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Lecture # 4
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الحمد لله رب العالمين والصالة والسالم على خاتم
النبيين
Geometric Design ndash Basic Principles Safety for all users Functionality ndash the need for access and mobility Accessibility for people with disabilities ndash as a prerequisite to
access to employment recreation and healthcare Mutual support and compatibility between transportation
facilities and services and the adjacent land uses and associated activities they serve
Consistency with transportation plans and policies and environmental regulations that guide the community the region the province and the Federal government
Transportation facility design and operational requirements established by others
Input and participation from local constituents and the appropriate local regional and state reviewing agencies 1048708
Cost effectiveness ndash the value returned for the investments made in transportation
GEOMETRIC DESIGN ndash Course Heads
Cross-Section Elements Horizontal Alignment Vertical Alignment Intersections Interchanges helliphelliphelliphellip helliphelliphelliphellip
500
1000
1500
2000
2500
3000
3500
4000
4500
3-D Model
Curves Straight segments are called Tangents Horizontal curves help change from one
tangent to another
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Geometric Design ndash Basic Principles Safety for all users Functionality ndash the need for access and mobility Accessibility for people with disabilities ndash as a prerequisite to
access to employment recreation and healthcare Mutual support and compatibility between transportation
facilities and services and the adjacent land uses and associated activities they serve
Consistency with transportation plans and policies and environmental regulations that guide the community the region the province and the Federal government
Transportation facility design and operational requirements established by others
Input and participation from local constituents and the appropriate local regional and state reviewing agencies 1048708
Cost effectiveness ndash the value returned for the investments made in transportation
GEOMETRIC DESIGN ndash Course Heads
Cross-Section Elements Horizontal Alignment Vertical Alignment Intersections Interchanges helliphelliphelliphellip helliphelliphelliphellip
500
1000
1500
2000
2500
3000
3500
4000
4500
3-D Model
Curves Straight segments are called Tangents Horizontal curves help change from one
tangent to another
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
GEOMETRIC DESIGN ndash Course Heads
Cross-Section Elements Horizontal Alignment Vertical Alignment Intersections Interchanges helliphelliphelliphellip helliphelliphelliphellip
500
1000
1500
2000
2500
3000
3500
4000
4500
3-D Model
Curves Straight segments are called Tangents Horizontal curves help change from one
tangent to another
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
500
1000
1500
2000
2500
3000
3500
4000
4500
3-D Model
Curves Straight segments are called Tangents Horizontal curves help change from one
tangent to another
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Straight segments are called Tangents Horizontal curves help change from one
tangent to another
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed mph Maximum Deflection
25 5deg30
30 3deg45
35 2deg45
40 2deg15
45 1deg15
50 1deg15
55 1deg00
60 1deg00
65 0deg45
70 0deg45
Source Ohio DOT Design Manual Figure 202-1E
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Design Elements Curves
Simple Circular Curvesbull Compound Curvesbull Broken Back Curvesbull S or Reverse Curves
Transitions
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Horizontal curves are circular to minimize steering
effort Curves need to be long enough to avoid unsafe or
uncomfortable conditions
Additional features can help reduce the driving effortbull Super Elevationbull Transition (or spiral) curves which slowly
transition from an infinite radius (a tangent) to the radius of the circular curve
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Design Elements Design Questions
Which one to be used where and how What should be the minimum radius
bull without Transitionbull with Transition
With minimum design radius what should bebull Type of Transitionbull Length of Transitionbull Components of Transition
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Simple Circular
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Compound Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curves
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curve Sight Distance
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Horizontal Curve Sight Distance
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Minimum Radius
Rmin = ____V2____
15 (e + f) where Rmin is the minimum radius in feet
V = velocity (mph) e = superelevation f = friction 15 = gravity and unit conversion
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curvesbull Rmin uses max e and max f (defined by AASHTO DOT
and graphed in Green Book) and design speed
bull f is a function of speed roadway surface weather condition tire condition and based on comfort ndash drivers brake make sudden lane changes and change position within a lane when acceleration around a curve becomes ldquouncomfortablerdquo
bull AASHTO 05 20mph with new tires and wet pavement to 035 60mph
bull f decreases as speed increases (less tire pavement contact)
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves Max e is controlled by 4 factors
bull Climate conditions (amount of ice and snow)bull Terrain (flat rolling mountainous)bull Type of area (rural or urban)bull Frequency of slow moving vehicles who might be
influenced by high super elevation rates Max e
bull Highest in common use = 10 12 with no ice and snow on low volume gravel-surfaced roads
bull 8 is logical maximum to minimize slipping by stopped vehicles considering snow and ice
bull For consistency use a single rate within a project or on a highway
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
TRANSITIONSTRANSITIONS
SuperelevationSuperelevationSpiral CurvesSpiral Curves
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Image
httptechalivemtuedumodulesmodule0003Superelevationhtm
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Transitioning Incorporating superelevation into a roadwayrsquos
design may help avoid roadside obstacles that might otherwise be impacted by the alignment
In contrast superelevation may not be desirable for low-speed roadways to help limit excessive speeds or in urban settings to limit impacts to abutting uses or drainage systems and utilities
Moreover superelevation may not be desirable when considering pedestrian or bicycle accommodations along the roadway segment Like other roadway design elements designers must consider the trade-offs of introducing superelevation in a roadwayrsquos design
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Although superelevation is advantageous for traffic
operation various factors often combine to make its use impractical in many built-up areas (such as Suburban High Intensity Suburban Town Centers and Urban Areas)
Such factors include wide pavement areas the need to meet the grade of adjacent property surface drainage considerations and frequency of cross streets alleys and driveways
Therefore horizontal curves on low-speed roadways in urban areas may be designed without superelevation counteracting the centrifugal force solely with side friction
Designing without superelevation is often a suitable design practice for low-speed roadways (below 35 mph) or roadways in urban developed settings
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Attainment of Superelevation - General
bull Must be done gradually over a distance without appreciable reduction in speed or safety and with comfort
bull Change in pavement slope should be consistent over a distance
Tangent Runout Section Superelevation Runoff Section bull Methods
bull Rotate pavement about centerline bull Rotate about inner edge of pavement bull Rotate about outside edge of pavement
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Tangent Runout Section
Length of roadway needed to accomplish a change in outside-lane cross slope from normal cross slope rate to zero
For rotation about centerline
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Runoff Section
Length of roadway needed to accomplish a change in outside-lane cross slope from 0 to full superelevation or vice versa
For undivided highways with cross-section rotated about centerline
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Transitioning The development of superelevation on a horizontal curve requires a
transition from a normal crown section which is accomplished by rotating the pavement
The pavement may be rotated about the centerline or either edge of the travel lanes Five basic cross section controls mdash (-a-) through (-e-) superelevation
Cross section (-a-) is the normal crown section where the transitioning begins
Cross section (-b-) is reached by rotating half the pavement until it is level
Cross section (-c-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section at a cross slope equal to the normal crown slope
Cross section (-d-) is the rate of the cross slope at any intermediate cross section between (-c-) and (-e-) is proportional to the distance from Cross section (-e-)
Cross section (-e-) is achieved by further rotation of the planar section the entire pavement section to attain the full superelevation at a cross slope equal to (e)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Transitioning Rotation about the centerline profile of traveled way
This is generally the preferred method for two lane and undivided multilane roadways and when the elevations of the outside of roadway must be held within critical limits such as in an urban area to minimize the impact on adjacent properties This is also the method that distorts the edge line profiles the least
Rotation about the inside-edge profile of traveled way This is generally the preferred method when the lower edge profile is of concern such as when the profile is flat and the inside edge of the roadway needs to be controlled for drainage purposes This method is suitable for ramps
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Superelevation Transitioning Rotation about the outside-edge profile of traveled way
This method is similar to inside edge rotation except that the change is effected below the outside-edge profile instead of above the inside edge profile This method is used when the higher edge profile is critical such as on divided highways where the median edge profiles are held
Rotation about the outside-edge profile of traveled way when the roadway has a straight cross-slope at the beginning of transition (-a-)
The outside-edge rotation is shown because this point is most often used for rotation of two-lane one-way roadways with profile along the median edge of traveled way or for the traveled way having a typical straight cross-slope
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
39
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
40
Source CalTrans Design Manual online httpwwwdotcagovhqoppdhdmpdfchp0200pdf
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Same as point E of GB
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Attainment Location - WHERE
Superelevation must be attained over a length that includes the tangent and the curve
Typical 66 on tangent and 33 on curve of length of runoff if no spiral
Super runoff is all attained in Spiral if used
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Minimum Length of Runoff for curve
Lr based on drainage and aesthetics
rate of transition of edge line from NC to full Superelevation traditionally taken at 05 (1 foot rise per 200 feet along the road)
current recommendation varies from 035 at 80 mph to 080 for 15 mph (with further adjustments for number of lanes)
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
eNC = normal cross slope rate ()
ed = design superelevation rate
Lr = minimum length of superelevation runoff (ft)
(Result is the edge slope is same as for Runoff segment)
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Length of Superelevation Runoff
α = multilane adjustment factor adjusts for total width
r
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Relative Gradient (G)
Maximum longitudinal slope Depends on design speed higher speed =
gentler slope
For example For 15 mph G = 078 For 80 mph G = 035 See table next page
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Maximum Relative Gradient (G)
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Multilane Adjustment
Runout and runoff must be adjusted for multilane rotation
See Iowa DOT manual section 2A-2 and Standard Road Plan RP-2
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Length of Superelevation Runoff Example
For a 4-lane divided highway with cross-section rotated about centerline design superelevation rate = 4 Design speed is 50 mph What is the minimum length of superelevation runoff (ft)
Lr = 12eα
G
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
50
Lr = 12eα = (12) (004) (15)
G 05
Lr = 144 feet
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Tangent runout length Example continued
Lt = (eNC ed ) x Lr
as defined previously if NC = 2
Tangent runout for the example is
LT = 2 4 144rsquo = 72 feet
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
52
From previous example speed = 50 mph e = 4
From chart runoff = 144 feet same as from calculation
Source A Policy on Geometric Design of Highways and Streets (The Green Book) Washington DC American Association of State Highway and Transportation Officials 2001 4th Ed
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Spiral Curve TransitionsSpiral Curve TransitionsSpiral Curve TransitionsSpiral Curve Transitions
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Spiral Curve Transitions Vehicles follow a transition path as they enter or
leave a horizontal curve
Combination of high speed and sharp curvature can result in lateral shifts in position and encroachment on adjoining lanes
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Spirals Advantages
Provides natural easy to follow path for drivers (less encroachment promotes more uniform speeds) lateral force increases and decreases gradually
Provides location for superelevation runoff (not part on tangentcurve)
Provides transition in width when horizontal curve is widened
Aesthetic
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Minimum Length of Spiral
Possible Equations
Larger of (1) L = 315 V3
RC
Where
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration (fts3) use 1-3 fts3 for highway)
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Minimum Length of Spiral
Or (2) L = (24pminR)12
Where
L = minimum length of spiral (ft)
R = curve radius (ft)
pmin = minimum lateral offset between the tangent and circular curve (066 feet)
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Maximum Length of Spiral
L = (24pmaxR)12
Where
L = maximum length of spiral (ft)
R = curve radius (ft)
pmax = maximum lateral offset between the tangent and circular curve (33 feet)
Safety problems may occur when spiral curves are too long ndash drivers underestimate sharpness of approaching curve (driver expectancy)
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Length of Spiralo AASHTO also provides recommended spiral lengths
based on driver behavior rather than a specific equation See Table 1612 of text and the associated tangent runout lengths in Table 1613
o Superelevation runoff length is set equal to the spiral curve length when spirals are used
o Design Note For construction purposes round your designs to a reasonable values eg
Ls = 147 feet round it to
Ls = 150 feet
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source Iowa DOT Design Manual
SPIRAL TERMINOLOGY
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source Iowa DOT Design Manual
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Source Iowa DOT Design Manual
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
Attainment of Superelevationon spiral curves
See sketches that follow
Normal Crown (DOT ndash pt A)
1 Tangent Runout (sometimes known as crown runoff) removal of adverse crown (DOT ndash A to B) B = TS
2 Point of reversal of crown (DOT ndash C) note A to B = B to C
3 Length of Runoff length from adverse crown removed to full superelevated (DOT ndash B to D) D = SC
4 Fully superelevate remainder of curve and then reverse the process at the CS
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
65Source Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
With Spirals
Tangent runout (A to B)
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
With Spirals
Removal of crown
With Spirals
Transition of superelevation
Full superelevation
69
With Spirals
Transition of superelevation
Full superelevation
69
69
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