5_Superelevation & Transition Curves

7/27/2019 5_Superelevation & Transition Curves

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stanbul Teknik niversitesi 26.07.2012

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Chapter 3:

Horizontal Alignment

Superelevation Application

&

Transition Curves

In the actual design of a horizontal curve, the engineer

must select appropriate values of e and fs . The value selected for superelevation, e, is critical

because high rates of superelevation can cause

vehicle steering problems on the horizontal curve, and

in cold climates, ice on the roadway can reduce fssuch that vehicles traveling at less than the design

speed on an excessively superelevated curve could

slide inward off the curve due to gravitational forces.

AASHTO provides general guidelines for the selection ofe and fs for horizontal curve design, as shown in Table3.5.

The values presented in this table are grouped by fivevalues of maximum e. The selection of any one of thesefive maximum e values is dependent on the type of road(for example, higher maximum e's are permitted on

freeways compared with arterials and local roads) andlocal design practice. Limiting values of fs are simply afunction of design speed. Table 3.5 also presentscalculated radii (given V, e, and fs) by applying Eq. 3.34.


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Transition Design Controls

The design of transition sections includes consideration

of transitions in the roadway cross slope and possible

transition curves incorporated in the horizontal

alignment.

The former consideration is referred to as superelevation

transition and

The latter is referred to as alignment transition.

Where both transition components are used, they occur

together over a common section of roadway at the

beginning and end of the mainline circular curves.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001


The superelevation transition section consists of the

superelevation runoff and tangent runout sections.

The superelevation runoff section consists of the length of

roadway needed to accomplish a change in outside-lane

cross slope from zero (flat) to full superelevation, or vice

versa.

The tangent runout section consists of the length ofroadway needed to accomplish a change in outside-lane

cross slope from the normal cross slope rate to zero

(flat), or vice versa.

from AASHTOsA Policy on Geometric Design of Highways and Streets 2001


These two elements are applicable to superelevation on

both simple circular curves and spiral transition curves,

but the manner of application is somewhat different for

each.

General criteria for application of runoff and terminology

for both types of curves are shown in Figure.



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Superelevation Transition

from the 2001 CaltransHighway Design Manual

Transition Design Controls For reasons of safety and comfort, the pavement

rotation in the superelevation transition section should

be effected over a length that is sufficient to make such

rotation imperceptible to drivers. To be pleasing in

appearance, the pavement edges should not appear

distorted to the driver.

In the alignment transition section, a spiral or compound

transition curve may be used to introduce the main

circular curve in a natural manner (i.e., one that is

consistent with the drivers steered path).


Transition Design Controls Such transition curvature consists of one or more curves

aligned and located to provide a gradual change inalignment radius.

As a result, an alignment transition introduces the lateralacceleration associated with the curve in a gentlemanner.

While such a gradual change in path and lateral

acceleration is appealing, there is no definitive evidencethat transition curves are essential to the safe operationof the roadway and,

As a result, they are not used by many agencies.



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When a transition curve is not used, the roadway

tangent directly adjoins the main circular curve. This

type of transition design is referred to below as thetangent-to-curve transition.

Some agencies employ spiral curves and use their length

to make the appropriate superelevation transition. A

spiral curve approximates the natural turning path of a

vehicle.

One agency believes that the length of spiral should be

based on a 4-s minimum maneuver time at the design

speed of the highway.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001


Other agencies do not employ spiral curves but

empirically designate proportional lengths of tangent and

circular curve for the same purpose.

In either case, as far as can be determined, the length of

roadway to effect the superelevation runoff should be the

same for the same rate of superelevation and radius of

curvature.

Review of current design practice indicates that the

length of a superelevation runoff section is largely

governed by its appearance.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001

Transition Design Controls Spiral transition curve lengths as determined otherwise often

are shorter than those determined for general appearance, so

that theoretically derived spiral lengths are replaced with

longer empirically derived runoff lengths.

A number of agencies have established one or more control

runoff lengths within a range of about 30 to 200 m[100 to 650

ft], but there is no universally accepted empirical basis for

determining runoff length, considering all likely traveled way

widths.

In one widely used empirical expression, the runoff length is

determined as a function of the slope of the outside edge of

the traveled way relative to the centerline profile.

TANGENT-TO-CURVE TRANSITION


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Minimum length of superelevation runoff:

For appearance and comfort, the length of superelevation

runoff should be based on a maximum acceptable

difference between the longitudinal grades of the axis ofrotation and the edge of pavement.

The axis of rotation is generally represented by the

alignment centerline for undivided roadways;

However, other pavement reference lines can be used.

These lines and the rationale for their use is discussed

below in the section on Methods of Attaining

Superelevation.


Design Superelevation Tables

forth the basic design criteria based on design speeds for

the normal design superelevation rates of emax = 4 and 6percent as well as othervalues ranging up to 12 percent.

The criteria shown includes the minimum radius of

curvature, crown treatment and superelevation runoff

lengths (L), all of which are related to the number of

lanes to be rotated. The minimum rate of cross slope for

a traveled lane is determinedby drainage requirements.

from the 2005 WSDOTDesign Manual, M 22-01


Table 3-21 to 3-25 show, in addition to length of runoff or

transition, values of R and the resulting superelevation for

different design speeds for each of five values of

maximum superelevation rate (i.e., for a full range of

common design conditions).

The minimum radii for each of the five maximum

superelevation rates were calculated from the simplified

curve formula.



Under all but extreme weather conditions, vehicles can

travel safely at speeds higher than the design speed on

horizontal curves with the superelevation rates indicated

in the tables.

This is due to the development of a radius/superelevation

relationship that uses friction factors that are generally

considerably less than can be achieved.

This is illustrated in Exhibit 3-11,which compares the

friction factors used in design of various types of highway

facilities and the maximum side friction factors available

on certain wet and dry concrete pavementsfrom the 2005 WSDOTDesign Manual, M 22-01


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The term normal cross slope (NC) designates curves

that are so flat that the elimination of adverse cross

slope is not considered necessary, and thus the normalcross slope sections can be used.

The term remove cross slope (RC) designates curves

where it is adequate to eliminate the adverse cross slope

by superelevating the entire roadway at the normal

cross slope.



Table 3-21.Values forDesign

ElementsRelated to

DesignSpeed andHorizontalCurvature

Table 3-21.Values for

DesignElementsRelated to

DesignSpeed andHorizontalCurvature


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Location with respect to end of curve

In the tangent-to-curve design, the location of the

superelevation runoff length with respect to the point ofcurvature (PC) must be determined.

Normal practice is to divide the runoff length between

the tangent and curved sections and to avoid placing the

entire runoff length on either the tangent or the curve.

With full superelevationattained at the PC, the runoff

lies entirely on the approach tangent, where theoretically

no superelevation is needed.



At the other extreme, placement of the runoff entirely on

the circular curve results in the initial portion of the

curve having less than the desired amount of

superelevation.

Both of these extremes tend to be associated with a

large peak lateral acceleration.

Experience indicates that locating a portion of the runoff

on the tangent, in advance of the PC, is preferable, since

this tends to minimize the peak lateral acceleration and

the resulting side friction demand.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001


Observations indicate that a spiral path results from a

drivers natural steering behavior during curve entry or exit.

This natural spiral usually begins on the tangent and ends

beyond the beginning of the circular curve.

Based on the preceding discussion, locating a portion of the

runoff on the tangent is consistent with the natural spiral pathadopted by the driver during curve entry.



AASHTO does allow agencies to adopt a single value for

all design speeds and rotated widths. For simplicity,

DelDOT has adopted a runoff proportion of two-thirds in

the tangent section and one-third into the curve.

In the case of simple curves, the superelevation runoff

distance is applied with one-third on the curve itself and

two-thirds (or preferably as per Figure 5-7) on thetangent adjacent to the curve.



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Thus, full superelevation is not reached until slightly past

the P.C. and starts to reduce shortly before reaching the

P.T.

Where spiral transition curves are used, the

superelevation runoff is always coincident with the spiral

length (T.S. to S.C. or C.S to S.T.) and the designated full

superelevation is provided between the S.C. and the C.S.

The geometrics for spiral curves provide for a natural

introduction of superelevation without the compromise

necessary for circular curves.from AASHTOsA Policy on Geometric Design of Highways and Streets 2001

Simple Curve

Spiral TransitionCurve

Methods of Attaining Superelevation

There are three basic methods are used to transition the

pavement to a superelevated cross section. These methods

include:

(1) revolving a traveled way with normal cross slopes

about the centerline profile,


about the inside-edge profile,


about the outside-edge profile



The following figures illustrates these three methods.

The methods of changing cross slope are most

conveniently shown in the exhibit in terms of straight

line relationships,

but it is emphasized that the angular breaks between the

straight-line profiles are to be rounded in the finished

design, as shown in the figure.



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In fist figure, the profile reference line corresponds to

the centerline profile. In figures second and third, the profile reference line is

represented as a theoretical centerline profile as it

does not coincide with the axis of rotation.

The cross sections at the bottom of each diagram in

Figures indicate the traveled way cross slope condition at

the lettered points.



The first method, as shown in following figure, revolves

the traveled way about the centerline profile. This method is the most widely used because the change

in elevation of the edge of the traveled way is made with

less distortion than with the other methods.

In this regard, one-half of the change in elevation is

made at each edge.



Methods of Attaining Superelevation Methods of Attaining Superelevation

The second method, as shown in Fig 3-37B, revolves the

traveled way about the inside-edge profile.

In this case, the inside-edge profile is determined as a

line parallel to the profile reference line. One-half of the

change in elevation is made by raising the actual

centerline profile with respect to the inside-edge profile

and the other half by raising the outside-edge profile anequal amount with respect to the actual centerline

profile.



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Methods of Attaining Superelevation Methods of Attaining Superelevation

The third method, as shown in Fig. 3-37C, revolves the

traveled way about the outside-edge profile. Thismethod is similar to that shown in Exhibit 3-37B except

that the elevation change is accomplished below the

outside-edge profile instead of above the inside-edge

profile.




TRANSITION CURVES


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A properly designed transition curve provides a natural,

easy-to-follow path for drivers, such that the lateralforce increases and decreases gradually as a vehicle

enters and leaves a circular curve.

Transition curves minimize encroachment on adjoining

traffic lanes and tend to promote uniformity in speed.

A spiral transition curve simulates the natural turning

path of a vehicle.


The principal advantages of transition curves

The transition curve length provides a suitable location

for the superelevation runoff. The transition from the normal pavement cross slope on

the tangent to the fully superelevated section on the

curve can be accomplished along the length of the

transition curve in a manner that closely fits the speed-

radius relationship for vehicles traversing the transition.




Where superelevation runoff is introduced without a

transition curve, usually partly on the curve and partly

on the tangent, the driver approaching the curve may

have to steer opposite to the direction of the

approaching curve when on the superelevated tangent

portion in order to keep the vehicle within its lane.

A spiral transition curve also facilitates the transition inwidth where the traveled way is widened on a circular

curve. Use of spiral transitions provides flexibility in

accomplishing the widening of sharp curves.



The appearance of the highway or street is enhanced by

the application of spiral transition curves.

The use of spiral transitions avoids noticeable breaks in

the alignment as perceived by drivers at the beginning

and end of circular curves.

Figure 3-32 illustrates such breaks, which are made

more prominent by the presence of superelevation

runoff.



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Figure 3-32

illustrates such

breaks, which are

made moreprominent by the

presence of

superelevation

runoff.


Terminology

Types of Transition Curves

Clothoid the one

that we will examine

in more detail, most

commonly used

Lemniscate used

for large deflection

angles on high

speed roads

Cubic Parabola

unsuitable for large

deflection angles

Curvature of Transition Curve

Generally, the Euler spiral, which is also known as the

clothoid, is used in the design of spiral transition curves.

The radius varies from infinity at the tangent end of the

spiral to the radius of the circular arc at the end that

adjoins that circular arc.

By definition, the radius of curvature at any point on anEuler spiral varies inversely with the distance measured

along the spiral.


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The beginning of thetransitioncurve istangential to the alignment,

end of the transition curveis also tangential to thehorizontal curve.

At begining of thetransition curve radiusof curvature, RT=

(infinite)At end of the transitioncurve radius ofcurvature, RT=R (radius ofhorizontal curve)


The curvature of the transition curve at any point (Lx) from thestart point of the transition curve (TS );

=

=

At the end of the transition curve(SC), the curvature, k = 1 / R ;kx can be expressed as:

=

Term of (Lp.R) is constant, so this is an indication of increasedcurvature in linear

Transition Length (Lp)

In the case of a spiral transition that connects two circular

curves having different radii, there is an initial radius

rather than an infinite value.

The following equation, developed for gradual attainment

of lateral acceleration on railroad track curves, is the basic

expression used by some highway agencies for computing

minimum length of a spiral transition curve:


The length of plan transition (Lp) is determined by

the rate of change of radial acceleration, and

rate of change of rotation of pavement


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Transition Length (Lp)-Radial Acceleration Method

At begining of the transition curve a=0

At end of the transition curve a=

Time of radial accelaration change t=

The radial accelaration changeover time:

=

=


=

Radial acceleration will vary with design speed and design

authority.

Typical values for a lie between (0.3 -0.6 m/sec3) for V from 40-

140 km/h respectively

Lp = length of plan transition

V = design speed (km/h)

R = radius of circula r curve

a = radial acceleration


If Vkm/h =

.

Lp = length of plan transition

Vp = design speed (km/hr)

R = radius of circular curve a = radial acceleration

R : Length of throw or thedistance from tangent that the

circular curve has been offset(m),

S : Chord of Clothoid (m),

: Deflection angle from TS to

SC (degree),

Geometry of Clothoid


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L : Length of clothoid (m),

X : Distance along tangent fromTS to point at right angle to SC

Y : Offset distance (right angledistance) from tangent to SC(m),

: Spiral angle from tangent toSC (raydan),

Xm, Ym : Coordinates ofhorizontal curve

Tu : Long tangent of clothoid(m),

Tk : Short tangent of clothoid

(m),


=

L = Length of Plan Transition

R = radius of circular curve

A = constant of clothoid(clothoid parameter)


Spiral angle from tangent to SC

(raydan) ;

=

2Distance along tangent from TS to

point at right angle to SC ;

X =

40

=

40

Offset distance (right angle

distance) from tangent to SC ;

Y =

6=

6


Coordinates of horizontal curve ;

=

= +

Long tangent length of clothoid;

= Short tangent length of clothoid ;

=

Length of throw or the distance from

tangent that the circular curve has been

offset ;

= = 1



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Chord of Clothoid ;

= +

Deflection angle from TS to SC (degree);

= tan


R : Radius of simple curve

T : Spiral tangent distance (m),

: Angle of intersection

C : Angle of intersection of thesimple curve (degree),

Dc : Degree of simple curve.


Angle of intersection of the simple

curve ;

= 2Spiral angle from tangent to SC

(raydan);

=

2Degree of simple curve ;

=2

360Spiral tangent distance ;

= + + tan


In the selection of clothoid parameter, Themaximum value of radial accelaration change overtime (sademe) is taken into account in terms ofcomfort.

Clothoid parameter A that provides following

conditions are determined according to a maximumvalue of a

Then clothoid length are calculated using theparameter.

Selection of Clothoid Parameter


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Optical Requirement:

Dinamic Requirement: = 0.17

Superelevation Requirement: =

.


b: platform width

d : full superelevation,

q : normal crown

R: raius of the circular curve,

After determining clothoid parameter, calculate length ofclothoid by following equation ;

=

Clothoid Length should be consistent the length ofsuperelevation runoff ;

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In order to application of the clothoid, the horizontal curvemust be a certain length ;

2

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5_Superelevation & Transition Curves