CEE 320Winter 2006Geometric DesignCEE 320Steve Muench CEE
320Winter 2006Outline1. Concepts2. Vertical Alignmenta.
Funamentals!. Crest Vertical Curvesc. Sag Vertical Curves.
E"amples3. #ori$ontal Alignmenta. Funamentals!. Superelevation%.
&ther 'on()esta!le Stu** CEE 320Winter 2006ConceptsAlignment is
a 3+ pro!lem !ro,en o-n into t-o 2+ pro!lems #ori$ontal Alignment
.plan vie-/ Vertical Alignment .pro*ile vie-/Stationing Along
hori$ontal alignment 12000 1 12200 *t.Piilani Highway on Maui CEE
320Winter 2006StationingHorizontal AlignmentVertical AlignmentFrom
Perteet Engineering CEE 320Winter 2006Vertical Alignment CEE
320Winter 2006Vertical Alignment&!3ective4 +etermine elevation
to ensure 5roper rainage Accepta!le level o* sa*et65rimar6
challenge)ransition !et-een t-o graesVertical curvesG1G2G1G2Crest
Vertical Cure!ag Vertical Cure CEE 320Winter 2006Vertical Curve
Fundamentals5ara!olic *unctionConstant rate o* change o*
slope7mplies e8ual curve tangents6 is the roa-a6 elevation "
stations .or *eet/ *rom the !eginning o* the curvec bx ax y + + 2
CEE 320Winter 2006Vertical Curve
FundamentalsG1G2PV"PV#PVC$$%2&c bx ax y + + 2'Choose Either(
G1) G2 in *ecimal +orm) $ in +eet G1) G2 in ,ercent) $ in stations
CEE 320Winter 2006RelationshipsChoose Either( G1) G2 in *ecimal
+orm) $ in +eet G1) G2 in ,ercent) $ in
stationsG1G2PV"PV#PVC$$%2&'1and 0 : PVC At the G bdxdYx c Y x
and 0 : PVC At theLG GaLG GadxY d22: Anywhere1 2 1 222 CEE
320Winter 2006ExampleA -.. +t/ e0ual tangent crest ertical cure has
a PVC station o+ 1..1.. at 23 +t/ eleation/ #he initial gra*e is
2/. ,ercent an* the +inal gra*e is 4-/2 ,ercent/5etermine the
eleation an* stationing o+ PV") PV#) an* the high ,oint o+ the
cure/G162/.7G26 4 -/27PV"PV#PVC( !#A 1..1..E$ 23 +t/G162/.7G26
4-/27PV"PV#PVC( !#A 1..1..E$ 23 +t/ CEE 320Winter 2006Other
PropertiesG1G2PV"PV#PVC'8m8+82200xLAY 800ALYm 200ALYf2 1G G A G1)
G2 in ,ercent$ in +eet CEE 320Winter 2006Other Properties9(Value
.e*ines vertical curvature/)he num!er o* hori$ontal *eet neee *or a
1: change in slopeALK 1. / G K x pt low high CEE 320Winter
2006Crest Vertical CurvesG1G2PV"PV#PVCh2h1$!!5( )( )22 122 2 100 h
hSSD AL+( )( )Ah hSSD L22 12002+ For SS+ ; < For SS+ = s e6e
height 1 3.? *t. h2 1 tail light height 1 2.0 *t.Simpli*ie
E8uations( )21582SSD AL ( )ASSD L21582 For SS+ ; < For SS+ =
< CEE 320Winter 2006Crest Vertical CurvesAssuming < =
SS+@21582SSDK CEE 320Winter 2006Design Controls for Crest Vertical
Curves +rom AA!H#9:s A Policy on Geometric Design of Highways and
Streets 2001 CEE 320Winter 2006Design Controls for Crest Vertical
Curves+rom AA!H#9:s A Policy on Geometric Design of Highways and
Streets 2001 CEE 320Winter 2006Sag Vertical
CurvesG1G2PV"PV#PVCh26.h1$$ight ;eam 5istance eam y ? *egrees= CEE
320Winter 2006Sag Vertical CurvesAssumptions *or esign h1 1
healight height 1 2.0 *t.A 1 1 egreeSimpli*ie E8uations( )( )
SSDSSD AL5 . 3 4002+ ( )( )
,_
+ A SSDSSD L5 . 3 4002For SS+ ; y her hea*lights) is it
reasona>le to e',ect the *rier to >e a>le to sto,
>e+ore hitting the treeA CEE 320Winter 2006Example !!imilar to
E'am,le 1 >ut +or a crest cure/A car is traeling at @. m,h in
the country at night on a wet roa* through a 12. +t/ long crest
ertical cure/#he entering gra*e is @/. ,ercent an* the e'iting
gra*e is 4@/- ,ercent/A tree has +allen across the roa* at
a,,ro'imately the PV#/"s it reasona>le to e',ect the *rier to
>e a>le to sto, >e+ore hitting the treeA CEE 320Winter
2006Example "A roa*way is >eing *esigne* using a -2 m,h *esign
s,ee*/9ne section o+ the roa*way must go u, an* oer a small hill
with an entering gra*e o+ @/2 ,ercent an* an e'iting gra*e o+ 42/.
,ercent/How long must the ertical cure >eA CEE 320Winter
2006#ori$ontal Alignment CEE 320Winter 2006#ori$ontal
Alignment&!3ective4 Beometr6 o* irectional transition to
ensure4 Sa*et6 Com*ort5rimar6 challenge)ransition !et-een t-o
irections#ori$ontal curvesFunamentalsCircular curvesSuperelevationB
CEE 320Winter 2006#ori$ontal Curve FundamentalsC#5C5)57MECBB%2
B%2B%2R RD 000 , 18180100
,_
2tan R TDR L 100180$ CEE 320Winter 2006#ori$ontal Curve
Fundamentals
,_
12 cos1R E
,_
2cos 1 R MC#5C5)57MECBB%2 B%2B%2$ CEE 320Winter 2006Example %A
horizontal cure is *esigne* with a 12.. +t/ ra*ius/#he tangent
length is -.. +t/ an* the P# station is 2.1../Dhat are the P" an*
P# stationsA CEE 320Winter 2006Superelevationcp f pF F W + cos sin
cos sin2 2v vsgRWgRWW f W
,_
+ +FcFcn!!nF"F"Fc!1 "teE #$ CEE 320Winter 2006Superelevation cos
sin cos sin2 2v vsgRWgRWW f W
,_
+ +( ) tan 1 tan2svsfgR
f +( ) ! fgR
f !svs + 12( ) ! f g Rsv+2 CEE 320Winter 2006Selection of e and
fs5ractical limits on superelevation
.e/ClimateConstructa!ilit6A3acent lan use Sie *riction *actor .*s/
variationsVehicle spee5avement te"ture)ire conition CEE 320Winter
2006Side Friction Factor+rom AA!H#9:s A Policy on Geometric Design
of Highways and Streets 2004Few Gra,h CEE 320Winter 2006&inimum
Radius 'a(lesFew #a>le CEE 320Winter 2006)SDO' Design Side
Friction Factors+rom the 2..2 D!59# Design Manual) M 224.1Few
#a>leFor 9,en Highways an* Cam,s CEE 320Winter 2006)SDO' Design
Side Friction Factors+rom the 2..2 D!59# Design Manual) M 224.1For
$ow4!,ee* Gr>an Manage*Access HighwaysFew Gra,h CEE 320Winter
2006Design Superelevation Rates * AAS#'O+rom AA!H#9:s A Policy on
Geometric Design of Highways and Streets 2004Few Gra,h CEE
320Winter 2006Design Superelevation Rates * )SDO'+rom the 2..2
D!59# Design Manual) M 224.1ema' 6 H7Few Gra,h CEE 320Winter
2006Example +A section o+ !C 222 is >eing *esigne* as a
high4s,ee* *ii*e* highway/#he *esign s,ee* is I. m,h/Gsing D!59#
stan*ar*s) what is the minimum cure ra*ius structionMs( )vsRSSD180
DR SSDss v 100180!!51]1
,_
vv sRSSDR M%0cos 11]1
,_
vs v vRM R RSSD1cos%0 CEE 320Winter 2006Supplemental Stu,Cross
sectionSuperelevation )ransitionCuno**)angent runoutSpiral
curvesE"tra -ith *or curvesFD7 E '&) )ES)AF
