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+ ( )( )

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+ 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

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2tan R TDR L 100180$ CEE 320Winter 2006#ori$ontal Curve Fundamentals

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12 cos1R E

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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

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+ +FcFcn!!nF"F"Fc!1 "teE #$ CEE 320Winter 2006Superelevation cos sin cos sin2 2v vsgRWgRWW f W

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+ +( ) 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

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vv sRSSDR M%0cos 11]1

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vs v vRM R RSSD1cos%0 CEE 320Winter 2006Supplemental Stu,Cross sectionSuperelevation )ransitionCuno**)angent runoutSpiral curvesE"tra -ith *or curvesFD7 E '&) )ES)AF