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GeometricDesignofHighways

AAlignmentDesign

ofaroadisshownontheplaneviewandisaseriesofstraightlinescalledtangentsconnectedbycircular.Inmodernpracticeitiscommontointerposetransitionorspiralcurvesbetweentangentsandcircularcurves.

Alignmentmustbeconsistent.Suddenchangesfromflattosharpcurvesandlongtangentsfollowedbysharpcurvesmustbeavoided;

otherwise,accidenthazardswillbecreated.Likewise,placingcircularcurvesofdifferentradiiendtoend（compoundcurves）orhavingashorttangentbetweentwocurvesispoorpracticeunlesssuitabletransitionsbetweenthemareprovided.Long,flatcurvesarepreferableatalltimes,astheyarepleasinginappearanceanddecreasepossibilityoffutureobsolescence.However,alignmentwithouttangentsisundesirableontwo-laneroadsbecausesomedrivershesitatetopassoncurves.Long,flatcurvesshouldbeusedforsmallchangesindirection,asshortcurvesappearas“kink”.Alsohorizontalandverticalalignmentmustbeconsideredtogether,notseparately.Forexample,asharphorizontalcurvebeginningnearacrestcancreateaseriousaccidenthazard.

Avehicletravelinginacurvedpathissubjecttocentrifugalforce.Thisisbalancedbyanequalandoppositeforcedevelopedthroughcannotexceedcertainmaximums,andthesecontrolsplacelimitsonthesharpnessofcurvesthatcanbeusedwithadesignspeed.

Usuallythesharpnessofagivencircularcurveisindicatedbyitsradius.However,foralignmentdesign,sharpnessiscommonlyexpressedintermsofdegreeofcurve,whichisthecentralanglesubtendedbya100-ftlengthofcurve.Degreeofcurveisinverselyproportionaltotheradius.

Tangentsectionsofhighwayscarrynormalcrossslope;

curvedsectionsaresuperProvisionmustbemadeforgradualchangefromonetotheother.Thisusuallyinvolvesmaintainingthecenterlineofeachindividualroadwayatprofilegradewhileraisingtheouteredgeandloweringtheinneredgetoproducethedesiredsuperisattainedsomedistancebeyondthepointofcurve.

Ifavehicletravelsathighspeedonacarefullyrestrictedpathmadeupoftangentsconnectedbysharpcircularcurve,ridingisextremelyuncomfortable.Asthecarapproachesacurve,superbeginsandthevehicleistiltedinward,butthepassengermustremainverticalsincethereisoncentrifugalforcerequiringcompensation.Whenthevehiclereachesthecurve,fullcentrifugalforcedevelopsatonce,andpullstherideroutwardfromhisverticalposition.Toachieveapositionofequilibriumhemustforcehisbodyfarinward.Astheremainingsupertakeseffect,furtheradjustmentinpositionisrequired.Thisprocessisrepeatedinreverseorderasthevehicleleavesthecurve.Wheneasementcurvesareintroduced,thechangeinradiusfrominfinityonthetangenttothatofthecircularcurveiseffectedgraduallysothatcentrifugalforcealsodevelopsgradually.Bycarefulapplicationofsuperalongthespiral,asmoothandgradualapplicationofcentrifugalforcecanbehadandtheroughnessavoided.

Easementcurveshavebeenusedbytherailroadsformanyyears,buttheiradoptionbyhighwayagencieshascomeonlyrecently.Thisisunderstandable.Railroadtrainsmustfollowtheprecisealignmentofthetracks,andthediscomfortdescribedherecanbeavoidedonlybyadoptingeasementcurves.Ontheotherhand,themotor-vehicleoperatorisfreetoalterhislateralpositionontheroadandcanprovidehisowneasementcurvesbysteeringintocircularcurvesgradually.However,thisweavingwithinatrafficlane（butsometimesintootherlanes）isdangerous.Properlydesignedeasementcurvesmakeweavingunnecessary.Itislargelyforsafetyreasons,then,thateasementcurveshavebeenwidelyadoptedbyhighwayagencies.

Forthesameradiuscircularcurve,theadditionofeasementcurvesattheendschangesthelocationofthecurvewithrelationtoitstangents;

hencethedecisionregardingtheiruseshouldbemadebeforethefinallocationsurvey.TheypointofbeginningofanordinarycircularcurveisusuallylabeledthePC（pointofcurve）orBC（beginningofcurve）.ItsendismarkedthePT（pointoftangent）orEC（endofcurve）.Forcurvesthatincludeeasements,thecommonnotationis,asstationingincreases:

TS（tangenttospiral）,SC（spiraltocircularcurve）,CS（circularcurvetospiral）,andST（spiralgotangent）.

Ontwo-lanepavementsprovisionofawilderroadwayisadvisableonsharpcurves.Thiswillallowforsuchfactorsas

（1）thetendencyfordriverstoshyawayfromthepavementedge,

（2）increasedeffectivetransversevehiclewidthbecausethefrontandrearwheelsdonottrack,and（3）addedwidthbecauseoftheslantedpositionofthefrontofthevehicletotheroadwaycenter.For24-ftroadways,theaddedwidthissosmallthatitcanbeneglected.Onlyfor30mphdesignspeedsandcurvessharperthan22°

doestheaddedwidthreach2ft.Fornarrowerpavements,however,wideningassumesimportanceevenonfairlyflatcurves.RecommendedamountsofandproceduresforcurvewideningaregiveninGeometricDesignforHighways.

BGrades

Theverticalalignmentoftheroadwayanditseffectonthesafeandeconomicaloperationofthemotorvehicleconstituteoneofthemostimportantfeaturesofroaddesign.Theverticalalignment,whichconsistsofaseriesofstraightlinesconnectedbyverticalparabolicorcircularcurves,isknownasthe“gradeline.”Whenthegradelineisincreasingfromthehorizontalitisknownasa“plusgrade,”andwhenitisdecreasingfromthehorizontalitisknownasa“minusgrade.”Inanalyzinggradeandgradecontrols,thedesignerusuallystudiestheeffectofchangeingradeonthecenterprofile.

Intheestablishmentofagrade,anidealsituationisoneinwhichthecutisbalancedagainstthefillwithoutagreatdealofborroworanexcessofcuttobewasted.Allhaulsshouldbedownhillifpossibleandnottoolong.Thegradeshouldfollowthegeneralterrainandriseandfallinthedirectionoftheexistingdrainage.Inmountainouscountrythegrademaybesettobalanceexcavationagainstembankmentasacluetowardleastoverallcost.Inflatorprairiecountryitwillbeapproximatelyparalleltothegroundsurfacebutsufficientlyaboveittoallowsurfacedrainageand,wherenecessary,topermitthewindtocleardriftingsnow.Wheretheroadapproachesorfollowsalongstreams,theheightofthegradelinemaybedictatedbytheexpectedleveloffloodwater.Underallconditions,smooth,flowinggradelinesarepreferabletochoppyonesofmanyshortstraightsectionsconnectedwithshortverticalcurves.

Changesofgradefromplustominusshouldbeplacedincuts,andchangesfromaminusgradetoaplusgradeshouldbeplacedinfills.Thiswillgenerallygiveagooddesign,andmanytimesitwillavoidtheappearanceofbuildinghillsandproducingdepressionscontrarytothegeneralexistingcontoursoftheland.Otherconsiderationsfordeterminingthegradelinemaybeofmoreimportancethanthebalancingofcutsandfills.

Urbanprojectsusuallyrequireamoredetailedstudyofthecontrolsandfineradjustmentofelevationsthandoruralprojects.Itisoftenbesttoadjustthegradetomeetexistingconditionsbecauseoftheadditionalexpenseofdoingotherwise.

Intheanalysisofgradeandgradecontrol,oneofthemostimportantconsiderationsistheeffectofgradesontheoperatingcostsofthemotorvehicle.Anincreaseingasolineconsumptionandareductioninspeedareapparentwhengradesareincreaseingasolineconsumptionandareductioninspeedisapparentwhengradesareincreased.Aneconomicalapproachwouldbetobalancetheaddedannualcostofgradereductionagainsttheaddedannualcostofvehicleoperationwithoutgradereduction.Anaccuratesolutiontotheproblemdependsontheknowledgeoftrafficvolumeandtype,whichcanbeobtainedonlybymeansofatrafficsurvey.

Whilemaximumgradesvaryagreatdealinvariousstates,AASHTOrecommendationsmakemaximumgradesdependentondesignspeedandtopography.Presentpracticelimitsgradesto5percentofadesignspeedof70mph.Foradesignspeedof30mph,maximumgradestypicallyrangefrom7to12percent,dependingontopography.

Whereverlongsustainedgradesareused,thedesignershouldnotsubstantiallyexceedthecriticallengthofgradewithouttheprovisionofclimbinglanesforslow-movingvehicles.Criticalgradelengthsvaryfrom1700ftfora3percentgradeto500ftforan8percentgrade.

Longsustainedgradesshouldbelessthanthemaximumgradeonanyparticularsectionofahighway.Itisoftenpreferredtobreakthelongsustaineduniformgradebyplacingsteepergradesatthebottomandlighteningthegradenearthetopoftheascent.Dipsintheprofilegradeinwhichvehiclesmaybehiddenfromviewshouldalsobeavoided.

Maximumgradeforhighwayis9percent.Standardssettingminimumgradesareofimportanceonlywhensurfacedrainageisaproblemaswhenwatermustbecarriedawayinagutterorroadsideditch.InsuchinstancestheAASHTOsuggestsaminimumof0.35%.

CSightDistance

Forsafevehicleoperation,highwaymustbedesignedtogivedriversasufficientdistanceorclearversionaheadsothattheycanavoidunexpectedobstaclesandcanpassslowervehicleswithoutdanger.Sightdistanceisthelengthofhighwayvisibleaheadtothedriverofavehicle.Theconceptofsafesightdistancehastwofacets:

“stopping”（or“nopassing”）and“passing”.

Attimeslargeobjectsmaydropintoaroadwayandwilldoseriousdamagetoamotorvehiclethatstrikesthem.Againacarortruckmaybeforcedtostopinthetrafficlaneinthep