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ScientificReport

ANINVESTIGATIONOFTHEITEFORMULAANDITSUSE

CP =

t + +

AbstractThisworkingreportisastudyoftheuniversallyadoptedITEformulawhichcalculatesatrafficlight’schangeinterval.Itssolepurposeistoprovidesafepassagethroughanintersectionforawiderangeofvehicletypesandpedestrianswithhightrafficflow.However,duetomisinformationandmisunderstandings(bothpresentedandfoundinthemanuals5referencedinthisreport)andlackofknowledgeoftheITEformula’sintendantusewiththemanydifferentState’svehiclescodes,safetyiscompromised.ProperunderstandingofthebasiclawsofphysicsisneededandtheProfessionalEngineers(PE)thatareapplyingtheITEformulatosetthetimingofanintersection’strafficlightsarerequiredbylawtounderstandandapplythesciencetoprovidepublicsafety.ThisreportispresentingthedetailsofhowtheITEformula’stermsareusedtocalculatetheyellowandall‐redphasetimesforvehiclestravelingthroughanintersectionwithconflictingtrafficandespeciallyhowtoapplytheformula’sclearancetermwiththetwoyellowlaws;thepermissiveandrestrictiveyellowlaws.Thereportincludestheneededtoolstoinvestigateandillustrateavehicleinmotion.Greatefforthasbeentakentosimplifytheinvolvedmathematicsandphysics.Allthekinematicformulasarederivedfromthebasicdefinitionoftheaveragevelocityandacceleration.Theinvestigationshowstheinherentdesignoftheformulaandthatthecriticalstoppingdistanceisthesourceofitsdesign.Givenbyavehicle’sspeed,adriver’sreactiontimeandasafedecelerationrate;thecriticalstoppingdistanceistheonlypointreferencedtoanintersection’sentrywhereadrivercaneitherstopsafelybeforeenteringorgothecriticaldistancetoreachtheintersection’sentrypointonalegalyellow.However,thedesignoftheformulaisnotallowingthedrivertoslowdownwithinthecriticalstoppingdistanceandentertheintersection.ThustheformulaisdesignedtoONLYaccommodateavehiclestoppingbeforeenteringortravelingthroughanintersectionatconstantoracceleratedspeed.Thenextreportwillcovertheyellowphasetimerequiredforturns;atimewhichisgreaterthancalculatedbytheITEformuladuetoavehicleisslowingdownwithinthecriticalstoppingdistancewhenperformaturningmaneuver.AuthorMatsJärlströ[email protected]‐671‐0312Beaverton,Oregon,USARevision:14•September9,2014

mailto:[email protected]

MatsJärlström•[email protected]•503‐671‐0312•Beaverton,Oregon,USA Rev.14•September9,2014

Page1 AninvestigationoftheITEformulaanditsuse

Tableofcontents Tableofcontents.....................................................................................................................................................................1 1.TheITEformula...................................................................................................................................................................2

1.1TheITEformula’sthreeterms 2 2.TheusageoftheITEformulaterms............................................................................................................................3

2.1Theyellowphase 3 2.2Theall‐redphase 3 2.3Thepermissiveyellowlaw 3 2.4Therestrictiveyellowlaw 3

2.4.1Restrictivelawyellowtrafficlightviolation.........................................................................................3 2.5SummaryoftheITEformulaandthetwoyellowtrafficlightlaws 4

3.Perceptionandreactiontime........................................................................................................................................5 4.Stoppingandclearancetime..........................................................................................................................................5 5.Kinematics–Thegeometryofavehicleinmotion...............................................................................................6

5.1Vehiclemotionandthemathematics 6 5.2Motioninputvariables 6 5.3Constantdecelerationoracceleration 6 5.4Constantaccelerationgraphingoptions 7 5.5Thebenefitsofthevelocityversustimegraph 7

6.Firstmotionexample:Avehicletravelingwithaconstantvelocity..............................................................8 7.Secondmotionexample:Avehicletravelingwithaconstantacceleration................................................9 8.Thirdmotionexample:Avehicletravelingwithastoppingmotion...........................................................10

8.1Totaltraveleddistancecalculations 10 8.2Stoppingtimecalculations 12 8.3Totalstoppingtimecalculations 12 8.4ComparisontotheITEformula 12 8.5Whythedifference? 13

9.ITEformulaexampleusingtypicalinputvalues..................................................................................................13 9.1Speedunitconversion 13 9.2Calculationoftheyellowphasetime 13 9.3Preparingtographtheexample 14 9.4Calculationoftotalstoppingtime 14 9.5VerificationoftheITEdecelerationrate 14 9.6Calculationofthetotalstoppingdistance 14 9.7GraphoftheITEformulaexample 15 9.8Grapharea‐distancecalculations 15 9.9Driverdecisionsandoptionalbehavior 16 9.10TheITEformulaexample’sconclusions 16

10.Fourthmotionexample:Avehiclemakingarighthandturn......................................................................17 11.References.........................................................................................................................................................................18 12.AppendixA‐DefinitionoftheYellowTrafficSignalforVehiclesbyState............................................19 13.AppendixB‐EmergencyStoppingDistancesandTimeCalculations(Rev.10)..................................24 14.AppendixC‐DecelerationRatesandStoppingDistancesComparison(Rev.5).................................25

ThisreportisdedicatedtoMarianneJärlströmandDavidHodge.



AninvestigationoftheITEformulaanditsuse Page2

1.TheITEformulaTheInstituteofTransportationEngineers’ITEformulawasdevelopedbyDenosGazisfromGMResearchLabs,RobertHermanandAlexeiMaradudinandpresentedin1959inthepaper“TheProblemoftheAmberSignalLightinTrafficFlow”1.Todaytheformulaisusedworldwidetocalculatetrafficlightphasetimessuchastheyellowchangeandall‐redclearanceintervals.Hereisoneexampleofthisformula12345:

CP =

t +2 2

+ (1.1)

Where:CP = ChangePeriod,totalcombineddriverperceptionandreaction,vehiclestoppingand

clearancetimes,resultexpressedinseconds,(s).t = Perceptionandreactiontimeofthedriver,typically1.0secondsforanexpectedevent,(s).

V = Speedoftheapproachingvehicle,expressedinfeetpersecond,(ft/s).

a = Comfortabledecelerationrateofthevehicle,typically10feetpersecondsquared,(ft/s2).W = Widthoftheintersectionatwidestconflictpoint,expressed infeet,(ft).L = Lengthofvehicle,typically20feet,(ft).G = Accelerationduetogravity,32.2feet persecondsquared,(ft/s2).g = Gradeoftheintersectionapproach,inpercent(%)dividedby100,downhillisnegative

gradeanduphillispositivegrade.1.1TheITEformula’sthreetermsBystudyingtheITEformula(1.1)andtheindividualinputvariables,wecandeterminethatitconsistsofthreetermsandalltermsappeartospecifyorcalculatetimeinsecondsasfollows:

1. Perceptionandreactiontimeof the driver (1.2)

2. Decelerationtimeofthevehicle2 2

(1.3)

3. Intersectionandvehicleclearance time (1.4)

DescribingtheITEformula(1.1)anditsterms,theequationissimplifiedasfollows:

CP =

t +2 2

+

or

ChangePeriod = Perception

ReactionTime

+ DecelerationTime + Intersection&Vehicle

ClearanceTime

or

ChangePeriod = TotalStoppingTime + ClearanceTime




2.TheusageoftheITEformulatermsThissectionexplainshowthethreeITEformulatermsarecurrentlyused2toimplementthetimingoftrafficlightswithdifferentState’svehiclecodes5presentedinAPPENDIXA.2.1TheyellowphaseThedriverperceptionandreactiontime(1.2)andthedecelerationtime(1.3)termsaretypicallycombinedtocalculateatrafficlight’syellowphasetimewhichisalsothetotalstoppingtimeoftheITEformula.Thistotalstoppingtimeisalsodirectlylinkedtothe“onesafestoppingdistance”orGazis’“criticalstoppingdistance”whichwillbefurtherinvestigatedlaterinthisreport.2.2Theall‐redphaseTheremainingterm,theintersectionandvehicleclearancetime(1.4),iscommonlyusedtocalculatetrafficlightall‐redphasetimes.Theall‐redphaseisaclearancetimewhenalltrafficlightsareredandnovehiclesareallowedtoentertheintersectionfromanyofitsapproaches.Theall‐redphasetimeallowvehiclesthatarestillintheintersectiontoexitbeforeconflictingtraffic,includingpedestriansthataregivenagreenlighttoenter.Theclearancetermaddsanimportantsafetytimetoavoidtrafficaccidents.2.3ThepermissiveyellowlawThepermissiveyellowlightlawiswhenaState’svehiclecodeonlywarnsthatachangeofthetrafficlightfromyellowtoredisimminentandistherebypermittingadrivertoentertheintersectionduringthefullyellowphase.Forthislaw,theall‐redphaseismandatorysinceavehiclecanlegallyentertheintersectionattheveryendoftheyellowphaseandthusneedstimetodrivethroughandexittheintersectionduringtheprotectionoftheall‐redphase.Aviolationoccursifthedriverenterstheintersectiononaredtrafficlightsignal.2.4TherestrictiveyellowlawThereisalsoarestrictiveyellowlightlawwhereadriverfacingayellowlight“shallstop”andnotentertheintersectionunlessthedriver“cannotstopinsafety”.Adrivercannotstopinsafetyifthedriverisclosertotheintersectionthan“onesafestoppingdistance”orthe“criticalstoppingdistance”.SomeState’srestrictiveyellowlightvehiclecodesalsoaddinstructionsforadriver’soptionalbehaviorwhenfacingtheyellowlightsuchas“ifadrivercannotstopinsafety,thedrivermaycautiouslydrivethroughtheintersection”.Here,the“drivethroughtheintersection”istheITEformula’sclearanceterm(1.4)whichforarestrictiveyellowlightlawisaddedtothetrafficlight’syellowphasetime.Inaddition,theword“cautiously”isinstructingthedrivernottoacceleratetoreachandcleartheintersection’sexit.Anyunsafeaccelerationwouldalsoviolatethespeedlimitifthedriverapproachedtheintersectionatthespeedlimit.Fortherestrictiveyellowlightlawtheall‐redphaseisoptionalsincetheclearancetimeisalreadyincludedintheyellowphasetime.2.4.1RestrictivelawyellowtrafficlightviolationAjurisdictionhavingtherestrictiveyellowlightvehiclecodecanciteadriverrunningayellowlightbecausetheyellowphasetimeincludestheclearanceterm(1.4)andisthereforelongerthanjusttheITEformula’stotalstoppingtime.Thewords“shallstop”usedbytherestrictiveyellowlawisspecificallyaddedtoprohibitorrestrictthedrivertousetheaddedclearancetimetoenterthe




intersection.Thusacitationcanbeissuedifthedriverenterstheintersectionduringtheaddedyellowclearancetime.(Seealsothemarked“ViolationArea”infigure1).2.5SummaryoftheITEformulaandthetwoyellowtrafficlightlawsTosummarizetheITEformula’stermsandtheirusagewiththepermissiveandtherestrictiveyellowlightlawswehave:

ThePermissiveYellowLawWherethedriverispermittedtoentertheintersectionduringthefullyellowphase.

2 2

“TotalStopping” “Clearance”

TheRestrictiveYellowLawWherethe“drivershallstopfacingthelight”duetotheclearancetimeisaddedtotheyellowphase.

2 2

“TotalStopping+Clearance"

Thebelowfigure1illustratestheITEformulatermsandthetwoyellowtrafficlightlawsinascaledintersectionshowingrelativetrafficlightphasetimesforaconstantvelocityvehicle.Thetiminggraphsofthetrafficlightsalsoshowhowtheall‐redphaserelatestotheconflictingtrafficsignalandwhenatrafficlightviolationoccurswiththetwodifferentlaws:

Crosswalk

RESTRICTIVEYellowLaw

PERMISSIVEYellowLaw

ConflictingTrafficSignal

t V2a+2Gg

W+LV

ConstantVehicleVelocity,V

Car&PedestrianConflictingTraffic

+ +

CAR CARCAR

Fig.1‐TheITEFormulaRelativeaTrafficLightIntersectionandtheTwoYellowLightLaws

All‐RedPhase

CAR

TRAFFICSIGNALS:

Entry

PedestrianPath

Time,t

CP=

ClearanceTime

"OneSafeStoppingDistance"

"OneSafeStoppingDistance"

ClearanceTime

ClearanceTime

Confli ct ingCar

&

Perception

Reaction

"Critical

Stopping

Distance"

Exit

Clearance

ViolationArea




3.Perceptionandreactiontime Driverperceptionandreactiontime67isatimewherenochangesaretakingplacetoavehicle’smotion.Thisisduetoittakesadriversometimetoperceiveandreactto,forexampleatrafficsignalchangingfromgreentoyellowandtomakeadecisionwhetherheorsheshouldmakeanychangessuchasstoporgo.Thetimeittakescanbebrokendownintothreecategoriesdependingonwhattypeofeventthedriverisreactingtoorismaking.ThreelowcomplexitytypeofeventsandsometypicalperceptionandreactiontimesusedbyITEwithexamplesareasfollows:

1. Unexpectedexternalevent: 2.5seconds‐Adeerenteringtheroadway.

2. Expectedexternalevent: 1.0seconds‐Achangingtrafficlightortrafficcontroldevice.

3. Plannedinternalevent*: 0.0seconds‐Adriverismakingalanechangeoraturn.

*Eventintroducedbyauthor.Note:Atrafficlightisconsideredanexpectedeventbutanincorrectlytimedtrafficlightintersectioncancauseunexpectedeventssuchaspedestrianorvehicleinterferences.Inaddition,differentvehiclebrakingsystemssuchastractor‐trailer,schoolandpublicbusairbrakeswilladdanextrareactiontimedelayof0.5secondsormore8.4.StoppingandclearancetimeBystudyingthestoppingandclearancetermsoftheITEformula,weseethefollowinginputvariables;vehiclelength,vehiclespeedandvehicledeceleration,plusintersectiongradeandintersectionclearancewidth.Distance,velocityandaccelerationcanbepresentedingraphformtohelpusvisualizeandinvestigatethetruephysicalnatureoftheITEformula.Thenextstepistointroducevisualtoolssuchasvehiclemotiongraphs.Note:Sincethisisworkingreport,nextversionwillincludedmoredetailedstudiesoftheindividualinputvariablesofITEformulainthissection.AppendixBandCareincludedatthistimewhichpresentsomeofthisinformation:AppendixBispresentingtheeffectsofdifferentstoppingdistancesbasedonmaximumroadwayfriction(emergencystopping)67andairbrakedelaysneededbytrucks,publicandschoolbusses8.AppendixCispresentingacollectionofmaximumdecelerationsratesfordifferentvehicletypesandalsotheir“cargo”whichincludesbuspassengersandtherelatedstoppingdistances.




5.Kinematics–ThegeometryofavehicleinmotionThegoalistoinvestigatetheITEformulaandhowitrelatestoavehicle’smotionintimeandspacebyusingbasicmathematicsandalsopresentitsmotionusingvisualgraphingtools.5.1VehiclemotionandthemathematicsAvehiclehasthreetight‐coupledvariablesofmotion;distance(d),velocity(V)andacceleration(a).Thebelowflowdiagraminfigure2illustratesthesestatesofmotionandhowtheyarelinkedthroughmathematicalcalculusfunctionswhicharecalleddifferentiationandintegration.Differentiationislookingataplottedcurve’sslopeandintegrationislookingattheareaunderaplottedcurve.However,thisdocumentisgoingtopresentasimplifiedmethodtouse“calculus”toanalyzetheITEformulabyavoidingadvancedmathematicsoncurves.

Integration(Area)

∆

∆

∆∆

∆∆

Differentiation (Slope)

Fig.2‐FlowDiagramofMotionoverTimeandtheirMathematicalRelationships

Figure2presentsthatthethreevariablesofmotionarecloselyconnectedthroughmathematics.Wecanmathematicallyconvert,forexample,accelerationtovelocitybyintegratingaccelerationoverelapsedtime(Δt),(thesymbol“Δ”represents“change”).Wecanalsoconvertdistanceovertimetovelocitybyusingdifferentiation.Usingwords,wecanalsodescribedifferentiationandhowitrelatestoadriverofavehicle:Thevehicle’svelocityisthefirstderivativeofthedistance.Steppingontheacceleratororthebrake,weexperienceasecondderivative‐accelerationordeceleration.5.2MotioninputvariablesWearefamiliarwithbothdistanceandvelocitysincemostvehiclesareequippedwithbothanodometerfordistanceandaspeedometerforspeed.Typicallywehavenostandard“meter”installedinourcarstomeasureacceleration,eventhough“g‐meters”arepopularasanaccessoryforperformancecarenthusiasts.IntheUnitedStates,vehicleodometersmeasuredistanceinmilesandthespeedometersmeasurevelocityinmilesperhour(mph).Asadriver,wecontinuouslymonitortheinstantaneousvehiclespeed(V),ifnot,wemightgetaspeedingcitation.5.3ConstantdecelerationoraccelerationTheITEformulaisusingvehiclevelocity(V)asoneimportantinputvariable.Theformulaisalsoincludingaconstantdecelerationrate(a)definedwithatypicalvalueof10ft/s2.Thisconstantdecelerationrate(a)istellingushowfastavehicleisslowingorisabletoslowdownorstop.OneimportantfactortounderstandisthattheITEformula’saveragedecelerationrateisaconstantrateorvalueovertimeandcaneasilybeplottedinagraph.

Velocity,VDistance,d Acceleration,a




5.4ConstantaccelerationgraphingoptionsLetuslookatthegraphingoptionsbasedonanaverageconstantacceleration(a)andseehowthecloselyrelatedvelocity(V)anddistance(d)arevisuallypresentedversustime.

Slope=Velocity

0

Distance

0

Fig.3‐GraphingOptionsforMotionwithConstantAcceleration

ftVelocity

Time

ft/sAcceleration

Time

ft/s2

0 0

aV

Time

t s

d

0 t s 0 t s

ConstantAcceleration

Cons

tnat

Acceleration

ConstantAcceleration

Area=Velocity

Area=DistanceSlope=Acceleration

(Area)

(Slope)

Integration

Differentiation

(Area)

(Slope)

Integration

Differentiation

A B C

Figure3showshowtheaverageconstantacceleration(a)isplottedusingthethreevariablesofmotionversustime.Studyingtheabovegraphsinfigure3A,BandCwesee:

A. Distance(d)versustime(t)graphshowsconstantacceleration(a)plottedasacurve.

B. Velocity(V)versustime(t)graphpresentstheconstantacceleration(a)asastraightlineraisingovertime.

C. Acceleration(a)versustime(t)graphrepresentstheconstantacceleration(a)asastraighthorizontalline.

Wecanalsoseeinfigure3thatsomeareasundertheplottedlinesareshapedastrianglesorrectangles.Wealsoknowthatwecanmathematicallytransform,forexample,accelerationtovelocityorvelocitytodistanceusingthecalculusfunctioncalledintegration.Integrationisthesameascomputingtheareaunderaplottedcurve.Bycarefullychoosingagraphingmethodthatwillavoidcurvesandonlyusesstraightlineswecansimplifythemathematicsforthe“integration”orareacalculationstobasicgeometryareacalculationsofrectanglesandtriangles:

Areaofarectangle Height Width

AreaofatriangleHeight Width

2

Width

HeightArea

Rectangle

Width

HeightAreaTriangle

Forexampleinfigure3C,velocity(V)istheintegrationofacceleration(a).Thus,integrationistheareaundertheplottedlineintheaccelerationversustimegraphwhichisequaltothe“height”constantacceleration(a)timesthe“width”elapsedtime(Δt).5.5ThebenefitsofthevelocityversustimegraphFromthethreegraphingoptionswecanseethatbychoosingavelocity(V)versustime(t)graphwegetthesekeybenefits:

1. Theconstantacceleration(a)definedbytheITEaveragedecelerationrate,isvelocity(V)plottedasastraightlineinavelocityversustimegraph.




2. Singleintegrationwhichistheareaundertheplottedlineofthevelocityversustimegraphwillcalculatetraveleddistance(Δd)duringtheelapsedtime(Δt).

3. Theintegrationofthevelocityversustimeplotbecomessimplesincethegraphonlyhavestraightlinesandwecanusebasicmathematicssuchasareaandgeometrycalculationsofrectangularandtriangularshapes.Thusavoidingusingadvancedcalculusfunctionsormathematicsoncurves.

4. Velocityorvehiclespeedistheinstantaneousmeasurementweasdriversaremostfamiliarwith.

BeforewegraphtheITEformulaitselfwecanstarttolookatsimplevehiclemotionprofilesusingthisgraphingmethodandseewithexampleshowvehiclevelocityorspeedversustimerelatetodistanceandaccelerationandtheircorrespondingmathematicalformulas.6.Firstmotionexample:Avehicletravelingwithaconstantvelocity

Velocity,V

Time,t

t0 t100

V0

Fig.4‐ConstantVelocity

Area

Variables:

Δ Δ Δ

Formulas:

ΔΔ

Δ Δ

ΔΔ

Figure4showsavelocityversustimegraphofavehicletravelingataconstantspeedV0fromtimet0totimet1.Theconstantspeedisrepresentedasastraighthorizontallineovertime.Speedorvelocityisdefinedasdistancetraveledoverelapsedtimeaswealsoseeintheunitsweuseforspeedsuchasmilesperhour(mph).Basedonthedefinitionofaveragevelocitywehave:

,, Δ, Δ

(6.1)

Rearrangingaboveequation(6.1)wealsoget: , Δ Δ (6.2)

And:

, ΔΔ (6.3)

Area Distance, ∆




Wecanalsoseethattheareaunderthegraphistheheight(velocity,V0)multipliedwiththewidth(elapsedtime,Δt=t1‐t0).Thisareaunderthegraphisthesameasthetraveleddistance(Δ )ofthevehicleasshowninequation(6.2).Thisvisualunderstandingthattheareaundertheplottedlineinavelocityversustimegraphequalsdistancewillbeveryusefulwhenwestarttolookatmorecomplexmotionprofileswithchangingvehiclespeedsovertime.Thischangeofvelocityovertimeisalsoreferredtoasaccelerationordeceleration.7.Secondmotionexample:Avehicletravelingwithaconstantacceleration

Velocity,V

V

Time,t

Fig.5‐ConstantAccelerationt0 t1

00

1

Acceler

ation,a

V0

Area

Variables:

Δ Δ Δ

Formulas:

Δ

Δ

Δ

Δ Δ2

Δ2

Figure5showsavelocityversustimegraphofavehicleacceleratingataconstantrate(a)fromastandstill.Attimet0thevehiclehasreachedaspeedV0andattimet1thevehiclehasreachedspeedV1.Theaverageacceleration(a)ofthevehicleisdefinedaschangeinvelocity(V1‐V0)overelapsedtime(Δt=t1‐t0).Thedefinitionofaverageaccelerationis:

,,, Δ

(7.1)

Whenthevehiclespeedisincreasingovertime,aspresentedinfigure5,thetermV1‐V0informula(7.1)becomespositiveandwehavepositiveacceleration.IfthevehiclespeedisdecreasingovertimethetermV1‐V0becomesnegativeandwegetnegativeacceleration.Negativeaccelerationisalsocalleddecelerationandoccurswhenthevehicleisslowingdownorstopping.

Rearrangingaboveequation(7.1)wealsoget:

, Δ (7.2)

And:

, Δ (7.3)Note:Asfigure5shows,V1representsendvelocityandV0initialvelocity.

Area Distance, ∆




Infigure5,theareaunderthegraph,whichisalsothedistancethevehicleistravelingduringtheelapsedtime(Δt=t1‐t0),isnotaseasytocalculateaswiththepreviousconstantvelocityvehicleexample.Tosolvetheproblemwewilllookatthetwospeedvaluesattimet0andt1andcalculatetheaveragevelocity.TheaveragevelocityissimplethesumofV1+V0dividedby2.Theareaunderthecurveisthentheaverage“height”orvelocitytimestheelapsedtime“width”.Theformulaforthetraveleddistance(Δ )duringtheelapsedtime(Δt)isthen:

, Δ Δ2

(7.4)

Ifwedonotknowthetime(Δt)wecancombinetheabovedistanceformula(7.4)withtheformulaforelapsedtime(7.2)asshownhere:

Take(7.2) Δ andcombinewith(7.4) Δ Δ2

whichgives:

, Δ2

(7.5)

Hint:Usetheconjugaterule tocombinetheaboveformulas.8.Thirdmotionexample:Avehicletravelingwithastoppingmotion

Velocity,V

Time,t

t0 t2=00

V1

Fig.6‐ConstantVelocityandDecelerationt1

Deceleration,aArea1 Area2

V2

V0,

Area1formulas:

, ∆Δ

, Δ ∆ Area2formulas:

, ∆

, Δ ∆2

, Δ2

Figure6showsavehicletravelingwithaninitialconstantvelocity(V0)upuntiltimet1.Thevelocity(V1)attimet1isstillV0sowehaveV0=V1.Fromt1thevehicleisdeceleratingataconstantrate(a)toacompletestopattimet2.Ifwealsointroduceaninitialtimet0whichisanaddedtimebeforethevehicleisdeceleratingweseethatthisisavehiclemotionprofilethatistakingtheshapeofthefirsttwotermsoftheITEformula(1.1)–driverperceptionandreactiontime(t1–t0)plusvehiclestoppingtime(t2–t1).8.1TotaltraveleddistancecalculationsTheITEformula’sfirsttermisthedriverperceptionandreactiontime.Infigure6wecansettheelapsedtime(Δt1)betweentimet0tot1tobethedriverperceptionandreactiontimevalue.Area1

Area1 Distance, ∆

Area2 Distance, ∆




isthenthedistancethevehiclewouldtravelduringthisperceptionandreactiontime.Wecanusethefirstmotionexampleanduseitsinformationwithformula(6.2)sincebetweentimet0tot1bothmotionexamplevehiclesaretravelingataconstantvelocity.Thearea1anddistance(Δd1)traveledduringtheperceptionandreactiontime(Δt1=t1‐t0)isthen: Δ Δ Δ (8.1)Fromtimet1tot2,figure6isshowingavehicle’smotiontoslowdowntoacompletestop.Attimet1thevehicle’sspeedisV1anditstartstodeceleratewithanaveragenegativeacceleration(a)untilithascometoacompletestopattimet2.Area2isthedistance(Δd2)thevehicleistravelingduringthestoppingordecelerationtocometoacompletestop.Tocalculatearea2whichisthedistance(Δd2)infigure6wecanusethesamemethodsandformulasasinthesecondmotionexamplewherethevehiclechangevelocityovertime.Inthisexample,thevehicleisdeceleratingtoacompletestopsoattimet2thevelocityiszero(V2=0).Therefore,thetwodistanceformulas(7.4)and(7.5)thenbecome:

2 Δ2

or 2 Δ2

SetV2=0(sincevehiclestoppedcompletely)andweget:

Δ2 or Δ

2

Since(a)isdecelerationornegativeacceleration,wechangethesignof(a)toget:

Δ2 or Δ

2

Thetotaltraveleddistance( d)infigure6fromtimet0totimet2isthen:

Δ Δ Δ andset

Δ2 or Δ

2

IfwecomparetheITEformulawiththetwoabovedistanceequationsweseethattheequationincludingthedecelerationterm(a)isthebestchoiceduetothisvariableispartoftheITEformulaasoneofthespecifiedinputvalues.Wecanalsosimplifytheformulabyusingthevariable(t)forthedriverperceptionandreactiontimeinsteadoftheelapsedtime(Δt1=t1‐t0).Thetotalstoppingdistanceformulaforthismotionexamplethanbecomes:

, Δ2 (8.2)

Theabovedistanceformula(8.2)isalsotheITE“onesafestoppingdistance”orthe“criticalstoppingdistance”ifthevehicleisstoppingonalevelapproachgrade(g=0),travelingataconstantapproachspeed(V),settingthedriverperceptionandreactiontimeto(t)andtheroadconditionsandvehiclebrakeswillallowadecelerationrate(a).




8.2StoppingtimecalculationsLetusnowtakealookatthetimeittakesforthevehicletodeceleratefromtimet1tot2infigure6.Inthesecondmotionexamplewestudiedaccelerationandweusedthedefinitionoftheaverageaccelerationtoderivetheelapsedtimeformula(7.2)againseenhere:

Δ

Inthecurrentexampleweareusingdifferentreferencestotheinitialvelocityandtheendvelocity.Wecanrewriteformula(7.2)tomatchthisexample’sarea2asfollows:

Δ

WealreadysetV2=0inthisexamplesincethevehiclehascompletelystoppedattimet2.Wealsoknowthattheaverageacceleration(a)isnegativesincethevehicleisdecelerating.SettingV2=0andchangingthesignofvariable(a)torepresentdecelerationinsteadofaccelerationweget:

Δ (8.3)

Theaboveformula(8.3)calculatesthestoppingtimeofthevehicleinfigure6whichisdeceleratingatrateof(a)toacompletestopfromaninitialvelocityof(V1).8.3TotalstoppingtimecalculationsByaddingthedriverperception‐reactiontime(t)(Area1,Δt1=t1‐t0infigure6)toformula(8.3)wegetthetotalstoppingtimeΔtfromtimet0totimet2.Thus,thisformulawouldcalculatethetimeittakesforavehicletotravel“onesafestoppingdistance”orthe“criticalstoppingdistance”asperequation(8.2).Addingtheperception‐reactiontime(t)toformula(8.3)weget:

, Δ (8.4)

8.4ComparisontotheITEformulaLetusnowcompareequation(8.3)forthevehicle’sstoppingordecelerationtimeinfigure6withtheITEformula’ssecondterm(1.3)whichiscalculatingthevehicle’sdecelerationtimeusedforyellowtrafficlightchangeintervals.

Deriveddecelerationtimeformula (8.3): ITEformuladecelerationtimeterm(1.3):

Δ 2 2

SetV1=V(vehicleapproachspeed)andweget Ifgradeislevel,setg=0andweget

2

Theabovecomparisonshowthatthederivedstoppingtimeformula(8.3)isNOTmatchingtheITEformula’sdecelerationterm(1.3)andthetimeittakestodeceleratetozerofromaninitialspeed(V)foragivendeceleration(a).




8.5Whythedifference?TheITEformula’sdecelerationterm(1.3)showanextra“2”initsdenominatorcomparedtoformula(8.3)whichiseffectivelydoublingthedecelerationrate(a)ordividingthevehicle’sapproachspeed(V)by2.Factis,theITEexpressionwillreducethecalculatedstoppingtimebyafactoroftwo.Weneedtoinvestigatewhythis“2”isaddedandalsowhateffectsithastothetimingofatrafficlight’schangeintervalrelatedtoavehicle’smotion.ItisnowtimetouseallthederivedformulasandthevisualgraphingtoolsbycalculatinganactualexampleusingthetypicalinputvaluesrecommendedbytheUSFederalHighwayAdministrationandtheinternationalInstituteofTransportationEngineers.

9.ITEformulaexampleusingtypicalinputvaluesForthisexamplewewillcalculatetheyellowtrafficlight’sstoppingtimeinapermissiveState(noclearancetimeaddedtotheyellowphase)fora30mphapproachspeedatalevelintersection.TheITEformulaandtheinputvaluesareasfollows:

2 2

(9.1)

Where:t = Perceptionandreactiontimeofthedriver,typically1.0secondsforanexpectedevent,(s).

V = Speedoftheapproachingvehicle,expressedinfeetpersecond,(ft/s).

a = Comfortabledecelerationrateofthevehicle,typically10feetpersecondsquared,(ft/s2).G = Accelerationduetogravity,32.2feetpersecondsquared,(ft/s2).g = Gradeoftheintersectionapproach,inpercent(%)dividedby100,downhillisnegative

gradeanduphillispositivegrade.9.1SpeedunitconversionFirstweneedtoconvertthe30mphvehicleapproachspeedtoft/ssoweworkwiththecorrectunits.Todothisconversionwelookattheunitmphwhichismilesperhour.Weknowthatonemileis5280feet.Wealsoknowthatonehourissixtyminutesandoneminuteissixtysecondssowecansetupthemphtoft/sconversionlikethis:

1 1528060

528060 60

52803600

1.466667 /

Theexamplehasanapproachspeedof30mphandifweapplythemphtoft/sconversionconstantweget:

1.466667/

30 44 /

9.2CalculationoftheyellowphasetimeNext,wecanaddtheinputvaluestotheITEformulafortheexamplecalculation:

2 2

1.044 /

2 10 /1.0 2.2 3.2

Note:Theterm“2Gg”becomeszerosincethisexamplehasalevelapproachgrade(g=0).




LetusnowplottheexampleinavelocityversustimegraphusingthetypicalITEformulainputvaluesandalsovisuallypresenttheabovecalculatedtrafficlight’syellowphasetimeof3.2secondsreferencedtothevehicle’smotionprofile.9.3PreparingtographtheexampleToplottheexampleweshouldfirstinvestigatethedatatosetthevelocityandtimescalesappropriately.Hereisaninitiallistofthekeyeventsordatapointstoplot:

Vehicleapproachspeed,V=44ft/s(30mph) Driverperception‐reactiontime,t=1.0s Vehicledecelerationrate,a=10ft/s2 Yellowphasetime=3.2s

9.4CalculationoftotalstoppingtimeThepreviouslistpresentamaximumvelocityof44ft/sandamaximumITEyellowphasetimeof3.2seconds.Letusinvestigatethevehicle’sstoppingtime,Δ basedontheapproachspeed(V)anddeceleration(a)usinginformationandthederivedformula(8.3)fromthethirdmotionexample.Addingtheexamplevaluesweget:

, Δ44 /10 /

4.4

Ifwecanalsocalculatethetotalstoppingtimeusingformula(8.4)whichincludesthe1.0secondsdriverperception‐reactiontime(t)andwehave:

, Δ 1.044 /10 /

5.4

Basedonthisweseethatthehorizontaltimescaleshouldbeaminimumof5.4seconds.9.5VerificationoftheITEdecelerationrateWecanalsocheckthattheITEdecelerationrate,a=10ft/s2iscorrectbyusingtheformulaforthedefinitionofacceleration(7.1).Setvehiclestoppingtime,Δ =4.4s,vehicleapproachspeed,V0=44ft/sandV1=0sincethevehiclecomestoacompletestopinformula(7.1):

, ,

, ∆

Addvaluespluschangeaccelerationtodeceleration(changesignofV0andsetV1=0)andweget:

∆44 /4.4

10 /

Theaboveresultshowsthatthestoppingtime,∆ =4.4sandtheITEdecelerationrate,a=10ft/s2areverifiedcorrectlyat44ft/s(30mph)vehiclespeed.9.6CalculationofthetotalstoppingdistanceLetusalsocalculatetheexamplevehicle’stotalstoppingdistancewhichisalsoincludingthedistancethevehicleistravelingduringthedriverperception‐reactiontime.Herewecanusethe“onesafestoppingdistance”orthe“criticalstoppingdistance”formula(8.2)whichwasderivedinthethirdmotionexample.




Theformulaandaddingtheexamplevaluesweget:

Δ2

1.0 44 ⁄44 ⁄

2 10 ⁄44 96.8 140.8

Thecalculated“criticalstoppingdistance”of140.8feetisthedistanceittakesforavehicletostopifitistravelingat30mphandthedrivertakesonesecondtoreactandrespondtoachangeofatrafficcontroldevicebasedonthecomfortableornonemergencyITEdecelerationrateof10ft/s2.Wenowhaveallinformationneededtoplottheexamplewithvalues.9.7GraphoftheITEformulaexample

‐1.0

Velocity,V

Time,t

Fig.7‐ITEFormulaExample‐30MPHVehicleMotionandTheYellowPhase

10

20

30

40

50

0

20

30

5

15

25

35

45

55

10

5

15

25

35

0.0‐0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 seconds

ft/smph

V=44ft/s(30mph)

a=10ft/s,ITEDecelerationRate

TheITEFormulaYellowPhaseTime

3.2s

Area1 Area2

INPUTVALUESApproachSpeed,V=30mphITEPerception‐ReactionTime,t=1.0sITEDecelerationRate,a=10ft/sApproachGrade,g=0

Area3

Area4

"Stop"

"Go"

"StoporGo"DecisionPoint

"Go"DistanceArea1+2+4

"Stop"DistanceArea1+2+3

22ft/s

NOTE:Area3=Area4

5.4s1.0s0.0s

2

2

9.8Grapharea‐distancecalculations

Figure7 AverageVelocity,V(Height) ElapsedTime,Δ (Width) Distance,Δd(Area)

Area1: 44 / × 1.0s = Δd1=44.0ft

Area2:44 ⁄ 22 ⁄

233 / × 2.2s = Δd2=72.6ft

Area3:22 ⁄ 0 ⁄

211 / × 2.2s = Δd3=24.2ft

Area4:0 ⁄ 22 ⁄

211 / × 2.2s = Δd4=24.2ft




Summaryofcalculateddistanceresultsfromfigure7

Driverperception‐reactiondistance: (Area1) Δd1=44.0ft

Vehicle“Stop”distance: (Area2+3) Δd2+Δd3=96.8ft

Total“Stop”distance: (Area1+2+3) Δd1+Δd2+Δd3=140.8ft

Total“Go”distance: (Area1+2+4) Δd1+Δd2+Δd4=140.8ft

9.9DriverdecisionsandoptionalbehaviorFigure7showsavehicletravelingataspeedof30mphor44ft/s.Attime0.0secondsthedriverseesachangeofatrafficcontroldevice‐atrafficsignalischangingfromgreentoyellow.Thedrivertakes1.0secondstoperceiveandreacttothetrafficlight’sphasechange.Duringthedriverperceptionandreactiontimeof1.0secondsthevehicleistraveling44ft(Area1).Afterthistimethedrivershallhavedecidedtoeither“stop”or“go”asfollows:

“Stop”decisionAt1.0secondsthedriverdecidestostopandthevehicleisdeceleratingatthetypicalrateof10ft/s2.Ittakes4.4secondstodeceleratetoacompletestopandduringthedecelerationthevehicleistraveling96.8ft(Area2and3infigure7).Thetotaltimeanddistancetraveled(includingthedistancethevehicletraveledduringthe1seconddriverperception‐reactiontime)is5.4secondsand140.8feet.Thistotal“Stop”distancetraveledisequivalenttoaddingArea1,2and3infigure7.

“Go”decisionAt1.0secondsthedriverdecidestomakenochangesandcontinuesattheconstantvehiclespeedof30mphor44ft/s.Duringtheyellowlight’stotalphasetimeof3.2secondsthevehiclewilltraveladistancedefinedinthefirstmotionexampleusingformula(5.2):

Δ Δ 3.2 44 ⁄ 140.8

Thetotal“Go”distanceof140.8feetisequivalenttoaddingArea1,2and4foundinfigure7.Wecanseethatthisconstantvelocitytraveleddistanceduringtheyellowlightphasetimeisthesameasforthedriverandvehiclethatdecidedtostopanditstotalstoppingdistance.

Usingtheunderstandingthattheareasundertheplottedlinesinfigure7areequaltothedistancetraveled,wehave:

Area1+2+3=Area1+2+4,sinceArea3=Area4

9.10TheITEformulaexample’sconclusionsBystudyingtheexamplewecanseethatthe“Go”vehiclewilltravelthesamedistanceduringtheITEformula’syellowphasetimeasthe“Stop”vehiclewilltraveltoacompletestop.However,the“Stop”vehiclewilltake5.4secondstocompleteitstraveleddistanceversus3.2secondsforthe“Go”vehicle.WecannowdrawtheconclusionthattheITEformulafortheyellowlight’stotalstoppingtimeisactuallyNOTbasedontime–theformulaisbasedonequaldistancetraveledfora“Stop”ora“Go”vehicleuptoaspecificpoint–theintersection’sentrypoint.Thisunderstandingexplainstheadded




“2”inthedenominatoroftheITEformula’sdecelerationterm(1.3)sincetheformulaitselfviolatesthebasiclawsofphysics.Yet,theITEformulaiscalculatingthetrafficlight’syellowphasestoppingTIMEforapermissiveStateintheexampleandwefindthatthe“onesafestoppingdistance”orthe“criticalstoppingdistance”isthereforethemostimportantformulatounderstandfortheexampleisasfollows:

Ifadrivertravelingat30mphfacesayellowlightwhenheiscloserthan“onesafestoppingdistance”totheentryoftheintersectionhemust“Go”andcontinueatthesameconstantspeedwithoutslowingdownreachingtheintersection’sentry.IfthedriverisslowingdownhemightnotbeabletoreachtheentryduringthetimeallocatedbytheITEformula’scalculatedyellowphasetimeandwillthusviolatetheredlight.

Ifadrivertravelingat30mphfacesayellowlightwhenheisfartherawaythan“onesafestoppingdistance”totheentryoftheintersectionhe“shallstop”andthedriverisabletostopcomfortablyandsafelybasedontheinputvariablesfortheITEformula.

Finally,basedontheunderstandingthattheITEformulaisnotcalculatingactualdecelerationtimeperthebasiclawsofphysics,weseethatthedecelerating“Stop”vehicleisstillmovingat15mphwhichishalftheapproachspeedwhentheyellowlight’sphasetimeendsanditistakinganother2.2secondstocometoacompletestop.Thetrafficlight’sphasechangetoredandtheextratimeisnotaproblemforthestoppingvehiclesinceitstillhas24.2feet(Area3)toreachthefull“onesafestoppingdistance”ortheintersection’sentrypoint.Thusthestoppingvehiclewillnotentertheintersectiononaredlight.However,whathappens,whenforinstance,avehicleiswithinthe“criticalstoppingdistance”andisslowingdowntomakearighthandturn?Letusinvestigate.10.Fourthmotionexample:AvehiclemakingarighthandturnTobecontinued…




11.References

1. “TheProblemofTheAmberSignalLightinTrafficFlow”,(DenosGazis,RobertHermanandAlexeiMaradudin),Nov.1959:http://jarlstrom.com/PDF/The_Problem_Of_The_Amber_Signal_Light_In_Traffic_Flow.pdf

2. “TrafficSignalTimingManual”,(USDepartmentofTransportation,FederalHighway

Administration&InstituteofTransportationEngineersITE),June2008,(Page119safestoppingdistances,permissive/restrictiveyellowlaws&ITEformula;pages137‐138):http://ops.fhwa.dot.gov/publications/fhwahop08024/fhwa_hop_08_024.pdf

3. “TrafficSignalTimingManual”,(InstituteofTransportationEngineers,ITE),2009,(Pages5,12&13):http://jarlstrom.com/PDF/Traffic_Signal_Timing_Manual_ITE_2009_p5_12_13.pdf

4. “MakingIntersectionsSafer:AToolboxofEngineeringCountermeasurestoReduce Red‐LightRunning”,(FederalHighwayAdministration&InstituteofTransportationEngineersITE),2003,(ITEformula,documentpage33,Chapter3,YellowChangeInterval):http://safety.fhwa.dot.gov/intersection/resources/fhwasa09027/resources/Making%20Intersections%20Safer%20‐%20A%20Toolbox%20of%20Engineering%20Count.pdf

5. “NCHRPReport731;GuidelinesforTimingYellowandAll‐RedIntervalsatSignalizedIntersections”,(NationalCooperativeHighwayResearchProgram),2012,(SeeChapter6,page44:"ShouldYellowChangeandRedClearanceIntervalTimingPracticesVaryBasedonStateVehicleCode?"anddifferencesbetweenStatespage64:"AppendixC"):http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_731.pdf

6. “StoppingSightDistanceandDecisionSightDistance”,(TransportationResearchInstituteOregonStateUniversityforODOT),Feb.1997:http://www.oregon.gov/ODOT/HWY/ACCESSMGT/docs/stopdist.pdf

7. “StoppingSightDistanceDiscussionPaper#1”,(OregonStateUniversity,RobertLayton,KarenDixon),April2012:http://cce.oregonstate.edu/sites/cce.oregonstate.edu/files/12‐2‐stopping‐sight‐distance.pdf

8. “2014‐2015OregonCommercialDriverManual”,(OregonDepartmentofTransportation,ODOT&DMV),2014,(Section5:AirBrakes):http://www.odot.state.or.us/forms/dmv/36.pdf


http://jarlstrom.com/PDF/The_Problem_Of_The_Amber_Signal_Light_In_Traffic_Flow.pdf

http://ops.fhwa.dot.gov/publications/fhwahop08024/fhwa_hop_08_024.pdf

http://jarlstrom.com/PDF/Traffic_Signal_Timing_Manual_ITE_2009_p5_12_13.pdf

http://safety.fhwa.dot.gov/intersection/resources/fhwasa09027/resources/Making%20Intersections%20Safer%20-%20A%20Toolbox%20of%20Engineering%20Count.pdf

http://safety.fhwa.dot.gov/intersection/resources/fhwasa09027/resources/Making%20Intersections%20Safer%20-%20A%20Toolbox%20of%20Engineering%20Count.pdf

http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_731.pdf

http://www.oregon.gov/ODOT/HWY/ACCESSMGT/docs/stopdist.pdf

http://cce.oregonstate.edu/sites/cce.oregonstate.edu/files/12-2-stopping-sight-distance.pdf

http://cce.oregonstate.edu/sites/cce.oregonstate.edu/files/12-2-stopping-sight-distance.pdf

http://www.odot.state.or.us/forms/dmv/36.pdf



12.AppendixA‐DefinitionoftheYellowTrafficSignalforVehiclesbyState

Source5:NCHRPReport731“AppendixC”

State Definition SteadyYellowSignalVehicleCode

Alabama PermissiveVehicular traffic facing a steady circular yellow or yellow arrow signal is thereby warned that the related green movement is being terminated or that a red indication will be exhibited immediately thereafter.

Alaska Permissive Nospecificinformationavailable,assumeUniformVehicleCodeasdefault.

Arizona PermissiveVehiculartrafficfacingasteadyyellowsignaliswarnedbythesignalthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Arizona Permissive

Vehiculartrafficfacingthesignaliswarned thattheredor"STOP"signalwillbeexhibitedimmediatelythereafter,andvehiculartrafficshallnotentertheintersectionwhentheredor"STOP"signalisexhibited.

California PermissiveAdriverfacingasteadycircularyelloworyellowarrowsignalis,bythatsignal,warnedthattherelatedgreenmovementisendingorthataredindicationwillbeshownimmediatelythereafter.

Colorado PermissiveVehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.

ConnecticutPermissive(Correctedbyauthor)

Vehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter,whenvehiculartrafficshallstopbeforeenteringtheintersectionunlesssoclosetotheintersectionthatastopcannotbemadeinsafety.

Delaware PermissiveVehiculartrafficfacingthecircularyellowsignalistherebywarnedthataredsignalforthepreviouslypermittedmovementwillbeexhibitedimmediatelythereafter.

Florida PermissiveVehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Georgia Permissive

Traffic,exceptpedestrians,facingasteadyCIRCULARYELLOW orYELLOWARROWsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Hawaii PermissiveVehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Idaho PermissiveAdriverfacingasteadycircularyelloworyellowarrowsignalisbeingwarnedthattherelatedgreenmovementisending,orthataredindicationwillbeshownimmediatelyafterit.

Illinois PermissiveVehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.


http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_731.pdf



Indiana PermissiveVehiculartrafficfacingasteadycircularyelloworyellowarrowsignaliswarnedthattherelatedgreenmovementisbeingterminatedandthataredindicationwillbeexhibitedimmediatelythereafter.

Iowa Restrictive

A"steadycircularyellow"or"steadyyellowarrow"lightmeansvehiculartrafficiswarnedthattherelatedgreenmovementisbeingterminatedandvehiculartrafficshallnolongerproceedintotheintersectionandshallstop.Ifthestopcannotbemadeinsafety,avehiclemaybedrivencautiouslythroughtheintersection.

Kansas Permissive

Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Kentucky Permissive

Vehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

LouisianaPermissive(Correctedbyauthor)

Vehiculartrafficfacingasteadyyellowsignalaloneistherebywarnedthattherelatedgreensignalisbeingterminatedorthataredsignalwillbeexhibitedimmediatelythereafterandsuchvehiculartrafficshallnotenterorbecrossingtheintersectionwhentheredsignalisexhibited.

Maine PermissiveIfsteadyandcircularoranarrow,meanstheoperatormusttakewarningthatagreenlightisbeingterminatedoraredlightwillbeexhibitedimmediately

Maryland Permissive

Vehiculartrafficfacingasteadyyellowsignaliswarnedthattherelatedgreenmovementisendingorthataredsignal,whichwillprohibitvehiculartrafficfromenteringtheintersection,willbeshownimmediatelyaftertheyellowsignal

Massachusetts Permissive Nospecificinformationavailable,assumeUniformVehicleCodeasdefault.

Michigan Restrictive

Ifthesignalexhibitsasteadyyellowindication,vehiculartrafficfacingthesignalshallstopbeforeenteringthenearestcrosswalkattheintersectionoratalimitlinewhenmarked,butifthestopcannotbemadeinsafety,avehiclemaybedrivencautiouslythroughtheintersection.

Minnesota Permissive

Vehiculartrafficfacingacircularyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection,exceptforthecontinuedmovementallowedbyanygreenarrowindicationsimultaneouslyexhibited.

Mississippi Restrictive

Vehiculartrafficfacingthesignalshallstop beforeenteringthenearestcrosswalkattheintersection,butifsuchstopcannotbemadeinsafetyavehiclemaybedrivencautiouslythroughtheintersection.




Missouri Permissive

Vehiculartrafficfacinga steadyyellowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

Montana Permissive

Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignaliswarnedthatthetrafficmovementpermittedbytherelatedgreensignalisbeingterminatedorthataredsignalwillbeexhibitedimmediatelythereafter.Vehiculartrafficmaynotentertheintersectionwhentheredsignalisexhibitedaftertheyellowsignal.

Nebraska Restrictive

Vehiculartrafficfacingasteadyyellowindicationistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection,andupondisplayofasteadyyellowindication,vehiculartrafficshallstopbeforeenteringthenearestcrosswalkattheintersection,butifsuchstopcannotbemadeinsafety,avehiclemaybedrivencautiouslythroughtheintersection.

Nevada Permissive

Vehiculartrafficfacingthesignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthatasteadyredindicationwillbeexhibitedimmediatelythereafter,andsuchvehiculartrafficmustnotentertheintersectionwhentheredsignalisexhibited.

NewHampshire Permissive

Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.

NewJersey Restrictive

Amber,oryellow,whenshownalonefollowinggreenmeanstraffictostopbeforeenteringtheintersectionornearestcrosswalk,unlesswhentheamberappearsthevehicleorstreetcarissoclosetotheintersectionthatwithsuitablebrakesitcannotbestoppedinsafety.Adistanceof50feetfromtheintersectionisconsideredasafestoppingdistanceforaspeedof20milesperhour,andvehiclesandstreetcarsifwithinthatdistancewhentheamberappearsalone,andwhichcannotbestoppedwithsafety,mayproceedacrosstheintersectionormakearightorleftturnunlesstheturningmovementisspecificallylimited.

NewMexico Permissive

Vehiculartrafficfacingthesignaliswarned thattheredsignalwillbeexhibitedimmediatelythereafterandthevehiculartrafficshallnotentertheintersectionwhentheredsignalisexhibitedexcepttoturnashereinafterprovided.

NewYork Permissive

Traffic,exceptpedestrians,facing asteadycircularyellowsignalmayentertheintersection;however,saidtrafficistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.




NorthCarolina Permissive

Whenatrafficsignalisemittingasteadyyellowcircularlightonatrafficsignalcontrollingtrafficapproachinganintersectionorasteadyyellowarrowlightonatrafficsignalcontrollingtrafficturningatanintersection,vehiclesfacingtheyellowlightarewarnedthattherelatedgreenlightisbeingterminatedoraredlightwillbeimmediatelyforthcoming.

NorthDakota Permissive

Vehiculartrafficfacingasteadycircularyelloworyellowarrowindicationistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficmaynotentertheintersection.

Ohio Permissive

Vehiculartraffic,streetcars,andtracklesstrolleysfacingasteadycircularyelloworyellowarrowsignalaretherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartraffic,streetcars,andtracklesstrolleysshallnotentertheintersection.

Oklahoma Permissive

Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.

Oregon Restrictive

Adriverfacingasteadycircularyellowsignallightistherebywarnedthattherelatedright‐of‐wayisbeingterminatedandthataredorflashingredlightwillbeshownimmediately.Adriverfacingthelightshallstopataclearlymarkedstopline,butifnone,shallstopbeforeenteringthemarkedcrosswalkonthenearsideoftheintersection,orifthereisnomarkedcrosswalk,thenbeforeenteringtheintersection.Ifadrivercannotstopinsafety,thedrivermaydrivecautiouslythroughtheintersection.

Pennsylvania PermissiveVehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreenindicationisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.

RhodeIsland Permissive

Vehiculartrafficfacingthesignaliswarned byitthattheredor"stop"signalwillbeexhibitedimmediatelyafterwards,andthevehiculartrafficshallnotenterorbecrossingtheintersectionwhentheredor"stop"signalisexhibited.

SouthCarolina Permissive


SouthDakota Permissive

Vehiculartrafficfacingthesignalistherebywarnedthattheredor"stop"signalwillbeexhibitedimmediatelythereafterandsuchvehiculartrafficshallnotentertheintersectionwhentheredor"stop"signalisexhibited.




TennesseePermissive(Correctedbyauthor)

Vehiculartrafficfacingthesignaliswarned thattheredor"Stop"signalwillbeexhibitedimmediatelythereafterandthatvehiculartrafficshallnotenterorcrosstheintersectionwhentheredor"Stop"signalisexhibited.

Texas PermissiveAnoperatorofavehiclefacingasteadyyellowsignaliswarnedbythatsignalthat:(1)movementauthorizedbyagreensignalisbeingterminated;or(2)aredsignalistobegiven.

Utah PermissiveTheoperatorofavehiclefacingasteadycircularyelloworyellowarrowsignaliswarnedthattheallowablemovementrelatedtoagreensignalisbeingterminated.

Vermont Permissive

Vehiculartrafficfacingasteadyyellowsignalistherebywarnedthattherelatedgreensignalisbeingterminatedorthataredsignalwillbeexhibitedimmediatelythereafter,whenvehiculartrafficshallnotentertheintersection.

Virginia Restrictive

Steadyamberindicatesthatachangeisabouttobemadeinthedirectionofthemovingoftraffic.Whentheambersignalisshown,trafficwhichhasnotalreadyenteredtheintersection,includingthecrosswalks,shallstopifitisnotreasonablysafetocontinue,buttrafficwhichhasalreadyenteredtheintersectionshallcontinuetomoveuntiltheintersectionhasbeencleared.Theambersignalisawarningthatthesteadyredsignalisimminent.

Washington Permissive

Vehicleoperatorsfacingasteady circularyelloworyellowarrowsignalaretherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafterwhenvehiculartrafficshallnotentertheintersection.VehicleoperatorsshallstopforpedestrianswhoarelawfullywithintheintersectioncontrolareaasrequiredbyRCW46.61.235(1).

WestVirginiaPermissive(Correctedbyauthor)

Vehiculartrafficfacingthesignalistherebywarnedthattheredor"stop"signalwillbeexhibitedimmediatelythereafterandsuchvehiculartrafficshallnotenterorbecrossingtheintersectionwhentheredor"stop"signalisexhibited.

Wisconsin RestrictiveWhenshownwithorfollowingthegreen,trafficfacingayellowsignalshallstopbeforeenteringtheintersectionunlesssoclosetoitthatastopmaynotbemadeinsafety.

Wyoming Permissive





13.AppendixB‐EmergencyStoppingDistancesandTimeCalculations(Rev.10)

Note:DistancesmarkedinREDviolatethe30mphcriticalstoppingdistanceof141feet.

COMMONINPUTDATA Value

Perception/ReactionTime,tpr (s): 1.0 (t=1.0secondsforEmergencyStoppingorITE,ExpectedEvent).

AirBrakeDelay,tb (s) 0.5 (t b=0.5+secondsairbrakedelay‐tractor‐trailers,schoolandpublicbuses)Grade,g (%): 0.0 (g isnegativefordowngradeandpositiveforuphill).

30MPHNOMINALDESIGN ITE,CarCriticalStoppingDistanceNonemergencyDecelerationRateDesignSpeed,V (mph): 20 25 30 35 40 45 50 55

AASHTOCoefficientofFriction,f : 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31

DecelerationRate,a (ft/s2): 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00CriticalStoppingDistance,d c (ft): 72.3 103.8 140.7 182.9 230.5 283.5 341.8 405.5

TotalStoppingTime,T (s): 3.9 4.7 5.4 6.1 6.9 7.6 8.3 9.1

Car‐DRYPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55

AASHTOCoefficientofFriction,f : 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60DecelerationRate,a (ft/s2): 19.32 19.32 19.32 19.32 19.32 19.32 19.32 19.32

EmergencyStoppingDistance,d (ft): 51.6 71.5 94.1 119.5 147.7 178.7 212.4 248.9TotalStoppingTime,T (s): 2.5 2.9 3.3 3.7 4.0 4.4 4.8 5.2

Car‐WETPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55



30MPHNOMINALDESIGN ITE,Truck/BusWITHairbrakedelayNonemergencyDecelerationRateDesignSpeed,V (mph): 20 25 30 35 40 45 50 55


CriticalStoppingDistance,d c (ft): 87.0 122.2 162.7 208.7 259.9 316.6 378.6 446.0TotalStoppingTime,T (s): 4.4 5.2 5.9 6.6 7.4 8.1 8.8 9.6

Truck/Bus,NOairbrakedelay‐DRYPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55



Truck/Truck/Bus,NOairbrakedelay‐WETPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55



Truck/BusWITHairbrakedelay‐DRYPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55



Truck/Truck/BusWITHairbrakedelay‐WETPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55



IntersectionComparisonData: East&westboundSWAllenatSWLombard30mph,141ftcriticalstoppingdistance.

ReferencesAirbrakedelayandstoppingdistances:ODOTCommercialDriverManual:http://www.odot.state.or.us/forms/dmv/36.pdfStoppingdistances:ODOT/OSUFebruary1997:http://www.oregon.gov/ODOT/HWY/ACCESSMGT/docs/stopdist.pdfODOT/OSUApril2012:http://cce.oregonstate.edu/sites/cce.oregonstate.edu/files/12‐2‐stopping‐sight‐distance.pdf

Note:BothOSUreportsshowantypographicalerrorinTable3B(97report)and5A(2012report)forwetpavementemergencystoppingat50mph.(Correctvalue:351vstypo.error:357feet)




14.AppendixC‐DecelerationRatesandStoppingDistancesComparison(Rev.5)

Note:DistancesmarkedinREDviolatethe30mphcriticalstoppingdistanceof141feet.

(NoAirBrakeDelayAdded)

FederalandStateStandards ft/s2 g mph/s (t=1.0s,grade=0%) 25mph 30mphITE&ODOT"ComfortableRate": 10.00 0.31 6.82 → StoppingDistance,ft: 103.8 140.7

ODOT/OSUEmergencyStopping ft/s2 g mph/s (t=1.0s,grade=0%) 25mph 30mphCarDryPavement: 19.32 0.60 13.17 → StoppingDistance,ft: 71.5 94.1

CarWetPavement25mph: 12.24 0.35 7.68 → StoppingDistance,ft: 91.6 ‐CarWetPavement30mph: 11.27 0.35 7.68 → StoppingDistance,ft: ‐ 129.8CarWetPavement35mph: 10.88 0.34 7.42 → StoppingDistance,ft: ‐ ‐

Truck/BusDryPavement: 14.80 0.46 10.09 → StoppingDistance,ft: 82.1 109.4Truck/BusWetPavement25mph: 7.37 0.23 5.02 → StoppingDistance,ft: 127.8 ‐Truck/BusWetPavement30mph: 6.83 0.21 4.66 → StoppingDistance,ft: ‐ 185.5Truck/BusWetPavement35mph: 6.41 0.20 4.37 → StoppingDistance,ft: ‐ ‐

0.5sAirBrakeDelayAdded

ODOT/OSUEmergencyStopping ft/s2 g mph/s (t=1.5s,grade=0%) 25mph 30mphTruck/BusDryPavement: 14.80 0.46 10.09 → StoppingDistance,ft: 100.5 131.4

Truck/BusWetPavement25mph: 7.37 0.23 5.02 → StoppingDistance,ft: 146.1 ‐Truck/BusWetPavement30mph: 6.83 0.21 4.66 → StoppingDistance,ft: ‐ 207.6Truck/BusWetPavement35mph: 6.41 0.20 4.37 → StoppingDistance,ft: ‐ ‐

BusPassengerStanding ft/s2 g mph/s (t=1.5s,grade=0%) 25mph 30mphMaximumUnsupported: 2.25 0.07 1.54 → StoppingDistance,ft: 353.3 495.5

LossofEquilibrium: 5.47 0.17 3.73 → StoppingDistance,ft: 177.8 242.7UsingHandhold: 6.43 0.20 4.39 → StoppingDistance,ft: 159.5 216.4

UsingVerticalStanchion: 8.69 0.27 5.92 → StoppingDistance,ft: 132.3 177.3

BusPassengerSeated ft/s2 g mph/s (t=1.5s,grade=0%) 25mph 30mphVeryUncomfortable: 7.08 0.22 4.83 → StoppingDistance,ft: 149.9 202.6

DislodgedUntiltedSeat: 15.12 0.47 10.31 → StoppingDistance,ft: 99.5 130.0DislodgedTiltedSeat: 16.73 0.52 11.41 → StoppingDistance,ft: 95.2 123.9

NOTE:SWAllenBlvdatSWLombardAve,BeavertonOregonDesignvalues:V=30mph,a=10ft/s2,t=1.0sandg=0%→141feetcriticalstoppingdistance(ITE).(DistancesmarkedinREDviolatethe30mphcriticalstoppingdistanceof141feetatSWAllenBlvd)

ReferencesODOTandOSU,Emergencystoppingdistancesforwetanddryroadconditions:February1997:http://www.oregon.gov/ODOT/HWY/ACCESSMGT/docs/stopdist.pdfApril2012:http://cce.oregonstate.edu/sites/cce.oregonstate.edu/files/12‐2‐stopping‐sight‐distance.pdfAirbrakedelayandstoppingdistances:ODOTCommercialDriverManual:http://www.odot.state.or.us/forms/dmv/36.pdfStandingandseatedbuspassengermaximumdecelerationrates:http://ntl.bts.gov/lib/33000/33300/33313/33313.pdfhttp://ntl.bts.gov/lib/33000/33300/33340/33340.pdf

MaximumDeceleration,a VehicleSpeed,V

MaximumDeceleration,a VehicleSpeed,V


Download - Scientific AN INVESTIGATION OF THE ITE FORMULA AND ITS USE · This working report is a study of the universally adopted ITE formula which calculates a traffic light’s change interval

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