Scientific AN INVESTIGATION OF THE ITE FORMULA AND ITS USE · This working report is a study of the...
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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
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.
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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
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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
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AninvestigationoftheITEformulaanditsuse Page4
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
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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.
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AninvestigationoftheITEformulaanditsuse Page6
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
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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.
MatsJärlström•[email protected]•503‐671‐0312•Beaverton,Oregon,USA Rev.14•September9,2014
AninvestigationoftheITEformulaanditsuse Page8
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, ∆
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Page9 AninvestigationoftheITEformulaanditsuse
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, ∆
MatsJärlström•[email protected]•503‐671‐0312•Beaverton,Oregon,USA Rev.14•September9,2014
AninvestigationoftheITEformulaanditsuse Page10
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, ∆
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Page11 AninvestigationoftheITEformulaanditsuse
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).
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AninvestigationoftheITEformulaanditsuse Page12
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).
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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).
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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.
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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
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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
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“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…
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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
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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.
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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.
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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.
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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
Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.
SouthDakota Permissive
Vehiculartrafficfacingthesignalistherebywarnedthattheredor"stop"signalwillbeexhibitedimmediatelythereafterandsuchvehiculartrafficshallnotentertheintersectionwhentheredor"stop"signalisexhibited.
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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
Vehiculartrafficfacingasteadycircularyelloworyellowarrowsignalistherebywarnedthattherelatedgreenmovementisbeingterminatedorthataredindicationwillbeexhibitedimmediatelythereafter.
MatsJärlström•[email protected]•503‐671‐0312•Beaverton,Oregon,USA Rev.14•September9,2014
AninvestigationoftheITEformulaanditsuse Page24
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
AASHTOCoefficientofFriction,f : 0.40 0.38 0.35 0.34 0.32 0.31 0.30 0.30DecelerationRate,a (ft/s2): 12.88 12.24 11.27 10.88 10.30 9.98 9.66 9.66
EmergencyStoppingDistance,d (ft): 62.7 91.6 129.8 172.3 225.5 283.9 351.3 417.0TotalStoppingTime,T (s): 3.3 4.0 4.9 5.7 6.7 7.6 8.6 9.4
30MPHNOMINALDESIGN ITE,Truck/BusWITHairbrakedelayNonemergencyDecelerationRateDesignSpeed,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 0.31DecelerationRate,a (ft/s2): 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00
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
AASHTOCoefficientofFriction,f : 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46DecelerationRate,a (ft/s2): 14.80 14.80 14.80 14.80 14.80 14.80 14.80 14.80
EmergencyStoppingDistance,d (ft): 58.4 82.1 109.4 140.3 174.9 213.0 254.9 300.3TotalStoppingTime,T (s): 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
Truck/Truck/Bus,NOairbrakedelay‐WETPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55
AASHTOCoefficientofFriction,f : 0.25 0.23 0.21 0.20 0.19 0.18 0.18 0.17DecelerationRate,a (ft/s2): 8.05 7.37 6.83 6.41 6.12 5.86 5.64 5.51
EmergencyStoppingDistance,d (ft): 82.7 127.7 185.6 256.6 339.5 437.0 549.7 670.5TotalStoppingTime,T (s): 4.7 6.0 7.5 9.0 10.6 12.3 14.0 15.7
Truck/BusWITHairbrakedelay‐DRYPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55
AASHTOCoefficientofFriction,f : 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46DecelerationRate,a (ft/s2): 14.80 14.80 14.80 14.80 14.80 14.80 14.80 14.80
EmergencyStoppingDistance,d (ft): 73.1 100.5 131.4 166.0 204.3 246.1 291.6 340.7TotalStoppingTime,T (s): 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Truck/Truck/BusWITHairbrakedelay‐WETPavementDesignSpeed,V (mph): 20 25 30 35 40 45 50 55
AASHTOCoefficientofFriction,f : 0.25 0.23 0.21 0.20 0.19 0.18 0.18 0.17DecelerationRate,a (ft/s2): 8.05 7.37 6.83 6.41 6.12 5.86 5.64 5.51
EmergencyStoppingDistance,d (ft): 97.4 146.1 207.7 282.4 368.9 470.1 586.4 710.9TotalStoppingTime,T (s): 5.2 6.5 8.0 9.5 11.1 12.8 14.5 16.2
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)
MatsJärlström•[email protected]•503‐671‐0312•Beaverton,Oregon,USA Rev.14•September9,2014
Page25 AninvestigationoftheITEformulaanditsuse
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