Report the Art of the Speed

8/10/2019 Report the Art of the Speed

1/27

2009

Efficientuseofprofessionalsensorsincar

andtire

performance

measurement

and

comparison

3/3/2009

The art of the speed


2/27

Summary(Workinprogress)

Companiesinvolveddescription

o CorrsysDatronSystem

o OresteBertaS.A.

o OptimumG

Testpresentationandbriefdefinition

Summaryoftestandsensorsrequired

Slipangleo Definitions

Descriptionandimportanceoftheparameter

SlipAnglewithsteering

Yawcenter

Lateralaccelerationincornering

Stabilityandresponse

o Sensors

Sensorsused

Hintsandadviceforsensorssetup

o Calculation

Geometricalmethod

Mathematicalmethod

o Datadiscussion

Turncentermigration

Slipanglevariationwithspeedinskidpadtesting

Bodyslipangleandbodyslipanglespeed

Understeergradiento Definitions

o Sensors

Sensorsused

o Datadiscussion

Influenceofthesetup

Influenceofthespeed

.(MoreTest)

AppendixA:Mathchannelcreation

AppendixB:summarysymbolsusedinthisreport


3/27

Summary

of

tests

and

sensors

required

Slip AngleFront

Slip AngleRear

Dynamic CamberAng le (DCA)

Ride Height -Laser

WheelPulse

3 wayAcceleromet er

TireTemperatu

SlipangleFrontaxle x x

SlipangleRearaxle x x

BodySlipangle x x

WheelsSlipangle x x

TurnCenter x x

CGradius x x x x

FrontRadius x x

RearRadius x x

Yawrate x x

Yawacceleration x x

Yawmoment x x

Yawcenter x x

Yawdamping x x

LongitudinalSpeed x x x

LateralSpeed x x

UndersteerGradient x x x x

Ackermanangle x x x x

WheelCamber x

Suspension

compliance x x

FrictionCircle x

LoadTransfer x x

TireTemperature x

Camberandpressure

evaluation x

TireStability x x x

Rideheight x

Tiresrollangle x


4/27

Tirevertical

deflection x

Longitudinal

acceleration x

Verticalacceleration x

Lateralacceleration

front x x

Lateralaccelerationrear x x

Lateralacceleration

CG x

Accelerometerbias

error x x x

SlipRatio x x x x

Wheelpulse

harmonics x

Rollangle x

Pitchangle x

Slipanglespeed x x

Steeringangle

smoothness

Steeringsensitivity x

CornerWeight x x

Chassistorsion x

Chassisstiffness x

Tiresverticalstiffness x

DamperFrequency


5/27

SLIPANGLE:

DEFINITIONS

Descriptionandimportanceoftheparameter:

The slipangle is theanglebetweenapoints speedvectorand its longitudinal component inagiven

coordinate system.A slip angle sensoruses anopticalmethod to calculateboth componentsof the

velocity vector. As it is shown in the following picture the slip angle changes with the system of

coordinates.Therefore,thexaxisofthesensormustbealignedwiththelongitudinalaxisofthecarin

ordertoobtainreliableresults.

Inthepreviousfigure,xandyaretheaxisinthesensorscoordinatesystemwhilexandyare

theaxis inthecarcoordinatesystem. Ifanangle existsbetweenthetworeference frames,theslip

anglemeasuredbythesensorwillnotbetheslipangleinthecarcoordinatesystem.

The importance of measuring this parameter arises from the fact that there is a direct relationship

betweenthelateralforcecreatedbyatireanditsslipangle.Besides, thebodyslipanglegivesanidea

oftheattitudeofthecaruponthetrajectorypath,whileacomparisonbetweenthefrontandrearaxles

slipanglesmeasuresthechangeinthatattitudeandifthecarifdriftingorrotatingabouttheCG.

Whenslipangleispresentinbothfrontarearaxlesitcouldbeduetobodydrifting,bodydriftingwith

rotationandpurerotationwithoutbodydrifting.Figures2to5analyzesthosecasesinabicyclemodel.

Figure1.Slipanglemeasurementindifferentcoordinatessystem

FRONTREARCG

b a

Vyf=Vyr=VyCGVehicleinpuredrifting.

YawRate=0

VyfVyr VyCG

Figure2.Vehicleinpuredrift,noyawrate


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FRONTREARCG

b a

Vyf>Vyr;butsamesign

VyCG>0

Vyf

Vyr

VyCG

Figure3.Vehicledriftingandwithyawrate

Vehicledrifting.

YawRate>0

FRONTREARCG

b a

Vyf>Vyr;butdifferentsign

VyCG>0

Vyf

Vyr

VyCG

Figure4.Vehicledriftingandwithyawrate

Vehicledrifting.

YawRate>0

FRONTREARCG

b a

Vyf*a=Vyr*b

VyCG=0

Vyf

Vyr

VyCG

Figure5.VehiclewithyawrateandnotCGlateralSpeed

CGLatSpeed=0

YawRate>0


7/27

Slipanglewithsteering:

Whensteeringangleispresent(infrontwheelsduetodriverinput,inrearwheelsduetoinitialtoeand

bumpsteer),theslipangleofthetireisnottheslipangleofthecaratthatpoint.Asitwasmentionat

thebeginningofthissection,theslipangle isdifferent ineachcoordinatesystem.Theanglebetween

onereferenceframeandtheother(steeringangle)maygeneratenegativetireslipanglewhiletheslip

angleinthecarispositive.Figures6to9showaprogressioninthesteeringangleandhowthetireslip

anglechangeswhilethecarslipangleremainsconstant. Inthose figures c istheslipangle inthecar

coordinatesystem,t istheslipangle inthetirecoordinateangleand isthesteeringangle(orangle

betweenthechassislongitudinalaxisandthedirectionwherethetireispointing).

t=c t>0c>0

t=0 c=t0

>c

Figure6.Slipangleforzerosteeringangle Figure7.Carslipangleandtireslipangle,bothpositive

Figure8.Steeringangleequalscarslipangle Figure9.Tireslipanglenegative,carslipanglepositive


8/27

Yawcenter:

Fromfigures3to5 it iseasytoconcludethat ifyawrateexist,thenthere isapointwherethe lateral

speediszero.Thispointiscalledtheyawcenteranditisthepointwherethecarisrotatingaboutina

coordinateframewhichismovingwiththesamevehiclesinlinespeed.Thus,theyawcenterpointitis

inpurelongitudinalmotion.

Thereare3possibilitiesfortheyawcenterlongitudinallocation:

Infrontof thecar (Abs(FrontLateralSpeed)Abs(RearLateralSpeed)andbothwiththesamesign)


9/27

Lateralaccelerationincornering

An accelerometer placed in the CG of the car pointing transverse to the inline axis of the car will

measurethelateralaccelerationrelatedtothechassisframe.However,whenacarisnegotiatingaturn,

theCG lateralacceleration is in linewiththe instantradiusandtherefore ifbodyslipangle ispresent,

theaccelerometerwillnotbeabletomeasurethetotal lateralacceleration.Figure10showsthiswith

moredetail.

Note that there is a component of the lateral acceleration in the radius direction measured by the

longitudinal accelerometer. However, the body slip angle is not the angle between the lateral and

longitudinalacceleration,sincethe longitudinalaccelerometeralsomeasures thechange in thespeed

magnitude. If recognizing each contribution to the longitudinal acceleration would be possible, still

wouldnotbe recommendable tocalculate the slipangleusingaccelerometers.The reasonsare, first

becauseofallthenoiseregisteredbythosedevices(thatiswhythelongitudinalspeedisnotmeasured

by integrating the longitudinal accelerometer, and second due to the inertial nature of the sensor,

making the measurement in transient extremely inaccurate (the same reason why it is not

recommended touseone slipanglesensorandagyro).Anothercommonmistake is to think thatby

integratingthelateralaccelerometerispossibletofindthelateralspeed.Thefactisthatthevariationin

thelateralspeedmultipliedbythemasswillgiveyouthesumofalltheforcesactingattheCG,however

thelateralaccelerometerisonlymeasuringareactionforceduetothecartryingtochangeitsvelocity

vector. Ifyouattachanaccelerometertoyourbodypointingto theground, itwillmeasure1G.The

integration of that signal will have as result a time increasing speed, however your speed is zero,

becauseyouarenottakingintoaccountthereactionforcegeneratedbythegroundinyourfeet.

Figure10.Accelerationindifferentframes

Lateral accelerometer

Component of the total lateral

acceleration measured by the

longitudinalaccelerometer

TurnCenter

Body

Slip

angle


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Stabilityandresponse:

Stability istheabilityofthecartominimizethe impactofanydisturbanceandtoremain inthesame

state that itwas in the instantprevious to the disturbance appearance. The input couldbe internal

(driversteeringorbraking)orexternal(wind,abumpintheroad). Ontheotherhand,response isthe

abilitytoreachanewstateassoonastheconditionschange.Stabilityisrequiredinsituationscloseto

steadystate, forexampleaNASCARrace,withstraightlinesandlongcurveswherethespeedofchange

of the driver inputs (steering angle) is not so big.However, if the car is required to take a chicane

response isdesiredandnotstability. It iseasytounderstandthatthemorestabilitythe lessresponse

andviceversa. Vehicleswithlowyawinertia(massconcentratedneartheCGorsmallwheelbase)have

moreresponsesincesmalleryawmoment isneededtodisturbtheirequilibriumstate.Forthiskindof

carsthebodyslipanglespeedshouldbebigforasmallrangeofbodyslipangles.ThescatterplotofCG

slipanglerateversusCGslipanglelookslikeanovalinverticalposition,asshowninfigurenumber11

Vehicleswithhighyaw inertia(massconcentratedontheaxlesor longwheelbase)areverystableand

are not affected too much by any disturbances. Therefore, the body slip angle speed is smaller

comparedtoacarwithhighresponse,andtherangeofbodyslipangles iswider.Figure12showsthe

CG slipangle rateversus thebody slipangle for thiscar.Note that it looks likeanoval inhorizontal

positionduetothelessbodyslipangleratethatcanreachincomparisonwiththebodyslipangles.

Body

slip

angle

[deg]

Bodyslipanglerate[deg/s]

Bodyslipangle[deg]

Bodyslipanglerate[deg/s]

Figure11.Bodyslipangleratevsbodyslipangleforacarwithhighresponse

Figure12.Bodyslipangleratevsbodyslipangleforacarwithhighstability


11/27

SENSORS

Sensorsused:

A slip angle sensor is designed to measure the lateral and longitudinal components of a vehicles

velocity.CorrsysDatronCorrevitS350was thesensor selected tomeasure the slipangles in thecar.

Thisdeviceisanoncontactopticalsensorwitharesolutionof2.47mm.Amongotheradvantagesithas

thepossibilityofdirectconnectiontoaPCandvirtuallyalldataacquisitionsystem.

Usingtwoslipanglesensorsitispossibletocalculate(amongstotherthings):

Slipangleofthefrontandrearofthevehicle

Locationoftheyawaxis

Yawrate

Balanceofthevehicle Realturnradius

When used in conjunction with other common vehicle sensors, slip angle sensors also allow you

calculate:

Slipangleofthefrontandreartires

Longitudinalslipratio

Tiremodel

Responseofthevehicletoinputs(steering,throttle,brake,gearchange,etc.)

Drivingstyleandresponse

Thereforeonesensorwaspositionedatthefrontandanotheroneattherearofthevehicle.Figure13

showstheinstallationofbothsensors.

Figure13.Slipanglesensorssetup


12/27

Hintsandadvicesforsensorssetup:

1) Each slip angle light unit is calibrated by Corrsys

Datron to a specific signalconditioning unit. If an un

matchedpair isused together it is likely that the recorded

slipangleswillbe incorrect(e.g.theoutputwillbescaledor

offset). It is important to label light/signalconditioningunit

pairs.

2)Accesstotheserialportonthesignalconditioningunit is

needed at least before the first use, if not continuously

during testing (for setup and calibration). If the units are

placed in an inaccessible place it may be necessary to run

jumperwirestoanaccessiblelocationtoallowquickchanges

ofsensitivity/calibration.

3)With the sensor / lampboxplugged into the signalconditioningunit the resistanceof the system

(measuredat thepower supplywires)wasmeasured tobeapproximately1.The resistancewillbe

significantlyhigherifabulbhasblown.

4) When using the Lemo connectors (analog voltage outputs,

Figure15),itiseasytosetupanundesirableearthloopcondition

between the data logger and the signalconditioning unit. The

outercasingsofthetwoLemoconnectorsareelectricallyjoined,

andiftwo0Vwiresareruntoeachofthesefromthedatalogger,

anearth loop conditionexists.The solution is to runa single0V

wire,twistedwiththetwosignalwires,inasinglewiringloomand

connectittooneoftheLemocasings.

5)The sensorsare ratedatapproximately40Weach (theywere

measured at 3.26A at 11.9V 38.8W), therefore it may be

necessary touse individual switches foreachsensor tominimize

batterydrainduringsetup/test.Appropriatewireshouldbeused

(i.e.donotruntwoormoresensorsusingasingle22gageTefzel

wire). If individualswitchesareusedforthe lightunits, it iseasyforthedriver/engineertoforgetto

switchthemon.Abettersolutionistouseadigitaloutputchannelonthedataloggingsystemtoswitch

arelaywhichwillturntheunitsonandoffatthebeginningandendofeachsession.Analternativeon

vehicleswithaconfigurabledashboardistosetanalarmwhenwheelmotionisdetectedtoremindthe

drivertoswitchonthesensors.

6)Theanalogoutputof lateralvelocity (AV2) canonlyproduceamaximumvoltageof5V.Theusual

measurement range is 5V, however, some data acquisition systems (e.g. race systems such as the

MoTeCADL)canonlymeasurepositivevoltages.Thereforeitiseithernecessarytoscaleandoffsetthe

lateraloutputsignalto2.5V2.5Vviatheserialinterfaceonthesignalconditioningunits,orconnectthe

Figure 15.Lemoconnectors

Figure 14.Sensorlabeling


13/27

casingoftheLemoconnectorstoasuitable5Vreferencefromthedata loggertoallowthefull5V5V

output. When using the second approach it is important that the Lemo connectors are electrically

isolatedfromothercablesorthevehiclechassis.

7)Therearslipanglesensorlightconewasmeasuredatapproximately29C(85F)after10minutesof

running(ambienttemperaturewasapprox.15.5C(60F)).Thesensorbodywasnotashot.Thissensor

wasintheairflow.

8)WhenusingthesensorsonaFormulaFordZeteccar,occasionally(butconsistentlyatthesameplace

onthetrack)therearsensorwoulddropoutandreadzero longitudinaland lateralvelocity.Thiswas

attributedtostrongsunlightata lowangleonaparticularcorneratthattimeofday.Thistheorywas

reinforcedbythefactthatthefrontsensor(shadedwithinthenoseconeandbythefrontwing)was

stillreadingnormally.Itisthereforerecommendedthatthesensorsbeprotectedfromdirectsunlightif

sunlightinterferenceisfoundtobeaproblem.Asafurthernote,sensordropout/accuracydegradationmayalsooccurifadriverusesalargeamountofcurb(forexampleinV8SupercarsinAustralia)andthe

sensormovesoutofthe30050mmcalibratedrangefromtheground.Brightlycoloredcurbsmayalso

reflectmoresunlightintothesensorandcausesignaldegradation.Rearsensordropoutmayalsooccur

underheavybrakinginavehiclewithasignificantamountofdive.

9)Toensurethatthesensorswillnotbesubjectedtotemperaturesoutsidetheiroperatingrange,the

vehiclecan initiallybe runwithThermax indicatorsat thepointswhere thesensorswillbemounted.

Thiswillgivethemaximumtemperatureatthatlocationonthevehicle,andhelppreventdamagetothe

sensors.

10)Orderallconnectorsbeforebeginningwiring.

11)Whenusingracedataloggingsystems(e.g.MoTeC,Pi,etc.),ensureallpinassignments/changesare

recorded.

12)Allconnectorsshouldbeclearlylabeled.

13)Allwiring(particularlysignalwires)shouldbetwistedto

reduce the effect of electromagnetic interference. Twisted

wiresshouldthenbeprotected (withheatshrink tubing, for

example)toprotectfromheat,oil,etc.

5) Lizard Skins (used on bicycles to protect shock

absorbers/frames,figure16)canbeusefulforkeepinglarger

wiring looms tidy. Stretch the Lizard Skin around the loom

andfastentheVelcrostrip.Unlikeheatshrink,theyareeasy

toadjustandremove.

Figure 16.Lizardskinsprotectingabicycleframe


14/27

CALCULATION

Oncethedataisacquiredforthepointswherethesensorswereinstalled,itisnecessarytoextrapolate

the information totheremainingpoints inthechassis,speciallythe tiresand thecenterofgravity. In

thissection,twomethodswillbeexplained.For further informationaboutthemathchannelsused in

thiscalculationleasegotoAppendixA.

Geometricalmethod:

For a given point, its instant centerof rotationmustbe somewhere in the line perpendicular to its

velocityvector.Consequently,ifthespeedvectoroftwopoints (aandb)thatbelongtoarigidbody

isknown,theinstantcenterofrotationforthementionedbodycanbeeasilyfoundastheintersection

betweenthetwolinesperpendiculartoaandbspeedsvectors.

Ifthecarisinstrumentedwithonlyonesensor,theturncenterlocationinspacecannotbeknownasit

couldbeanypointalongsaidline.

Oncethe instantcenterposition isknown, theslipangleofeachpoint inthebodymaybecalculated

usingthe inversemethod.Thismeans,foranyselectedpoint,thespeedvector isperpendiculartothe

linepassingthroughtheICandthatpoint.

Thesame isappliedtothewheels.As itwassaidbefore,differentcoordinatesystems implydifferent

slipangles.Thereisananglebetweenthecarslongitudinalaxisandthefronttiresyaxis,whichisthe

steeringangle.Thus,theslipangleforanyofthetwofronttireswillbetheanglecalculatedusingthe

methodmentionedaboveminusthesteeringangleforthatwheel.Infact,thesamecouldbeappliedfor

both rear tires iftoe inor toeoutarepresent.Commonlytiredata isprovided inawheelcoordinate

Figure17 .GeometricalICcalculation


15/27

systemandnot inavehiclecoordinatesystem.That iswhy thisconversion is fundamental.Figure18

showstheslipangleforthetireandtheinfluenceofthesteeringangle.

Mathematicalmethod:

Thereisanalternativemethodtothegeometricalmethodthatisbasedonthekinematicofarigidbody

inrotationaltranslationalmotion.

Aslipanglesensormeasuresthelongitudinalandtransversalcomponentsofthevelocityvectorinorder

tocalculatetheslipangle,inthefollowingmanner:

= x

y

x

y

V

V

V

V

arctg (1)

UsingtwoslipanglesensorswecancalculatetheslipanglefortheCGandforthefrontandrearofthe

car. In figure5,wecanseethatthesensorcoordinates in thevehiclesreferencesystemare (ax,ay).

Thereforethevelocityvectorforthatpointis:

],[*)()]tan(*,[.

xyxx aaYVVV ++= (2)

Figure18.Tiresslipanglecalculation


16/27

Where

.

Y istheyawvelocityofthecarwithrespecttotheCG, istheangularvelocityoftheCGwith

respecttothecenterofthecornerand isthebodyslipangle.

Replacing(2)in(1)

yx

xxfs

aYV

aYV

*)(

*)()tan(*.

.

+

++=

(3)

Equation (3)has twounknowns. Ifagyro isused, the term )( . +Y canbe replacedwith the signal

coming from that sensor, and therefore, the system is solved for the body slip angle. This is the

advantageofthismethod,withonlyoneslipanglesensorandagyrotheslipangleofanypointcanbe

calculated byjust replacing its coordinates in equation 3. However, the accuracy of the gyro is not

comparabletotheaccuracyoftheslipanglesensor,andso,thismethod is lessaccurate.Besides,the

inertiaofthegyromakesthemeasurement intransientverypoorandwithabigerror,whentheslip

anglesensorsdonthave thisproblembecause theyuseanopticalmethod,and thus the response is

almostimmediate.

Figure19.Carconfiguration


17/27

Ontheotherhand,iftwoslipanglesensorsareused,theaccuracyisthesameasthepreviousmethod

andthesystemcanbesolvedforthebodyslipangleandtheterm )(.

+Y ,whichwedecidedtocallthe

virtual gyro since it is the angular speed of the car, theoretically calculated and not empirically

obtained.

Asthesensormeasuresthelateralandlongitudinalcomponentsofthespeed,anewsystemisproposed

inordertomaketheresolutioneasier:

Solving for and )(.

+Y , considering that both sensors are in the center line of the car (

):

Knowingthatthecoordinatesofthefrontofthecarare(a,0),wecanuseexpression(3)tocalculatethe

frontslipangle.

x

x

V

aYVf

*)(*)tan(.

++=

Thesamecanbedonefortherearandallfourwheels.

Anotheradvantageofthismethodisthepossibilitytocalculatetheyawacceleration.Since += .

Yr ,

byderivationoftheexpressionforthevirtualgyroweobtain


18/27

Figure20showshowtheslipanglesvarywithinalaponanovaltrackwithachicane.Redandyelloware

thenon filteredsignalsofthe frontand rearslipanglesensors, respectively.Greenandvioletarethe

calculated slipangles for the frontand rearaxle respectively. In thepoint selected, the frontaxle is

travelinginonedirectionwhiletherearaxleistravelingintheopposite.Thisbigdifferenceinbothaxle

speedsisaresultoftheyawraterequiredtotakethecorneratmaximumspeed.

Figure20.Axlesslipangleinanovaltrackwithchicane


19/27

DATADISCUSSION

TurnCenterMigration

Thenextpictureshowshowtheturncenterischangingalongalapinanovalcourseat50km/h.Inthe

straightline,Ycoordinateisfarawayfromthecarslongitudinalaxis.Theoreticallyitshouldbeinthe

infinite;however,even inthestraight linethecarstillhasa lateralspeedcomponentduetotransient

behavior.Thismeansthatbeforeitreachesthesteadystategoingoutofcornerone,thedriverstartsto

turnincorner2.

Corner1hasagreaterradiusthanCorner2.But,inthegraphtheradiusthattheCGdescribesissmaller

forCorner1becausethelateralaccelerationinthatpartofthecircuitissmallenoughtoconsiderthat

the car is rotating around the center of the corner. On the other hand, to negotiate the remaining

corner,thecarneedsagreaterbodyslipangleinordertoobtainthegripneeded,increasingtheradius

and trying to rotate the rear axle around the front axle (increase of X coordinate) to achieve the

desiredyawrate.

Figure21.Turncentermigrationinanovaltrack


20/27

Figure22showsaquasilinearrelationshipbetweenthexandycoordinatesoftheturncenter.Both

coordinatesarerelatedtothecenterofgravityofthecar,xpositiveistowardthefrontofthecarand

ypositive istothe left.Thenegativezoneofthexcoordinatecorrespondstothecarcornering.This

indicatesthatthevehicleneedstogeneratepositivebodyslipangletonegotiateaturn,withpositive

lateralspeed inthefront(tothe left)andnegative intherear(totherightofthechassis) inorderto

achievetherequiredyawrate. Thepositivezoneisthecarinthestraightline,wheretheradiusgoesup

alongwith the reduction of the lateral speed. The turn centermigrates toward the frontof the car

becausethefrontaxlereducesitslateralspeedfasterthantherearaxle.Thatcouldbeduetotraction

forceintheforcetryingtoalignthefronttireswiththedirectionofmotionoramisalignmentoftherear

slipanglesensor,where it ismeasuring lateralspeed inthestraight line.As the lateralacceleration is

small(peaksof0.9G)thelongitudinalforcesinthefronttiresareforcingthefrontofthecartotravelto

theinsideofthecorner,andthatiswhythelateralspeedofthefrontaxleispositive,plusthefactthat

thelongitudinalweighttransferissubtractingcorneringcapabilityintherearaxle.

Finally,thespreadofthepoints isgreater inthepositivezone,while incorneringthepointsaremore

closetoanactualline,showingthatthedriverhadmoreconsistencytohandlethecarattitudeanddrift

duringthecornersthaninthestraights.

Figure22.Scatterplotoftheturncentermigration

y>0

x>0CG

x=1.092x=1.508


21/27

SlipAnglevariationwithspeedinSkidPadtesting:

Forthistest,thedriverwasaskedtodrivearoundthe50mradiusskidpadat20,40and60km/hand

thenatthemaximumspeedpossible(90km/h inthiscase).Inallthecasesthedirectionofrotation is

counterclockwise

As the speed is increased the body slip angle decreases, going from positive values to negative at

maximumspeed. Toexplainthis isnecessarytogobacktoFigures2to5. Ifthe longitudinalspeed is

considered the same for the front, rear and CG (the car is a rigid body), then the slip angle is a

measurementofthe lateralspeedofeachpoint.Thus,therearaxlehasalwaysits lateralspeedvector

pointingtotheoutsideofthecorner,whilethefrontitisalmostpointingtotheinsideofthecorner.The

lateralspeedintherearmighthavebeenduetotheweightdistributiontowardsthefront,sincethereis

nolongitudinalaccelerationforbrakingintheskidpad(atthispointitisimportanttonotethatthetire

isthesameforthefourwheels).Athigher lateralaccelerationsthefrontstarttodriftfortworeasons,

beingthefirstonetheneedofmoregriponthefront(thetireislikeaspring,togeneratemoreforce,

Figure23.Slipangledifferentspeedintheskidpad

Speed:20km/h Speed:40km/h

Speed:60km/h

Speed:maxpossible


22/27

more displacement is needed). The second one is that at grater speeds, even though there is no

longitudinalacceleration,theaerodynamicdragmustbeequilibratedbyaddingthrustinthefronttires,

reducing their cornering force capability (goingback to the springexample, the longitudinal forceat

lowerlateralaccelerationsworksasapreloadbutathigherlateralaccelerationactslikeitwasreducing

thestiffnessofthespring).

Thus, to find the equilibrium at higher lateral acceleration the car needs to point in the direction

tangenttothecorner.Anotherwaytosaythat isthatlesspositivebodyslipanglesmeansthatthe

turncenterismovingtowardthefront,andthereforethecarisundersteer. From20km/hto90km/h

thevariationinthefrontaxleslipanglewas3.1degwhileintherearwas2.8deg,andsothefrontend

ofthecardneededmoredisplacementinordertogenerategrip,againthecarisundersteer.

At60km/h it isclosetozeroandsotheturncenter is insomepoint inthe lineperpendiculartothe

chassispassingthroughtheCG.

Figure24containstheslipangleineachtireforeachcase.Notethatthefronttiresslipanglestakeinto

accountthesteeringangle,whichisthereasonoftheoscillationofthosevaluesinthegraphs.Yetagain

thevariationofthefronttiresslipangleisgreaterthanintherear.

Figure24.Tiresslipangles,differentspeedintheskidpadtest

Speed:20km/hSpeed: 40km/h

Speed:60km/h

Speed:maxpossible


23/27

Bodyslipangleandbodyslipanglespeed

Figure25showsthescatterplotofthebodyslipanglerateofchangevsthebodyslipangleforseveral

lapsintheovaltrack,withthespeedvaryingfrom40to80km/h.

TheenvelopeofthescatterplotlooksliketheFigure12indicatingthatthecarmighthavegoodstability.

However, inthezoneofhighdensityofpointsthecarseemstohaveverygoodresponse. Infact,the

envelope isformedforasuccessionofverticalovalscorrespondingtodifferentequilibriumstates.For

eachsituation(inthiscasespeed)thecarreachesanequilibriumstateanditmovesarounditwithhigh

response. If the situation requires more body slip angle, the vehicle will settle itself in a new high

responsestate.

Fi ure 25. Bod sli an le s eed vs bod sli an le

Scatterplotenvelope

Zoneofhighdensityof

points.

Lowlateralacceleration


24/27

UNDERSTEERGRADIENT:

DEFINITIONS

Descriptionandimportanceoftheparameter:

TheAckermanangleistheidealrequiredsteeringanglethatacarneedstonegotiateacornerwhenthe

lateral forcesat the tiresarenegligible (slipanglesclose to zero),anda smallangleapproximation is

suitable.Consequently, thedeviationof thesteeringangle from theAckermananglemaybeusedan

evaluationof theundersteer/oversteer characteristicsof the car.However,as theAckermanangle is

definedfornegligiblelateralaccelerations,acorrectionfactor isintroducedtoevaluatetheundersteer

characteristic at any acceleration. That is whywedefined theparameterundersteer gradient (UG),

whichisthedeviationweightedbythelateralacceleration.

TheexpressiontocalculatetheAckermansteeringangleis:

Andtheundersteergradientis:

If thecar isundersteering,moresteeringangle isrequiredas the lateralacceleration increases.Thus,

theundersteergradient inthiscase isgreaterthanzero.Thebiggerthisnumber,themoreundersteer

willthevehiclebe.

y

manAcsteered

AUG

ker =

3.57*kerRadius

WheelbasemanAc =

Radius

Wheelbase

(l)

Radius

Wheelbase

=

Figure26.Ackermanangle


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SENSORUSED

In the Ackerman angle calculation the wheelbase

remainsconstant,sotheonlyvariableistheradius.

The radiusat theCGwascalculatedusing theslip

angle sensors mentioned in the previous section

(CorrsysDatronCorrevitS350).

Thesteeredanglewasmeasuredusingastandard

steeringanglesensor,sofurtherconsiderationsare

notneeded.

Finallythelateralaccelerationwasmeasuredusing

a Corrsys Datron 3 way accelerometer. More

informationaboutthissensor intheAcceleration

andSpeedsectionofthisreport.Figure 27.CDS3wayaccelerometer

Figure28.Installationoftherearslipanglesensor.Notethelightontheasphalt


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DATADISCUSSION

Influenceofthesetup:

Thisparameter isusefultoviewthesensibilityofthecarsbalanceandhandlingwithsetupchanges.

During the test, the front antiroll

stiffness was increased, not by

changing the ARB, but by changing

one of the ARB drop link pick up

point position and therefore the

motion ratio. The latter has two

effects, the first one is more front

antiroll stiffness, and the second is

more weight transfer due to thesteering geometry since theantiroll

bar drop link was attached to the

upright. Figure 29 represents the

dataobtainedontheovaltrackwith

thebaselinesetup(redline)andwiththenewpositionfortheARBsdroplink(blackline).

TheUGiszerointhestraightlinebecausethemathchannelwascreatedtoevaluatethisfunctionwhen

thelateralaccelerationisaboveathresholdvaluesincetheUGisonlydefinedincornering.

After the test the driver commented that he did not like the new configuration because it created

oversteeron cornerentryandundersteeron cornerexit.On thegraph, theblack line isnegativeon

cornerentry(oversteer)andposiviteoncornerexit(understeer).Thedriverscommentandthegraph

areconsistent.

Oversteerbehavior iscausedbythefrontaxlecreatinggripfasterthantherearone(trianglebetween

lateralacceleration,rollangleandgrip).Understeerincornerexitisduetothesteadystatebehaviorof

thecarandmore lateral loadtransfer inthe fronttires (insteadystatemore loadtransferonanaxle

reducesitscorneringcapabilityduetothenonlinearitiesinthetiremodel).

Influenceofthespeed:

Toanalyzetheinfluenceofthespeedtwotestsweremade,bothwiththebaselinesetup,thefirstonein

the25mSkidPad(steadystate),asshowninFigure30.Inthegraph,thefrontsensorslipangleisinred,

therearsensorslipangle is inorange,thefrontaxleslipangle is ingreen,therearaxleslipangle is in

purpleandthebodyslipangleisinblue.Theretheundersteertendencyofthecarisveryclear,asthe

speedgoesup (form40to60km/h)moresteeringangle isneededandtheattitudeofthecar inthe

cornerchanges(bodyslipangleapproachingtozero).

Figure29.InfluenceofthesetupintheUG


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Thesecondtestwasontheovaltrack,ataspeedof30km/h(blackline),50km/h(greenline),70km/h

(lightblueline),andmaximumpossible(redline).Thevehiclehaslessoversteerasthedriverincreases

the speed. This could be due to more aero load in the rear wing, which means more lateral force

capability intherearaxle.However,atmaximumspeedthecar isundersteeringoncornerentry.The

reasonforthisisthatthedriverbrakeshardwhilegoingintothecorner(atlowerspeedshardbrakingis

notneeded)andeventhoughthereismorevertical loadinbothfronttires,therearealsolongitudinal

forcesactingatthecontactpatchandso, lesslateralgripmaybedeveloped.

Figure30.Bodyslipanglevariationwithspeed

Figure31.InfluenceofthespeedintheUG

Report the Art of the Speed

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