studyontheinfluenceofroadgeometryonvehicle...

Research ArticleStudy on the Influence of Road Geometry on VehicleLateral Instability

Yanna Yin 1 Huiying Wen1 Lu Sun 12 and Wei Hou34

1South China University of Technology School of Civil Engineering and Transportation No 381 Wushan Road Tianhe DistrictGuangzhou 510641 China2Department of Civil and Environmental Engineering University of Maryland College Park MD 20742 USA3Qilu Transportation Development Group Co Ltd Lixia District Jinan China4Shangdong Binlai Freeway Ltd Zibo Shandong Province China

Correspondence should be addressed to Lu Sun workingworking123163com

Received 17 November 2019 Revised 24 June 2020 Accepted 17 September 2020 Published 7 October 2020

Academic Editor Maria Castro

Copyright copy 2020 Yanna Yin et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

According to the accident analysis of vehicles in the curve the skidding rollover and lateral drift of vehicles are determined asmeans to evaluate the lateral stability of vehicles -e utility truck of rear-wheel drive (RWD) is researched which is high accidentrate Human-vehicle-road simulation models are established by CarSim -rough the orthogonal experiment method the effectsof different road geometries speed and interaction factors between road geometries on vehicle lateral stability are studied In thispaper skidding risk of the vehicle is characterized by the Side-way Force Coefficient (SFC) Rollover risk of the vehicle ischaracterized by lateral acceleration and the load transfer ratio Lateral drift risk of the vehicle is characterized by the sideslip angleof wheels-e results of orthogonal analysis reveal that the maximum tire-road friction coefficient and speed are highly significantin skidding of the vehicle -e effects of the combination of horizontal alignment and superelevation on vehicle skidding areimportant -e effects of horizontal alignment and speed on vehicle rollover risk are highly significant -e effects of super-elevation on vehicle rollover risk are significant -e effects of the interaction of horizontal alignment and superelevation are alsoimportant on vehiclesrsquo rollover risk-e speed and the maximum tire-road friction coefficient have highly significant effect on thevehiclersquos lateral drift -e superelevation has a significant effect on the vehiclersquos lateral drift -e effects of the interaction ofhorizontal alignment and superelevation and longitudinal slope are also important on the lateral drift of the vehicle

1 Introduction

Road accidents caused by lateral stability of the vehicle havealways been a tough concern of vehicle safety in the world Inorder to solve this problem many experts and scholars workon studying how to reduce or even avoid the safety riskcaused by lateral stability -e significant results have beenachieved but traffic accidents are still serious -e lateststatistical data from the National Highway Traffic SafetyAdministration of United States [1] are shown in Table 1 Of52200 fatal automotive vehicle accidents 315 of death tollwas caused by rollover [1] -e number of rollover occur-rence caused by single-vehicle crashes is greater thanmultiple-vehicle crashes -erefore there is an urgent need

to investigate the accident of rollover caused by single-ve-hicle crashes

In the recent years study on lateral stability of vehiclesmainly focus on driving assistance using a vehicle stabilitycontrol system such as an antilock brake system (ABS)electronic stability controller (ESC) and acceleration slipregulation (ASR) When vehicles are in the transverse un-stable state the vehicle stability control system activelycontrols and corrects vehicle movement [2ndash5] -ese sys-tems have brought about a striking effect in antisideslipHowever most of the driving assistance systems are con-cerned about the antiskid risk of vehicles paying less at-tention to the hidden dangers caused by vehicle rolloverRelying on the vehicle stability control system only cannot

HindawiJournal of Advanced TransportationVolume 2020 Article ID 7943739 15 pageshttpsdoiorg10115520207943739

solve the road traffic safety problems completely Moreattention needs to be paid to the ultimate and differentcauses of road traffic accidents [6]

Road traffic accidents are mainly caused by three factorsroads drivers and vehicles Road environment-relatedfactors cause 27 of accidents in the United States [7] Roadgeometric factors cause 34 of vehicle collisions in theUnited States and Britain [8] -ese studies show that badroad conditions or improperly designed roads are the majorcauses of vehicle accidents [9]

-e shortcomings of the existing research on the impactof road factors on vehicle accidents caused by lateral stabilityare reflected in threefold

Firstly the method of the influence of road geometry onvehicle safety is mainly the accident black spot analysismethod -at is to say accident statistics are carried out foraccident-prone roads [10] -e references were seldom onthe effect of road geometry on vehicle dynamics and thenextended to vehicle lateral stability

Secondly the existing research studies on the effect ofroad geometry on vehicle lateral stability mainly considervehicle rollover or skidding Vehicle lateral drift has not beentaken into account It has not been reported that the threeindexes of rollover skidding and lateral drift are consideredat the same time Stergios Mavromatis focuses on the studyof road factors on vehicle skidding and stopping sightdistance [11ndash13] Our research group has systematicallystudied the influence of road geometry skid resistance sightdistance and three-dimensional vision on vehicle rolloverskidding and stopping sight distance [14ndash16]

-irdly the existing road design parameters based on themass point model of are designed -e radius parameters ofcurves are based on the minimum radius formula (1) ofcurves based on the classical mass point model in highwaydesign code -e model ignores the parameter differencesbetween vehicles such as vehicle type mass and center ofgravity position

R V

2

127 fR + e( 1113857 (1)

where fRmdashlateral friction demand of the mass point modelV(kmh)mdashvehicle speed R(m)mdashthe radius of a circularcurve and emdashsuperelevation

Based on the NHTSA data [1] 95 of 522000 auto-motive vehicle accidents are passenger cars or light trucks

As shown in Table 1 compared with passenger cars pickupvans large trucks and buses utility trucks have the highestrollover occurrence caused by single-vehicle crashes(647) Based on the analysis of vehicle accidents and theshortcomings of existing researches this paper takes theutility trucks as the research target A human-vehicle-roadsimulation model is established by CarSim -e orthogonalexperimental method is adopted -rough orthogonal ex-periment the effects of different road geometries speed andinteraction factors on vehicle lateral stability are studiedSignificance analysis of skidding rollover and lateral driftare carried out to characterize vehicle lateral stability

2 Methods

21 Road Model -e road geometric alignment mainlyincludes horizontal alignment longitudinal slope superel-evation road crown and their combination -e horizontalalignment is shown in Figure 1(a) which usually consists ofstraight lines transition curves and circular curves -eradius of the circular curve is R -e longitudinal slopeincludes straight lines and vertical curves as shown inFigures 1(b) and 1(c) It refers to the ratio of the heightdifference of two points of the same slope to its horizontaldistance on the vertical section of a route [17] Longitudinalslope is expressed by islope In order to offset part or even allof the centrifugal force generated while vehicles negotiate acurve the curve section is usually designed to a one-waycross slope with lateral high and medial low It is calledsuperelevation As shown in Figure 1(d) the superelevationslope is isuperelevation In order to facilitate the drainage of theroad surface the road is designed into an arch with highcenter and low sides which is called the road crown Asshown in Figure 1(e) the gradient is i0 -e slope is called asthe composite longitudinal slope with overlapping super-elevation and of longitudinal slope sections as shown inFigure 1(f ) -e formula of calculating the composite lon-gitudinal slope is [17]

icombination

i2superelevation + i

2slope

1113969

(2)

Because of the superelevation and longitudinal slope aresmall in road design code the angle of the roadrsquos cross slopeis approximately equal to the superelevation e asymp isuperelevationFor the same reason the angle of the longitudinal slope isapproximately equal to its longitudinal slope e asymp islope -e

Table 1 United States Traffic Accident Statistics [1]

Vehicle type Rollover occurrence caused bysingle-vehicle crashes ()

Rollover occurrence caused bymultiple-vehicle crashes () Death toll caused by rollover ()

Passenger car 417 71 22Light truck-pickup 571 216 433Light truck-utility 647 266 485Light truck-van 50 16 28Other 638 25Total 509 129 315

2 Journal of Advanced Transportation

angle of the composite longitudinal slope is approximatelyequal to its longitudinal slope θc asymp icombination

22 Vehicle Model

221 Full Vehicle Model In the past two decades expertsand scholars have developed various vehicle dynamicsmodels [12] the mass point model bicycle model [18 19] 8degrees of freedom model [20] and 11 degrees of freedommodel [21] -e complexity of the models increases grad-ually ADAMS is a multibody dynamics simulation tooldeveloped by MSC Software -e main function of ADAMSis to model and simulate multibody dynamics -e vehicledynamics module of ADAMSCar can be used for vehicleperformance simulation However the complexity of thevehicle modeled by ADAMSCar is very high and thesimulation speed may be very slow -e multibody vehiclesimulation software CarSim developed by UMTRI is mainlyused in the automobile industry -e software has beenvalidated for many years -e simplified model includes 27degrees of freedom -e stability and reliability of the modelare very high and the simulation speed is fast

-e vehicle types studied in this paper are light truck-compact utility defined in CarSim [1 22] CarSim simplifiesthe vehicle model into 10 parts one body part four un-sprung mass parts four wheel parts and one enginecrankshaft part -e simplified model consists of 27 degreesof freedom as shown in Figure 2(a) three degrees offreedom of movement (x y z) three degrees of freedom ofrotation (X Y Z) four degrees of freedom of unsprungmass four degrees of freedom of wheels one degree offreedom of the transmission system eight degrees of free-dom of transient characteristics of tires and four degrees offreedom of braking pressure Specifically vehicle modeled

by CarSim is shown in Figure 2(b)-emodel includes sevensubsystems the body aerodynamics transmission assemblybrake system steering system tire and suspension In thispaper the utility truck of the rear-wheel drive is selected asthe research target -e specific parameters of the utilitytruck are shown in Table 2 [21 22]

222 Tire Model -e ldquoMagic Formulardquo tire model ofPacejka [23ndash25] with high fitting accuracy is used in thispaper -e expressions are as follows

y D sin C arctan[Bx minus E(Bx minus arctanBx)] (3)

In the formula y can be a longitudinal force a lateralforce or an aligning torque while the independent variablecan represent the sideslip angle or the longitudinal slip rateof the tire in different cases Based on our previous research[26] this paper considers the tire with good quality as theresearch object ignoring the zero drift in the horizontal andvertical directions of tires -e longitudinal force formulaunder the pure slip condition is fitted by the algebraicpolynomial method [27 28]

Fx(λ) Dx sin Cxarctan Bxλ minus Ex Bxλ minus arctan Bxλ( 1113857( 1113857( 1113857( 1113857

(4a)

where Cx PCx1 Dx (PDx 1 + PDx 2dfz) middot Fz Ex PEx1 +

PEx2dfz Kx Fz middot (PKx1 + PKx2dfz) middot exp(PKx3dfz) andBx (Kx(CxDx))

Under the condition of pure sideslip the formula oflateral force is as follows

Fy(α) Dy sin Cyarctan Byα minus Ey Byα minus arctan Byα1113872 11138731113872 11138731113872 11138731113872 1113873

(4b)

QDZH

HY YHHZ

ZDRStraight Straight

Transition

curveTransitioncurve

Circular curve

(a)

islope

θ

(b)

R1 R2

i2i1

(c)

isupereleveation

e

(d)

i0 i0

(e)

i slope

isupereleveationi combin

ation

(f )

Figure 1 Road geometric design (a) Horizontal curve (b) Longitudinal slope (c) Vertical curve (d) Superelevation (e) Road crown(f ) Composite longitudinal slope

Journal of Advanced Transportation 3

where Cy PCy1 Dy (PDy 1 + PDy 2dfz) middot Fz Ey PEy1 +

PEy2dfz Ky PKy1 middot Fz0 middot sin 2 tanminus 1[(Fz(PKy2Fz0))]1113966 1113967and By (Ky(CyDy))

Here α is the wheel sideslip angle λ is the wheel slip rateFx(λ) is the longitudinal force calculated in the pure slipcondition Fy(α) is the lateral force of the tire in pure

Sideslip angle

Front

Wheel rotation

Unsprung mass degreesof freedom

Unsprung mass degrees of freedom

6 spring mass degrees of freedom

Rear

(a)

BodyVehicleshape

AerodynamicsElastodynamics

Elastodynamics

Kinematics

Kinematics

Engine

Clutch

Steeringsystem

Brakingsystem

Power trainsystem

Transmission

Differential

Suspension

TireDrivingsystem

Steeringbraking

power trainsystems

Vehiclemodel

(b)

Figure 2 (a) Twenty-seven DOFs vehicle model (b) CarSim vehicle structure

Table 2 Vehicle simulation parameters [21 22]

Parameter (unit) Value (utility vehicle)Sprung mass ms (kg) 600Full vehicle m (kg) 768Moment of inertia of sprung mass around X-axis Ixx (kgm2) 3840Moment of inertia of sprung mass around Y-axis Iyy (kgm2) 6242Moment of inertia of sprung mass around Z-axis Izz (kgm2) 6869Horizontal distance between the center of mass and front wheels a (mm) 550Horizontal distance between the center of mass and rear wheels b (mm) 1373Centroid height h (mm) 700-e height between the center of mass and the center of roll hc (mm) 573Front wheelbase cf (mm) 1260Rear-wheelbase cr (mm) 1260Wheel radius R (mm) 347Wheel moment of inertia Iw (kgm2) 09


sideslip movement and Fz is the vertical force of the tire thevalue of fitting parameters is shown in Table 3

23 Driver Model -ere are two kinds of vehicle dynamicssimulation systems the open-loop simulation system andclosed-loop simulation system -e open-loop simulationsystem regards the vehicle itself as an independent controlsystem -e system does not consider the driverrsquos feedbackcharacteristics as shown in Figure 3(a) -e closed-loopsimulation system incorporates the driverrsquos feedback intothe system -e driver continuously corrects the steeringwheel angle through track estimation to form a closed-loopsystem as shown in Figure 3(b) -e closed-loop system cansimulate the influence of road factors on vehicle dynamicsmore realistically In this paper a closed-loop simulationoptimal preview model raised by Charles C Macadam isused which can correct the trajectory [22 29 30] Driversget information about the road ahead and vehicles throughldquopreviewrdquo and ldquoperceptionrdquo Drivers make judgments basedon the acquired information and adjust the motion state ofvehicles -is forms a closed system

-e station formula of the target position [22] is

Stargi S +iVx T

m (5)

S refers to the station of the center line of the roadrsquoshorizontal geometric figure defined by coordinates X and YFor any station S it corresponds to unique X and Y coor-dinates Route S is defined as a function of X and Y through alinear connection point For each pair of XndashY coordinatesthe Pythagorean theorem is used to calculate the corre-sponding s-increment

Si Siminus 1 +

Xi minus Ximinus 1( 11138572

+ Yi minus Yiminus 1( 11138572

1113969

(6)

-e calculation of the controller uses a special coor-dinate axis system as shown in Figure 4 In this coordinateaxis the center of the front axle of the vehicle should belocated at x 0 and y 0 -e yaw angle of a vehicle isdefined as ψ 0 the alignment of the X and Y axles with thelongitudinal and lateral axes of the vehicle respectively Inthe coordinate axes of the driverrsquos controller the motion ofthe vehicle is predicted based on these axes -e axis is fixedin the inertial reference and rotates ψ degree based on theinertial axis

-e target translates transversely in this coordinatesystem First the inertia of X and Y coordinates of the pathare calculated as the path function of the target position(Starg) -en applying the transformation [22]

Ytarg Y Starg1113872 1113873 minus YV1113960 1113961cos(ψ) minus X Starg1113872 1113873 minus XV1113960 1113961sin(ψ)

(7)

Within the coordinate range of the steering controllerthe vehicle is always at the origin of the axis shown inFigure 4 -e time is 0 and the target path is known fromtime 0 to preview time T

3 Safety Margin Analysis of Lateral Stability

-is paper uses the safety margin from our previous study asa variable to reflect the extent of the index approaching thethreshold As shown in Figure 5 the safety margin-stationcurve of the vehicle dynamics index is obtained from thevehicle dynamics simulation It can be seen that the largerthe value of Ij(t) is the closer it is to the threshold I0j and thegreater the possibility of rollover skidding and lateral driftare-erefore this paper uses formula (8) to define the safetymargin of index J to measure the probability of accident riskcaused by lateral unstability of vehicles

Mj I0j minus max Ij(t)

11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leMj le I0j (8)

31 SafetyMargin ofVehicle Skidding Risk When a vehicle istraveling on a curve the lateral force perpendicular to thedirection of the vehicle will be produced due to the influenceof centrifugal force and cross slope When the lateral force isequal to or exceeds the maximum lateral adhesion forceprovided by the road surface it will cause lateral slip of oneor both axles of the vehicle which is called skidding Vehicleskidding includes skidding of four wheels skidding of thefront wheel and skidding of the rear wheels -e phe-nomenon that the trajectory tracking ability is lost due to theskidding of the front axle in a curve is called the front-wheelskidding

-e phenomenon of instability caused by skidding offour wheels is called lateral drift [31] Lateral drift is studiedseparately below According to the definition of the skiddingthe lateral force coefficient of wheels is taken as the indicatorof vehicle skidding in this paper -e lateral force coefficient[32] formula of the vehicle is

μl maxFyi

FZi

11138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113888 1113889 i 1 2 3 4 (9)

where Fyi is the tire lateral force FZi is the tire vertical forcei 1 2 3 4 are the left-front wheel left-rear wheel right-front wheel and right-rear wheel respectively

When the lateral force coefficient of any wheel is greaterthan the lateral maximum tire-road friction coefficient thevehicle will skid Let μ0l be the adhesion coefficient providedby the pavement when skidding is about to occur It alsorequires the lateral maximum tire-road friction coefficient toavoid skidding When μl gt μ0l skidding will occur-e testedmaximum tire-road friction coefficient fp is 08 05 and 02[32] which correspond respectively to dry wet and snowconditions of the asphalt pavement According to [33] thelateral maximum tire-road friction fRmax 0925fp

Table 3 Fitting parameters of the ldquoMagic Formulardquo [20]

PCx1 PDx 1 PDx 2 PEx1 PEx2 PKx1 PKx2 PKx3162 1035 minus 00487 05 minus 0122 194 minus 013 0171PCy1 PDy 1 PDy 2 PEy1 PEy2 PKy1 PKy2129 minus 09 018 minus 107 068 minus 1295 172


However the vehicle is at a high slip value in this paper andthe brake is blocked or the slip is accelerated [32 34] In sucha situation the maximum tire-road friction coefficient isequivalent to the sliding adhesion coefficient fs Namelyfp fs -erefore fRmax 0925fs Table 4 shows themaximum tire-road friction coefficients slip friction coef-ficient and lateral maximum tire-road friction coefficient ofasphalt pavements under dry wet and snow conditions

-e safety margin of vehicle skidding on curves is de-fined as the difference between the lateral maximum tire-road friction coefficient provided by the available tire-roadand the lateral friction demand [35] So the correspondingsafety margin of vehicle skidding is obtained

M1 μ0l minus max μl( 1113857 0leM1 le μ0l (10)

Inertial Y

Inertial X

Target path

Predicted path(constant steer)

Driver model X axis

Driver model Y axis

Origin (front axle)

XV YV(inertial coordinates)

ab

Mass center

ψ

Figure 4 Axis system of the steering controller

S

I j0

Mj

Ij (t)

Figure 5 -e station curve of index j

Driverroad inputVehicle dynamics

outputVehicle dynamicssimulation

(a)

VehicledynamicsresponseVehicle dynamics

simulation

Externalinterference

Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)

Figure 3 Flow chart of simulation (a) Open-loop simulation (b) Closed-loop simulation


32 Safety Margin of Vehicle Rollover Risk -ere are twotypes of vehicle rollover nontripping rollover and trippingrollover When vehiclesrsquo lateral acceleration exceeds thecompensation limit of lateral tire weight transfer the vehiclerotates 90 degrees or more around its longitudinal axiswhich is called nontripping rollover Another is that when avehicle slips the vehicle loses control -e vehicle is im-pacted by the cross slope the curb and mollisol so as toldquotriprdquo the vehicle and rotates 90 degrees or more around itslongitudinal axis which is called tripping rollover Becausethe risk of skidding occurs before tripping rollover andskidding has been expressed above this paper only studiesnontripping rollover Based on the abovementioned defi-nition of rollover the lateral acceleration and load transferratio are selected as the indicators to measure vehiclerollover risk -e load transfer ratio is defined as the ratio ofthe amount of load transferred from the inside to the outsideto the total load [36] as shown in the following equation

LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)

When the inner wheel load is zero that is the innervehicle leaves the ground at this time LTR 0 and thethreshold of the load transfer ratio is thus obtained -ecorresponding safety margin of rollover is

M2 LTR0minus max(|LTR(t)|) 0leM2 le LTR

0 (12)

In this paper the quasistatic model of a rigid vehicle isused -e rigid vehicle means neglecting the elastic defor-mation of the vehicle and tire [32] Quasistatic refers to thevehicle steady-state steering [32] -e quasistatic model of arigid vehicle is shown in Figure 6 -e torque formula of thecontact point between the outside wheel and the ground is asfollows

(F cos α minus mg sin α)hg + Nxi middot B minus (F sin α + mg cos α) middotB

2 0

(13)

Here F is the centrifugal force α is the bank angle ofroads Nyi and Ny0 are the lateral forces on the inner andouter tires respectively Nxi and Nx0 are the vertical forceson the inner and outer tires respectively ay is the lateralacceleration and B is the wheel base

As the bank angle α of the road is generally smallsin α asymp tan α α isuperelevation cos α asymp 1 Moreover

F cos α minus mg sin α may which can be derived fromequation (13) as follows

mayhg + Nxi middot B minus (Fα + mg) middotB

2 0 (14)

When Nxi becomes 0 the vehicle begins to rollover -elateral acceleration when the vehicle begins to rollover iscalled the rollover threshold which can be derived fromequation (14) as follows

ay Fα + mg middot (B2)

mhg

(15)

Clearly when the bank angle is α 0 the rolloverthreshold is ay (B2hg)g -e parameters in Table 2 aresubstituted into equation (15) to obtain the resulting rolloverthreshold ay 09g -e quasistatic model of the rigid ve-hicle is reasonable only when the lateral acceleration changesslowly [32] When the lateral acceleration changes rapidly aphysical model of roll is needed However modeling is notcritical in this paper and this paper directly applies theconclusion of [32] For the utility truck the rolloverthreshold value of the physical model of roll is lower 30than that of the quasistatic model of rigid vehicle [32]-erefore the rollover threshold value of the physical modelof roll is a0

y (1 minus 30) middot ay 063g which can be derivedfrom equation (8) as follows

M3 a0y minus max ay(t)

11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)

33 Safety Margin of the Vehiclersquos Lateral Drift Risk Highsideslip cornering is also called drift [37] When vehicles aretraveling in curves when the speed is too high (eg racingactivities) or the radius of the curves is too small theirwheels will lose grip-e sideslip angle of the vehicle exceedsits control limit and the vehicle runs at the tire-road ad-hesion limit [38] At this time the vehicle is turning in theopposite direction of bend with large sideslip angle and the

Table 4 -e maximum tire-road friction coefficients slip frictioncoefficient and lateral maximum tire-road friction coefficient[32ndash34]

Maximum tire-roadfriction coefficients

Slip frictioncoefficient

Lateral maximum tire-road friction coefficient

fp fs fRmax 0925fs

08 075 06905 045 04102 015 013fp maximum tire-road friction coefficient fs slip friction coefficient theslip friction coefficient is equal to the braking force coefficient when thesliding rate is 100 fRmax lateral maximum tire-road friction coefficient

B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay

Figure 6 -e free-body diagram of the quasistatic model of a rigidvehicle


wheels are nearly saturated -is state of the vehicle is calleddrift [39]

According to the definition of lateral drift the sideslipangle of a vehicle is determined as the indicator of vehiclelateral drift Sideslip angle is the angle between the directionof movement of the wheel center and the lateral velocity[34 37] -e expression is as follows

β arctanVy

Vx

(17)

where β- vehicle sideslip angle Vy- lateral speed of the tire-road contact point and Vx- longitudinal speed of the wheelrotation center

Based on the literature of Yu [32] and the definition oflateral drift when the lateral friction coefficient of the rearwheels of the vehicle reaches the critical value of skidding therear wheel is close to saturation state and the sideslip angle atthis time is defined as the threshold of lateral drift -e roadmodel is developed by CarSim -e radius of the road isdesigned as 250m the longitudinal slope is designed as 006and the superelevation is designed as 008 (the road model isthe most unfavourable road condition on the basis ofltHighway Engineering Technology Standard (JTG B 01-2014)gt when the design speed is 80 kmh) -e peak adhesioncoefficient of the pavement is 08 05 and 02 -e vehiclespeed starts at 80 kmh and increases continuously everyother 5 kmh until the vehicle is about to skid At this time thevehiclersquos sideslip angle is 371deg 234deg and 059 respectivelyand this value is defined as the lateral drift threshold of ve-hicles -e safety margin of lateral drift of the vehicle is

M4 β0 minus max(|β|) 0leM4 le β0 (18)

4 Numerical Analysis

41Orthogonal ExperimentalDesignwith Interaction In thispaper the method orthogonal experimental design is used toanalyze the influence of the roadrsquos horizontal alignment (A)longitudinal slope (B) superelevation (C) maximum tire-road friction coefficient (D) and vehicle speed (E) on vehiclelateral stability -e interaction of horizontal alignment andthe longitudinal slope (AB) the interaction of horizontalalignment and superelevation (AC) and the interaction ofhorizontal alignment and the pavement friction coefficient(AD) are also considered -e levels of factors are shown inTable 5 and each factor contains three levels-e orthogonaltable of L27(313) (this form can be seen in the supplementarydocument (Experimental data) -e supplementary docu-ment is the selected orthogonal table and the experimentaldata for orthogonal analysis) is selected in this paper Basedon literature [40] we can get the location of the interactionfactors column -e headerrsquos design of the table is shown inTable 6 with blank columns as error items

42 Analysis of Experimental Results Tables 7ndash10 are thevariance analysis table of skiddingrsquos safety margin rolloverrsquossafety margin and lateral driftrsquos safety margin-e influence

of some factors on the experimental results is not obviousNamely mean square value Sj lt Se -erefore the sum ofsquares of row of these factorsrsquo location is incorporated intothe error line e and a new error line is obtained As shown inTable 7 SA lt Se SB lt Se SAtimesB lt Se SAtimesD lt Se therefore weshould incorporate SA SB SAtimesB SAtimesD into Se New sum ofsquares of errors and degrees of freedom are obtained SeΔ

Se + SA + SB + SAtimesB + SAtimesD and feΔ fe + fA + fB+ fAtimesB +

fAtimes D Analysis of variance is carried on by the formulaF ((Sjfj)(SeΔ feΔ)) If FgeF1minus α(fj feΔ) the signifi-cance of this factor on the experimental results is inferredfrom the significance α If Fj geF1minus 001(fj feΔ) the influenceof this factor on the experimental results is highly significantIf F1minus 001(fj feΔ)gtFj geF1minus 005(fj feΔ) the influence ofthis factor on the experimental results is significant IfF1minus 005(fj feΔ)gtFj geF1minus 01(fj feΔ) the influence of thisfactor on the experimental results is commonly significant IfF1minus 01(fj feΔ)gtFj the influence of this factor on the ex-perimental results is not significant For the same reasonTables 8ndash10 are available

For the safety margin of skidding M1 analysis of variancebased on orthogonal Table 6 is carried on Because the skiddingsafety margin obtained is small the original value is multipliedby 1000 in the calculation process Table 7 is FD gtF1minus 001(2 16)

obtained by the analysis of variance In the tableF1minus 001(2 16)gtFC geF1minus 005(2 16 ) FD gtF1minus 001(2 16) FE gtF1minus 001(2 16) and FAC ltF1minus 01(2 16) it shows that themaximum tire-road friction coefficient and vehicle speed have ahighly significant influence on the vehiclersquos lateral force coef-ficient -at is to say the impact on vehicle skidding is highlysignificant-e superelevation has a significant influence on thevehiclersquos lateral force coefficient -at is to say the impact onvehicle skidding is significant Other factors have no significanteffect on vehicle skidding

In this paper the range Rj of the safety margin ofskidding is calculated to determine the order of primary andsecondary factors affecting skidding From main to sec-ondary RD gtRE gtRAC gtRC gtRAB gtRA gtRB gtRA D Obvi-ously except for a single factor the maximum tire-roadfriction coefficient vehicle speed and superelevation theinteraction of horizontal alignment and superelevation hasan important effect on vehicle skidding It cannot beignored

-e results from two analyses suggest that the maximumtire-road friction coefficient and vehicle speed have a highlysignificant effect on vehicle skidding -e superelevation hasa significant influence on the vehiclersquos skidding -e in-teraction of horizontal alignment and superelevation has animportant influence on vehiclersquos skidding

Figure 7 shows the effect of the significant single factoron the safety margin of vehicle skidding Figure 7(a) showsthe effect of superelevation on the safety margin of vehicleskidding -e speed v 100(kmh) radius of the circularcurve R 700m and the maximum tire-road friction co-efficient fp 08-e 600mminus 1200m road section is selectedas the research object -e 600ndash800m road section is thetransition section from a straight line to a circular curve(clothoid curve section) -e 800ndash1200m road section is acircular curve section -e values of superelevation are


e 004 006 008 As can be seen in the Figure 7(a) withthe increase in superelevation values the safety margin ofvehicle skidding increases -erefore it is more difficult forthe vehicle to skid

Figure 7(b) shows the effect of the maximum tire-roadfriction coefficient on the safety margin of vehicle skidding-e speed v 80(kmh) radius of the circular curveR 700m and the superelevation e 006 -e

Table 5 Factors and level table [40]

Level A B C D EHorizontal alignment (m) Grade () Superelevation () Maximum tire-road friction coefficient Speed (kmh)

1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120

Table 6 Headerrsquos design with factors interaction and mixed levels

Factor A B (AB)1 (AB)2 C (AC)1 (AC)2 D (A D)1 (A D)2 E

Column 1 2 3 4 5 6 7 8 9 10 11 12 13

Table 7 -e table of variance analysis of skiddingrsquos safety margin M1

Sources of variation Square sum Sj Freedom f Mean square Sj F value Significance Critical value

A 3630 2 1815

F1minus 005(2 16) 363F1minus 001(2 16) 623F1minus 01(4 16) 233F1minus 005(4 16) 307

B 4519 2 2259C 22296 2 11148 4704 SignificantD 14507630 2 7253815 306068 Highly significantE 132741 2 66370 28004 Highly significant(AtimesB) 7703 4 1926AtimesC 19926 4 4982 2102 Nonsignificant(AtimesD) 3926 4 0982e 18148 4 4537e 37926 16 2370

Table 8 -e table of variance analysis of rolloverrsquos safety margin M2


A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431

B 6586 2 3293C 55352 2 27676 3455 SignificanceD 15278 2 7639E 76289 2 38144 4761 Significance(AtimesB) 21514 4 5379(AtimesC) 49634 4 12406(AtimesD) 11623 4 2906E 64258 4 16065E 176249 22 8011



A 1636093 2 8180037 99669 Highly significant


F1minus 005(4 22) 282F1minus 001(4 22) 431

B 0069 2 0345C 0023 2 00115D 0041 2 00205E 19248217 2 9624108 117264 Highly significant(AtimesB) 071 4 01775(AtimesC) 0117 4 0029(AtimesD) 0092 4 0023E 1804547 4 451137e 1805599 22 82072


600mndash1200m road section is selected as the research object-e 600ndash800m road section is the transition section from astraight line to a circular curve (clothoid curve section) -e800ndash1200m road section is a circular curve section -emaximum tire-road friction coefficients are fp 02 05

08 As can be seen from the Figure 7(b) with the increase inthemaximum tire-road friction coefficient the safety marginof vehicle skidding increases -erefore it is more difficultfor the vehicle to skid

Figure 7(c) shows the effect of vehicle speed on the safetymargin of vehicle skidding Radius of the circular curveR 700m the superelevation e 006 and the maximumtire-road friction coefficient fp 08 -e road section oftime at 16 sndash40 s is selected as the research object whichincludes two sections the transition section (clothoid curvesection) and circular curve section -e vehicle speeds arev 80(kmh) 100(kmh) 120(kmh) As can be seen fromFigure 7(c) with the increase in vehicle speed the safety

Table 10 -e table of variance analysis of the safety margin of vehicle lateral drift M4


A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431

B 40831 2 20416C 442258 2 221129 448 SignificantD 447987 2 2239935 454007 Highly significantE 2207725 2 1103862 22374 Highly significant(AtimesB) 38041 4 9510(AtimesC) 275292 4 68823(AtimesD) 43575 4 10894e 474172 4 118543e 1085415 22 49337

v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding

v = 80kmhv = 100kmhv = 120kmh

R = 700 e = 006 fp = 08

(c)

Figure 7 -e effect of the significant single factor on the safety margin of the vehiclersquos skidding (a) Effect of superelevation on the safetymargin of skidding (b) Effect of the pavement friction coefficient on the safety margin of skidding (c) Effect of speed on the safety margin ofskidding


margin of vehicle skidding reduces -erefore vehicles aremore prone to skidding

For the safety margin of vehicle rollover M2 analysis ofvariance based on orthogonal Table 6 is carried out Becausethe safety margin of vehicle rollover obtained is small theoriginal value is multiplied by 100 in the calculation processTable 8 is obtained by variance analysis In the tableFC gtF1minus 005(2 22) FE gtF1minus 005(2 22) and it shows thatsuperelevation and vehicle speed have a significant effect onthe lateral load transfer ratio of vehicles that is the su-perelevation and vehicle speed have a significant effect onthe vehiclersquos rollover

In this paper the range Rj of the safety margin of vehiclerollover is calculated to determine the order of primary andsecondary factors affecting rollover From main to sec-ondary RAC gtRE gtRC gtRAB gtRA D gtRD gtRA gtRB Obvi-ously except for a single factor superelevation and vehiclespeed the interaction of horizontal alignment and super-elevation has a significant effect on vehicle rollover It cannotbe ignored

For the safety margin of vehicle rollover M3 analysis ofvariance based on orthogonal Table 6 is carried out Becausethe safety margin of vehicle rollover obtained is small theoriginal value is multiplied by 1000 in the calculationprocess Table 9 is obtained by variance analysis In the tableFA gtF1minus 001(2 22) FE gtF1minus 001(2 22) and it shows thathorizontal alignment and vehicle speed have a highly sig-nificant effect on the vehicle lateral acceleration -at is thehorizontal alignment and vehicle speed have a highly sig-nificant effect on the vehiclersquos rollover

-e variance analysis from M2 and M3 suggests that thehorizontal alignment and vehicle speed have a highly sig-nificant effect on the vehiclersquos rollover -e superelevationhas a significant influence on the vehiclersquos rollover -einfluence of the interaction of horizontal alignment andsuperelevation cannot be neglected and also an importantfactor

Figure 8 shows the effect of the significant single factoron the safety margin of vehicle rollover Figure 8(a) showsthe effect of superelevation on the safety margin of vehiclerollover (M2) -e speed v 100(kmh) radius of thecircular curve R 700m and the maximum tire-roadfriction coefficient fp 08-e 600mndash1200m road sectionis selected as the research object-e 600ndash800m road sectionis the transition section from a straight line to a circularcurve (clothoid curve section) -e 800ndash1200m road sectionis a circular curve section -e values of superelevation aree 004 006 008 As can be seen from Figure 8(a) with theincrease of superelevation values the safety margin of thevehiclersquos rollover increases-erefore vehicles are less proneto rollover

Figure 8(b) (M2) and Figure 8(d) (M3) show the effect ofvehicle speed on the safety margin of vehicle rollover -eradius of the circular curve R 700m the superelevatione 006 and the maximum tire-road friction coefficientfp 08 -e road section of time at 16 sndash40 s is selected asthe research object which includes two sections the tran-sition section (clothoid curve section) and circular curvesection -e vehicle speeds are v 80(kmh) 100(kmh)

120(kmh) As can be seen from the Figures 8(b) and 8(d)with the increase of vehicle speed the safety margin ofvehicle rollover reduces -erefore vehicles are more proneto rollover As can be seen from Figure 8 the safety marginof vehicle rollover expressed by the load transfer ratio (M2)is greatly affected by the clothoid curve section and therollover safety margin expressed by the lateral acceleration(M3) is less affected by the clothoid curve section

Figure 8(c) shows the effect of horizontal alignment onthe safety margin of vehicle rollover -e speed v 80 kmhthe superelevation e 006 and the maximum tire-roadfriction coefficient fp 08 -e radii of the circular curveare R 700m 1000m 1500m -e 600mndash1200m roadsection is selected as the research object-e 600ndash800m roadsection is the transition section from a straight line to acircular curve (clothoid curve section)-e 800ndash1200m roadsection is a circular curve section -e values of superele-vation are e 004 006 008 As can be seen fromFigure 8(c) with the increase in the radius of the circularcurve values the safety margin of vehicle rollover increases-erefore vehicles are less prone to rollover

For the safety margin of the vehiclersquos lateral drift M4analysis of variance based on orthogonal Table 6 is carriedout Because the safety margin of the vehiclersquos lateral driftobtained is small the original value is multiplied by 100 inthe calculation process Table 10 is obtained by varianceanalysis In the table FC gtF1minus 005(2 22) FD gtF1minus 001(2 22)FE gtF1minus 001(2 22) and it shows that the superelevation has asignificant effect on the vehicle sideslip angle -erefore thesuperelevation has a significant effect on the vehiclersquos lateraldrift -e vehicle speed and maximum tire-road frictioncoefficient have a highly significant effect on the vehiclesideslip angle -erefore the vehicle speed has a highlysignificant effect on the vehiclersquos lateral drift

In this paper the range Rj of the safety margin of thevehiclersquos lateral drift is calculated to determine the order ofprimary and secondary factors affecting the vehiclersquos lateraldrift From main to secondary RD gtRB gtRE gtRAC gtRC gtRA D gtRA gtRAB Obviously except for a single factorsuperelevation vehicle speed and maximum tire-roadfriction coefficient the interaction of horizontal alignmentand superelevation also have an important effect on thevehiclersquos lateral drift It cannot be ignored

-e results from two analyses suggest that the vehiclespeed and maximum tire-road friction coefficient have ahighly significant effect on the vehiclersquos lateral drift -esuperelevation has a significant effect on the vehiclersquos lateraldrift -e interaction of horizontal alignment and superel-evation and longitudinal slope has an important effect on thevehiclersquos lateral drift It cannot be ignored

Figure 9 shows the effect of the significant single factoron the safety margin of the vehiclersquos lateral drift Figure 9(a)shows the effect of superelevation on the safety margin of thevehiclersquos lateral drift-e speed v 100(kmh) radius of thecircular curve R 700m and the maximum tire-roadfriction coefficient fp 08-e 600mndash1200m road sectionis selected as the research object-e 600ndash800m road sectionis the transition section from a straight line to a circularcurve (clothoid curve section) -e 800ndash1200m road section


600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)

Figure 8-e effect of the significant single factor on the safety margin of vehicle rollover (a) Effect of superelevation on the safetymargin ofrollover (b) Effect of speed on the safetymargin rollover (c) Effect of the radius of the horizontal curve on the safety margin of rollover (M3)(d) Effect of speed on the safety margin of rollover (M3)

600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued


is a circular curve section -e values of superelevation aree 004 006 008 As can be seen from Figure 9(a) with theincrease in superelevation the safety margin of the vehiclersquoslateral drift increases -erefore vehicles are less prone tolateral drift

Figure 9(b) shows the effect of the maximum tire-roadfriction coefficient on the safety margin of lateral drift -espeed v 80(kmh) radius of the circular curve R 700mand the superelevation e 006 -e 600mndash1200m roadsection is selected as the research object -e 600ndash800m roadsection is the transition section from a straight line to acircular curve (clothoid curve section) -e 800ndash1200m roadsection is a circular curve section -e maximum tire-roadfriction coefficients are fp 02 05 08 As can be seen fromFigure 9(b) with the increase in the maximum tire-roadfriction coefficient the safety margin of lateral drift increases-erefore it is more difficult for the vehicle to drift

Figure 9(c) shows the effect of vehicle speed on the safetymargin of the vehiclersquos lateral drift Radius of the circularcurve R 700m the superelevation e 006 and themaximum tire-road friction coefficient fp 08 -e roadsection of time at 16 sndash40 s is selected as the research objectwhich includes two sections the transition section (clothoidcurve section) and circular curve section -e vehicle speedsare v 80(kmh) 100(kmh) 120(kmh) As can be seenfrom the Figure 9(c) with the increase in vehicle speed thesafety margin of the vehiclersquos lateral drift reduces -ereforevehicles are more prone to lateral drift

5 Conclusions

Based on the analysis of vehicles accident in a curve theskidding rollover and lateral drift of vehicles are determined asthe means to evaluate the lateral stability of vehicles Aiming atthe high accident rate of utility trucks with rear-wheel drive(RWD) simulation models of Human-Vehicle-Road areestablished by CarSim -rough the orthogonal analysis designmethod the effects of road geometry speed factors and in-teraction between road geometries on the lateral stability ofvehicles are studied

In this paper the lateral force coefficient is used to char-acterize the safety margin of vehicle skidding Synthesizing theresults of orthogonal analysis and range analysis of the safetymargin of vehicle skidding it is suggested that the maximumtire-road friction coefficient and vehicle speed have a highlysignificant effect on vehicle skidding -e superelevation has asignificant influence on vehiclersquos skidding -e interaction ofhorizontal alignment and superelevation has an important effecton vehicle skidding It cannot be ignored

Significant single factor analysis shows that with theincrease of superelevation and the maximum tire-roadfriction coefficient the safety margin of vehicle skiddingincreases and the vehicle is less prone to skidding With theincrease of vehicle speed the safety margin of vehicleskidding decreases and the vehicle is more prone to skid

In this paper lateral acceleration and the load transferratio are used to characterize the safety margin of vehiclerollover -e results of orthogonal analysis and rangeanalysis show that horizontal alignment and vehicle speedhave a highly significant impact on vehicle rollover risk -esuperelevation has a significant impact on vehicle rolloverrisk and the interaction between horizontal alignment andsuperelevation is also an important factor

Significant single factor analysis shows that with theincrease of superelevation and the radius of horizontalcurves the safety margin of vehicle rollover increases andthe rollover of vehicles is less prone to occur With theincrease of vehicle speed the safety margin (M2 M3) ofvehicle rollover decreases and the vehicle is more prone torollover

In this paper the safety margin of the vehiclersquos lateraldrift is characterized by the sideslip angle From the resultsof orthogonal analysis and range analysis we can get theseconclusions -e vehicle speed and maximum tire-roadfriction coefficient have a highly significant effect on thevehiclersquos lateral drift -e superelevation has a significanteffect on the vehiclersquos lateral drift -e interaction of hori-zontal alignment and superelevation and longitudinal slopehas an important effect on the vehiclersquos lateral drift It cannotbe ignored

16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)

Figure 9 -e effect of the significant single factor on the safety margin of the vehiclersquos lateral drift (a) Effect of superelevation on the safetymargin of lateral drifting (b) Effect of the peak friction coefficient on the safety margin of lateral drifting (c) Effect of speed on the safetymargin of lateral drifting


Significant single factor analysis shows that with theincrease in superelevation the safety margin of vehiclesrsquolateral drift increases and the lateral drift of vehicles is lesslikely to occur With the increase in vehicle speed and themaximum tire-road friction coefficient the safety margin ofthe vehiclersquos lateral drift decreases and the lateral drift ofvehicles is more likely to occur

-e results of the abovementioned analysis show that thevehicle traveling risk can be reduced through improving andlimiting the significant adverse factors for the lateral stabilityof vehicles In our future research besides considering theinfluence of a single factor on vehicle lateral stability weshould also consider the interaction among multiple factors

Data Availability

Some or all data models or code generated or used duringthe study are available in a repository or online in accor-dance with funder data retention policies (provide full ci-tations that include URLs or DOIs)

Conflicts of Interest

-e authors declare no conflicts of interest

Authorsrsquo Contributions

L S conceived the study Y Y and L S conducted thenumerical experimental design Y Y H W and L Sanalyzed the data and wrote the paper and W H partici-pated in the revision of the study and providing suggestionson incorporation of technical specifications of road geo-metric design and policy recommendations

Acknowledgments

-is study was sponsored in part by the National NaturalScience Foundation of China under grants 51050110143 and51250110075 and by Qilu Transportation DevelopmentGroup to which the authors are very grateful

Supplementary Materials

-is form can be seen in the supplementary document(Experimental data) -e supplementary document is theselected orthogonal table and the experimental data fororthogonal analysis (Supplementary Materials)

References

[1] NHTSA National Highway Traffic Safety Administration2016 httpwwwnhtsadotgov

[2] D Chu Z Li J Wang C Wu and Z Hu ldquoRollover speedprediction on curves for heavy vehicles using mobilesmartphonerdquo Measurement vol 130 pp 404ndash411 2018

[3] S Yim ldquoDesign of a robust controller for rollover preventionwith active suspension and differential brakingrdquo Journal ofMechanical Science and Technology vol 26 no 1 pp 213ndash2222012

[4] S Yim K Jeon and K Yi ldquoAn investigation into vehiclerollover prevention by coordinated control of active anti-rollbar and electronic stability programrdquo International Journal ofControl Automation and Systems vol 10 no 2 pp 275ndash2872012

[5] A B Dunwoody and S Froese ldquoActive roll control of a semi-trailerrdquo SAE International Warrendale PA USA SAETechnical Paper 933045 1993

[6] J Shin and I Lee ldquoReliability-based vehicle safety assessmentand design optimization of roadway radius and speed limit inwindy environmentsrdquo Journal of Mechanical Design vol 136no 8 Article ID 081006 2014

[7] T Sayed W Abdelwahab and F Navin ldquoIdentifying acci-dent-prone locations using fuzzy pattern recognitionrdquoJournal of Transportation Engineering vol 121 no 4pp 352ndash358 1995

[8] K Rumar ldquo-e Role of Perceptual and Cognitive Filters inObserved Behaviorrdquo Human Behavior and Traffic SafetySpringer Boston MA USA pp 151ndash170 1985

[9] J Shin and I Lee ldquoReliability analysis and reliability-baseddesign optimization of roadway horizontal curves using afirst-order reliability methodrdquo Engineering Optimizationvol 47 no 5 pp 622ndash641 2015

[10] F Malin I Norros and S Innamaa ldquoAccident risk of roadand weather conditions on different road typesrdquo AccidentAnalysis amp Prevention vol 122 pp 181ndash188 2019

[11] S Mavromatis and B Psarianos ldquoAnalytical model to de-termine the influence of horizontal alignment of two-axleheavy vehicles on upgradesrdquo Journal of Transportation En-gineering vol 129 no 6 pp 583ndash589 2003

[12] S Mavromatis F Mertzanis G Kleioutis et al ldquo-ree-di-mensional stopping sight distance control on passing lanes ofdivided highwaysrdquo European Transport Research Reviewvol 8 no 1 p 8 2016

[13] S Mavromatis A Laiou and G Yannis ldquoSafety assessment ofcontrol design parameters through vehicle dynamics modelrdquoAccident Analysis amp Prevention vol 125 pp 330ndash335 2019

[14] K S You L Sun and W J Gu ldquoRisk analysis-based iden-tification of road hazard locations using vehicle dynamicsimulationrdquo Journal of Southeast University (Natural ScienceEdition) vol 42 no 1 pp 151ndash155 2012

[15] K S You L Sun and W J Gu ldquoReliability design theory andmethod of highway horizontal curve radiusrdquo Journal of Trafficand Transportation Engineering vol 12 no 6 pp 1ndash6 2012

[16] K You and L Sun ldquoReliability analysis of vehicle stability oncombined horizontal and vertical alignments driving safetyperspectiverdquo Journal of Transportation Engineering vol 139no 8 pp 804ndash813 2013

[17] Y Liu R You and Y Yang Road Reconnaissance Design (InChinese) China Electric Power Press Beijing China 2010

[18] M Kontaratos B Psarianos and A Yiotis ldquoMinimumhorizontal curve radius as a function of grade incurred byvehicle motion in driving moderdquo Journal TransportationResearch Record vol 1445 pp 86ndash93 1994

[19] H B Pacejka Tire and Vehicle Dynamics Society of Auto-motive Engineers Butterworth ndash Heinemann London UK2006

[20] K S You Vehicle Dynamic and Reliability Reliability BasedHighway Safety Analysis and Design Optimization SoutheastUniversity Nanjing China 2012

[21] W Zhang Vehicle Dynamics Analysis of Single Vehicle RoadTraffic Accident and Regression Model Xiamen UniversityXiamen China 2017


[22] Mechanical Simulation Corporation CARSIM ReferenceManual Mechanical Simulation Corporation Ann ArborMI USA 2016

[23] E Bakker L Nyborg and H B Pacejka ldquoTyre modelling foruse in vehicle dynamics studiesrdquo pp 190ndash192 SAE Inter-national Warrendale PA USA 1987 SAE Technical PaperSeries

[24] E Bakker H B Pacejka and L Lidner ldquoA new tire modelwith an application in vehicles dynamics studiesrdquo pp 101ndash113 SAE International Warrendale PA USA 1989 SAEPaper 890087

[25] F Yu and Y Lin Automotive System Dynamics China Ma-chine Press Beijing China 2016

[26] L Sun K S You Y Wang et al ldquoInfluence analysis of roadconditions on vehicle rolloverrdquo Journal of Southeast Uni-versity (Natural Science Edition) vol 43 no 3 pp 645ndash6482013

[27] D Wang L He X J Sun et al ldquoParameters identification ofmagic formula of vehicle tire using genetic algorithmrdquo Bus ampCoach Technology and Research vol 2 2015

[28] C Zhang L Meng and S J Wang ldquoSideslip risk simulationanalysis of passenger car braking behavior on expresswaycurved sectionsrdquo China Journal of Highway and Transportvol 28 no 12 pp 134ndash142 2015

[29] C C Macadam ldquoApplication of an optimal preview controlfor simulation of closed-loop automobile drivingrdquo IEEETransactions on Systems Man and Cybernetics vol 11 1981

[30] C C Macadam ldquoAn optimal preview control for linearsystemsrdquo Journal of Dynamic Systems Measurement andControl ASME vol 102 no 3 1980

[31] M Abe Vehicle Handling Dynamics Ieory and ApplicationChina Machine Press Beijing China 2016

[32] Z S Yu Automobile Ieory China Machine Press BeijingChina 2011

[33] R Lamm B Psarianos and T Mailaender Highway Designand Traffic Safety Engineering Handbook McGraw-HillCompanies New York NY USA 1999

[34] S Dieter H Manfred and B Roberto Vehicle DynamicsModeling and Simulation Springer-Verlag Berlin HeidelbergBerlin Germany 2018

[35] D W Harwood and J M MasonHorizontal Curve Design forPassenger Cars and Trucks pp 22ndash33 Transportation Re-search Board Washington DC USA 1994

[36] Z C Su Study on Vehicle Dynamic Stability Control onSteering and Braking Maneuvers Chongqing UniversityChongqing China 2007

[37] F Zhang J Gonzales K Li et al ldquoAutonomous drift cor-nering with mixed open-loop and closed-loop controlrdquo IFACPapers On Line vol 50 pp 1916ndash1922 2017

[38] E Velenis ldquoFWD vehicle drifting control the handbrake-cornering techniquerdquo in Proceedings of the 2011 50th IEEEConference on Decision and Control and European ControlConference (CDC-ECC) pp 3258ndash3263 Orlando FL USADecember 2011

[39] R Y Hindiyeh and J C Gerdes ldquoDesign of a dynamic surfacecontroller for vehicle sideslip angle during autonomousdriftingrdquo in Proceedings of the 6th IFAC Symposium Advancesin Automotive Control Munich Munich Germany July 2010

[40] C Q Zhang and C X He Fundamentals of MathematicalStatistics South China University of Technology PressGuangzhou China 2013


solve the road traffic safety problems completely Moreattention needs to be paid to the ultimate and differentcauses of road traffic accidents [6]

Road traffic accidents are mainly caused by three factorsroads drivers and vehicles Road environment-relatedfactors cause 27 of accidents in the United States [7] Roadgeometric factors cause 34 of vehicle collisions in theUnited States and Britain [8] -ese studies show that badroad conditions or improperly designed roads are the majorcauses of vehicle accidents [9]

-e shortcomings of the existing research on the impactof road factors on vehicle accidents caused by lateral stabilityare reflected in threefold

Firstly the method of the influence of road geometry onvehicle safety is mainly the accident black spot analysismethod -at is to say accident statistics are carried out foraccident-prone roads [10] -e references were seldom onthe effect of road geometry on vehicle dynamics and thenextended to vehicle lateral stability

Secondly the existing research studies on the effect ofroad geometry on vehicle lateral stability mainly considervehicle rollover or skidding Vehicle lateral drift has not beentaken into account It has not been reported that the threeindexes of rollover skidding and lateral drift are consideredat the same time Stergios Mavromatis focuses on the studyof road factors on vehicle skidding and stopping sightdistance [11ndash13] Our research group has systematicallystudied the influence of road geometry skid resistance sightdistance and three-dimensional vision on vehicle rolloverskidding and stopping sight distance [14ndash16]

-irdly the existing road design parameters based on themass point model of are designed -e radius parameters ofcurves are based on the minimum radius formula (1) ofcurves based on the classical mass point model in highwaydesign code -e model ignores the parameter differencesbetween vehicles such as vehicle type mass and center ofgravity position

R V

2

127 fR + e( 1113857 (1)

where fRmdashlateral friction demand of the mass point modelV(kmh)mdashvehicle speed R(m)mdashthe radius of a circularcurve and emdashsuperelevation

Based on the NHTSA data [1] 95 of 522000 auto-motive vehicle accidents are passenger cars or light trucks

As shown in Table 1 compared with passenger cars pickupvans large trucks and buses utility trucks have the highestrollover occurrence caused by single-vehicle crashes(647) Based on the analysis of vehicle accidents and theshortcomings of existing researches this paper takes theutility trucks as the research target A human-vehicle-roadsimulation model is established by CarSim -e orthogonalexperimental method is adopted -rough orthogonal ex-periment the effects of different road geometries speed andinteraction factors on vehicle lateral stability are studiedSignificance analysis of skidding rollover and lateral driftare carried out to characterize vehicle lateral stability

2 Methods

21 Road Model -e road geometric alignment mainlyincludes horizontal alignment longitudinal slope superel-evation road crown and their combination -e horizontalalignment is shown in Figure 1(a) which usually consists ofstraight lines transition curves and circular curves -eradius of the circular curve is R -e longitudinal slopeincludes straight lines and vertical curves as shown inFigures 1(b) and 1(c) It refers to the ratio of the heightdifference of two points of the same slope to its horizontaldistance on the vertical section of a route [17] Longitudinalslope is expressed by islope In order to offset part or even allof the centrifugal force generated while vehicles negotiate acurve the curve section is usually designed to a one-waycross slope with lateral high and medial low It is calledsuperelevation As shown in Figure 1(d) the superelevationslope is isuperelevation In order to facilitate the drainage of theroad surface the road is designed into an arch with highcenter and low sides which is called the road crown Asshown in Figure 1(e) the gradient is i0 -e slope is called asthe composite longitudinal slope with overlapping super-elevation and of longitudinal slope sections as shown inFigure 1(f ) -e formula of calculating the composite lon-gitudinal slope is [17]

icombination

i2superelevation + i

2slope

1113969

(2)

Because of the superelevation and longitudinal slope aresmall in road design code the angle of the roadrsquos cross slopeis approximately equal to the superelevation e asymp isuperelevationFor the same reason the angle of the longitudinal slope isapproximately equal to its longitudinal slope e asymp islope -e

Table 1 United States Traffic Accident Statistics [1]

Vehicle type Rollover occurrence caused bysingle-vehicle crashes ()

Rollover occurrence caused bymultiple-vehicle crashes () Death toll caused by rollover ()

Passenger car 417 71 22Light truck-pickup 571 216 433Light truck-utility 647 266 485Light truck-van 50 16 28Other 638 25Total 509 129 315



22 Vehicle Model








(4a)





(4b)

QDZH

HY YHHZ


Transition


Circular curve

(a)

islope

θ

(b)

R1 R2

i2i1

(c)

isupereleveation

e

(d)

i0 i0

(e)

i slope


ation

(f )






Sideslip angle

Front

Wheel rotation




Rear

(a)

BodyVehicleshape


Elastodynamics

Kinematics

Kinematics

Engine

Clutch

Steeringsystem

Brakingsystem

Power trainsystem

Transmission

Differential

Suspension

TireDrivingsystem

Steeringbraking

power trainsystems

Vehiclemodel

(b)








Stargi S +iVx T

m (5)


Si Siminus 1 +



1113969

(6)




(7)





11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leMj le I0j (8)



μl maxFyi

FZi

11138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113888 1113889 i 1 2 3 4 (9)









Inertial Y

Inertial X

Target path


Driver model X axis

Driver model Y axis

Origin (front axle)


ab

Mass center

ψ


S

I j0

Mj

Ij (t)




(a)


simulation


Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)




LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References












































22 Vehicle Model








(4a)





(4b)

QDZH

HY YHHZ


Transition


Circular curve

(a)

islope

θ

(b)

R1 R2

i2i1

(c)

isupereleveation

e

(d)

i0 i0

(e)

i slope


ation

(f )






Sideslip angle

Front

Wheel rotation




Rear

(a)

BodyVehicleshape


Elastodynamics

Kinematics

Kinematics

Engine

Clutch

Steeringsystem

Brakingsystem

Power trainsystem

Transmission

Differential

Suspension

TireDrivingsystem

Steeringbraking

power trainsystems

Vehiclemodel

(b)








Stargi S +iVx T

m (5)


Si Siminus 1 +



1113969

(6)




(7)





11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leMj le I0j (8)



μl maxFyi

FZi

11138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113888 1113889 i 1 2 3 4 (9)









Inertial Y

Inertial X

Target path


Driver model X axis

Driver model Y axis

Origin (front axle)


ab

Mass center

ψ


S

I j0

Mj

Ij (t)




(a)


simulation


Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)




LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References














































Sideslip angle

Front

Wheel rotation




Rear

(a)

BodyVehicleshape


Elastodynamics

Kinematics

Kinematics

Engine

Clutch

Steeringsystem

Brakingsystem

Power trainsystem

Transmission

Differential

Suspension

TireDrivingsystem

Steeringbraking

power trainsystems

Vehiclemodel

(b)








Stargi S +iVx T

m (5)


Si Siminus 1 +



1113969

(6)




(7)





11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leMj le I0j (8)



μl maxFyi

FZi

11138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113888 1113889 i 1 2 3 4 (9)









Inertial Y

Inertial X

Target path


Driver model X axis

Driver model Y axis

Origin (front axle)


ab

Mass center

ψ


S

I j0

Mj

Ij (t)




(a)


simulation


Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)




LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References














































Stargi S +iVx T

m (5)


Si Siminus 1 +



1113969

(6)




(7)





11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leMj le I0j (8)



μl maxFyi

FZi

11138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113888 1113889 i 1 2 3 4 (9)









Inertial Y

Inertial X

Target path


Driver model X axis

Driver model Y axis

Origin (front axle)


ab

Mass center

ψ


S

I j0

Mj

Ij (t)




(a)


simulation


Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)




LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References














































Inertial Y

Inertial X

Target path


Driver model X axis

Driver model Y axis

Origin (front axle)


ab

Mass center

ψ


S

I j0

Mj

Ij (t)




(a)


simulation


Driverexecution

linkDriver model

Driver feedback

Targetpath

(b)




LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References












































LTR 1113944

2i1 FZR( 1113857i minus FZL( 1113857i1113858 1113859

11139442i1 FZR( 1113857i + FZL( 1113857i1113858 1113859

(11)



0 (12)



2 0

(13)





2 0 (14)



mhg

(15)




11138681113868111386811138681113868

111386811138681113868111386811138681113874 1113875 0leM3 le a0y (16)






fp fs fRmax 0925fs


B

α

y

x

Nxo

Nyo

NxiNyi

hgmg cosα

F cosα

F sinα

mg sinα

ay





β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References













































β arctanVy

Vx

(17)




















1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References















































1 700 minus 4 4 02 802 1000 0 6 05 1003 1500 4 8 08 120



Column 1 2 3 4 5 6 7 8 9 10 11 12 13



A 3630 2 1815





A 7356 2 3678


F1minus 005(4 22) 282F1minus 001(4 22) 431






F1minus 005(4 22) 282F1minus 001(4 22) 431








A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References
















































A 213504 2 106752


F1minus 005(4 22) 282F1minus 001(4 22) 431


v = 100kmh R = 700m fp = 08

600 700 800 900 1000 1100 1200Station (m)

056058

06062064066068

Skid

ding

safe

ty m

argi

n

e = 004e = 006e = 008

(a)

v = 80kmh R = 700m e = 006

600 700 800 900 1000 1100 1200Station (m)

001020304050607

Skid

ding

safe

ty m

argi

n

fp = 02fp = 05fp = 08

(b)

16 18 20 22 24 26 28 30 32 34 36 36 40Time (s)

05

055

06

065

07

Safe

ty m

argi

n of

skid

ding


R = 700 e = 006 fp = 08

(c)

















600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References

























































600 700 800 900 1000 1100 1200085

09

095

1Sa

fety

mar

gin

of ro

llove

r v = 100kmh R = 700m fp = 08

Station (m)

e = 004e = 006e = 008

(a)

085

09

095

1

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 4008


Time (s)

(b)

600 700 800 900 1000 1100 1200Safe

ty m

argi

n of

rollo

ver v = 80kmh e = 006 fp = 08

Station (m)

R = 700mR = 1000mR = 1500m

03032034036038

04

(c)

Safe

ty m

argi

n of

rollo

ver R = 700m e = 006 fp = 08

16 18 20 22 24 26 28 30 32 34 36 38 40


Time (s)

02

025

03

035

(d)


600 700 800 900 1000 1100 1200Station (m)

191817161514

Late

ral d

riin

g sa

fety

mar

gin

e = 004

e = 008e = 006

v = 100kmh R = 700m fp = 08

(a)

600 700 800 900 1000 1100 1200Station (m)

0051

152

253

354

Late

ral d

riftin

g sa

fety

mar

gin v = 80kmh R = 700 e = 006

fp = 02fp = 05fp = 08

(b)

Figure 9 Continued





5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References














































5 Conclusions







16 18 20 22 24 26 28 30 32 34 36 38 4012141618

2

Time (s)

R = 700m e = 006 fp = 08


Late

ral d

riftin

g sa

fety

mar

gin

(c)





Data Availability






Acknowledgments




References













































Data Availability






Acknowledgments




References











































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