WINSEM2013 14 CP0776 TB05 Road Vehicle Safety in Windy Environments

Journal of Wind Engineering

and Industrial Aerodynamics 95 (2007) 14451462

presented is applied to a multitude of scenarios to explore the interrelation between the various basic

variables and how they affect the probability of accident given in terms of the so-called accident index.

In the developed countries worldwide, road accidents are causing more injuries andcasualties than any other man-made or natural hazard. The associated socio-economic

ARTICLE IN PRESS

www.elsevier.com/locate/jweia

0167-6105/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jweia.2007.02.020

Corresponding author. Tel.: +354 525 4128; fax: +354 525 4140.

E-mail address: [email protected] (J.Th. Snbjornsson).The analysis demonstrates that wind-related accidents are the consequence of a combination of several

basic variables as represented by the accident index. The study suggests that available methods of

probabilistic mechanics and theory of reliability can be of value for analysis of wind-related trafc

accidents and potential applications of the presented methodology are outlined.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Wind; Pressure; Aerodynamics; Road vehicles; Dynamics; Reliability; Accident risk; Safety index

1. IntroductionProbabilistic assessment of road vehicle safetyin windy environments

J.Th. Snbjornssona,, C.J. Bakerb, R. Sigbjornssona

aEngineering Research Institute, University of Iceland, Hjardarhaga 2-6, 107 Reykjavk, IcelandbSchool of Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Available online 28 March 2007

Abstract

Several wind- and weather-related accidents of road vehicles occur every year, especially at exposed

locations where topographical features magnify the wind effects. The most notable ones involve high-

sided vehicles. The objective of this paper is to investigate parameters inuencing wind-related

accidents of road vehicles. A general probabilistic model, based on reliability approach, is outlined and

applied for assessment of road vehicle stability in windy environments. The numerical model is dened

on a nite set of basic variables with prescribed probabilistic characteristics. The basic variables are

wind velocity and direction; frictional coefcient; camber of the road and vehicle speed. The accident

point is dened in the space of basic variables and the probability of accident is assessed. The theory

The state of knowledge on the engineering aspects of wind-related accident risk of road

ARTICLE IN PRESSnon-linear effects related to the frictional contact problem arising from the properties ofthe road surface and tyres. The quantication of the probability of accident is hencederived using appropriate stability criteria including side slip and overturning limit states.The theoretical outline is followed by a numerical study to quantify and visualise theeffects of the basic variables on the probability of accidents.

2. Modelling

The procedure adopted herein for the assessment of road vehicle accidents consists ofthe following four main steps: (1) denition of basic variables that are modelled asindependent stochastic variables; (2) numerical model of the vehicle is obtained includingfrictional contact between road surface and tyres; (3) denition of suitable performancecriteria that ensure stability and controllability of the vehicle; (4) assessment of stochasticwind-induced response followed by a quantication of the probability of accident.Formally, in the following the probability of safety, PS, is dened as: PS 1PA, where

PA is the probability of accident. It should be stressed that PS dened in this way shouldnot be used to represent probability of safe driving in the corresponding derivedenvironmental conditions. In that case, introduction of a reasonable safety margin shouldbe applied, corresponding to conservative estimates of near-accidents.

2.1. On the basic assumptions

The equations of motion of the coupled vehicle-road system in windy environmentshave been put forward by several investigators with a various degree of renement (Guoand Xu, 2006; Chen and Cai, 2004; Baker, 1991, 1994). These equations containvehicles is under constant development and has been established through many papers andreports dealing with accidents measures (Baker, 1994; ARC, 1997). In an accident riskanalysis (Blaeij et al., 2003; Lindberg, 2005), the key instruments used can be summarisedas follows: (1) severity or cost are intended to quantify the extent of harm; (2) probabilitygives the rate of occurrence of events that creates accidents and (3) risk expresses theimpact of accidents in terms of cost and rate of occurrence.In the present paper, we do not go into the cost issue and touch, therefore, only

indirectly upon the concept of risk, which has strong socio-economic relations through thecomplex issue of acceptability of risk. Our concern is mainly the quantication ofprobabilities as a measure of the rate of occurrence of accidents.The central objective of this paper is to present a comprehensive model, in general

probabilistic settings, of road vehicle safety in windy environments. Special emphasise isput on cross-wind conditions. This includes a presentation of the engineering mechanicsaspects dealing with the equations of motion accounting for the aerodynamic actions andconsequences are of growing concern for the responsible authorities (Blaeij et al., 2003).The natural wind does inuence the road accident risk in various ways. A recent study inIceland (Thordarson and Snbjornsson, 2004), at a windy location, indicates that windmay be a causative factor in up-to 20% of road accidents at that location. However,accident reports may not express this fact accurately in all cases.

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621446the mechanical properties of the environment and the vehicle, and some even model the

of the vehicle. In the following, we assume that the deformations of the body of the

coar

byrec

recorded simultaneously with a GPS receiver. An example of these recordings is

ARTICLE IN PRESSshown in Fig. 3. The layout of the road is given through measured latitude andlongitude, and the evaluated driving direction. The variables R, V and W shown in Fig. 1are measured relative to the driving direction. Using the vector relation displayed in Fig. 1,the wind velocity and wind direction can then be evaluated, as demonstrated in Fig. 3.Although some vehicle-induced turbulence is clearly added to the natural turbulence inthe evaluated wind velocity, the results are found to compare well with xed recordingstations in the vicinity, which validates the vector relation put forward in Fig. 1.Furthermore, they give a good view of how variable the wind can be along a relativelyspeshThe coordinate system adopted in this study is dened in Fig. 1. The origin of theordinate system is located at the centre of gravity of the vehicle. The equations of motione referred to the centre of gravity, which leads to decoupling of the inertia terms.The actuality of the vector system shown in Fig. 1 has been tested in full scaleattaching a sonic anemometer to the roof of a driving car (see Fig. 2). The anemometerorded the effective airow above the roof of the car (V, W), whereas the vehicleed (R), driving direction (f) and momentary geographical location of the car istopography of the road.velocity and direction as well as vehicle speed and direction are required to dene theaerodynamic forces in addition to the shape of the vehicle and the surroundingprovide the necessary stability for controllability and safe performance. These forces aretreated in the following as being non-linear which is related to loss of road contact ofthe wheels.Aerodynamic actions are due to the relative motion of the vehicle and the air. Windvehicle are negligible compared to that of the suspension system.Inertia forces are due to changes in vehicle speed and direction. These include the so-called centrifugal forces that arise when vehicle is driving through curves.Frictional forces are contact forces that act between the tyres and the road surface andpsycho-physiological characteristics and reactions of the driver (Baker, 1988, 1994;Maruyama and Yamazaki, 2006; Chen and Ulsoy, 2001).In this study, the emphasis is to develop a model that gives a balanced measure of

accuracy considering the various uncertainties in the mechanical, aerodynamic andenvironmental properties.The basic forces of mechanical origin accounted for in the modelling of road vehicles in

windy environment are as follows:

Gravity forces are due to the attraction induced by the gravitational eld of theEarth. Hence, the gravity forces are static and induce the reference state for whichthe dynamic response is measured from. In dening the gravity force components,it is important to account for the slope and camber of the road. They may bothcontribute directly to reduction of stability of vehicle performance through the tyrereaction forces.

Elastic and damping forces are primarily related to the suspension system and the tyres

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1447ort stretch of road.

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Fig. 1. Denitions (a) coordinate system applied in this study, with origin located in centre of gravity and sign

conventions for aerodynamic actions on the vehicle. (b) Addition of the velocity vectors, where R represents the

relative velocity of air caused by the vehicle speed, U is the mean wind velocity, f is wind direction, u and v are thehorizontal turbulence components (the vertical w-component is not shown), V is the effective wind velocity and Wis the angle of incidence. It is assumed for simplication that the mean wind is acting in the horizontal xz-plan.

Fig. 2. A xed weather station and a car equipped with a sonic anemometer attached to the roof and a GPS

receiver for positioning during recordings in route.

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621448

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J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 14492.2. Aerodynamic actions

The aerodynamic forces and moments are dened as follows:

Fx 12rCFxAV 2 drag force;Fy 12rCFyAV 2 lift force;Fz 12rCFzAV 2 side force;Mx 12rCMxAV 2h rolling moment;My 12rCMyAV 2h yawing moment;Mz 12rCMzAV 2h pitching moment; 1

where r is the density of air, A is the reference area, V is the reference speed taken as therelative velocity of the air (see Fig. 1), h is the reference arm, CFx ; CFy ; CFz are force

Fig. 3. An example of a 9min long segment from measurements with a sonic anemometer attached to the roof of

a driving car, which is equipped with a GPS receiver.

ARTICLE IN PRESScoefcients and CMx ; CMy ; CMz are moment coefcients. The force and momentcoefcients are dependent on the selection of the reference parameters. In thefollowing, the reference area, A, is taken as the frontal area of the vehicle and thereference height, h, is the height of the centre of gravity above the surface of the road. Thatimplies that the point of action used for the aerodynamic forces and moments is the centreof gravity.In the general case, when the reference wind speed is selected as the mean wind

velocity blowing in the mean wind direction, the force and moment coefcients can berepresented as a multi-dimensional stochastic process. This process has a complexcorrelation structure, which presently is not well known. Recent full-scale experimentson the cross-wind forces on trains (Baker et al., 2004) suggest high degree ofcorrelation between rolling moment and side force, and pitching moment and lift forcewith values of the correlation coefcient around 0.95. The correlation between sideand lift force is poorer (in the range 0.800.85) because the uctuations are to someextent caused by different ow mechanisms. However, the above mentioned full-scale workon trains suggested that a second order quasi-steady assumption can work quite well torelate uctuating wind velocities to uctuating forces. Therefore, due to lack ofinformation on the multi-dimensional aerodynamic action process, we adopt a simpliedmodel where the force and moment coefcients are represented as deterministic functionsdepending only on the mean wind direction. The stochastic nature of the aerodynamicaction process is then accounted for by treating the wind velocity as a locally stationaryGaussian process.The aerodynamic coefcients adopted for the present study are based on formulas from

(Baker, 1987, 1994), but modied according to results from wind tunnel experimentscarried out by Coleman (Coleman and Baker, 1994). The coefcients are expressed asfollows:

CFx 0:51 sin3W,CFy 0:751:5 0:9 cos4W 0:6 cos2W,CFz 5:5 sinW,CMx 2:2 sinW,CMy 7:2 sin2W,CMz 1:01 cos4W, 2

where W is the angle of incidence dened in Fig. 1. The coefcients are referred tothe centre of gravity and the coordinate system dened in Fig. 1. These coefcients areplotted in Fig. 4 along with wind tunnel data. It is seen that the agreement is fair. Theabove coefcients are an enhancement of the earlier relationships put forward by Baker(1987, 1994).It should be noted that the aerodynamic characteristics of vehicles under crosswinds

do not only depend on the shapes of the vehicles but also on the aerodynamicsof the infrastructure, such as bridges and embankments (see for instance Suzukiet al., 2003). In addition, any aerodynamic data is to some degree dependentupon the technique and methodology used to acquire that same data (Baker andHumphreys, 1996). A single unied set of aerodynamic coefcients may, therefore, be an

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621450unrealistic goal.

ARTICLE IN PRESS2.3

tyrwhtem

Stfrimofo

en

Fig

tunJ.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1451. Contact between tyres and road surface

The operational safety and controllability is governed by stable static contact betweenes and road surface (Bradley et al., 2004). This is assumed acquired by frictional forces,ich unfortunately depend on several environmental factors, such as precipitation andperature (see for instance Xu and Guo, 2003).

Friction is a contact property that is divided into static friction and kinetic friction.atic friction refers to the case when there is no slip between the contact surfaces. Kineticction, on the other hand, describes the case when the two surfaces, i.e. tyre and road, areving with respect to each other. The friction is commonly modelled applying thellowing simplifying assumptions (Gillespie, 1992):

The magnitude of the frictional force is proportional to the normal force acting on thecontact surface.The magnitude of the frictional force is independent of the size of the area of contact.The magnitude of the frictional force is independent of the direction of action.The magnitude of the frictional force is independent of the velocity of motion.

These assumptions do not fully represent the real situation, as is the case with mostgineering models, however, they lead to a simple and practical approximation given by

. 4. Aerodynamic coefcients for high-sided lorry. The solid curves refer to Eq. (2) and the circles are wind

nel data from Coleman and Baker (1994).

the following expression:

Fi mNi, (3)where Fi is the frictional force transmitted by wheel no. i, Ni is the vertical force insuspension no. i and m is the frictional coefcient. The frictional coefcient can either beinterpreted as the static frictional coefcient, mS, or the kinetic frictional coefcient, mK. Ingeneral, we can assume that mS4mK. The difference between the two depends on the roadsurface and types of tyres. In the case of wet or icy surface, the difference can be great, butis normally small for dry road surfaces.

ARTICLE IN PRESSJ.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621452The frictional forces have to resist lateral and longitudinal wind forces arising from theaerodynamic action, traction forces, acceleration forces and deceleration (braking) forces.Furthermore, a rolling wheel requires a certain amount of frictional resistance to preventthe surface of contact from slipping. Hence, the amount of traction, which can be obtainedfor a given tyre on a particular road surface, is dened by the static frictional coefcient. Ifthe wheel is locked and slides, the friction is controlled by the kinetic frictional coefcient,which is smaller than the static one (Gustafsson, 1997). In the following, we assume thatthe frictional coefcient is the static coefcient if not otherwise stated.The rolling resistance is assumed given by the following equation:

FR mgf R, (4)where fR is the rolling resistance coefcient (Gillespie, 1992), that is generally dependent onthe driving velocity, m is the spring mass of the vehicle and g is acceleration of gravity.The limit state of safe performance is checked using the friction circle, radius of which is

dened by Eq. (3), by requiring that the traction eld is inside this circle (Gillespie, 1992).

2.4. Basic variables

The quantities governing the motion of the vehicle are in most cases uncertain, thatmeans they cannot be determined with nite certainty. Depending on the degree ofuncertainty, these quantities are in this study either modelled as stochastic variables ordeterministic parameters. The stochastic variables selected in this study are the windvelocity and wind direction (measured relative to the direction of the vehicle), vehiclespeed, frictional coefcient and camber of the road (see Table 1). In all cases, the basicvariables are taken as being normally distributed, except in the case of the frictioncoefcient which is assumed, on physical grounds, to be a positive quantity. Hence, forsimplication it is taken as being truncated normally distributed. Quantities describing the

Table 1

The basic variables used in this study

Name of quantity Basic variables Notation Distribution

Wind velocity X1 U Normal

Wind direction X2 W NormalCoefcient of friction X3 m Truncated normalDriving speed X4 R Normal

Camber of road X5 e Normal

ARTICLE IN PRESSThe side slip of a given wheel is checked using the equilibrium equation of acting andresisting horizontal forces through the following criterion:

f Fy2 Fx FR2

q mNi, (6)

where Fy is the total side force, Fx is the frontal drag force, FR is the rolling resistance(friction) from Eq. (4), m is the frictional coefcient and Ni is the axial force acting on wheelno. i. If f40 then there is no slip, if fo0 the wheel will slip and critical state is emergingwhich potentially may result in an accident, if f 0 the state is indifferent and the stabilitylatent (neutral). This model is used to quantify the rst three of the above-mentionedcriteria.The state of potential rollover arises when one wheel looses road contact (Baker, 1986).

The potential point of rollover can be reached if the friction is high enough to prevent slip.This happens when the moment created by the wind-induced forces exceeds the resistingmoment due to gravity. Then the relative velocity is given as follows:

V rollover

2amg

rAhCMx hCFz aCFy

s, (7a)

where m is the mass of the vehicle, g is acceleration of gravity, a is half of the lateraldistance between the centres of the wheels, r is the density of air, A is the frontal area and hisside slip of rear wheels androllover.

side slip of front wheels,

side slip of all four wheels,mechanical properties of the vehicle are taken as deterministic parameters. Other variablesused in modelling the behaviour of the vehicle are treated as derivatives. Theirdistributions deviate from normality when the system behaviour becomes non-linearwhich may be the case when the vehicle approaches instability.

2.5. On the limit states of safe performance

The limit states of safe performance can be dened in terms of loss of controllability andstability. Typically, loss of controllability will result in difculty to follow a specic lane onthe road, while loss of stability implies overturning or loss of traction resulting in side slip.The solution of the equations of motion along with appropriate stability criteria denes

the limit states of safe performance in terms of a response hyper-surface in the space ofbasic variables. This can be written formally as

f X f X 1;X 2;X 3; . . .Xn 0, (5)where X {X1, X2,y} refers to the above dened stochastic basic variables. In fact, thishyper-surface of safe performance divides the space of basic variables in two sub-spaces,that is a safe domain, DS fx : f x40g, and an unsafe or accident domain,DA fx : f xo0g.The present study utilizes the following stability criteria:

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1453the height of the centre of gravity. The force coefcients have to be evaluated using the

PA Fb, (10)

ARTICLE IN PRESSwhere F denotes the standardised Gaussian distribution function.In general, the limit state of safe performance cannot be expressed in terms of a single

function. Hence, the hyper-surface of safe performance is modelled as a set of functionswhere each function corresponds to a particular stability criterion as described above.From a computational view, this leads to one safety index for each limit state function. Thelowest of those safety indices corresponds to the point on the combined response hyper-surface with the highest probability density, i.e. the most probable accident point in theangle of incidence (see Figs. 1 and 3). The critical wind velocity can be obtained as

U rollover R cosW V 2rollover R2 sin2W

q, (7b)

where W denotes the wind direction relative to the driving direction. It should be noted thatthe above equation would only produce real values for the wind speed provided that wehave V2rolloverXR

2 sin2W.

2.6. Quantification of accidents

The probability of accident can now be assessed as follows (Sigbjornsson andSnbjornsson, 1998). The stochastic basic variables dened above, X {X1, X2, y},are transformed into (independent) normalised Gaussian variables, U {U1, U2, y},implying that Ui can be treated as normally distributed with zero mean and unit standarddeviations. The response hyper-surface, Eq. (5), can be expressed formally in thenormalised variable space as

f gU f gU1; U2; U3; . . .Un 0. (8)

The point on the response surface with the highest probability density is dened as theaccident point, uA, that is the most probable point on the surface. In the normalised space,this is the point on the response surface that is closest to zero. The Euclidean norm of thebasic variables at the accident point, measured in the normalised space, is a measure of theprobability of an accident. This leads to the following denition of the accident index, b,(Sigbjornsson and Snbjornsson, 1998)

b sign nA uAuA uA

p,

uA 2 fu : f gu 0g,nA nuA 2 fn : n rf gug, 9

where n denotes the normal to the response hyper-surface and o denotes scalarmultiplication.It should be stressed that the accident index can be both positive and negative. Positive

b-values correspond to 0oPAo0.5, b 0 gives PA 0.5 and negative b-values yield0.5oPAo1, where PA is the probability of accident which can be approximated as follows:

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621454space of basic variables.

Fig. 6 demonstrates the interrelation between wind velocity, wind direction and the

ARTICLE IN PRESSaccident index. It is seen that the probability of accident increases with increased windvelocity, and for wind velocity above 30m/s, PA exceeds 0.5 for a wide range of winddirections. Otherwise, b is at minimum for wind direction around 901, although it is not aclear cut picture because of the aerodynamic coefcients and the fact that the driving speedaffects the effective angle of incidence to a varying degree depending on the wind velocity.For certain conditions, it is therefore conceivable that b is reduced with increased drivingspeed relative to the wind velocity (Baker, 1987). This can, for example, be seen in Fig. 7,which displays the relationship formed by driving speed and wind direction as parametersin the accident index. As in Fig. 5, it is seen that b safety decreases with increased drivingspeed for wind directions below 901, but increases with increased driving speed for winddirections above 901. This means that although decreased driving speed generally reducesthe probability of accident when the wind is blowing towards the front of vehicle. Theopposite is true in cases where the wind is blowing at the back of the car, then increasingthe vehicle speed increases safety. Furthermore, it is seen that b is primarily inuenced bythe driving speed for wind directions below 901.Fig. 8 illustrates the association between driving speed and wind velocity in generating

the accident index. In principle, increased wind velocity decreases b, although for wind3. Numerical study

3.1. Overturning

Rollover velocity can be dened as the wind velocity which results in aerodynamic forcesthat give a rollover moment greater than the restoring moment provided by gravity forces(see Eq. (7a)). Evaluating Eq. (7a) in a deterministic fashion gives the relation betweendriving velocity, wind velocity and wind direction that is shown in Fig. 5. As can be seen byinspecting Fig. 5, the critical rollover wind velocity is reduced by increased driving velocityfor wind directions below 901 to a minimum of about 20m/s for wind directions of about601. However, for wind directions above 901, the critical rollover wind velocity increaseswith increased driving velocity. Clearly, overturning can only be expected for winddirections between 301 and 1201. This is as expected, since the effective velocity vector is acombination of the wind vector and the vehicle driving speed vector as demonstrated inFig. 1. At the same time, Fig. 5 is both a demonstration of predicted behaviour and a testof the underlying mechanics of the model applied.

3.2. Cases studied

The combinations of parameters applied for the basic variables in this study are given inTable 2. The study further assumes that the basic mechanical quantities of the road vehicleused are the same as for the lorry found in Coleman and Baker (1994).Figs. 610 show the interrelation between the various basic variables and how they affect

the accident risk, herein measured via the so-called accident index, b, dened in Eq. (9).Each Figure shows a three-dimensional view of the accident index as a function of two pre-chosen variables with the other three, xed around certain mean value with a prescribedstandard deviation.

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1455velocities around 25m/s b is almost constant; but for wind velocities around and above

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J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462145630m/s, the probability of accident increases rapidly especially for the higher drivingspeeds.Fig. 9 shows the accident index as a function of driving speed and frictional coefcient.

It clearly demonstrates the dramatic inuence of frictional resistance on the driving safety.For snowy and icy condition, i.e. for friction coefcient below 0.4, the probability of

Fig. 5. Two plots demonstrating the relation between rollover wind velocity, wind direction and driving velocity

as evaluated deterministically using Eq. (7a).

ARTICLE IN PRESSTable 2

Characteristic parameters for the stochastic variables

Name of quantity Notation Range of mean values Standard deviation

Wind velocity (m/s) U 0:7.5:112.5 2

Wind direction (1) W 8:4:40 0.15UCoefcient of friction m 15:15:165 7.5Driving speed (km/h) R 0.1:0.1:0.7 0.05

Camber of road e 0.045:0.01:0.045 0.005

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1457accident is about 0.5 or more for a wide range of driving velocities at the wind velocity of25m/s and wind direction of 601.Fig. 10 depicts the interaction of driving speed and road camber on the accident index.

On traditional straight two lane highways, the road is highest in the middle and then slopestowards the embankments on each side. As can bee seen in Fig. 10, the road camber canhave signicant effect on driving safety. In fact, the conditions may be quite differentdepending on which lane the vehicle is driving, even when driving in the same direction.For instance, decreasing the vehicle speed down to 60 km/h for camber of 0.035, results ina b value of the same order as for 90 km/h on ground with zero camber. The effect of

Fig. 6. The accident index as a function of wind velocity and wind direction. The mean values used for the other

basic variables are as follows: V 90 km/h, W 601, m 0.5 and e 0.035.

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Fig. 7. The accident index as a function of driving speed and wind direction. The mean values used for the other

basic variables are as follows: U 25m/s, e 0.035 and m 0.5.

Fig. 8. The accident index as a function of driving speed and wind velocity. The mean values used for the other

basic variables are as follows: W 601, e 0.035 and m 0.5.

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621458

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Fig. 9. The accident index as a function of driving speed and friction coefcient. The mean values used for the

other basic variables are as follows: U 25m/s, W 601 and e 0.035.

Fig. 10. The accident index as a function of driving speed and road camber. The mean values used for the other

basic variables are as follows: U 25m/s, W 601 and m 0.5.

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 14451462 1459

interrelation between the various basic variables and how they affect the probability of

ARTICLE IN PRESSaccident or the so-called accident index. The analysis demonstrates how wind-relatedtrafc accidents are the consequence of a combination of several basic variables asrepresented by the accident point.The probability of accident increases with increased wind velocity, although for wind

velocities around 25m/s the accident index, b, is almost constant but for wind velocitiesaround 30m/s PA exceeds 0.5 for a wide range of wind directions, especially for higherdriving speeds. The accident index is generally at minimum for wind direction around 901,although it is not a clear-cut picture because of the aerodynamic coefcients and the factthat the driving speed affects the effective angle of incidence to a varying degree, dependingon the wind velocity.Although decreased driving speed generally reduces the probability of accident when the

wind is blowing towards the front of vehicle, the opposite is true when the wind is blowingat the back of the car when increasing the vehicle speed increases safety. However, b isprimarily inuenced by the driving speed for wind directions below 901.The frictional resistance has dramatic inuence on the driving safety, and may warrant a

more detailed modelling. Unfortunately, although considerable information is available onthe characteristics of friction, information on the mechanics of frictional resistance of tyrescamber on the measurements of aerodynamic coefcients as indicated in Coleman andBaker (1994) is not addressed herein.It can be informative to study the behaviour of the basic variables to see how they adjust

as the limit state is reached. Such observation reveals, which variables are contributingmost to the accident index. Studying the overturning accident limit state (rollover criteria),the friction and camber are found to be relatively inactive parameters. The activeparameters, considering the limit state values, are primarily wind velocity and drivingspeed. For the slip accident limit state (slip on at least two wheels), different behaviour isseen as the friction and camber values are adjusted throughout the convergence process,according to the freedom given by their assigned standard deviation. Their values at theaccident limit state seem to depend primarily on the wind velocity. The friction values atlow wind velocities go down, whereas for the higher wind velocities no adjustment isneeded and the friction approaches its predened mean value. The camber is similarlyadjusted to increase probability of accident at low wind velocities, whereas the predenedmean value is approached for the higher wind velocities. The limit state wind velocity anddriving velocity largely follow their mean values.

4. Discussion and conclusions

An outline of a general probabilistic model is presented for assessment of road vehiclestability in windy environments. The model presented herein is an extension andimprovement of model developed earlier by Sigbjornsson and Snbjornsson (1998). Thenumerical model is dened on a nite set of basic variables with prescribed probabilisticcharacteristics. The basic variables are wind velocity and direction; frictional coefcient;camber of the road and vehicle speed. The limits of safe performance are discussed and theaccident point is dened in the space of basic variables and the probability of accident isassessed. The theory presented is applied to a multitude of scenarios to explore the

J.Th. Snbjornsson et al. / J. Wind Eng. Ind. Aerodyn. 95 (2007) 144514621460to side forces under driving conditions is limited.

information and further modelling renement. The aerodynamic properties of road

aerodynamic and environmental properties applying a simplied balanced model.

ARTICLE IN PRESSThe study suggests that available methods of probabilistic mechanics and theories ofreliability can be of value for analysis of wind-related trafc accidents. Using methods ofthis type to set up computer simulations to analyse scenarios can be helpful in post-evaluation of accidents and to improve the design of roads and highways. For instance, itis possible to analyse the accident index at locations where wind data is available along theroad systems.The Road Authority in Iceland has installed data acquisition systems along the

highways at several locations to monitor weather conditions and trafc. The data is madeavailable as an online information system for drivers on the Internet and on computer-controlled information boards along the roads. Based on the wind data gathered by thesestations, time series of accident index can be evaluated at each monitoring location. Thiscan then be used as input in statistical analysis of the probability of wind-related accidentsalong the roads in question and correlated with accident reports. This type of informationshould at least give a more complete view on the wind-related hazard for road vehiclesthan is currently available and could even be used to point out potential accident spots aswell as to devise and evaluate preventive measures to improve trafc safety in windyenvironment.

Acknowledgments

This work was in part supported by a research grant from RANNUM (The IcelandicResearch Board for Trafc Safety).

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Probabilistic assessment of road vehicle safety in windy environmentsIntroductionModellingOn the basic assumptionsAerodynamic actionsContact between tyres and road surfaceBasic variablesOn the limit states of safe performanceQuantification of accidents

Numerical studyOverturningCases studied

Discussion and conclusionsAcknowledgmentsReferences