influence of aerodynamics on the fatal crash in le ... - ansys · influence of aerodynamics on the...

Influence of Aerodynamics on the Fatal Crash in Le Mans 1955 Peter Gullberg, Lennart Löfdahl and Zhiling Qiu Department of Applied Mechanics Chalmers University of Technology, 412 96 Göteborg, Sweden ABSTRACT

In the 1955 Le Mans race one of the worst crashes in motor racing history occurred and this accident changed the face of motor racing for decades to come. However, still fifty years after the fatal accident a number of questions remained unsolved. One open issue is the influence of aerodynamics on the scenario, since the Mercedes-Benz 300 SLR involved in the crash was equipped with an air-brake. In a recent work [1], it was shown that the air-brake in operation generates a significant drag increase, but also under certain conditions a down force on the vehicle. In the current work, CFD is utilized as a tool for the investigation of the aerodynamic aspects of the accident. More advanced parameters like the pitch angles are computed, and a simple model for the flight path is derived. It is found that the pitch angles, which were largely affected by the air brake, had a significant influence on the length of the flight path. 1. INTRODUCTION

The 1955 Le Mans 24 hour race changed the world of motor sport entirely, and many persons have the opinion that this accident moved the sport from innocence to moderny. After roughly two and a half hours of the race the largest accident in motor racing history occurred; two cars crashed into each other just outside the former pilots and motor dealers stands. The crash was a race incidence, however, also a consequence of the combination of fast and slow cars moving on the same track as well as traffic in and out of the pit lane. A fast Mercedes-Benz 300 SLR clipped the rear part of an Austin Healy 100 when the Austin Healy 100 did an evasive maneuver to avoid a collision with Jaguar who was going for a pit stop. The weighty Mercedes, driven by Pierre Bouillon (a Frenchmen who raced under the name “Pierre Levegh”) caught fire and was catapulted into the crowd of spectators, while the Austin Healy driven by the Englishman Lance Macklin could stay on the track. Unfortunately, the Mercedes-Benz went up in the air and at the end of its flights path it hit a concrete tunnel, and spitted up in parts which killed more than 80 people. A brief summary of the race and the accident scenario may be found on the web sites; http://www.youtube.com/watch?v=FXtb5eDUuQw http://www.youtube.com/watch?v=IuKP-rNyiOQ Through the years this fatal accident has been much discussed, analyzed thoroughly and numerous investigations have been accomplished in order to sort out the real accident scenario. In 2005, fifty years after the accident, a vast amount of papers and books were published to elucidate the catastrophe further and also put it into a modern perspective. To mention a few good publications; Hilton [2] and Bonte [3] summarize the course of events in an excellent way and point out several interesting political observations which not were so obvious to anyone in the mid-fifties. It should be remembered that the event took place only

EASC 20094th European Automotive Simulation Conference

Munich, Germany6-7 July 2009

Copyright ANSYS, Inc.

ten years after the end of the Second World War, and at that time England, Germany and France were nations under strong pressure to recover from the war damages. These political effects are most interesting, but will not be discussed further in this paper. More relevant issues for the present paper are the large number of technical questions and unclear statements which still remain, and a few of these constitute the kernel of this paper. The aerodynamic performance and documentations of the Le Mans cars used in the fifties is, with today’s measure, rather inadequate. From the archives it may, however, be concluded that the Mercedes-Benz 300 SLR used during the end of the “Silberpfeile-era”, was a most interesting car. It had an extremely powerful drive line, good road holding, but a weak point on the brakes since the cars were equipped with drum brakes which on long distance races like Le Mans had an obvious tendency to fade. In order to match the braking force of their main competitors, the Jaguar D-type that was utilizing disc brakes, Mercedes-Benz had developed an air-brake system which, on this particular model, was located just behind the driver. This device was complex but most efficient. Mike Hawthorn [4] wrote that;”…he (Juan Manuel Fangio) could leave his braking (on the Mercedes) just about as late as I could on the disc-braked Jaguar…”. Similar statements are found in Ludvigsen [5]. In addition, the Mercedes works drivers at that time, Juan Manuel Fangio and Stirling Moss, were joined in the statement that this version of Mercedes-Benz 300 SLR, “had a much better cornering with the air-brake in operation”, see Moss and Nye [6] and the aforementioned short movies for further illustrations.

Figure 1: Smoke visualizations in the Daimler-Benz tunnel, from Motor Klassik [7] All three Mercedes-Benz 300 SLR used in Le Mans 1955 were equipped with air-brake. One remaining question from the race event is whether Pierre Levegh was able to raise his air-brake before the crash. No one will ever know; so in this paper it is assumed that the air brake was in full operation just before and during the course of the accident. Another key issue is how the aerodynamics of the whole vehicle changes when the air-brake was in




operation; even though a heavy vehicle like the Mercedes-Benz 300 SLR creates a substantial momentum it is difficult to explain how it could fly such a long distance as it did before it hit the concrete barricade? Reliable aerodynamic data on old racing cars are, due to the experience of the authors, very difficult to find, however, in the late eighties, smoke visualizations and drag coefficients on the Mercedes 300 SLR were published in the German motor magazine, Motor Klassik [7], see figure 1. A drag coefficient of 0.437 with the air-brake down, and 1.090 with the brake in operation were measured. It was claimed that the data were from measurements in the Daimler-Benz Wind tunnel in Unterturkheim, 1978 and 1986, respectively. Relatively good agreement between these reported experimental data, and computations were found and discussed in a recent paper by Gullberg and Löfdahl [1]. Figure 2 shows the computed total pressure distribution of the Mercedes Benz 300 SLR on the ground and with the air-brake in operation from the Gullberg and Löfdahl’s work [1].

Figure 2: Total pressure, wing high vehicle on ground The objective of the present work is to continue to use CFD in order to elucidate some un-clear questions of the accident scenario in the 1955 Le Mans race. This paper relies on, and is an extension of the previously reported work by Gullberg and Löfdahl [1], however, in the present case focus is extended from drag and lift coefficients at zero pitch angle to the computation of the aerodynamic coefficients at different pitch angles and other quantities necessary for the determination of the flight path. To estimate this path, a number of assumptions on initial and boundary conditions have been made, and a highly simplified model for the flight path has been derived and used. The assumptions made are discussed in detail in the next sections, but here it could be remarked that the objective of the flight path calculations was not to determine an exact flight path in terms of height and length but rather to find the influence from aerodynamic forces on the flight length of the vehicle. In addition, a common goal of this paper and the previous work of Gullberg and Löfdahl [1] are to establish CFD as a tool for the reconstruction of un-explained race accidents. Like many other non-commercial projects this project also suffers of limited recourses in terms of computer as well as man time. Hence, it is important to keep this in mind when evaluating results and conclusions made, since better resolutions, more sophisticated flight models and additional adequate input data might change some statements. At this point it is natural as well to remark that no information or data used in this paper have been supplied by Daimler Benz. So all data utilized have been found in the open motor sport literature, and estimates of inertial moments etc. are based on the laws of classical mechanics.




2. METHODOLOGY

2.1 Generation of Surface Geometry

To get a representative geometry of the Mercedes-Benz 300 SLR, a 1:24 die-cast model of the 1955 Le Mans car of Fangio / Moss was purchased from the model maker, Pauls Model Art, who is well known for their high level of details and representative models; see Figures 3 and 4 for further details.

Figure 3: 1:24 model of the Fangio/Moss Mercedes-Benz 300 SLR

Figure 4: Side view of the model with detail features This model car was laser scanned with and without the air brake in operation, and the obtained surface data was prepared in ANSA version 12.1.3 to generate a dense and clean surface model suitable for CFD simulations. To make realistic computations a driver CAD model was prepared in ANSA, and located in the driver position inside the cockpit, Ludvigsen [5]. The corresponding surface model is shown in Figure 5.




2.2 Gen

The surversion extendeof the twhere trefinemrefinemthe surfmesh isrange fr

Finally, These realizabmoving driver wclearanConfigupitch anthat thedefined

neration of

rface geom3.1 was us

ed three cartunnel was he car was ent zone oent around face in ords seen in From 11 to 16

the mesh flow cases

ble k-epsilonground and

was brakingce of this

urations withngle of ± 30e air brake

in Figure 7

Figure

a CFD Mod

metry in Figsed to gener lengths ah2.5 car lenplaced in t

of the meshthe air-bra

der to repreFigure 6, an6 million ce

Fi

was imports were set-n turbulencd stationaryg the vehicvehicle, a h different p0° and ± 60

was in op7, and Table

e 5: Surface

del

ure 5 was erate a Hex-head of thengths for ththe free-streh just arouake region. esent the bnd the total ells.

igure 6: A ty

ted into Flu-up using

ce model. Ey wheels asle during thflat underbpitch angles0°, were simeration dur

e 1 shows th

e model for

then triang-dominated vehicle an

he cases weam, total wnd the vehAs usual, t

boundary lamesh size

ypical mesh

uent versioa standard

Each case ws boundary che acciden

body was as ranging fr

mulated. All ring the acche configura

CFD simula

gulated in A volume med seven caith floor an

width of the hicle and whe finest myer properl

es, dependin

h density us

n 6.3.26 wd Fluent inwas solvedconditions dt. Because

assumed anrom -20° to configuratio

cident. Theations studi

ations.

ANSA, and esh. The tur lengths bed 5 car lentunnel was

wake was umesh cells a

ly. A magnng on diffe

sed

where the cacompressib at a velocdue to the a of the reland used in 20° in 5° s

ons were ce pitch angled.

after this Hnnel was siehind it. Thngths for th 4 car lengt

used, and aare found clnified picturrent configu

ases were ble solver wcity of 200 kassumptionatively high

the compustep, and acomputed asle of the ve

Harpoon imulated

he height he cases ths. One a further losest to e of the urations,

studied. with the kph with that the

h ground utations. dditional ssuming ehicle is




Figure 7: Vehicle pitch angle definition

Condition Vehicle with wing high in vicinity of floor Vehicle with wing high in free-stream

Pitch angle 0°, ± 5°, ± 10°, ± 15°, ± 20°, ± 30°, ± 60°

Table 1: Configurations calculated in CFD

To normalize the forces, the wheelbase was used as reference length, see Figure 8, where also the centre, located midway between the wheel axles, used for moment calculations is shown. The frontal area of the vehicle with the airbrake in low position was used for normalization and the numerical values are found in Table 2.

Figure 8: Reference length used is wheelbase and reference position for moment is midway between the wheel axles.

Ref. area: 1.951 m2 Ref. velocity 55.55 m/s Ref. density 1.2 kg/m3 Ref. length 2.363 m

Table 2: Input data used for normalization

3. FLIGHT PATH CALCULATION AND DISCUSSION

3.1 CFD Simulation Results

Some of the aerodynamic coefficients used are shown in Figure 9, and a cubic interpolation is utilized. As expected, the aerodynamic drag force and moment rise significantly with the increase of the absolute value of pitch angle. Moreover, the results show that the aerodynamic lift increases when pitch angle reduces and vice versa, see Figure 7 and 9. At large negative pitch angles, the rear aerodynamic lift coefficient increases significantly due to




the blockage between the rear end of the vehicle and the ground as is shown in Figure 9. The same effect is found on the front for positive pitch angles. Of course, these effects are not present when the vehicle is off the ground.

Figure 9: Aerodynamic coefficient change with pitch angle

3.2 Calculation Model

In the model for the flight path, the vehicle is simplified as a rigid rod which represents the wheelbase length and center of gravity (CG). The coordinate system used and the forces acting on the vehicle are shown in Figure 10. Equation [1], [2] and [3] below describes the motion of the model in terms of linear accelerations in X and Z direction, and the angular acceleration around an axis through CG in Y direction.




Figure 10: Simplified model and free body diagram

1 ( )x Da F N fM

= + ⋅ [1]

1 ( )z Lf Lra F F N M gM

= + + − ⋅ [2]

1 {[ ( ) ( ) ( )] cos

[ ( )] sin }

Lf Lr rY

D r

F L k F L k N L k LI

F k N f L k L

θ θ

θ

= ⋅ − − ⋅ + − ⋅ + + ⋅ −

⋅ + ⋅ ⋅ + + ⋅

&& [3]

DF , LfF and LrF are the aerodynamic drag, front and rear aerodynamic lift force respectively. The definitions of these forces can be seen in Equation [4], [5] and [6]. The normal force N is created in case the vehicle rear end touches the ground during the flight. Since velocity in Z direction of vehicle rear end is fairly small during the flight, the normal force from ground is estimated into Equation [7].

212D DF C A Vρ= ⋅ ⋅ ⋅ ⋅ [4]

212Lf LfF C A Vρ= ⋅ ⋅ ⋅ ⋅ [5]

212Lr LrF C A Vρ= ⋅ ⋅ ⋅ ⋅ [6]

Lf LrN M g F F= ⋅ − − [7]




The values of the vehicle model properties used in the flight path calculation are shown in Table 3, where the total mass of the vehicle includes the net mass of the vehicle (880 kg) [9] and the assumed mass of driver (70 kg). The moment of inertia is estimated by assuming the vehicle to be a regular box shape with the dimensions shown in Figure 11 and calculated according to Equation [8]. However, given that the engine is located close to vehicle front end and the gear box is near the vehicle rear end [10], the moment of inertia used for calculating flight path shown in Figure 13 and 14 is estimated by using 120% of the value from Equation [8] according to authors’ experience.

Figure 11: Moment of inertia calculation model

2 2 2 21 1( ) ( 4 ) ( ) ( 4 )

12 2 12 2Yr fI M H f M H rL L

= ⋅ ⋅ ⋅ + ⋅ + ⋅ ⋅ ⋅ + ⋅ [8]

The vehicle weight distribution is set to be 58% on the front axle and 42% on the rear axle [11]. Hence, the value of k, see Figure 10, will be 0.189 m.

Total mass 950 kg Moment of inertia 480.24 kg ⋅m2 k (distance between CG and midpoint) 0.189 m f (friction coefficient) 0.5 g (gravity acceleration) 9.8 kg/s2

Table 3: Input data used for simplified vehicle model properties

A Matlab Simulink model based on Equation [1], [2] and [3] was set up for the calculation of vehicle motion in real time. The aerodynamic coefficients used in the model were taken from the cubic interpolation; see Figure 9, in steps of one degree of the pitch angle. The aerodynamic coefficients used for the flight path calculation were determined through a linear interpolation between the condition of in-vicinity-of-floor and in-free-stream, according to Equation [9] and [10] so the ground effect on vehicle aerodynamics disappears completely when the height of vehicle lowest point reaches one meter from the ground. The initial motion of the vehicle is defined in Figure 12, more details may be found in Bonté [3].

1 height of vehicle lowest point1

p −= (Length unit: m; Minimum: 0) [9]




. . Value-in-vicinity-of-floor (1 ) Value-in-free-streamAeroCoeff p p= ⋅ + − ⋅ [10]

Figure 12: Initial motion of the vehicle model

3.3 Calculation Results

In figure 13 and 14 one computed flight path with and without the influence of the aerodynamic forces are shown. The flight path is most sensitive to the initial conditions, pitch angle, take off angle and velocity. In the shown example the pitch and take off angle is the same (-5 degrees) as is shown in figure 12. As is evident from the example shown in figure 13 and 14, the aerodynamic forces have a significant influence on the length of the vehicle flight. Without any aerodynamic forces the vehicle model can only fly approximately 55 meters, but including aerodynamic effects this distance increases to at least 100 meters. With aerodynamic forces acting on the vehicle, it has a tendency to quickly increase its pitch angle due to the large rotating moment generated by the aerodynamic lift force. The aerodynamic lift force rises in proportion to the increasing pitch angle and due to this effect the flight path is prolonged. The pitch angle reaches its peak value around the midway of the flight path due to the increasing aerodynamic drag.

Figure 13: Flight path without aerodynamic forces

Figure 14: Flight path with aerodynamic forces (upper) and aerodynamic coefficient change (below)




In order to estimate sensitivity of the flight path calculations a brief sensitivity analysis was conducted. Table 4 shows three different take off angles, 2.50°, 3.75° and 5.00° together with three different values of the moment of inertia, 100 %, 120 % and 140 %. The flight path model seems to be quite insensitive to variation in the latter quantity, but the take off angle influences the flight length. However, the tendency shown in figure 13 and 14 remains i.e. that the flight length is longer when the aerodynamic forces are included in the model.

Initial pitch angle Moment of inertia 100 % 120 % 140 %

-2.50° with aero. eff. 35 m 35 m 36 m without aero. eff. 29 m



Table 4: Flight distance change with initial pitch angle and moment of inertia

4. CONCLUSION

In this work CFD has been used to establish some of the aerodynamic performance of a Mercedes-Benz 300 SLR with the specification used in the 24 hours Le Mans race of 1955. Raising the air-brake increases drag and pitch coefficient significantly and this certainly influenced the car handling as has been described in the Gullberg and Löfdahl work [1]. In addition, the current work confirms the general trend that the drag coefficient decreases as the vehicle moves away from the ground, a well-known effect for slender bodies see for instance Barnard [8]. The results also indicate that the pitch angle has significant influences on the aerodynamic drag, lift and especially the rotating moment. The aerodynamic drag and moment arise significantly with an increase of the absolute value of pitch angle. The flight path calculations show that the aerodynamic influences of the vehicle with air-brake in operation are significant. Although the flight path estimations were based on a highly simplified model a clear tendency of a much longer flight path was found when including aerodynamic effects. A full determination of the accident scenario of the 1955 Le Mans accident will, however, require more sophisticated and detailed CFD studies to be conducted. So the current work should be considered as an introductory part with the objective of forming a few cornerstones for future computations. ACKNOWLEDGE

The authors appreciate David Söderblom for supporting this work with Matlab model input data and driver CAD model for the CFD simulations.




REFERENCES

1. Gullburg, P. and Löfdahl, L., The Role of Aerodynamics in the 1955 Le Mans Crash, SAE 2008-01-2996

2. Hilton, C., (2004), Le Mans´55, Breedon Books Publishing, ISBN 1 85983 441 8. 3. Bonté, M., (2005), 11 June 1955, B.A. Editions, ISBN 2-915744-01-7. 4. Hawthorn, M. (1958) Challenge Me The Race, London 5. Ludvigsen, K. (1971) The Mercedes-Benz Racing Cars, Bond/Pankhurst Book, ISBN 0-

87880-0093-3. 6. Moss, S. & Nye,D., (1999) My cars, my career, Haynes publish., ISBN 1 85960 661 X. 7. Motor Klassik, “Das aktuelle Magazin fur alle Freunde klassicher Automobile” Issue #3

1987 8. Barnard, R.H., (2001), Road Vehicle Aerodynamic Design, Mechaero Publishing, ISBN

0-9540734-0-1 9. http://www.conceptcarz.com/vehicle/default.aspx?carID=2252&i=2#menu, available on April

2009 10. Engelen, G. and Riedner, M., (1999) Mercedes-Benz 300 SL, Vom rennsport Zur

Legende, ISBN 3-613-01268-5 11. http://www.classicandperformancecar.com/features/octane_features/222306/mercedes_300slr.ht

ml, available on May 2009 CONTACT

Peter Gullberg: [email protected] Lennart Löfdahl: [email protected] Zhiling Qiu: [email protected]




influence of aerodynamics on the fatal crash in le ... - ansys · influence of aerodynamics on the...

Documents