Aerodynamic Model of a Hill Climb Racing Carmb4/xin_zhang/55.pdfThe basemodel line for aerodynamic development was a Pilbeam MP88 raced in the British Hill Climb Championship. This

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Aerodynamic Model of a Hill Climb Racing Car

Xin Zhang$, Paul Blyth, Paul Dunning, Mark Gardiner and Christian Wood School of Engineering Sciences

University of Southampton, Southampton, SO17 1BJ, UK

$ - Author for correspondence. Email: [email protected]

Abstract

The aerodynamics of a generic hill climb car was studied through wind tunnel model tests and

computational fluid dynamic (CFD) simulations. A racing car is a highly interactive aerodynamic system

with vortex flows dominating the flow field. Components such as the front wing, the sidepod/diffuser, and

the rear wing play important roles in deciding the performance of the car. Through a systematic process

of component design, a high level of overall downforce with a balance (the percentage of the total

downforce acting through the front wheels) around 40% was achieved. The pitch sensitivity of the car

was also constrained to within 1.5% variation across the range of front and rear ride heights tested. The

use of CFD during the study further enhanced the understanding of the flow characteristics. The

combination of wind tunnel testing and CFD provided an effective tool to study the aerodynamics of a hill

climb racing car.

Preface by Willem Toet

The original idea had been for University of Southampton to try and develop the model of a Formula 1 (F1) car.

However, as this would require far too many man hours of testing and the F1 rules are strict and difficult to

interpret, it was obvious that the exercise would have been very frustrating for students. The rules for the

British Hill Climb Championship are simpler and more liberal and far less research has been carried out. This

gave more scope for improvement with the limited testing that could be carried out in a single year of a

University course and enabled the students to see a result at the end of their project. Students were also able to

benefit from the parallel use of the physical testing of a car in the wind tunnel and theoretical modelling using

computational fluid dynamics.

I. Introduction

The aim of the work was to develop the aerodynamic performance of a generic, open wheel, hill climb car

through both wind tunnel tests and CFD using practical and realistic modifications. Various parts were designed,

produced and tested that took advantage of the aerodynamic regulations used by the hill climb formula.

The baseline model for aerodynamic development was a Pilbeam MP88 raced in the British Hill Climb

Championship. This series is governed and run by the British Motor Sports Association (MSA) and as such it is

subject to the MSA and Federation Internationale De L’Automobile (FIA) regulations [1, 2]. Hill climb races

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take place over a weekend and the championship is stretched out over 17 events, which is attended by a wide

variety of cars ranging from modified road cars to the full unrestricted racing cars of ‘Class L’. A typical event

consists of a staggered time trial, where each car races from the bottom of the hill to the top of the hill in the

shortest time possible. The courses are short, with times of around one minute and top speeds reaching 150mph

(240kph). A typical course contains many twisting corners connected by relatively short straights, limiting the

car’s potential to reach top speeds. This means that lap times are largely governed by how quickly a driver can

negotiate the corners. This can be achieved by a) preventing lateral tyre slip caused by the car’s inertia in the

corners, and b) improving the car’s acceleration out of a corner, i.e. emphasis is on the desire for more ‘grip’,

which can be achieved either mechanically or aerodynamically. The provision of aerodynamic grip (via

downforce) in an effort to provide a performance increase was the focus of this study.

As the car is designed to compete in the British Hill Climb Championship; any new designs must comply with

the regulations. The objectives for the development of the car were as follows:

- To fully exploit the comparatively liberal aerodynamic regulations imposed on the car

- To increase the downforce available to the car

- To reduce the pitch sensitivity of the car

- To increase the quantity and quality of the airflow to the rear of the car

II. Overview of aerodynamic requirements

As with all modern racing cars, aerodynamics is an intrinsic part of a hill climb car’s development. However,

without the budgets available to the likes of top Formula 1 teams the approach is very different, albeit with the

same ultimate goal - a faster car. Different design considerations come into play, for instance, whereas in other

formulae an ‘optimal’ solution is close to the edge of the performance envelope a more conservative approach is

beneficial to manufacturers of hill climb cars. Without resources to fully investigate the flow physics of a car,

any component that can have a detrimental effect is avoided and so the aerodynamics package is relatively

simple. That is not to say that hill climb cars are poorly equipped aerodynamically. The FIA and the MSA rules

[1, 2] allow for many aerodynamic techniques that have been outlawed in other formulae.

The three main areas that generate the majority of the downforce on a racing car are the front wing, rear wing

and diffuser [3, 4]. These parts are only limited to dimensional constraints and may take any form the designer

wishes. The front wing may be placed as little as 40mm away from the ground allowing it to take full advantage

of ground effect. The diffuser curvature is unlimited and could take a full airfoil shape if the designer so wished.

Also the number of rear wing elements is unlimited (Figure 1). The use of multiple elements allows for higher

level of rear downforce and can also be used to drive the diffuser. Any one of these components can produce

significant gains. The relatively liberal rules and regulations, in the hill climb category, mean that there is more

scope for significant improvements in the downforce levels than those achieved in other formulae.

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The style of hill climb races and the courses over which they take place dictate aerodynamic design of the cars.

The characteristic track layouts dictate that the wing configurations are almost always at maximum downforce,

save for a few balancing tweaks. In addition as the top speeds are rarely maintained for more than a few seconds

and the engines are unlimited, penalties for high drag configurations are small. For this reason aerodynamic

efficiency is not critical, and is normally lower for hill climb cars. Another consequence is that the complete

design of a car can be optimized for maximum downforce without fear of adverse consequences in lower

downforce configurations.

III. Description of the aerodynamic model

The wind tunnel model used for this study is based on a Pilbeam MP88 racing car at 35 percentage scale

(Figures 2 and 3). In its baseline configuration it has a wheel base of 0.896m and a frontal area of 0.15m2.

Regulations state that over a race event the mass of the car must not be lower than 560kg. The total downforce

for the baseline configuration is 5800N with 40% front balance at 30m/s. After development the wheel base

remains the same and there is no change in frontal area. The tunnel blockage ratio is approximately 2%. The

model is constructed around an aluminium spine in which the internal balance is housed and is suspended in the

tunnel from an overhead balance. The model is a ‘wheels off’ design; the wheels are separately suspended in the

tunnel and their drag is measured independently. This reduces the complexity of the model but does not allow

testing under extreme cornering conditions. There are three main aerodynamic devices, the front and rear wings

and the diffuser. Of these the front wing and sidepod/diffuser endured the most intensive development. The

baseline and the final model configurations are shown in Figures 2 and 3.

Based on the aforementioned development directions and the allowances within hill climbs the evolution of the

external aerodynamics took a number of avenues that are highlighted below:

Higher nose to maximize flow to the underbody, as well as to allow a range of other tests to be

conducted such as a front wing height survey, vortex generation via guide vanes, and the effect of a

splitter plate.

Lower engine cover to increase flow to the rear wing assembly.

One piece monoflap for the front wing, replacing the multi-element wing configuration.

Roll hoop wings mounted to the engine cover, which can either be stand alone downforce devices or

used as a lifting section to induce a greater downwash to the rear wing assembly.

Airfoil shaped sidepods capable of a range of positions and angle adjustments.

IV. Development tools: wind tunnel and computational fluid dynamics

Wind tunnel. The University’s R J Mitchell wind tunnel (http://www.windtunnel.soton.ac.uk) was used for the

study. The tunnel is a closed loop design with a 3.5m × 2.6m working section capable of wind speeds up to

50m/s and a road speed of 45m/s. The working section is equipped with a 6-component overhead balance. As

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well as being highly suited for marine and aerospace applications, the wind tunnel is fully adept at catering for

automotive simulations with its moving ground facility. The tests on the hill climb model were conducted at

wind and road speeds of 30m/s. The working section comprises a number of flow control mechanisms intrinsic

to realistic testing of racing cars, such as a fore and aft suction box and a raised suction plenum that maintains

the belt’s contact with the reference plane. Such boundary layer control mechanisms remove ‘tired’ air and re-

energize the near wall profile with a resultant 99.8% of freestream velocity at only 2mm above the belt;

ultimately true ground effect can be simulated. Due to the work done by the fan on the returning volume of air,

closed return tunnels can create inaccuracies when the air temperature invariably increases. The R J Mitchell

wind tunnel incorporates a cooling system that maintains a constant air temperature whilst still conserving the

freestream turbulence level of less than 0.2%.

The tests conducted include overhead balance and surface oil flow visualization. The Reynolds number, based

on the freestream flow speed and model wheel base of 0.895m, was 2.2×106.

CFD. Although the wind tunnel tests played the major role in developing and studying the aerodynamics of the

hill climb car, CFD also played an active role in the study - primarily providing a 1st estimate in the design

process and a secondary interpretation when analyzing the wind tunnel results. The CFD package FLUENT was

used in the study to solve steady Reynolds-averaged Navier-Stokes equations. The Spalart-Allmaras turbulence

model, a one equation model that solves for eddy viscosity was used mostly for its inherent robustness. Grid

dependency studies were also conducted to ensure that the results were fully independent of the grid number (up

to 3.5 million cells) and domain size. For some cases, a shear stress transport k-ω turbulence model was also

employed. The majority of the CFD analysis was conducted on the front wing and the sidepod.

V. Results and discussion

In this section, some selected aerodynamic results are discussed. In presenting the results, all numbers are scaled

to the full scale values, unless otherwise stated in the text.

Aerodynamic development trend. The aerodynamic development of a hill climb car should focus on the areas

that are most likely to yield the greatest reduction in lap time for minimal effort. Any alteration permissible is

dependent on the locations of major car components, driver, legality boxes and the mechanical setup. The three

important considerations are the total downforce (the body force, taken as positive minus any wheel lift), the

drag (the retarding force) and the balance (the percentage of the total downforce acting through the front wheels

determined by the front wing flap angle(s)).

The flow surrounding a racing car is highly complex because each part is affected by the flow from the upstream

and surrounding components and the extent of ground effect experienced [3, 4]. The flow field changes with

ride height, which alters the body forces and the car’s handling characteristics. Furthermore, transient effect,

cross wind and cornering angle of the front wheels will change the flow field. Therefore, it is impossible to

know the flow field around a car exactly. Wind tunnel tests use simplified flow fields (no transient effects etc.)

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at model scale in order to reduce cost. Wind tunnel model development involves aerodynamic insight and the

pursuit of testing directions, which hopefully would yield positive results. Recently CFD analysis has become

increasingly important. In this study it was used as a secondary design tool.

A racing car is generally set up for the mean aerodynamic balance to follow the weight distribution of the car,

which is determined by the speed characteristics of the circuit and the car's mechanical setup. Track results

show that drivers generally set up their car to a front balance of approximately 40%±2%, depending on the car,

track and driver preferences. The study tried to develop the aerodynamic performance of the car whilst

maintaining a mean aerodynamic balance, to the front wheels, of 40%.

A plot of the downforce values against the front and rear ride heights for a fixed Reynolds number is referred to

as a downforce map; similarly for balance and drag maps. For hill climbs, the cars are predominantly traveling

at relatively low speeds (<60mph) when the downforce is required; that is, in cornering. Additional downforce

at high speeds is detrimental when a car is traveling down a straight (a typical unlimited class car is able to put

all of its power onto the ground by about 80mph), which does not require downforce, and thus the induced drag

will retard the car. As there are not enough data points to produce a contour plot, the overall downforce and

balance data for the baseline and final models are given in tabulated format in Tables 1 and 2. It should be

noted that the downforce is proportional to the square of the velocity. The results shown are for a constant

Reynolds number of 2.2×106.

The relatively high power to weight ratios of hill climb cars coupled with the low top speeds ultimately put less

emphasis on the drag and therefore efficiency (defined as the downforce divided by the drag force) of the car

though within reason, especially at high ride heights. Generally speaking the pitch sensitivity, that is the balance

change across the balance map, should be minimized. For low speed racing at moderate downforce levels,

reducing the pitch sensitivity can be more beneficial to a car's aerodynamic development than additional

downforce. In a pitch sensitive car the driver will be forced to compromise his setup, reducing his/her

confidence and ultimately increasing lap time. A common complaint is under-steer on corner entry coupled

with over-steer on corner exit. Simply put, this can be thought of as a balance shift as the car finishes its

deceleration and starts its acceleration traveling through a corner. Another common driver complaint is the lack

of confidence under braking from high speed, owing to the balance position being too far forward. The ride

heights experienced by the car as it negotiates a track can be overlaid onto the balance map so that the car can be

developed to minimize the shift in balance. This, in turn, should minimize transient handling effects. For the

final design, the car's balance shift across the ride height map for a mean balance of 39% is kept to within 1.5%.

This represents a significant improvement over the baseline design (see Table 1) where the balance shift is

5.3%.

Front wing. The front wing assembly works in ground effect by increasing the low pressure region on the

underside (suction surface) of the wing compared with a similar inverted wing in freestream conditions [5, 6, 7].

The flow is sucked towards this low pressure region, from both upstream of the wing and outboard of the front

wing end-plates. The flow separates on traveling under the end-plate and wraps up, forming a vortex under the

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inboard part of the front wing assembly, commonly referred to as an edge vortex (Figure 4) [8]. The edge

vortex has a three-fold effect: it creates its own downforce, owing to a low pressure core; it generates local

upwash, assisting the local flap attachment and it can interact with the vortices created by the tyre downstream,

reducing wheel drag.

With a 60mm increase of the nose height (scale model) a range of studies could be conducted, including a front

wing height survey for the baseline and new front wing assembly. It was found in several studies [5, 6, 7] that a

reduction in ground clearance dramatically increases downforce. Hence, the new front wing supports were

designed such that the lowest point of the end-plate pushed the limits of the regulations. Figure 5 shows the

front wing assembly. Results, based on the ground height defined in terms of mainplane chord, showed that as

the height clearance was reduced there was an increase in front downforce (Figures 6 and 7). As downforce is

ultimately characterized by the turning of the flow, a greater front wing downforce may well deflect the air

enough to compromise the flow to the sidepods; the results supported this hypothesis.

Surface oil flow visualization was conducted to highlight surface flow patterns. It was found that even with a

gurney flap on the trailing edge of the mainplane, that was believed to increase the total circulation by Jeffery et

al. [9] and hence keep flow attached, separation at 80% chord occurred along the centerline of the wing. It is

believed that the edge vortex, highlighted in Figure 4, created an upwash that reduced the wing’s effective angle

of attack. The point on the wing that was subjected to the least upwash was on the centerline, and hence

separation was more common there (Figure 8). This belief was confirmed both by Zerihan and Zhang [5] and by

CFD analysis where a shear stress transport k-ω turbulence model was utilized to capture the points of

separation (Figure 8(a)).

Sidepod. One region of interest was the use of an under body curvature. There is ubiquitous use of diffuser type

devices in racing car aerodynamics and hill climbing is of no exception. The airfoil shaped sidepods developed

by Colin Chapman and employed on the 1978 world championship wining Lotus 78 were especially effective

[4]. It is also noted, however, that this car employed sliding skirts to further enhance downforce, which were

banned due to the spectacular and dangerous losses in downforce that were caused by very small increases in

skirt/ground separation. Wright [10] found that ground separations of just 20mm could result in a 50% loss of a

car’s downforce. This kind of characteristic is especially dangerous for hill climb cars, where the tracks are

especially bumpy. Unsurprisingly the use of sliding skirts is also outlawed by the MSA regulations. Fortunately,

this does not totally eliminate the effectiveness of the sidepod when compared to a flat under tray. The upswept

leading edge permits an increase in the mass flow beneath the car and therefore creating a greater potential for

downforce generation.

Work on the car’s diffuser included changing it to be more like an airfoil shape. New sidepods for the car

(Figure 9) were developed that blend in the design of a diffuser to continue behind the car’s rear wheels (the

airfoil sidepods used in the late 1970s simply ceased before the wheels). It was hoped that this would recover

some of the losses incurred by not employing sliding skirts. However, two new problems were created. Firstly

the flow path would become more tortuous and secondly there would be significant mechanical interaction with

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the suspension components if built to full scale. For investigative purposes the sidepods on the wind tunnel

model were designed to be adjustable in height and angle.

Despite the potential problems, the new sidepods produced the largest gains in downforce of the components

tested (Figures 10 and 11). It was found that the largest downforce was achieved with the sidepods placed into

their lowest position and at the smallest angle of attack. Whilst it was expected that lowering the ground height

would increase downforce in line with previous work that had been done on wings and diffusers in ground effect

[6, 11], it was also intuitively expected that increasing the sidepods’ angle of attack (nose down positive) would

increase downforce. The opposite was found to be true for this particular design. Two reasons for this behaviour

are proposed below.

Firstly in their highest ground clearance configuration the sidepods were observed to be disrupting flow to the

car’s rear wing. This effect got worse with increasing sidepod angle. This effect is shown by an overall forward

balance shift forwards (Figure 11) as the rear wing downforce decreases. In viewing Figure 11, it should be

noted that the tests of the airfoil sidepods were conducted with a very small front flap angle in order to ensure

best flow conditions to them during testing. When the 'optimum' configuration for the sidepods was found, the

front flap angle was increased and the front wing was lowered to achieve the target balance of around 40%.

Consequently the results obtained for the sidepod tests are at a lower value than 40%. In their lowest ride height

configuration the sidepods were clear of the rear wing but it was observed that the downforce decreased with

increasing angle. The proximity to the ground and the increased angle is thought to stall the sidepods [11]. This

hypothesis was strengthened by a CFD study. From Figure 12(a) it can be seen that at the lowest installation

height the edge vortex in the sidepods is incoherent and has greatly reduced velocities when compared to the

Figure 12(b) where the sidepod height is increased to twice the lowest height. This indicates that the edge vortex

has broken down at the lowest installation height.

The observations made in the sidepod study highlight the highly interactive flow field around a racing car and

the design problems that arise from it. In isolation the sidepods, as designed, would produce more downforce at

a higher ground clearance as this would alleviate the stall observed [11]. However, when installed on the model

at a higher ground clearance they block flow to the rear wing and therefore have a detrimental effect on the car’s

total downforce.

VI. Summary Wind tunnel tests and CFD were used to develop a generic, open wheel, hill climb racing car model and to

enhance the aerodynamic performance of the car. The aerodynamic performance of the car was improved

through a systematic study of the nose assembly, the sidepods, and the front wing assembly. The model

generated high levels of downforce with a front balance of 40%. The pitch sensitivity of the car was reduced,

with a variation of 1.5% across the range of ride heights tested, by properly positioning the front wing and the

airfoil sidepods. It is believed that the effect on reducing track times, as a result of increased driver confidence

through better drivability, would be more substantial than that caused by the downforce increases alone. The use

of CFD during the study further enhanced the understanding of the flow characteristics expected. The generic

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wind tunnel model and CFD represent an effective tool to develop the aerodynamic performance of a hill climb

racing car.

An observation of the study is that a racing car is a highly interactive aerodynamic system. Components that

produced individual downforce gains were not necessarily beneficial to the overall performance of the whole car.

Vortex flows and flow interactions dominate the flow field about a racing car, which is highly dependant on ride

height and pitch.

Acknowledgements

The article is dedicated to the memory of Dr Charlie Williams. Charlie tragically passed away during the course

of this work, but without his dedication and expertise the project would not be successful.

The idea of the project came from Mr Willem Toet. We wish to thank Mr Toet for his time, technical advice and

financial support. The School of Engineering Sciences provided initial funding to build the wind tunnel model.

We also wish to thank the assistance provided by Dr S Chan, Mr M. Thomas, Mr D. Coe, Mr D. Marshall and

Mr T. Westbury. The authors would also like to thank the staff at Pilbeam Racing Design and Gould Racing for

their help. The authors acknowledge www.2t4t.co.uk for permission to use the photo shown in Figure 1.

References [1] “Specific regulations for sprints, hill climb and drag racing,” Motor Sports Association, UK. http://www.msauk.org. [2] “2007 FIA European hill-climb championship standard regulations updated: 08.06.2007,” Federation Internationale De L’Automobile, http://www.fia.com. [3] Zhang, X., Toet, W. and Zerihan, J., “Ground effect aerodynamics of racing cars”, Applied Mechanics Review, 59(1), 2006, pp. 33-49. [4] Katz, J., “Aerodynamics of race cars”, Annual Review of Fluid Mechanics, 38, 2006, pp. 27-63. [5] Knowles, K., D. Donahue, D. and Finnis, D , “A study of wings in ground effect” Loughborough University Conference on Vehicle Aerodynamics, 1994, pp. 22.1-22. [6] Zerihan, J. and Zhang, X., “Aerodynamics of a single-element wing-in-ground effect,” Journal of Aircraft, 37(6), 2000, pp. 1058-1064.

[7] Zhang, X. & Zerihan, J., “Aerodynamics of a double element wing in ground effect,” AIAA Journal, 45(6), 2003, pp. 1007-1016. [8] Zhang, X. & Zerihan, J., “Edge vortices of a double element wing in ground effect,” Journal of Aircraft, 41(5), 2004, pp. 1127-1137. [9] Jeffrey, D.R., Zhang, X. & Hurst, D.W., “Some aspects of aerodynamics of Gurney flaps on a double-element wing,” ASME Journal of Fluids Engineering, 123, 2001, pp. 99-104. [10] Wright, P., “The influence of aerodynamics on the design of Formula One racing cars.” International Journal of Vehicle Design, Impact of Aerodynamics on Vehicle Design SP3:158-172, 1983

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[11] Zhang, X. & Senior, A., “Force and pressure of a diffuser equipped bluff body in ground effect,” ASME Journal of Fluids Engineering,” 123, 2001, pp. 105-111.

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Ride Height (mm) Total Downforce (N) Balance

Front Rear 35.00 65.00 5555 38.4 27.14 51.43 5912 38.2 20.00 40.00 5826 38.7 12.86 28.57 5647 39.1 12.86 40.00 5912 40.6 12.86 51.43 6167 41.6 27.14 40.00 5718 36.3

Table 1: Ride height map for the baseline model.

Ride Height (mm) Total Downforce (N) Balance

Front Rear 35.00 65.00 5852 38.3 27.14 51.43 5742 38.7 20.00 40.00 5722 38.7 12.86 28.57 5899 39.1 12.86 40.00 6099 38.5 12.86 51.43 6237 38.3 27.14 40.00 5948 39.8

Table 2: Ride height map for the final design.

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Title figure

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Figure 1: A view of Pilbeam MP88 driven by Willem Toet at Prescott hill climb May 2006 exiting Ettore's Bend.

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Figure 2: Development trend: baseline model (top) and current design (bottom).

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Figure 3: Sideview of baseline model (top) and current design (bottom).

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Figure 4: CFD simulation of edge vortex produced from front wing assembly; main picture is viewed from behind.

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Figure 5: Comparison of baseline (red) and new front wing (blue) assemblies showing greater variation in height achievable with the new assembly.

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Ground Clearance Ratio (h/C)

Dow

nfor

ce(N

)

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1000

2000

3000

4000

5000

6000

7000Total Down-forceFront Down-forceRear Down-force

Figure 6: Downforce vs non-dimensional ground clearance. h – Distance from ground plane to bottom of wing, C – Chord of the main front wing element.

Ground Clearance Ratio (h/C)

Tota

lDra

g(N

)

L/D

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.452225

2230

2235

2240

2245

2250

2255

2260

2265

2.3

2.4

2.5

2.6Total DragL/D

Figure 7: Total force and efficiency (L/D) vs ground height.

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(a)

(b)

Figure 8: Surface streaklines on the suction surface of the front wing observed by (a) CFD and (b) oil flow; final assembly with Gurney. Flow from bottom to top.

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Figure 9: Sidepod design.

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Angle (degrees)

Tota

lDow

nfor

ce(N

)

2.5 3 3.5 4 4.5 5 5.5 64800

5000

5200

5400

5600

5800

6000

6200

Full scale ground clearance = 168mmFull scale ground clearance = 110mm

Figure 10: Downforce vs sidepod angle (nose down positive).

Angle (degrees)

Bal

ance

(%)

2.5 3 3.5 4 4.5 5 5.5 622

23

24

25

26

27

28

29

30

31

32

33Full scale ground clearance = 168mmFull scale ground clearance = 110mm

Figure 11: Balance vs sidepod angle (nose down positive).

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(a)

(b)

Figure 12: CFD investigation of sidepod stall. Pathlines are coloured by velocity magnitude at a ground height of (a) ground clearance = 40mm (b) and ground clearance = 80mm.