Being open-wheeled vehicles, the tyres of a Formula One car play a major role in its aero performance and, as such, understanding their impact here is an important part of optimising the car’s overall aero package. Tyres are dynamic entities though, so their shape and size changes when loaded by the car on track. Along the straights, they will grow in diameter and get narrower; in corners, vertical and horizontal loads will cause them to deform laterally.

To ensure that the impact of this deformation is accounted for in aerodynamic testing – both in CFD and the wind tunnel – requires some clever methodologies. Most Formula One teams keep such testing secrets close to their chest; however Honda has revealed some of the techniques it used during its last stint in the sport.

For scale-model wind tunnel testing, scale rubber tyres are used to replicate the behaviour of their full-scale counterparts. In most wind tunnels though, it is only possible to apply vertical forces to the tyres, and perhaps a small amount of side force by yawing the car on the wind tunnel’s moving belt. To combat this problem, Honda devised various testing methods based on deformation measurements taken from its cars on track. This data could then be fed into its CFD simulations to gauge the impact of this deformation on overall aerodynamic performance.

The actual data for deformation was gathered using a tyre test rig, with the inputs for side loadings derived from load cell measurements of the car’s suspension when on track. The measurement of the deformation was achieved by scanning the tyres as they were on the test rig, and using this information to create 3D models of the tyres. These models could then be fed in to Honda’s CFD simulations. As an example of the level of deformation present, a side loading of 7000 Nm on the tyres’ tread caused a deflection of the side wall of about 20 mm.

The impact of this deformation on the flows around the tyre were considerable. Looking at the front tyres, CFD simulation showed that as the tyre deformed, the separation point of the flow at the base of the tyre sidewall moved backwards. As a result, flow that moved around the tyre when it was not deformed, started to flow under the car, reducing the effectiveness of the underfloor aerodynamics.

With this new-found knowledge, Honda went on to replicate the tyre deformations as accurately as possible in the wind tunnel, using both scale and full-sized vehicles. It was verified, through force measurements and PIV (particle image velocimetry) visualisation, that the changes to the flow in CFD correlated with the real-world effects. It is interesting to note that one method suggested by Honda to more accurately replicate tyre deformation in the wind tunnel involved fitting a roller inside the test wheels that could be used to load the sidewall of the tyre to produce the same deformation as seen on track.

It is more than likely that current teams have various other methodologies for assessing problems such as tyre deformation, no doubt helped by advances in CFD and other simulation methods. However, Honda’s study provides an interesting example of the amount of effort needed to accurately quantify just one area of a Formula One car’s overall aero behaviour.

Written by Lawrence Butcher

The option to couple solvers is not limited to structural solvers. The new set of technical regulations in Formula One has put greater emphasis on cooling, and in turn on understanding heat transfer. This is an area where CFD methodology has been developed extensively by roadcar manufacturers, with engine bay cooling airflow and exhaust modelling simulations now commonplace. Such coupling would also allow Formula One teams to evaluate their cooling package as part of their aero simulations and accurately model the flow of the air escaping from the rear of the car. 

This methodology could also have proved more effective in recent years, with the prominence of exhaust-blown diffusers. Wind tunnel models are rather limited in their ability to mimic how the exhausts truly behave, as it is impossible to put a scale engine in a wind tunnel model that produces the same mass flow and temperatures through the exhaust. Even accounting for the correct temperature of an exhaust, it would have been hard to correctly model the mass flow through it. In reality, an exhaust’s behaviour is linked to what the engine is doing, and what the engine is doing is changing at an alarming rate. 

This again leads to the argument for using transient methods, although it should be noted that a fully transient coupled simulation – where ride heights, yaw, steer and roll trajectories and exhaust parameters are changing – is still beyond the time constraints of a Formula One team. However, a compromise has been developed by at least one automotive OEM. 

This was developed by taking a car around a race track and monitoring the velocity and dynamics of the car together with the exhaust parameters. A filtering process is then applied to identify the most significant velocities and exhaust parameters, and from this a sample of points is taken to simulate 20 or so steady-state RANS simulations. From these results an understanding can be developed of how the car is truly behaving around a circuit. The time needed to complete this analysis is within a working week – a potentially acceptable timeframe in Formula One – although at the moment this approach would take up most of the restricted CPU time available just to analyse a single car configuration. 

Staying with the theme of coupling with a heat transfer solver, brakes obviously get hot and cool down, and it is important to keep a racecar’s brakes within a specific operating temperature range. In recent years, front and rear brake ducts have been an area of aggressive aerodynamic development for teams, but when optimising these ducts for aerodynamic gain it is perhaps easy to overlook their cooling requirements. Coupling the braking system geometry with a heat transfer solver would allow teams to analyse the extent to which they are keeping within operating temperatures, while also analysing the aerodynamic effect of modifying their brake duct design. 

The CPU time penalty incurred by coupling solvers implies though that this is not a methodology that is currently attractive to Formula One teams. Moreover, brake cooling effect is inherently associated with wheel shape, so modelling the rotation of the wheel as accurately as possible via sliding mesh techniques should greatly enhance the accuracy of such simulations. 

Formula One has undoubtedly added to mainstream automotive technologies over the years, with ABS and semi-automatic gearboxes being prime examples, and the modification of the powertrain regulations for 2014 will hopefully once again improve the series’ relevance to roadcar technology. In terms of manufacturing, Formula One also continues to drive the development of new techniques. 

With regard to aerodynamics and CFD, however, Formula One’s relevance to the wider world is arguably diminishing. The 2014 regulations aim to reduce costs, but by linking the wind tunnel usage limit to the CFD usage limit, the FIA is surely overlooking the fact that CFD is cheaper than using a wind tunnel. So, in the context of cost-efficient development, should CFD not be encouraged? 

The phrase in the regulations most damning to the development of CFD methodology is surely the one that states that the CFD limit line will change every three years “to take account of changes to CFD hardware ownership and running costs”. This suggests that the FIA is being naive in its view of the rate of development of both CFD methodology and computational hardware, so Formula One needs to ensure that the rule makers are not prejudiced about the benefits of CFD. 

The fact remains though that some teams are not using their current hardware to its full potential. The hardware is expensive but brain power is free – provided you are employing the right brains!

Written by Sam Wakelam

The regulations impose a limit on the combined use of CFD and wind tunnel time must fall below a limit line. The natural implication of this is that, for most teams, CFD use is compromised to an extent in favour of wind tunnel time, given that it remains the primary development tool of the teams.

It follows then that one of the most desirable attributes for a CFD simulation is fast turnaround. This has led to a great deal of convergence of methodology between teams to using commercial Reynolds averaged Navier Stokes (RANS) solvers with wall modelling, high under-relaxation factors and high-quality meshes capable of producing steady values of lift and drag within a few hundred iterations.

While this methodology can produce well-correlated results in a timely fashion, however, it does not represent the forefront of development in CFD methodology, and arguably shows that teams are heading towards a stagnation in accuracy improvements. Practicality governs the use of this methodology but the regulations prohibit more accurate and more computationally expensive methodologies. Now let’s examine the possibilities the teams are dissuaded from pursuing.

First, if we discount methods such as direct numerical simulation, large eddy simulation and (to an extent) detached eddy simulation as being impractical – particularly in terms of providing a result within an acceptable timeframe for a Formula One team – then we are still left with main ways of simulating the unsteady flows characterised by a Formula One car: the unsteady RANS and Lattice-Boltzmann methods.

Both provide a wealth of data beyond steady-state RANS solvers, as the ability to look at transient data makes it is easier to visualise how flow structures interact with one another and how vortices generated at the front of the car propagate downstream. Both are available in existing commercial software, the Lattice-Boltzmann method in particular allowing transient data to be obtained at a relatively low computational cost, and because it is inherently transient and has greater numerical stability, it is harder to make the simulation crash. These methods could realistically be used by Formula One teams on a daily basis to drive development; it is primarily the regulations that stop them exploring them further.

Aside from using new methods, teams are equally restricted in trying to maximise the information they can generate in conjunction with their existing RANS solvers. In recent years there has been more emphasis on creating aero-elastic bodywork, which allows teams to set up their car with minimum compromise or (depending on your opinion) completely flout the regulations. Rightly or wrongly, aero-elastic bodywork is an area of interest to Formula One teams, and much of the focus on it has concerned the front wings, specifically flexing the wing to move the ends closer to the floor to further exploit the ground effect or to place the wing into a stall condition to reduce drag.

Aero-elasticity is particularly difficult to model in a wind tunnel: the materials used and the size of the (scale) models are different from the car they mimic, and hence behave differently. Computationally it is possible to model aero-elasticity, although at present it invariably involves coupling a fluid dynamics solver with a structural solver. This presents its own difficulties: scripting is needed to couple the solvers, as is potentially the need to re-mesh the geometry after it has altered shape and skewed some elements. Naturally though, the passing of information between solvers and the need to run longer to achieve convergence for each iteration of geometry change means this is not currently an attractive way for Formula One teams to run their solvers on a daily basis.

It is often said by technical writers that the wheels and tyres account for around a third of the drag on a Formula One car, so modelling the flow interaction with the wheels is seen as crucial to being able to engineer an efficient car. There are currently two main ways of modelling wheel rotation – using a moving reference frame, and using a sliding mesh. The former is the norm for Formula One teams, and relies on assigning a constant speed of rotation to a volume region. The latter is generally out of reach to teams as it invariably requires a transient simulation to be run, although neglecting its use means teams are not modelling the true rotation of the wheel.

Aside from modelling the rotation, another key area teams seek to optimise to improve their correlation is the squash shape of the tyre. Modelling the deformation of the tyre would again involve coupling the simulation with a structural solver, and is hence not possible within the framework of the regulations. So while teams model different trajectories of yaw, steer, roll and ride heights, their accuracy is limited by their grasp of tyre squash.

Next edition’s article on this keyword will continue to examine what the current regulations implicitly prohibit, focusing predominantly on thermal applications. 

Written by Sam Wakelam

The restrictions were introduced by FOTA, with the teams having to submit a declaration at the end of each testing period summarising the resources used. There are two principle measures:

• WT wind-on hours per week. This is the length of time the WT is switched on, with the speed above a nominal value. The longer the WT is running for, the more parts that can be tested, or the more data points that can be sampled for each part.
• Average CFD teraflops. This is a measure of the computational usage of a CFD cluster. For a given cluster and CFD model, the more teraflops that are available, the more CFD runs/geometry changes that can be made.

These measurements are averaged over eight-week periods, so teams typically own CFD clusters that have a peak capacity rated as significantly faster than the restrictions. This allows them to cope with periods of high demand, as long as they operate at reduced capacity later on in the eight-week cycle.

New restrictions for 2014

For 2014, the testing restrictions are now an appendix to the sporting regulations, and are enforceable by the FIA; they are no longer optional or as open to abuse. Beyond this, the two main changes for 2014 are:

• A reduction in the WT and CFD limits to 30 hours and 30 teraflops (see Fig. 1).
• The number of WT runs is limited to 80, and occupancy time is restricted to 60 hours (the length of time a model can be installed in the WT, having parts changed or ready to be tested)

It is the limit on the number of WT runs that is incredibly restrictive, rather than the reduction to ‘30/30’. A Formula One wind tunnel will typically run for close to 24 hours a day, six or seven days a week, during which it can perform upwards of 200 runs, so the new restriction cuts this down to roughly a third of the current run rate. Assuming that each WT run is testing a new part, this is a dramatic reduction in the number of components that can be tested in the tunnel.

Implications of the new restrictions

With fewer parts being tested in the WT, the development rate is likely to drop. One way to counteract the reduction in the number of parts tested would be to test each part for longer, sampling more detailed data. However, occupancy limits will limit this, as it works out to be only 45 minutes per run, which must include the time taken to change parts on the model.

The reduction in WT testing could also lead to a greater emphasis on the use of CFD in the development process. Designing parts in CFD prior to tunnel testing allows all but the most promising directions to be filtered out without wasting tunnel runs and time.

General implications of aero restrictions

While restrictions on aerodynamic testing make sense from a financial point of view, particularly in the field of CFD, they have also removed a lot of the industrial relevance. In the past, the needs of Formula One have pushed CFD developments forwards, and this has led to faster clusters along with faster and more efficient CFD software for the wider community. The recent restrictions have led Formula One teams to put major resources into tailoring their individual CFD process to provide the highest throughput for their limited computational capacity, but most of these optimisations have no relevance in the wider industry, which can now call on greater computing power than in Formula One. Also, other promising CFD simulation techniques that are gaining traction in industry, such as design of experiments or design optimisation, are no longer viable in Formula One owing to their large computing requirements.

Fig. 1 - Aerodynamic resource restrictions (Source: FIA 2014 Formula One sporting regulations) 

Written by Matt Layton

By far the most efficient method of heat transfer from the brakes is through convection. This is achieved by blowing cold air over a hot component – usually the disc, pads and caliper – as well as any nearby electronic sensors. The plethora of vented brake disc designs, with their large number of flow paths drilled or moulded radially through the disc, are designed to increase convection. As flow passes through these holes, heat is transferred from the hot disc into the colder air, and as this flow heads out of the wheel it can be up to 400 C hotter than it went in.

The brake discs must be run at around 400 C (although peak temperatures may hit 1200 C at points in the lap). Too hot and they rapidly oxidise, resulting is excessive wear; too cold and the braking performance is poor. Teams alter their cooling set-up on a race-by-race basis, using a range of inlet sizes, using taping or blanking for fine tuning.

An easy way to increase the cooling level is to increase the mass-flow through the brake duct. This can usually be achieved by increasing the inlet size of the duct, but that usually leads to worse external aero performance. Contrary to popular opinion, it is not the drag from a large inlet scoop that is detrimental to the car’s performance; rather it is the effect of the larger duct on the myriad of flicks, winglets and flow-conditioners that surround it. In general, minimising the size of the cooling inlet for a required cooling level leads to greater aero performance, and this can be achieved through the design of the internal ducting and brake disc.

Historically, all high-temperature flow is expelled from the outboard side of the wheel without further use. However, the temperature-sensitive performance of the Pirelli tyres over the past couple of seasons has led teams to experiment with redirecting the hot flow coming out of the brakes as a way to affect tyre temperature.

The only component of the car in direct contact with the tyre is the wheel rim, which provides a conduction path into tyre’s carcass. The external surfaces of the wheel rim, within the tyre cavity, face the internal surfaces of the tyre, which allows it to be heated through radiation from the inside. Heating up the wheel rim can give a small but measurable increase in tyre temperature and, vice versa, cooling the wheel rim can reduce tyre temperature.

The leading teams pursue a strategy of heating the front wheel rims, particularly to increase front tyre temperatures for qualifying. One mechanism that has been used by several teams is to remove a large amount of the brake shroud and directly expose the brake disc to the inside of the wheel rim. When combined with surface coatings on the inside of the rim, this can lead to significant increases in rim temperature through radiation.

The aim with the rear wheels is to generate a cooling effect – or at least minimise any heating effect from the brakes – to avoid the dramatic drop-offs in race performance experienced by some teams as a result of overheating the tyres. In an effort to control their rear tyre temperatures, the teams take steps to isolate the brakes from the wheel rim, including:

• The brake disc is contained with a carbon shroud, accurately controlling the hot and cold flow paths
• All the hot brake disc flow can be ducted back out inboard of the wheel, preventing it from passing over the wheel rim
• Channels are recessed into the brake shrouds, allowing cold flow to be directed into the small air gap between the shroud and the wheel rim, and helping to isolate the wheel rim.

Development and simulation of the brake cooling flows is primarily conducted using a combination of physical dyno testing and CFD. Track testing is too limited, and wind tunnel testing of components within the wheels is problematic because of the need to accommodate load cells, part modularity and clearances. CFD has the advantage of being able to model and separate out the importance of the various levels of physics at work. Brake components, in particular discs and calipers, are usually tested on a full-size test rig over an entire race simulation before being signed off for use on the racecar. Data from this testing is fed back into the simulation process. 

Fig. 1 - The most efficient method of heat transfer from the brakes is by blowing cold air over hot components such as the caliper (Photo: Michael D)

Written by Rob Lewis

Rate of change of car state: This is best illustrated by the braking event at the end of a straight. Here the car changes from a low ride height (high downforce pushing the car into the track at high speed) to a pitched high rear/low front as the brakes are applied. This change in attitude is very quick and happens on almost the same time scale it takes for the air to travel from the front of the car to the back. It is a true transient bit of aerodynamics that can’t be reliably modelled as a series of steady-state car attitudes during the braking phase.

The effect of ignoring this physics is that well behaved diffusers (designed in tunnel and CFD) may start to stall at the track as the brakes are applied; also they may not re-attach that quickly either. This is one example of rate of change of car attitude, but there’s also rate of change of yaw, roll and steer.

The options for measuring this effect are fairly limited. CFD is only starting to be able to model this transient, moving body, type of simulation. Tunnels have motion systems and can replicate the braking pitch change but the challenge comes in separating out the aero forces during the pitch change from the inertial forces needed to pitch the car itself – very tricky indeed, and also very important as diffuser design gets more complex and closer to the limit of transient stall effects.

Exhaust flow rate: Recent years have seen exhaust flow playing an important part in Formula One aero, and these days the effects of exhaust gases are included routinely in tunnel and CFD testing. CFD probably has the upper hand here as it can model hot gases at the right flow rate, whereas most tunnel tests are limited to cold flow and reduced flow rates. Similar to the rate of change of car state described above, the exhaust gas flow can change very quickly, and true transient analysis of rapidly changing exhaust flow rates could become important too.

Airbox intake flow: As for exhaust flows this is routinely included in CFD and tunnel tests. It is simpler than exhaust flows though as there is no hot flow. Scale tunnels can often be limited in airbox intake work because the mounting strut for the model tends to sit in front of the air intake. Again, transient effects of rapidly changing intake flows could become important, but this is unlikely.

Corner curvature: When the car is cornering, the air flowing over it isn’t travelling straight but in a curve, so the approach angle varies from the front to the back of the car. This effect was until recently considered to be negligible, but teams have realised that it becomes important as we look deeper for more aero gains. CFD was able to simulate curved flow back in 2001, so has had the capability for a long time. Tunnel testing, however, is capable of straight wind only. So to predict true cornering aero forces CFD has a significant advantage here. Most teams are looking at cornering flow; few though are prepared to make a cornering CFD simulation the definitive test before the track – yet.

Rate of change of corner curvature: Continuing with the theme of it not being just about steady flow but the rate of change of flow or attitude, the rate of change of corner curvature will have an influence on aero forces. It’s probably safe to say that none of the teams are looking at dynamic curvature of flow, and it’s likely that the effect is small compared to the dynamic braking event. Eventually a CFD run will perhaps be a dynamic simulation of straight, brake, turn in, corner and exit – throughout which tyre shape, flow curvature, wing deflections and exhaust flows are all dynamically changing. With current CFD tools, such a simulation is difficult but not out of reach.

Wake onset from a leading car: Wake effects have been studied extensively recently with regard to overtaking performance. Rarely are wake effects considered when optimising a car’s aerodynamics; rather, this is done in clean flow. Testing two cars in a wind tunnel is not impossible, and in CFD as well interactions can be studied. Again it’s not important enough to look at routinely, and the DRS button has reduced that importance further.

Atmospheric conditions: In other words, wind and its velocity, direction, boundary layer profile and how all that changes with time. Aerodynamics is often about creating a robust design, something that performs under a range of operating conditions. Making a car well behaved aerodynamically under varying car attitudes is not the same as designing aero to work on a windy day – again, the nasty non-linearity of aerodynamics pops up, where a small change can cause a finely optimised device to switch flow modes and effectively fail.

Some roadcar wind tunnels can create ‘wobbly wind’ though, to simulate transient wind conditions using moving vanes ahead of the car. Formula One tunnels haven’t applied this technique and have focused on steady, clean flow. On the other hand, CFD can easily do some of the elements of transient atmospheric conditions (like boundary layer profile) but some aspects are still challenges. The chances are that the teams aren’t looking at this with CFD or tunnels but are probably thinking about it for their next wind tunnel upgrade or purchase.

Heat rejection from brakes and radiators: As air is heated it expands and so becomes less dense, and if it’s in a duct it will accelerate. Wind tunnel testing rarely sees hot brakes or radiators as these factors are very difficult to implement or control. CFD can solve thermal problems and include the effects, but these tend to be specialist cooling models rather than routinely incorporated into the standard CFD aerodynamic simulation. Most of the time the assumption of cold flow is valid but, as above, at some point it will be important and standard.

So in summary these are the various levels of physical phenomena that contribute to aero forces. Some are routinely included in Formula One tunnels and CFD tools; some are simply missing. The question of validating CFD versus tunnel versus track becomes somewhat academic in contrast to the missing physics from the CFD and tunnel tests. Arguing over a 2% balance difference between CFD and tunnel should be seen in context of what the balance shift would be from straight to curved flow, hot to cold or static to dynamic. The last point to make is that CFD will only ever be a mathematical approximation of real air and turbulence, and although the above may paint an advantage for CFD, its biggest downside is the fake wind.

Fig. 1 - The wake behind a Formula Three car in straight flow (Courtesy of TotalSim)

Fig. 2 - The wake behind a Formula Three car in curved or cornering flow. Here the wake can be seen to be following an arc along the path the car would have taken. Notice also that the air has more energy (colours are total pressure) the further away from the centre of the turn you are (Courtesy of TotalSim)

Written by Rob Lewis

Of the four toolsets, only one – track testing – is truly correct, the rest being approximations of real-car aerodynamics at the track. But track testing is restricted, expensive and has poor repeatability/resolution due to changing conditions (weather, temperature, tyre and so on). So the track has all the physical processes that contribute to or influence aerodynamic forces and moments.

At first glance this is simply car design and set-up, car state (ride, roll, steer, yaw) and wind speed. But there are other factors that drive aero forces too. As the need for higher-fidelity aerodynamics increase, so does the importance of looking further than car design, car state and speed. The mind map below aims to illustrate some – hopefully most – of the other physics or influences on aerodynamic forces.

Working through the list on the left-hand side, the first three are the obvious ones, as stated above. Given a car design, attitude and speed we can get steady aero forces from either tunnel testing (scale or full) or CFD. From there we’ll see differences and debate CFD turbulence models, wind tunnel design and geometry differences forever. But the bigger picture is: what else should we be looking at to get the real forces and moments the car would see on the track? Let’s go back to the mind map and work through the list.

Acceleration of the car: There are two things happening here. The first is that the air around the car has mass, so to accelerate the car you need to accelerate that air too – it’s a small but significant force change that steady flow won’t show. The second is where aerodynamics can play tricks, where a sudden change in flow speed can cause a different flow structure compared to a slow increase in flow speed. This doesn’t happen often but imagine the effect of having a front wing that works at a range of speeds but stalls if the acceleration of the air is greater than, say, 1 g.

Using wind tunnels it is probably very hard to match the high accelerations seen on track, whereas with CFD it’s fairly straightforward. Are the teams looking at this as part of their process? Probably not, as it is considered low priority and tricky.

Static aero-elastic bodywork deflections: The pressure exerted by the air on the car as it passes over it causes things to bend or deflect under load. ‘Static’ means these deflections move and stay moved – that is, no flutter. It’s pretty routine using today’s tools to take forces from CFD and plug them into stress analysis codes and calculate the deflected shapes. These shapes can then go back into CFD or wings made for tunnel testing that are “as deflected at 180 mph”.

So the effects can be studied, gains exploited and front wings that peek outside rule boxes created. This has led to more stringent load tests on car components, and so the game continues.

Given the deflected shape, the tunnel or CFD toolset can equally perform a role. Full-scale tunnel testing has the upper hand in that the wings will naturally deflect in the right way. Most static aeroelastic work in Formula One is probably done in CFD, since the link to the stress codes can be made slick and seamless. It is very likely that all teams are using these tools as part of their standard process.

Dynamic aero-elastic bodywork deflections: This is similar to the above but here the deflection doesn’t stay put and things flutter. This motion can be all aero-driven, like a flag in the wind, but the motion of the car (bumps and vibration) can contribute too. The full dynamic aeroelastic problem is very difficult in either scale of tunnel. Even in CFD with complex stress codes, this problem is only just becoming solvable, largely because the motion (such as pitching) of the car is very hard to model. Very few teams will be looking at true dynamic aeroelastic work, and probably fewer will be including the car motion in the calculation.

Tyre shape, roughness, flash and deformation: At the track the tyres don’t stay smooth, the edges get sharp with rubber flash from wear, and they deform significantly under load. Structural models of the tyre can help to predict and provide tyre shape under load, and these can then be fed into CFD directly.

For scale tunnel testing, the tyres used are designed to try to mimic the shape changes seen on track. In either part-scale or full-scale tunnel testing it is possible to get tyre deflections through vertical load, but generating correct lateral forces and deflections in the tunnel is very difficult or impossible.

Tyre shape is a key driver for a car’s aero performance; the tyre sheds vortices and wakes, and interacts strongly with wings and underfloors. Flash and roughness can be applied in CFD or tunnels, and the effects shown. True cornering tyre shape control can probably only be achieved in CFD; tunnel testing can get close but struggles to fully match the track. Most teams put large efforts into getting tyre shapes right in tunnels and CFD.

Track roughness: As the air is squeezed under the car it can be travelling faster (or even slower) than the track, so the surface finish of the track can play an important role in the car’s aero. Teams run rough belts in their tunnels and apply roughness to the ground in their CFD models. It’s mostly straightforward stuff, and tuning of track roughness for different circuits isn’t really necessary.

Dirt build-up, surface finish: Tunnel testing and CFD tends to be done with a clean model. At the track, the cars can build up dirt and rubber deposits in key aerodynamic places. Mostly this makes little difference and can be ignored, but a finely tuned front wing might fall over if there are a few specs in the wrong places. This sort of flow change is largely small-scale boundary layer physics, which CFD struggles to resolve, and tunnel testing provides an easier route to gluing dead flies in the wrong places. Teams have probably rarely looked at this in the past, although this has almost certainly changed now given the amount of rubber build-up of recent years!

In Part 2 we’ll continue through the list and discuss how the curvature of the wind in a corner can make a big difference to Formula One aerodynamics.

Written by Rob Lewis

If we go back to the late 1990s then CFD was starting to be capable of full car analysis, with models that looked pretty complete but in fact weren’t really resolving the general external aerodynamics accurately. The models were around one-hundredth of the size they are these days and would take weeks to build and days to calculate the airflow around it. But in the background was always Moore’s Law, which states that the number of transistors on a chip roughly doubles every two years. In other words, computers become exponentially quicker. So CFD has been tracking the digital revolution and the power/price of the home PC.

Hardware aside, these days there are a few other areas where progress must be recognised. The software tools for building the CFD models have improved massively. Ten to 15 years ago, meshes had to be almost hand-stitched together, but now we can drive CFD directly from CAD in some cases where CFD runs are built, configured, computed, post-processed and reported automatically from a “go CFD” button in CAD. The tricky bit will always be figuring out what the results all mean and what to do next!

The other change is that open source CFD tools have arrived. We now have a choice between commercial codes and open source alternatives. This means two things: we can reduce the cost of doing CFD, and we can take the lid off the CFD code and poke around, change things and make it our own special version. Remember that commercial codes are closed; you can request modifications but you can’t get the source code and play around with it. All in all, great progress for the power, cost and ease of use for CFD over the past 15 years, and the gradient of progress is still there pinned to Mr Moore’s coat tails.

The world outside of Formula One is using CFD to tackle bigger and more complex problems. Roadcar companies are using CFD to solve unsteady flows rather than the time-averaged flow solutions that most Formula One teams still bank on. This means they can look at the unsteady wake and turbulence around a vehicle, giving them greater insight and a much more accurate tool to measure drag, noise, cooling, soiling of the car by dirt particles and aero stability.

Optimisation has become a widespread tool for many CFD users too. This is a process where the shape or design is parameterised, and CFD plus some maths works to morph the shape automatically to maximise a goal. Optimisation needs lots of computing power, and these days it is achievable even with complex full-car models.

Most Formula One teams, on the other hand, are working to a cap on the use of wind tunnels and CFD, either through previous FOTA agreements or in the future with incoming FIA regulations. There is a sliding scale between wind-on hours and CFD computing power, where a team can choose a balance between CFD and tunnel use, then work to that budget.

Most teams go for a sensible balance, with probably around 20 ‘units’ – teraflops of theoretical peak computing power – of CFD. The definition of a teraflop is a trillion (one followed by 12 zeros) floating-point operations per second. That sounds simple enough, but it’s the “theoretical peak” phrase where it all goes fuzzy. In theory, a current Intel 3.4 GHz six-core CPU can carry out six of these floating-point calculations per cycle, 3.4 GHz means 3,400,000,000 cycles per second, and there are six cores, so this chip is capable of 122.4 gigaflops, or 0.1224 teraflops.

With a budget of 20 teraflops, a Formula One team would max out at 163 of these CPUs, (or 980 cores) – not many really. But the real twist is how close a CPU can perform compared to its theoretical  peak, and this is where some of the games start. So if one chip manufacturer produces a chip tweaked for Formula One that loses 25% of its theoretical power, but in reality for CFD calculations it loses only 5%, then it becomes a must-have for the teams. Just like working around rules for blown diffusers, the teams can find ways to stay within the 20 teraflop budget but still get more real computing power. This drives them to buy very specific hardware, often discarding perfectly good hardware at the same time. So while the rest of the CFD world is using the current quickest, best-value hardware, the Formula One teams using capped computing power are doing something else, and it’s not saving them money.

Another consequence of the computing power cap is that Formula One ‘can’t afford’ to follow the rest of the CFD world in doing real transient simulations. It is stuck largely with the teraflop-friendly steady-state science that for most vehicle aero research is becoming old school. Also, optimisation is becoming a no-go for Formula One, as it burns more computing budget than teams can afford to spare. It is steering them back to guys drawing parts and running them manually, rather than letting the computer take the strain. Formula One CFD solvers are being tweaked for efficiency, previous runs are being scoured for useful info, while new ways not to use computing power but solve more CFD are being sought at some cost. All the while, the rest of the world is asking the opposite question: “What can we do next with all this computing power?”

So what’s the real answer to budget-capping CFD? It isn’t simple; Formula One teams could do proper benchmarks of their hardware using standard CFD codes and models rather than relying on ‘theory’. In the end though there will be ways to tweak the benchmarks and work around any new rules. Perhaps the teams could all be allocated computing power from a central computing ‘cloud’ and be asked to make the most of it.

None of this is ideal, but there has to be a sensible solution somewhere that gets Formula One back on Moore’s law and using or evolving tools that the rest of the world would want. One solution could be financial budget caps that would drive the teams to seek productivity per £/€ spent on solutions, thus developing tools and processes that will have more appeal outside Formula One.

Fig. 1 - Unsteady CFD simulation and shape optimisation techniques were used to make gains for wheelchair and track cycling in 2012 (Courtesy of UKSport and TotalSim)

Written by Rob Lewis