Technical Article #1: Race Car Tyre Pressures - A Comprehensive Guide
One of your responsibilities as a race engineer is to set tyre pressures for your race car. At first glance, this may seem straightforward, but as I found out, it’s a rabbit hole which is worth exploring. This article will cover everything one should know about tyre pressures including, the motivation behind setting tyre pressures, how to find the optimal pressure for your tyre, the pressure-temperature relationship of a tyre, calculating cold pressures to reach your desired target, and managing the uncertainties surrounding tyre pressures.
The Motivation Behind Setting Tyre Pressures
Before learning how to set tyre pressures, one must first understand why it’s so important to do so. Fundamentally, a tyre is a deformable body made of many materials which contribute to its stiffness, durability, and wear characteristics. One of the largest contributors to a tyre’s overall vertical stiffness is tyre pressure, and the effects of varying pressure by even 0.1 bar can be quite significant. To quantify this, the spring rate of a typical GT3 car tyre in a pressure range of 1.7-2.0 bar is anywhere from 250-350N/mm. It’s also worth mentioning that in terms of stiffness distribution front to rear, a rear tyre for a GT car is typically stiffer than the front. From previous calculations, a variation in tyre pressure of 0.1 bar can change the stiffness by about anywhere from 5-15 N/mm. This seems insignificant at first, but one must realize that when dialling in the balance of a race car, you may make spring rate changes on the same order of magnitude. As their temperature increases over a stint, tyres will rise in pressure, and this increase in stiffness can be substantial from when the vehicle left the pitlane. One must also remember that a tyre acts as a spring in series with the rest of the suspension, meaning it influences a corner’s wheel rate and respective natural frequencies. Looking at wheel rate as a function of tyre pressure, we see the following.
Table 1 took the upsprung mass of a single corner to be 45kg and the sprung mass to be 305kg. It also assumes that the growth in tyre pressure is linear with respect to laps spent in the stint. The results are clear though, and as the pressure increases, every parameter of interest increases by a noteworthy amount. From a race engineering standpoint, having an understanding that these vehicle parameters are evolving on track is vital to building a complete understanding of the race car’s performance. As an example of a real application of this principle, if one were to make a damper change during a red flag period, you would need to ensure that enough laps have been run after the session resumes to ensure that tyres reach the target pressure so that the data collected, and the driver’s feedback is relevant.
Moving away from how the tyre influences suspension characteristics, to the tyre’s performance itself reveals some other interesting motivations for tightly controlling tyre pressures. Fundamentally, a tyre produces a higher peak μ (friction coefficient) as you reduce its contact pressure. The contact pressure is defined as:
Where P is the contact patch pressure, F is the vertical load on the tyre, and A is the contact patch area. Therefore, for a fixed vertical load, if the contact patch area is increased, P is reduced, and by association, μ rises. This is clearly illustrated in Figure 1. In general, the contact area increases as tyre pressure decreases. This is only true to a certain point, and there is such a thing as running your tyre pressures to low which will be explored shortly.
One could imagine then, that with tyre pressures directly influencing contact patch pressure, you can directly control the grip a tyre produces. This becomes critical when one considers the grip across an axle, or front to rear grip which dictates vehicle balance. It is easy to imagine that, for left and right tyres of the same compound but at different operating pressures, the normalized tyre force produced will not be the same, causing asymmetric handling characteristics. If the driver mentions this in their post-session feedback, it can be really easy to be misled into making a setup change to compensate for this, even though everything will look normal in your post-session set-down numbers. Therefore, ensuring that tyre pressures plateau during the stint to be as equal as possible across an axle is critical to vehicle stability and performance.
Normalized tyre force (NTF) is a critical concept to grasp in vehicle dynamics, and essentially, increasing the normalized tyre force improves tyre performance. Normalized tyre force is a useful parameter as it describes the maximum force a tyre can produce while normalized for the vertical load exerted on it. Using this metric in our analysis of a tyre’s performance not only accounts for any tyre load sensitivity (for models that include it) but also allows for a fair method of comparison for tyres from data sets that have different applied vertical loads. The left-side plot of Figure 2 suggests that regardless of the sprung damping ratio, a higher tyre spring rate, and therefore tyre pressure, increases the NTF. The trend of increasing NTF with damping ratio is also quite encouraging, as it suggests that, as the sprung mass damping ratio, and therefore the vehicle’s body control improves, so does the tyre’s NTF. The results displayed in the right-side plot of Figure 2 aren’t so straightforward, suggesting that a lower tyre spring rate improves NTF at lower frequency suspension oscillations. Conversely, above the natural frequency of the vehicle body, a stiffer tyre produces a higher NTF. It’s worth noting that these plots were generated in response to a random road profile input, using Matlab code provided by Dr. E Velenis who is a Reader in Vehicle Dynamics and Control at Cranfield University.
Manipulating tyre pressures is also an effective way to try and change the limit behaviour of a vehicle. If a race car was reported to have a neutral balance, bleeding or adding tyre pressure to an axle can change the maximum tyre performance of that axle, which will alter the balance. It is common to try this when working in a series where the vehicles have limited balance tunning tools, or if you have professional drivers who can decipher if they prefer their rear tyres at say, 2.1 or 2.15 bar. If one were to run a set of tests to determine how pressure variation affects the tyre’s grip factor, it could also be used during a race. During an endurance race, if the driver were to complain about balance, but there was not enough time during a pit stop to make a balance change, one could prescribe a tyre pressure for the next tyre set which would be slightly staggered at their plateau, allowing for the balance to be corrected. This isn’t something that’s very commonly used, but it’s another tool to store in your race engineering toolbox for when it is eventually needed in your career.
The importance of controlling tyre pressure also has to do with its effects on the vehicle’s ride height. Fundamentally, each tyre has a defined unloaded radius, and at a given speed and vertical load, a loaded radius. For a given rotational speed, and vertical load, the tyre experiences a deformation proportional to its spring rate, which as defined previously, is also proportional to the tyre’s inflation pressure. The vertical load and speed the tyre experiences are dictated by the nature of the vehicle it is fitted to, its setup, and the track on which the race car is being driven. Therefore, tyre pressure is the remaining variable that a race engineer needs to be concerned with when analysing ride height data. As an example, if one were to calculate the end of a straight vehicle rake using laser ride height sensors, then it can change early on in a stint when tyre pressures are still growing. Furthermore, it could be difficult to define a setup that produces the desired end of straight rake if tyre pressures are not tightly controlled. For an order of magnitude estimation, the delta between loaded tyre radius at minimum and maximum tyre pressures in the same stint may be on the order of a few millimetres. This may not seem significant for your standard GT4 car, but for a Hypercar, that could mean the difference between excessive plank wear causing the team to fail post-race technical inspection. Ride height control for optimal downforce production has become increasingly important for modern F1 and LM(D)H cars that have seen recent regulation changes that emphasise downforce generation through devices in ground effect. Therefore, devising a process that returns tyre pressures consistently at their target not only ensures a more consistent race car but will be more likely to remain legal throughout an event as well. Tyre deflection on track can be estimated by comparing the roll gradient measured at your suspension potentiometers, with the roll gradient calculated by using laser ride heights. Subtracting the laser-based roll from the potentiometer-based roll exposes the increase in the roll due to tyre deflection alone. Without any tyre data, this can aid in a first estimation of tyre spring rate due to tyre deflection.
One final comment on the motivation behind tyre pressure control is due to safety concerns. At the beginning of a stint, to achieve your target hot pressures, you may need to start excessively low when the tyres are still cold. In extreme cases, if rules allow it, starting a set below 1.0 bar is not uncommon. As can be seen in the figure above, as the tyre pressure is lowered, the contact patch pressure begins to increase at the tyre’s shoulder. On an out lap, when the tyres are cold, pressures are low, and the contact patch pressure is concentrated at the shoulder, debris, or the excessive use of curbs can cause a puncture. In this case, the most common failure mode is a puncture through the tyre receiving a cut near the sidewall, where most of the vehicle’s load was being carried. This is why it’s common to tell drivers to avoid the use of curbing on their out lap. This safety concern is also something that must be considered by series when removing the use of tyre warmers, where sets of rubber can be mounted on the car hot, and therefore much nearer to their final pressures. The reality is, in the quest for ultimate performance, you’ll almost always start the tyre pressures as low as the series will let you, regardless of the chance of punctures, because the reward is typically higher than the risk.
In summary, if you can effectively set your tyre pressures such that you can ensure your tyre’s spring rate, contact patch area, and vehicle ride height will remain consistent over multiple runs while refining your setup, you’ve eliminated a set of variables in your equation for setting up the perfect race car.
Which Pressure Is The Best Pressure For Your Tyre?
With the motivation behind tyre pressure control cemented, the discussion around finding the optimal tyre pressure for a given compound and circuit can now be discussed. The word optimal can occasionally be misleading as it presents one solution as the outright best solution without consideration for some other important factors. As was alluded to previously, a race car tyre typically produces peak forces at a pressure much lower than that of a road car tyre. Finding this pressure can sometimes be difficult, as it requires lots of carefully planned track testing, plenty of sensory instrumentation, and ideally, a driver that can drive with high consistency and provide good feedback about the vehicle’s behaviour. Firstly, we must define a metric which describes tyre performance. A common method of assessing tyre, and vehicle performance, is looking at the value of the traction circle radius. The traction circle, commonly known as the G-G diagram, provides insight into the vehicle’s lateral, longitudinal, and combined performance. Therefore, the increase in traction circle radius denotes an improvement in vehicle performance. The computation of the traction circle radius is as follows:
When using traction circle radius as a calculated math channel in your data analysis program of choice, it computes the instantaneous traction circle radius of the vehicle for every logged data point over a lap. Taking a lap average or lap maximum value for TCRadius can reveal some interesting trends when plotted against data obtained from TPMS sensors.
The data above was taken from a race session during a race weekend in 2023, with the actual tyre pressure values removed. The trend is quite clear though, and there exists a set of tyre pressures that maximise the traction circle radius.
Looking at the same data set concerning temperature, it is clear once again that there is certainly a tyre temperature at which the tyre compound performs best. It is important to note that due to the potential difference in the compound, tread width, and diameter of the front and rear tyres, the optimal operating pressure and temperature for each may be different. For a simplified analysis, this article makes the above acknowledgement but assumes them to be identical.
Though the graphs above can seem quite convincing, it’s important to remember the caveats that surround this method of analysis. Firstly, the traction circle radius is highly dependent on the driving style of the driver, especially in combined loading conditions such as corner entry and corner exit. This is easily seen by the fact that two different drivers in the same car can have different G-G diagrams, even if the lap time they produce is nearly the same. Leaning further into driver consistency, it’s always wise to expand the data set to include as many relevant data points as possible to negate any inconsistencies from one lap to the next. As the traction circle radius is pace-dependent, different sessions may skew the data in different directions due to variations in session objectives and fuel load. In qualifying, the driver may spend a few laps bringing the tyres up to temperature before a push lap, which disproportionally represents lower tyre pressures and temperatures as having lower average TC values. Conversely, while near the limit on an early flying lap, the driver may happen to set a faster lap time with the tyres just outside the working window and then may make a mistake on the flying lap where the tyres were in their best operating region. In a race, one would need to consider the effects of pace management, fuel saving, a large fluctuation in ambient conditions as seen in endurance racing, the use of multiple tyre compounds, and multiple drivers sharing the same vehicle. Critically, one must not forget the data source from which they are obtaining pressure and temperature values. The dataset used for the graphs was gathered using a TPMS sensor which was mounted inside the tyre, on the inner shoulder of the rim, which measures internal tyre air temperature and pressure. As it’s mounted to the rim, the measurement from the sensor can be influenced by any heat source that can be radiated to the rim, such as the brakes. This is quite a significant effect, as while the vehicle is stationary in the pitlane after a long run, tyre pressures can be seen to artificially rise slightly as the rim heats up by absorbing the radiated brake heat, which is then transferred by conduction to the TPMS sensor. Finally, the temperature measured is the internal air temperature and is not an exact representation of the bulk temperature of the tyre carcass, which would be the ideal parameter to measure for tyre temperature and vehicle performance correlation.
Overcoming these sources of error is important for putting together a data set which is reliable enough to be analysed. From a data acquisition perspective, it’s important to equip your race car and its multiple rim sets with the same TPMS sensors such that the qualitative and quantitative concepts of the pressure measurement remain constant. When putting together a test plan to assess what the optimal tyre pressure is, it’s important to select a consistent driver, and a time of day when the track and ambient conditions stay relatively constant. It may be wise to prepare three new sets of tyres which target three different plateau pressures, and then complete long runs to not only assess peak performance but also the effect that different pressures have on tyre degradation. A more common, and cost-effective method, is to have the driver start on a set with a given target pressure, then come into the pitlane after a handful of laps, bleed the tyre set by a constant amount, and then resume running. In my opinion, it’s wise to make a substantial pressure change, on the order of say 0.137 bar, such that the changes in performance are not only easy to notice in the data, but it's also something the driver can feel. A shortcoming of the final method of tyre testing is that during the first stint, a good driver will use the peak of the tyre, and then subsequent pressure changes will never display peak traction circle values above the first run. Therefore, it’s important to ensure that comprehensive driver feedback is gathered to supplement any ambiguities one may find during their post-test data analysis.
Tyre pressures play a substantial role in driver confidence, and just because the data suggest that a certain tyre pressure is the best, the driver may not necessarily agree. In my experience, although being quicker on lower tyre pressures, drivers have reported feeling more vagueness through the steering wheel, when compared to tyres set to a higher pressure. The lack of feeling through the wheel can be detrimental to global performance, especially for amateur drivers. For this reason, with non-factory drivers, it may be important to consider how the drivers feel about different tyre pressures.
Defining The Window Of Performance
Though a tyre has a theoretical temperature and pressure which produces the highest traction circle radius, we must define how far we can deviate from the target before performance drops significantly. A common phrase I’ve used in the past is “in the window”, which more descriptively, is the vehicle’s optimal performance window. In this article, I propose a more mathematically rigorous definition of the performance window.
Figure 6 shows a significant correlation between traction circle radius and lap time from the same dataset, which means there is a mathematical relationship between the two variables which can be used for the next step. Here, the gradient of the graph represents the lap time sensitivity to the traction circle radius in units of seconds per acceleration measured in g. By fitting a second-order polynomial, the relationship can be quantified.
Similarly, fitting a second-order polynomial for each tyre, and then taking an average for each term of the quadratic equation yields a general representation of the traction circle radius sensitivity to tyre pressure. The gradient of this function is the traction circle radius per unit of pressure.
Now that we have both parameters modelled, we have to define an allowable lap time loss due to missing the pressure target which produces the maximum traction circle radius. This can be done by quantifying the consistency of your driver over multiple data sets to understand what the typical lap time variation would be when the setup, and ideally ambient conditions are held constant. A good measure of driver consistency is the average delta of a set of laps with respect to the stint average pace. By dividing this value by the mean lap time, we can quantify a normalized consistency value that is independent of the overall lap time. This means that this measure of consistency should be fairly constant from one track to the next, but this will never completely hold due to the discrepancy in driver confidence at each circuit. The results for my data set were as follows.
So from Table 2, it’s clear that the variation in lap time due to the driver’s capabilities alone is nearly three-tenths and a half per lap, but this will vary based on the driver’s skill. Something worth mentioning here is that the data used for these calculations does not use fuel-corrected lap times, or lap times corrected for predicted tyre degradation, as these topics will be covered in a future article. Correcting the lap times for those key parameters will provide a better indication of your driver’s actual consistency capabilities, independent of those external factors. Table 2 also suggests that if we can limit the absolute variance of vehicle performance to within the value suggested by the table, then it would be relatively insignificant with respect to the consistency contribution from the driver.
Referring back to Figures 6 & 7, with this lap time variation, we can compute the allowable variation in the traction circle radius, and the associated required tyre pressures to achieve that traction circle radius.
Table 3 demonstrates that by calculating the window of the traction circle radius due to lap time inconsistency, there exists an associated range of pressure that, if exceeded, the contribution of the performance loss due to the tyres is larger than the performance variability from the driver. Due to the parabolic nature of the TC Radius – Tyre Pressure relationship, two tyre pressures satisfy the desired traction circle radius, each lying equidistant from the tyre pressure that produces the highest traction circle radius. This assumes that the relationship is perfectly parabolic, even though in reality it likely isn’t, but with many data sets, this relationship could be further refined, and the same principles can be applied. Importantly, the sets of pressures that satisfy the desired traction circle radius form the basis for the window of performance. It’s quite clear that, as the traction circle radius increases, the range of tyre pressures that allow the tyre to perform in this manner, decreases. The trend of the decreasing size of the tyre pressure window continues until the window size shrinks to zero when the tyre pressure that produces the largest traction circle radius is reached. At this maximum, any change in tyre pressure may cause a loss in global vehicle performance, especially if the magnitude is larger than the error bounds defined in the chart. Lastly, by estimating a peak traction circle radius from the TC Radius – Tyre Pressure, we can estimate what lap time we would achieve at that peak value, and the tyre pressure required to achieve it.
So essentially, we’ve defined how much we can over/undershoot the tyre pressure target before the performance loss is significant. We’ve also characterized a window of performance that describes not only how forgiving the tyre is, but also which pressures are associated with certain performance targets. The reason behind devising a method to quantify a performance window is to improve communication with our drivers. The best drivers can intuitively feel when it’s time to push in qualifying, but for those who need it, we can instruct drivers to push once the pressures have surpassed a certain threshold. When speaking with the driver about the window of performance, we can explain that when the tyres are +/- 0.160 bar away from the target, we can achieve a lap time 1.1 seconds away from our theoretical best, and the closer we are to our target pressures, the faster our pace will be. It’s worth mentioning that in scenarios where peak performance is not always required, such as during endurance racing, the pressure window to deliver consistent lap times approximately 0.500s off ultimate pace only requires one to be with +/- 0.118 bar of the pressure target. Of course, you should always do everything possible to achieve the pressure target, and any extra peak performance gained is useful as for a given required cornering force, tyres producing a higher μ require less energy to do so. Tyre energy spent over a stint directly correlates with tyre degradation, so the goal is very clearly to generate the maximum μ possible at all times.
One final note is that the range of tyre pressures required to meet a certain lap time offers insight into how forgiving the tyre compound is. One brand of tyre might produce a higher peak traction circle radius while offering a narrow window of performance, while another tyre might be ultimately slower while offering a wider range of performance. This is critical to consider when working with the same race car across multiple series that may use different tyre compounds.
Tyre Pressure & Temperature Behaviour
With the methodology behind finding the best tyre pressure for your compound sorted, it’s important to talk about the relationship between tyre pressure and tyre temperature, and tyre behaviour on track. Assuming no leakage, a tyre can be said to have a finite and consistent volume, meaning the ideal gas law can be applied to quantify the relationship between pressure and temperature.
This equation shows that pressure and temperature are directly proportional to each other. While holding tyre volume constant, the isochoric state change from an initial state to a final state can be represented as follows.
This equation suggests that, with an initial temperature and pressure known, we can predict a final pressure if we know a final temperature, and vice versa. The point of measurement of the temperature here is the temperature of the air in the tyre, which is a function of the tyre’s bulk temperature. In racing, it’s very common to select a pressure to accompany an expected temperature because the tyre temperature is directly proportional to the expended tyre energy. The tyre energy is largely dependent on the circuit layout, which dictates the distribution of tyre energy around the race car. The asphalt compound and circuit layout also determine the magnitude of tyre temperature from one circuit to the next. Furthermore, a tyre’s temperature is also influenced by the vehicle’s setup, driver capability, and critically, both the track and ambient temperatures.
In Figure 8 we quantify our tyre’s pressure–temperature relationship by truncating the data to only the linear region of tyre growth as shown in Figure 9 and plotting a scatter plot of tyre pressure with respect to temperature. Additionally, by plotting a trendline for each, we can take the slope of each trendline to represent the increase in tyre pressure per unit of tyre temperature. The values you receive for the slope of this trendline must be nearly identical for tyres that have the same internal volume. We will later discuss what is happening if this is not the case. In my experience, even though front and rear tyres rarely have the same dimensions, the increase in pressure per unit of temperature is almost the same regardless.
Figures 9 and 10 represent the general behaviours of tyre pressure and temperature over a stint, respectively. Looking further at Figure 9, the three distinct phases of pressure behaviour have been labelled accordingly. Tyre pressure typically grows linearly, until it reaches a plateau, and at the point of the plateau, if the pressures were set correctly, they all would have converged at the target. This specific graph is a very good example of this, with pressures reaching the target, and the spread across the set was no more than 0.027 bar. In reality, given all the factors previously mentioned, this can be difficult to achieve consistently. Fundamentally, since the pressures are driven by the tyre temperatures, if the driver has a sudden burst in pace, and more energy is exerted by the tyres to match the load demanded by the driver, the tyre temperatures rise, and the pressures rise with them. On the other hand, tyre pressures are known to drop significantly during a safety car period, once again due to a lack of energy being put through them. Therefore, it’s clear that the driver’s pace plays a very important role in dictating the spread of temperatures and pressures.
Diving deeper into Figure 10 reveals some interesting phenomena. The green trace had a relatively low starting temperature, but climbed quickly and was by far the hottest tyre at the plateau. Conversely, the blue tyre was the second hottest at the start, but after having the slowest buildup, it was the coolest tyre in the plateau region. In the initial linear pressure growth region, we see that, although the tyre pressures are almost all identical, the pressures are growing at different rates. This suggests that, in terms of the vehicle balance and the tyre µ correlation with temperature quantified in Figure 4, this growth region is quite a transient period for vehicle balance as it changes until the tyre temperature plateaus. The spread of the tyre temperatures and the difference in their growth rate is due to the layout of the track. It’s clear from the trace that the green tyre is heavily stressed, while the blue tyre is the least stressed, suggesting that the green tyre is typically the outside tyre for most corners, while the blue is usually the inside tyre of one of the axles.
In the final race weekend of 2023, a gearbox failure after the second qualifying forced the team to use a spare car from another team for the second race. As there was a very limited amount of time from when we received the car to the start of the race, we never had the chance to apply our setup to the new car. In Figure 9, the green traces are from the Saturday race, while the red traces are from the Sunday race. First and foremost, it’s important to comment on the magnitude of the tyre temperatures, and the general trend is that values from the Sunday race were lower than those of the Saturday Race. Looking at the ambient temperatures, on Saturday the air temperature was 10o C warmer, and the track temperature delta between the Saturday and Sunday races was 5 o C due to extra sun exposure. It’s quite clear then, that even seemingly small changes in external temperatures can vary tyre temperature significantly. Interestingly, the right rear tyre temperature was the only tyre temperature that increased relative to that same tyre’s temperature the day before. Looking at the balance metrics from that race shows that the driver experienced in excess of 10% more oversteer during Sunday’s race. This suggests that the extra tyre temperature generated in that corner was likely due to excessive rear sliding. It’s worth mentioning that with excessive sliding, one would expect both rear tyre temperatures to increase significantly, but this is still a partial explanation for what is been seen in Figure 11. Furthermore, a setup with more oversteer suggests that the spare car was running a stiffer combination of springs, anti-roll bars, or possibly even higher ride height at the rear, with respect to the setup run the day before. When compared to a soft setup, a stiffer rear end would also be responsible for a higher proportion of the lateral load transfer distribution during cornering, increasing the rear tyre vertical loads, and therefore increasing their temperature.
Since the setup of the vehicle plays some role in dictating the tyre temperature distribution, this concept can be applied when making setup decisions. There is a good thought experiment that can be carried out to help understand how tyre temperatures can be used to tune vehicle balance. Say the driver is consistently complaining of understeer at most corners around the lap, in the steady state mid-corner region of the cornering phase. In your experience, you choose to soften the front anti-roll bar to move the lateral load transfer distribution rearwards, effectively making the front end more “powerful”. After the change, the driver goes out for another stint and the understeer is reportedly worse. Initially, this is concerning, as this vehicle behaviour can come down to many factors, including the driver misreporting what they feel, or a mechanic going the wrong direction with a setup change. After looking at the data though, the TPMS data suggests that the front tyres were not hot enough to reside within their optimal window of operation, therefore causing them to underperform, and the driver to report understeer, with the softening of the front bar worsening this effect. In this scenario, a beneficial setup change would be to do something counterintuitive and stiffen the front anti-roll bar such that the front tyres would see more load due to the increase of lateral load transfer distribution on that axle. The increase in load would be followed by an increase in tyre temperature, which would then bring the tyres back into a window where they’re generating a higher µ. This phenomenon isn’t a common occurrence, but in situations where external temperatures are too cold, this may be something to consider if setup changes to correct the vehicle balance aren’t performing as expected.
As tyre energy coincides with the area under the graph of the lateral force-slip angle curve, it can also be said that increasing your static toe value may directly increase your tyre temperatures as well as your rolling resistance. Rolling resistance itself plays a significant role in tyre temperature generation, as an increase in rolling resistance is associated with more tyre deformation and the additional stress and strain cause the tyre to heat up. It’s been said that, upon the introduction of the thinner sidewall 18 in tyres for the F1 2022 season, the reduction in rolling resistance from the old tyre construction was so significant, that this factor alone contributed to an approximate 10 C drop in tyre temperatures for equivalent compounds.
So tyre temperatures and therefore pressures are demonstrably sensitive to ambient and track temperatures, but why is this the case?
In Figure 12 we assume that the graph follows a single point on the surface of the tyre as it completes a full rotation. Area one represents the decrease in tyre temperature due to the heat transfer by the method of conduction of the tyre with the asphalt surface. In this region, the contact patch is not yet sliding and generating any heat, therefore as the tyre is assumed to be hotter than the track surface, it loses heat to the track and cools slightly. The amount of heat transferred to the track in this region is very sensitive to the temperature delta between the tyre and the track. In the second region, significant heat is generated when the contact patch begins to slide. The point we’re monitoring on the tyre is still in contact with the track, but the heat transfer to the track is insignificant with respect to the heat generated, and therefore the tyre temperature increases. In area three, there is heat transfer with the surrounding air, but the heat transfer method is by convection at this point. The delta to the right of the graph shows that, before thermal equilibrium is reached, the tyre ends the cycle with a higher temperature than it started it with. Thermal equilibrium is reached when the heat generated at the contact patch, is equal in magnitude to the heat rejected to the track and surrounding air. Since, over a short period, say a lap, track and ambient temperatures can be assumed to be constant, the increase in tyre temperature is directly related to the heat generated at the contact patch. As the driver’s pace increases, the energy at the contact patch increases as well, which is why the driver has a direct influence over their tyre temperatures. It must be noted that there are other more important methods of tyre temperature generation, notably bulk temperature generation through tyre carcass strain. This has been covered by Pat Symonds in his tyre articles in Race Tech magazine, so I invite you to read those as they are very compelling. With that said, this surface representation of tyre temperature still offers an intuitive explanation of the phenomenon of tyre temperature sensitivity to track and ambient temperatures. As Figure 10 shows, in reality, tyre temperatures may never reach a thermal equilibrium, especially in transient scenarios such as qualifying. It’s important to keep this in mind, as although these academic explanations are effective, they can be scarcely experienced in practice.
In summary, the track layout and asphalt compound used, the track and ambient temperatures, and the driver’s pace dictate the global magnitude of the tyre temperatures. The track layout, vehicle setup, and driver’s driving style dictate the temperature distribution of the tyre temperatures around the vehicle.
Setting Tyre Pressures
Without further ado, we must discuss how to calculate and set tyre pressures as a race engineer. The previous sections up to this point have been critical to build a complete understanding of why we want to set tyre pressures in the first place, how to find the best ones for your tyre and car, and the relationship between tyre temperature and pressure. With these concepts solidified, one should now be able to approach setting tyre pressures with sound methodologies and should be able to clearly explain their choice in target pressure, as well as expected results given a set of starting pressures.
Before we continue it's imperative that we establish some of the terminology used at the race track surrounding tyre pressures. The phrase “cold pressures”, represents the initial pressure that you set your tyre to before it gets mounted to the car. On the other hand, “hot pressures” is a term used to describe the pressures that are reached in the plateau region.
The Process
The general process of setting your tyre pressures is as follows:
1. Make an initial estimation of the tyre pressure required to reach your target pressures
2. Set your cold pressures with a desired hot target pressure in mind
3. Record session metadata
4. Use data to confirm the plateau pressures and temperatures
5. Adjust, iterate, and scale accordingly
Initial Tyre Pressure Estimation
If your team has solid documentation, then assuming you’ve been to this track in the past, making an initial estimation on where to start your tyre pressures for that weekend should be dependent on what worked during previous race weekends. If you have been to this track but your records are poor, yet you have some TPMS data available, it is possible to back-calculate the tyre pressures required using the plateau temperatures. This can be done by using the following equation:
Where all pressures and temperatures are expressed in bar and Celsius, respectively. In this equation, represents your cold pressure at temperature , and signifies your desired target hot pressure which occurs at a temperature of . If you have previous TPMS data from a circuit, you can use this equation by inputting the target hot pressure, and final tyre temperature for that specific tyre, and it will return a cold pressure for an associated temperature. Doing this for all four tyres using four different plateau temperatures yields four starting cold pressures. Explicitly, tyres require different cold pressures because they reach different plateau temperatures. At this point, it’s critical to remember that due to the pressure–temperature relationship in Figure 8, there exists a cold pressure for every initial temperature. In this case, the initial temperature is usually taken as the ambient temperature, but there are several cases where this approximation doesn’t hold. Oftentimes, the temperature of the air inside the tyre, and the ambient temperature are different. One common example of this is when tyres are left in the sun, their internal temperature increases due to the black colour of the rubber absorbing a high percentage of the incident radiation emitted from the sun. A common remedy to this is to always keep tyre sets in a shaded area, such as under a tent or in a garage, such that they are at equilibrium with their surroundings. If you must place the tyres in a sunny area, it is good practice to set the tyre pressure before they leave the shaded area. Another example of this delta between ambient and internal tyre temperatures can occur when the tyres are mounted to the car before being set, and then the car is switched on and warmed up. In my experience with mid-engine race cars, this is of particular concern with the rear tyres, with the nearby engine and exhaust manifolds radiating their heat to the tyres. This is where communicating with the mechanics to ensure that pressures are set before the tyres leave the shaded area, or are mounted to the car, is so important. It is possible to measure a tyre’s internal temperature using handheld TPMS scanning devices, but I prefer to reduce as many sources of error as possible rather than compensate for them by adding extra processes to an already stressful work environment.
You may be wondering, if you have TPMS data, why not go back to the beginning of the data file and take the first data point as your starting pressure? This may seem tempting, but in practice, I haven’t found that the data points match exactly what I prescribed the pressures to be. This may be due to a difference in the tyre pressure gauge reading and the TPMS sensor reading, or more likely because the datalogger wasn’t recording when pressures were set as the vehicle was switched off. By the time the logger and vehicle are switched on, the tyre pressures would have been influenced by the vehicle’s warm-up performed before exiting the garage.
If you haven’t been to a track before and have no data, then it is still possible to make some initial estimations of cold tyre pressure distribution. Firstly, surrounding the magnitude of the cold pressures, the growth rate of the pressures from their cold state to stabilization is a fairly consistent value. Dividing the target hot pressures by an estimated growth rate from other data sets should allow for an initial approximation of what the mean cold pressure will be before there is any compensation for tyre energy distribution. The primary method of determining how much each tyre deviates from that mean is by looking at the distribution of left - and right-hand corners, and how much time is spent in each.
Using my home track of Mosport as an example, it has 6 right-hand corners (we usually separate 5a/b) and 3 left-hand corners and the rest of the curves have insufficient curvature to be classified as a proper corner. Furthermore, most of the right-hand corners produce high tyre vertical loads such as turns 1, 3, and 8. When turning right, some vertical load is transferred off the right-inside tyre, and to the left-outside tyre. Since the side that typically sees more vertical load and will exert more lateral force, it will generate more tyre temperature. To compensate for this additional temperature, and to ensure the left side tyres don’t overshoot the pressure target, we lower the left side tyre pressure with respect to the mean pressure discussed before. Since the right-side tyres generate less mean lateral force over a lap, and therefore less temperature, we can raise tyre pressures on the right side to compensate for this as well. Using this logic, we’ve just arrived at a basic starting pressure prescription for a track we have no data for.
In modern motorsports, the days of arriving at a circuit with little to no understanding of how your vehicle will perform there are long gone. Many advanced simulation tools have tyre energy as a data output, or at the very least return the slip angles at every instance in time. Even the most basic of simulation tools would allow you to better quantify the percentage of time spent in left- and right-hand corners, allowing you to refine your predictions with respect to the method above. Furthermore, the use of driver-in-the-loop simulators allows for more accurate characterization of tyre energy usage due to differences in driving styles, which once again, only improves your predictions of vehicle and tyre pressure behaviour.
Back to the more practical side of things, when selecting your first set of cold pressures, it’s important to leave some margin such that the pressure plateau is surpassed during the first on-track session. It’s easy to bleed down to your target in the pitlane if you’ve got it wrong, but inflating a tyre in the pitlane can be difficult to do and time-consuming.
Setting Your Pressures
As previously mentioned, you need to set your target pressures while the tyre set is still in the shade, or before the race car is put through a warm-up cycle. When you do go to physically set the tyre pressures you need to be mindful of a few things. Firstly, once the tyre pressure is set, do not go back and check it again. After setting the tyre pressure, if you go back to measure it, it will always be slightly higher than what you set it to. So then if you bleed it again to match your pressure prescription, you reduce the amount of air in the tyre. The best philosophy when setting pressures is to always remain ultra-consistent in how you physically set them. If you are consistent, the error in setting tyre pressures from one set to another is strictly absolute, and your calculations are more likely to align with your expectations. This is why, when setting tyre pressures, if the mechanics do it, I always have them tell me when it’s done, just so I don’t go check myself, see a different value than I requested, and do a secondary bleed down. When you do set the pressures, ensure that you record the internal temperature (typically ambient temperature) at which you set them, this will be needed for pressure compensation due to ambient temperature change from one set to the next, which will be discussed soon.
Recording Session Metadata
With the car now out on track, your ability to accurately and consistently record metadata may be one of the most important factors that will dictate how successful you are in setting tyre pressures for your next tyre set. As mentioned in the previous section, the first temperature-related data point that needs to be recorded is the internal temperature of the tyre when initially setting the pressure. When the tyre set is being used during the session, it is good practice to take multiple samples of track and ambient temperatures to understand their magnitude, and how they evolve during the session. When measuring track temperature, it is common to walk into the pitlane and take a reading but one must pay attention to where the tip of the pyrometer is placed. Consider if the area of the track you’re probing was recently in the shade, or if the colour of the asphalt in the pitlane is different from the track. If there is a difference in asphalt colour, there will be a difference in the amount of radiation absorbed from the sun, and your reading won’t be representative of how hot the track surface is. However, as long as the track temperature reading is taken from a consistent spot, the error associated with the measurement will be low. Your run sheets should also keep detailed records of what the tyre pressures were measured at when they arrived in the pitlane, whether that measurement was taken through a gauge or TPMS, and what you bled them down to if you decide to do so.
The Calculation Process
With initial pressures set, and data gathered from the previous session, it’s time to discuss the process of calculating your tyre pressures for the next session. The general process of calculating tyre pressures for the next tyre set is as follows.
Figure 14 displays the parallel workflows required to effectively and consistently calculate tyre pressures for the next tyre set, given recorded data from the previous set. It’s typical to re-create this workflow in a program such as Excel or Matlab, which not only makes the calculation instantaneous but also provides a method of storage for each tyre pressure data set. So far, in the writing of this article, the topic that hasn’t been covered as of yet, but makes up the majority of the intellectual property of the pressure calculator, is related to Figure 12’s cells 7 and 9. The temperature compensation due to changes in track and ambient temperature is effectively the most important part of every tyre pressure calculator, so it’s important to tune those to how you see fit. The units for the compensation values are your pressure unit of choice per unit temperature, and when multiplied by the delta taken from the previous cell, the final result is a compensation value in pressure.
Something interesting that I spent a lot of time developing during the 2023 season was cells 10 and 11. In motorsports, it’s common to set your tyre pressures for the first session early in the morning just after arriving at the track, when the ambient temperature is still very cool. When doing the same in the afternoon, the ambient temperature could have climbed significantly, so it’s worth investigating what effect that has on cold tyre pressure migration throughout the day. As a thought experiment, let’s say you set your cold tyre pressures to be 1 bar in the morning when the internal tyre temperature is 15 C. You want to use the same cold pressure for an afternoon session, but the temperature is now 30 C and your tyre's internal temperature matches ambient conditions. In this scenario, if you were to set your cold pressures at the higher temperature to 1 bar, you would not reach your target pressures.
Figure 15 illustrates the problem at hand. To set your cold pressure when the temperature is 30 C you must compensate them for the temperature increase with respect to your old set. I call this phenomenon, respecting the line of growth. The method of compensation is performed by multiplying the pressure-setting temperature delta between tyre sets, with the pressure-temperature relationship obtained by plotting a trendline in Figure 8. For this example, say that for every degrees Celsius increase in temperature, the increase in pressure is 0.01 bar. Therefore, with a 15 C delta in temperature between setting the first tyre set, to the second, the required pressure compensation is 0.01 bar/ C * 15 C, which yields 0.15 bar. That’s a very significant change in pressure, as your new starting pressure at 30 C would have to be 1.15 bar. It’s important to note that this final pressure is solely pressure compensation for the sake of tyre set temperature, and would need to be further compensated for the ambient and track temperature differences between sessions. Regardless, the effect is quite significant, and without this temperature compensation, you may find yourself missing the tyre pressure target quite often at tracks that have large daily temperature swings.
Tyre Temperature Scaling
Another process I spent much of 2023 studying was scaling tyre pressures to effectively reach the target pressure at a specified lap in qualifying. In a pre-qualifying engineering brief, you have discussions with your driver about how many warm-up laps, and how many push laps you expect them to do during the session. After the target number of laps is set, one must calculate the cold pressures required to reach the target pressures at the start of the push laps. The reason this pressure scaling is needed is because typically, the driver won’t reach the pressure-temperature plateau in the small number of laps completed in qualifying. To calculate the new cold pressures required to reach the target in the defined number of laps, the calculation process is nearly identical. In this scenario though, instead of looking at the pressure values in their plateau state, you input your pressures achieved in the previous session at your target lap, into cell 2 from Figure 14. This will return the required qualifying cold pressures, which should be higher than your cold pressures from the previous non-qualifying sessions. It is important to consider, however, that since the pressures will not plateau at the push lap, subsequent laps will continue to see pressure growth. Using the principles described in Table 3, one should be able to estimate the window around your target pressures where running additional laps is still beneficial for performance.
Baking Tyres For Qualifying
In the previous section, it was mentioned that due to the small number of laps completed in qualifying, the tyres may never reach their pressure-temperature plateau. Therefore, a qualifying tyre is effectively temperature-limited, and any attempts to boost the initial tyre temperature can increase the final tyre temperature closer to what would be seen at the plateau, which would improve performance. A higher initial temperature means fewer laps are required before the push laps begin, allowing for fewer total laps to be completed in qualifying, which is a concept that is especially important at tracks with higher tyre degradation. One common method that is legal in most series is the practice of “baking” the qualifying tyre set in the sun. The process of doing this is as follows; set the qualifying tyre pressures in the shade, place them in the sun on top of a black blanket with the inside of the rims facing up, and check on them every once and a while to ensure they’re still in the sun and not being covered by shadows. The second method is the same, except the pressure setting is done just before the session starts. Then, using the value of the baked tyre’s internal temperature in the pressure-temperature compensation cell, you adjust for the fact that you’re setting pressures on a hot tyre. Both of these methods are just suggestions, and further experimentation is required to select the one that works the best, but I used both methods in 2023. In general, the findings surrounding the tyre baking experiments performed in 2023 were that a substantial increase in initial temperature was obtained. So much so, that the increase in temperature over a set that was not baked, was on the order of temperature gained by completing an extra lap in qualifying. The temperature increase would not only allow the driver to complete a push lap earlier in the run, but reducing the amount of laps necessary to reach the tyre’s operating window also means one could potentially prescribe a shorter qualifying run, allowing for a lighter fuel load. Tyre baking is a semi-controversial topic up and down any paddock, and while some swear by it, others choose not to utilize it. The results obtained from baking experiments in 2023 objectively suggest that tyre baking is a positive practice, but completing tests to validate these findings is always suggested.
Wet Tyre Pressures
One of the most widely discussed topics surrounding tyre pressures is how to set cold pressures for rain. Before even proposing a solution for a rain tyre, one may find themselves running a slick tyre in damp conditions. In my experience, it's safe to increase your cold pressure for a slick tyre on a damp track by a fixed amount. This is because, with a damp track, the cooling effect of the water on the asphalt will lower the maximum achievable tyre temperature and pressure. The amount by which this occurs is very difficult to quantify, so in this situation, you may want to err on the side of caution and increase the cold pressure values by approximately 0.07 bar. Fundamentally, you know that left unadjusted, the tyre set won’t hit your desired target, so the bump in pressure is a safe decision. Though the proposed value must be taken with a grain of salt, as, with all damp tracks, they inevitably dry out. Having a thorough understanding of the weather trends of the day is always helpful, and this is true for tyre pressure setting in general regardless of whether it rains or not. This is a scenario where having experience is invaluable, and that experience will guide you to adjust the cold pressures based on what you’ve encountered in the past.
Wet tyre pressure methodology follows the same philosophy as tyre pressures for slicks on a damp track, except tyre manufacturers may provide a target pressure for their wet tyres, making the process slightly easier. Apart from trying to get the wet tyre pressures in their desired window, one must also consider the other effect that tyre pressures have on rain tyres, their ability to clear water. In general, the higher the tyre pressure of a wet set, the stiffer the tread block becomes, and their ability to clear water improves. For this reason, there have also been discussions of running front-to-rear pressure splits for wet tyres as running higher pressures in the front improves the water-clearing ability of the lead axle. I have no experience using this tactic, but it is certainly something worth considering the next time it rains. When deciding on a global scaling factor for your wet set there are a few important things to consider. The first is the amount of water on the track, and as this increases, the tyre pressure required to clear it does as well. Secondly, one must once again think about the change in weather and the potential formation of a dry line. If you’re expecting the track to dry up by the end of the stint, then you may want to start slightly lower than you would if the rain was persistent. There is also the so-called quenching effect, which is once again hard to quantify, but it’s the principle that the extreme amount of water on the track seriously reduces the build-up of any meaningful tyre temperature. With these considerations, we can arrive at the following wet pressure suggestions.
Table 4 presents suggested values for wet tyre pressure scaling. These values are based on my own experience, and may not reflect what is required for your specific tyre compound or vehicle. While the table does not provide the ultimate solution for every scenario, it should serve as a strong starting point that can be refined for your application.
Managing Uncertainties
One of the most difficult aspects surrounding tyre pressures is managing the uncertainties that inevitably arise with trying to repeatably achieve accurate and precise results. One of the first choices you will make as a race engineer with tyre pressures is whether you set your pressures with data obtained with TPMS, pressure gauge data as measured in the pitlane, or a combination of both. From experience gathered from personal testing, it is not uncommon to see differences in measurement between the sensor installed within the tyre, and a pressure gauge, so which one is correct? In theory, the discrepancies between the two are minor enough such that, in reality, it doesn’t matter. What is more important is that, whichever method you select, you remain consistent with that method over a race weekend, and over a season. If available, TPMS data can offer certain advantages that a pressure gauge reading doesn’t. Firstly, even assuming the driver was pushing on their in-lap, pressure gauge data is inherently skewed by the distance from the pit entry to the pit box, where pressures will drop slightly as the tyres cool in the pitlane. Secondly, say there were two left-handed corners right before pit entry, then the pressures measured in the pit box will show the right-side pressures to be artificially inflated due to the lateral force they exerted just before the pitlane. If available, TPMS data can help to overcome these inconsistencies by allowing for analysis using lap-average pressure values, which is what should be considered when looking at plateau pressures and temperatures. Referring back to Figure 9, the spikes in the pressure trace represent the rise and fall of tyre pressures as tyres are more heavily loaded in one corner, and less heavily loaded in the next. Looking at lap average pressure values helps give a global picture of how the tyres are building temperature and pressure, without focusing on aspects out of our control.
It was mentioned earlier that tyre pressures are significantly affected by the pace, and driving style of the driver. This can cause issues when some tyre pressures will plateau differently than expected, even when the cold pressure split didn’t deviate much from the previous set. Therefore, it can be said that there is a stochastic element to tyre pressures, so it’s worth touching on the methodology we use to cope with this uncertainty. From the first set of pressures prescribed at the beginning of the weekend to the last, every time cold pressures are set, it’s effectively an iterative guess at the pressures required to reach the target pressure, with the intent of reducing your error to the target each time.
Plotting tyre pressures in a manner similar to Figure 16 allows you to better understand the direction you’re trending in with respect to your prescribed cold pressures. Occasionally, when a pressure reading from a run is much different than expected, it’s worth investigating why that difference occurred, rather than just instantly compensating for it in your next set of cold pressure values. If the cold pressure trend has been consistent all weekend, and it’s clear the error to the target has been reducing, then one outlier shouldn’t skew the remaining calculations. By the end of a race weekend, it’s typical that the adjustments being made for cold pressures are purely for ambient condition compensation, and not for adjusting the front-back/left-right split amongst a set as the pressure trend has strongly converged. Data can be misleading, so understanding the evolution of tyre pressure, set-up, fuel consumption, and other aspects of the vehicle are all important in helping to avoid being deceived by one-time occurrences.
How To Confirm If Your Tyres Were Filled With Nitrogen (Or Dried Air)
One of the most prominent tyre pressure uncertainties you’re bound to face at some point is investigating whether your tyres were prepared correctly. In Figure 8, we discussed that the tyre has a quantifiable and consistent pressure-temperature relationship, but this only holds if the tyre is inflated with a gas containing as little humidity as possible. Humid air can drastically increase the expansion of a gas per unit of temperature, so the effective growth rate for a tyre filled with a humid substance is much higher than one with zero humidity. In North America, to get around this issue, it is commonplace to have tyres purged multiple times, and filled with nitrogen which is a stable gas that, in my experience, has offered a high consistency in terms of the growth rate of the tyre due to the gas alone. I understand that the trend in the UK and Europe is to use dried air to achieve the same effect. Regardless, after receiving an errant pressure data point, one of the first questions we ask the tyre team was if the tyres were filled with nitrogen. As engineers, we can answer this question ourselves by re-creating Figure 8 and comparing the growth rate of the questionable tyre set, with the previous tyre sets that behaved more uniformly. Something to keep in mind is that tyres are also seemingly sensitive to having been exposed to rain before being mounted. There is a general understanding up and down the paddock that once water makes contact with the inner lining of the tyre, it gets absorbed, and then continuously released after the tyre is inflated. This causes the gas in the tyre to be humid, and therefore that tyre will have an inconsistent growth rate. It’s common practice to not only have good coverage of the tyre technicians' work area but to also pay close attention to loose tyre sets when the weather is looking ominously like rain.
Working As A Team
Last but certainly not least, being a strong communicator within your team is one of the most important aspects of not only effectively setting tyre pressures, but being a talented race engineer in general. Many speak about the act of setting tyre pressures but don’t acknowledge whose responsibility it usually is to do so, the mechanics. Therefore, it is your job as the engineer to present the desired cold pressures to the mechanics, such that they have enough time to set them before a session begins. Furthermore, sometimes the mechanics are responsible for collecting the necessary metadata for setting pressures when you’re not present in the pitlane, so helping them build an understanding of what you need and why you need it often helps reduce the frequency of missing data points. All of the tyre pressure and tyre baking experiments that we conducted in 2023 were only made possible because everyone on the team was aware of the plan to do so before it was executed. After tyre baking became a common practice for us, it was often reiterated in that race weekend’s pre-event report so the team entire team would know what to expect beforehand. Working with your tyre team to talk about which tyre sets can be discarded, and what sets need to be ready for the upcoming sessions is critical. You have to be considerate of the workload that others have, not just what is at hand for you. Expressing to colleagues ahead of time, when wet or dry sets need to be ready in the pitlane helps to keep the team calmer when situations are highly transient. A calmer team thinks with more clarity, makes fewer mistakes, and achieves the highest results.
Conclusion
What was originally intended to be a short blog post discussing tyre pressures, quickly spiralled into something much deeper than I could have ever expected. When all is said and done, the tyres are the only four points at which the race car makes contact with the track, so improving tyre performance through any means possible will always lead to a pace improvement. This article has set the motivations behind effectively setting tyre pressures and finding the best tyre pressures for your tyre. It describes the tyre pressure-temperature relationship, and once this knowledge has been absorbed, we can then knit everything together to discuss how to calculate your desired tyre pressures. This post has truly been a pleasure to write, and I’m not only thankful for the topics I’ve learned but also for everyone who has helped me develop my own set of trackside methodologies since starting my career in motorsports back in 2020.
Acknowledgements
I must thank my team at R. Ferri Motorsport who stood by me during my moments of madness during the 2023 season. Working within an experienced team and constantly discussing these topics with the team manager Enrico, really helped to solidify my methodology. I also always had support from everyone on the team when I wanted to experiment, which is something that I’m very grateful for. All the data in this article is taken from my time at R. Ferri Motorsport, specifically during the 2023 season, but all sensitive information has been removed out of respect for the team.
A final acknowledgement goes to my professors of Advanced Motorsports Engineering at Cranfield University, who have provided me with the knowledge to produce some of the figures in this article, or the code required to generate some of the data. To find out more about the Advanced Motorsports Engineering program, visit www.cranfield.ac.uk/courses/taught/advanced-motorsport-engineering.