The Engineer's Handbook to Racecar Tyre Inflation Pressure
The Engineer's Handbook to Racecar Tyre Inflation Pressure
In the high-stakes motorsport arena, tyre pressure is critical in determining a racecar's performance, directly impacting handling, grip, and overall tyre life on the track. Optimal tyre inflation pressure ensures the best possible contact patch, providing maximum traction and stability, while incorrect pressures can lead to excessive heat buildup, increased rolling resistance, or reduced grip. Additionally, tyre pressure is a dynamic variable influenced by track temperature, driving style, and track conditions, requiring continuous monitoring and adjustment throughout a race. This article explores the intricacies of racecar tyre pressures, examining the underlying science, methods for precise measurement and adjustment, and best practices for different racing conditions. It provides valuable insights for engineers and drivers striving for optimal performance.
How do tyres generate grip?
How do tyres generate grip?
When a race car navigates a turn, two primary forces come into play: centripetal force and centrifugal force. Understanding these forces is crucial for grasping how a car maintains its path and how drivers and engineers optimize the performance of the car. ("For drag racers, these forces are irrelevant distractions—because turning corners is a challenge they’ll never face.")
Centripetal Force:
Centripetal force keeps a race car on its curved path by acting towards the turn's center, preventing the car from continuing straight due to inertia. In racing, this force is generated by tyre friction with the track, providing the lateral grip, also known as cornering force, essential for maintaining the car's intended trajectory.
Centrifugal Force:
Centrifugal force is an apparent force that feels like it pushes a car outward when it goes around a turn. This sensation is caused by the car's inertia, which is the tendency to continue moving in a straight line. Essentially, as the car turns, the inertia makes it feel as though there's a force pulling it away from the turn's center. In reality, there's no actual force pushing the car outward; it's just the car resisting the change in direction. This perceived force is equal in strength but opposite in direction to the centripetal force, which is the real force pulling the car towards the center of the turn to keep it moving along the curved path.
For perfect cornering, each tyre has to balance lateral and centrifugal force to have optimal lateral force at CG. If one of the axles, let's say the rear one has less lateral force than centrifugal force it can result in an oversteer condition, the same happens in the front axle (understeer condition). Now, the question is how does each tyre generate lateral force?
The simple answer is slip angle. It is defined as the angle between the direction in which a tyre is pointed and the actual direction in which the tyre is moving. When a tyre operates at a slip angle, both the tread and carcass experience distortion near the tyre contact patch. Essentially, the tread aligns with the direction of motion while the carcass adjusts its shape to accommodate this alignment.
The relationship between slip angle and lateral force is given below:
Fy=Cα*α (1)
where, F_y is the lateral force, Cα = Cornering Stiffness of the tyre and α = slip angle of the tyre
Higher cornering stiffness is required to increase lateral force but not the slip angle. As tyres project non-linear characteristics, the lateral force of a tyre doesn't increase in the higher slip angles phase. This can be well understood in Image 1.2 below. At higher slip angles, the adhesiveness of rubber starts degrading, resulting in the sliding of the contact patch's rear part, resulting in lower lateral force.
Influence of tyre pressure on the handling balance:
Influence of tyre pressure on the handling balance:
Tyres function similarly to anti-roll bars and springs in a vehicle by influencing the lateral load transfer distribution during cornering. Like springs, tyres have vertical stiffness, which determines how much they compress under load. This stiffness affects the vehicle's ride comfort and responsiveness to road irregularities. When it comes to lateral load transfer— the shifting of weight from the inner to the outer wheels during a turn—tyres also play a crucial role. By adjusting tyre pressures, which alters the tyre stiffness, engineers can fine-tune the vehicle's balance and handling characteristics, similar to how changes in spring rates or anti-roll bar settings would affect the vehicle dynamics.
C_total = ( Cs * Ct ) / ( Cs + Ct ) (2)where, Cs = spring rate of the construction spring, Ct = Tyre spring rate, Ms = sprung mass and Mus = unsprung mass
However, the spring rate of the tyre is higher than the construction spring rate but it will have a significant impact on the overall stiffness of the system.
From eq (1), it is clearly understood that to improve handling criteria of racecar we have to increase the cornering stiffness of the tyre. But the big question is"How to relate inflation pressure with the cornering stiffness of a tyre".This article describes the relationship between cornering stiffness and tyre vertical stiffness to predict the cold pressure of the tyre required in a race. Given that inflation pressure accounts for more than 80% of a tyre's overall stiffness, we can use this factor to improve the handling of our race car.
Let's do a simple simulation:
Let's do a simple simulation:
This article aims to provide a comprehensive and technical guide on setting the pressure of your race car's tyres while maintaining optimal grip balance. Let's start:
The data that I am going to show is replicated from a real-life scenario stint at Silverstone National Racetrack. The car used for this case is a poorly set Radical SR3 running on Hankook 200/580R15 (front) and 200/610R16 (rear). The starting cold pressure of the front tyres was set to24 psi front and 23 psi rear.The track temperature and ambient air temperature were 27.8 Cand 15.9 C respectively at the start of the stint and evolved up to 30.3 C and 17.7 C at the end of the stint.
From Images, it can be seen that after lap 7, the front tyre pressure was well over Hankook's recommended hot targets and the rear tyres were below their recommended hot targets. From this workbook, we can actually assess vehicle balance as the front axle tyre pressures are higher than the rear ones even if the car is a rear-wheel drive racecar. The front tyres display higher values as the vehicle is understeering and the front axle has a higher load transfer distribution.
Assessing the vehicle's grip balance:
To understand overall vehicle behaviour, whether the car is understeering or oversteering, we need to compare the yaw rate at COG of the car at each degrees of steering at the front tyres to that of vehicle speed.
Image Ψ(dot) represents the yaw rate at the centre of gravity(COG) upon δsteer which rotation (steering) angle of the outer wheel. The understeer graph indicates that as the vehicle's speed rises, the steering angle of the front wheels gradually increases without resulting in additional yaw. Eventually, the steering angle becomes excessive, leading to increased resistance. Generally, cars are slightly biased towards the understeer side to make them stable. This graph gives a good understanding of vehicle balance in both low-speed and high-speed section. One can note that in the 20-25m/s region, it understeers heavily. The next aim is to find a relation between vehicle balance with driving style of the driver so that setup changes would be developed around him.
Jorge Segers in his book proposed a method to measure the understeer/oversteer effect of racecar by finding the difference between the outer wheel steered angle and Ackermann steering angle. If the outer wheel steered angle equals Ackermann steering, the vehicle is neutral steer condition. Similarly more positive values denote understeer conditions and negative values denote oversteer conditions.
Image compares lap times with the average understeer angle to comprehend the driver's driving style. From the trend line plot, it is well understood that with higher levels of average understeer angle, the lap times are lowered. This means the driver is more confident with understeer setup. Of course, too much understeer will make him slow but giving him a slightly front-limited setup will make him faster and more confident.
The driving style and vehicle performance are well-understood now. To make the tyres perform the best, we need to make sure, they achieve the manufacturer's hot pressure targets quickly and then get stabilized at that temperature bracket. Tyre pressures increase linearly and then get stabilized at a range of pressure shown in Image, setting the cold pressures correctly will help us reach the plateau quickly and will allow the tyres to stay in the plateau region which will maximize the tyre's performance.
Predicting cold pressures of the tyres using the ideal gas equation:
Predicting cold pressures of the tyres using the ideal gas equation:
Let's assume our tyres are filled up with nitrogen or dry air which behaves like an ideal gas, by using ideal gas equation we can calculate the cold pressure targets of the tyre. For this article, I would show only for front tires to keep the article short. This can be applied to all four tyres of the car. The ideal gas equation gives us a fixed relation between a particular gas's temperature, volume and pressure.
Where, p1 = desired cold pressure targets, p2 = optimum performing pressures (manufacturers hot pressure targets), t1 = temperature measured inside the pits/ ambient air temperature and t2 = optimum performing temperature. All units are in bar and Celsius, 1 here is atmosphere pressure in bar
Except for t2 which is the optimum performing temperature and p1 which desired cold pressure target, every other value is known to us or can be measured in the pits. To find t2, we generally look at the data from the tyre temperature Infrared sensors projected towards the tread of the tyre. Plotting GSUM values against front and rear axle tyre temperature will give us an idea of optimum performing temperatures.
GSUM is the combined acceleration of the racecar, higher values of GSUM show higher cornering potential of a racecar. Image 1.8 gives peak GSUM values at 66°C at the front axle and 56°C at the rear axle. ("tyre temperatures are quite low because the damping ratio is way lower than 1.0. I will make a different article about dampers"). As t2 is known from this plot, we can calculate the cold pressure for front tyres using MATLAB code.
From the code, the cold pressure of the front tyre is 21.93 psi ≈ 22 psi.And rear tyre cold pressure is 22.83 ≈ 23 psi
"Are we done? Not yet !!"
From Eq (1), it is clear the higher cornering stiffness increase the lateral force generation capability of a tyre, hence improves handling. As tyre pressure affects vertical stiffness which in turn affects the cornering stiffness of the tyre, in the next section, a relationship will be made between the three different factors to maximize tyre performance.
Cornering Stiffness vs Vertical Stiffness vs Inflation Pressure:
Cornering Stiffness vs Vertical Stiffness vs Inflation Pressure:
The direct relationship between tyre pressure and cornering stiffness was first given the Magic Formula tyre model introduced by Pacejka in 1997.
where cornering stiffness was calculated using tyre load, nominal tyre pressure, some magic formula and fitting parameters.
"We are not using this equation because lot of parameters are unknown!!"I will give a workaround to relate cornering stiffness with inflation pressure.
First of all, let's find the cornering stiffness of a tyre, for that, we need two things: Lateral forces acting on a tyre and the slip angle of a tyre. Lateral force can be calculated using chassis accelerometers and suspension displacement. There's a whole lot of literature available on this topic. The second challenge is calculating slip angle if you don't have optical sensors to find carcass deflection in tyres.
Calculation of tyre slip angle:
where, αfl = Slip angle of the front left tyre, αfr = Slip angle of the front right tyre, αrr = Slip angle of the rear right tyre, αrl = Slip angle of the rear left tyre δf= Steering angle at the front wheels, vy=" Lateral" velocity of the vehicle, vx: Longitudinal velocity of the vehicle, γ= Yaw rate of the vehicle, lf=" Distance" from the centre of gravity to the front axle, d="Track" width of the vehicle.
Using the equations mentioned above, respective math channels can be created to determine the slip angle of front tyres. One thing to note, these are calculated values, accuracy may be low but gives a good understanding of vehicle performance.
The data can be viewed when plotted against the lateral force of each tyre.
Cornering Stiffness:
Now, we can easily calculate the dynamic cornering stiffness of the tyre by dividing lateral force by slip angle. Modifying eq (1) as a math channel:
Fy/α = Cα
Point to note that this cornering stiffness is a dynamic one not actual Tyre data. It does not have a fixed value but when plotted against a tyre's vertical stiffness gives the best operating bracket of the tyre. It is beneficial to make sure that tyres perform in these optimum brackets.
To find tyre vertical stiffness we divide the tyre load (from strain gauges) by tyre vertical deflection.
Image gives the best vertical stiffness bracket of the tyre. From these data density regions onwards, any increase or decrease in the tyre's vertical stiffness decreases the tyre's cornering stiffness. The highest cornering stiffness occurs around254 N/mm for FL, 257 N/mm for FR, 249 N/mm for RL, and 250 N/mm for RR of vertical stiffness.
Vertical Stiffness vs Pressure:
To find the influence of inflation pressure on vertical stiffness, we can do FEA testing using Ansys Workbench. By applying varying vertical loads during braking, cornering and accelerating on quarter-car model with different tyre pressures, we can find a tyre's vertical stiffness.
