
The Engineer's Handbook of Inflation Pressure
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LPϟ9Engineering® at the 68th Rally Coppa Valtellina with Biella-Serventi
LP9Engineering is pleased to announce its collaboration with John Biella and Marco Serventi to manage tire pressure on their Peugeot 106 Rallye, prepared by Alien Cars, for the 68th Coppa Valtellina Rally. Drawing on my experience in motorsport engineering, I will be responsible for analyzing and optimizing tire pressure choices, aiming to maximize grip, consistency, and performance throughout all special stages.
The Engineer's Handbook of Inflation Pressure
Credits to Shirshak Pattnaik and Ludovico Di Lorenzo
In the high-performance world of motorsports, tire pressure is a crucial parameter in determining a racing car's performance, directly impacting handling, grip, and tire life on the track. Optimal inflation pressure ensures the best possible contact patch, offering maximum traction and stability, while incorrect pressures can lead to excessive overheating, increased rolling resistance, or loss of grip. Furthermore, tire pressure is a dynamic variable, influenced by asphalt temperature, driving style, and track conditions, requiring continuous monitoring and adjustment throughout the entire race. This article delves into the science behind racing tire pressure, methods for precise measurement and adjustment, and best practices to adopt in different racing conditions. This content is packed with useful insights for engineers and drivers seeking maximum performance.
How do tires generate grip?
When a racing car takes a turn, two main forces come into play: centripetal force and centrifugal force. Understanding these forces is essential to understanding how a car maintains its intended line and how drivers and engineers can optimize cornering performance.
( "For drag racers, these forces are irrelevant distractions—since cornering is a problem they will never have to face." )
Centripetal force:
Centripetal force keeps the car on a curved path, acting toward the center of the curve and preventing the car from continuing straight due to inertia. In racing, this force is generated by the friction between the tires and the asphalt, and is what provides the lateral force , also called cornering force , needed to maintain the desired trajectory.
Centrifugal Force:
Centrifugal force is an apparent force that feels like a push toward the outside of a curve. It's due to the vehicle's inertia, or its tendency to continue in a straight line. In practice, as the car turns, inertia makes it feel like a force pushing it out of the curve. In reality, there's no actual outward force: it's the body's resistance to changing direction. This apparent force is equal and opposite to the centripetal force, which is real and keeps the car on its trajectory.
Overall lateral force and cornering behavior
To achieve a perfect corner, each tire must balance lateral and centrifugal forces to ensure optimal CG force. For example, if the rear axle generates less lateral force than centrifugal force, oversteer can occur; the same applies to the front axle in the opposite case ( understeer ).
But how does each tire generate lateral force?
The answer lies in the slip angle .
This is defined as the angle between the direction the tire is oriented and the actual direction of motion. When a tire operates at a certain slip angle, both the tread and the casing deform in the contact patch. Essentially, the tread aligns with the direction of motion, while the casing deforms to compensate.
The relationship between slip angle and lateral force
The initial linear relationship is expressed by the following equation:
Fy = Cα · α
Where:
- Fy is the lateral force,
- Cα is the cornering stiffness of the tire,
- α is the drift angle.
Greater stiffness in cornering allows for more lateral force to be obtained without excessively increasing the slip angle .
However, since the tire behavior is non-linear, the lateral force does not increase indefinitely as the slip angle increases.
Evolution of the track:
"Track evolution" describes how the condition and performance characteristics of a circuit change over the course of a race weekend. This phenomenon can significantly impact both the performance of the cars and the strategies employed by drivers and teams. Track evolution occurs for various reasons, such as changes in asphalt temperature, increased rubber deposits on the track, weather conditions, and so on. This article will discuss the influence of track temperature on tire pressure.
We'll go into a bit more technical detail about tire thermal modeling, but this will give you an idea of why we care so much about track temperature. ( "We're engineers, we have to deal with equations and numbers!!" )
Danny Nowlan explained how temperature builds up on the surface of the tire tread through a formula used in tire thermal modeling.
Therefore, the evolution of the track temperature has a significant importance in managing tyre temperature and pressure during an entire stint or race.
The Ideal Gas Law (PV = nRT) (“I explained it earlier in the section on cold pressure prediction”) is often used to understand the relationship between pressure (P) , volume (V) , and temperature (T) of gases. However, in the context of setting tire pressures in motorsport, relying solely on this law can be problematic due to track evolution and other factors, such as the complex thermal conductivity between the rubber and the track surface.
While the ideal gas law provides a basic understanding of the relationship between pressure and temperature, it is not sufficient to accurately predict tire pressure in the dynamic environment of a race .
To understand the evolution of the track, we need to find a relationship between track temperature and tire pressure .
By performing a linear regression for all four tires, we can plot the best-fit lines for each tire pressure as a function of track temperature.
We will use these equations to predict tire pressure at different track temperatures.
Note : Tire pressure curves are not completely linear , but slightly logarithmic . However, by isolating the linear region, we can use the equation
y = mx + c
.
The resulting equations are:
- Tire Pressure (FL) = 1.6943 × Track Temperature − 20.8074
- Tire Pressure (PR) = 1.3368 × Track Temperature − 11.3200
- Tire Pressure (RL) = 1.4062 × Track Temperature − 14.9203
- Tire Pressure (RR) = 1.2905 × Track Temperature − 11.7724
Evaluation of all the above methods:
In this section, the different cold tire pressure prediction methods described above were used to evaluate the car's performance.
The best method is to evaluate the stopwatch : each improvement in lap time gives an idea of which is the best setup among those proposed.
Analyzing tire wear for the various setups, it was discovered that the fastest setup (the one based on cornering stiffness) also showed the highest wear rate . The other two setups experienced significantly less wear.
The setup that took into account the evolution of the track was the one that showed the lowest wear rate .
This happens because at lower pressures the tire's shoulders flex more , causing greater heat and mechanical stress in the structure, which leads to accelerated wear and degradation.
This is crucial when deciding what pressure to set for a qualifying session or race:
- Setups that optimize grip and lap time with lower pressures should be preferred in qualifying .
Since tire wear matters little in a single lap, the cornering stiffness method can be chosen , despite the increased wear. - However, in racing , it is better to opt for a setup that balances performance and tire life .
The method based on track evolution, with the lowest wear rate , is the best choice for maintaining competitive times while limiting pit stops .
Conclusion:
Tire energy management is a crucial component in motorsport. It impacts grip, wear, consistency, safety, strategy, and adaptation to conditions . Teams invest heavily in researching and improving tire performance, as it directly impacts speed, handling, and the final outcome of the race .
Final conclusion:
To balance grip, handling and tyre life for optimum performance , properly managing tyre pressure is essential.
This article examined pressure management theories and techniques and showed the effects of different strategies on lap times and wear.
Lower pressures maximize speed and grip in qualifying, but in the race a compromise is needed to ensure durability and consistency.
Efficient pressure management offers strategic advantages, reliability and competitive performance.
Further information on tire energy will be covered in a dedicated article.
I hope you enjoyed this article. Stay tuned for more on track engineering.
References:
- Soltani, A., Goodarzi, A., Shojaeefard, M.H., & Saeedi, K. – Optimization of tire vertical stiffness based on comfort, handling, performance and fuel consumption criteria
- Nam – Application of novel tire lateral force sensors for electric vehicle parameter estimation
- Nowlan – Deriving a Tire Model from Nothing , ChassisSim Technologies
- Segers, J. (2008) – Analysis Techniques for Racecar Data Acquisition , SAE International
- Ralph and Ton – Race Car Handling Optimization: Magic Numbers to Better Understand a Race