Understanding Car and Tire Dynamics in Motorsport Handling
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Chapter 1: Introduction to Cornering Dynamics
This article continues from "Car and Tire Dynamics at the Limits of Handling (Part I)," where we established the fundamentals of tire grip and its impact on a vehicle’s acceleration in a straight line. However, cars are also required to navigate corners, which is the focus of this second installment.
To comprehend advanced concepts such as understeer and oversteer, one must first grasp how tires function at their handling limits. These concepts are often simplified as "when the car doesn't want to turn" or "when the car turns more than intended." If you’re eager to delve deeper into the science behind these phenomena, you're in for an enlightening experience.
Before we proceed, it's essential to recognize that cornering also requires acceleration. Acceleration is the change in velocity, and during cornering, a car alters its direction. Specifically, cars need lateral acceleration to navigate turns, which is again generated by the tires' grip.
Section 1.1: The Mechanics of Tire Grip
Let’s revisit how tires generate grip, this time focusing on lateral forces.
“When the tire contact point has nonzero sliding velocity relative to the road surface, it creates grip in the opposite direction of this motion.”
In Part I, we discussed longitudinal grip, which arises when the tire's angular velocity differs from the ideal (ω≠v/R). A tire accelerates when it rotates faster than this ideal and decelerates when it rotates slower.
An effective analogy for this situation is to consider rolling a metal sheet around the tire. As the tire moves forward, it will unfold the sheet back onto the road, assuming the forces acting on it are sufficient to cause deformation. Thus, we can think of the forces acting on the tire as a reaction to the metal sheet's deformations.
The animation illustrates how lateral grip is produced when the tire slides perpendicularly to its primary plane. When the tire slides to the right, grip pushes it back to the left, similar to how the folded metal sheet resists deformation.
The amount of lateral grip is dictated by the lateral slip angle, which is the angle formed between the tire's velocity and its main plane. The factors affecting lateral grip include the vertical load on the tire, the lateral slip angle (lambda), and the longitudinal slip (kappa).
For the purposes of this discussion, we will set kappa to zero, which simplifies our analysis. If kappa = 0, you may notice that the relationship between lateral grip and slip mirrors that of longitudinal grip.
Section 1.2: Lateral Grip and Load Factors
Lateral grip increases with vertical load, meaning how heavily the car presses the tire against the road. Additionally, grip increases with lateral slip for moderate values, exhibiting a linear and predictable behavior. However, larger slip angles lead to a non-linear variation in grip until reaching a peak, typically found in Formula 1 cars at lateral slip angles below 10º.
The vertical load is influenced by various factors, including downforce, mass distribution, and suspension settings, while the driver controls lateral slip through steering input.
To maximize grip, drivers aim to operate as close to the grip peak as possible. However, this zone is delicate; exceeding it can lead to a sudden loss of grip.
When accelerating in a straight line, this may result in wheel spin or lock-up. In cornering scenarios, losing grip can lead to instability, causing either the front or rear of the car to lose traction, potentially resulting in a spin.
Chapter 2: Simulating Cornering Dynamics
Now, let's take a look at how cars behave on the track while navigating turns. In this section, we will explore simulations of an infinite corner loop where the driver strives to achieve maximum speed and extract all available grip from the tires.
Section 2.1: Neutral Handling Characteristics
A car is considered to have neutral handling when both front and rear tires are able to achieve their maximum grip simultaneously.
The following simulation illustrates this balance, showing the grip produced by both front and rear tires during a cornering maneuver. The external (right) tires are monitored, as the grip in left-handed corners is primarily dictated by the rear tires due to inertia forces that lift the inner tires.
Notably, the total vertical load of the tires can exceed 1.0g due to aerodynamic downforce enhancing grip. A neutral balance allows drivers to extract the maximum performance from their tires.
In this scenario, the rear tires achieve their slip angle through a combination of the chassis sideslip angle and the chassis angular rate, while the driver directly controls the front tires' slip with steering input.
Section 2.2: Understanding Understeer and Oversteer
While neutral handling is ideal, most cars exhibit either understeer or oversteer.
Understeer occurs when the front tires have less grip than the rear tires, leading to wider trajectories. Conversely, oversteer happens when the rear tires lose grip, resulting in an unstable handling condition.
Drivers often push the limits in pursuit of grip, but in an understeering situation, increased steering input can lead to a loss of front grip, causing the car to drift wide. This scenario, while stable, can be frustrating for drivers eager to maximize speed.
In contrast, oversteering is precarious. If a driver pushes too far, the rear tires lose grip, leading to a rapid increase in the car's angular rate and further loss of grip, often culminating in a spin or collision.
Conclusions
In summary, understanding tire lateral forces is crucial for mastering car dynamics in motorsport. A neutral balance allows drivers to maximize grip, whereas understeering and oversteering present distinct challenges. With understeer, drivers can regain control with minimal adjustments, while oversteer requires swift reactions to avoid losing control entirely.
For these simulations, I utilized my open-source laptime simulator, Fastest-lap. You can find the MATLAB scripts and data for these simulations linked in my profile. Follow me on Twitter (@fastestlap_f1), LinkedIn, YouTube, and Medium for more insights into motorsport dynamics.