| For part 3 in this Car Control Fundamentals lesson series, we’re going take a deeper look at slip angle and vehicle rotation. We’ll begin by discussing front tire slip angle and take a close-up look at what exactly is happening at the tire as a driver turns. We’ll then move on to take a closer look at rear tire slip angle and learn how it directly changes a vehicle’s angle in a corner as well as how this affects rotation. Lastly, we’ll finish up by examining how a vehicle’s rotation relates to its ability to change direction. |  1. The Limit Defined 2. The Understeer Limit 3. Slip Angle & Rotation 4. The Oversteer Limit 5. Load Transfer |
Slip Angle and Car Control
Tire slip angle is relatively easy to understand from a technical standpoint, as it is simply the difference between the direction a tire is facing and the direction it is traveling. It’s also fairly common knowledge amongst drivers that a tire’s lateral force peaks at a certain slip angle, usually in the neighborhood of 5-10 degrees, after which it starts to drop.
Tire slip angle is relatively easy to understand from a technical standpoint, as it is simply the difference between the direction a tire is facing and the direction it is traveling. It’s also fairly common knowledge amongst drivers that a tire’s lateral force peaks at a certain slip angle, usually in the neighborhood of 5-10 degrees, after which it starts to drop.
| There is a lot of misunderstanding however, surrounding how a driver should use this knowledge. Firstly, it’s important to understand that slip angle is not something a driver must induce with a special technique. Although it can be hard to perceive during normal driving, all car tires, front and rear, experience at least some slip angle during a corner. Once a vehicle approaches the limit however, slip angle starts to become much more noticeable and so at race speeds, driving effectively requires an understanding of what slip angle affects… as well as what it doesn’t. |  |
Front Tire Slip Angle
When a driver turns the steering wheel, the front tires create a “slip” angle with the direction of travel. This produces a lateral force that pushes the front tires to the side, similarly to how a skier angles their skis against the snow or water to turn. If the tires were solid, like on a child’s ride-on toy with plastic wheels, maximum lateral force would be achieved almost instantly at a very low slip angle. Car tires are flexible however, and so as the vehicle turns, the contact patch seeks the path of least resistance and tries to keep going straight ahead. This causes the part of the tire near the contact patch to not quite turn as much as the central part near the wheel and so the tire will actually start to twist, which increases the slip angle.
When a driver turns the steering wheel, the front tires create a “slip” angle with the direction of travel. This produces a lateral force that pushes the front tires to the side, similarly to how a skier angles their skis against the snow or water to turn. If the tires were solid, like on a child’s ride-on toy with plastic wheels, maximum lateral force would be achieved almost instantly at a very low slip angle. Car tires are flexible however, and so as the vehicle turns, the contact patch seeks the path of least resistance and tries to keep going straight ahead. This causes the part of the tire near the contact patch to not quite turn as much as the central part near the wheel and so the tire will actually start to twist, which increases the slip angle.
| At the same time this tire twisting is taking place however, the rear of the contact patch will also start to break away and slide. Once a tire reaches its peak slip angle and has achieved maximum lateral force, it has twisted as much as it is going to and a fair amount of the contact patch will be sliding. Any additional steering at this point will continue to increase the tire’s slip angle, but this will simply cause more of the contact patch to start sliding and lateral force would now start to drop. | |
A tire still typically produces a significant amount of force past the peak slip angle, but lateral force would be dropping at this point and rearward longitudinal force would be increasing as the driver continues to turn the steering. This rearward longitudinal force is called induced drag and essentially acts as if the driver is applying the brakes. You can learn more about induced drag in our tire science article.
Although there is a lot happening as a tire approaches and then goes past the peak slip angle, we can use the method learned in the last lesson to guide us in finding that peak. When a driver tests for the understeer limit by using their steering to find the point of maximum lateral force at the front tires, they are essentially searching for the front tires’ peak slip angle. While there are many factors that influence exactly where that peak will be at any given moment, a tire’s peak slip angle is primarily determined by how flexible it is. A more flexible tire will typically peak at a higher slip angle than a stiffer one because it will twist more before achieving maximum force.
Before moving on, I also want to point out that front tire slip angle doesn’t affect a vehicle’s line, speed or rotation. Only a change in the force produced by the tire would. Whether a car has tires that peak at two degrees or twenty, the front tires would travel along the same path if the force produced by the tires is the same. This is because it is really only the contact patch that is traveling along this line. Differing peak slip angles will simply determine how much more turned the front wheels need to be in relation to the path the contact patch is on.
Vehicle Rotation Without Slip Angle
Looking now at the rear of the vehicle however, while the same tire twisting and sliding happens just as it does at the front, slip angle will change the rear tires’ path of travel, which directly affects the rotation of the vehicle. Unfortunately, this effect on rotation also makes it the source of most of the misunderstandings surrounding slip angle.
Looking now at the rear of the vehicle however, while the same tire twisting and sliding happens just as it does at the front, slip angle will change the rear tires’ path of travel, which directly affects the rotation of the vehicle. Unfortunately, this effect on rotation also makes it the source of most of the misunderstandings surrounding slip angle.
To explore this subject, let’s begin by looking at a theoretical example of a car going through a corner using solid tires so that we can first examine vehicle rotation while taking slip angle out of the equation. These solid tires won’t twist as a normal tire does and so peak lateral force will be achieved at near zero slip angle. Also note that this example corner will be done following the principles discussed in the Racing Line Fundamentals series, so please refer back to those lessons if needed.
| We will start our example at the turn-in point of the corner, where the driver would begin to reduce braking and increase steering, which would cause the car to start taking a path of steadily decreasing radius in the shape of an Euler spiral. The turn-in point is where vehicle rotation begins, as the direction the car is facing has started to change. The car’s rate of rotation would then steadily increase as the driver continued to slow down throughout corner entry and progressively tighten their turning radius. |  |
It’s useful to realize here that our example car’s increasing rotation rate would directly coincide with its decreasing speed during corner entry, because as we learned in previous lessons, speed and turn radius (and therefore rotation rate) are linked when a vehicle is at the limit. For example, our driver could take a completely circular path through the corner, allowing a constant speed at the limit and therefore a constant rate of rotation. When using an ideal Euler spiral shaped corner entry however, the rotation rate will progressively increase as speed progressively decreases. Once the car reaches the apex, it will then be at its minimum speed (and therefore maximum rotation rate) in the corner. At this point, the car will begin to gain speed as it progresses through corner exit, which will coincide with a decrease in its rotation rate, until by the end of the corner, the vehicle’s rotation rate will drop to zero as it reaches the following straightaway.
Vehicle Rotation With Rear Tire Slip Angle
So with our solid tires, we now have a baseline, where the car’s rotation rate steadily increases throughout corner entry and then decreases during corner exit, all without the influence of slip angle. Let’s now do it again with a different set of tires that can produce the same maximum force as our solid tires, but are now realistically flexible.
So with our solid tires, we now have a baseline, where the car’s rotation rate steadily increases throughout corner entry and then decreases during corner exit, all without the influence of slip angle. Let’s now do it again with a different set of tires that can produce the same maximum force as our solid tires, but are now realistically flexible.
| Starting again at the turn-in point, as we learned in previous lessons, the driver’s spiral-shaped entry would cause the vehicle’s rearward longitudinal force from braking to steadily decrease and lateral force from steering to steadily increase as the tires’ force direction moved around the car. This progressive increase in lateral force would push our now flexible rear tires outward, causing them to twist and gain slip angle. Although the front tires are now flexible as well and also gain slip angle, remember that this would not change their path of travel. The rear tires are pushed outward however, and this would steadily increase the angle of the entire vehicle. |  |
This increasing angle will add to the vehicle’s baseline rotation rate, so that throughout corner entry, it would now progressively rotate even more than it had on the solid tires. Then during corner exit, as lateral force starts to decreases, rear tire slip angle and therefore vehicle angle would decrease as well, which would now subtract from the car’s rotation rate. From the outside of the car, we would see all this as the front tires remaining on the same path as before, while the rear of the car steadily swung outward during corner entry and then moved back in during corner exit.
What’s most important to understand here however, is that although our two examples may look different, nothing has fundamentally changed in how the vehicle completed the corner. While the flexible tires would cause the car to rotate more throughout corner entry and be at a higher angle as corner exit began, the two apexes would actually still be the same. This is because an apex isn’t defined by the direction a vehicle is facing, but by the direction it is moving. Although the two sets of tires would be at different angles throughout the corner, the amount and direction of force they produce would be the same, and therefore the car’s movement throughout the corner would be the same. So even though the higher rear slip angle might make it look like the car has turned more by point it reaches the apex, the vehicle would still be moving in the exact same direction in both cases, and they would both have just as much direction change left to do during corner exit.
Movement Direction Vs Rotation
It’s important to remember that a driver’s primary goal is to maximize the tire forces pushing a vehicle in the ideal directions. In both of our examples, our driver is simply trying to maximize and optimally direct the force available from the tires. Although those forces might cause the flexible tires to twist and gain slip angle, further affecting vehicle rotation, the driver is primarily only concerned with the vehicle’s resulting change in movement direction. This is because rotation isn’t part of racing line optimization.
It’s important to remember that a driver’s primary goal is to maximize the tire forces pushing a vehicle in the ideal directions. In both of our examples, our driver is simply trying to maximize and optimally direct the force available from the tires. Although those forces might cause the flexible tires to twist and gain slip angle, further affecting vehicle rotation, the driver is primarily only concerned with the vehicle’s resulting change in movement direction. This is because rotation isn’t part of racing line optimization.
| In my first book The Perfect Corner, I use an example of an astronaut in space to illustrate this principle. In this example, the astronaut uses a fire extinguisher to propel themselves through a series of obstacles by maximizing and properly aiming the thrust from their extinguisher. The astronaut’s goal is to change the direction they are moving in as quickly as possible and they do this by following the same principles and producing the same ideal racing line shape as a car would, all while not needing to rotate to accomplish this. You can read the astronaut section in its entirety in The Perfect Corner book preview here. |  |
I bring up the astronaut example because, it is not only helpful in understanding the physics of the racing line, but it can also be a very useful way to think about car control. By visualizing how we can direct tire forces with our steering, brakes, and throttle in the same way that the astronaut aims their extinguisher, we can optimize our driving based on the core principles that determine the ideal line. I started calling this visualization technique the Universal Cue because it can provide a complete guide for a driver that will eventually take precedence over all other driving cues. This doesn’t mean that a driver can ignore vehicle rotation however. In order to effectively use the Universal Cue, a driver must first learn to drive at the limit, and when driving at the oversteer limit, sensing vehicle rotation is very important. That will be the subject of our next lesson however, where we will look at another exercise from our Academy series designed to teach a driver how to get the most out of their rear tires.
| Up Next - Oversteer I hope you enjoyed this third installment in the Car Control Fundamentals lesson series, and if you have any questions, please use the comments section below. Up next, we’ll dive into oversteer and then finish up our final lesson by learning about the role load transfer plays in car control. If you are interested in a complete guide to the physics of racing, we also offer The Science of Speed book series, available through our bookstore or at popular retailers such as Amazon. Adam Brouillard |  1. The Limit Defined 2. The Understeer Limit 3. Slip Angle & Rotation 4. The Oversteer Limit 5. Load Transfer |
