How do understeer and oversteer work? (the math and the physics)

• hari00968
In summary, the book discusses how understeer and oversteer works, using a formula derived from lateral acceleration. The formula is: Steer Angle = 57.3 L/R + K*(lateral acceleration). There is also a formula for K as well, depending on the front and rear curb weights of the car, in addition to tire properties.
hari00968
I am reading 'Fundamentals of Vehicle Dynamics' by Gillespie. In the chapter 'Steady State Cornering', it explains how under-steer and over-steer works, using a formula, which is also derived. I can understand the derivation of the formula reasonably well. The formula is:

Steer Angle = 57.3 L/R + K*(lateral acceleration)

where:
L = wheelbase
R = radius of curvature of curve
K = understeer gradient (+ve if the car has understeer, -ve if oversteer, 0 if neutral)

There's a formula for K as well, depending on the front and rear curb weights of the car, in addition to tire properties, which is easy, no problems with that.

This is what the book says (page number 203):

"In the understeer case the lateral acceleration at the CG causes the front wheels to slip sideways to a greater extent than the rear wheels. Thus to develop the lateral force at the front wheels necessary to maintain the radius of turn, the front wheels must be steered to a greater angle."

"In the oversteer case, the lateral acceleration at the CG causes the slip angle on the rear wheels to increase more than at the front, thus diminishing the radius of the turn. The increase in lateral acceleration that follows causes the rear to drift out even further and the process continues unless the steer angle is reduced."

It's obvious from the formula that you would need to increase the steering angle with increase in speed, in the case of understeer, and vice versa. But I don't understand what's happening physically, with respect to the force due to the tire slip angles. I'm very confused with their explanations. Please help.

When making a corner with a 4 wheel car, the inner front and back wheels have less of a radius to follow than the outer front and back wheels.
Ideally, the inner wheel will turn just a little bit more than the outer, so that both follow the arc prescibed by the above mentioned radii.

For understeer:
If both front wheels turn the same amount, and the outer wheel follows its arc, the inner wheel will subsequently not be following its arc and will skid a bit forward or sideways if you like, while trying to turn. You will have to turn the steering wheel a bit more to follow the curve.

Also, the car has inertia with a CG and wants to move in a straight line.
The wheels want to roll along a path that they point.
The two are in conflict with each other when making turn.

Its not a very thorough explanation, but I hope it clarifies some aspects of your inquiry.

Hard to say exactly what you're after with this:
"But I don't understand what's happening physically, with respect to the force due to the tire slip angles."

The force generated by the tire varies with the slip angle. To generate more lateral force, more slip angle is required from the tire (front or rear). The amount of force generated by the slip angle is fairly linear until the tire is getting close to its peak, then the line curves over and starts back down as more of the tire's contact patch slides.

If the car is understeering at the limit, the front tires will be at a higher slip angle than the rear tires and are the limiting factor that determines the maximum cornering rate. Adding more steering results in more slip angle but if the tire is already at the peak, the force generated will be less than at a lower steering angle.

Here's an excerpt from one of the books I have:
http://insideracingtechnology.com/tirebkexerpt2.htm

Last edited:
@mender,

"If the car is understeering at the limit, the front tires will be at a higher slip angle than the rear tires"

And like you said, up to a certain point, lateral force increases with slip angle. Assuming we're still within that range, if the slip angle in front is higher, the lateral force in front should also be higher, which should cancel the understeer right? I mean, if you further increase the steer angle (and hence the slip angle), you're only making the difference in slip angle between the front and rear higher right?

Besides, why is this difference a bad thing in the first place? Because it looks like it will cancel the understeer!

Sorry if my questions seem very trivial, but I'm really confused here!

1. What is the difference between understeer and oversteer?

Understeer and oversteer are two terms used to describe the handling characteristics of a vehicle. Understeer occurs when the front wheels lose traction and the vehicle tends to continue straight instead of following the intended turn. Oversteer, on the other hand, happens when the rear wheels lose traction and the vehicle tends to rotate more than intended. Both can be caused by a variety of factors such as speed, weight distribution, and tire grip.

2. How does understeer and oversteer affect a vehicle's handling?

Understeer and oversteer can greatly impact a vehicle's handling and stability. Understeer can make it difficult to steer through corners, while oversteer can lead to a loss of control and potential spinouts. It is important for drivers to understand how to properly handle both situations to maintain control of their vehicle.

3. What are the physics behind understeer and oversteer?

The physics behind understeer and oversteer involve the principles of weight transfer and tire grip. When a vehicle turns, weight is transferred to the outside wheels, reducing the grip on the inside wheels. This can lead to understeer. Oversteer can occur when the rear wheels have more grip than the front, causing the rear of the vehicle to swing out. This can be caused by factors such as excessive speed or abrupt steering inputs.

4. How can understeer and oversteer be corrected?

If a vehicle is experiencing understeer, easing off the accelerator or gently applying the brakes can shift weight to the front wheels and improve traction. For oversteer, countersteering (turning the wheels in the opposite direction of the slide) can help regain control of the vehicle. It is important to remain calm and make smooth, controlled adjustments to avoid exacerbating the situation.

5. Can understeer and oversteer be prevented?

While understeer and oversteer can be corrected, it is best to prevent them from occurring in the first place. This can be achieved by properly maintaining your vehicle's tires, avoiding excessive speeds, and being aware of your vehicle's weight distribution. It is also important to be familiar with how your vehicle handles in different situations and to adjust your driving accordingly.

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