Vehicle Dynamics 101 (incomplete)

The faster a car can go around the corners, the less its lap time would be for two reasons. The first and obvious reason is simply that the faster vehicle will cover the set distance in a shorter amount of time. And the Second more important reason is that a faster car through the corners has a head start in speed and will take less time to reach its maximum speed on the straight. - Carrol Smith, Tune to Win
Vehicle dynamics in motorsports is the study and application of the theory, kinematics and dynamics of how a car behaves in pitch, roll, dive and heave. The aim is to maximize tire contact patch and acceleration in the appropriate direction, at all times on the race track. As a driver, it is useful to understand a few basic concepts behind vehicle dynamics and handling.

The first lesson is tyres. Everyone is familiar with the saying that the tyres are the most important component of the car, however is is also arguably one of the most complex components also. It is where all the forces from braking, accelerating and turning are reacted to the ground, and it is also where feedback is channelled to the driver via the front wheels to the steering wheel.

The important thing to note about tyres is the concept of slip angles (coincidently where we got the name from). A tyre produces grip by generating slip angles. The slip angle is basically the angle between the direction in where the steering wheel is pointing, and the direction where the wheel is travelling. It is the result of complex deformation and wear in the rubber compound contacting the road surface when the wheel is turned. For the mathematically inclined, slip angle is the arctan of Vy/Vx (with respect to the tyre). By SAE (the Society of Automotive Engineers) definition, X is the longitudinal (front-back) direction, Y is the lateral (left-right) direction, and Z is the vertical direction.

Source: Milliken & Milliken

If we were able to slow time down, this is the process of turning a car: When the steering wheel is turned, the wheels start turning being linked to the steering via a universal joint and steering rack. At this point, the car is still going on in its original direction. It takes less than a revolution of the wheel for a slip angle to be generated, which causes a side ways force that pushes the front of the car left, for example.

At this moment, the rear does not know what the front is doing yet. This concept is important and will be unveiled later so remember this first. As the car yaws or rotates about its instant center (instant because it is only valid for that instant), the rear tyres now see a slip angle and begin to generate grip. The car then reaches a state known as steady state cornering where it settles down (even for a split second), and the yaw moment is zero.

Now, the rate at which the tyres generate grip can be obtained from tyre characteristic curves. Often, these information are not shared openly by tyre companies, but it is important to recognize that different types of tyres have different characteristic curves.

Source: Milliken & Milliken

You can now see clearly in this graph that slip angle is the primary reason for lateral grip in a tyre. As the slip angle increases, the lateral grip of the tyre increases till it reaches a peak, then begins to fall off. This is when 'understeer' or 'oversteer' happens depending on which end of the car reaches past the peak first. Also note that past the peak, the tyre does not completely lose grip, the grip level reduces at a rate depending on the tyre characteristics.

Tyre load sensitivity

Most of us are familiar with the classic friction equation:
Which shows that the amount of lateral force or grip a tyre generates is linearly proportional to the coefficient of friction of the tyre, and the amount of vertical load on the tyre. In other words, taking the friction coefficient as constant, the more vertical load a tyre experiences, the more sideways grip it produces.

However there is a catch because of the visco-elastic properties of rubber, which results in a non-linear relationship in reality, between the amount of vertical load Fz and sideways grip Fy. This is known as Tyre Load Sensitivity, and is an important concept in vehicle handling and suspension design. The following graph illustrates this fact.
Source: Milliken & Milliken


Another way to put it would be that twice the amount of vertical load does not produce twice the amount of grip. In short, you lose grip and cornering ability with more weight transfer to the outside wheel, than you would gain from the inside wheel.

This theory would suggest that contrary to popular belief, weight transfer is a negative result and should be minimized for maximum performance. We'll deal with weight transfer in another post.