Well, first of all I am by no means a physics expert.
Regarding your question, Your observation is correct, faster cars should have higher lateral forces, well but that's not the whole story.
I think your problem is that the question that needs to be asked, where does the lateral force come from in the first place?
In normal circumstances the car's engine generates force that makes the car moves forward. This force along with other forces that act on the car movement direction (or opposite) is called longitudinal forces.
On the other hand, in high speed cornering scenarios, the tires develop lateral forces also known as the cornering or side force. Which means this force is only generated when the tires have an angle between the tire's heading and its direction of travel.
Now the important point is, the angle between the tire's heading and its direction of travel is called
alpha. When the movement direction is the same as the tires heading direction then Alpha is Zero. This results in a lateral force that equals zero.
When there is an angle between heading direction and the tire's traveling direction the velocity vector of the car is now split into two components:
- The longitudinal vector has magnitude cos(alpha) * velocity.
- The lateral vector has magnitude
sin(alpha) * velocity and causes a
resistance force in the opposite direction: the cornering force.
Which means that lateral force depends on the As the slip angle grows, so does the cornering force. Now the point is, at low slip angles, the relationship between slip angle and cornering force is linear.
Flateral = Ca * alpha
Now, since this equation is only true for small angles, I believe this equation is using small angle approximation where:
Hence, dropping the sin and the velocity from the equation. Keep in mind that the linear relation is only true for small angles, otherwise the linear relation doesn't apply anymore. But I might be wrong someone with more knowledge might correct me.