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Attempting to write a simple racing game with a deeper physical simulation than "RotateBody()" for steering. I've looked in a few books, yes those physical things of paper, and some of the game physics books are too simplified to give me my desired "lateral force from turning a wheel" and the vehicle dynamic books either require the radius or I get completely lost, still working on math skills.

I've also looked around online and this is the best source I've found so far but even it seems to confuse me, and may also be simplified to 2D where my problem space is 3D.

Among my search I've found:

lateralForce = corneringStiffness * tireLoad

where corneringStiffness is a constant for small slipAngle values or for higher values a table lookup, (I compute it via 3 linear functions), tireLoad being the weight / corner load on the tire and slipAngle is the angle between the car velocity and the tire heading. My issue with this approach is, that the speed of the car is not considered so even if the car is moving very slowly, the applied force creates a rotation.

How do I calculate the lateral force of a tire based on the slipAngle and velocity of the car? (Obviously static/dynamic friction will get involved which I have yet to get modeled).

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You're always going to need the radius, one way or another. If you are calculating from the angle of steering, you will also need the vehicle's wheelbase (the distance between the front and back tires). The radius of turning is going to be (approximately) the wheelbase length divided by the angle of steering in radians. Given the radius and the speed of the vehicle, the force acting on the tires is just the centripetal force $mv^2/r$, divided by the number of tires.

In practice I expect in a tight turn, the force is unevenly distributed, with the outer tires applying more force.

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  • $\begingroup$ Ahh. That may have, finally, clicked. So the lateralForce I've computed above should actually be "maximumAllowedLateralForce" due to the friction, and the centripitalForce (= mv^2 / r) would be applied in full if less than maximum, or capped to max. I'll give that a go. $\endgroup$
    – Tim Beaudet
    Commented Oct 26, 2016 at 17:09
  • $\begingroup$ Seems I can't continue to edit the comment, but I suspect the tireLoad would handle the situation with outer tires applying more force than inner tires. $\endgroup$
    – Tim Beaudet
    Commented Oct 26, 2016 at 18:13
  • $\begingroup$ Though it isn't behaving exactly how I'd like I am accepting the answer at current time. $\endgroup$
    – Tim Beaudet
    Commented Oct 29, 2016 at 20:08

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