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# Car Wheel Skidding

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Alright I need to find out at any moment in time if a wheel is skidding or not, for example if you slam on the pedal of a 2000 horsepower car, your wheels will just spin like crazy. Also how much force do the wheels output to push the car whether skidding or not.

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Something to do with the max value of friction maybe?

Are you going for exact modelling or some fancy looks?

If know the revolutions for sec of the wheel (some direct calculation from the gear box and engine output) and it''s radius then you could find the speed of the edge of the wheel. Then if the edge of the wheel is travelling faster than the car, it must be spinning.

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Alright, but if it is spinning it''ll still move the car a little. How do I find how much force of a skidding wheel goes to pushing the car?

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You will need to use a co-efficient of friction, you can then calculate how much of the force will be applied in the direction of motion and how much will be lost.
I dont know where to find the numbers, but there is probably a look up table of typical co-efficients of friction between two surfaces (say rubber and stone) somewhere on the net.

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quote:
Original post by Mynock
Alright, but if it is spinning it''ll still move the car a little. How do I find how much force of a skidding wheel goes to pushing the car?

This is dynamic friction. Typically dynamic friction is a lot worse than stati friction, which is why spinning the wheels does not get a car going fast and why locked wheels are a lot worse for stopping the car.

The amounts of static and dynamic friction depend on the coefficients of static and dynamic friction. The calculations are the same for static and dynamic friction, but the forces generated by dyanmic friction are a lot less as the coefficient of dynamic friction is less. This is quite complex to model for a car because you want to model each wheel seperately, and for realism want to take into account a number of factors such as road surface type, tyre type, tyre temperature, etc.

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A car moves because the friction between the tyres and the road pulls it along (if there where no friction the wheels would just spin backwards). The maximum this force can be is given by:

F = u*W (where u is the coefficient of friction and W the weight of the car)

Now if the torque at the point of transmission of power to the wheels T > r*F (where r is the radius of the wheel), the wheel will spin as a greater force than the max possible frictional force at point of contact is required to stop any relative motion between the tyre surface and the road. At the point that the wheel is spinning at a constant angular speed v say, the tyre surface will be moving at speed s = r*v and the car can only accelerate at a = F/m (remember F = max frictional force, m = mass of car).

F/m = a constant so the wheels will stop spinning after time t when:

s = (F*t)/m and the speed of the tyre surface relative to the road matches the cars translational speed along the road.

Now F = u*W = u*m*g where g is the acceleration due to gravity so substituting this into the above and cancelling m in the numerator and denominator gives:

s = u*g*t

Hope this helps :-)

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quote:
Original post by Newton
F = u*W (where u is the coefficient of friction and W the weight of the car)

Actually, W is the normal force, which is usually the weight of the car, but not always (for example, it''s not the weight of the car when going down a hill).

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Of course you are absolutely right SpaceRook, I just thought I''d get the wagon rolling with a simple model ;-)

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