Friction and turning angle relation

[Adamolesiak]

Hi there,
Suppose we had a car going in a circle. We know that the turning angle(angle between the movement direction and the wheel axis) and the friction are connected, because friction determines the centripetal force and it determines the radius of the circle that we make with our car. I need to know the relation(equation) between that angle and the friction.
We can split it into 2 cases:
1) the centripetal force is not too large for the maximum friction for given materials to be achieved
2) the centripetal force is too big - the car starts drifting

Mostly need the 1), but if someone would be so nice to explain to me the math behind the 2) i would be very grateful.
The computer program I'm writing establishes the movement direction as the direction a sitting still driver would face. In 2), this direction isn't movement direction anymore, which would complicate it

English is my secondary language, so if you could use symbols instead of their spoken equivalents, that would be great.
Thanks in advance!

 

[Lance219]

suppose you mean on level ground. $$ \mu N=\frac {m v^2} r $$
$$\mu m g = \frac {m v^2} r$$
$$r = \frac {v^2} {\mu g} $$

so your radius is determined by the static friction constant as well as your car's speed.

 

[Adamolesiak]

Yes, ground level and i got to that equation: r = V*V/g*f.
But I need to determine the angle between movement axis and wheel facing axis.
For example you have a car moving at constant speed, with constant friction constant and a constant steering wheel position(which determines the angle).
How to connect the angle with the rest. I think there were some circular acceleration equation or something like that that was giving you a result in radians, but it was so many years ago, I don't remember so well.

Need it to calculate where my car is going to be on my x/y plane in next frame so that i can draw it there and have a working car simulator

 

[Lance219]

The way I see it, the angle between the lines of your front and rear wheel tells the car what radius you are asking for, but where the ground condition (friction) and your car's speed will be able to support that is a different issue. You might end up drifting or even worse.

 

[Lance219]

The angle between front left wheel and rear left wheel, the distance between the 2 wheel will determine the radius of your circular movement, provided no drifting occurs.

Then $\omega = \frac v r$, you have your speed, you have your radius (when the angle you mentioned is determined), then $\theta = \omega t$ can be determined for given t (assuming intial $\theta$ is 0)

 

[Adamolesiak]

Thanks man, that's what I was looking for.
Wasn't even considering the distance between wheels before, but yes you're right.
Thanks again!

 

[Lance219]

Determine the radius from front&rear left wheel and distance between them is a geometry problem. suppose front left wheel touch the ground at A, rear left wheel touch ground at B, front wheel's direction line meet rear wheel's direction line at C, then the center of the circle O will satisfy OA is perp to AC, and OB is perp to BC.