# Turning radius and wheel speed difference

I am trying to fitgure out the turning radius of a simple car with front wheel steering based on the velocity difference between the front wheels. Unfortunately, I could not figure out how this could be done. I figured out the relationship between steering angle and turn radius but I am unable to relate that to the wheel speed difference. Any help is greatly appreciated.

Thanks and Regards
Rana Basheer

tiny-tim
Homework Helper
Welcome to PF!

I am trying to fitgure out the turning radius of a simple car with front wheel steering based on the velocity difference between the front wheels.

Hi Rana! Welcome to PF!

I think the turning radius depends only on the angle of the front wheels.

I expect you're thinking that the outer wheel has to go further than the inner wheel, and so must go faster … but I think there's some sort of tracking arrangement on the front axle so that that doesn't happen (I honestly don't really understand that part of it )!

Anyway, imagine a three-wheeled car, with only one front wheel … it still turns, doesn't it?

He is referring to the purpose of the differential in the car. Basically that the outer wheel (wrt the turn) must turn faster than the inner wheel and this relationship or ratio of the two speeds is a function of the turning radius of the car.

It can be easily shown that

wt * rt = ww * rw
and
rt = ro - wb/2, rt = ri+wb/2

where:
wt = angular velocity of the car
wb = wheel base of the car (width)
rt = radius of the turn
ww = angular velocity of the wheel (wo,wi as outside and inside)
rw = radius of the wheel
ro = outside radius of tire
ri = inside radius of tire

With a little coaxing and simple algebra you get this:

rt = $$\frac{-Wb}{2}$$ $$\frac{wi+wo}{wi-wo}$$

Last edited:
Thank you topher,
I appreciate your help. I never looked at that way. I will test your equation on my RC car and let you know how accurate my turning radius are.

hey Topher925

i jus read ur post cos i had the same question.. now can u explain how did u derive it.. ? cos according to my calculation rt= rw - (Wb/2)(wi+wo)/(wi-wo) but urs say differently.... lemme know how u got the equation.