How to calculate the radius of a curve based on vehicle wheel speeds of a car I have data of the 4 differen wheelspeeds of a vehicle during driving time. Based on that I want to calculate the radius of a curve it is taking. The following are my current thoughts that seem to be errorneuos:


*

*Each curve or at least each part of a curve can be approximated by a circle, so:


      B = Width of the vehicle
      r = Radius of any Curve
      UI = Circumference of inner curve the vehicle takes
      UO = Circumference of outer curve the vehicle takes
      UD = Differences in circumferences of the curves 
      UD = 2 * pi * (r + B) - 2 * pi * r = 2 * pi * B
      Now I have the differences in distance the wheels of the car take in a clean circle.


*With this Distance I want to calculate the speed difference:


      VI = Inner Speed
      VO = Outer Speed
      t = Time
      VD = Speed Difference  
      VI = UI/t
      VO = (UI + UD)/t = (UI + 2 * pi * B)/t
      VD = VO - VI = UD/t = (2 * pi * B)/t  
Now the problem is that I lost every circle parameter (besides B) on my calculation. The interpretation would be that no matter the curve, the Speed difference is always 2 * pi * B per time. This is kinda contraintuitive as I thought, that the speed difference of wheels should be way higher for smaller radiuses.
Can someone help me to understand where I am wrong?
Regards 
 A: There is nothing wrong with your calculation. 
The two wheels roll around different circles in the same time. The difference in speed is proportional to the difference in circumference, which is always $2\pi$ times the difference in radius, which is the width $B$ of the vehicle : $$C=2\pi R$$ $$\Delta C=2\pi \Delta R=2\pi B$$ The difference in circumference, and therefore also the difference in the speed of the wheels, is independent of the radius $R$. So it is impossible to find radius from difference in speeds.
However, you can determine the radius $R$ of the turning circle from the ratio of speeds of the two wheels, as follows :
Suppose that the car turns through a small angle $\theta$ on a circle of radius $R$ as measured from the centre of the vehicle, which has width $2b$. Then the wheels trace out arc lengths $s_1=(R-b)\theta, s_2=(R+b)\theta$. Their speeds are in the ratio $$\frac{v_2}{v_1}=\frac{s_2}{s_1}=\frac{R+b}{R-b}$$ The radius of the turning circle is therefore $$R=\frac{v_2+v_1}{v_2-v_1} b$$ 
