Can height of a curb be determined by the angles of scratches on the perimeter of a wheel that struck a curb? With any level of certainty, can the angles of scratches on the outermost edge of a wheel of known diameter be used to calculate the height of a curb, which the wheel struck at low velocity?
The wheel didn't strike the curb head on, but rather scraped against the curb while approaching (So, imagine rolling forwards or backwards beside the curb and then attacking it at an angle less than perpendicular).
It comes to mind that the type of curb is unknown, but suspected to be either semi-circular or perpendicular to the ground.
  
 A: Let us imagine that only one point of the curb scratches the wheel.  If we let the wheel radius be r, the height of the curb h, and the horizontal distance of the contact point of the wheel to the point below the point scratching, and measure $\theta$ as wheel rotation from the point where the contact point of thwe wheel is just below the scratcher, we have $d=r \theta$ and the distance from the scratcher to the center is $\sqrt{r^2\theta^2+(r-h)^2}$.  Then the distance in from the circumference is $r-\sqrt{r^2\theta^2+(r-h)^2}$.  The angular position of the momentary scratch is not $\theta$, however because the scratcher moves only at horizontal velocity $\frac {r-h}rv$.  So the angular poistion on the wheel is $\phi=\arccos \frac {r-h}{\sqrt{r^2\theta^2+(r-h)^2}}$If the scratch goes from one side of the wheel to the other, you can just take $h$ to be the maximum distance in from the circumference the scratch attains.  But without that, if you have two ends of a scratch the angular distance between them will give $h$ or you can use the angle which the scratch meets any given radius.
