I know that when a car is taking a turn, the front 2 wheels trace out 2 arcs having the same centre. I also know that the steering angle for the outside wheel is more than that of the inner wheel to prevent the car from skidding. My question is during the turn do the rear wheels trace out the same arcs as the front wheels.

enter image description here

  • 2
    $\begingroup$ Possible duplicate physics.stackexchange.com/q/169274/26076 $\endgroup$ May 13, 2015 at 14:40
  • $\begingroup$ @WetSavannaAnimalakaRodVance - I agree the two are related but I don't think the answer given in your possible dup is the answer that OP is looking for here. $\endgroup$
    – Floris
    May 13, 2015 at 15:05
  • $\begingroup$ If you're looking into steering geometry I should note that in real driving conditions the tires always slip slightly at a velocity dependent rate, called the slip angle. $\endgroup$
    – Rick
    May 13, 2015 at 15:11

1 Answer 1


No they won't. while they may be circles that are centered on the same point, the radius of the four circles is different. This diagram ought to convince you:

enter image description here

The four wheels trace out circles with radius $r_1 ... r_4$, and each of these will be different (in general). It is possible, for certain combinations of $L$, $W$ and $D$ that the front right and bottom left wheel trace the same arc; but the others will always be (slightly) different.

$$\begin{align}\\ r_1 &= \sqrt{L^2 + D^2}\\ r_2 &= \sqrt{L^2 + (W+D)^2}\\ r_3 &= W+D\\ r_4 &= D\\ \end{align}$$


Not the answer you're looking for? Browse other questions tagged or ask your own question.