# How does a car turn without any skidding?

The rear wheels of a car always face in the direction the car is moving. The front wheels are able to turn left or right and thus can point in the direction the car is moving towards. What I don't understand is how a car can turn with all four wheels rotating (not skidding). That is, how is it possible that the front two tires can face in one direction, the rear two tires in another direction, with the four tires all connected by rigid rods and with all four tires rotating without skidding?

I'm trying to visualize this assuming the car is moving very slowly, but even then the situation just seems impossible to me. Is it in fact that the rear tires are skidding in just very small micro-steps so that we don't actually observe it happening?

• I was going to give a wikipedia link to differential (en.wikipedia.org/wiki/Differential_%28mechanical_device%29) but I think the article there unnaturally lacks obvious visual explanation. Commented Aug 17, 2012 at 13:24
• maybe I misunderstood the question. Do you concerned that while turning outer wheels accomplish greater path than the inner ones? Commented Aug 17, 2012 at 13:35
• No, I was not concerned with the fact that the outer wheels rotate at a different speed than the inner wheels via a differential. What I'm asking is the following: Let the rear tires be facing 0 degrees and the front tires be turned to 5 degrees with the car moving at some reasonably slow velocity such that all of the tires are rotating. How is it that the rear tires can (after some time) be facing 5 degrees without any skidding? How is this possible since the rear tires cannot turn? Commented Aug 17, 2012 at 13:42
• How is it that the front tires can (after some time) be facing 5 degrees without any skidding? Both front and rear tires have to turn and skid around the vertical axis to actually turn. Is that the skidding around the vertical (not horizontal) axis you were concerned about? Commented Aug 17, 2012 at 13:48
• I might think about it like from a horse pulling a sleigh (which is not a bad model for a front wheel drive car). The sleigh skids, no matter what direction it's going -- it has no wheels, so everything is a skid. When we put some wheels on the back of the sleigh, it is able to move without skidding in (and only in) the direction of the wheels' rotation. If the sleigh is moving in a direction other than straight ahead, the sleigh still skids, except that now it's actually the tires that skid since they're in contact with the road instead of the sleigh. Commented Aug 17, 2012 at 20:08

The key here is that you think there is no skidding. In fact, there is skidding, although for normal automobiles this is barely noticeable. For normal cars, the rear wheels simply skid a lot less than would the front wheels when a turn would be fully forced.

You can see this also in trucks, where it becomes necessary to have dual or triple-axle steering when doing tight turns while manoeuvring.

• You can hear the sound when they slowly turn tight. Commented Aug 17, 2012 at 13:31
• that's true, good one Commented Aug 17, 2012 at 13:34
• Although this isn't completely an answer, it is a correct start to the answer. I remember spending countless hours trying to formalize the problem in basic calculus. If solved fully and correctly, it may not so much describe how a car turns, but instead give an optimal algorithm for a car cornering system, as a naive solution would wear down the tires surprisingly fast. Commented Aug 17, 2012 at 13:41
• @AlanSE Not to sound condescending, but why would such an algorithm be so complicated that it required countless hours? Commented Aug 17, 2012 at 13:44
• mcFreid, youtube.com/… (time 1.29) She throws a hoop. It rotates and skids for a certain time, then stops skidding and rotating comes back. I couldn't find a better video, maybe youtube.com/… too Commented Aug 17, 2012 at 15:31

Simplify it. Think bicycle, not car.

The two axle lines intersect at a point C. Each wheel travels in a circle about that point. There's no skidding involved.

EDIT: As a result of comments, I thought it might be helpful to show what I think the road looks like from the viewpoint of the tire. This is an exaggerated view of the contact patch of the tire against the road. From the tire's point of view, the roadway material is traveling in a circle about center C. So a piece of rubber comes down straight, makes contact with the road, travels in an arc, and then breaks contact with the road and continues in a straight line. It can do this because it's made of flexible rubber.

At no time does it slide against the road - i.e. skid, except for the tiny amount due to the material at the outside edge of the patch actually having to travel farther than the material at the inside edge of the patch.

• Actually, we can simply my question even further. Let there be one wheel on a road which is fixed at the origin upon which it pivots about the vertical axis. Clearly upon spinning the rod, the wheel does rotate (assuming a small enough wheel and a long enough rod). However, I just can't see how the wheel actually changes direction without skidding. I'm trying to visualize the process in small steps, and it seems to me that the wheel must skid. From Rody's answer above this appears to be the case. Now I am trying to understand how both skidding and rotation can occur at the same time. Commented Aug 17, 2012 at 14:24
• @mcFreid: As long as we're simplifying, idealize the wheel to be zero width (a knife edge of super-hard material). It rolls forward and backward without slipping. The path on which it rolls does not have to be perfectly straight, does it? From instant to instant, it can turn a little bit without slipping, because it contacts the road at an infinitessimal point. Commented Aug 17, 2012 at 14:32
• @mcFreid: Actually, since a tire contacts the road in a patch, not a point, the side of the patch away from C does have to travel a larger distance. So it does skid a little bit that depends on how wide the tire is. Commented Aug 17, 2012 at 14:40
• At zero width, I still can't seem to visualize it turning without slipping. I can accept the fact without understanding it, but I'd much rather understand it :/ It just seems to me that a rotation has to be in a straight line. If it's not in a straight line, there has to be some kind of movement that isn't a rotation... Commented Aug 17, 2012 at 14:43
• @RodyOldenhuis: Then it can turn in a circle about the center of the rear wheel. Then what I said earlier about there being some skidding at the rear wheel due to the width of the contact patch applies. Commented Aug 17, 2012 at 16:20

Mind you also that the front wheels, which are turning, do not turn to one direction. Both front wheels will be aligned separately, to ensure that the curvature of the trajectory they follow leads to no skidding (see Ackermann steering geometry). The rear wheels, as stated above, are prevented from skidding by the rear differential.

In four wheel driven cars, you typically find three differentials: one for rear wheels (left+right), one for front (left+right), one for front+rear overall.

• This is not exactly what I was asking (see comment in original post). Thanks for pointing this out anyway as I did find the link interesting! Commented Aug 17, 2012 at 13:45
• @mcFreid: Indeed this is one of the Ackermann geometry properties: the rear wheels are always just going "straight", as the center of curvature is aligned with the rear wheel axes. I think the illustration in Wikipedia shows this quite neatly. With this geometry, it is only the front wheel steering angles that need to be considered. Commented Aug 17, 2012 at 13:50
• I think the point that the OP is uncomfortable with is that the rear wheels (and indeed the front wheels on Ackermann steering geometry too!) are slipping (minimally...) due only to their having nonzero width. Commented May 6, 2014 at 16:26

The way skidding is minimized is by using a differential steering system. Here's an article about the topic and an awesome 1937 video which gives a good explanation about the concept.

You are correct. Turning/cornering wheels slide/skid on the road. This is because the cornering wheel is changing direction which means rotating on a vertical axis. With the contact patch having some length and or width there will be sliding on the road.

At 40 seconds into the following video there is an experiment that reveals a cornering car wheel is rotating on a vertical axis and sliding/skidding.