# What is the axis of rotation of a turning car?

I was wondering while parking my car, what is the axis of rotation/pivot of a turning car? Does it differ when it is turning frontwards of backwards?

Is it different for a 4x4?

• This wikipedia page explains the idea. Instant center of rotation. The illustration to the right can be thought of as a car, with the links running parallel to the wheel axes. In this model of motion (quasi static), velocity and direction are actual properties of the object at the instant rendered as opposed to being derived from trajectories in time. So the concept is pretty much limited to basic dynamics. Jan 4, 2018 at 14:53
• Yes, in the real world, it differs depending on if you are going forward or reverse. The difference in the direction of rolling resistance changes the sideslip of the tires. Try backing up a trailer on soft ground, then driving back out. RVers get their rigs locked into camping sites all the time because of this. Side-slopes also function the same way, biasing side-slip so the path isn't reversible. Minor contributors include fwd vs rwd, Steering alignment (ackerman angle, toe, and linkage slop), and any torque bias in the differential. Jan 4, 2018 at 15:04
• Slightly relevant: youtube.com/watch?v=iFwfexZstO4 Jan 4, 2018 at 15:24

Turning center of the cars with fixed rear wheels is on a line extending from rear axel inward to the point interesting with the two front wheel axel lines. Providing two tracks, one inside for rear wheel and one outside for front wheel. Only in some rough terrain vehicle which have both the rear and front wheels attached to steering system this does not apply!

This creates a larger radius of turning for the front wheels, usually in the order of 3-4 feet tracking at a position on a tangent to the rear wheel turn circle.

Normal range of rdius of turn for midsize seddans is 16-20 feet inside dimension and 34-40 feet outside dimension!

Going back up same pattern applies! Unless you make the car skid by going too fast or doing stunt turns.

This discrepancy in radius is critical when designing turning ramps and driveways! one hase to allow for gradual increase in the width of the lane to accomodate this extra radius asthe car travels into the turn! All graphic standard enging/architectural handbooks have digrams for different residential and commercial settings!

Our driveway is both turning and sloping up. Many times in hot summer days I see the intricate dark track of our cars turning on the driveway. They start from two parallel lines, then separate into four track lines with the ones arcing outsid left by front wheels then they merge back and become two lines after the ramp ends in front of the garage space.

When turning/banking the steering mechanism linkage design e.g., Ackerman, is such that axes of rotated front wheels intersect on fixed rear wheel axis line at P, so around P the entire vehicle instantaneously rotates in the plane of the ground. Operates same way for 4X4 or 2X4 driven wheels.

Take the axles of all the wheels and extend them. Where they all intersect is the pivot point of the car.

In a front-wheel-steering car that will be somewhere in line with the rear wheels.

• I don't think so -- the axles don't move! Perhaps you meant the axis of the steered wheel itself? And then, due to toe-in and camber, the two front wheels rotate different amounts about each axis, so we need to identify exactly which axis matters. Jan 5, 2018 at 14:57

To elaborate on Narasimham's answer a bit, assuming a four-wheeled vehicle with fixed rear wheels, the rotation axis (which is normal to the plane on which the vehicle is moving) intersects a point (the center of rotation) on the axle line of the rear wheels. The front wheels must be rotated such that each of their rotation axes intersect the center of rotation.

Here's an image from Wikipedia's article on Ackermann steering geometry:

Here's another image (source):

Note that the two front wheels are rotated by different angles.

The Wikipedia article on steering in general may also be of interest.

• A differential between the front wheels is not needed on a rwd car... Oct 14, 2018 at 19:37
• @SolarMike True, although it's necessary for front-wheel drive. Since the question didn't specify front- or rear-wheel drive, I've removed the comment about differential drive from my answer as it's not really relevant. Oct 14, 2018 at 21:23