How to find the radius of the circle that a car will follow

[dpapadim]

TL;DR

I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity?

I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity? For example, if i turn the wheels of my car by 12 degrees to my current direction, how large of a circle will the car perform

 

[jrmichler]

When confronted by a problem like this, it helps to look at if from different directions. Keep trying until you find a direction that allows you to derive the equation(s). Expect that you will have to derive the equation(s), rather than finding "the" equation(s) in a book or online.

Hint 1: The front and rear tires are tangent to the circle.

Hint 2: The inside front tire and inside rear tire are tangent to the same circle. The outside tires are tangent to a different circle.

Hint 3: Lay it out in a sketch and the math will follow.

Hint 4: The two front tires are turned to different angles because they roll on different circles.