Calculation of Turning radius of vehicle, Minimum turning radius

　・In Japanese

■Definition of turning radius

The turning angle of the tire when turning the steering wheel is slightly different between the front, back, left and right, and the inner ring is more angled. If the angles of the outer and inner tires are the same, the tires will slip because the turning radii are different. Ackermann geometry is the difference between the turning angles of the outer and inner rings. By doing this, the center of turning will be the point of intersection when lines are drawn vertically on the left and right tires. The turning radius is defined as the distance between the outer tire and the turning center.

■How to calculate turning radius

＜For extremely low vehicle speeds＞
In many cases, the Ackermann geometry is not actually achieved, and the turning radius is the value obtained by adding the red line and the blue line and dividing by 2, as shown in the figure below. The red line is drawn from the intersection of the lines drawn vertically from the inner ring toward the center of the outer ring. It is different from the line drawn vertically from the outer ring. L is the wheel base, T is the tread, which can be found from the vehicle specifications, and θ can be found from the steering angle. The turning radius at this time is called the minimum turning radius.



＜Simple method＞
For simple calculation, use only the outer ring. The turning radius R is as follows.


＜For steady turning＞
As the vehicle speed increases, centrifugal force is added, and the tire is given a small slip angle outward, and this angle becomes the traveling direction angle of the vehicle. Also, as shown in the figure below, the turning center of the tires is slightly shifted upward compared to when the vehicle is at extremely low speeds.



The turning radius R is as follows. For the sake of clarity, the drawing is simplified and supplementary lines are also drawn. Trigonometric approximations are explained here.

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