Turning Radius calculation

This article describes the calculation of the turning radius of a car or bicycle.
This radius depends on two things:
    - the wheelbase w , which is the distance between the front- and the rear wheel
    - the angle a of the front wheel
We suppose that only the front wheel is able to turn.
See figure below:
    side view top view

The front and rear wheel follow a circle with the same center.
At all times, the direction is perpendicular to the radius.
See figure below:

The radius of the front wheel is R, the rear wheel r.
From the figure above we conclude: