Radius of the turn of leaning bike (for small steering angles)

Description

This lean of the bike decreases the actual radius of the turn proportionally to the cosine of the lean angle. The resulting radius can be approximated (within 2% of exact value) by the wheelbase, the lean angle, the steer angle and the caster angle. Wheelbase is the horizontal distance between the centers (or the ground contact points) of the front and rear wheels and the caster angle, is the angle that the steering axis makes with the horizontal. The steering axis is the axis about which the steering mechanism (fork, handlebars, front wheel, etc.) pivots.

Related formulas

Variables

rRadius of the turn (m)
w Wheelbase (m)
θThe lean angle (radians)
δThe steer angle (equal to tangent) (dimensionless)
ϕThe caster angle (radians)