Radius of the turn of an upright bike (for small steering angles)

Description

In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any front-wheel steered vehicle.The radius of the turn of an upright (not leaning) bike is related to the wheelbase, the steer angle and the caster angle of the steering axis. 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 (mm)
wThe wheelbase (mm)
δThe steer angle (equal to the tangent ) (dimensionless)
ϕThe caster angle (radians)