Drive: the trail is the rear-axle path. Dashed lines = wheel axes; red dot = instant centre of rotation.

Ackermann Steering Lab - 2D

Top view: turning circle, instant centre and inner/outer wheel angles.

-Turning radius (m)

-Inner wheel angle (deg)

-Outer wheel angle (deg)

-Parallel-steer angle error (deg)

-Yaw rate (deg/s)

-Rack travel (mm)

-Heading (deg)

-Distance (m)

Independent checks

The science

At low speed a wheel rolls without sideways slip only if its axis points along the circle it travels. All four wheel axes must therefore pass through one point, the instant centre of rotation (ICR), which lies on the extension of the rear axle. For wheelbase L and track t the rear-axle centre follows radius R = L / tan(delta_mean).

Ackermann condition. The inner wheel must turn more than the outer: cot(delta_outer) - cot(delta_inner) = t / L, with tan(delta_inner) = L / (R - t/2) and tan(delta_outer) = L / (R + t/2). With parallel steering both wheels take the same angle, their axes do not meet, and one tyre must scrub sideways; the page reports that wheel-angle error.

Rack and pinion. Rack travel is steering-wheel angle times the pinion pitch radius; the steering ratio (13:1) divides the wheel angle to give the mean road-wheel angle. Yaw rate is v / R.

Honest simplifications: kinematic model only (no tyre slip angles, no suspension, no speed-dependent understeer); the tie-rod linkage is replaced by the ideal Ackermann mapping; no steering effort or friction.