Motion ratio, wheel rate and ride frequency

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Motion ratio is how far the spring (or damper) moves for each millimetre the wheel moves. Because the ratio applies once to the spring's travel and once to its force, the stiffness the wheel feels, the wheel rate, is the spring rate times the motion ratio squared.

Formulas

MR = \frac{d L _{spring}}{d s _{wheel}} k_{wheel} = k_{spring} MR^{2}

The tire is a spring in series, so the ride rate at the contact patch is

k_{ride} = \frac{k _{wheel} k _{tire}}{k _{wheel} + k _{tire}}

and the corner's ride frequency, with $m$ the sprung mass on that corner, is

f = \frac{1}{2 π} \frac{k _{ride}}{m}

Use N/m and kg in the last formula (multiply N/mm by 1000).

Worked example: the Formula SAE front

The Formula SAE example drives a 60 N/mm coilover through a pushrod and rocker. opensus measures the motion ratio at ride height as 0.674:

k_{wheel} = 60 \times 0.67 4^{2} = 27.2 N/mm

With a 120 N/mm tire:

k_{ride} = \frac{27.2 \times 120}{27.2 + 120} = 22.2 N/mm

Each front corner carries 58 kg of sprung mass:

f = \frac{1}{2 π} \frac{22 190}{58} = 3.11 Hz

All three match the Ride, at design section of the readout. A 2.6 to 3.5 Hz ride frequency is typical of a winged FSAE car; road cars are usually between 1 and 1.5 Hz.

Rising and falling rate

A rocker's geometry makes the motion ratio change with travel. If it rises in bump, the wheel rate rises faster than the motion ratio itself (it goes with the square). Kinematics → Heave → Motion ratio plots it across travel. Pushrod and rocker angles are the usual way to tune it.

Damping

The same squared ratio applies to the damper: the damping the wheel feels is the damper's coefficient times its motion ratio squared. The readout shows the resulting damping ratio in bump and rebound, and Open 3D detail and damper curves on any spring or damper lets you draw its force-velocity curve directly.

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Last updated 2026-11-07 · View as Markdown