Motion Ratio Explained: Spring Rate vs Wheel Rate
Spring rates are quoted at the spring. The tire does not feel that number. Between the two sits the suspension linkage, which works as a lever, and the motion ratio describes that lever. It is the reason the same 8 kg/mm spring is stiff on one car and soft on another.
The definition
If the wheel moves up 100mm and the spring compresses 65mm, the motion ratio is 0.65. A MacPherson strut, where the spring sits almost directly over the wheel, is typically between 0.9 and 1.0. A double-wishbone or multi-link suspension with the coilover mounted part-way along the lower arm is often between 0.55 and 0.8. Some sources quote the inverse (wheel travel ÷ spring travel); a value above 1 is the sign of that convention.
Wheel rate: why the ratio is squared
The lever acts twice. It reduces how far the spring moves for a given wheel movement, so the spring produces less force. It then reduces that force again on its way back to the wheel. Two reductions by the same factor is the factor squared.
| Spring rate | Motion ratio | Wheel rate |
|---|---|---|
| 8 kg/mm | 0.95 (typical strut) | 7.2 kg/mm |
| 8 kg/mm | 0.75 | 4.5 kg/mm |
| 8 kg/mm | 0.65 | 3.4 kg/mm |
| 12 kg/mm | 0.65 | 5.1 kg/mm |
So a double-wishbone car at 0.65 needs roughly a 17 kg/mm spring to match the wheel rate of a strut car on 8 kg/mm. Comparing spring rates between different cars, or between the front and rear of the same car, means nothing until both are converted to wheel rate. Dampers and anti-roll bars have their own motion ratios and follow the same rule.
Ride frequency: comparing setups fairly
Wheel rate still depends on how heavy the car is. Ride frequency removes that: it is how fast a corner of the car would bounce on its spring, and it lets very different cars be compared on one scale.
A wheel rate of 7.2 kg/mm is about 70,600 N/m. With 300kg of sprung mass on that corner, the frequency is about 2.4Hz. The same corner on the 3.4 kg/mm wheel rate is about 1.7Hz.
| Ride frequency | Typical character |
|---|---|
| 1.0–1.5 Hz | Comfort-oriented road cars |
| 1.5–2.0 Hz | Sports cars and firm road setups |
| 2.0–3.0 Hz | Track-focused cars on road tires or without much downforce |
| Above 3 Hz | Race cars with significant aerodynamic load |
These bands are general guidance, not targets for a particular car. The relationship between front and rear frequency matters as much as either number.
Measuring it
- Support the car safely and remove the spring from one corner, leaving the damper in place.
- Move the hub through its travel in steps with a jack, for example every 10mm of wheel travel.
- At each step, measure the damper's length between its mounts.
- Divide the change in damper length by the change in wheel height. Use the steps around normal ride height.
- The ratio usually changes through the travel; a ratio that rises as the wheel moves up gives a rising rate.
- Lowering the car changes the arm angles and therefore the ratio at the new ride height.
- A coilover that leans in at the top loses a little more: multiply by the cosine of its lean from the direction the mount moves.