Motion ratio: the lever between the spring and the road

Your spring rate is not your wheel rate. The linkage sits in between as a lever, and because the effect goes as the square, a small ratio change makes a big difference — 400 lb/in can arrive as 196.

Here is a question that has embarrassed a lot of people at the track: you fitted 400 lb/in springs, so the car has 400 lb/in at the wheel, right?

No. On one of the layouts in this course it has 196.

The spring doesn’t sit on the wheel. It sits on the control arm, or the strut, or a rocker — somewhere partway along a lever. Motion ratio is how far the spring moves for a given wheel movement:

\text{MR} = \frac{\text{spring compression}}{\text{wheel travel}}

Mount the spring halfway along the arm and MR is about 0.5: the wheel moves 20 mm, the spring squashes 10 mm.

Why it’s squared

The temptation is to think a 0.5 motion ratio halves the wheel rate. It quarters it, and the reason is worth understanding rather than memorizing.

The lever does two things at once. It reduces the displacement the spring sees — so the spring generates less force. And it reduces the force that reaches the wheel, because the wheel is on the long end of the lever. Each effect scales with MR, and they multiply:

k_{\text{wheel}} = k_{\text{spring}} \times \text{MR}^2

That square is the single most useful fact in spring selection. Watch it bite on one layout, by sliding one mount.

The wishbone layout mounts its shock partway along the lower arm, giving MR 0.700. Move that lower mount 40 mm inboard, toward the chassis, and nothing else:

Shock lower mount	MR	MR²	400 lb/in spring becomes
as designed	0.700	0.490	196 lb/in
40 mm inboard	0.616	0.379	152 lb/in

Forty millimeters along an arm — a change you could make by drilling a second hole — took 22% off the wheel rate. Not 12%, which is what the ratio change alone suggests. The square is what turns a modest geometric change into a large spring-rate change.

For contrast within the same course, the strut layout runs MR 0.936, so that same 400 lb/in spring arrives as 350 lb/in. A strut’s near-1.0 ratio is one of its genuine advantages: the spring sits almost directly on the wheel’s path, so little is lost — and it’s why strut cars need softer-looking spring numbers than wishbone cars for the same ride.

Working backwards is the useful direction

In practice you rarely start from a spring. You start from a wheel rate you want — usually from a target ride frequency, which is chapter 12 — and you need to know what to order:

k_{\text{spring}} = \frac{k_{\text{wheel}}}{\text{MR}^2}

Worked example. You’ve decided you want 24.5 N/mm at the wheel. On the wishbone layout (MR 0.700, MR² 0.490) you need 50 N/mm of spring. Move that same target to a corner with MR 0.936 and you need only 28 N/mm.

Put the other way round: a corner with MR 0.70 needs a spring 1.8× stiffer than a corner with MR 0.94 to reach the same wheel rate. That factor is why spring rates from one car mean nothing on another, and why “what springs do you run?” is close to a useless question without the motion ratio beside it.

It isn’t a constant either

By now you can guess. As the wheel travels, the arm rotates and the angle between the spring and the arm changes, so MR changes through travel. The app reports the current value beside the shock: MR 0.94 · Travel 142 mm on the strut layout.

A ratio that rises with compression gives a naturally progressive spring rate at the wheel — soft around ride height, firmer deep in bump — which is often exactly what you want and is how many race cars get progression without progressive springs. A ratio that falls does the opposite and is usually a mistake.

Go look at it

Open the wishbone layout — the rear axle of the Mini preset, which mounts its shock on the lower arm.

Just under the suspension type, find the MR readout. It should say about 0.70.

Drag the Shock Lower Mount inboard along the arm, toward the chassis, by roughly 40 mm. MR should fall to about 0.62.

Do the arithmetic as you go. At MR 0.70 a 400 lb/in spring gives 196 lb/in at the wheel; at 0.62 it gives 152. You just removed 22% of the wheel rate without touching the spring.

Now feel it. Go to the Springs/Shocks tab and run the car over Urban Road, noting RMS Accel (g). Change the motion ratio back in Geometry, then run the identical road again.

For contrast, look at the strut layout on the front axle — MR 0.94, because the strut carries the spring almost directly.

The spring sits partway along the arm, so it moves less than the wheel does. That ratio reduces both the travel the spring sees and the force it delivers — which is why wheel rate goes as MR squared.

Drag the shock mount and watch MR — Mini front →

What it costs you

A low motion ratio isn’t only a spring-rate problem — it’s a force problem. The spring and damper have to react the same wheel force through a shorter lever, so the loads in the spring, the shock, the mount and the arm all go up. Halve the motion ratio and you roughly double the force through that hardware for the same wheel rate. On a kit car, that’s the difference between a bracket that lasts and one that tears out of the chassis.

It’s a damper problem too, and this catches people: the damper sees wheel velocity multiplied by MR, so a low ratio means the damper operates at lower velocities, where its valving is least consistent. Two cars with identical wheel damping can feel completely different because one is working its damper in a useful part of its range and the other isn’t. That’s chapter 15.

The upside of a low ratio is packaging and progression — inboard springs, rocker suspensions, and everything tucked out of the airflow. Formula cars accept high forces to get exactly that.

Rules of thumb

MacPherson strut: 0.90–0.98. The spring is nearly on the wheel.
Double wishbone, coilover on the lower arm: 0.55–0.75, depending on how far outboard you can mount it.
Rocker / pushrod: 0.5–1.2 and tunable by design, which is most of the reason to accept the complexity.
Rear multilink: often 0.6–0.8.
Design target: get MR as high as packaging allows unless you specifically want progression, because high MR means lower forces, more consistent damper velocities and smaller springs.
Rally-raid and desert: frequently run two dampers per wheel, and this is why. With 350–600 mm of travel the energy per corner is enormous, and a single unit at a modest motion ratio cannot absorb it without overheating. Splitting the load across two shocks halves the force each one carries — and bypass shocks add position-sensitive damping on top, which is chapter 15’s territory.

Try this

Find the highest motion ratio the wishbone layout can package. What did you have to move, and does the shock still fit inside the wheel arch?
Set up a corner where MR clearly rises through compression. What does that do to the ride over a rough road versus a constant ratio?
Take a spring rate you actually own and compute its wheel rate at MR 0.70 and MR 0.94. Would you have guessed the difference?

Next, and last in this module: Ackermann — why the inside front wheel should turn more than the outside one, and why race cars often refuse to do it.

Preset hardpoints are illustrative sketches, not measured factory specs.