February 19, 2020 2 min read

What the heck is a motion ratio? It's not the size of the shock, it's the ratio of the motio(n). (?)

Vehicles with different suspension layouts can make it difficult to compare settings between cars. A spring rated at 8 kg/mm on a Honda S2000 will not act the same as it would on a Subaru BRZ. In fact, an 8 kg/mm spring on the front suspension of a Subaru BRZ will work differently than it would on the rear suspension.

The wheel rate, or the spring rate “at the wheels”, can be calculated using a car’s motion ratio to allow for a better understanding of what the spring is actually doing.

The Subaru BRZ has a rear multi-link suspension. While the front has a coilover strut mounted at the hub, the rear spring is mounted inwards on the control arm towards the center of the car. With the spring closer to the pivot point, it needs to be stiffer to have the same effect as it would if it were mounted at the end of the arm or at the hub.

This effect can be quantified with the motion ratio. For the front suspension on a BRZ, it's close to 1. In the rear, it's around 0.75.

The motion ratio can be approximated by taking a few measurements under the car.

  • d1 is the distance from the control arm inner pivot point to the spring centerline.
  • d2 is the distance from the control arm inner pivot point to the outer ball joint.
  • motion ratio = d1 / d2
  • The motion ratio can also be measured directly by looking at how far the wheel moves as the spring compresses.
  • motion ratio = wheel travel / spring travel
  •  To get the "wheel" rate of the spring, or the spring rate at the wheel, multiply the spring rate by the square of the motion ratio.
  • Wheel Rate = Spring Rate * (Motion Ratio2)
  • 4.5 = 8 * (0.752)

So a set of coilovers on a BRZ with 8 kg/mm springs in the front and rear really means that you’ll have about 8 kg/mm in the front and 4.5 kg/mm in the rear in terms of wheel rate.

*If the spring is mounted at an angle, then a correction factor must be applied. This is not necessary for this example.

Is that bad? If it's not what you were planning on then, yes, it’s a problem. Spring rates aren’t the only variable in a suspension system, but they are an important part of setting up a car.

Other variables, such as sway bars and alignment settings, should be tuned in conjunction with the main springs to produce the desired handling and ride characteristics.

Ultimately, spring rates and wheel rates are used to calculate a suspension frequency, but that’s a topic for another time.