Springs

Springs are used to control the vertical motion (z-direction) of the wheels, as well as pitch and roll. This page will focus only on the vertical motion, sometimes called ride.

Spring Rate

Springs produce force based on how much they are stretched or compressed. The stiffness of a spring is represented in its spring rate, which is in units of Force/Displacement. For example, if it takes 100 Newtons to compress a spring 1 millimeter, its spring rate would be 100 N/mm. If you are using air springs, the spring rate will be non-linear.

Motion Ratio

The effective spring rate of the wheel is not the same as the rate of the spring itself (unless the spring is positioned directly over the wheel). This is because of something called the motion ratio. It is defined as the ratio of spring displacement to wheel displacement. If the wheel moves up one inch, and the spring compresses two inches, the motion ratio would be 2:1.

You should design your suspension so that the spring connects to the lower control arm as far outboard as possible. This gives the spring maximum leverage over the wheel, and allows you to use softer springs.

Wheel Rate

Wheel rate is the effective spring rate at the wheel. If you assume the definition of motion ratio is Spring displacement : Wheel displacement, then the formula for wheel rate is (Spring Rate)*(Motion Ratio)^2. See the video above for an explanation of this. You can see that as the motion ratio goes down, you need a stiffer spring to achieve the same wheel rate.

Ride Rate

Ride rate is wheel rate with the tire's stiffness taken into account. This can be represented as two springs in series.

let K_w be wheel rate and K_t be the spring rate of the tire
- Ride Rate = (K_w * K_t) / (K_w + K_t)

Sprung Mass Natural Frequency

This is a parameter of a vehicle's suspension suspension system that is often used as a rule of thumb to select spring rates. In my opinion, it is better to select spring stiffness based on what roll stiffness and pitch stiffness you want. Sprung mass natural frequency is an indicator of how stiff a car's ride will be, but since this is a race car we aren't really concerned with that.

Spring Calculator - Mathcad

How to Spring the Car?

Springs: Design Matrix

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