Movement Ratio Calculator

The motion ratio indicates how far a suspension spring or damper moves relative to the wheel it controls. Because of the way that the wishbones act as levers, in most cases the spring does not move exactly as much as the wheel. This geometric relationship determines how the chosen spring actually feels on the road.

This calculator allows calculations in both directions. You can enter the spring travel and wheel travel to find the ratio, or you can enter the spring rate and ratio to find the effective wheel travel. Enter the known values and leave the unknown fields blank. The calculator will then determine the remaining results.

What is the motion ratio?

The motion ratio, also called the motion factor, installation ratio or lever ratio, is a value that results from the relationship between spring travel and wheel travel.

If the wheel moves by 100 mm and the spring shortens by 50 mm, then the movement ratio is 0.5. This value has no unit and in automotive engineering it usually lies between 0.3 and 1.0.

A low motion ratio means that the spring only sees a fraction of wheel movement so a stiffer spring is needed to achieve the desired rate. A high motion ratio close to 1.0 allows for a softer spring but as the spring carries almost all of the load on the wheel, the suspension mounting points must be robust enough to carry this load.

This is how this calculation tool works:

Start with the travel path. Measure how far the wheel moves vertically and at the same time measure how much the spring is compressed during this movement. This way you can directly calculate the motion ratio. This is a useful method when examining an existing suspension or designing a new geometry.

In the reverse direction calculations you can enter the spring constant and motion ratio to find the effective wheel rate at ground contact. You can also enter the desired wheel rate and motion ratio to back calculate the required spring constant. Any field can be used freely so simply select which calculation method you want by leaving fields blank.

Understanding of formulas.

The first relationship is a simple division. In the formula for wheel rate, the motion ratio is squared.

The square term comes because the motion ratio affects both force and displacement. On the force side it acts like a mechanical advantage from a lever, and on the displacement side as well. Let's look at some numbers. Suppose that a double wishbone suspension has a spring mounted between the pivot point and the ball joint. If the wheel moves 100 mm, then the spring shortens by 50 mm so the motion ratio is 0.5. A spring with a stiffness of 50 N/mm is used:

At the position of the tires, the suspension acts like a spring with a stiffness of 12.5 N/mm. Although when installing it is used a spring with a stiffness of 50 N/mm, in reality it only has one quarter of that.

Each input is described below, with the value it takes in the linkage above:

From spring constant to suspension natural frequency

The spring constant is only a middle value. What engineers actually adjust when developing chassis is the natural frequency of the suspension, i.e. the natural frequency of the spring package that supports each wheel and which is determined by the spring constant.

Here 'm' is the mass of the spring package that supports the wheel. If you enable the suspension natural frequency calculation option and enter the mass here then the calculator will perform the entire calculation for you. Roughly speaking, comfort oriented vehicles have a natural frequency below 1.0 Hz, typical street cars are between 1.0 and 1.5 Hz, sports suspensions are between 1.5 and 2.0 Hz, race cars are between 2.0 and 3.0 Hz or higher, and high performance race cars have even higher values.

The role of the motion ratio.

The kinematics affect all phases of suspension function. In the early design phase positions for springs and dampers are determined with available space and performance requirements constraining each other. Once a vehicle is built it informs which spring rate should be ordered to achieve desired wheel rate. This is the method used in most tuning work. The choice of damper also depends on kinematics as damper speed relates to wheel speed through kinematics. Wheel rates produced by the damper are also data required for adjusting suspension natural frequency and understeer/oversteer characteristics.

Measuring and adjustment tips:

To measure the motion ratio on a real vehicle, an angle sensor is mounted at the center of the wheel and another one on the housing of the spring or shock absorber. The suspension is then moved through its full travel and both values are checked. There's one point that can be easily overlooked: On many modern suspensions, the motion ratio changes with the travel as the angles of the wishbones change. So this single number model is only a snapshot of the vehicle at its original ride height.

A higher motion ratio means more efficiency and allows for the use of smaller springs and dampers, but also increases the load on the chassis mounting points. A lower motion ratio makes assembly easier, but requires stiffer springs and faster dampers. Regardless of the calculation results, you should always verify the spring rate by actual measurements.