Wheel Centre Stiffness / Longitudinal Compliance

Wheel centre stiffness (the inverse of wheel centre compliance) is a measure the equivalent longitudinal stiffness of the suspension system at the wheel centre. It is measured in Newtons per metre (N/m) or Newtons per millimetre (N/mm). Wheel centre longitudinal stiffness is tuned on production cars to deliver a level of longitudinal impact isolation and energy absorption from potholes, bumps, road joints, etc.

Production cars usually have a wheel centre longitudinal stiffness between 300 – 700 N/mm, with comfort orientated cars towards the lower end of this scale. In practice longitudinal stiffness is tuned as shown below. A lower control arm will have a stiff bush to manage lateral cornering loads and a soft bush tuned to manage longitudinal loads. When the suspension system is subject to a longitudinal impact, the lower control arm will pivot around the stiff bush. The resultant travel in the soft push provides the longitudinal isolation in the system.

If you regularly drive over a small bump on your daily drive, try the following scenarios as a simple demonstration of the influence of this bush on the comfort of a suspension system. Drive over the bump as normal and notice the impact you feel. Now drive over the obstacle at the same speed but this time brake sharply before the obstacle and hold the brake as you hit it. Braking before the obstacle applies a longitudinal load to the suspension and takes up the travel in the soft bush. Now when you hit the obstacle, the soft bush is stiffer than usual as it will be pre-loaded and will no longer have the same travel as before. The impact will be more noticeable in this second scenario.

As always with suspension systems, delivering low longitudinal stiffness comes with some trade-offs against other suspension characteristics. The most prominent is castor wind up or castor compliance under braking.  This can result in degraded brake response and brake feel, so like many suspension design parameters the designer needs to find the right balance for their vehicle.

There are some suspension systems which can decouple wheel centre longitudinal stiffness and castor wind up, the most widely used is the integral link suspension which is found on some high-end saloon cars and SUVs.