The vertical deflection of a tyre is closely proportional to the applied vertical force. It is convenient to refer to this as vertical stiffness or tyre spring rate. The actual vertical stiffness of the tyre depends upon several factors:

• Size

• Construction

• Inflation Pressure

• Camber

• Temperature

• Speed of Rotation

• Lateral and Longitudinal Forces

However 90% of the tyre stiffness comes from inflation pressure, the tyre is effectively a gas spring, although not a very honest one.

The tyre companies normally issue dynamic rolling radius and circumference data at various speeds, loads, pressures, and cambers so that dynamic ride heights and gearing can be calculated. A dynamic rolling radius tyre model can be constructed from this data so that the tyre dynamic spring rate and amount of tyre growth can be obtained based upon the operating conditions.

The geometric and dynamic effects of high and low vertical stiffness tyres on the car with heave are shown in the diagrams below.

## The geometric and dynamic effects of high and low vertical stiffness tyres on the car with heave:

## The geometric and dynamic effects of high and low vertical stiffness tyres on the car with roll:

A large proportion of the total dynamic ride height change with speed is due to tyre deflection. The options are either to increasing the static ride heights or increase the heave rate by stiffer springs / third springs / packers. The later options will only increase the proportion of tyre to suspension deflection even more. The diagram shows a very simple model of rubber.

If a sinusoidal varying displacement is applied to the top point A, then the consequent force amplitude at A will depend on the frequency. At low frequency, both springs will act in series with the damper exerting little force. At high frequencies, only the upper spring will move as the damper will now exert a large force and hardly move. However, there must be an intermediate frequency where energy dissipation is at a maximum. Hence the development in F1 of mass damper systems and "J" dampers, in an effort to try to alleviate the problem.

If a sinusoidal varying displacement is applied to the top point A, then the consequent force amplitude at A will depend on the frequency. At low frequency, both springs will act in series with the damper exerting little force. At high frequencies, only the upper spring will move as the damper will now exert a large force and hardly move. However, there must be an intermediate frequency where energy dissipation is at a maximum. Hence the development in F1 of mass damper systems and "J" dampers, in an effort to try to alleviate the problem.