Analytical expression to calculate the suspension sag of vehicles.

The suspension system of a vehicle is essentially conceived with two objectives: to provide comfort to the passengers and maintain tires in contact with the ground (roadholding). It is well known, however, that optimal comfort and roadholding cannot be achieved simultaneously since they require a different set of stiffness and damping. Simple models are used to comprehend the variables involved with which the response acceleration, tyre force and suspension displacements due to random roads had been derived, together with optimal suspensions. Nonetheless the required suspension travel and suspension sag have not been extensively discussed. In this article we derive expressions to determine the suspension travel and suspension sag (static compression) required to transit a random road. It was also analysed the case when the optimal suspensions are used, and the expressions where simplified. Lastly, a numerical example show that the derived equations provide reasonable values for a first approximation.