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.

In the preliminary design of a motorcycle suspension, simple equations are used to calculate optimal stiffness and damping for comfort or roadholding, to conceive and evaluate first prototypes in a short time. The spring deformation in static equilibrium, known as suspension sag, with the calculated stiffness needs to be revised to minimize reaching any of the suspension ends on the expected transients. The general practice is to set the suspension sag on 33% of the overall stroke by adding an appropriate preload of the springs, but significantly different values are also recommended for specific disciplines. The determination of the specific sag value for a given application seems unresolved in the literature. The aim of this paper is to propose a simple, yet general model to calculate the suspension sag needed for a specific discipline, particularly for the preliminary design stage of motorcycles and bicycles. To achieve this, we calculate the expected suspension stroke needed on random roads with a linear half-motorcycle model, from which we find an expression to determine the minimum sag required in terms of road class and longitudinal speed. The proposed procedure is general, in the sense that it is not bounded to a specific discipline or driving style, though representative road class and longitudinal speed of each discipline need to be further studied.