Analytical expression to calculate the suspension sag of vehicles.

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.