Analytical expression to calculate the suspension stroke and sag of vehicles

Suspension stroke and sag are important to provide comfort to the passengers and to maintain contact of the tyres with the ground (road holding), nonetheless, they have not been extensively discussed in the literature. In this article, we aim to obtain elementary expressions to calculate the stroke and sag. To this end, we use the suspension displacement variance found in the literature, which has been derived for continuous road excitations, and by introducing a reliability interval, we are able to find the desired expressions. We extended the analysis to the case when the optimal suspensions are used, and furthermore, we simplified the expressions using two approximations. Lastly, a numerical example shows that the derived equations yield reasonable values for a first approximation, highlighting that they are valid for continuous excitations.