Wragge-Morley, R., Herrmann, G., Burgess, S., and Barber, P., "Modelling and Simulation of Rapidly Changing Road Gradients," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):392-401, 2016, doi:10.4271/2016-01-1663.
In vehicle dynamics modelling, the road profile is generally treated in one of two ways; either the gradient is a property that changes over a length scale far greater than that of the vehicle's wheelbase, or as a very detailed road surface model for determining the behaviour of vehicle suspensions. Occasionally, for modelling the behaviour of off-road vehicles, step-climbing manoeuvres are modelled. We propose an extension of these step-climbing models to a general, continuously varying road gradient model for cases where the distance over which the large gradient change occurs are of similar length-scale as the vehicle wheelbase. The motivation behind this work comes from a road gradient and vehicle mass estimation problem where it was noticed that very sudden gradient changes have a significant impact on the powertrain, but in a way that is not proportional to the attitude change of the vehicle. We present an analysis applicable to these cases where the road gradient change is substantially different from the vehicle attitude change. The analysis is built up from a very basic step climbing exercise to a general case solution for two dimensional longitudinal vehicle dynamics. Methods of handling road gradient and gradient change for modelling purposes are discussed. A method is proposed that defines the gradient change as an input to a backwards dynamic model that allows us to compute torque required to achieve a pre-defined datum speed during a gradient transition. The results of simulations for simple gradient change cases are shown. We discuss the implication of these road gradient transients for vehicle parameter estimation based on powertrain behaviour.