Calculation of vehicle aerodynamic drag coefficients from velocity fitting of coastdown data

Abstract

Analysis of coastdown data is a useful tool for the extraction of rolling resistance and aerodynamic drag coefficients of a road vehicle. Cenek and Shaw [1], from Central Laboratories, Works Consultancy Service, New Zealand, published velocity-time profiles incorporating continuous on-board anemometry and road slope measurement. This paper discusses the mathematical and statistical techniques used for the extraction of parameter values and their confidence limits from these profiles. The vehicle rolling resistance F R and aerodynamic drag F D are assumed to have the respective forms at speed v F R = a 0 + a n v n F D = a D[ V cos Ψ] 2 where a 0, a n , and a D are functions of the relative vehicle speed V and yaw angle Ψ. Optimal values of the related rolling resistance and drag coefficients for a given data set are found from a non-linear least-squares fitting procedure. In the case n = 1, confidence limits on the aerodynamic drag coefficient, as well as a measure of the suitability of the model, are obtained. Also considered is the sensitivity of the coefficients to variations in the input data. Overall confidence limits on the coefficients may be reduced by averaging values over many separate runs. On the question of the value of n, ref. 1 presents experimental evidence, based on driving torque data, for taking n=2, a value used in road-load calculations, and the implication of this from the coastdown analysis point of view is discussed.