Proposal of a coast-down model including speed dependent coefficients for the retarding forces

Coast-down techniques are widely used on bicycles and motorized vehicles in order to estimate retarding forces and respective coefficients. The mathematical model behind coast-down data analysis is usually based on the assumption that both drag and rolling resistance coefficients do not depend on the vehicle speed. This assumption restricts the model validity to the specifically tested range of speeds and provide averaged values for the force coefficients. In the attempt to overcome this limit, the proposal of a complete polynomial equation of motion is developed, evaluated and discussed on a human powered vehicle case study. The analysis points out that the extended model is adequate for experimental data fitting and could potentially provide a more reliable power-speed prediction outside the testing range. However, the expressions included in the model in order to account for speed dependent coefficients is a first approximation with limited capability to represent these complex phenomena. As a consequence, further experimental testing is needed in order to achieve a validation. Advantages and side effects of both the classical and the complete polynomial models are discussed, concluding that the two approaches could be complementary and could answer different needs that specifically depend on the purpose of the coast-down analysis.