What is Slowing Me Down? Estimation of Rolling Resistances During Cycling

In this paper, we present a method to estimate the current rolling resistance coefficient of a four-wheeled electric bicycle. We derived linear regression models between the velocity of the bicycle and the vibrations at the handlebars to be able to classify the current road surface and consequently the rolling resistance coefficient. To derive the models, we performed experiments on three different surfaces typical for cycling - asphalt, fine gravel and coarse gravel. A cyclist performed five test rides on each surface on different days at varying velocities. During the experiments power output at the pedals and velocity were measured. Additionally, vibrations at the handlebars were measured using a smartphone. Then, a curve consisting of the mathematical representation of rolling and air resistance was fitted to the experimental data and the rolling resistance coefficients of the surfaces and the effective frontal area of bicycle and cyclist were estimated. The magnitude of the vibrations at the handlebars was calculated for each test ride and each surface. From this data the linear regression models for each surface were derived using velocity as the predictor. Analyzing the data yielded rolling resistance coefficients of 0.01221, 0.01468 and 0.01832 for asphalt, fine gravel and coarse gravel, respectively, and showed significant difference. The magnitude of vibrations increases significantly with velocity and is higher for surfaces with higher rolling resistance. To validate the model the outdoor experiments were repeated with a similar prototype of a four-wheeled electric bicycle. The results can be used to classify the current surface and therefore estimate the rolling resistance coefficient. We believe that this system can help improve the estimation of the residual range of electric bicycles by providing more detailed information about the environment and consequently enhance their operating distance and the usage of the bicycle.