To simulate bicycle traffic accurately, it is essential to capture how bicyclists react to features of the infrastructure such as the longitudinal gradient of a bicycle path. Bicycling requires humanpowered motion, and the power output provided by bicyclists differs significantly among bicyclists due to physical capabilities and preferences. Therefore, the objective of this paper is to investigate the connection between gradient and power output in bicycle traffic, with the purpose of developing a power-based model that accurately predicts the speed of bicyclists. Based on trajectory data of free-riding bicyclists travelling on a non-flat bicycle path segment, we estimate changes in power output as a function of gradient considering the physical forces acting on a bicycle. The results suggest a linear correlation between gradient and power output; while bicyclists increase their power output on the uphill as gradient increases, they decrease their power output on the downhill as gradient increases. By implementing this correlation into a traffic simulation algorithm, we show that the simulation captures well the impact of gradients in a population of bicyclists as it reproduces similar speed profiles. We conclude that bicyclists adapt their power output to compensate for the gradient, and that the impact of gradient varies greatly among bicyclists. Furthermore, we conclude that power-based modelling of free-riding bicyclists is an attractive alternative to investigate further.