Wind speed, wind yaw and the aerodynamic drag acting on a bicycle and rider
Keywords:Bicycles, bicycle instrumentation, cycling, aerodynamics, air drag, CdA, wind yaw, apparent wind, power meter, OFPM, iBike.
A large portion of a cyclist’s power is consumed by air drag. Opposing force power meters measure air drag with a wind sensor. In cross winds the bicycle and rider experience a different air drag than that informed by a conventional wind sensor. The main objective of this study is to quantify this error as a function of wind yaw. Additionally, if power is independently measured with a direct force power meter, we estimate the drag area (CdA) as a function of wind yaw without using a yaw sensor. 1- We use exact equations to estimate air drag from airspeed and wind yaw instead of approximate equations and a conventional wind sensor that responds to the axial component of the airspeed called inline airspeed. 2- We describe a novel method for estimating air drag using a conventional wind sensor under naturally-occurring wind conditions, where the missing wind yaw data is inferred from ground speed, heading and the prevailing wind velocity. The prevailing wind is identified as a vector by analyzing ground speed, inline air speed and heading data. Wind yaw that is estimated by this method is called the virtual wind yaw. Our test results suggest that a state-of-the-art opposing force power meter, namely the iBike Newton, systematically underreports the total power when the wind yaw is large. We show that the virtual wind yaw approximation often returns a more accurate estimate of instantaneous power than a conventional opposing force power meter. When a bicycle is equipped with a speedometer, an inclinometer, a conventional wind sensor and a direct force power meter, the redundancy in the data allows us to determine the constituent components of the total power including the aerodynamic power. It also allows us to determine the CdA as a function of wind yaw, as well as the time and energy spent within a given range of wind yaw angles. The accuracy of an opposing force power meter can be improved by using exact equations with input from a wind yaw sensor (e.g., a wind vane).
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