Am I correct in assuming that the cycling industry absorbs the cosine error in their yaw sweeps?
My interpretation of Paul Lew’s writings is that he simply making a statement that exposes this inaccuracy in testing at one wind velocity while yawing the bicycle and rider.
Let’s ignore any tailwinds for the sake of discussion here ( -90 deg <= Beta <= 90 deg) , since otherwise this would require vector analysis. For a cyclist to see a 30 mph relative wind at a yaw angle Beta, the cyclist-to-ground speed must be at most 30cos(Beta), with an Air-to-Ground relative wind speed being at least 30sin(Beta) in magnitude, depending on if the the cyclist and the wind velocities with respect to ground are at right angles to each other or smaller. In a practical sense, ignoring this cosine means underpredicting power-required from a cyclist at any given speed.
I’ve never seen any company get into the details of how they crunch this out, but ignoring this cosine error is a convenient standard that paints yaw in a more favorable light than it should be. Consider that at 10 degrees, this error paints drag favorably by 1.5%, at 20 degrees 6.5%. While some argument can be made for “sailing effects” and isolating one’s concern to opposing forces in the cyclist longitudinal axis, it seems too convenient that the industry has chosen to ignore the true power cost of side winds on a cyclist*. If I’m wrong in assuming that this is the de facto standard, then I will gladly retract this statement.
*I’d assume this cost to be on the order of: sin(cyclist’s roll angle into wind) * height at center of pressure * weight * crr_y(cyclist’s roll angle into wind) * Ucyclist-to-ground. Not including any cost to control rolling-into-wind, particularly for gusts.
I’ve never seen any bicycle wind tunnel data that was not corrected to the appropriate frame-of-reference for a ground-based vehicle.