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Subject: Headwinds, Crosswinds and Tailwinds

From: Jobst Brandt

Date: December 21, 2004

Overcoming wind resistance (ærodynamic drag) presents the main effort for bicyclists, although climbing hills is more daunting. Unlike wind resistance, climbing effort does not diminish at lower speeds, which is partly why bicycles are used mostly in the flatlands. The effort of pushing one's way through the atmosphere is so limiting that most bicyclists ride in a fairly narrow speed range below 20mph. Regardless of whether racing, touring or shopping, ærodynamic analysis reveals some unexpected effects.

Common knowledge has bicyclists always riding into the wind, regardless of direction, a perception that is not as wrong as it may seem. On level ground, one rides as fast as is comfortable and because the bicycle is highly efficient, speed is limited by wind resistance. With a tailwind, speeding up until the wind is in one's face is fairly easy, and at that point it becomes a headwind.

With strong tailwinds, speeds are attainable at which wind drag in wheels (parts of which move at twice the speed of the bicycle) together with rolling resistance, can prevent going faster than the wind. This is similar to the limit on a stationary bicycle without a power dissipater. However, riding in such strong tailwinds is uncommon.

Crosswinds, unlike tailwinds, can only be made into partial headwinds because forward speed cannot diminish the crossing speed of the wind, besides which controlling the bicycle also becomes a hindrance.

Wind drag is a nonlinear function of the relative wind. That is, drag does not increase in proportion (linearly) to wind but rather with the square of its speed relative to the rider. Relative wind-speed is the sum of wind and rider speed, which in still air is equal to rider speed. Direct head- and tailwinds can be combined by addition with rider speed to give relative wind-speed.

Although inline winds add to or subtract directly from drag, they do not similarly affect the power required to overcome that drag. For instance, standing still in a 15mph wind requires no power because power is the product of inline drag and rider speed.

Drag is proportional to the square of relative wind-speed while power is the product of the inline portion of that drag and rider speed. Thus, required power (in still air) increases as the cube of rider speed. Computing power from wind and rider speed, even for other than in-line winds, requires only addition, multiplication and a bit of trigonometry, but working back from a given power to rider speed is more complex. This requires solving for coefficients of cubic equations. Computer techniques can readily solve for and graphically display these results.