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Have any of you cycled against 40mph headwind? Is it even possible? If 90% of resistance to moving forward, is wind resistance, then you would have to be able to average 36mph in still air, to be able to make forward progress. I have cycled through a tropical storm, where I was moving very, very slowly, and there was water lapping the bottom bracket. What would it take to not make any progress at all?
Aside from spokes spinning into the wind, I don't see a difference in drag between a 20mph direct headwind, and rider moving through still air at 20mph. However, the following equation from http://www.kreuzotter.de/english/espeed.htm disagrees with this belief.
|The following equations take into account all of the relevant resistance components: Rolling friction including the dynamic (speed-dependent) rolling friction, air drag including the influence of wind speed, mechanical losses, and uphill/downhill forces.
|V||Velocity of the bicycle|
|Hnn||Height above sea level (influences air density)|
|T||Air temperature, in ° Kelvin (influences air density)|
|grade||Inclination (grade) of road, in percent|
|β||(“beta”) Inclination angle, = arctan(grade/100)|
|mbike||Mass of the bicycle (influences rolling friction, slope pulling force, and normal force)|
|mrider||Mass of the rider (influences rolling friction, slope pulling force, and the rider's frontal area via body volume)|
|Cd||Air drag coefficient|
|A||Total frontal area (bicycle + rider)|
|Cr||Rolling resistance coefficient|
|CrV||Coefficient for velocity-dependent dynamic rolling resistance, here approximated with 0.1|
|CrVn||Coefficient for the dynamic rolling resistance, normalized to road inclination; CrVn = CrV*cos(β)|
|Cm||Coefficient for power transmission losses and losses due to tire slippage (the latter can be heard while pedaling powerfully at low speeds)|
|ρ||(“rho”) Air density|
|ρ0||Air density on sea level at 0° Celsius (32°F)|
|p0||Air pressure on sea level at 0° Celsius (32°F)|
|Frg||Rolling friction (normalized on inclined plane) plus slope pulling force on inclined plane|
In order to solve this Power equation for Velocity V, we write it in the implicit form
so we can use the cardanic formulae to obtain the solutions:
|If a2 + b3 ≥ 0:
If a2 + b3 < 0 (casus irreducibilis; in case of sufficient downhill slope or tailwind speed):