Okay, I'm almost certain this has been discussed here before in the context of doing laps on the track and hoping the wind effect would cancel. But I did a calculation of the effect of wind and bike speed fluctuations on power, in particular climbing power where the correlation between bike speed and wind speed is weak. The result, assuming zero average wind speed, and assuming the wind never becomes a net tail wind, to second order is:

<pw> / pw0 ? 1 ? ( 3 <?s²> + <?sw²> ) / s0²,

where <pw> is the expectation value of the wind resistance power, pw0 is the value calculated assuming constant speed, <?s²> is the average value of the square of the deviation in bike speed (not the deviation of the square of the bike speed), <?sw²> is similar for the wind speed, and s0 is the average bike speed.

This is intended as an estimate for the purpose of estimating power on a climb. For example, on a climb I did in the

Low-Key Hillclimbs, Soda Springs Road:

I got a 2 mph typical variation in speed with a 1 mph typical variation in wind speed yielded an increase in estimated power of 2.3 watts.

Way too much detail:

http://djconnel.blogspot.com/2009/11/ef ... speed.html
http://djconnel.blogspot.com/2009/11/ef ... ed_02.html
http://djconnel.blogspot.com/2009/11/ef ... ed_03.html