I hope you are not serious! Wind power is usually associated with wind turbines, not propellers (cough) and the turbines are designed to orient themselves so they are facing directly into the wind. That being the case, it is not necessary to consider RMS wind direction. But if you think it is ludicrous to consider it when the turbine, or in this case the propeller (chuckle) is not always aligned with the wind, than you are quite mistaken. In the case of varying wind direction, the wind power density depends as much on RMS wind direction as it does on velocity and the velocity in varying wind conditions is also calculated as an RMS value. Do you think only two people in the world advocate RMS wind calculations? Then which one of those two wrote this research paper?
http://www.gsmt.noao.edu/studies/wind_tests4/wprv_all.htm
Again, that measurement has nothing to do with direction, but pressure.
wrong on all counts, a propeller works best when the angle of attack of the blades is optimized all the way around their arc, that can only happen when the disk is normal to the air stream. Anything else and each blade will have either higher or lower angles of attack in the crosswind portions of their arc.Furthermore, a propeller is the antithesis to a turbine. Think about that for a moment. If the turbine works best when it is aligned with the wind direction, doesn't that indicate the propeller will work worst when similarly aligned? I think it is obvious that if a propeller is used to gather wind energy, it will do it best when it is not aligned with the wind direction. It only requires common sense to see that, but I'm sure I can find some supporting mathematics as well.