swoosh said...Ian K said...
The power that can be extracted from the wind goes up with the cube square of wind speed. The kinetic energy in a unit, say a cubic metre, of wind goes up with the square of velocity, and then the amount of wind that goes past in a unit of time goes up with speed again.
I think you made a typo here, don't wanna confuse the masses!
No this time it's not a typo. It is the cube of windspeed for power. The
force on a wind turbine blade goes up with the
square of velocity, but then the blade can also spin faster. Power = force times velocity, so there you get the cube. Not quite that way in a turbine as many are synchronised to the mains voltage and have variable pitched blades, but the result is the same.
en.wikipedia.org/wiki/Wind_energyBetz' law looks at this from an interesting perspective.
en.wikipedia.org/wiki/Betz'_law
You can argue whether force or power is more important to get planing. Most likely it is power as the power required to push a non-planing hull thru the water also goes up with the cube of hull speed. But then the force to push that hull only goes up with the square - so it's a bit of a circular argument.
It's all a bit academic for something as complicated as a windsurfer. All sorts of issues with apparent wind, what angle do you bear away at, and then there's the pumping power of weet-bix. Doing the calculations for powering a 40 watt light bulb with a stationary turbine is relatively easy.