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gorgesailor said..
These wind "speed" measuring devices are actually measuring the same mechanical forces as we feel on our sails. I understand the theoretical difference & factors as they relate to drag, but unless we are actually measuring the speed of the air molecules & comparing that to the forces they can exert, we can't really say a dense 20kt wind has more power than low density 20kt wind. Because the mechanical wind "speed" measuring device has already compensated for that.
Tell me I'm wrong & why!
You're (mostly) wrong. Think of typical wind meter that has cups that catch the wind. The cups are mounted on a center axis with little friction, so they will rotate at the speed of the wind, regardless of air density. The device measures the rotation speed, not the forces exerted on the cups. One wind meter I have even use bike speedometers for that, since those are cheap to get.
At a given wind speed and humidity, colder air is denser. More air molecules will hit the cups of the wind meter, so the force they hit with will be higher. But the cups won't rotate faster than the wind speed because they hit air molecules on their way back which slows them down. I'd guess that they actually move marginally slower than wind speed, which is compensated for in the calibration.
When sailing in moderate climates, the difference in air density between cold and warm air is barely noticeable, partly because cold weather sailing usually makes us quite a few pounds heavier from wearing thicker wet suits (and boots and gloves). Also, keep in mind that the kinetic energy is linear to density, but increases by the square of the wind speed. So a 20% difference in density is more similar to a 10% difference in wind speed (until you take into account apparent wind and board speed, at least).
But the difference is very noticeable when you sail high elevation lakes like Lake Silvaplana (about 1800 m / 5900 m above ocean level). You may have similar wind strengths and temperatures compared to nearby Lake Garda, but you
will need a sail that is one or two sizes larger, since air density is about 20% lower.