Chad - (resurrecting an old thread here, but the debate still rages on) Bottom line is, you guys were correct in your suppositions and observations of an anemometer mounted on an airplane. I've been unsuccessfully arguing this point over on wattflyer. I keep telling myself to just drop it, but I can't seem to. I'm about to break out the diagrams and equations! ( I have already drawn them up).
There seems to be an alternate issue at heart, that you guys weren't even intending to address, and that is the "myth of the downwind turn." The controversy seems to be centered around this "myth." The confusion of this issue comes from the frame of reference that one is using. In fact, using anything other than a frame of reference outside of the airplane (even if it is two African swallows, which are non-migratory, carrying a coconut on a string-that's a reference^2) is necessary to understand the heart of the issue. And, again it is an issue that you guys didn't even bring up.
You intended to compare ground speed vs indicated airspeed. Y'all kinda did a poor job of summarizing that (its a teacher thing) at the end of your video. I doubt anyone would argue that there is a difference between indicated airspeed (airplane frame of reference) and ground speed (ground frame of reference) as long as there is wind. Folks have run with that and are saying that the airplane doesn't care about its groundspeed (true) and only cares about its IAS (true). But, they fail to understand that, as you said, aircraft have inertia and don't instantaneously assume the speed of the wind. Ok, our rc planes do. But real planes don't, due to inertia. If you are flying into the wind then kick hard rudder, your ground speed increases, but IAS decreases as you turn downwind.
Back to the "myth." If you are in an aircraft that has sufficient inertia (real one) and are flying REALLY close to stall (within the ground measured wind speed), then you likely will spin in to your death if you turn downwind without increasing throttle. Simple mechanical physics.