John, the multiple flaws in your diagram give you away. The master will tear you to shreds if you let him see those. ...
Ah yes. When I went to bed last night, I had actually deluded myself that humber might just find my approach incontrovertible. I'm seeing the doctor today anyway, so I'll mention it.
I'm the "Chief Scientist" at "The Hall of Science".
Is that the one in Scienceville, near the Empirical State Building?
The observer does not matter, John. It's not a matter of a tree falling in the forest without a witness, or the sound of one hand clapping.
But surely you do understand that wind velocities change for an observer, depending on whether they travel and at what velocity w.r.t. the wind. Surely you also know that the forces on a body from that wind will change with their relative velocities. Surely you know that these are the velocities we are interested in, those experienced by the thought-experiment observer on the belt, since they are the forces "experienced" by a cart. Surely also those were the velocities you were eager to show involved a reversal within the boundary layer, this being the basis of one of your contentions that the cart on a treadmill is significantly different from one blown along a road outside. Surely also, it is those relative velocities that would affect your paddle, and thus pertained to your earlier calculations. Surely, we were trying to work out the very same values, even though we disagree about them.
Or was your paddle magical, as I suspected, and able to measure the velocity of a wind relative to the ground when it is itself moving relative to the ground?
The flows are there if you are aware of them or not. Pitot tubes, paddles, anemometers, or some other measurement device, will contradict your conclusion.
They absolutely obviously will not. But if I obtained some under strict scientific scrutiny and subjected them to years of peer review (not that anyone would be interested in measuring the speed of things we already know), you would still contradict the conclusion.
Also, an observer of the kind you suggest, but on the ground or somewhere else, will also contradict your cart observer, whereas all will agree with the direct measurements and the calculations. My solution is correct, if only because it is the same for all observers, and quite clearly not like real wind.
You forgot "QED". But your solution wasn't the same for all observers. Your paddle spun backwards, because the flow on a treadmill was reversed compared with that on the ground! I (and several others) corrected your mistakes, and WE showed that the flows were identical, both between scenarios and no matter whether moving or at rest through the wind, since its relative velocities do not change.
My diagram shows precisely what you said an observer feels - 10 back of head, 6 lower down from front. You were quite clearly working out what that observer would experience. Surely, you're not going to do that low trick of pretending you were stating something different from what everyone thought you were stating? Not you, humber!