Since humber made a clear statement and a question, I'll just exercise my fingers a bit. (I'm quite fustrated with my present work assingment, you see.)
To make the model complete, moving with the belt must be the equivalent of being stationary in the real world, with the wind to his back.
Yes, moving with the belt must be equivalent of being stationary in the real world. You must compare _being still_ in real wind and _movin with belt_ in treadmill. Being still in real wind must NOT be equivalent with being still above the belt. And moving in real wind must NOT be equivalent with moving above the belt (same speed ofcourse). Agreed?
Realwind:
Wind from the back, with the laminar wind flowing from heel to toe. Like the wind. Correct?
Yes, being still in real wind.
Now, become an imaginary observer, which way does the flow move?
From heel to toe. It passes from heel to toe, like the wind.
Yes, the imagynary obeserver continues being still in real wind.
Treadmill:
Wind to the back, with laminar wind flowing from heel to toe. Correct?
Yes, moving with the belt.
Now, become an imaginary observer.
Which way does the laminar flow go?
From toe to heel. It passes from heel to toe like the belt (road), not the wind.
No, the imaginary obeserver must continue moving with the belt. In your realworld example, becoming imaginary does not change observers velocity. In your treadmill example, becoming imaginary changes observers velocity. That is the fallacy.
Here is your mistake. Your imagynary observer suddenly stops, it is no more moving with the belt, and therefore the situation is no more equivalent with real world.
If the observer is not moving, the wind passes from toe to heel.
If the obeserver is moving with the belt, the wind passes from heel to toe.
The latter is the situation that should be and is equivalent with real wind.
Which part do you not agree with?
I hope I made it clear, but feel feel to ask for a line number or something.
Two separate "winds" that are only "correct" in two limiting cases. When fixed to the belt, or at "windspeed". At other velocites, the ratio will change.
The treadmill and real wind are identical in any practical sence at all possible speeds. It is true though, that the treadmill can be used to model ONLY the situation, were the cart is already going at windspeed or just a bit over or under it. Nobody claims otherwise.