You try to make similar claims as Alex (that university professor in Derks second video).
No, that's just what I know when trying to model physical phenomena. My own scientific field is molecular dynamics modelling software and their development –– i.e., I'm a toolmaker more than I use those tools to do research ––, and this sort of thing, or oversimplified models and trying to find the correct complexity level where things are still understandable and simulatable, but not so simple that they no longer reflect reality, is a daily encountered problem.
Like I said, I am
not interested in the equilibrium case. To me, it's like investigating automobile fuel consumption by assuming that all roads are straight without intersections and all travel at the posted speed exactly. In the real life, different types of vehicles' fuel consumption varies very differently due to repeated accelerations and decelerations, which is the reason why fuel mileage is usually reported separately for "city driving" and "long-distance driving": one being constant acceleration and deceleration, the latter with relatively stable speeds. Those who teach economical driving, always emphasize how big of a beneficial impact keeping to a constant speed makes.
To put it more simply, the case where the vehicle is traveling at exactly the speed of wind is not interesting.
Instead, divide the examination into two: One, when the vehicle is traveling slower than the speed of wind. Parametrise the scenario, and especially examine how acceleration changes as the vehicle speed approaches wind speed. Two, do the same examination, but in the case where the vehicle is already traveling faster than the speed of wind. Next, using the parameters (coefficients and such) you established, find out if and when the vehicle already traveling faster than the speed of wind can keep a nonnegative acceleration (ie., zero or positive).
The equilibrium case, where the vehicle has exactly the same speed as the wind, has zero acceleration, and has no exploitable energy storage, just doesn't happen in nature: it is an unstable state, and will always fall into one of the above two cases, sooner or later.
If, and only if, it turns out that the vehicle has always nonpositive acceleration when already traveling faster than wind, will that unstable state always fall to the lower speed side, and only then is it impossible for that vehicle to travel directly downwind faster that the wind. If you can find a mechanism or model and parameters, where the vehicle can keep a nonnegative acceleration while already traveling faster than wind, then that vehicle can keep traveling faster than wind almost indefinitely (barring similar unstable points, possibly an infinite number of them, as the exactly-same-speed-as-wind case).
So, as unintuitive as it might seem, the entire scenario seems to depend on exactly how the vehicle behaves when it is already traveling faster than wind directly downwind. In my mind, this is well in the realm of fluid dynamics; and indeed if a simple propeller-like arrangement can achieve that, the actual underlying mechanism is almost certainly more interesting than just flywheel-like energy storage.
I wouldn't trust a treadmill (either way!), because the static charge buildup in the belt can cause all kinds of wonky stuff. Depending on the materials, it can act like a big but not very good Van De Graaff generator, for example.
I'm sure people will still deny that energy storage being used up is the reason.
I'm not making any such claims, for or against. I am saying you are looking at the issue from the completely wrong angle.
The exact point where the vehicle speed matches wind speed is an unstable point state, which will immediately change. It is not interesting or useful to examine it, at least not before you have some kind of models that describe the two different situations around that state, depending on the speed.
I'm not saying anyone is cheating, either, but it would be easy to do,
even unwittingly. You might make a very lightweight vehicle, but use heavy natural rubber wheels, which would definitely behave like an energy storage (flywheels, literally). A model that can describe multiple different such vehicles is the way to go.
Note that since the faster-than-wind-speed case is critical, it is not sufficient to show one model that works that shows it cannot be done; that only proves that
that vehicle cannot do it. Considering sail boats (that can jig faster than wind nearly-downwind), I suspect it is possible, certainly possible enough to do research on, but I wouldn't be overly surprised to find out it would be unfeasible somehow either, say requiring a 1m long but 100m wide vehicle, for example.
Some kind of
vertically rotating wane system would be what I'd look into myself, simply based on existing sailing techniques.