When I get back to NZ I plan to build new device for a turntable that has two single wheel carts directly opposite each other that share the same tether for balance. The main thing I want to test is whether the carts are hovering or travelling relative to whatever surface they get their energy from with stored or sustainable energy.
The opposite-side carts design is an interesting touch, ynot, which is intuitively appealing to 'balance' the forces, but I wonder if it does that significantly in practice. The centrifugal force of the single cart moving in a circle would be balanced at the central bearing, but it probably wouldn't be rotating very fast (unless you get a really efficient design) - windspeed, of course, being when it is at rest w.r.t. the ground - so the force won't be very great. However, the fact that you have doubled the motive force by having two mechanisms with two props, your twin cart should have twice the power, even if none of the losses are offset by better balanced bearing forces.
I believe you are totally wrong. When the cart is prevented from travelling backwards only on the moving surface the propeller will develop enough thrust to allow the cart to "hover". When the cart is prevented from travelling forwards as well as backwards on the moving surface however the propeller will develop more than enough enough thrust to "hover" and it will travel forwards against the surface. In other words the cart will be able to travel faster than the moving surface that gives it it's energy. As I said above, the question I'm interested in is this "extra" energy stored or constant?
Like fredriks, I can't see that this is a correct analysis. For sure, when the cart is held still on the treadmill, the prop will generate whatever force it has to, whether that represents too little for FTTW travel or more, but then, when it is let go of, the fact that it progresses forwards seems conclusive unless it arrived at that position after first being driven forwards to accelerate the whole mechanism beyond belt-speed. This would be utterly impossible without being clearly visible, and would dissipate very quickly. It is not the same as the acceleration that the mechanism undergoes from being placed on the moving belt at rest and reaching windspeed.
It can help to translate back to a humberian 'real wind' scenario, assuming you believe in the equivalence. Then, we can imagine the land cart driven along, held next to a powered vehicle so the whole thing is going exactly windspeed, and uncoupled. If it moved off ahead of your powered vehicle, it's even more difficult to imagine that it could have gained enough momentum from the setup conditions to do so.
Ah, but I suppose I can imagine how the setup acceleration
could give it momentum that is translated into further motive power (or how one could imagine such a thing), but it would require a significant mass, a flywheel, say, and very slow losses. Then, after the machine is driven up to windspeed and released, the flywheel's energy would return to the system.
Let's do this in imagination. If we imagine first doing this with just a simple cart with a flywheel driven by the wheels, pushed up to 10 mph in still air, we know that it won't just suddenly stop when we let go. It's momentum will cause it to continue into the headwind, a motive force against the resistance (indeed, any mass will, even just a cart freewheeling). So the question is, if we did so up to 10 mph in a 10 mph wind, downwind, would whatever momentum is in the machine cause it to continue accelerating and outpace the wind, if, for instance, it hasn't reached 'steady state' when we let go - we've given it a shove so far, does that shove continue?
I think this is the sort of principle you identify as a possible reason for temporary gains of velocity, and (as you say) it depends on how quickly the steady state is reached. In the treadmill situation, it could be tested by holding the cart at windspeed for a 'suitably' long time (whatever that is), before letting go.
However, imagining the land cart again, with no prop but a flywheel as big as you like, if we have acceleration forces of a tailwind and an outside force (push by the pilot vehicle), and resistance of friction only, when we reach windspeed and uncouple, there is now no driving force (we've uncoupled) and no tailwind or headwind. There is only the friction.
Now, here's the important consideration. While we were accelerating the machine, the flywheel was being accelerated (and the whole thing was harder to push). When we stop pushing, the flywheel is just going round without any acceleration,
immediately. That seems to be how long it takes to reach that initial steady state before launching. So if we push a flywheel cart into a tailwind up to windspeed and let go, it doesn't outpace the wind just because of that pushing of a moment ago, or any amount of momentum so gained. Acceleration isn't translated into the next moment. Velocity is, but
the moment you stop accelerating something (take the force away), it stops accelerating. Now we have a cart going windspeed and it will take longer to slow down because it has a ruddy great flywheel rotating, but it can't beat the wind.
Similarly, it seems hard to conceive that the prop could gain a sort of aerodynamic equivalent that is magically different. There is only its tiny plastic mass and the momentum of the air it is moving, which would very soon lose any excess energy.
In either frame, it seems even more impossible that holding it back could give it more momentum to do the trick. This is even more convincing in the treadmill videos, to me. The natural result for every other object (wheeled or otherwise) is to be slung off the back end of the treadmill, unless zero friction can be attained. The plastic spork pushes the cart that way, and then it repeatedly advances again. Clearly, the wheels are going slower when it is pushed back, so the only thing that could gain 'momentum' or other stored energy to cause it to come back (like a pendulum), is the prop or the propelled air (which is what you suggest, I think). But the free-spinning prop stops in 7 seconds. Besides, when this advance is balanced by the cart's own weight (component thereof) by tilting the belt, it generates an excess forward force to hold itself in position for minutes.
No, I really think all these momentum arguments are wrong. I value your experiment and expect it will verify the claim once again.
), but if the cart isn't efficient enough, it may not work. If your cart does not advance against the direction of the treadmill, it will not be a proof that DDWFTTW is impossible: it will simply demonstrate that your particular cart can't manage it. Should that happen, I hope you'll keep tweaking the design of the cart.
