Trust me, it is a fucking HUGE battery. But if it pleases you we can make it nuclear-powered instead, just in case you're worried about the thing running out of charge.
So, are we at this point agreed that, ignoring how the propeller is powered, the vehicle with a 1m/s prop and a 2m/s tail wind will move forward at close to 3m/s?
It is obvious I will agree. You can drive at almost any speed you want if you have a battery.
So what is next ?
OK. Well sorry we have to take this a small step at a time but with all the distractions and other comments possibly confusing and obscuring things we do need to be able to reflect on where we were in order to make the next move.
Which, right now, is realising that the propeller is essentially equivalent to the moving sail. That is, just as the wind pushed against the sail moving backwards, the wind is pushing against the prop wash similarly moving backwards. Still with me?
The prop wash moving at 1m/s from a prop of radius r is pretty much the same as the sail moving backwards at 1m/s of area πr
2. You OK with that? Speak up if not.
The other thing to ponder at this point is that the vehicle in our scenario is moving at 3m/s ground speed with a 2m/s wind. It follows, then, that if the vehicle was moving at only 2.5m/s there would be 0.5m/s of wind available to power things. Note that
we are still using a battery as a power source so this is 'spare' wind power. Nevertheless, it shows that the
vehicle as a whole can be moving faster than the wind yet still make use of wind power.
We can change this: travel at 2.1m/s and we have 0.9m/s available wind despite still going faster than the wind. But, again,
we are still using battery power to turn the prop so this IS NOT powering the prop from the available wind. You will be dying to point out that the 0.9m/s we have available isn't quite the 1m/s the prop is putting out to make that available. In other words, this is not the explanation for the Blackbird.
OK so far? If you're still happy at this point we will make a sideways move and press on, but if you're not then it's important that we sort these two issues out here.