Is it possible to get an summary from start to finish about why it is impossible?
Examples and illustrations along to way would be helpful so that I can follow all the steps.
I'm really struggling to follow the thought process here. Guess I'm not smart enough. So please put it as plainly as possible.
In any case I will try to make a summary.
The easiest part will be to show that directly down wind faster than wind is not possible without some sort of energy storage device or an external energy source.
That can be proved with the correct equation for wind power available to any wind powered vehicle
Pw = 0.5 * air density * area * (wind speed - vehicle speed)3
It is irrelevant how vehicle is build as long as wind power is the only source then the above is the correct formula for an ideal system (so absolutely best case scenario).
The air density can be considered a constant so not very relevant and then there are just two other therms the area of the vehicle that in the particular case of blackbird will increase with speed up to a max of swept area of the propeller but while that increase in area helps make more power available to vehicle it will only be valid as long as vehicle speed is smaller than wind speed since as it can be seen in the equation if vehicle speed equals wind speed the wind power will be zero.
This formula is all that is needed in order to demonstrate that any wind powered only vehicle will need an energy storage device in order to exceed wind speed directly down wind.
It seems that many people do not work with power and prefer to work with force and speed separately and this is how a wrong equation ended everywhere.
The equation for force is correct
Fw = 0.5 * air density * area * (wind speed - vehicle speed)2
But then when they want to calculate wind power they just multiply by vehicle speed and leave the wind speed out of the equation. The most likely reason they do that is because someone made this mistake first and they just copy paste the same wrong equation everywhere without thinking to much or testing to see if it is true.
They just think that if vehicle speed is zero the wind power available to that vehicle is zero and they think that since they imagine zero speed as a vehicle with brakes engaged. That seems as a super silly mistake to make is like saying that a sail boat has zero wind power available when boat speed is zero because the boat is anchored to the ground.
Let me know if you agree with the above and then I can continue with how the Blackbird can actually exceed wind speed for a limited amount of time using energy storage in pressure differential created by the propeller with part of the wind power.
Ah ok. So the only thing relevant to the vehicle speed is the air pushing it (assuming everything else ideal). The part that is confusing me is the spinning propeller. I know from experience that those do push or pull air depending on orientation when spinning. And spinning this does since it is driven by the wheels (which are also spinning), So shouldn't this factor into the problem in some way? And sorry I don't have access to youtube here.
The propeller is a wheel for traveling trough a medium instead of traveling on top surface of a medium like a regular wheel.
Propeller is powered by wind and or pressure differential depending on vehicle speed.
Since output power of the propeller is lower than input power from the wheel there could not be any net gain.
The role of the propeller is to compress air creating that pressure differential where energy is stored to allow vehicle to exceed wind speed for a limited amount of time.
Wind power is split between accelerating the vehicle and powering the propeller that in turn creates pressure differential.
Say at some particular moment there are 100W available as wind power and say this is for 1ms
then say 40W is used to accelerate the vehicle so vehicle kinetic energy will increase by 40W * 0.001s = 40mWs thus the vehicle speed has increased a little bit.
The other 60W is taken by the wheel that sends it to propeller that say it is 70% efficient so 60W * 0.7 = 42W are available as propeller output and they end up stored as pressure differential so 42mWs of stored energy.
If this continues in the same way the vehicle will be storing about the same amount of energy in pressure differential as there is stored in vehicle kinetic energy maybe just slightly more.
In ideal case all this stored energy can then end up as vehicle kinetic energy and thus vehicle peak speed can be even multiple times larger than wind speed but from that max speed the vehicle will just start to decelerate as there is nothing more to power it.