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Mess with your minds: A wind powered craft going faster than a tail wind speed.

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electrodacus:

--- Quote from: IanB on December 28, 2021, 05:40:33 am ---
--- Quote from: electrodacus on December 28, 2021, 05:34:20 am ---They rotate as long as the vehicle moves as they are connected to wheels. But the vehicle will get to a peak speed / kinetic energy when all stored energy (pressure differential) is used up then it will start to slow down well below wind speed.

--- End quote ---

This kind of response, overshooting and then coming back down again, can only be observed in a system with second order dynamics, and a second order system requires some kind of inertia or momentum term. A compressed gas is a first order system, so it cannot explain this kind of system behavior. Where is the second order inertial term found in Blackbird?

--- End quote ---

What are you even talking about.
Of course energy stored in pressure differential will exactly result in this sort behavior where as the pressure differential drops the rate of acceleration drops until there is no longer any acceleration and deceleration phase will start.   

Brumby:

--- Quote from: electrodacus on December 28, 2021, 05:34:20 am ---They rotate as long as the vehicle moves as they are connected to wheels. But the vehicle will get to a peak speed / kinetic energy when all stored energy (pressure differential) is used up then it will start to slow down well below wind speed.

--- End quote ---
But won't the propeller still be pushing back and causing another pressure differential?

IanB:

--- Quote from: electrodacus on December 28, 2021, 05:43:59 am ---What are you even talking about.
Of course energy stored in pressure differential will exactly result in this sort behavior where as the pressure differential drops the rate of acceleration drops until there is no longer any acceleration and deceleration phase will start.   

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But where does the stored energy in the pressure differential come from? There is no external power source to charge it up. The vehicle starts from a standstill and gets blown along by the wind like a sail, until it speeds up and goes faster than the wind. Until this point, all the wind energy is being used to make Blackbird go faster. Where does the extra energy come from to charge up a pressure bubble?

electrodacus:

--- Quote from: Brumby on December 28, 2021, 05:45:52 am ---
But won't the propeller still be pushing back and causing another pressure differential?

--- End quote ---

The entire vehicle is pushed by this pressure differential not by the propeller. Propeller is powered by this pressure differential so part of the power from the pressure differential is used to accelerate the vehicle and another part is used by propeller to put something back in to increasing the pressure differential but net pressure differential drops as much more is used (for acceleration and friction losses) than it is put back.
Propeller itself is just a device allowing to store energy in surrounding air.

In the beginning is the wind pushing the vehicle part of the wind power will go to (accelerating the vehicle and friction losses) and the other part will be used by propeller to increase the pressure differential and even before vehicle gets to half the wind speed the stored pressure differential will take most of the part of powering the vehicle but still some small percentage will also be covered by wind and when vehicle above wind speed there is no more wind power available so all acceleration is done by the remaining pressure differential.
The higher the percentage of push power will go to propeller the more energy will be stored (resulting in a slower acceleration rate to allow more time to charge) and then also after exceeding wind speed the power from pressure differential will just be "recycled" meaning push the vehicle then take big part of that trough the wheel maybe 60 or 70% of that ending back as pressure differential. Process is not efficient but good enough that it can keep this pressure differential pushing the vehicle for a few minutes.

In a very simplistic way you can think of natural wind speed providing the initial energy and part of that will be used to increase the artificial wind speed (made by propeller) and so max speed the vehicle can reach is no longer the natural wind speed but the artificial wind speed (a bit less of course as there are multiple losses) still way above "natural wind speed"

electrodacus:

--- Quote from: IanB on December 28, 2021, 05:56:39 am ---
But where does the stored energy in the pressure differential come from? There is no external power source to charge it up. The vehicle starts from a standstill and gets blown along by the wind like a sail, until it speeds up and goes faster than the wind. Until this point, all the wind energy is being used to make Blackbird go faster. Where does the extra energy come from to charge up a pressure bubble?

--- End quote ---

It comes from the wind while vehicle is well below wind speed. As soon as the vehicle starts to move pushed by the wind the propeller will start to rotate and not only push air back but increase the equivalent sail area. So in the initial phase the sail size increases from the vehicle back are plus the propeller blades area up to full propeller swept area.
Only small part of the wind energy is used to accelerate the Blackbird that ratio is given by the gear ratio between wheel and propeller and the propeller pitch.
So wind pushes against vehicle body and later propeller swept area and that power is split say 60% to propeller and 40% to acceleration so even more time spend charging as the acceleration is slowed then from those 60% say about 70% (assuming 70% efficient propeller) is stored but that stored energy will increase a bit the pressure differential so part of what you just stored a moment ago also starts to power the vehicle and at some point (below half wind speed according to my calculations) the pressure differential becomes more significant than the wind power.
So most of the charged energy happens well before vehicle gets to half the wind speed.

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