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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 12, 2021, 06:29:00 pm ---And as I keep telling you, that is not the correct formula. The correct formula is:

available power from wind = 0.5 * air density * area * (wind speed − ground speed)^3

If you keep putting vehicle speed in there you will get the wrong conclusion.

--- End quote ---

ground speed relative to what ?

fourfathom:

--- Quote from: electrodacus on December 12, 2021, 06:34:29 pm ---ground speed relative to what ?
--- End quote ---
Speed of the ground, relative to the ground.  In other words, zero.

fourfathom:

--- Quote from: IanB on December 12, 2021, 06:29:00 pm ---the vehicle is in contact with the ground using wheels that do not slip.
--- End quote ---

And even if the wheels did slip, as long as there's some traction (friction) the vehicle can still draw energy.  Of course the system efficiency will be less with slipping wheels.

But for the sake of analysis, and for all practical purposes, the wheels do not slip.

electrodacus:

--- Quote from: fourfathom on December 12, 2021, 06:45:18 pm ---
--- Quote from: electrodacus on December 12, 2021, 06:34:29 pm ---ground speed relative to what ?
--- End quote ---
Speed of the ground, relative to the ground.  In other words, zero.

--- End quote ---

Then why even mention that?

electrodacus:

--- Quote from: fourfathom on December 12, 2021, 06:49:41 pm ---
--- Quote from: IanB on December 12, 2021, 06:29:00 pm ---the vehicle is in contact with the ground using wheels that do not slip.
--- End quote ---

And even if the wheels did slip, as long as there's some traction (friction) the vehicle can still draw energy.  Of course the system efficiency will be less with slipping wheels.

But for the sake of analysis, and for all practical purposes, the wheels do not slip.

--- End quote ---

Think about this way.  The thing that converts the wind power to kinetic energy is on the vehicle (you do not have an extension cord to a stationary location).
So wind speed relative to vehicle will be (wind speed - vehicle speed).

The wind power equation as you describe 0.5 * air density * area * w^3 is valid for a stationary device like a wind turbine or for a vehicle that travels perpendicular to the wind direction not directly downwind.

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