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Mess with your minds: A wind powered craft going faster than a tail wind speed.
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bdunham7:

--- Quote from: electrodacus on December 13, 2021, 02:26:27 am ---You have a 100% efficient wind turbine so output will be 0.5 * air density * swept area * w^3
Now you put that wind turbine on top of a vehicle and drive directly downwind at say at a quarter wind speed
Then your wind turbine will output this 0.5 * air density * swept area * (w -(w/4))^3
Anyone that has ever calculate the wind power available to a sail vehicle going directly downwind will know the equation
0.5 * air density * area * (wind speed - vehicle speed)^3
That is the reason a sail vehicle can never exceed wind speed directly downwind.

--- End quote ---

The Blackbird is neither a sail vehicle nor a vehicle with a wind turbine on it.
fourfathom:
I was wrong -- a fast sailboat *can* beat a balloon directly downwind. 

Here are the polars for one of the 2013 America's Cup races (you may recall that these were extremely fast catamarans):


Look at the polar diagram for 20 kts true windspeed at a true wind angle of 135 degrees (TWS and TWA are ground-referenced values shown here, not the boat-referenced AWS and AWA).  You will see that with a 20 kt wind the boat can sail 45 kts at 135 degrees (180 degrees is directly downwind).  Jibing +/- 45 degrees, to beat the balloon the boat would only have to exceed (20  / 0.707) or 28.28 kts.  I haven't tried to figure out the optimum downwind jibing angle, but at 45 degrees off DDW there is plenty of margin.  By the way, these conditions would give you (on each 180 +/- 45 degree jibe) an AWS of 33.9 kts, AWA 34 degrees.

So this is a jibing boat, similar in many ways to a spinning propeller.
IanB:

--- Quote from: electrodacus on December 13, 2021, 01:33:34 am ---A propeller can create a pressure differential in air and that is where energy is stored.
See below graph   https://en.wikipedia.org/wiki/Axial_fan_design


--- End quote ---

You misunderstand that graph. It does not show what you think it shows. In fluid flow theory, there is static pressure and total pressure. Total pressure is the sum of the static pressure and the velocity component of the fluid. The total pressure may be higher downstream of the fan, but it is pointing in a direction away from the fan, so there is no way it can act as a store of energy. The static pressure points in all directions, and could potentially be a store of energy behind the fan. Except the static pressure is lower than the surroundings, and therefore it is more like a vacuum dragging the fan backwards. To store energy in a compressible fluid you need to  contain it within walls, as in a storage tank. There is no tank here, there are no walls, there is no containment, therefore no store of pressure energy. Once the air leaves the fan, its energy quickly dissipates in all directions away from the fan.

I showed you a video where someone measured the pressure in the air stream leaving a fan to verify that it is lower than the surroundings. Unless you can show how that video was somehow faked or manipulated, you have to accept experimental evidence as fact.
electrodacus:

--- Quote from: IanB on December 13, 2021, 03:18:44 am ---
--- Quote from: electrodacus on December 13, 2021, 01:33:34 am ---A propeller can create a pressure differential in air and that is where energy is stored.
See below graph   https://en.wikipedia.org/wiki/Axial_fan_design


--- End quote ---

You misunderstand that graph. It does not show what you think it shows. In fluid flow theory, there is static pressure and total pressure. Total pressure is the sum of the static pressure and the velocity component of the fluid. The total pressure may be higher downstream of the fan, but it is pointing in a direction away from the fan, so there is no way it can act as a store of energy. The static pressure points in all directions, and could potentially be a store of energy behind the fan. Except the static pressure is lower than the surroundings, and therefore it is more like a vacuum dragging the fan backwards. To store energy in a compressible fluid you need to  contain it within walls, as in a storage tank. There is no tank here, there are no walls, there is no containment, therefore no store of pressure energy. Once the air leaves the fan, its energy quickly dissipates in all directions away from the fan.

I showed you a video where someone measured the pressure in the air stream leaving a fan to verify that it is lower than the surroundings. Unless you can show how that video was somehow faked or manipulated, you have to accept experimental evidence as fact.

--- End quote ---

Are you able to read a graph? or are you saying that the graph is incorrect ?

Is P2 higher than ambient pressure PA and much higher than P1 ? Thus a pressure differential potential energy.
IanB:

--- Quote from: electrodacus on December 13, 2021, 03:38:12 am ---Are you able to read a graph? or are you saying that the graph is incorrect ?

Is P2 higher than ambient pressure PA and much higher than P1 ? Thus a pressure differential potential energy.

--- End quote ---

Yes, the graph is incorrect. For a typical fan in the open air, P2 < PA, as you can verify yourself by experiment.

When you have two pieces of evidence, being (A) a pretty picture someone posted on the internet, and (B) the results of a physical experiment you can perform yourself, you have to take (B) every time. Reality is always more reliable than a picture.

Please do the experiment, so you can satisfy yourself that the picture is wrong.
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