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

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PlainName:

--- Quote ---If it has stored energy say that 0.07mWh I calculated
--- End quote ---

Stored where?

Kleinstein:

--- 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 ---
This calculation neglegts the force on the turbine. This gives an additional energy as drag force times vehichle speed.
Even for just a passive sail the energy is vehichle speed times force and thus
0.5 * air density * area * (wind speed - vehicle speed)^2 * vehicle speed

The passive sail is however not the best that can be done. So the theoretical available energy can be larger than that. The blackbird vehicle showed one way to do that. A sail boat going at a suitable angle is another way - though it complicates the area part. Anyway it still gets power when the speed component parallel to the wind is faster than the wind speed so there is no inherent zero at that speed. Yes it is sideways, but for a though expoeriment one can consider the sideways area as still part of the vehicle size, so the movement would be only inside (like the fan going in circles).
One could consider the fan blades as sails going zig-zag.  So this kind of circumvents the going straight in the direction of the wind.
 

electrodacus:

--- Quote from: dunkemhigh on December 13, 2021, 08:05:35 am ---
--- Quote ---If it has stored energy say that 0.07mWh I calculated
--- End quote ---

Stored where?

--- End quote ---

Pressure differential created by the propeller.

bdunham7:

--- Quote from: fourfathom on December 13, 2021, 03:04:35 am ---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.

--- End quote ---

I knew iceboats can do that, and I suppose the wheeled equivalents like a the Blackbird chassis, but to get near ideal numbers like that those catamarans must have hulls coated with buttered teflon.

electrodacus:

--- Quote from: Kleinstein on December 13, 2021, 09:54:53 am ---This calculation neglegts the force on the turbine. This gives an additional energy as drag force times vehichle speed.
Even for just a passive sail the energy is vehichle speed times force and thus
0.5 * air density * area * (wind speed - vehicle speed)^2 * vehicle speed

The passive sail is however not the best that can be done. So the theoretical available energy can be larger than that. The blackbird vehicle showed one way to do that. A sail boat going at a suitable angle is another way - though it complicates the area part. Anyway it still gets power when the speed component parallel to the wind is faster than the wind speed so there is no inherent zero at that speed. Yes it is sideways, but for a though expoeriment one can consider the sideways area as still part of the vehicle size, so the movement would be only inside (like the fan going in circles).
One could consider the fan blades as sails going zig-zag.  So this kind of circumvents the going straight in the direction of the wind.

--- End quote ---

The turbine is supplied by wind power so you can not add that again.
Everything on a wind only powered vehicle is supplied by the wind power.
You can search research papers or similar and see that any direct down wind sail vehicle powered only by the wind will use this wind power formula
0.5 * air density * area * (wind speed - vehicle speed)^3

For a wind turbine the same formula is used except you do not need that vehicle speed subtracted as the wind turbine is fixed to the ground and this is the ideal wind power so to this you will add turbine and generator efficiency.
I designed my own turbine so I worked with this sort of formulas before.

The passive sail is actually the most efficient and an ideal one will be 100% efficient.
That is why no vehicle exceeding wind speed directly downwind (special case) powered only by the wind can not exceed wind speed.
The way blackbird is doing that is by storing energy in pressure differential while it is below wind speed and then use that stored energy to be able to accelerate well past wind speed.

Sail boat going at an angle is a geometric problem as the sail will still have access to wind speed since it will not be driving faster than wind relative to wind direction. Best case is driving perpendicular to wind direction as then you have always access to same wind power as vehicle is not moving at all in the wind direction.
And while driving at an angle the vehicle kinetic energy is what will store energy and then in an ideal case no friction you can just change direction to direct down wind and maintain that higher wind speed indefinitely (no losses) in real vehicle they will slow down same as blackbird will also slow down.
Since kinetic energy is directly related to vehicle speed as soon as a real sail vehicle changes direction to direct down wind it will start to slow down but on the blackbird energy is stored in a separate energy storage device the pressure differential.
If you have some electrical knowledge the equivalent of kinetic energy is a capacitor and the analog to pressure differential is an inductor.
 

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