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

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Kleinstein:

--- Quote from: electrodacus on December 29, 2021, 08:31:09 pm ---
--- Quote from: IanB on December 29, 2021, 07:42:33 pm ---It's a very circular argument:

"Why can no vehicle go downwind faster than the wind speed? Because this correct formula says so."

"Why is this formula correct? Because no vehicle can go downwind faster than the wind speed."

Each conclusion depends on the other.

--- End quote ---

Provide an equation that you think is the correct one for a wind powered vehicle.
The one I provided is valid for any case and it perfectly predicts what happens in reality.
Even the incorrect formula used by many predicts no wind power available above wind speed so that is not an argument either.

--- End quote ---
I don't think there is an generally accepted ready made formula for the maximum available wind power for the moving vehicle. At least I don't know one.
It is not up to us to provide a formula for a rather tricky problem. Chances are you would not understand or accept it anyway. It is your turn to show a good source, ideally with a good explaination.

The formula with the (w-v)²*v is the power available to a simple sail for velocities lower than the speed of the wind. However this does not have much relevance to a vehicle driven by a prop. It shows that going faster than the wind does not work with a simple (e.g. spinnacker like) sail, when going straight down the wind.
This is not really surprising and know for a long time.

electrodacus:

--- Quote from: Kleinstein on December 29, 2021, 09:22:53 pm ---I don't think there is an generally accepted ready made formula for the maximum available wind power for the moving vehicle. At least I don't know one.
It is not up to us to provide a formula for a rather tricky problem. Chances are you would not understand or accept it anyway. It is your turn to show a good source, ideally with a good explaination.

--- End quote ---

It will be ridiculous if there was none but I mentioned many times. Problem is not that tricky if you know that equation

Pw = 0.5 * air density * area * (wind speed - vehicle speed)3


--- Quote from: Kleinstein on December 29, 2021, 09:22:53 pm ---The formula with the (w-v)²*v is the power available to a simple sail for velocities lower than the speed of the wind. However this does not have much relevance to a vehicle driven by a prop. It shows that going faster than the wind does not work with a simple (e.g. spinnacker like) sail, when going straight down the wind.
This is not really surprising and know for a long time.

--- End quote ---

Blackbird is not driven by the propeller it is driven by wind power that pushes against the equivalent back area of the vehicle and it is also pushed by the pressure differential.
So what energy you take from the wheel is provided by the combination of wind + stored energy in pressure differential that basically push the vehicle same as any sail vehicle as that is the only way air can interact with the vehicle. Above wind speed is the stored pressure differential alone that "pushes"/powers the vehicle.
When that stored energy is all used up the vehicle will just slow down (decelerate).

PlainName:

--- Quote --- it is driven by wind power that pushes against the equivalent back area of the vehicle
--- End quote ---

So close! It's pushing against the rearward-moving airflow from the propeller, not any part of the vehicle (which would be receding forwards).

electrodacus:

--- Quote from: dunkemhigh on December 29, 2021, 10:27:28 pm ---
--- Quote --- it is driven by wind power that pushes against the equivalent back area of the vehicle
--- End quote ---

So close! It's pushing against the rearward-moving airflow from the propeller, not any part of the vehicle (which would be receding forwards).

--- End quote ---

Yes as the vehicle speed increases the equivalent area of the propeller increases up to the max swept area of the propeller.
Still air density and of course pressure is increased at the back of the propeller and decreased on the front and this pressure differential stored energy is powered by wind power.
But while vehicle is above wind speed there is no more wind power available so the pressure differential that now pushes the vehicle will start to drop reducing the acceleration rate up to the point pressure differential is small enough that can no longer cover the vehicle frictional losses and then the vehicle will start to slow down.

PlainName:

--- Quote ---But while vehicle is above wind speed there is no more wind power available
--- End quote ---

You're falling into your hole again. When the vehicle is at or above wind speed, the airflow from the propeller is still going backwards at slower than wind speed. Thus the wind is still pushing against that airflow and generating power.

The prop doesn't need much power to do that. Just enough to turn it and move the vehicle through almost static air - any drag is from the vehicle going faster than the wind, and we only need it to be tiny to score.

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