General > General Technical Chat
Mess with your minds: A wind powered craft going faster than a tail wind speed.
bdunham7:
--- Quote from: electrodacus on December 18, 2021, 10:44:10 pm ---We are drifting in all sort of analogies but to try and answer what happens imagine that vehicle with the solar panel having the solar panels rotate away from the sun as the speed increases. That is what happens to a wind powered vehicle that drives directly downwind.
--- End quote ---
I'll agree that analogies are often problematic, but that one is the worst I've seen in a long time.
--- Quote ---Here are the correct equations for wind power available to a vehicle traveling directly down wind
0.5 * air density * area * (wind speed - vehicle speed)^3 yes this is the correct equation. Notice how you have highest power at low vehicle speed and power drops to zero by the time vehicle speed equals wind speed.
--- End quote ---
So surely you agree that the total available wind power at a certain point (no vehicle or sail involved) is 0.5*airdensity * windspeed3, correct?
So where does the rest of that wind power go if you can only get the fraction of it that your formula specifies? That power is still there somewhere, isn't it?
electrodacus:
--- Quote from: bdunham7 on December 18, 2021, 11:09:17 pm ---
--- Quote ---Here are the correct equations for wind power available to a vehicle traveling directly down wind
0.5 * air density * area * (wind speed - vehicle speed)^3 yes this is the correct equation. Notice how you have highest power at low vehicle speed and power drops to zero by the time vehicle speed equals wind speed.
--- End quote ---
So surely you agree that the total available wind power at a certain point (no vehicle or sail involved) is 0.5*airdensity * windspeed3, correct?
So where does the rest of that wind power go if you can only get the fraction of it that your formula specifies? That power is still there somewhere, isn't it?
--- End quote ---
Please read again my formula as you forgot a very important part and that is the area that wind pushes against.
0.5 * air density * area * windspeed3
This is the formula anyone designing a wind turbine will use except that is is ideal 100% of available wind power and to this they need to add the turbine efficiency usually around 40% and the generator efficiency that can be over 90%
For a vehicle driving directly down wind ideal case all you need is to subtract vehicle speed from wind speed since wind speed relative to vehicle is what can power the vehicle.
This formula
0.5 * air density * area * (wind speed - vehicle speed)3 is what will apply to any wind only powered vehicle driving directly downwind.
This is also the ideal case so absolutely max that is available to the vehicle meaning that if you do not add an energy storage device to this vehicle or some external energy source like gasoline and an engine then your vehicle can not exceed wind speed.
For direct downwind blackbird is clear to me that energy is stored in pressure differential generated by the propeller and that is what allows it to exceed wind speed even if it may be for just a few minutes depending on the design, how fast it will use that stored energy.
bdunham7:
--- Quote from: electrodacus on December 19, 2021, 01:02:47 am ---Please read again my formula as you forgot a very important part and that is the area that wind pushes against.
0.5 * air density * area * windspeed3
This is the formula anyone designing a wind turbine will use except that is is ideal 100% of available wind power and to this they need to add the turbine efficiency usually around 40% and the generator efficiency that can be over 90%
For a vehicle driving directly down wind ideal case all you need is to subtract vehicle speed from wind speed since wind speed relative to vehicle is what can power the vehicle.
This formula
0.5 * air density * area * (wind speed - vehicle speed)3 is what will apply to any wind only powered vehicle driving directly downwind.
This is also the ideal case so absolutely max that is available to the vehicle meaning that if you do not add an energy storage device to this vehicle or some external energy source like gasoline and an engine then your vehicle can not exceed wind speed.
--- End quote ---
Mea culpa, I forgot to put in 'area'. But you've dodged the actual question. Since all of the energy in the first question represents the total wind energy available for that particular area and the second equation represents only part of that energy, where does the rest of it go?
Brumby:
--- Quote from: electrodacus on December 18, 2021, 06:31:44 pm ---Clearly shows you do not understand power and energy. 20km/h ~ 5.5m/s
If you take 5.5W form the wheel (1N * 5.5m/s) and put all that in to propeller (ideal case) the most propeller can output is 5.5W
--- End quote ---
Using this, you have 5.5W spinning a propeller. This propeller creates a thrust force against an air mass which is stationary with respect to the vehicle.
--- Quote ---thus no acceleration possible even in ideal case.
--- End quote ---
How can a non-zero force NOT create a change in velocity?
IanB:
It's really necessary to work with power, rather than energy.
For a vehicle to travel at any steady speed, v, the power it requires is the power required to overcome the frictional resistance--the rolling resistance on the ground and the drag from the surrounding air.
Let's suppose that a vehicle wants to travel at a speed, v, that is faster than the wind, then it will require some motive power, Pv.
If a vehicle can obtain at least that much power from the wind, using a turbine or other mechanism, then it can travel at that speed. It becomes an engineering problem of how to design that mechanism, that will necessarily include such items as turbines, fans, gears, shafts, even possibly a motor-generator combination.
There is no violation of conservation of energy implied, since clearly the wind has unlimited power available (if you want more power, just use more area for your fan/turbine).
To be clear, sailors know this, since they routinely sail downwind faster than the wind, as noted by my example earlier in the thread. If the wind speed is 20 mph due west, then racing yachts can travel 20 miles due west at an average speed greater than 20 mph. And they can do this indefinitely. Energy storage cannot be claimed for a boat that is travelling for an hour or more at these speeds.
(Specifically, if point B is 20 miles due west of point A, and the wind is blowing at 20 mph due west, then a boat can travel from A to B in less than 1 hour.)
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