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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: Kleinstein on December 15, 2021, 07:41:34 pm ---Recongnizing that the equation should conver different cases without changing the equation is a good point: this also applies to looking at the vehicle moving a snails speed aroung zero. The correct equation incudes this case.

The slow speed case does not directly apply to the vehicle going faster that the wind. However it clearly shows the the equation proposed by electrodacus is flawed and leads to obvious problems there. Looking at this point may also help him correcting his understanding of force and power.  Doing the calculations only with power can be tricky if there are processes with less than 100% efficiency (e.g. like the sail).

--- End quote ---

The equation I use perfectly matches reality. For some reason you think that is not the case but it can fairly easily be proven.
If your vehicle has no mechanical brakes and you want to keep the vehicle from moving in 10m/s wind with a 1m^2 sail then you will need to apply 600W to that motor (all ideal case so ideal motor and no friction losses).
If you apply no power to the motor the vehicle will accelerate towards wind speed.
If you want to go directly upwind with 0.001m/s then you need to supply the motor with 0.5 * 1.2 *1 *(10 + 0.001)^3 = 600.18W
If you want to go directly downwind with 0.001m/s then you can use the motor as a generator and take out 0.5 * 1.2 *1 *(10 - 0.001)^3 = 599.82W (you can just waste this as heat and you can maintain that low speed).



--- Quote from: Kleinstein on December 15, 2021, 07:41:34 pm ---Having an equation with (w-v) or (v-w) is not such a big difference, it is just the sign and this may be different depending on how one defines the direction of force or an axis.  One has to look not just at the one line with the formula, but also the explaination fo the symbols.

I don't think Derek's proof has a major mistake in the equations, as it leads to the right conclusion - just getting a result that is not obvious to everybody is no proof that there is an error. Usually math is way more reliable than intuition.

--- End quote ---

Not sure why you think a change in sign is not a huge difference.  It is the difference between being able to accelerate instead of decelerate.
That is the problem the conclusions are totally wrong. The vehicle is not powered by wind directly but by stored energy.
PlainName:
Does anyone have access to a treadmill and propeller model? ISTM the way to settles this is to get that model doing its thing, but have it tethered by some string so it can't move forward. Either the string is kept taught and energy storage is rubbish, or it goes loose and some store has clearly run out of puff.
IanB:

--- Quote from: dunkemhigh on December 15, 2021, 08:17:13 pm ---Does anyone have access to a treadmill and propeller model? ISTM the way to settles this is to get that model doing its thing, but have it tethered by some string so it can't move forward. Either the string is kept taught and energy storage is rubbish, or it goes loose and some store has clearly run out of puff.

--- End quote ---

It doesn't matter if you do that. Our friend will just find some way to reject the experiment or the results. So it would be a waste of time to try.
bdunham7:

--- Quote from: electrodacus on December 15, 2021, 07:59:06 pm ---If your vehicle has no mechanical brakes and you want to keep the vehicle from moving in 10m/s wind with a 1m^2 sail then you will need to apply 600W to that motor (all ideal case so ideal motor and no friction losses).

--- End quote ---

That's the point of contention.  I'm saying that this statement is not true.  What is your theory/proof/argument/evidence that supports it?
electrodacus:

--- Quote from: bdunham7 on December 15, 2021, 08:25:12 pm ---
--- Quote from: electrodacus on December 15, 2021, 07:59:06 pm ---If your vehicle has no mechanical brakes and you want to keep the vehicle from moving in 10m/s wind with a 1m^2 sail then you will need to apply 600W to that motor (all ideal case so ideal motor and no friction losses).

--- End quote ---

That's the point of contention.  I'm saying that this statement is not true.  What is your theory/proof/argument/evidence that supports it?

--- End quote ---

So what do you think is needed if not 600W to prevent the vehicle from being pushed by the wind ?
We can do this test relatively easily.

The equation showing that is simple and it is this one you can find everywhere for ideal case  0.5 * air density * area * (wind speed)^3
So 0.5 * 1.2 * 1 * 10^3 = 600W

Here I found an image supporting my case ciclist frontal surface area around 0.5m^2 and 10m/s = 36km/h notice that requires about 300W


https://ridefar.info/bike/cycling-speed/air-resistance-cyclist/
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