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Newton's third law problem.
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electrodacus:

--- Quote from: IanB on November 29, 2022, 08:28:37 pm ---We covered this in another thread, and it appears that a simple square sail is not very efficient at all. A sail self-evidently has zero efficiency when stationary, and zero efficiency when moving at the same speed as the wind. It seems the maximum efficiency of a simple square sail occurs somewhere in between, and is not much more than 15% at best. See this post for an explanation:

https://www.eevblog.com/forum/chat/mess-with-your-minds-a-wind-powered-craft-going-faster-than-a-tail-wind-speed/msg3888830/#msg3888830

Yacht sails are clearly much more efficient, but that is because they use angles and aerodynamics to do a better job.

--- End quote ---

What you call a stationary sail is not stationary it moves at the same speed as the earth move as it is anchored to earth.
When you release the brakes what is the acceleration power that the vehicle experiences assuming no rolling resistance ?

Measure the distance the vehicle moved in one second after the brakes were released and calculate based on that the amount of kinetic energy vehicle gained then work backwards to calculate the amount of average power the wind applied in order to gain that amount of kinetic energy.

Also calculate the amount of brake power needed (energy to be wasted as heat) to maintain vehicle speed at 1m/s while wind speed is 11m/s
See what you think about the efficiency of a sail after that.
Kleinstein:

--- Quote from: electrodacus on November 29, 2022, 08:27:54 pm ---That is not good enough.
If you want to say that equation is wrong you need to provide the correct one so we can compare the prediction each of them makes.

--- End quote ---
No, to proof that the euqation is wrong it is enough to show an example where the equation is wrong. That example is given (both with the math and as real world example in the videos in several examples).

The true burden is to you to show that the equation is correct to start with. Just a link to a dubious web site that seems to do the same mistake or a remotely similar equation for the stationary vehicle is not a proof. Given that it is pooven wrong there no hope to find a proof.
electrodacus:

--- Quote from: Kleinstein on November 29, 2022, 09:12:51 pm ---No, to proof that the euqation is wrong it is enough to show an example where the equation is wrong. That example is given (both with the math and as real world example in the videos in several examples).

The true burden is to you to show that the equation is correct to start with. Just a link to a dubious web site that seems to do the same mistake or a remotely similar equation for the stationary vehicle is not a proof. Given that it is pooven wrong there no hope to find a proof.

--- End quote ---

You (all) are talking nonsense.

It is time for you to make a real world prediction and we will find a way to setup the experiment.

So say a small maybe toy like vehicle with a simple shape say a cube on wheels.

Say a cube with 20x20x20cm should be fine but we can change the dimensions if it makes it easier to do the experiment.

Drag coefficient for a cube is 1.05
 
Say cube will need to move upwind at a slow speed of 1m/s and wind speed is 10m/s

Based on all this I say the electric motor driving the cube requires this amount of power to overcome drag

Pd = 0.5 * 1.2 * (0.2*0.2*1.05) * (10+1)3 = 33.5W

Time for your prediction and please show how it is calculated and we will find a way to do the experiment so that we all agree it is done correctly.
Kleinstein:
The (..)³ equation is wrong by having the wind speed inside for all 3 factors. One factor is only the vehicle speed. So the toy would only need 1/11 the power.

The difference gets even larger, when we assume a smaller speed, like 1 mm/s and than 11 m/s of wind. In this relatively extreme slow speed example it gets obvious that your prediction is wrong:
The mechanical power is speed times force and the force thus power divided by speed. So the froce would be 33.5 W /0.001 m/s = 33.5 kN. That would be way too much force to be produced by the wheels. So your equation would predict that a vehicle can not go slow against a heat wind. With the cazy prediction of needing more force the slower it wants to move and thus no way to start from a standstill as this naturally innitially is very slow.
electrodacus:

--- Quote from: Kleinstein on November 29, 2022, 09:33:03 pm ---The (..)³ equation is wrong by having the wind speed inside for all 3 factors. One factor is only the vehicle speed. So the toy would only need 1/11 the power.

The difference gets even larger, when we assume a smaller speed, like 1 mm/s and than 11 m/s of wind. In this relatively extreme slow speed example it gets obvious that your prediction is wrong:
The mechanical power is speed times force and the force thus power divided by speed. So the froce would be 33.5 W /0.001 m/s = 33.5 kN. That would be way too much force to be produced by the wheels. So your equation would predict that a vehicle can not go slow against a heat wind. With the cazy prediction of needing more force the slower it wants to move and thus no way to start from a standstill as this naturally innitially is very slow.

--- End quote ---

You are right about one thing and that is 1m/s is still way to fast for such a small vehicle especially if we will test this in a small DIY wind tunnel.
Will still use 10m/s for wind as I think that should be possible even in DIY wind tunnel and use 0.02m/s (2cm per second) this way a 30cm run will take about 15 seconds enough to see the power measurement.

With this new data we have

Pd = 0.5 * 1.2 * (0.2*0.2*1.05) * (10+0.02)3 = 25.3W

I is time for your prediction as it makes no sense to discuss since you have a wrong idea of how air particles and the object/vehicle interact.
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