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Newton's third law problem.
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electrodacus:

--- Quote from: Kleinstein on November 29, 2022, 09:33:03 pm ---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 ---

I see no prediction from you. Do you need more time ?

In the meantime I can show how that what you think as the correct equation violates the energy conservation law.
Say you had a 100% efficient wind generator (obviously a wind turbine will be only around 40% efficient but the discussion is ideal case).
For easy calculation say the wind generator swept area is 1m2 and there is nothing more. It is on wheels but we consider those super narrow so they do not add to wind drag. Also wind speed is 10m/s
A stationary vehicle with this characteristics can generate 0.5 * 1.2 * 1 * (10)3 = 600W again ideal case 100% efficiency.
What happens if vehicle moves very slowly upwind say 1m/s upwind ?
The wind turbine will see a 11m/s wind speed so it can now generate 798W that is 198W more than when stationary.

According to your equation only 0.5 * 1.2 * 1 * (11)2  * 1m/s = 72.6W are needed.

So inputting 72.6W and getting out 198W will violate energy conservation. Keep in mind we already discuss about an ideal 100% efficient system.

While the equation I consider to be the correct one will predict that you need 798W for the motor to drive at 1m/s against a 10m/s headwind (just drag power) so there is no energy conservation conflict.

Also if you want to travel down wind powered by the wind at 1m/s you need to apply a brake at the wheel with the power equal with 0.5 * 1.2 * 1 (10-1)3 = 437W so you can do what you want with those 437W say light some incandescent lamps and be able to maintain a constant 1m/s downwind powered by the wind.

So a stationary vehicle in 10m/s wind with 1m2 capture area has 600W available to accelerate downwind and if it wants to move upwind it needs to add extra on top of that 600W to start accelerating the mass in that direction. 
AVGresponding:
I do enjoy a good circular argument   :popcorn:

Kleinstein:

--- Quote from: electrodacus on December 03, 2022, 02:46:13 am ---
--- Quote from: Kleinstein on November 29, 2022, 09:33:03 pm ---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 ---

I see no prediction from you. Do you need more time ?

In the meantime I can show how that what you think as the correct equation violates the energy conservation law.
Say you had a 100% efficient wind generator (obviously a wind turbine will be only around 40% efficient but the discussion is ideal case).
For easy calculation say the wind generator swept area is 1m2 and there is nothing more. It is on wheels but we consider those super narrow so they do not add to wind drag. Also wind speed is 10m/s
A stationary vehicle with this characteristics can generate 0.5 * 1.2 * 1 * (10)3 = 600W again ideal case 100% efficiency.
What happens if vehicle moves very slowly upwind say 1m/s upwind ?
The wind turbine will see a 11m/s wind speed so it can now generate 798W that is 198W more than when stationary.

According to your equation only 0.5 * 1.2 * 1 * (11)2  * 1m/s = 72.6W are needed.

So inputting 72.6W and getting out 198W will violate energy conservation. Keep in mind we already discuss about an ideal 100% efficient system.

--- End quote ---

This is a good, but tricky point. By moving against the wind the volume of wind that is used is increased.  So there is extra air to use. The exact calculation is tricky as the wind interacts with the slowed down air.  The limited efficiency of a wind turbine is not just for technical reasons, the Betz limit is there for prociple reasons and a 100% efficient wind turbine thus already in in conflict with theroy and by itself cause contradictions.




--- Quote from: electrodacus on December 03, 2022, 02:46:13 am ---While the equation I consider to be the correct one will predict that you need 798W for the motor to drive at 1m/s against a 10m/s headwind (just drag power) so there is no energy conservation conflict.

Also if you want to travel down wind powered by the wind at 1m/s you need to apply a brake at the wheel with the power equal with 0.5 * 1.2 * 1 (10-1)3 = 437W so you can do what you want with those 437W say light some incandescent lamps and be able to maintain a constant 1m/s downwind powered by the wind.

--- End quote ---
Your prediction is also causing a problem with energy conservation. You predict the 437 W from the vehicle moving down wind, but the wind turbine on the vehicle still sees 9 m/s of wind and could use that wind to creat additional power. Chances are it could gain more than 170 W from this - likely even with an efficiency within the Betz limit. When moving with the wind, there is less (at least not more) of the wind actually used - so that point does not work here either.  So it is your prediction that violates the conservation of energy.
electrodacus:

--- Quote from: Kleinstein on December 03, 2022, 09:05:28 am ---
This is a good, but tricky point. By moving against the wind the volume of wind that is used is increased.  So there is extra air to use. The exact calculation is tricky as the wind interacts with the slowed down air.  The limited efficiency of a wind turbine is not just for technical reasons, the Betz limit is there for prociple reasons and a 100% efficient wind turbine thus already in in conflict with theroy and by itself cause contradictions.

--- End quote ---

Sorry but Benz limit only refers to wind turbines. And even if we used the 59% Benz limit the problem is not changed. You add a small amount of energy to an a system and you get more in return (significantly more but even just 1% extra will violate the energy conservation law).
The example is there just to prove that equation you and others proposed is not correct.
 




--- Quote from: Kleinstein on December 03, 2022, 09:05:28 am ---Your prediction is also causing a problem with energy conservation. You predict the 437 W from the vehicle moving down wind, but the wind turbine on the vehicle still sees 9 m/s of wind and could use that wind to create additional power. Chances are it could gain more than 170 W from this - likely even with an efficiency within the Betz limit. When moving with the wind, there is less (at least not more) of the wind actually used - so that point does not work here either.  So it is your prediction that violates the conservation of energy.

--- End quote ---

There is no extra power. Those 437W are all that it is available and you are already extracting everything that is it available to be extracted with the generator at the wheel.
At 9m/s which is the wind speed relative to vehicle (all that is important) you have 0.5 * 1.2 * 1 * (10-1)3 = 437.4W  There is nothing more.
A wind turbine as you already mentioned can extra way less than this if it was to be used.
So whatever a wind turbine where to extract it will be subtracted from those 437.4W.

You can say that a sail vehicle on wheels is much more efficient than a propeller but the vehicle is moving and so you will need a flexible cable to connect the vehicle and at some point you need to stop and come back and you will wasting time not generating and use energy to return to a start point.
So overall efficiency if it was to be used as a wind turbine will not be that great and way more expensive. Plus it will be close to the ground where wind speed is much lower.
That is the reason I say a sail is as close to 100% efficiency as possible in using wind power to accelerate a vehicle.
All that calculated drag power is available to accelerate the vehicle.
So staying with this example when stationary the vehicle has available 600W of wind power so as soon as you remove the brakes say for 1ms the kinetic energy of the vehicle will increase by  600W * 0.001s = 0.6Ws (0.6J) so the speed of the vehicle after 1ms will depend on vehicle weight.
I know I use unusual methods of calculating all this compared to how this things are teached in schools but I think talking only about forces in schools while correct is the wrong approach in properly understanding what happens and human intuition about this things is wrong thus the wrong equation circulating around.
I wish people still did experiments in the classrooms then it will be easy to spot this incorrect equations.

I also think this has way more implications than in this highschool level physics as you can not work in any field of physics or engineering and not be affected by wrongly understanding this subject.
I really want for this misinformation to be corrected if possible. But no idea how to do this. The only thing that will convince most people will be the real world experiment.
The simplest I can think of is a vehicle driving slowly in a head wind and measuring the motor consumption. 
 
Kleinstein:

--- Quote from: electrodacus on December 03, 2022, 04:24:27 pm ---
--- Quote from: Kleinstein on December 03, 2022, 09:05:28 am ---Your prediction is also causing a problem with energy conservation. You predict the 437 W from the vehicle moving down wind, but the wind turbine on the vehicle still sees 9 m/s of wind and could use that wind to create additional power. Chances are it could gain more than 170 W from this - likely even with an efficiency within the Betz limit. When moving with the wind, there is less (at least not more) of the wind actually used - so that point does not work here either.  So it is your prediction that violates the conservation of energy.

--- End quote ---

There is no extra power. Those 437W are all that it is available and you are already extracting everything that is it available to be extracted with the generator at the wheel.
At 9m/s which is the wind speed relative to vehicle (all that is important) you have 0.5 * 1.2 * 1 * (10-1)3 = 437.4W  There is nothing more.
A wind turbine as you already mentioned can extra way less than this if it was to be used.
So whatever a wind turbine where to extract it will be subtracted from those 437.4W.

--- End quote ---
The moving wind turbine would still see the 9 m/s wind can it can thus still extract power from that wind.  It gets even more obvious when you consider moving the turbine only at snails pace. That would chance essentially nothing with the wind. So there would still be nearly the full wind and with correct formular also only very little power on the wheels. Your formular has just way too much power for the wheels and than the problem that there is overall too much power to be gained.

Too much power from the wheels comes with another problem: the force gets too large: 437 W with a speed of 1 m/s would mean a force of 437 N , which is too high by about a factor of 10. The errir gets even more rediculous if slower. Essentially constant power even at slow speed just does not work.  :horse:
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