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

[electrodacus]

Aside from the fact that 10W is not a 'force', OK.  Say a force such that 10W is dissipated. So what?

Obviously is not just a force is better as it contains more information.

What does all that have to do with the example we are talking about? 

One thing about physics is that often different sets of rules apply to the same problem and the solutions have to work in all of them, otherwise you have made an error.  You can try to solve an energy equation here if you like, but you should also be able to come up with a solution in simple mechanics, Newton's laws and so forth, and if the methods don't yield the same result, then one of them hasn't been done right or doesn't apply.  The simplest trick exam question involves firing a bullet into a pendulum and then determining the resulting motion of the pendulum afterwards.  In that case, the common mistake is to use conservation of energy instead of conservation of momentum to try and solve the problem.  That doesn't work because (coherent) kinetic energy is not conserved in that case. You're making a similar mistake here--this is not a closed system and you cannot use conservation of energy laws to solve it.

The example was meant to show that if you take energy out of the vehicle kinetic energy by breaking you need to put all that back just to maintain current speed.
Yet blackbird type vehicle is superposed to break this rule (obviously is not as that will be impossible).
Pushing against the ground using a wheel or pushing against the air using a propeller will have the same result as long as the air particles are stationary (vehicle same speed as wind). If vehicle speed higher than wind in the exact same direction then you will be able to put less kinetic energy back in to vehicle meaning even ideal vehicle will slow down.

[electrodacus]

Knowing the mass "m" (ie. 1000kg) of the vehicle you can, imho.
KE=p^2/(2m)
KE=10Ns*10Ns/(2m)=100/2000=0.05Ws
500-0.05=499.95Ws

I intentionally not mentioned the mass or the speed of the vehicle to make the point that Force alone is no useful while Power alone is.
Using power will make the calculation simpler and easier than using force and speed since you can wrongly interpret the results as it seems the case here.
You could have used my 10Ws example to keep things consistent and find the mass that way not just take a random number.
m= 10Ns*10Ns/(2*10Ws) = 5kg
In any case that is not the point.
The point is that taking energy from vehicle wheel and then transferring all that to another wheel or to a propeller will not allow you to accelerate the vehicle.
Not in the example where vehicle is only powered by wind and it is at wind speed or higher and vehicle direction is exact same as wind direction.

[bdunham7]

The point is that taking energy from vehicle wheel and then transferring all that to another wheel or to a propeller will not allow you to accelerate the vehicle.
Not in the example where vehicle is only powered by wind and it is at wind speed or higher and vehicle direction is exact same as wind direction.

OK.     Would you like to bet $10,000? 

[electrodacus]

OK.     Would you like to bet $10,000? 

What is up with people and obsession with gambling.

[Ian.M]

OK.     Would you like to bet $10,000? 

What is up with people and obsession with gambling.

Perhaps they see an easy mark who if they believe their pet theory strongly enough may take a sucker bet!   The physics is validated by the existence of several types of wind powered vehicles that have been demonstrated to sustainably exceed the wind speed down wind when the vehicle's velocity is resolved in the true downwind direction.  Smells like a potentially profitable bet to me . . . .

Perhaps you were a deprived child and never had the chance to play with a flywheel powered toy car.   Although it is clearly obvious that no energy can be extracted from the wind by a vehicle that is travelling at exactly the same speed as the wind in the exact same direction,  you need to prove that net energy cannot be extracted from the wind when travelling faster than the wind speed.

[electrodacus]

Perhaps they see an easy mark who if they believe their pet theory strongly enough may take a sucker bet!   The physics is validated by the existence of several types of wind powered vehicles that have been demonstrated to sustainably exceed the wind speed down wind when the vehicle's velocity is resolved in the true downwind direction.  Smells like a potentially profitable bet to me . . . .

I had not claimed blackbird and similar vehicle can not exceed wind speed in the same direction as the wind. Problem is that is not indefinitely it is just for at most a few minutes depending on amount of stored energy and amount of vehicle friction.
Vehicle will get to peak speed and then slowly decelerate until it is below wind speed.

I propose people test the wheel only vehicle I show in my diagram so they can see an example (if that is what it takes).
That may still not be convincing so another test a bit harder to do is push a vehicle like blackbird or the small treadmill model to sufficient speed (designed speed) then release it in a day with no wind and see how vehicle exceed the speed the vehicle was pushed at while there is no wind at all.

In fact this is demonstrated already by the treadmill model the one with propeller since there the wind speed is zero and treadmill just simulates a vehicle at a certain speed (I think it was 10mph) then vehicle accelerated forward thanks to stored energy while vehicle was restrained with the hand.
If the vehicle had a wheel as propulsion instead of a propeller that as an inductor can store energy in pressure differential instead of magnetic field around the coil then with wheel only since there is no storage there is no forward motion left to right in my diagram.
Some like that guy on youtube thinks that his vehicle is what I show in my diagram when it is not.
His vehicle in both cases shows a vehicle traveling against the wind direction at lower than wind speed and of course that is possible.

I say a bet is a gamble because winner is not necessarily the one with the correct explanation but the one that is believed by the judge. 

[Ian.M]

I believe the real limit is the length of downwind track available before they run out of salt pan!   

[David Hess]

Running out of track on the salt pan is not a problem if your oscillation overthruster is functioning properly.  Contact Yoyodyne Propulsion Systems for pricing and availability.

[IanB]

Goodness, I thought this thread was long ago gone to sleep! Crazy to see it woken up again after such a long time.

[IanB]

Problem is that is not indefinitely it is just for at most a few minutes depending on amount of stored energy and amount of vehicle friction.

Except that you are not able to demonstrate or prove this to the satisfaction of others.

It has been shown both by experiment and mathematics that a vehicle with a trailing wind can travel faster than  the wind speed indefinitely, if the vehicle is constructed appropriately.

The vehicle does of course need to have the correct design. A simple sailboat cannot do this.

[ejeffrey]

Perhaps they see an easy mark who if they believe their pet theory strongly enough may take a sucker bet!   The physics is validated by the existence of several types of wind powered vehicles that have been demonstrated to sustainably exceed the wind speed down wind when the vehicle's velocity is resolved in the true downwind direction.  Smells like a potentially profitable bet to me . . . .

I had not claimed blackbird and similar vehicle can not exceed wind speed in the same direction as the wind. Problem is that is not indefinitely it is just for at most a few minutes depending on amount of stored energy and amount of vehicle friction.
Vehicle will get to peak speed and then slowly decelerate until it is below wind speed.

But that is manifestly not what is observed.  The vehicle keeps accelerating when the apparent wind switches direction to become a headwind.  Because it keeps accelerating, the wheels and propeller also are also accelerating -- their kinetic energy is also increasing, not being depleted to make the vehicle go faster.  Your description could be accurate if they were using a mutli-speed transmission and effectively slam shifting into higher gear to get the kart to go faster while the propeller slows down but that isn't what is happening.  Instead they vary the effective gear ratio by feathering the blades which has negligible impact on the stored kinetic energy.  And the blackbird team has gotten to well over 2x the wind speed, that can't be from some energy storage.

Anyway, all the talk about the wind is almost a red herring.  It is a simple problem of gear ratios, and the mechanical model shown near the end of the Veritasium bet resolution video (around 13:30) is all you actually need to see.  The two floor / wood plank in that demo have a relative speed difference, and a car with the right gear ratio can extract energy from that difference to go faster than either of them.  The fact that in the blackbird one of the "gears" is replaced with a propeller and the "board" is the wind is mostly just a head fake.  Yes to get the actual numerical answer you need to figure the efficiency of the propeller, but the underlying reason it works doesn't change.

It is also very similar to the problem problem "if I attach a rope to a bike pedal and pull backwards, which direction will the bike roll" (https://www.scientificamerican.com/article/mathematical-impressions-the-bicycle-pulling-puzzle/ ) -- and the answer there is that it will usually go backward but with the right gearing can go forward.

[ejeffrey]

If an ice yacht can tack downwind with a velocity made good (VMG) of over double the wind speed, which is very well documented^*, its obvious that a land vehicle with a  variable angle of attack wind turbine geared to wheels can also beat the wind downwind if its got sufficient blade area and great care is taken to minimize friction.

The problem is getting past the stagnation point in a steady wind where the velocity is equal to the wind which is going to demand some sort of mechanism so stored energy in the rotor can briefly accelerate the vehicle past the wind speed, then flipping the angle of attack will let the rotor continue to draw power from the relative wind.   

There is no stagnation point because the propeller is spinning fast enough that the angle of attack of the blade is always from the same side.  They do adjust the prop pitch to get the most efficient operation, but it is not directly related to the apparent wind speed seen by the body of the vehicle.  A fixed pitch prop can also work but would be less efficient.

[electrodacus]

Except that you are not able to demonstrate or prove this to the satisfaction of others.

It has been shown both by experiment and mathematics that a vehicle with a trailing wind can travel faster than  the wind speed indefinitely, if the vehicle is constructed appropriately.

The vehicle does of course need to have the correct design. A simple sailboat cannot do this.

If you have at least basic understanding of physics then my theoretical explanation should be more than good enough to disprove their claims.
The mathematics they used is flawed as they wrongly assume vehicle has any access to wind power when they are above wind speed in the exact same direction as the wind.
Not sure what most people thing when they think about air or propellers as it seems a lot of you think they are magic.
The treadmill prototype test alone if interpreted correctly show exactly what I say and that is stored energy in the form of pressure differential is what powers the vehicle. There is no wind indoor and the treadmill just simulates a vehicle traveling at wind speed (so as far as vehicle is concerned no wind to extract energy from).
I guess while almost exactly the same a test where they push this small propeller powered cart to 10mph (same as treadmill speed) maybe 12mph to be sure (as there is extra drag compared to treadmill test) in a day with no wind and see vehicle accelerate forward will be more convincing even if it is almost the exact same test minus less drag as the pushed vehicle will experience an apparent head wind equal with vehicle speed.
So what I say is already proven people just do not understand the experiments that where already done.
Also an experiment with wheels only cart like the one in my diagram will show anyone that can not calculate from the diagram what will happen that vehicle can not travel from left to right.
If wheels G and M are free spinning in ideal case with no friction vehicle will not move at all then if power is taken from wheel G and all of it (again ideal case) is transferred to wheel M vehicle will still be in the same place.
Any sort of friction basically a real vehicle will result in vehicle moving from right to left so the reverse of the claim with is clearly impossible.
I can not see how the problem can be simplified more and how can someone claim there is some gear combination that will make this vehicle move from left to right.
It is a simple as motor wheel "M" is powered from generator wheel "G".   



Anyone will ridicule the device in the image below but not the one in my diagram above.
Claims made are exactly the same so energy from nothing since vehicle above wind speed in the wind direction will have no access any wind power.

[Kleinstein]

The vehicle still has access to wind power independ of the speed. It works when moving faster than the wind and also when movong at the speed of the wind. The way the vehicle is extracting energy is a bit counter-intuitive and it takes some careful thinking to understand . Even the professor who lost the initial bet was wrong, but he finally understood.  This is not just because the judge was convinced but the professor also got the idea. Understanding the idea is not so difficult, once one opens the mind to new ideas.

One basic point to make clear is that the power is force times speed. So at a lower speed one has a higher force at the same power level. Confusing power and force is a mistake sometimes made by beginners.

The basic idea behind the vehicle is to take up power from the wheels and use this power to drive the prop. The prop than produces force relative to the wind.

So it looks a bit like the fake over unit devices, but there is a twist to it, as the two parts have different systems to act on:

With the vehicle moving in the direction of the wind, the speed of the wheels to the ground is relatively high.
With the vehicle moving with about the speed of the wind, the relative speed between the prop and wind is relatively low and with a speed lower than the wind speed the wind is even driving the prop. So even with a not so good efficiency of the prop it is possible to create more forward force ( = power / speed)  than the backward force from the wheels. So the net force can be forward. 

The energy comes from slowing down the wind. This is seen as the backwards force from the wheels. With the fan blowing in reverse this even works when moving faster than the wind or also when moving at the speed of the wind. So there is no dead point or special case when the speed is the same.

The difficulty in actually making this work comes from getting good enough an efficiency from the prop and gears. No need for over unity, just not too small (e.g. < 30%) to not overcome the friction forces and parasitic drag.


One can test the easy purely mechanical (no aero dynamic) analog. The nice point here is that it does not depend on speed so much and can be done hands on on the desk:  Have a spool of thread with the outer rims larger than the diameter where the thread is. To improve the gearing ratio maybe add some rubber rings to the outer rims.  With the spool on the desk slowly pull the thread horzontally.  The thread is the analog to the wind.

With the thread on the top side the spool moves slower the thread is pulled, so nothing funny happening.
With the thread on the bootom side the spool moves faster than the thread is pulled.  On a slippery surface it may slip.

[electrodacus]

One basic point to make clear is that the power is force times speed. So at a lower speed one has a higher force at the same power level. Confusing power and force is a mistake sometimes made by beginners.

The basic idea behind the vehicle is to take up power from the wheels and use this power to drive the prop. The prop than produces force relative to the wind.

So it looks a bit like the fake over unit devices, but there is a twist to it, as the two parts have different systems to act on:

With the vehicle moving in the direction of the wind, the speed of the wheels to the ground is relatively high.
With the vehicle moving with about the speed of the wind, the relative speed between the prop and wind is relatively low and with a speed lower than the wind speed the wind is even driving the prop. So even with a not so good efficiency of the prop it is possible to create more forward force ( = power / speed)  than the backward force from the wheels. So the net force can be forward. 

The energy comes from slowing down the wind. This is seen as the backwards force from the wheels. With the fan blowing in reverse this even works when moving faster than the wind or also when moving at the speed of the wind. So there is no dead point or special case when the speed is the same.

The difficulty in actually making this work comes from getting good enough an efficiency from the prop and gears. No need for over unity, just not too small (e.g. < 30%) to not overcome the friction forces and parasitic drag.


One can test the easy purely mechanical (no aero dynamic) analog. The nice point here is that it does not depend on speed so much and can be done hands on on the desk:  Have a spool of thread with the outer rims larger than the diameter where the thread is. To improve the gearing ratio maybe add some rubber rings to the outer rims.  With the spool on the desk slowly pull the thread horzontally.  The thread is the analog to the wind.

With the thread on the top side the spool moves slower the thread is pulled, so nothing funny happening.
With the thread on the bootom side the spool moves faster than the thread is pulled.  On a slippery surface it may slip.

This is where you (all) make the mistake. No wind energy can be extracted above wind speed when vehicle drives in the same direction as wind direction or opposite to wind direction.
Traveling in any other direction of course is not a problem to get energy from the wind at any speed as you always have access to wind energy.
Using force and speed (while not fully understanding how they work is what creates the wrong conclusion).
The main reason I used a wheel to replace the propeller is so that the misery of how a propeller works is eliminated. Propeller is nothing more than a wheel for air.


But why not use an example.
Say there is no wind and vehicle travels at 5m/s and say kinetic energy of the vehicle at that point is 500Ws and a break of 10W is applied for 1 second.
Vehicle will end up at 490Ws and say all this energy is then transferred to propeller that is 70% efficient (fairly good propeller efficiency).
Now there will be just 7Ws available for the propeller and no matter how you set the angle of the propeller blades to get more force and lower speed or higher speed and lower force you will still end up putting back 7Ws in to vehicle thus you end up with less than you started 497Ws vs 500Ws so lower speed.
Hope you fully agree with my example above and understand that 7Ws is all you have available and no matter how you use that you will not end up with more.
Now if there is a wind speed say 20m/s and vehicle is above that speed say 25m/s and you break the vehicle with 10W for 1 second then you have available 10Ws with a 70% efficiency means 7Ws to use for the propeller. Since wind speed is in exact same direction and lower than vehicle speed the wind can not contribute with anything to the equation thus you again end up with a deficit no matter what force vs propeller speed you select.
And I used energy instead of power as maybe it is more helpful but for power it will work in the exact same way.
Using forces and speed will just complicate things for you and you will come to wrong conclusions.

In my wheels only example there is a G (generator) wheel and a M (motor) wheel and say there is a 2:1 gear ratio that means the generator wheel will make 2 full rotations while the motor wheel will do just one.
So say treadmill speed is 5m/s and say you apply 10W of breaking power that will mean a breaking force of 2N now if you look at the motor wheel you will see that spins at half the speed 2.5m/s but twice the force 4N assuming ideal vehicle where all 10W from generator are available at the motor wheel.
Now if you look just at the forces you will think that since there are 4N at the motor wheel and only 2N breaking force at generator the vehicle will advance forward but that will be the wrong conclusion to make as the force at the wheel is not transferred to the body but to the other wheel.
Say wheels are mechanically connected with a chain then those forces will be transferred to the chain not to the vehicle body and so since power is equal on G and M wheels the vehicle will actually not move in any direction. The same happens with the propeller based vehicle as propeller is just an air wheel.

I will expect here there are more electrical engineers and they understand that power is a more important unit than current and voltage (speed and force).
And as far as vehicle is concerned as soon as it is at same speed as the wind or above wind speed (same direction) is not accessible at all to the vehicle.
You can imagine air as small fling balloons that if they have higher speed than vehicle can push the vehicle by bumping in to it and as soon as vehicle has higher speed all the balloons that vehicle will see will come from the opposite direction of travel thus not only they will not help but they will be counterproductive.
This is a long reply and maybe not very organised but I hope you take the time to read. Especially the part with the example.
You can not claim that if you use forces and speed in your calculation the result will be different than if you use power as if applied correctly the result will need to be exactly the same.

[iMo]

I think the trick comes from the propeller construction itself. It has nothing to do with wheels or gears..
The propeller's blades are built in form of a wing.
A wing works such it creates a difference in pressures (top vs. bottom) thus it forces the wing "up" (in case of an airplane).
Thus when the propeller on that vehicle "already rotates" it creates a push, and even the speed of wind is equal or lower than the speed of the vehicle, the "wing effect" still pushes the vehicle in forward direction. That adds up to the speed of the vehicle, and the vehicle goes faster than the wind.
The sailing with a boat faster than wind works the same way, imho (the boat's sail works the same way as an "airplane wing" when positioned properly, pressure diff creates a push).
The energy conservation law works of course, even in this case.. 

[Kleinstein]

You can not claim that if you use forces and speed in your calculation the result will be different than if you use power as if applied correctly the result will need to be exactly the same.

This is true, but so far the calculation based on power alone is wrong.

In my wheels only example there is a G (generator) wheel and a M (motor) wheel and say there is a 2:1 gear ratio that means the generator wheel will make 2 full rotations while the motor wheel will do just one.
So say treadmill speed is 5m/s and say you apply 10W of breaking power that will mean a breaking force of 2N now if you look at the motor wheel you will see that spins at half the speed 2.5m/s but twice the force 4N assuming ideal vehicle where all 10W from generator are available at the motor wheel.
Now if you look just at the forces you will think that since there are 4N at the motor wheel and only 2N breaking force at generator the vehicle will advance forward ...

Up to this point the argument is correct. Just accept it not just think it must be wrong, because is contradics intuition and the misconception that the systen should not work.   The net force is real and it will move the vehehicle - that's it.

Say wheels are mechanically connected with a chain then those forces will be transferred to the chain not to the vehicle body and so since power is equal on G and M wheels the vehicle will actually not move in any direction.

A chain drive as a gear will just transfer power. The force of the chain is balanced by the structure between the axels. So there is no magic force to stop the vehicle.  Otherwise a simple chain drive could move a space craft.

Having the same power does not mean it would not move - power is not moving things, it is force.  Power is only needed to generate a force in the direction of the movement.  Head-lights are incresddibly inefficient breaks.

[Brumby]

           

This is embarrassing.  Please stop.

You have clearly misunderstood the mechanism and continue to argue "physics" when you are not using a model which describes the system that has actually demonstrated the effect.

Yes, there are parameter constraints for the propeller and gearing for this to work, but within those constraints, it does work as claimed.

... and - as other have stated - no energy storage is required and as long as the wind is consistent and there is room to drive, it will continue, unabated.

[electrodacus]

I think the trick comes from the propeller construction itself. It has nothing to do with wheels or gears..
The propeller's blades are built in form of a wing.

This is where you (and others) are wrong. A propeller is nothing than a wheel equivalent for a gas, liquid or even solid's
The only difference is the amount of friction as gases have way lower density than a liquid plus even more important for this problem is that a gas is compressible so energy can be stored by creating a pressure differential on each side of the propeller.
The shape of the propeller blades can make the propeller more or less efficient as it reduces the friction with improved shape but it will never create a propeller with higher than 100% efficiency.

If you put 10W as input to a propeller you can not expect more than 10W of trust in fact a generous value for a real propeller may be around 7W worth of thrust.
Now if you take out 10W from the wheel basically slowing the vehicle down and put that in to a propeller as 7W of thrust will you not see a slow down of the vehicle.
It really is a simple as that.
A wheel is more efficient than a propeller so unless you need to travel trough air like an airplane you will not see propellers on ground based vehicles. 

[electrodacus]

This is true, but so far the calculation based on power alone is wrong.

What do you mean by that ?  I made a mistake in my calculations, or are you saying this vehicle is a special case and this clear rule will not apply to it.

Up to this point the argument is correct. Just accept it not just think it must be wrong, because is contradics intuition and the misconception that the systen should not work.   The net force is real and it will move the vehehicle - that's it.

No it will not and if you do not believe that I encourage you to test it. Forces at the wheel act on the transmission not directly on the vehicle body.
In my example with 2N and 4N the force on the vehicle will not be higher than 2N (maybe this was not a good example as I mean force on vehicle can not be higher tan force of the Generator wheel but you can also by chance consider that as difference between forces)
So say gear ratio is modified so that at 2N on generator wheel can result in 6N on motor wheel the force on vehicle body will be 2N from each side but opposite direction (and this is for ideal vehicle) so vehicle will not move in any direction.

A chain drive as a gear will just transfer power. The force of the chain is balanced by the structure between the axels. So there is no magic force to stop the vehicle.  Otherwise a simple chain drive could move a space craft.

Having the same power does not mean it would not move - power is not moving things, it is force.  Power is only needed to generate a force in the direction of the movement.  Head-lights are incresddibly inefficient breaks.

Yes having same power it means vehicle will not move. And in real world tests the vehicle will move the opposite way you are predicting.
That is why I asked the question about two vehicle with same exact motor power and different gear ratio and nobody was brave enough to answer.  The answer to that is also that none of the vehicle will win and it will be a tie.

[electrodacus]

This is embarrassing.  Please stop.

You have clearly misunderstood the mechanism and continue to argue "physics" when you are not using a model which describes the system that has actually demonstrated the effect.

Yes, there are parameter constraints for the propeller and gearing for this to work, but within those constraints, it does work as claimed.

... and - as other have stated - no energy storage is required and as long as the wind is consistent and there is room to drive, it will continue, unabated.

I have not ever denied that tests are not real and my explanation predicts exactly the same thing observed in the experimental results.
The difference is my explanation is correct and you just modify the formulas to fit the data.
So the one misunderstanding physics is you.
You just do not understand that with vehicle above wind speed in the exact same direction or opposite direction to wind there is no power available from the wind.  I can think on only one reason of why you will think that way and that will be that you do not understand what air is or maybe also propeller.

That is why I came up with the analog of that and that is wheels based only.
1) Do you claim that my wheel based analog is not correct ? If it is not how it will need to be corrected ?
2) Or do you think it is correct and that vehicle in my drawing will be capable to move from left to right ?

[Kleinstein]

That is why I asked the question about two vehicle with same exact motor power and different gear ratio and nobody was brave enough to answer.  The answer to that is also that none of the vehicle will win and it will be a tie.

  - there still is the misconception about force and power. 
Under normal condition (e.g. no ice) one gets a higher maximum force in the lower gear and thus the lower gear car wins.
This is why you don't drive up a steep hill in the higherst gear.

Please  do a little more reading on the basics, before wirting even more stupid and wrong claims.

[electrodacus]

  - there still is the misconception about force and power. 
Under normal condition (e.g. no ice) one gets a higher maximum force in the lower gear and thus the lower gear car wins.
This is why you don't drive up a steep hill in the higherst gear.

Please  do a little more reading on the basics, before wirting even more stupid and wrong claims.

My problem was setup in ideal conditions meaning no wheel slip allowed on any of the vehicle's. The vehicle perfectly identical except for the gear ratio.
I guess you can not solve a problem as you need to see an experimental result to know what will happen in a system.
And keep in mind that your example of a vehicle climbing a hill has no relevance here at all.
That vehicle has the power source on board it is not taking power from one wheel and transferring it to another so as long as it has traction it can always move forward.

Look again at my diagram and answer this simple question.
Can the vehicle as shown in the diagram using any gear ration you want between G wheel and M wheel be able to move from left to right with no external power source?

If your answer to my question is yes then you do not understand physics and since my words will not convince you the only thing you can to is test it in real life.
I will have tested this for you but I do not own a treadmill and also if I will do the test you will think I cheat in some way.

The way you need to look at that diagram is that breaking the G wheel will push the vehicle backwards (right to left) and then this breaking power (more is not possible) will be transferred trough a gearbox of your choosing to wheel M that will try to push the vehicle in the other direction (left to right) but since power on wheel M can not be higher than breaking power at G wheel the net movement of the vehicle can only be from right to left so the opposite of what you will want or claim.
And yes power in vs power out is the easiest way to look at the problem and also correct. Looking at forces and speeds will also give you the same exact and correct result if you where able to understand what the relation between them is.

And I hope I do not sound to condescending but I do not have great social skills and on top of that I see this sort of wrong answers from people for the past few weeks. Even people that should understand this like university level physics professors and science communicators like Derek.
You maybe can understand why I can not let this go until it is properly explained and corrected else you have people that waste 15 years of their life designing and building a vehicle that is not working as they think and there are smart people that fail a university entrance exam while solving this sort of problem correctly (yes I saw this exact problem mentioning blackbird on some exams).   I was not joking when I said this gave me PTSD.

[bdunham7]

If your answer to my question is yes then you do not understand physics and since my words will not convince you the only thing you can to is test it in real life.
I will have tested this for you but I do not own a treadmill and also if I will do the test you will think I cheat in some way.

You don't need a treadmill, you can just substitute a sliding block as you won't have to move it very far to prove yourself wrong.  If you make the gear ratio 2:1, so the M turns one revolution for every two of G, in the same direction, you will find that as you slide the right hand block towards the fixed block, the car will move to the right with equal speed.  Or you could prove your skills at math and physics by solving the very basic equations I gave you.  Either experimentally or mathematically these should be trivially easy for someone claiming to be knowledgeable about physics.

And I hope I do not sound to condescending but I do not have great social skills and on top of that I see this sort of wrong answers from people for the past few weeks. Even people that should understand this like university level physics professors and science communicators like Derek.

I don't think the problem is a lack of understanding of physics by forum members--there are fairly accomplished people here, some with actual degrees in the subject.  I also no longer think the actual issue here is your lack of understanding of physics, rather it is a fixation on one particular aspect of this that you think you understand intuitively, but are wrong about.  The amazing part is that you yourself have provided a blindingly obvious way to demonstrate a correct solution and understanding of the issue--which boils down to the fact that power equals force x speed--and yet you not only don't recognize it, but won't even respond directly when it is explicitly pointed out.  Several times I thought I had clearly explained this in the past--both to you and previously--but apparently my explanations aren't clear enough or something.

[electrodacus]

You don't need a treadmill, you can just substitute a sliding block as you won't have to move it very far to prove yourself wrong.  If you make the gear ratio 2:1, so the M turns one revolution for every two of G, in the same direction, you will find that as you slide the right hand block towards the fixed block, the car will move to the right with equal speed.  Or you could prove your skills at math and physics by solving the very basic equations I gave you.  Either experimentally or mathematically these should be trivially easy for someone claiming to be knowledgeable about physics.

This is where you make the mistake. A sliding block is not the same thing with a treadmill. Please try to understand the difference to know what I mean.
The results of the experiment will be very different with the treadmill compared to the sliding block.
You can just imagine the treadmill in my diagram as powered off and then moved from right to left. Since you move the treadmill both relative to the vehicle but also relative to the ground this is a totally different scenario from a treadmill that will not move as it is fixed to the ground.
Say wheels are all free spinning and have no friction then in the treadmill experiment the vehicle will not advance on the treadmill so no movement from left to right or any movement at all in relation with treadmill but if you power off the treadmill so it is not spinning and instead you move it from right to left it will look like vehicle drove on to the sliding block and you wrongly interpret the results.
When you connect the wheels trough a gear ten what happens is even more confusing and you will not be able to interpret the data correctly if you use a moving block as there are to many things to track.
So yes what you will see is very different and that is where the mistake is made.

I don't think the problem is a lack of understanding of physics by forum members--there are fairly accomplished people here, some with actual degrees in the subject.  I also no longer think the actual issue here is your lack of understanding of physics, rather it is a fixation on one particular aspect of this that you think you understand intuitively, but are wrong about.  The amazing part is that you yourself have provided a blindingly obvious way to demonstrate a correct solution and understanding of the issue--which boils down to the fact that power equals force x speed--and yet you not only recognize it, but won't even respond directly when it is explicitly pointed out.  Several times I thought I had clearly explained this in the past--both to you and previously--but apparently my explanations aren't clear enough or something.

Working with force and speed will give you the same results as working with power. But working with forces and speeds you need to be way more careful on how you use them and interpret the results sort of in a similar way a moving block and a treadmill problems above.

So just accept for a minute that you are wrong and look closer at what I'm saying and do not try to change the type of units I use or replace a treadmill with a moving block since all of this will provide the same result if you can interpret correctly. But I selected the most simple to understand examples that is why I use the treadmill and also why I use power.
I think you are very close to understand what I'm saying you just need to put a bit of effort in reading what I write.