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

[bdunham7]

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.

Like I said, your purported understanding of basic principles--as represented here--is highly flawed, but that's not the real problem.  At this point, from my perspective you are failing the Turing test....

[electrodacus]

Like I said, your purported understanding of basic principles--as represented here--is highly flawed, but that's not the real problem.  At this point, from my perspective you are failing the Turing test....

Have you read my reply ? Where are your disagreements ?
Maybe let me know what is your area of expertise/education so I know how to better reply to you.

The way peoples brain work is very different likely way more different than you imagine.  You should search about Aphantaisia that affects maybe 1 to 3% of the population the others have a spectrum of capabilities in creating a mental image. And you should also look-up "Internal monologue" where an estimated 30% of the population has no internal monologue.  You will be blown away.
I can create a mental image (sort of average) and I sure have an internal monologue so I think more abstract using language.
I can simulate fairly accurately in my head how a simple cart like those in my diagram will work including what wheel is the generator and witch is the motor and I can know the outcome.
I can also imagine air as a multitude of small particles moving at a relatively constant speed above the ground and that have elastic forces keeping them apart like repelling magnets and then imagine a vehicle driving in the same direction at higher speed than this air molecules and can see that air molecules can no longer help accelerate the vehicle (impossible) but I can also imagine this now higher pressure behind the vehicle meaning higher density (more air particle in the same volume now with higher forces keeping them apart same as force increases when you try to bring two opposing magnets closer).
This is the so called stored energy and as vehicle continues to accelerate this pressure will reduce meaning the density of air molecules drops up to the point that there is not enough pressure to cover the vehicle losses and so vehicle will start to decelerate until it will get below wind speed.
If this description created for you a mental image (visualizing this moving animation) then you will also know vehicle can not be powered by wind when vehicle speed is higher than wind speed in the same direction.

[IanB]

you will also know vehicle can not be powered by wind when vehicle speed is higher than wind speed in the same direction

You keep writing lots and lots of words trying to explain that this is not possible. The difficulty you face is that the universe does not agree with you. It is provably possible to construct a vehicle that does what you claim is impossible. Your challenge, should you accept it, is to explain how actual experiments, in the real world, do this "impossible" thing, since they actually do work.

Theory is good up to a point, but all of physics is backed by experiment. Every theory, every formula, every equation, is consistent with experimental evidence. Here, the experimental evidence is clear--a suitably constructed vehicle can run forever at a speed faster than the wind when the wind is directly behind it. If you want to disagree with the experiments, you need to show what is wrong with the experimental evidence. You can't do that with theory. You have to do it with practice. What part of the experiment has the wrong method, and why?

[electrodacus]

You keep writing lots and lots of words trying to explain that this is not possible. The difficulty you face is that the universe does not agree with you. It is provably possible to construct a vehicle that does what you claim is impossible. Your challenge, should you accept it, is to explain how actual experiments, in the real world, do this "impossible" thing, since they actually do work.

Theory is good up to a point, but all of physics is backed by experiment. Every theory, every formula, every equation, is consistent with experimental evidence. Here, the experimental evidence is clear--a suitably constructed vehicle can run forever at a speed faster than the wind when the wind is directly behind it. If you want to disagree with the experiments, you need to show what is wrong with the experimental evidence. You can't do that with theory. You have to do it with practice. What part of the experiment has the wrong method, and why?

There is no experiment showing vehicle runs forever above wind speed. The most I think was about one minute for the blackbird when they did the 28mph record.
If you do not have a theory of how it works then of course you can wrongly interpret the limited experimental data and that is what happens here.
There is just no mechanism to allow a vehicle be powered by wind when above wind speed in same direction as the wind.
Unless you want to have a very long extension cord to power the vehicle but then that will also not be unlimited it will end when the cord is no longer long enough

The theoretical explanation made by the designer of the Blackbird and Derek on how this is supposed to work is flawed.
My theory fully explains the practical results and what will come next if the test where to run for longer duration.
Also my theory can be tested both with the simple wheel only cart that will show no wind energy is available above wind speed (not sure why that is not obvious) and also as mentioned wind is not necessary at all you can just push the Blackbird or the smaller treadmill model to speed and it will continue to accelerate for maybe two minutes or so depending on how much energy was stored during the push phase then it will slow down for another 2 minutes or so before it gets below pushed speed and then slow down to zero as there is no wind.
This second one is harder to do but will be more convincing for some of you even if the actual treadmill test is exactly this just not run for long enough to see the full result since treadmill is to short for that.

[Brumby]

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.

There is just no mechanism to allow a vehicle be powered by wind when above wind speed in same direction as the wind.

Oh, but there IS.

The fact you can't see this simply underlines your understanding of the system is lacking.  Any "examples" that do not include the propeller are fundamentally wrong and discussion on such is completely irrelevant.

[ejeffrey]

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 answer is yes, yet surprisingly I *do* understand physics.  This is a simple 1st year mechanics problem, and again the answer is 100% yes, you can make the cart move in either direction by changing the gear ratio.  This is actually exactly equivalent to the demo from the veritasium video.

In your example, I define positive velocity to the right and positive angular frequency to be clockwise.  Both wheels are assumed to have radius r, although you could let that radius vary instead of the gear ratio.  Then I can write three equations:

$$v = \omega_G \cdot r \\
v = \omega_G \cdot r + v_t\\
\omega_G = X\omega_R
$$

The first two are the center of mass velocity of the two wheels (which both must be equal to v).  $v_t$ is the velocity of the treadmill.  The third is the gear ratio constraint where X is the gear ratio.

The solution to these three equations is:

$$v = v_t / (1 - X)$$

If $v_t$ is negative but you want positive velocity X must be >1.  If X < 1, the cart will move in the same direction as the treadmill.  If X equals 1, then you get divide by zero but that just means there is no solution: the cart will just slip.  Close to the 1:1 gear ratio you can theoretically generate arbitrarily high speed in either direction but the forces involved will be quite high and it will likely slip.  If you want to build this yourself, a 1:2 or 2:1 ratio should work well, although as I said the video above already does exactly this demonstration.

Any "examples" that do not include the propeller are fundamentally wrong and discussion on such is completely irrelevant

That is not actually true, or at least you don't have to include any fluid dynamics.  The airfoil shape of the sail is necessary for the boat because it doesn't have wheels, but the blackbird is fundamentally a simple gear ratio problem and doesn't need any aerodynamics to understand the basic operation.  If you stood behind the blackbird and poked the propeller blade with a stick, it would move forward faster than your stick, because the propeller would turn "into" the stick as you pushed.  Of course you couldn't go very far before the stick would run off the edge of the blade so the wind is a lot more convenient.

[electrodacus]

Oh, but there IS.

The fact you can't see this simply underlines your understanding of the system is lacking.  Any "examples" that do not include the propeller are fundamentally wrong and discussion on such is completely irrelevant.

Please explain what IS ?
The explanation I heard is that since there is relative motion between air and ground energy can be extracted and that is a silly explanation for when vehicle is above air speed traveling on ground in exact same direction.  That explanation works only when vehicle travels in a direction different from wind direction.
Sorry but if you think a propeller is in any way different (other than ability to store energy when in a compressible medium) then you do not understand what a propeller is. For example under water (not compressible) a propeller based vehicle will not be able to exceed water speed not even for a limited time like in air.
And a propeller will be less efficient than a wheel.   

[electrodacus]

The answer is yes, yet surprisingly I *do* understand physics.  This is a simple 1st year mechanics problem, and again the answer is 100% yes, you can make the cart move in either direction by changing the gear ratio.  This is actually exactly equivalent to the demo from the veritasium video.

In your example, I define positive velocity to the right and positive angular frequency to be clockwise.  Both wheels are assumed to have radius r, although you could let that radius vary instead of the gear ratio.  Then I can write three equations:

$$v = \omega_G \cdot r \\
v = \omega_G \cdot r + v_t\\
\omega_G = X\omega_R
$$

The first two are the center of mass velocity of the two wheels (which both must be equal to v).  $v_t$ is the velocity of the treadmill.  The third is the gear ratio constraint where X is the gear ratio.

The solution to these three equations is:

$$v = v_t / (1 - X)$$

If $v_t$ is negative but you want positive velocity X must be >1.  If X < 1, the cart will move in the same direction as the treadmill.  If X equals 1, then you get divide by zero but that just means there is no solution: the cart will just slip.  Close to the 1:1 gear ratio you can theoretically generate arbitrarily high speed in either direction but the forces involved will be quite high and it will likely slip.  If you want to build this yourself, a 1:2 or 2:1 ratio should work well, although as I said the video above already does exactly this demonstration.

My vehicle is not the same with what Derek demonstrates in his video even if he claims so.
What he has is the equivalent of a vehicle driving at lower than wind speed in the opposite of wind direction.
The wind in this case (power source) is the floor with the small wheels the generator turning the large wheel (motor wheel) that drives on the lumber at about 2.8x lower speed than the wind (floor).

No gear ratio will make the vehicle in my diagram move from left to right. I also demonstrated with a much simpler formula where power at wheel M can not be higher than power at wheel G because wheel G powers the wheel M
That is all you need to know to understand this vehicle can never move from left to right just the other way around.

My definition of understanding physics is the ability to predict what the result should be even before applying any formula. Not sure how come so many intelligent people can not see how this simple vehicle in my diagram will move and also how it wrongly interprets what that lumber, wheels, floor vehicle represents.
When you look at the cart in Derek's video can you not see that small wheels are the generator wheels powered by the floor and that vehicle travel in the opposite direction on the lumber ?

It was annoying for me at first to see people do not understand this (simple systems) but since I get the same answers here on a forum where nobody has any invested interested, I starting to think this sort of problems are not easy for most people of the education system is failing.
Build this model that I showed you exactly as it is since is nowhere near the same as what you see in Derek's video and if you manage to have the vehicle move from left to right I will pay for all your expenses building it.

[Kleinstein]

The point of the controversy is that the vehicle demonstated that it is possible to extract energy from the wind when moving at the speed and direction of the wind.  It is not easy to understand, but it works.  It is proven by experiment and also the calcultions show that is should work, if the prob is reasonable efficient.

One can not understand a system when one starts with the proposition that the system does not work.

The idea of looking at the case with 2 platforms is a way to get away from the complications of aerodynamics. So it is a good way to understand the principle. Even electrodacus did the math correct on this  .  For some reason he just refused to accept the result and than argued that the force is not real.

If you replace the 2nd platform with a string / thread, one can easily do the experiment hands one.   A nearly empty spool of thread on a not so slippery desk is all it takes to try. The gear ratio is replaced with different diamaters.

When I first saw this effect it confused me for a short time - like 5 minutes for 5 year old.

[electrodacus]

The point of the controversy is that the vehicle demonstated that it is possible to extract energy from the wind when moving at the speed and direction of the wind.  It is not easy to understand, but it works.  It is proven by experiment and also the calcultions show that is should work, if the prob is reasonable efficient.

One can not understand a system when one starts with the proposition that the system does not work.

The idea of looking at the case with 2 platforms is a way to get away from the complications of aerodynamics. So it is a good way to understand the principle. Even electrodacus did the math correct on this  .  For some reason he just refused to accept the result and than argued that the force is not real.

If you replace the 2nd platform with a string / thread, one can easily do the experiment hands one.   A nearly empty spool of thread on a not so slippery desk is all it takes to try. The gear ratio is replaced with different diamaters.

When I first saw this effect it confused me for a short time - like 5 minutes for 5 year old.

I think I mentioned this before but I'm not denying that blackbird vehicle works as shown in the videos and that it exceed wind speed.
What I say is that the reason is energy storage so it is not directly powered by wind energy when above wind speed.
The explanation of why it works as seen in test is wrong. The vehicle will not travel indefinitely above wind speed but only for at most a few minutes until stored energy is used up.

The two diagrams I showed are for conditions where none of the mediums are compressible like a vehicle driving at the bottom of a river using a propeller for water (since water is not compressible water speed can not be exceeded by vehicle at all not even for a few seconds).
The second wheel vehicle that is almost identical with the first contains a spiral spring connecting the wheel to the motor and that if build will show the exact same behavior as the treadmill propeller prototype.
So my two diagrams as meant to show why the vehicle works by using just wheels (propellers and air seems to be confusing for people).
Bellow just the spring based vehicle the one with energy storage that can move from left to right but just for a limited amount of time same as blackbird

[Brumby]

Oh, but there IS.

Please explain what IS ?

Seriously?   

Then let me be direct: There IS a mechanism to allow a vehicle be powered by wind when above wind speed in same direction as the wind.

You just can't seem to see it - or are refusing to.

[Brumby]

Any "examples" that do not include the propeller are fundamentally wrong and discussion on such is completely irrelevant

That is not actually true, or at least you don't have to include any fluid dynamics.

I wasn't going to go quite that far - I simply meant to say that the propeller is a key part of how this mechanism works.

.... but the blackbird is fundamentally a simple gear ratio problem and doesn't need any aerodynamics to understand the basic operation.  If you stood behind the blackbird and poked the propeller blade with a stick, it would move forward faster than your stick, because the propeller would turn "into" the stick as you pushed.  Of course you couldn't go very far before the stick would run off the edge of the blade so the wind is a lot more convenient.

I quite like this explanation. 

[IanB]

There is no experiment showing vehicle runs forever above wind speed. The most I think was about one minute for the blackbird when they did the 28mph record.

In both the Blackbird and treadmill experiments the vehicle accelerated. Blackbird accelerated so vigorously they had to put the brakes on to slow it down. If an unpowered vehicle accelerates it is gaining energy from the surroundings. If it accelerates under its own steam, it will run forever, by definition.

no wind energy is available above wind speed (not sure why that is not obvious)

If there is a velocity difference between the air and the ground, then a vehicle in contact with both air and ground can extract energy from the system. This can happen even if the vehicle is moving faster than the differential velocity.

and also as mentioned wind is not necessary at all

If course wind is necessary! If there is no wind, there is no motive power for the vehicle, and it will coast to a standstill and stop moving.

[richard.cs]

If there is a velocity difference between the air and the ground, then a vehicle in contact with both air and ground can extract energy from the system. This can happen even if the vehicle is moving faster than the differential velocity.

This was the concept that made it "click" for me, originally stated a few pages back.

[electrodacus]

In both the Blackbird and treadmill experiments the vehicle accelerated. Blackbird accelerated so vigorously they had to put the brakes on to slow it down. If an unpowered vehicle accelerates it is gaining energy from the surroundings. If it accelerates under its own steam, it will run forever, by definition.

Blackbird is build at the limit as they wanted to keep the weight down so that is the reason it looked it will self destroy as it was close due to vibrations.
The acceleration is from the stored energy and highest stored energy (full storage) is at around 0.7x the wind speed on blackbird and of course for the treadmill model highest acceleration is immediately after you release the vehicle from your hand.
You will be able to feel the force of the stored energy on your had as an elastic type force from the compressed (higher density) air behind the propeller.
As the model advances on treadmill stored energy will decrease and so will the acceleration rate but if you stop the vehicle by blogging it going forward with your hand the energy storage will be again filled up so as long as you keep the vehicle from moving you have just a treadmill powered propeller.

If there is a velocity difference between the air and the ground, then a vehicle in contact with both air and ground can extract energy from the system. This can happen even if the vehicle is moving faster than the differential velocity.

As far as vehicle is concerned when you are at exact same speed as wind speed (like in the treadmill example) air molecules do not move relative to the vehicle meaning air molecules can not transfer any energy to the vehicle. The only way vehicle accelerates from that point is due to stored energy as there is that high density air in the back of the propeller.
As vehicle accelerates past wind speed that pressure will slowly decrease. Slowly because most of the stored energy is put back in the propeller to maintain part of this pressure differential (that is what the connection between wheel and propeller will do).
At peak speed there will very little pressure differential between the front and back of the propeller, so small that it can no longer cover the vehicle losses and have extra to accelerate and that is the point where propeller and vehicle will have the highest speed and vehicle will start to slowly decelerate.
This part after peak speed is where the kinetic energy both the one in the vehicle body but also the propeller (flywheel) will start to be used thus the reason it will take probably as long to decelerate below wind speed as it took to get to peak speed.
 

If course wind is necessary! If there is no wind, there is no motive power for the vehicle, and it will coast to a standstill and stop moving.

If you push one of this propeller based vehicles either blackbird or the treadmill models (needs to be pushed to a minimum speed probably around 10mph maybe 11mph due to extra drag) then when released the vehicle will accelerate well past that speed before slowing down to zero and no wind at all is needed.
I think this is already shown in the treadmill example if you interpret that correctly as test is done in a room with no wind and so you keeping the vehicle on the treadmill is the same with pushing the vehicle to 10mph (small difference is the extra drag when pushed) and so when you let go while there is no wind you notice vehicle accelerates and it can not use energy from treadmill as vehicle advances on the treadmill thus that means it is not slowing down (or try to slow down) the treadmill. Meaning energy comes from the compressed air behind for lack of a better description.
This stored energy will eventually be transferred to vehicle in form of kinetic energy minus the losses trough friction. That means that if you where to add weight to the vehicle the vehicle will be able to travel less on the treadmill and if you add weight almost perfectly the vehicle will accelerate forward so slowly that you will be able to see how it slows down before it gets to the end of the treadmill.

[electrodacus]

This was the concept that made it "click" for me, originally stated a few pages back.

I'm starting to think that is what "click" for most but it is just wrong when you are referring to wind in exact same direction as vehicle.
This works perfectly for any other vehicle direction other than same as wind direction or opposite to wind direction.
Should (it is for me) be easy to visualize that no air molecules moving at wind speed in same direction as vehicle can hit a vehicle that moves faster than the wind. But if there is even a slight angle between wind direction and vehicle direction then there will be at least some air molecules hitting the vehicle no matter how fast the vehicle moves and energy from those molecules can be used by the vehicle.

Best case will be vehicle perpendicular to wind direction then full wind power is available no matter the vehicle speed and in this case a vehicle powered only by wind can get to any speed as long and is limited only by the vehicle losses / friction.

[Ian.M]

...
Should (it is for me) be easy to visualize that no air molecules moving at wind speed in same direction as vehicle can hit a vehicle that moves faster than the wind. ...

Really?  If that was the case, then an airplane flying exactly downwind faster than the wind speed would drop out of the sky!

[bdunham7]

As far as vehicle is concerned when you are at exact same speed as wind speed (like in the treadmill example) air molecules do not move relative to the vehicle meaning air molecules can not transfer any energy to the vehicle.

You make so many mistakes in your analysis that it is hard to keep track of them all, let alone the glaring inconsistencies in your reasoning.  But here is at least one lucid example of where you have gone wrong.  The air molecules movement relative to the vehicle is not the point, it is the movement of the air molecules relative to the parts of the propeller with which they are interacting.  That is the whole reason the propeller is there.  Now you may say that the propeller as a whole is moving at the same speed as the vehicle, which is true, but from the perspective of an air molecule, the surface of the propeller will still appear to be coming at it as the propeller rotates.  That is how propellers work.

And as to previous comments about your "intuitive understanding" of physics, give it up--that's a delusion.  The rule in physics and similar sciences is that if you can't do the math, you don't really understand it.  Period. ejeffrey has laid out clearly the equations that I wanted you to find and solve on your own--which you didn't even attempt.  Look at those and if you don't understand them, your 'intuition' is worthless.  One of your other misconceptions has to do with your own example where you claim that analyzing the power at M and G proves your point.  You've simply miscalculated because you just don't grasp the implications of the fact that power is force x speed, or in another form, torque x rpm (or ω for actual science types).  In your own diagram it is obvious that G will be spinning faster than M, thus at equal force (any steady state where the car is not accelerating) G will always produce more power than is consumed by driving M.   

[electrodacus]

Really?  If that was the case, then an airplane flying exactly downwind faster than the wind speed would drop out of the sky!

Yes the airplane will drop if is a wind only powered airplane but if that was the case it will not have exceeded the wind speed in the first place. Planes have stored energy in the form of fuel and a propulsion system that can use that fuel.

[electrodacus]

As far as vehicle is concerned when you are at exact same speed as wind speed (like in the treadmill example) air molecules do not move relative to the vehicle meaning air molecules can not transfer any energy to the vehicle.

You make so many mistakes in your analysis that it is hard to keep track of them all, let alone the glaring inconsistencies in your reasoning.  But here is at least one lucid example of where you have gone wrong.  The air molecules movement relative to the vehicle is not the point, it is the movement of the air molecules relative to the parts of the propeller with which they are interacting.  That is the whole reason the propeller is there.  Now you may say that the propeller as a whole is moving at the same speed as the vehicle, which is true, but from the perspective of an air molecule, the surface of the propeller will still appear to be coming at it as the propeller rotates.  That is how propellers work.

And as to previous comments about your "intuitive understanding" of physics, give it up--that's a delusion.  The rule in physics and similar sciences is that if you can't do the math, you don't really understand it.  Period. ejeffrey has laid out clearly the equations that I wanted you to find and solve on your own--which you didn't even attempt.  Look at those and if you don't understand them, your 'intuition' is worthless.  One of your other misconceptions has to do with your own example where you claim that analyzing the power at M and G proves your point.  You've simply miscalculated because you just don't grasp the implications of the fact that power is force x speed, or in another form, torque x rpm (or ω for actual science types).  In your own diagram it is obvious that G will be spinning faster than M, thus at equal force (any steady state where the car is not accelerating) G will always produce more power than is consumed by driving M.

The air molecules relative to vehicle are exactly the point. Propeller is part of the vehicle so at the same speed as the vehicle. The rotation part will not help and the air molecules it hits come from the front of the propeller and they are pushed back to maintain the pressure created before vehicle was above wind speed (of course that pressure will continue to drop as it powers the vehicle loses plus adding kinetic energy to vehicle). When all that pressure differential is gone vehicle will start to slow down.
My math was done quite a few times here and that is power at the propeller is smaller than power taken from the wheel thus vehicle will slow down without any form of energy storage.

G can spin way faster than M say if G and M are not connected and they are ideal so there is no friction then wheel G will spin at same speed as the treadmill and wheel M will not spin at all be stationary still vehicle will stay where it is not move in any direction and power at both wheels will be zero as one wheel has zero speed and the other wheel has zero force.
To get power from G you will need to break and that breaking force will move the vehicle backwards from right to left then transferring that power to wheel M even if all of it ideal case will only be able to bring the vehicle back to the same place so ideal vehicle either with disconnected G and M or with connected G and M (any gear ratio) will not move in any direction.
In real world there is friction so vehicle will always move from right to left and no matter what you want to do vehicle will not be able to move from left to right.
If testing this is the only way for you to be convince do that and if you can prove I'm wrong I will pay for your experiment cost.
 

[bdunham7]

My math was done quite a few times here and that is power at the propeller is smaller than power taken from the wheel thus vehicle will slow down without any form of energy storage. accelerate.

You've done no math, but you have just accidentally actually stated the reason that the vehicle in question works as advertised.  The horizontal force from the propeller is greater than the horizontal force the other way at the wheels, yet the power generated at the wheels is greater than what is used by the propeller. 

[electrodacus]

You've done no math, but you have just accidentally actually stated the reason that the vehicle in question works as advertised.  The horizontal force from the propeller is greater than the horizontal force the other way at the wheels, yet the power generated at the wheels is greater than what is used by the propeller.

I'm fairly certain your expertise is not in electrical engineering else you will not make such a statement.
At starting point the vehicle has zero kinetic energy since it is stationary and in order to increase the kinetic energy (also vehicle speed) you will need have an imbalance of power not forces.
Since the only imbalance of power you can have is lower power at M motor wheel  and higher power at G generator wheel that means kinetic energy will increase but not in the direction you will like meaning vehicle can only move from right to left and not the other way around.

That is why I repeat so many times to stop thinking in therms of forces and speed as you do not know how to apply the formula in that case and it just makes things more complicated when all you want to know is if vehicle can advance forward (left to right).
And no mater if you like or not that I use power the result using power is very clear and you can not get a different result by using forces and speeds if you apply the formula correctly.
Using a propeller instead of the motor wheel will not change anything if propeller was in a non compressible medium like say water. But propeller being in air you can store energy by basically compressing air and that is emulated in my second diagram with the spiral spring (like those used in a retractable tape measure).

[ejeffrey]

You've done no math, but you have just accidentally actually stated the reason that the vehicle in question works as advertised.  The horizontal force from the propeller is greater than the horizontal force the other way at the wheels, yet the power generated at the wheels is greater than what is used by the propeller.

I'm fairly certain your expertise is not in electrical engineering else you will not make such a statement.
At starting point the vehicle has zero kinetic energy since it is stationary and in order to increase the kinetic energy (also vehicle speed) you will need have an imbalance of power not forces.

But the power doesn't have any directionality.  That is one of your fundamental misunderstandings.  The backwards force on the wheels is less than the forward force of the prop.  Net force: forward.  The power input at the wheels is less than the power consumed by the prop.  Net power: positive.  The fact that the force at the wheels is backwards is *irrelevant*

Since the only imbalance of power you can have is lower power at M motor wheel  and higher power at G generator wheel that means kinetic energy will increase but not in the direction you will like meaning vehicle can only move from right to left and not the other way around.

Kinetic energy is not a vector and has no direction.  No equation in units of energy or power tells you anything about direction of motion.  You need to look at force or velocity.  I worked out your treadmill problem above.  You haven't addressed it.  Can you find a *mathematical* flaw in it?  Or you can actually do the experiment.  You obviously haven't done it.

[bdunham7]

I'm fairly certain your expertise is not in electrical engineering else you will not make such a statement.

Well perhaps, but it isn't an electrical engineering question, it is at best a slightly tricky exam question from a 1st year introductory physics course or possibly a high school AP class.  The concepts are not difficult, but I think what probably hangs up most people is the propeller--and in the case of anyone with any real understanding of physics, once the solution is presented decently, they'll understand it.

At starting point the vehicle has zero kinetic energy since it is stationary and in order to increase the kinetic energy (also vehicle speed) you will need have an imbalance of power not forces.

You need both.  Newtons laws still apply and if both forces are equal, the motion will remain constant (zero in this case) and if there is acceleration, there must be a net force--meaning they don't balance.

Since the only imbalance of power you can have is lower power at M motor wheel  and higher power at G generator wheel that means kinetic energy will increase but not in the direction you will like meaning vehicle can only move from right to left and not the other way around.

That's gibberish.  Really.  But if I take a wild guess at what you are saying, what is the basis for your notion that the car will somehow only travel in the direction of the wheel with 'lower power'? 

as you do not know how to apply the formula in that case
you can not get a different result by using forces and speeds if you apply the formula correctly.

Real men don't apply formulas, they derive everything from first principles! 
Indeed you should get the same result if you use two different methods to determine the same thing, but the trick is in figuring out which one is most appropriate given the problem.  I cannot fathom why you don't understand Newton's laws of motion, or at least are ignoring them.  Do you actually not believe that the car is going to go in whatever direction the net force is?

[ejeffrey]

That's gibberish.  Really.  But if I take a wild guess at what you are saying, what is the basis for your notion that the car will somehow only travel in the direction of the wheel with 'lower power'? 

Yes.  As near as I can tell, what they are saying is that one wheel acts as power input, the other as "output".  Because of conservation of energy, the output must be less than or equal to the input.  All this is correct so far.  The next step is "the vehicle must accelerate in the direction of the force of the input wheel because the power is greater".  That just isn't any kind of physical law, and ignores the entire point of the classic simple machines such as the wheel, lever, wedge, etc. which is to change the direction or magnitude of force without producing or consuming energy (except for friction losses).