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

[Kleinstein]

When going at the speed of the wind or faster than the wind, the wheels are driving the propeller, not the other way around.

It is a nice graphics from electrodacus, but for the formulars one has too look at what they actually calculate, and what the symbols stand for:
In the pictures the vehicle is standing still with respect to the picture and the belt like platforms should show the relative movements.

The right side is easy, that is the power generated by generator. Positive power giving power given off.

For the left side it is a bit more complicated: The "belt" velocity is (w-v). The power of the motor is F_m*(w-v). Here a negative sign means the motor takes up power and a positive sign means the motor works as a generator and produces power.
Together with the power from the genrator side this gives the net power. A postive values means excess power available.
So the lable P_out is a bit misleading here. P_net would be more suitable.

The center formula gives the power from the motor, as the generator power is again subtracted.

So the labels there are somewhat mixed up ! And thus the wrong conclusions.

In the upper case both side produce power and thus the high excess power.
In the middle case the motor stands still, and thus no power and thus the 10 W power from the generator.
In the lower case there is still a 6 W of excess power.

So all three cases show net power excess to overcome friction. So all 3 cases are possible.

[electrodacus]

Here is the formula for wind power

0.5 * air density * area * (w-v)^3

air density is usually around 1.2kg/m^3
area is the sail area or equivalent (the area facing the wind direction) so direct down wind this is also a constant for a sail
and then is that w (wind speed) minus v (vehicle speed) so there there is max power when vehicle just starts moving super low vehicle speed and decreases significantly as vehicle approaches wind speed and equal with zero when at wind speed.

This formula is quite wrong. It is not w (wind speed) minus v (vehicle speed), it is w (wind speed) - g (ground speed), where g is usually zero (unless on a treadmill).

This means the available power from the wind does not depend on the speed of the vehicle, and so it does not matter if the vehicle is travelling at the speed of the wind or faster than it. As long as the vehicle has contact with the ground (wheels with friction), and contact with the air (some kind of sail, fan or propeller), then the vehicle can extract power from the wind/ground system and can go faster then either.

Wheel friction is important here. If the vehicle was skating on ice, then it couldn't go faster than the wind speed, since it would have no grip on the surface between it.

Similarly, it is easy to make a wheeled vehicle run directly into a headwind, and any number of experiments can be built to demonstrate this.

Not sure how you came out with that formula.
Also there was never a sail based vehicle demonstrated to exceed wind speed directly down wind (not even close not even in ideal case).
Unless you have an energy storage device you can not exceed wind speed directly down wind.

Directly upwind is a completely different story but there also energy storage is needed else it will be impossible to go up wind at any speed.
All demonstrations including the one I did and showed in this video I just posted uses energy storage plus stick slip hysteresis.  Is clear to see charge and discharge of the energy storage in the slow motion video.

[electrodacus]

Wind is powering the propeller not the wheels .
The wind tread mill is not correct .
Sorry you can't emerlate wind with a tread mill

The propeller was replaced by the M wheel here not to have any confusion about what a propeller is (just a wheel for traveling trough materials instead of on the material surface).
People think propellers have magical proprieties so I prefer to use wheels as people have less misunderstandings about how those work.

[electrodacus]

When going at the speed of the wind or faster than the wind, the wheels are driving the propeller, not the other way around.

What powers the wheels ?
When below wind speed wind pushes the vehicle similar to how a sail is pushed.
That power  0.5 * air density * area * (w-v)^3  can be divided in to power to accelerate the vehicle and power for the propeller.
If say that available wind power at some fixed point in time is 100W and say 50W is used to accelerate the vehicle and 50W is sent to propeller by taking energy from the wheel what actually powers the propeller ? The wheel or the wind ?
If air was not a compressible fluid then this wheel to propeller connection will be useless but since air is compressible energy can be stored this way by increasing the pressure differential.
Then above wind speed this stored pressure differential is what pushes the vehicle but this time since this is a limited resource the vehicle will accelerate for a few seconds even minutes and then it will start to slow down as all stored energy will be used.   

It is a nice graphics from electrodacus, but for the formulars one has too look at what they actually calculate, and what the symbols stand for:
In the pictures the vehicle is standing still with respect to the picture and the belt like platforms should show the relative movements.

This is a snapshot of the condition at a fixed moment in time same way that Derek made his explanation from the vehicle reference point.
What is showed in my 3 examples is A vehicle lower speed than wind speed, B vehicle at same speed as wind speed and C vehicle at higher speed than wind speed.
And since with wheels only on solid surfaces there is no compressible fluid to store energy the C version will decelerate. Showing that without energy storage it is impossible to accelerate above wind speed

The right side is easy, that is the power generated by generator. Positive power giving power given off.

For the left side it is a bit more complicated: The "belt" velocity is (w-v). The power of the motor is F_m*(w-v). Here a negative sign means the motor takes up power and a positive sign means the motor works as a generator and produces power.
Together with the power from the genrator side this gives the net power. A postive values means excess power available.
So the lable P_out is a bit misleading here. P_net would be more suitable.

The center formula gives the power from the motor, as the generator power is again subtracted.

So the labels there are somewhat mixed up ! And thus the wrong conclusions.

In the upper case both side produce power and thus the high excess power.
In the middle case the motor stands still, and thus no power and thus the 10 W power from the generator.
In the lower case there is still a 6 W of excess power.

So all three cases show net power excess to overcome friction. So all 3 cases are possible.

I wanted to make sure is clear Pout includes Pin that is why a Pnet was need to show what the state of the vehicle will be.
Derek used the wrong formula with (v-w) instead of correct (w-v) and only looked at the case C so vehicle speed above wind speed.
The G wheel is a generator only and M wheel is a motor only same as with blackbird where wheel is only a generator and propeller is only for propulsion (they even have a freewheel device installed to make sure power from propeller can not be transferred to wheel).
In case B that is at the limit so in real world you can not get exactly zero speed but all power from generator is needed at the motor else vehicle will move backwards (decelerate if any power is generated at G wheel and not all of it is put in the M wheel).

[fourfathom]

Also there was never a sail based vehicle demonstrated to exceed wind speed directly down wind (not even close not even in ideal case).

True.  I don't think that a sailboat can beat a balloon to a goal directly downwind -- even if the boat jibes.

Unless you have an energy storage device you can not exceed wind speed directly down wind.

Using a sail.  But a propeller is not a sail, and a boat on the water is not a wheeled vehicle on the land.

[Labrat101]

Wind is powering the propeller not the wheels .
The wind tread mill is not correct .
Sorry you can't emerlate wind with a tread mill

The propeller was replaced by the M wheel here not to have any confusion about what a propeller is (just a wheel for traveling trough materials instead of on the material surface).
People think propellers have magical proprieties so I prefer to use wheels as people have less misunderstandings about how those work. 

I have no problem understanding a propeller . I was flying twin engine Doves out of Hurn airport UK  in the 60s . ( Not the white birds that flap around going tweet tweet )
WE used the wheels to keep the fuselage from scraping along the ground .  They also came in handy for Landing ..
A wheel is a wheel .. Propeller is a propeller that's it .
The design  of a propeller is an important factor the one they use was a variable pitch . ie the blades can have their pitch altered
this is not in your formulae..  There for you are wrong .  Angle , degree etc etc etc Please add these in .
Then the Bumble Bee will fly 

PS    Quote "" People think propellers have magical proprieties ""    and you don't understand the magic  IT's a Propeller

[electrodacus]

I have no problem understanding a propeller . I was flying twin engine Doves out of Hurn airport UK  in the 60s . ( Not the white birds that flap around going tweet tweet )
WE used the wheels to keep the fuselage from scraping along the ground .  They also came in handy for Landing ..
A wheel is a wheel .. Propeller is a propeller that's it .
The design  of a propeller is an important factor the one they use was a variable pitch . ie the blades can have their pitch altered
this is not in your formulae..  There for you are wrong .  Angle , degree etc etc etc Please add these in .
Then the Bumble Bee will fly 

I hope not to sound rude but unis something is different from understanding how it works.
Variable pitch is the equivalent of a gearbox before the wheel.
A propeller has no "magic" proprieties and it is the exact analog of a wheel just that a wheel is much more efficient than a propeller.
So if you wanted to be more efficient you will have just took the power from the back wheel on blackbird and put that in the front wheel. But doing so provides you with no energy storage as road is not compressible like air.
 
If someone suggested you take energy from back wheel and power the front wheel it will have been considered stupid (by most not all) but suggesting taking power and supplying a propeller is even worse if you exclude that energy storage in pressure differential that nobody seems to understand.

[Kleinstein]

When going at the speed of the wind or faster than the wind, the wheels are driving the propeller, not the other way around.

What powers the wheels ?

The wind power the vehicle and thus the wheels. The power from the wind is given as thrust from the propeller times speed of the wind.

I wanted to make sure is clear Pout includes Pin that is why a Pnet was need to show what the state of the vehicle will be.
Derek used the wrong formula with (v-w) instead of correct (w-v) and only looked at the case C so vehicle speed above wind speed.
The G wheel is a generator only and M wheel is a motor only same as with blackbird where wheel is only a generator and propeller is only for propulsion (they even have a freewheel device installed to make sure power from propeller can not be transferred to wheel).
In case B that is at the limit so in real world you can not get exactly zero speed but all power from generator is needed at the motor else vehicle will move backwards (decelerate if any power is generated at G wheel and not all of it is put in the M wheel).

For the math it does not matter if one has a motor or generator. Esepcially wheels and gears work in both directions. In the examples generator power was fixed positive and there is no porblem ignoring the possible extra power in case 1, it works without it too.
Whether one uses (v-w) or (w-v) is only a question of the direction of the force, so it depends which side of the balance to look at.
The case B is very easy: one needs no power to stop the motor. So here zero power for the motor is obvious.

[Kleinstein]

If someone suggested you take energy from back wheel and power the front wheel it will have been considered stupid (by most not all) but suggesting taking power and supplying a propeller is even worse if you exclude that energy storage in pressure differential that nobody seems to understand.

This is not stupid, but the way the vehicle works.  Of cause it only works because the wheels are not on the same surface, but with a velocity between them.

Excluding energy storrage is just making it simpler - in the steady state the energy storage does not contribute to the power. So far I see no form of energy storage that stores more energy when slower. The kinetic energy and the energy stored in the pressure difference around the propeller both go up when the vehicle goes faster. So these forms of energy storage can no explain a jo-jo type movement. Instead of chasing the red herrring energy storage just try to understand the explaination given. There is nothing wrong with the experiment with the large wooden beam on the roler vehicle. Just accept what you see.

[Labrat101]

I have no problem understanding a propeller . I was flying twin engine Doves out of Hurn airport UK  in the 60s . ( Not the white birds that flap around going tweet tweet )
WE used the wheels to keep the fuselage from scraping along the ground .  They also came in handy for Landing ..
A wheel is a wheel .. Propeller is a propeller that's it .
The design  of a propeller is an important factor the one they use was a variable pitch . ie the blades can have their pitch altered
this is not in your formulae..  There for you are wrong .  Angle , degree etc etc etc Please add these in .
Then the Bumble Bee will fly 

I hope not to sound rude but unis something is different from understanding how it works.
Variable pitch is the equivalent of a gearbox before the wheel.
A propeller has no "magic" proprieties and it is the exact analog of a wheel just that a wheel is much more efficient than a propeller.
So if you wanted to be more efficient you will have just took the power from the back wheel on blackbird and put that in the front wheel. But doing so provides you with no energy storage as road is not compressible like air.
 
If someone suggested you take energy from back wheel and power the front wheel it will have been considered stupid (by most not all) but suggesting taking power and supplying a propeller is even worse if you exclude that energy storage in pressure differential that nobody seems to understand.

Variable pitch is the equivalent of a gearbox before the wheel.   Your kidding for sure . 
This phrase just show how you have no idea of the properties and design that goes into a making a propeller .
 Its not a Fan that sits on the table in your house .
 There are many many factors that you have left out .
I suggest you take a course in aviation . . & leave the school book theory's to the kids with wind up elastic band planes  .

 Like every one here has already tried to explain this to you your maths is Wrong .

[fourfathom]

If someone suggested you take energy from back wheel and power the front wheel it will have been considered stupid (by most not all)

Yes, that would be stupid.

but suggesting taking power and supplying a propeller is even worse if you exclude that energy storage in pressure differential that nobody seems to understand.

Well, somebody doesn't understand, and it's you.  There is no speed difference between the road and the road.  There is a speed difference between the wind and the road.

[electrodacus]

The wind power the vehicle and thus the wheels. The power from the wind is given as thrust from the propeller times speed of the wind.

That wind power can be all used to accelerate your vehicle or you can take part of it and diverted to some other purpose.
But if you take say half that power and put it in to propeller then there is no net gain as far as acceleration go as it is better to just put that power in say front wheel as wheel is more efficient than a propeller.
But anyone (almost) suggesting taking power from back wheel and putting that in front wheel will realize how useless it is.

For the math it does not matter if one has a motor or generator. Esepcially wheels and gears work in both directions. In the examples generator power was fixed positive and there is no porblem ignoring the possible extra power in case 1, it works without it too.
Whether one uses (v-w) or (w-v) is only a question of the direction of the force, so it depends which side of the balance to look at.
The case B is very easy: one needs no power to stop the motor. So here zero power for the motor is obvious.

A motor or generator not connected to anything will spin freely so any attempt to take energy from generator wheel will result in vehicle moving backwards.
And all that energy generated putted back in the motor wheel will just bring you back from where you left.

[electrodacus]

Well, somebody doesn't understand, and it's you.  There is no speed difference between the road and the road.  There is a speed difference between the wind and the road.

Well yes that is what I showed in my 3 examples.
That difference at case C is not helping you so it will be even worse that putting that energy in the front wheel.

[Kleinstein]

Well, somebody doesn't understand, and it's you.  There is no speed difference between the road and the road.  There is a speed difference between the wind and the road.

Well yes that is what I showed in my 3 examples.
That difference at case C is not helping you so it will be even worse that putting that energy in the front wheel.

The 3 examples really show a lack of understanding.

[electrodacus]

The 3 examples really show a lack of understanding.

Are you saying that wrong formula was applied ?
If so please provide yours for all 3 cases.

[Kleinstein]

The motor power is given by force times velocity seen by the motor. The velocity seen by the motor is w-v, as the indicated speed in the graphics.
So this gives: P_motor = F_M * (W-V). For the steady state with no extra friction F_M = F_G.
A positive value would be power generated by the motor and one may want to set this to 0 instead. A negative power is actual power send to the motor.

The net power or excess power available to overcome friction is then P_net = P_in + P_motor.
So for the 3 example cases this would be 30 W (or 10 W if the motor is not allowed to generate power), 10 W and 6 W of net power.

[IanB]

The 3 examples really show a lack of understanding.

Are you saying that wrong formula was applied ?
If so please provide yours for all 3 cases.

You are wasting your time arguing with formulas, when actual, real-world experiments prove the case. All of us know we can build a craft that will run faster than the wind indefinitely, and all of us know we can build a craft that will run directly into the wind.

Since this is a fact that is provable by experiment, it doesn't really matter that you keep trying to say that it is "impossible". It is like trying to argue that it is impossible for airplanes to fly, when airplanes are flying over your head.

We don't need to prove anything to you, because we know already what the facts are. You are the one who needs to figure out for yourself how these things work. It is not our problem to convince you.

[electrodacus]

The motor power is given by force times velocity seen by the motor. The velocity seen by the motor is w-v, as the indicated speed in the graphics.
So this gives: P_motor = F_M * (W-V). For the steady state with no extra friction F_M = F_G.
A positive value would be power generated by the motor and one may want to set this to 0 instead. A negative power is actual power send to the motor.

The net power or excess power available to overcome friction is then P_net = P_in + P_motor.
So for the 3 example cases this would be 30 W (or 10 W if the motor is not allowed to generate power), 10 W and 6 W of net power.

Motor is what is says a motor not a generator. The back wheel is always powered by the front wheel that is the generator.
Same vehicle is used in all 3 case the vehicle construction can not be changed and will be the same for all 3 cases.

If I understand right your answer is net power acting against vehicle is always positive and this are the values.
A) 10W
B) 10W
C) 6W

Is that correct ?

It seems that you agree in steady state (referenced to vehicle) F_G = F_M due to Newton third law.
Without any connection between generator and motor both generator and motor will free spin with no friction (all ideal case).
You can decide what power you want to take out of generator and send to motor in my example I used 10W
Then if 100% of that generated power is sent to the motor Pout will always equal Pin plus or minus some extra depending on speed and direction of the wind treadmill.

To make it easier to replay I will post again the photo with the 3 cases

[electrodacus]

You are wasting your time arguing with formulas, when actual, real-world experiments prove the case. All of us know we can build a craft that will run faster than the wind indefinitely, and all of us know we can build a craft that will run directly into the wind.

Since this is a fact that is provable by experiment, it doesn't really matter that you keep trying to say that it is "impossible". It is like trying to argue that it is impossible for airplanes to fly, when airplanes are flying over your head.

We don't need to prove anything to you, because we know already what the facts are. You are the one who needs to figure out for yourself how these things work. It is not our problem to convince you.

Yes real case for B will be different but there is a good reason for that.  The reason is energy storage plus stick slip hysteresis and I have the videos to demonstrate that is the case.
So you see the real experiment but do not understand why you have that result.
No vehicle can exceed wind speed directly down wind or travel directly upwind without energy storage.
They are different case with direct upwind using small capacity energy storage and stick slip hysteresis with charge discharge cycles of many times per second.
The direct down wind uses large capacity pressure differential energy storage and can last for a few minutes depending on design.
For direct upwind you can travel forever using those mini charge discharge cycles and stick slip hysteresis as you always have access to wind energy
For direct downwind you can only travel for a limited amount of time as while above wind speed you have no access to wind energy only stored energy in pressure differential.

[Kleinstein]

The motor power is given by force times velocity seen by the motor. The velocity seen by the motor is w-v, as the indicated speed in the graphics.
So this gives: P_motor = F_M * (W-V). For the steady state with no extra friction F_M = F_G.
A positive value would be power generated by the motor and one may want to set this to 0 instead. A negative power is actual power send to the motor.

The net power or excess power available to overcome friction is then P_net = P_in + P_motor.
So for the 3 example cases this would be 30 W (or 10 W if the motor is not allowed to generate power), 10 W and 6 W of net power.

Motor is what is says a motor not a generator. The back wheel is always powered by the front wheel that is the generator.
Same vehicle is used in all 3 case the vehicle construction can not be changed and will be the same for all 3 cases.

If I understand right your answer is net power acting against vehicle is always positive and this are the values.
A) 10W
B) 10W
C) 6W

Is that correct ?

It seems that you agree in steady state (referenced to vehicle) F_G = F_M due to Newton third law.
Without any connection between generator and motor both generator and motor will free spin with no friction (all ideal case).
You can decide what power you want to take out of generator and send to motor in my example I used 10W
Then if 100% of that generated power is sent to the motor Pout will always equal Pin plus or minus some extra depending on speed and direction of the wind treadmill.

I don't agree with the red part: the net power is not acting against the vehicle - power has no geometric direction. A positive net power means there is power to spare, e.g. to turn on some lights or overcome friction. So not all power needs to be send to the motor in the steady state for the 3 cases shown. If all the power is send to the motor it would accelerate the vehicle and thus no longer the steady state.

The orange part is some-how self-contradicting, or I don't understand what it should mean: if all the power is send to the motor, Pout=P_motor= Pin and thus no net power.

[fourfathom]

[...] small capacity energy storage and stick slip hysteresis with charge discharge cycles of many times per second. [...]

This is all so wrong...   No wonder you can't figure it out.

[electrodacus]

I don't agree with the red part: the net power is not acting against the vehicle - power has no geometric direction. A positive net power means there is power to spare, e.g. to turn on some lights or overcome friction. So not all power needs to be send to the motor in the steady state for the 3 cases shown. If all the power is send to the motor it would accelerate the vehicle and thus no longer the steady state.

The orange part is some-how self-contradicting, or I don't understand what it should mean: if all the power is send to the motor, Pout=P_motor= Pin and thus no net power.

Power can be negative. Think a battery being charged vs discharged. How you will differentiate between the two ? as they sure do not mean the same thing.

What will you do with the excess of generated power ? heat air ?
Yes a net positive power means in this case power available at that fixed moment in time to accelerate the vehicle from left to right (I will say that is forward) so vehicle kinetic energy will increase relative to the road/ground.
A negative power means that will decelerate the vehicle so vehicle kinetic energy relative to road/ground will decrease.

Pout is the power provided by the wind (wind treadmill in this example) F_M * (w-v)  plus what you supply the motor with so Pin

[electrodacus]

[...] small capacity energy storage and stick slip hysteresis with charge discharge cycles of many times per second. [...]

This is all so wrong...   No wonder you can't figure it out.

See this video I made in slow motion (you can watch at 0.25x) and explain what you see https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8

[IanB]

To make it easier to replay I will post again the photo with the 3 cases

Case A: The vehicle can move to the right with zero power from the generator and zero power at the motor.

Case B: The vehicle can move to the right with any power greater than zero at the motor. Less than 1 W would be enough.

Case C: The vehicle can move to the right with a power greater than about 4 W at the motor. Since this is less than 10 W, the generator can supply it.

In each case, the pictures clearly show the cart being able to move to the right.

[Kleinstein]

Pout is the power provided by the wind (wind treadmill in this example) F_M * (w-v)  plus what you supply the motor with so Pin

Ok if P_out is supposed to be the power taken from the wind, than the formula on the left are correct, just a rather strange name for the power taken from the wind. This would however also include the motor running as a generator. Anyway the case of going slower than the wind should not be at question.

However  with P_out for the power from the wind the the formula in the middle don't make much sense. P_net would be than the power direktly transfered to the vehincle (without the power from the motor). In the ideal case with 100% efficiency and no friction loss all the power taken from the wind would also end up in the vehicle, as there is no other energy sink in the steady state.