Can a cart powered by wind travel faster than the wind itself?

[rcgldr]

It seems to me that the power budget is making a complete circle.

It might appear that way, but the power output can be significantly less than the power input because of the difference in the speed of the wind versus the speed of the ground. The power input is related to ground speed that the wheels interact with, while the power output is related to air speed that the prop interacts with. When there is a wind and the cart is doing downwind, the air speed is slower than the ground speed. Power equals force times speed, so the difference between air and ground speed allows the force on the air to be greater than the opposing force from the ground, but with an air speed much lower than the ground speed so that the power output, thrust times air speed, is less than the power input, ground force times ground speed.

 

[rcgldr]

I offer this extreme example of taking advantage of differing velocties in the same media, the air. By simply traveling back and forth across a reasonably small shear boundary between two differing air streams while circling in an angled loop, a radio control glider can achieve extreme speeds. This is called dynamic soaring.

In this youtube video a glider reaches 333 mph, and it's averaging over 270mph, with a wind flow differential around 50 mph or so. There's a high speed wind, around 50 mph flowing over a narrow ridge, so that on the downwind side of the ridge, there's a somewhat turbulent but relatively stagnant volume of air below the ridgeline, and a fast moving air stream above the stagnant air, separated by a reasonably small shear boundary.

http://www.youtube.com/watch?v=Vi0hrjqU15I&fmt=18

Last I read, the record for rc glider dynamic soaring was 365mph.

 

[A.T.]

A.T. : “What do you mean by "stationary"? The Earth moves around the sun at 30 km/s. There is no such thing in physics as absolute rest.”
So this cart harvests power from the rotation of the Earth around the sun?

I never said that, and you know it. That's why you sniped the relevant part:

"The ground outside can be assumed to be stationary just like the conveyor belt of the treadmill can be too. Both views are valid. Neither one is 'simulated' or less real."

I tried to explain to you that neither the ground not the conveyor belt are at absolute rest. But observers on either one will observe the same laws of physics. If the observer standing on the conveyor belt sees the cart moving faster that the air in the same direction as the air, the observer on the ground in a wind will see the same.

A.T. : “Yes there is a motor called sun. It drives the air masses just like the electric motor is driving the conveyor belt of the treadmill”
So now it is extracting solar energy as well?

Yes. No sun -> no wind -> no DDWFTTW

I don’t see that anything you have posted here has any relevance to this thread.

Because you have deliberately ignored the relevant parts of my post, in order not to have to address them:

When you look a http://de.youtube.com/watch?v=9Yt4zxYuPzI&feature=related" you see that not all parts of the cart are moving faster than the ruler. The top of the big gear has the same speed as the ruler, so it experiences no headwind. The same is true for the front surfaces of the propeller blades on the wind powered carts: they don't experience a headwind, even if the rest of the cart does.

 

[rcgldr]

I tried to explain to you that neither the ground not the conveyor belt are at absolute rest.

I don't think the frame of reference is the issue, it's the fact that the belts or turntable are powered. However the wind on the Earth is also powered (something had to accelerate the wind), so I'm not sure why the fact that the turntable is powered is an issue. The key thing here is that the carts are outruning the powered turntables and treadmills, while operating in an unpowered apparent headwind. Change this to unpowered ground and powered wind, and it should be the same.

video wheel ruler ... prop forward edges

I'm not sure what the point here is. The top wheel rolls forward on the "ruler" and doesn't move at the same speed. When the air based carts are going DDWFTTW, the prop experiences a headwind, but it's not an issue.

 

[A.T.]

I'm not sure why the fact that the turntable is powered is an issue.

It isn't an issue. It just the last straw of someone who said that he would accept a wind tunnel test. As if wind tunnels were not powered by a motor.

I'm not sure what the point here is. The top wheel rolls forward on the "ruler" and doesn't move at the same speed.

Read again what I wrote: "The top of the big gear has the same speed as the ruler".

If the ruler is not sliding over the big wheel, the very top of the big wheel (where it touches the ruler) has to move at the same speed relative to the ground as the ruler.

When the air based carts are going DDWFTTW, the prop experiences a headwind, but it's not an issue.

What I meant is the perspective of someone sitting on the surface of a propeller blade that faces (skew) forward. If he drills a small hole into the blade the air will flow from back to front trough that hole. So the propeller blade experiences a tailwind.

 

[zoobyshoe]

Except in this case the the torque pressed into service to accelerate the air ends up being converted by the propeller into thrust that is greater than the torque related opposing force from the ground. This works because the propeller interacts with a headwind that is much slower than the ground speed, and although force is higher, speed is slower still, and power output is less than power input.

I find it difficult to believe the prop will be anything but a useless fan in this situation.

The problem as I see it is that, although we still have a speed difference between the air and ground, the only energy available from that difference at this point is that represented by the cart's momentum. This is like a gust: it will only afford a brief period of continued forward motion till it is bankrupted.

The cart can extract energy from the relative speeds of the air and ground regardless of it's own speed, but that does not guarantee that the relative speeds of the ground and air always contain enough energy to do anything the cart wants it to do. Whittled down now to the cart's momentum, I think we may not have enough energy to proceed.

Therefore your claim that thrust greater than the slowing by friction will be generated does not strike me as what will actually happen.

Consider swerdna's set up. We replace the table with an ultra-lightweight table exactly equal in mass to the cart's mass. This can rotate but is not motorized. We lift the cart and set the table rotating (by some separate power source: a rubber wheel chucked into a drill, say.). Once it's up to speed, we remove the power source. Then we set the cart back down. Regardless of the speed we give the table it, and the cart, will come to a stop eventually, because it's running on stored energy being used up by the propeller. The propeller won't start to push the table adding energy to it.

Which is what is happening with the DDWFTTW cart. Repeating my previous example, the wind speed is 10 mph, the cart speed is 14 mph, Now it's encountering slow air and leaving it faster in its wake. The whole cart system is losing energy. And the prop accelerates the air by 6 mph upwind. The air speed at the prop is 14 mph - 6 mph = 8 mph. The prop is slowing down the wind from 10 mph to 8 mph, even though it's moving forwards at 14 mph. This 2 mph reduction in wind speed is what is powering this example cart. The videos we've seen appear to confirm that these DDWFTTW cart work.

It seems like you're stretching to show that somewhere some air was slowed. In a windmill energy is transferred by air slowing at the rotor. At your rotor, air was accelerated. The cart's propeller received no energy from the air; it gave energy to the air. The cart system lost energy (which you acknowledge).

 

[rcgldr]

The top of the big gear has the same speed as the ruler.

OK, the surfaces at the contact patch aren't moving during the time they are in contact (except there's motion perpendicular and compression related movment), but the "top" or contact patch of the big gear is moving.

Prop ... headwind ... What I meant is the perspective of someone sitting on the surface of a propeller blade that faces (skew) forward. If he drills a small hole into the blade the air will flow from back to front trough that hole. So the propeller blade experiences a tailwind.

The hole isn't needed. I'm guessing you're referring to the "upwash" that occurs at the separation point in front of the leading edge of the prop blades, or the tip vortices that include an upwash component.

I still don't get what this has to do with explaining how DDWFTTW carts work (but then again, it's late and I'm tired). When the carts are going DDWFTTW, the prop operates in an apparent headwind, but it's not an issue because the ground speed is faster still. The prop's purpose is to accelerate an apparent headwind faster still, an upwind acceleration of the air.

 

[vanesch]

It seems like you're stretching to show that somewhere some air was slowed. In a windmill energy is transferred by air slowing at the rotor. At your rotor, air was accelerated. The cart's propeller received no energy from the air; it gave energy to the air.

Yes, the propeller GAVE energy to the air *in the frame of the cart*. Now, in that same frame (I pointed out elsewhere that energetic relationships are frame-dependent, so one must not change frames while doing an energy balance: the balance only holds if we do it in one frame ; the balance will hold in any frame, but the different contributions will be different from frame to frame).

But in that same frame's reference, the ground is moving, and the wheels on the ground act like an old-time's water mill, extracting energy from the floor's motion.

So in the cart's frame, the air, which was initially at rest, won energy, and the floor lost some. However, the energy of the floor was replenished by the motor (which, from the cart's perspective, delivers power to the floor). And as the cart gave less power to the air than it took from the floor, it gained kinetic energy which allowed it to accelerate.

Now, from the *floor's perspective*, we have a different balance. Here, the motor is not delivering energy to the floor (which is not moving), but rather to the Earth and the room (which is rotating, powered by the motor). In this frame, the cart is *taking* some energy from the air, which is now moving less rapidly (but this is then compensated again by the motor speeding up the air again by rotating the room and the earth, which make the air blow over the fixed floor). With a part of that energy, the cart is accelerating.
It may seem strange that the motor "powers the wind through rotating the room and the earth", but in fact, what happens is that the air which was rotating with the room, has been slowed down by the cart's propeller, and is now sped up again by the room (which is powered by the motor). This would be similar in a doughnut-shaped wind tunnel with a ventilator. The cart's propeller would slow down the airflow, and the ventilator would have to spend extra power to speed the air up again. Here, we have a funny "wind tunnel" which is a rotating room with air in it, rotated by a motor which is fixed to the "fixed turntable".

In any case, the power comes from the motor.

The cart system lost energy (which you acknowledge).

 

[rcgldr]

The cart can extract energy from the relative speeds of the air and ground regardless of it's own speed, but that does not guarantee that the relative speeds of the ground and air always contain enough energy to do anything the cart wants it to do.

If wind turbines can extract mega-watts of energy from the wind, then it would seem that the potential energy from the wind would be more than enough for these relatively small DDWFTTW carts.

Consider swerdna's set up. We replace the table with an ultra-lightweight table exactly equal in mass to the cart's mass. This can rotate but is not motorized. We lift the cart and set the table rotating (by some separate power source: a rubber wheel chucked into a drill, say.). Once it's up to speed, we remove the power source. Then we set the cart back down. Regardless of the speed we give the table it, and the cart, will come to a stop eventually, because it's running on stored energy being used up by the propeller.

You don't need an ultra-light table. Without the motor driving the table, everyting will eventually come to a stop. However the stated conditions for the DDWFTTW cart is an existing tailwind that doesn't diminsh during the time the cart is in operation. Wind farms can suck hundred's of megawatts of power from the wind, and yet the effect is small compared to the total potential energy of the wind. The winds powersource (rotating earth, sun, ...) is huge and the DDWFTTW carts only require a tiny fraction of this potential energy.

Repeating my previous example, the wind speed is 10 mph, the cart speed is 14 mph, and the prop accelerates the air by 6 mph upwind. The air speed at the prop is 14 mph - 6 mph = 8 mph. The prop is slowing down the wind from 10 mph to 8 mph, even though it's moving forwards at 14 mph. This 2 mph reduction in wind speed is what is powering this example cart. The videos we've seen appear to confirm that these DDWFTTW cart work.

It seems like you're stretching to show that somewhere some air was slowed.

It's not a stretch, the videos are evidence that the carts work, which wouldn't be possible unless the carts slowed down the wind, the same as any wind powered device.

In a windmill energy is transferred by air slowing at the rotor. At your rotor, air was accelerated.

Relative to the prop yes, accelerated upwind. Relative to the ground, the air is decelerated by the prop.

The cart's propeller received no energy from the air; it gave energy to the air.

The wheels are receiving the energy, and they in turn drive the prop, which adds energy to the apparent wind. Kinetic energy includes a velocity factor, so it's sensitive to the frame of reference. From the prop + cart frame of reference the kinetic energy of the air is increased. From the wind's frame of reference the kinetic energy in also increased (speed changes from 0 relative to the wind to a non-zero upwind value). From the ground frame of reference the kinetic energy of the air is decreased.

If you're going to compare the cart to a windmill, you need to use the ground as a frame of reference, and my example situation from above describes the situation (10 mph wind, 14 mph cart, 6 mph upwind acceleration of air, 8 mph net wind at the prop, so the wind was slowed down).

 

[A.T.]

I still don't get what this has to do with explaining how DDWFTTW carts work

I was responding to schroder: "Let’s assume the cart is somehow pushed into a true transition to H-H. What exactly is supposed to keep it there? The ground is stationary, the wind is a headwind against the cart"

The key here is to understand that not all surfaces of the cart experience a headwind. Just like the top of the big gear doesn't experience the ruler as staying behind.

 

[rcgldr]

I still don't get what this has to do with explaining how DDWFTTW carts work.

The key here is to understand that not all surfaces of the cart experience a headwind.

I was referring to apparent headwind (relative to prop and cart here). Almost all surfaces of the cart experience an apparent headwind, and anything aft of the prop experiences even more of an apparent headwind. The point of the cart is to travel DDWFTTW, so an apparent headwind is expected. The point of the prop is to accelerate air upwind, so the apparent headwind is increased (relative to cart and prop).

From the ground frame of reference the only thing not traveling faster than the wind is the air accelerated upwind from the prop, unless you want to consider the tread surface of the wheels which cycle between zero to double the cart speed and back, but average the same speed as the cart. The net effect is all the parts of the cart go DDWFTTW and only the air at the prop is going DDWSTTW (S=slower).

 

[zoobyshoe]

If wind turbines can extract mega-watts of energy from the wind, then it would seem that the potential energy from the wind would be more than enough for these relatively small DDWFTTW carts.

Let's just take this point. The power available from the wind is dependent on its speed^3. The slower the wind, the power available drops off exponentially. At 1 mph a wind probably does not have the energy to start the cart. At 2 mph the wind is 8 times more powerful, and so on. The point is that the idea that the cart can extract energy from the relative motion of surrounding media regardless of its own speed breaks down when the cart wants to do something that requires more energy than either medium can supply. Below a certain wind speed the mega-watt turbines won't budge, despite the relative motion of ground and wind, and there is some speed at which the same turbine can only generate one watt.

 

[zoobyshoe]

Yes, the propeller GAVE energy to the air *in the frame of the cart*. Now, in that same frame (I pointed out elsewhere that energetic relationships are frame-dependent, so one must not change frames while doing an energy balance: the balance only holds if we do it in one frame ; the balance will hold in any frame, but the different contributions will be different from frame to frame).

But in that same frame's reference, the ground is moving, and the wheels on the ground act like an old-time's water mill, extracting energy from the floor's motion.

So in the cart's frame, the air, which was initially at rest, won energy, and the floor lost some. However, the energy of the floor was replenished by the motor (which, from the cart's perspective, delivers power to the floor). And as the cart gave less power to the air than it took from the floor, it gained kinetic energy which allowed it to accelerate.

Now, from the *floor's perspective*, we have a different balance. Here, the motor is not delivering energy to the floor (which is not moving), but rather to the Earth and the room (which is rotating, powered by the motor). In this frame, the cart is *taking* some energy from the air, which is now moving less rapidly (but this is then compensated again by the motor speeding up the air again by rotating the room and the earth, which make the air blow over the fixed floor). With a part of that energy, the cart is accelerating.
It may seem strange that the motor "powers the wind through rotating the room and the earth", but in fact, what happens is that the air which was rotating with the room, has been slowed down by the cart's propeller, and is now sped up again by the room (which is powered by the motor). This would be similar in a doughnut-shaped wind tunnel with a ventilator. The cart's propeller would slow down the airflow, and the ventilator would have to spend extra power to speed the air up again. Here, we have a funny "wind tunnel" which is a rotating room with air in it, rotated by a motor which is fixed to the "fixed turntable".

In any case, the power comes from the motor.

I am pretty sure I agree with this analysis of what is going on with swerdna's set up. (However, once you got to the floor's perspective I was afraid I might be drunk: the room was spinning.)

 

[A.T.]

Jeff, I agree with you. I just wanted to show the analogy to the simple mechanical cart propelled by the ruler:

Ruler: The very top of the big gear is pushed forward by the ruler, despite the fact that the ruler is moving back from the carts perspective.

Air: The rear surfaces of the propeller blades are pushed forward by the air, despite the fact that the air is moving back from the carts perspective.

Yes I know that it's the propeller that pushes back the air, but since action=reaction you can also see it this way to examine the forces: In both cases this forward force is transferred to the ground, where it creates a backward force on the cart. But due to translation via gears the backward force is smaller. So the net force on the cart points forward and accelerates it.

 

[vanesch]

Let's just take this point. The power available from the wind is dependent on its speed^3. The slower the wind, the power available drops off exponentially. At 1 mph a wind probably does not have the energy to start the cart. At 2 mph the wind is 8 times more powerful, and so on. The point is that the idea that the cart can extract energy from the relative motion of surrounding media regardless of its own speed breaks down when the cart wants to do something that requires more energy than either medium can supply. Below a certain wind speed the mega-watt turbines won't budge, despite the relative motion of ground and wind, and there is some speed at which the same turbine can only generate one watt.

The problem is again that your v^3 is dependent on the reference frame in which you are looking. If you are looking in the ground reference frame, then the only "moving medium" is the wind, but there's no problem: the wind is blowing at a steady pace.

Now, when you are looking at the situation from the cart's perspective (when it is exactly at the wind speed), then it is right that the *wind* medium doesn't allow any extraction, but in this reference frame, the floor is moving, and from *that* movement you can extract energy (like you can when you would have a running treadmill and you would put a wheel with a dynamo on it: you can extract power from this moving floor.

The problem is that you are applying your energy balance by using movements as seen in two different reference frames: you say that you cannot extract power from the floor (which is correct in the floor reference frame) AND you say that you cannot extract power from the air (which is correct in the cart's frame). So you say: there's no power source anymore (the floor is not moving, and the air is not moving). But you should do your balance in one and the same frame. It doesn't matter which one (although there will always be one where things are simpler), but once you've chosen it, you have to stick to it.

As pointed out already several times, when you reach the point where the cart is at (or beyond) windspeed, the propeller is DELIVERING power to the wind in the cart's frame, and TAKING that power from the motion of the floor (again, in the cart's frame). That's because it is *accelerating* the wind in its frame.

You get a similar analysis when you look at it from the wind's frame (but the numbers are different).

When looking at is from the floor's frame, the propeller is TAKING power from the wind (because in *this* frame, it is slowing down the wind). As in this frame the floor isn't moving, there' s no power to or from the floor.

 

[zoobyshoe]

The problem is again that your v^3 is dependent on the reference frame in which you are looking. If you are looking in the ground reference frame, then the only "moving medium" is the wind, but there's no problem: the wind is blowing at a steady pace.

Now, when you are looking at the situation from the cart's perspective (when it is exactly at the wind speed), then it is right that the *wind* medium doesn't allow any extraction, but in this reference frame, the floor is moving, and from *that* movement you can extract energy (like you can when you would have a running treadmill and you would put a wheel with a dynamo on it: you can extract power from this moving floor.

The problem is that you are applying your energy balance by using movements as seen in two different reference frames: you say that you cannot extract power from the floor (which is correct in the floor reference frame) AND you say that you cannot extract power from the air (which is correct in the cart's frame). So you say: there's no power source anymore (the floor is not moving, and the air is not moving). But you should do your balance in one and the same frame. It doesn't matter which one (although there will always be one where things are simpler), but once you've chosen it, you have to stick to it.

As pointed out already several times, when you reach the point where the cart is at (or beyond) windspeed, the propeller is DELIVERING power to the wind in the cart's frame, and TAKING that power from the motion of the floor (again, in the cart's frame). That's because it is *accelerating* the wind in its frame.

You get a similar analysis when you look at it from the wind's frame (but the numbers are different).

When looking at is from the floor's frame, the propeller is TAKING power from the wind (because in *this* frame, it is slowing down the wind). As in this frame the floor isn't moving, there' s no power to or from the floor.

First: just clarify for me if you are talking about an outdoor wind test or swerdna's table?

 

[vanesch]

First: just clarify for me if you are talking about an outdoor wind test or swerdna's table?

Both !
I'm talking in the abstract about a flat medium and a uniform air flow over it, whether that's in a lab, a train or whatever.

Imagine a train which contains a wind tunnel.

 

[zoobyshoe]

Both !
I'm talking in the abstract about a flat medium and a uniform air flow over it, whether that's in a lab, a train or whatever.

I notice there is a controversy raging over whether swerdna's table is the same thing as the outdoor, straight line test. Jeff and I have stayed out of that in talking to each other by always referring to an outdoor, straight line test.

 

[vanesch]

I notice there is a controversy raging over whether swerdna's table is the same thing as the outdoor, straight line test. Jeff and I have stayed out of that in talking to each other by always referring to an outdoor, straight line test.

If you want to. But do me a favor and consider it to be a windtunnel test.

A windtunnel test with the wind tunnel installed on a train.

 

[zoobyshoe]

If you want to. But do me a favor and consider it to be a windtunnel test.

A windtunnel test with the wind tunnel installed on a train.

Hehe. No thanks. My discussion with Jeff has just split into more issues than I want to handle at once. I fact, I limited my response to just one. As I said earlier:

... the zoobie brain is a slow, rust-encrusted, squealing, steam- emitting, gear-grinding, contraption with lots of loose hoses and shorted wires, and no one remembers the last oil change.

 

[vanesch]

Hehe. No thanks. My discussion with Jeff has just split into more issues than I want to handle at once.

But can you agree that a test in a (long) windtunnel is equivalent to an outdoor test ?

 

[zoobyshoe]

But can you agree that a test in a (long) windtunnel is equivalent to an outdoor test ?

The bait was delicious. Here's your hook back.

 

[vanesch]

The bait was delicious. Here's your hook back.

 

[Subductionzon]

But to change some of the wind speed so it is closer to ground speed it must take energy from the ground by slowing it down. The ground now has less speed. As soon as that happens we're back in a TH.

No, the relative energy of the wind to the ground is less after it passes through the propeller. The cart runs off of the difference in speed between the air and the ground. Try to look at it this way before the cart passes by all of the wind is moving at 10 mph with respect to the ground. After it passes by some of the air is now moving at let's say 8 mph. That air has less kinetic energy afterwords, where did the energy go? Into the cart propelling it faster than the wind. Please note this is not free energy, over unity or any other such nonsense. The cart is just extracting some of the energy of the wind in a unique fashion. If there is no wind there is no relative motion with the ground for the cart to work off of.

 

[schroder]

Alright, I will make yet another attempt to explain what my position is and why I say there is no equivalency between what is happening on the turntable (from now on TT) and what theoretically would happen outdoors. I apologize for the length of this; But if you have ever read some of my technical papers you would consider it to be very brief!
First, let me say that I believe we must isolate the system that we are talking about. Since we are talking about a wind-driven cart, I don’t see what purpose is served by including the rotation of the Earth around the sun, or the presence of the sun in the sky. How about we isolate the system to the wind? I think we all know what causes the wind to blow. If we were to carry the previous thinking to the extreme we can go all the way back to the Big Bang event as the ultimate source of energy for the cart. Hopefully, that is not necessary! In the case of the TT, in place of the wind, we have an electric motor driving the TT.
What I would like you recognize, is that there are two stages to the system operation. Initially there is an acceleration stage, and then there is the steady state or continuous running stage. Therein lays all the confusion, in my opinion. I believe that the acceleration or run-up stages are equivocal. I do not believe that the steady state stages or DDWFTTW stages are equivocal.
Let us first consider the run-up stage on the TT. Initially, everything is at rest. The motor is started, the TT turns. At first, due to the static friction between the wheel and the TT, the cart moves in the same direction as the TT. It is dragged backwards and experiences a Tailwind. Soon enough, the blunt force of the TW will slow and then stop the backwards motion of the cart. During this process, more and more torque is felt at the wheel and TT interface until the statics friction is overcome and the wheel begins to roll. The turning wheel then powers the propeller which starts to provide a forward thrust to the cart. The cart accelerates forward, opposite to the direction of motion of the TT. This is a regenerative feedback process, which continues the acceleration until the cart reaches some equilibrium speed which we will call “faster than the TT”. But here I only want to draw attention to the run-up process. The steady state faster than TT I would like to analyze separately as it is a different state as I will attempt to show.
OK, now let us consider the cart in an outdoor test, or if we could possibly have a circular wind around the TT, we could consider it indoors as well. Again, initially everything is at rest. The wind now starts to blow. It builds up a blunt force on the cart, on the crossarm I will even allow for a sail to be attached to the crossarm at this point, so as not to quibble. The blunt force of the wind makes the cart start moving in respect to the stationary TT or ground. As the cart moves, the static friction of the wheel is overcome and the wheel starts to roll. As the wheel rolls it generates a turning force through the flexishaft which turns the propeller. The propeller provides a thrust, cutting into the air ahead forcing it to the rear and the cart accelerates forward. At some point, the cart transitions into DDWFTTW as a steady state condition. Again, I will analyze the steady states separately. The point here is that the run-up stages in the motorized TT and the wind driven cart are completely equivocal as far as I can determine. I believe we have no dispute up to this point. Please correct me if I am wrong here.
Now I would like you to consider the steady state of the cart running in the faster than TT state (motor driven) The cart is already moving in the opposite direction to the TT. The wheel is in constant contact with the TT and is therefore constantly able to extract drive power from the TT and of course the motor which is driving the TT. As long as the wheel does not slip or slide, as long as it continues to roll against the TT, the cart has a continuous source of energy being supplied to it. There is now no blunt force Tailwind, as the cart is moving forward. There is a continuous headwind, which the propeller can make efficient use of to screw into and this also provides a driving force for the cart to continue to move forward indefinitely for as long as the motor is running. It is a true steady state condition.
Finally, let us now consider the cart in the outdoor (wind powered) situation at DDWFTTW. The cart is already moving downwind, having been accelerated to be going faster than the wind. The cart has lost contact with the Tailwind that was responsible for pushing it up to this state. It does not have a continuous source of power being provided to it completely unlike the cart on the motorized TT. The wheel is in constant contact with the ground, and if the cart can be kept moving forwards, the wheel would drive the propeller which would provide a forward acceleration to keep the steady state going. However, without the continuous source of power from the wind, the only thing the wheel/ground interface provides is a source of rolling friction.
The Big difference between the two steady states is: One has a continuous source of power (the motor) and one has disconnected from its source of power (the wind). I cannot see any way that you can justifiably say that the two steady states are equivalent. All the confusion, in my opinion, is that most everyone is comparing the two run-up states, which are equivalent. In fact, I believe you could connect a small DC generator to the axle of the wheel in the TT steady state and extract enough power to run a small lamp or some other device. The power is available until the wheel starts to slip. This is something that Swerdna could demonstrate as a science project! I find it inconceivable that anyone could believe that the downwind cart can not only run faster than the wind and with no apparent source of power also run a generator and power a light! This should emphasize that it is a mistake to consider the two steady states as equivalent! Yes a windmill can generate a Megawatt but it doesn’t drag itself along at wind speed as it is doing so!
My conclusion, it may be possible to bring a cart up to winds peed. It may even be possible to force it into a temporary transition to DDWFTTW, but it is not possible to keep it there for any length of time. DDWFTTW, at least as it is conceived here, is not possible.
Of course, I do not expect to convince everyone, especially those who almost religiously believe in this. But I do ask that you show me where my logic is flawed. Thank you!
Note: there may be some typos in here as well, but please try to follow the chain of thought.

 

[A.T.]

But I do ask that you show me where my logic is flawed.

Here:

The Big difference between the two steady states is: One has a continuous source of power (the motor) and one has disconnected from its source of power (the wind).

The direct source of power in both cases is the relative movement between air and ground (the wind). The cart is never disconnected from it.

 

[schroder]

Here:

The direct source of power in both cases is the relative movement between air and ground (the wind). The cart is never disconnected from it.

That makes no sense at all. The tailwind was driving it. It Has disconnected from the tailwind. Do you honestly believe the opposing headwind is now driving it forward into that opposing headwind?

 

[Subductionzon]

That makes no sense at all. The tailwind was driving it. It Has disconnected from the tailwind. Do you honestly believe the opposing headwind is now driving it forward into that opposing headwind?

Do you think that just because the cart is going at the same speed as the wind it is no longer in the wind? I will give you a clue here, it is not in a vacuum. Even at wind speed it is within the wind and can extract energy from a ground/wind interaction. In fact even when going faster than the wind the cart is still within the medium of the wind. Depending on prop advance and frictional forces the efficiency of this cart will vary, I have seen some aero people estimate that the cart may be able to approach twice the speed of the wind.

 

[schroder]

Do you think that just because the cart is going at the same speed as the wind it is no longer in the wind? I will give you a clue here, it is not in a vacuum. Even at wind speed it is within the wind and can extract energy from a ground/wind interaction. In fact even when going faster than the wind the cart is still within the medium of the wind. Depending on prop advance and frictional forces the efficiency of this cart will vary, I have seen some aero people estimate that the cart may be able to approach twice the speed of the wind.

I did not say the cart is not in any wind. I said it is not in a Tailwind. So far, although we have plenty of time, I see nothing that refutes my analysis. A reference to a mysterious magical air-ground interface or a reference to “some aero people” does not amount to anything at all. That is not a scientific argument. As far as the problem of the two steady state reference frames not being equivocal, that is not a violation of Galilean frames of reference either. Do you know why? It is because the DDWFTTW reference frame Does Not Exist! Only the Faster than TT frame can be shown to exist! You cannot equate to something that does not even exist.
I am finished for today, gentlemen.

 

[A.T.]

That makes no sense at all. The tailwind was driving it.

No, the relative movement between air and ground is driving it. It is not a sail boat.

It Has disconnected from the tailwind

It is not disconnected from the air.

Do you honestly believe the opposing headwind is now driving it forward into that opposing headwind?

Yes, just like the 'opposing ruler' is driving http://de.youtube.com/watch?v=9Yt4zxYuPzI&feature=related" forward relative to the ruler. The key is that the opposing headwind is passing by slower than the ground.