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Down wind faster than the wind

Humber, I may not have this right but feel free to correct me if needed and I apologize ahead of time if I don't use the correct terminology. I studied engineering decades ago but am not an engineer by trade.

It appears to me that you feel the cart in the video is in an equilibrium state and if disturbed from that in either direction, will tend back to that state. You also feel that the direction of the propeller's pitch or rotation can be reversed without altering the cart's ability to stay on the treadmill without assistance. Finally, you feel that the incline of the treadmill will affect the position of the cart on the treadmill but not its ability to stay on it.

I may have some of this wrong, this has been a very long thread! Would you please clarify your position on these?
 
Have you paid no attention at all? The answer is obvious:

There is only one line of force flowing from the input, and the velocity of the wheels will be determined by the input and retarding forces. But if the direction of the force is changed, then the velocity differential also changes. This means that the velocity differential averages to zero for the small wheel, but not for the large wheel - the rectified sine wave diagram shows this.

It all becomes clear when you realize that the absolute force that can be sustained is limited by friction, but reversing the direction would change the level of torque. Newton's laws cannot be circumvented. You make the error of thinking that the wheels are the velocities at which they turn. But mice are not elephants: if you change the signs, you change the speed. The situations are not equivalent.

Hope that cleared things up.

Thank you, Thabiguy: now I see my mistake. You do this much better than Humber.
 
Terry never gives his opinion: he is a strictly neutral observer who is there to ensure that no hanky-panky is going on.

I just assumed it was a Penn & Teller kind of thing. Only in this case we don't see Mike (save for the disembodied hands) and we don't hear from Terry. But I think we know who the brains of the outfit is. :D


P.S. The wife particularly like Terry.
 
Sorry if I did not make it clear. This is for the real environment. (0,0) is the trivial case of a motionless cart in still wind. The other
(0, Windspeed) downwind, is the assumed state when tested on the treadmill.
I say that the latter is conjecture. If not, then there must be states between, that have a non-zero dV. What is sought is a plot of that w.r.t. velocity.

I do understand what the treadmill represents. I considered that you could start from stasis with the cart held against the wind, rather than still wind, but there would still be a need to explain that latter case. If you would to start with dV= windspeed, then please do.

Of course a simple monotonic line would do, but where is the support ?

The (0,0) to (0, windspeed) case will then (presumably) have a maxima.
As you say, the treadmill does start from the other position. The fact that it can get instantaneously to windspeed, is one of its curiosities.
This not trivial, because it is of significant consequence regarding the power transfer.
I'd apologize for replying only after 2 pages of posts, except I've been away for only a day, so here goes:

I understand the graph now, but it's still a graph that misses the point. In both cases the cart is "travelling" at wind speed, except in one case te wind speed is zero. So if I interpret your grph literally ten there is no graph. I guess you could make a very similar graph though, and even learn from it, but not how this cart works. Let me explain:

You are comparing steady states in this graph. The terminal velocity of this cart for different wind speeds. The sleady state wind felt by the cart depends on whether of not the wind provides enough energy to overcome the friction in the system. Probably at lower wind speeds, this will not be the case, so dV will be non-zego there. The cart will be standing still or moving more slowly than the wind, simply because the energy is not sufficient.
Above some wind velocity the power will be enough to overcome the friction in the system, and the cart will always end up at (and beyond) windspeed.

Now this tells us that we need more than a certain windspeed (or conveyor belt speed) for the cart to work. But in your case that is assuming too much, since it assumes that the cat works.

I've thought of another, hopefully informative, case.
Let's say we have a very long treadmill in stil air. The treadmill is standing still and we put the cart on top.
Now we start the treadmill, the cart is moved backward and will therefore start feeling a tailwind. We've seen what happens when the cart is in a tailwind: it accelerates forward. As I've explained before, this acceleration is stable and strictly positive up to wind speed.
For us, the observers next o the treadmill, the cart will decelerate and come to a standstil a few metres back onthe treadmill.
At this point we have exactly the normal treadmill situation where the cart is standing still on a moving treadmill, and we've seen what happens then. it starts advancing.

If you do not agree that this situation is completely equivalent to setting the cart on the road in still air and then turning the wind on, please point out where the equivalence goes wrong.
 
Humber, I may not have this right but feel free to correct me if needed and I apologize ahead of time if I don't use the correct terminology. I studied engineering decades ago but am not an engineer by trade.

It appears to me that you feel the cart in the video is in an equilibrium state and if disturbed from that in either direction, will tend back to that state. You also feel that the direction of the propeller's pitch or rotation can be reversed without altering the cart's ability to stay on the treadmill without assistance. Finally, you feel that the incline of the treadmill will affect the position of the cart on the treadmill but not its ability to stay on it.

I may have some of this wrong, this has been a very long thread! Would you please clarify your position on these?

Yes, Mender, that is generally what I am claiming. If the cart is stationary, then it must be true that the force to carry is down the belt, be met by an opposing force up the belt. Being the only option, the up-hill force must come from the propeller, but that too comes from the belt. Because of the gearing, the up-hill and down-hill forces are in series and in opposition, leaving a net force upon the cart of zero, as expected.

If the load on the propeller is increased, say with a finger, then that too will me met by increased opposing force from the belt, but again the net force on the cart will be zero. The limit to the force is not the propeller, but the friction between the wheels and the belt. As can be seen from the video, the cart can be readily moved, indicating that friction is low, and the cart unstable.

The movement forward can be explained by an imbalance in the two opposing forces. Intermittent contact between the wheels and the belt for example, would allow the up-hill component from the propeller to be temporarily greater than down-hill component of direct drag from the belt.
Drive to the propeller from the belt would also be lost during this period, but the momentum of the propeller will keep it spinning for the short periods that it is disengaged, so generating a net force up the belt.

Additionally, when the wheels are connected, it is not possible for the down-force to exceed the up-force, so intermittent contact will be a bias in favour of going up the belt.

The propeller design is not important. It need only be capable of generating a suitable amount of force for a given rpm, (directly related to belt speed), but not so much as to permanently break traction.

If the angle is increased, that will increase the down-force, but also the up-force. The absolute level is increased, so the net force of imbalance likely to be greater, and the cart's progress even better. That is how I see the general operation of the system.

Detailed operation is difficult to define. The friction is low and dependent upon many factors, and may be non-linear. If so, then the wheels need not completely break contact, but only provide more friction when rotating clockwise than counter-clockwise, meaning that no airborne thrust would be required to cause forward motion. In this case, the propeller need only provide drag, and no thrust. Bigger devices may differ in detail, but the general argument would be the same.
 
Mender -- I'll summerize humber's position:

A: He believes the cart is hopping and therein lies it's secret to treadmill success.

B: The treadmill and the street are not the same thing.

JB
 
Thank you, Thabiguy: now I see my mistake. You do this much better than Humber.

So what is your conclusion Micheal_C? Thabiguy's "clarification" supports my argument that Ft= Fc. When reconstructed as in the animation, the wheels operate as I previously stated, to produce the desired 2:1 speed ratio.
The wheel ratios are 4 to 1. (1 turn of the top wheel = 4 turns of the bottom wheel, and the force is a single line, so the gearing affects only that ratio; the V/F ratio as you expect from any gearset.
Revering the direction of force applied to the top wheel, results in a speed of 2:1, also as you would also expect.

thabiguy
It all becomes clear when you realize that the absolute force that can be sustained is limited by friction, but reversing the direction would change the level of torque. Newton's laws cannot be circumvented. You make the error of thinking that the wheels are the velocities at which they turn. But mice are not elephants: if you change the signs, you change the speed. The situations are not equivalent.

Several errors;
1. Signs do not change the absolute level of friction.
2. The second point contradicts the single line of force precept.
3. The average velocity of a circle is zero. Speed is scalar.

You would not expect any gain your bicycle, would you?
 
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So what is your conclusion Micheal_C? Thabiguy's "clarification" supports my argument that Ft= Fc.

You would not expect any gain your bicycle, would you?

Dear god.

Humber - there's a secret message for you!

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Dear god.

Humber - there's a secret message for you!

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I only have to think of you driving the van to prove the treadmill. ROLF

ETA


Mender -- I'll summerize humber's position:

A: He believes the cart is hopping and therein lies it's secret to treadmill success.

B: The treadmill and the street are not the same thing.

JB
No hopping, and no success. The last statement is true. You can determine the level of debate from the above posts.
 
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I'd apologize for replying only after 2 pages of posts, except I've been away for only a day, so here goes:

I understand the graph now, but it's still a graph that misses the point. In both cases the cart is "travelling" at wind speed, except in one case te wind speed is zero. So if I interpret your grph literally ten there is no graph. I guess you could make a very similar graph though, and even learn from it, but not how this cart works. Let me explain:
No problem, this thread does move on.
I am saying that the behavior at windspeed is unproven, so the treadmill cannot be used to demonstrate it, because there is no cause that could explain it. To complete the graph (0, windspeed) to (windspeed, 0) would require that dv falls with speed, but that contradicts the general nature of drag.

You are comparing steady states in this graph. The terminal velocity of this cart for different wind speeds. The sleady state wind felt by the cart depends on whether of not the wind provides enough energy to overcome the friction in the system. Probably at lower wind speeds, this will not be the case, so dV will be non-zego there. The cart will be standing still or moving more slowly than the wind, simply because the energy is not sufficient.
Yes, that would be so with most carts.

Above some wind velocity the power will be enough to overcome the friction in the system, and the cart will always end up at (and beyond) windspeed.
And that is the magical bit. The drag will normally increase with velocity. To achieve "no force at windspeed", would mean that the drag must fall from the position you describe. Negative resistance, at least dynamically.

Now this tells us that we need more than a certain windspeed (or conveyor belt speed) for the cart to work. But in your case that is assuming too much, since it assumes that the cat works.

That is the assumption that is built into the experiment.
I say that the cart does not work to windspeed, but treadmill does nothing to deny or support that, because there is no wind to make the model valid. It is what it appears to be. A model climbing a belt in still air.

I've thought of another, hopefully informative, case.
Let's say we have a very long treadmill in stil air. The treadmill is standing still and we put the cart on top.
Now we start the treadmill, the cart is moved backward and will therefore start feeling a tailwind. We've seen what happens when the cart is in a tailwind: it accelerates forward. As I've explained before, this acceleration is stable and strictly positive up to wind speed.
For us, the observers next o the treadmill, the cart will decelerate and come to a standstil a few metres back onthe treadmill.
At this point we have exactly the normal treadmill situation where the cart is standing still on a moving treadmill, and we've seen what happens then. it starts advancing.

If you do not agree that this situation is completely equivalent to setting the cart on the road in still air and then turning the wind on, please point out where the equivalence goes wrong.

The cart moves backwards until the force to move it up the belt balances the drag with the belt. Devices can be constructed to balance in this way, using friction alone, and in a vacuum. The progress I have already explained, and most recently in reply to Mender.

The tailwind is the issue, if it were there, then the model would be more accurate, and perhaps indicative. It is clear that even pulling back against the supposed wind, creates no significant reaction. It always balances to a minimum. The friction is too low to see a reaction on the belt. It is an equivalent model, so there should be no significant scaling of force.
I have suggested that the cart could be pulled backwards on the floor in still air, and this could show the general forces required, and how they relate to velocity. The bias or rotation of the propeller could be changed to suit. A spring balance could measure the applied force.

You may infer the response from Sol_invictus' recent missives.
 
It's a freakin' mind bender.
sure is. I was intruiged to see one trucking down the road and had that gut feeling 'something must be wrong', but it didn't seem actually spooky. Your cart making headway up a slope against the treadmill powering it is just mental! I suppose I haven't felt such disbelief-vs-awe since I was a small child and got my first Ifel-Tower with a giro on top. We get used to these things that at first appear miraculous and 'break the laws of physics'. Still, I'm not convinced yet.

To be honest I would like to believe that being right and being convincing would be far better than offering my qualifications - but I realize on the internet that's not always the case.
For me it's a part of the drip-drip of many clues that I guess we all weigh up in these situations. Others are the quality of your explanations, the quality of contrary POVs expressed, etc.. Still, I'm not convinced yet.

How'd you like me to post another 30 brainteasers that will do the same? At least when you get a few in, you start to realize that you can't always trust your intuition. Physical intuition is a GREAT tool, but it's a great lesson to learn that it's far from perfect.
It's fine by me if you'd like to post more, but don't exhaust yourself with all this. You seem to be putting a lot into just this one.

I assure you there's no groundbreaking engineering here - just a really fun and bizarre novelty (whose only practical use is to start internet pissing matches).
Ah, so you wanted to start one!:p I wouldn't be so sure about the groundbreaking engineering question (but obviously you know the field). I doesn't have to be an undiscovered physical principle, just one that is very commonly overlooked, for opportunities to be missed in designing new inventions. It might not be a new mode of transport, but out of all these engineers who don't know about it, there might be a good few who would love to have it at their disposal.

Probably just displaying more ignorance here, but I wonder if there are patents that involve the principle. You say you weren't the first to discover it. Still, I'm....

Very unlikely. Perhaps it will indirectly lead to an internet forum troll filter.
No, I can't see that working, ever.:( If you can get an electronic version, it should give me a Retrieve button, to go and fetch my posts after I've submitted really stupid ones. Oooh, and if you manage this with photons, you should be able to travel faster than light. Nice.;)

Oddly, yes and no. I laughed when my father suggested I publish it a couple of weeks ago. Clearly no one in the field would be fooled for a moment by such a silly brainteaser. Since then I've had religious discussions with PhD's and engineering professors that are absolutely certain it can't do what we observe it doing. As a result, I think it is worthy of a journal writeup. I've met with some folks and am just starting that ball rolling. We'll see how it goes.
Good. I wish you luck.

When I originally concieved of this I was somewhat proud of myself (only for the novelty of it). As it happens I'm far from the first to have thought of it, or even demonstrated it. Publishing this will almost certainly cause a stir only because even the experts fall so hard on both sides of the issue. But there will be no prize or award.
Well, that sounds like the right motive. It's fascinating, and would cause a stir and educate other scientists. Still...

Explaining it to people that find it hard to believe is fun. The bad mouthing - not so much.
Ah well. You gain some you lose some. Conservation of mood.

But our intuition tells us that "outpacing our power source" means outrunning the wind. But this isn't the case. We are immersed in this fluid. And this fluid happens to be moving in an advantageous direction to allow us to extract some energy. The paper and spool demonstrates this very nicely. Even as it moves along faster than the paper, there is still paper there to apply the necessary force to continue to motivate the spool.
Yes. But it breaks the law of conservation of prejudice, unfortunately. You didn't notice that. :D

In our theoretical example let's make those spoke sails in the form of a japanese fan that extends and retracts - normal to the flow of the wind.

Alternately, you could build a cart like I show that has a belt that goes all way around (above and below) the deck. The vanes extend on the bottom and fold down on top.
Sure. I could design them myself. It's just that lack of physics knowledge again - for all I know, even if I use gravity to close the vanes, or they do so by pressure against the air somewhere else in the system, or indeed, if they're represented by the constant pitch of a prop, yet somehow doing the same kind of thing, it could all cancel out and give you no advantage, or it could give a net gain sufficient to do the DWFTTW trick. I don't know. I won't know, perhaps until I physically handle something that does it, or I finally get all the bits of the jigsaw sorted in my mind. Thanks for helping.

Again, there is not minimum inherent work done here. We can make that work be arbitrarily small by using the most clever materials and techniques. Folding them normal to the wind doesn't inherently take any specific amount of energy.
I see. But it's not about the absolute measure, is it? Isn't it the question of, wherever that energy is extracted, whether the mechanics have to push negatively against something to do it?

I don't know if this is relevant, but I'll put the question and see. I woke up this morning with this new invention fully formed: I've taken your cart and squished it and also made it radially symetrical, so that instead of running along a flat surface, it runs in a cylindrical pipe. It has spring-loaded wheels in two whorls, three in front, three behind, so as to locate it centrally in the pipe and maintain contact with the surface, one or more of these geared to a prop in the same fashion as per cart. I guess that's clear enough to 'see' it, but I'll draw it if you like. In a lossless mechanical system, I guess we could ignore springs and clearances of prop against the pipe, but no matter. I presume that this also hasn't changed the mechanical scenario too much. We may have different constraints on the air - I have now confined the column, and pressure might be able to build up, say, where in free-flowing air I guess this has a sideways dissipative ability. But I also imagine that such a device located in a pipe with fluid flowing along it would behave very much the same as your cart, outpacing the fluid by some amount. Ok so far?

Now, imagine three identical pieces of pipe with the same fluid conditions, a steady flow, and into one we magically materialize the device (pipe A) and in the other, we pop the same mass without any mechanical advantages of the device (pipe B). A control, C has just fluid.

So my question was going to be where the extra energy comes from for A to have a mass crawling through the fluid, so to speak, faster than the fluid itself? If I compare it with B and C, there is another requirement of energy, too, to propel the mass at the same speed as the fluid. I imagine that from rest it would be accelerated by the fluid, so the fluid would lose energy. I think the mass would approach the fluid velocity and 'eventually' match it. To maintain the same flow rate, I imagine, would require more power from the pump driving the fluid.

But in A, the device is pushing back on the fluid, accelerating to (say) twice the speed of the fluid, and the force, I guess, must translate into a similar reduction in energy of the fluid, and/or more juice to the pump to maintain the same speed.

Here again I am faced with my bootstrap levitation question. I think that doing this has made me more able to say that the cart slows the wind it is immersed in (as would a cart being blown along without a prop). So I guess the question forming in my mind from this is: is it true to say that, although the cart moves faster than the general windspeed, measured in the carpark or whatever, it never goes faster than the wind relative to itself? Does it in fact slow the column of air it moves through proportionally to however much faster it manages to go?

I'm sincerely sorry if I am just being dim again. This does seem in essence like a repeat of my original 'objection' (although put less arrogantly, I hope). I am still having a problem with the idea of the energy source not being 'the wind', but 'the wind relative to the ground'. To me they are the same. They represent different origins to measure stuff by. If we consider ground as fixed, there is only wind to extract energy from, nothing else at all. If we start taking about squeezing the machine between the wind and the ground to extract more energy, we're starting to move origins, it seems to me. We end up trying to measure windspeed relative to the craft, and now we don't have the SAME wind-ground speed, because where the craft is, it is now propelling air backwards. If we measure THAT airspeed relative to the ground, it is proportionally slower. No???

You say:
But for a given gear ratio you can only exceed the true wind speed by a fixed percentage. Remember that this is extracting energy from the true wind over the ground - not the wind over itself. We could in theory increase the gearing and therefore the speed indefinitely, in a perfect (lossless) world. But in the real world there will be a real limit.
What do you mean by 'the wind over itself'? If I am travelling at 200 mph in a 1 mph breeze, what about the headwind of 199 mph? You seem to suggest that we could continue to accelerate in a lossless world (I want one of those) with super gearing, but how can you not be lumping the 199 mph headwind into the description of 'loss' here to still extract energy from a 1 mph ground-windspeed?

I'm sorry, but I keep coming back to my problem. Maybe you can help explain it with another expression of it. I understand (roughly) the idea of the tacking. It seems to me that a land yacht can gain more and more energy because it is moving across the wind, and has an inexhaustible supply of it to tap. It picks up momentum by actually slowing the wind, yes? But it doesn't matter, because it moves on to another bit of wind to the side. I can translate this to a prop blade moving across the wind, but here it passes back to its original position with the period of rotation. Now, it may be that in that time a new piece of air has arrived from the rear, when the cart is going at lower than windspeed, but at windspeed it is now spinning through the same air as before, which it already extracted energy from and slowed.:confused:

Or maybe you can help me get beyond this by examining my earlier scheme (if you haven't done so already). If the cart on the treadmill slows rwt track (for whatever reason), its wheels turn slower, don't they? This was powering the prop, so doesn't it drop in power output? Doesn't that mean it doesn't move 'up' the tread as fast? Doesn't that give it less speed at the wheels? Etc. Of course, it's movement backwards through the air represents some kind of source of energy that might help it move forwards again, but...ugh?

Or this: A body in a stream of atoms, that's all we have (ok, next to stationary atoms). Atoms hit body. The body is mechanical and doesn't just get hit, absorbing energy to reach the speed of the passing atoms, but throws atoms backwards, changes their momentum. Still, to power whatever it is that's doing the throwing, it has to brace itself against something, (conservation again), and all there is to brace against is the same flow of atoms or the stationary ones. At atom-flow-speed, it has the motionless body of atoms next to it - how does it use that, or its relative velocity wrt the flow? That's now going at atomspeed backwards wrt the body and the flow. You can't shove a generator in the gap and let it wind up your speed, surely? Those 'stationary' atoms can only drag you.

If we have a wheel with the old vanes half speed below the axle. Isn't there something about the moment and pressure (I think someone mentioned this earlier), that means that even if the vanes are moving at v/2, and thus have a following wind of v/2, in order to increase the speed of the whole wheel (because it is rotating over the fulcrum of its contact with the ground?) would require more force than a v/2 wind can give it. If I push my bike wheel below the axle, it may go forward twice as fast as the point I'm pushing, but it's an inefficient lever compared with pushing the axle.

:boggled::boggled::boggled:
 
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Many good questions and observations. I'll answer as many as I can over my pop-tart. Stay tuned.
 
I only have to think of you driving the van to prove the treadmill. ROLF.

The best part about you is that you get absolutely everything wrong - even your insults. I didn't introduce the van (that was some other poster you've confused with me): I just answered a few questions you asked about it.

It's almost too perfect.... hmmm.... spork, is humber your sock puppet? Are you just trying to create dissent so you can get on mythbusters??
 
Or maybe you can help me get beyond this by examining my earlier scheme (if you haven't done so already). If the cart on the treadmill slows rwt track (for whatever reason), its wheels turn slower, don't they? This was powering the prop, so doesn't it drop in power output? Doesn't that mean it doesn't move 'up' the tread as fast? Doesn't that give it less speed at the wheels? Etc. Of course, it's movement backwards through the air represents some kind of source of energy that might help it move forwards again, but...ugh?

Let me try to help with this part. The cart reaches a maximum speed, which is determined by friction, the efficiency of the prop, etc. At that maximum speed it is not accelerating, which means that the total force on it is zero. There is a force pushing it up-tread (to the right, let's say), and some forces that total to the same (like friction in the wheel bearings) pushing it to the left.

Now suppose the cart moves a little slower. Several things happen: first, the prop rotates more slowly (which decreases the net force to the right as you said, all else being equal at least). But second, the apparent headwind decreases, changing the efficiency of the prop at a given rotational speed (and I think increasing it, although I'll have to think harder to be sure). Third, friction in the wheel bearings decreases (which increases the net force to the right).

So the net change could be in either direction - one needs to do a more careful analysis and add up all those effects. Video evidence confirms that the maximum speed is stable (i.e. the forces always accelerate the cart "towards" that max speed).

Does that help?
 
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John, I'll just address two of your points that seem, to me, to put the problem in a nutshell:

Here again I am faced with my bootstrap levitation question. I think that doing this has made me more able to say that the cart slows the wind it is immersed in (as would a cart being blown along without a prop). So I guess the question forming in my mind from this is: is it true to say that, although the cart moves faster than the general windspeed, measured in the carpark or whatever, it never goes faster than the wind relative to itself? Does it in fact slow the column of air it moves through proportionally to however much faster it manages to go?

No, it indeed goes faster that the "wind" around it: an imp sitting on the cart will feel a headwind. Look again at my little cotton reel: it is really going faster than the piece of paper that is pushing it. Once you have understood that the reason for this is that the piece of paper is always pushing at a specific part of the reel that is going slower than the centre of gravity of the reel, you can transfer this idea to the cart. I know it seems weird to say that a specific part of the cart is always going slower than the the centre of gravity of the cart, but this is what the propeller is effectively doing with respect to the air.

Think for a while on how a propeller works. I like this explanation: "A propeller moves through the air in a similar manner as a mechanical screw moves forward through a piece of wood". Imagine the propeller burrowing through the air: how far does it move in one complete rotation? If you think of the propeller as a screw, you'll see that it moves the equivalent of the width of the thread of the screw. This is the "pitch" of the propeller.

The gearing of Spork's cart is deigned so that the effective speed of the propeller through the air, defined by its pitch and its speed of rotation, is slower than the speed of the wheel on the ground, defined by the diameter of the wheel and its speed of rotation. This is a fixed ratio, like the fixed ratio of the speed of the point on the cotton reel to the speed of the centre of the reel.

I'm sincerely sorry if I am just being dim again. This does seem in essence like a repeat of my original 'objection' (although put less arrogantly, I hope). I am still having a problem with the idea of the energy source not being 'the wind', but 'the wind relative to the ground'. To me they are the same. They represent different origins to measure stuff by. If we consider ground as fixed, there is only wind to extract energy from, nothing else at all. If we start taking about squeezing the machine between the wind and the ground to extract more energy, we're starting to move origins, it seems to me. We end up trying to measure windspeed relative to the craft, and now we don't have the SAME wind-ground speed, because where the craft is, it is now propelling air backwards. If we measure THAT airspeed relative to the ground, it is proportionally slower. No???

The cart isn't propelling air backwards; it's moving through the air. The speed of the air relative to the ground stays constant.

It can be misleading to talk about "the wind". I prefer say that the energy source is the movement of the air relative to the ground. We can't extract energy from the motion of one thing (absolute motion has no meaning anyway); we can only extract energy from the relative motion of two things. As long as the cart is in contact with both the things (air and ground), there is the possibility of transforming this motion into a faster or slower motion, in theoretically any direction we please. That's all gears, pulleys, propellers and other such mechanical devices do: transform motion in one direction at a certain speed into motion in another direction, slower or faster than the original speed. It doesn't matter at what speed the cart is running: the speed of the air relative to the ground stays the same. Remember: we are not extracting the energy from the relative speed of the cart and the air, it's always coming from the relative movement between the ground and the air.
 
The speed of the air relative to the ground stays constant.

Unless I'm misunderstanding you, the above is incorrect.

The propeller of the cart definitely slows the speed of the air relative to the ground -- that's where it gets it's energy from.

JB
 
Yes, Mender, that is generally what I am claiming. If the cart is stationary, then it must be true that the force to carry is down the belt, be met by an opposing force up the belt. Being the only option, the up-hill force must come from the propeller, but that too comes from the belt. Because of the gearing, the up-hill and down-hill forces are in series and in opposition, leaving a net force upon the cart of zero, as expected.

I agree that the treadmill is providing all the energy that is being put into the system, but I'm curious about how you see that energy being dissipated. Obviously some is lost to friction in the various bearings and mechanisms. If the force produced by the propeller is matched by an equal drag on the belt, the cart would experience a net drag and move off the belt unless the treadmill were tilted forward to compensate for that. As the speed of the treadmill is increased, the amount of drag would also increase and the treadmill would need to tilted even more to compensate. Why is this not happening?
 
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