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You are lying right now. Not only did I state the absolute truth about Prof Whiteman, but I have a direct witness that will attest to the same. You do not get to call me a liar simply because you don't like the truth. This seems to be the same approach you take with science. Real world results don't count if they don't match with your intuition about how things "ought to be".
So I'll lay it on the line... You are wrong. You have been wrong from the start. You call me a liar when all evidence is clearly to the contrary, and you claim to understand things about this cart that we don't.
If your "theory" is any damn good at all you should be able to predict the outcome of a test we can run on our treadmill, and it should differ from what our understanding predicts. So I challenge you to make such a prediction and I will test it and post the results. Otherwise you effectively admit you're the troll that we all know you to be.
So make a prediction - a short concise prediction that is supported by your theory - or STFU (because science is nothing if it can't make predictions).
Sorry, Dan, but maybe you should think about those sentences again.
ETA: Sorry if that was a bit curt, but what I mean is that I don't think that asking for Humber's testable model is any less feeding the troll than a longer analysis of his writings here, a thorough criticism, trying to have a conversation with him, as H'ethetheth does, or asking him to provide answers to qute a number of questions raised by his assertions that he hasn't answered.
I also think it is fair, given the controversy around the issue and the number of newcomers to mechanics who happen upon this, to keep up the pressure on him. I'm open to the idea of us all ignoring him, but even then there's no certainty he won't respond to that by posting more.
Probably someone should nail him to a large treadmill and ask him if he's enjoying the breeze.
Humber is nothing but a troll. His writing is pure gibberish and doesn't deserve to be analyzed because the analysis is always invalid in his made up world (ie: tethers upset the balance so can't be used to measure force).
Humber won't submit to any test we propose so now it is up to him to propose a test between his reality and ours that can be verified in the real world. Until then, he is out of the conversation as far as I am concerned.
The cart operates in the differential motion between 2 mediums: a hard flat surface sometimes referred to as a road or a belt and a gas referred to as the air or wind.
If the difference in velocity between the two mediums is the same, what measurment can you make to differentiate between being on a treadmill or a road?
I'm far from an expert, but I think if you ave either a variable pitch propeller, or a multi-speed transmission, you can run something like this at any angle to the wind. There are two modes of operation: Wheels drive propeller, as in the DDWFTW, and propeller (or, more correctly, wind turbine) drives wheels. It can do two things a sail-propelled vehicle can't: Go directly down wind faster than the wind, and go directly upwind.
I suspect, but I'm not sure, that at an angle to the wind, upwind or down, a sail is more effective. A sail certainly has an advantage in simplicity: There are no gears, chanins. bearings or drive belts. This should make the sail more efficient, as long as you are far enough off the wind for it to act as an airfoil, not a simple drag device. The wind turbine drives wheels mode should move it in any direction, provided the wind turbine is allowed to pivot so its axis is aligned with the apparent wind. However, downwind, it will be limited to less than the speed of the wind in this mode. I suspect that in this mode the downwind component can't exceed wind speed. I am not nearly knowledgeable enough in aerodynamics to know what the optimum angle would be to switch from wind turbine drives wheels mode to wheels drive propeller mode, but clearly wheels drive propeller is faster downwind.
The folks hear and on other forums who know more about aerodynamics than I do seem to agree that a sail is more effective given a sufficient angle to the wind, but I really can't say at what angle the sail becomes more effective, upwind or down, or how much performance you lose with the propeller/wind turbine at an angle to the wind.
It shouldn't matter, if other factors are equal, which they probably won't be. A road is likely to have a rougher surface than a treadmill, which will increase rolling friction and make it somewhat slower. OTOH, the excercise treadmills people have been testing on are too short to allow the cart to self-start, or to achieve full speed without running off an end. The fact that the cart will move faster than the belt, or maintain position uphill demonstrates that they can move faster than the wind, but not really what the maximum speed is.
The trouble with outdoor tests is there are a lot of variables that are hard to control. Real winds gust and change direction, real roads are rarely completely level, and the wind rarely blows exacty aligned with the road. A large parking lot or, better, a dry lake bed could help with the surface, but doesn't stop the wind from gusting or changing.
(1) It's very difficult to control the circumstances, and
(2) it's virtually impossible to do it in such a way that a video will satisfy skeptics.
For instance, I would guess you weren't satisfied with the video of the big radio-controlled cart outside with the wind sock.
(3) The treadmill is equivalent to the point of being identical, plus it's easy to control, and easy to present.
The only problem is that not everyone understands that (3) is true.
(subject was building a push-driven analog of the DWFTTW cart by replacing the prop with a large screw)
Now that I think about it, you could just bend a wire coat hanger into a helix (by bending it around a rolling pin or something) then bend the ends to form the shaft ends.
Undoubtedly my post here will cover ground that has been well covered in this thread already. However I'd like to express my understanding of what is going on here in my own words. Please feel free to skip this post.
My first level of understanding happened when I realized that it wasn't an obvious violation (to me at least) of a physical law that restricted the energy gained by a propeller to less than the energy lost by pushing a propeller through the air. So this thinking coupled with the idea of the ice boats tied together with a piece of rope at least made me think the thing was plausible.
But then I hit a wall. What's going on here? For the propeller to spin and provide energy to the wheels there needs to be a pressure differential through it to drive the wind flow. But if the air is moving at 10 mph and the propeller is moving at 10 mph where's the air movement coming from to make the propeller spin?
That's when I developed my next level of understanding. When a propeller spins, the air is pushed through it faster than the surrounding air. The propeller creates its own environment. Initially I ignored this because it seemed like it was too small an effect to worry about and because it made things complicated. But to actually move faster than the wind the propeller must have air flowing through it to provide drive to the wheels and the only possible reason that air can flow through the propeller faster than the surrounding air is moving is that the propeller is affecting the air that is flowing through it.
At first this seems like it is violating the conservation of energy. The propeller is not only sucking out energy from the passing wind but it is making that wind blow faster. I think the answer here is that the net energy of all the wind flow is decreased by the propeller. Not only is the air moving through the propeller part of the energy balance but change in velocity of the air that is near the propeller is part of the energy balance.
Unfortunately, this qualitative level of understanding doesn't allow me to make any cool predictions including predicting that faster than downwind speed is possible. It does predict that the air speed through the propeller in net should be faster than the air that is making the propeller spin if faster than down wind speed travel is possible. This is sort of anti-intuitive in that one would expect that when one derives energy from the moving air the air should be slowed. The difficulty is that the net air flow might be difficult to measure since the air is churned up near the propeller and couldn't be easily accurately summed (possibly the sum of the squares of the velocities is what is relevant). I wonder if there's any computer modeling of propellers on the internet. I think I'll go look after this post.
First of all, let me say I appreciate you taking the time for this long reply, humber.
I accept it, but I'm having a hard time believing it when you say things like:You are saying here that none of the velocities involved influence the dynamics of the problem. I have a hard time believing that you believe this, as it woud actually preclude anything at all from happening. This is perhaps true on a cosmic scale, but then, we're not discussing celestial mechanics here.
No problem, H'ethetheth. All the velocities are too low to consider any effects that are not entirely local. The traveling object may as well be at your feet from that standpoint. Of course all of the usual laws of motion apply. I am telling you that all you need consider is the same physics that built the Concorde and your car.
I'm not sure, but I would rate your claim above close to 100%.
No. qualitatively. If taken literally, as a test of physics, then breaking the drag barrier requires a lot more energy than is normally considered available to the cart. This would mean that the gains from "equivalence" would be large. You would know about them. Your instruments would go nuts and you could never be sure of them because they may be moving a little faster relative to the moon or something. Not just for the treadmill, but all of the time. These forces, if they can be mustered, are tiny.
Some gravity devices are so sensitive, that motion of people in the surround ing rooms can be detected. Not for the cart, though.
Do you know that in topology, it is possible to cut a sphere into pieces like an orange, and then re-assemble it, so that its (solid) volume is significantly increased? Only on paper, so far.
I cannot tell you that, of course. In the last few pages of this thread, you will find him saying (something like) people believe it or not, and when that happens they are convinced.
a.k.a "Once people try our sausages, they never turn back"
The videos do not offer much evidence to begin with. One poster on You Tube, and probably here as well, said that the treadmill was evidence that the belt could make the prop. spin. That is about right.
I would add, without sarcasm, that if you replaced the treadmill with a fishtank, a goldfish would tell you as much about windspeed travel.
I am sure that a lot of what you know is solid, H'ethetheth, but it is the scientific method, and particularly experimental procedure that is not well understood at all. The errors are much more fundamental than you seem to appreciate.
As I have said, and it is not a matter of whether Newton's laws apply or not.
They always do for any objects you have to worry about in this case, but it is not a frame or anything like it. That is certain, I know nobody who would think otherwise.
However, when asking such questions, be careful that you get a commensurate answer, and that the answer given is not to another question.
A 50W heater consumes 50W? Generally true, but if you ask an expert, they may not want to say "yes" because they know that it is not quite true. It depends upon how you measure it, and so forth, and do you consider all of it being dissipated? What if the heat bends the chassis, and that stores some in an elastic component? Later perhaps, it will be released as sound. Correct only when you know all of the details.
Momentum cannot simply be arithmetically traded along with velocity vectors. There are laws of thermodynamics that do not allow that to happen. Perhaps you think I am being too dismissive in my rejection of frames, but if you take a look at the relevant equations, the differences would be tiny, if available to you. To worry about that trifling putative error, while accepting that an object can travel without KE, is a very bad bargain. I know of no circumstances where this is done, save for static models. Nothing in the real world does this. The real cart cannot give up or acquire KE at will, so the model cannot make its KE relative, and so disappear. Where does it go? Does it warm the air?
That would result in losses that could not be later recovered. See Carnot Cycle etc. Only figuratively is this vanishing KE possible, but the treadmill is said to be a real world test, a demonstration of real world performance.
That's fine, but regardless of who is right, your position is so alien to me that I'm having trouble putting myself into your train of thought. And you see, I'd like to. That's why I asked that question.
My position is not alien to you, you just think so. The change to Sporkian physics is one of "ah ha" but it is faux. Turning back on that new "insight", may be difficult, but don't put support for these ideas on your resume. Trust me on that.
But that's not what's going on here. The treadmill is not really a simplification of the dynamics. For a sufficiently large treadmill the dynamics become indistinguishable, and that's according to Newton and Einstein.
The treadmill is worse than the fishtank. To talk of border conditions is pointless, as the entire edifice is flawed. Really.
Despite that, you can always start a discussion with "assume that X is sphere.." The infinite version would be indistinguishable from a larger, but equally flawed model.
Noted. Thank you for offering me this window to your perspective. I'm going to have correct you, however: The wind we say is generated by the treadmill is not that. It is the airflow experienced by an observer standing still on the moving belt. I'm pretty sure you will feel this is preposterous, but I'm just telling you so we are talking about the same thing at least.
Yes, that is what I call the "other" wind. To be at all accurate, the belt should do it all. If it were a fan, you would expect that to be the case. The wind does not appear unless travel is present. Now, just on that point alone, the wind is no longer the independent force that it is in the real world. The treadmill wind does not blow unless the person experiencing it is moving. That depends upon how well the object is coupled to the belt, and that is via friction, so the wind is related to friction and witness velocity? This situation is either completely absent, or only so under specific circumstances in the real world.
One such case perhaps being actually tied to a treadmill belt, but not when it is a metaphorical road. Yes, if you break friction with a real road, you will be blown away, but then you are flying and have KE, and velocity etc. The natural wind force is not a function of the friction to the road, in the way it is on the treadmill. That is a huge difference, and is one thing that makes the model do what it does.
[/QUOTE]
Yes. Trust me on that.
It was a rhetorical question, H'ethetheth. Could you arbitrarily forget about pressure in general? What of environmental chambers? Don't you need to take into account that the lower the pressure, the worse become any thermally conductive paths? If you are not interested in thermal conditions at altitude, then you may leave it out, but that is a justified exclusion.
Can you leave out momentum exchange for a device that is entirely dependent upon it, such as a propeller? That's a hard sell.
If you do, then that must be justified by theory. Its absence must either be of limited effect, or otherwise accounted for. Simply wishing it away is not allowed.
Actually, the top-left figure represents my initial understanding of the cart. However, this is an incorrect understanding, because this is a cart that will never achieve wind speed. It's important to realize that the prop never acts as generator. This is precisely the counter-intuitive part.
Not so, but also correct. It will never reach windspeed. What I have drawn is how the cart works at low speeds. That is also how it works all the time. Some criticism has much softened the "backward" prop idea. BUT do not stray from the treadmill. It is a fishtank, so let's forget the real cart.
The top right figure is correct, and it is almost correct for the road case, except it is more difficult to interpret how the wind supplies the power. I realize that. You can think of it like this perhaps. In the acceleration phase, the wind inputs enough power to get it up to wind speed. When the cart has this much kinetic energy the combination of
(a) the rotation of the propeller and
(b) the lack of headwind
ensure that the blades still have the capacity to accelerate air backward. The resulting force makes up for the small losses in friction. In other words, if you draw a free body diagram of the cart, the two will be identical: The cart experiences a forward force on its propeller, and a backward force where the wheels meet the road.
Yes. I did say incomplete. I decided that I had no hope of changing minds, so I dropped it. I dragged it out of a USB stick to post to you. Moreover, it is illustrative. It shows just the primary differences of energy flow.
You forgot (c). The work that need be done.
The cart is a wholly different matter. This about the treadmill, and its value as a scientific tool. I do not look at the other groups, but I think misdirection leads to discussion about the cart in general, and the treadmill climbing effect, but not its principles. That is what I am doing,
The cart on the treadmill does no work. The propellor cannot exchange energy just because it is spinning. As I have said, take a small propellor in your hand against the wind. It will spin freely, but there is no work until you provide a load. Too much and you stall it, so no work. Too little and no work is done. Velocity is traded for force to do work. That transfer works both ways. A big engine makes no difference if the propellor cannot deliver its work to the air. All of this is basic physics. See Maximum Power Transfer Theorem. That pdf I linked to, is a mine of information about the relationship between the prop an its generator/motor equivalents.
The wind, through momentum exchanges energy with the propellor, via air.
That cannot be replicated by spinning a prop at the same rpm in still air.
In the cart's case, there is not a load that it can work against ( it does not move) then there simply will be no energy transfer. No significant thrust. Same cart in real wind is otherwise, there is moving wind and there is a load as the cart accelerates away. That fact coupled with the way the propeller is connected to the wheels, and the low value of friction, all conspire to make the cart sit there. It is nothing. It says nothing about travel at all. That is why user interference, simply placing it there, is "allowed". The system does not give a damn. Forget about frames, that is flannel. It is a normal (yet perhaps complex in detail) textbook statics and dynamics problem. A problem of working dynamics, not simplified models.
If the cart does travel fast, and I do not see why not, it has nothing to do with frames or the treadmill. I can offer you a much simpler explanation if you are interested, but I only have limited time, so please don't waste it.
As for being at windspeed, while ignoring the means of getting there? Do you study an egg by first scrambling it?
There is an mathematical attempt to explain post wind conditions.
Think so? Might not the very same line of argument prevent the cart from getting there?
A very interesting topic which, sadly, I have not been able to read in its entirety. Hopefully my thoughts haven't been repeated earlier.
Although I realized immediately that it was possible in principle to build a faster-than-wind machine, it wasn't clear that this particular machine would work until I thought about it some more. I think I have a simple argument why the machine works without resorting to anything tricky like vector analysis.
Let's assume we have a machine traveling exactly at the wind speed. We first ask how much work is being put into the vehicle over time. The definition of work is force times distance, so over some particular duration, the vehicle has traveled some distance, and the roadway has exerted force on the vehicle over that span. As such, the vehicle receives some finite, non-zero amount of work.
Based on conservation of energy, we know that the propeller can't perform any more work than that if there is no other energy source. So how much is it? The answer: exactly zero. Since the air is not moving relative to the vehicle, the propeller does not perform any work on the air, even with an arbitrarily large force. As such, it does not violate conservation to argue that the forward force from the propeller can greatly exceed the backwards force from the roadway--hence, the vehicle accelerates.
Of course, as soon as that happens, there is a net wind velocity, and the propeller now starts doing work. However, this amount is small at first, and the propeller can still exert a large force.
Given that the idea is plausible, let's look at it in more detail. Here's an equation for balancing work, taking efficiency into account:
[latex]
\begin{math}
\begin{subequations}
t = \mbox{time duration}\\
V_a = \mbox{air velocity}\\
V_g = \mbox{ground velocity}\\
F_p = \mbox{propeller force}\\
F_g = \mbox{ground force}\\
E = \mbox{system efficiency (number from 0 to 1)}\\
F_p V_a t = F_g V_g t E
\end{subequations}
\end{math}
[/latex]
Now, let's assume we're at steady state, with the vehicle neither accelerating nor decelerating, so that Fp = Fg. Also, if the wind velocity is Vw, then Va must be (Vg - Vw). Our new equation, after rearrangement and canceling, looks like this:
[latex]
\begin{math}
V_g - V_w = V_g E
\end{math}
[/latex]
The fraction Vg/Vw is just what multiple of wind velocity we can achieve, and here it's expressed in terms of system efficiency. As you can see, you don't need a particularly high efficiency to achieve noticeable gains: a 33% efficient system will get you 50% faster than wind velocity. A 67% efficient propeller system can go 3 times as fast as the wind.
So in conclusion, it's clear that the vehicles shown are not just plausible, but downright probable. A simple, inefficient mechanism is enough to demonstrate the effect.
As for the two boundary layers you (correctly) drew, I hope you will agree that in both cases the forces (per unit area) acting on the surface and on the air are identical, as action = -reaction.
Propellers can propel just fine when stationary, humber. Propeller aircraft do not need a push. And the cart does accelerate, so clearly the prop is producing thrust.
Does an outboard motor, drive a boat placed upon wheels in air, as well as it does in water?
Yes, you are right. But look at the energy path. In the real cart, the boundary exchange is there, but insignificant as far as the cart is concerned. The boundary is a system return that does not bother the cart too much.
The major flow is through the, propellor to the wheels and ground. Without this, the cart goes nowhere.
In the treadmill, there is also a boundary exchange. Does it get to the cart, or is it just a way of wasting energy? The primary path, the mechanically conductive path, from the motor to belt to wheels to prop to air is not sound. The last link is too weak, so energy cannot flow. Perhaps if the cart is dragged back, that would drive the prop, and so make good the circuit, but of course it does not. That test it will fail.
(1) If that wind is there, the cart must be moving down the belt. To avoid this fate, the cart would then need to accelerate against the belt, back to where? The top of the belt? "Where" is that exactly? Is windspeed a location?
(2) The entire power chain is choked by the friction to the belt. No friction, no power taken from the motor. It is not zero, but very low. That is not the case with a real road.
I was surprised to read that too. I guess he got somewhat callous.
Don't worry, it's neither (other than the videos, that is).
Not the insult, but its childishness, H'ethetheth. I really don't care. You saw how I taunted him over the professor. I told him outright what I thought. I gave him time to recant, he did not. He does not. If the argument is about personalities, and one traduces someone without right of reply, then I can do back. It is not acceptable at that level, that is beyond the usual bounds, even for knockabout discussions.
Forget about him. I was alluding to the way he argues his point. Either canned offerings or "stupid troll".
People like Spork bring out the worst in me. If I attack him, I am doing that, and not to deny his arguments. He lies, so I tell him so. A lot of promises, and so-called challenges and analysises that are either rubbish, or never actually delivered. His evidence may not be faked, but it is rubbish, and that shows complete contempt for his intended audience.
I hope I've at least clarified some of the differences between what we think and what you think we think.
As an aside, consider the company you keep. How the arguments are built.
Tsig wrote "this is not about belief". To most here, that is cryptic it seems, but to me, it is crystal clear. Science is not about belief, but knowledge, evidence and reason. So, where is it? It is bad from to offer, or to ask for anything else. It need not be dry, but that is the underpinning.
Don't let hot air make you say that you are 'just' an engineer.
ugh, I realize now that at least part of my understanding is wrong.
A propeller that was just sitting in non-moving air would spin indefinitely if my previous understanding was correct. OK, I realize now I need to think about the wheels some more and the part they play.
ETA:
OK, now some of the stuff people have been saying is beginning to make sense. As long as there is a mechanism to hold the cart in place the wheels can derive energy from the ground going by. So the energy the wheels derive is transferred to the prop which generates thrust to hold the cart at a steady speed at or somewhat above the ambient wind speed. So the wheels are actually driving the prop even though the cart is moving faster than the air that is hitting it.
ETA2:
I like my new understanding. I think based on it, even if I didn't tend to believe Spork et al, I would predict that faster than down wind speed is probably possible. Assuming low friction wheels and low mass, the cart is going to come very close to the down wind air speed by itself. There is very little drag on the cart to go a little faster than the down wind speed. Drag being proportional to the square of the velocity and all. So now all that is required is that the propeller be able to produce a little thrust to get the cart above the down wind speed when it is driven by the wheels which will provide drive as long as there is enough thrust to hold the card from being pushed back to just wind speed.
ugh, I realize now that at least part of my understanding is wrong.
A propeller that was just sitting in non-moving air would spin indefinitely if my previous understanding was correct. OK, I realize now I need to think about the wheels some more and the part they play.
On the downwind cart the wheels provide the torque to spin the prop - not the other way around.
humber: you sure spew a lot of words, but it seems your brilliant theories aren't able to produce any predictions - so they really aren't scientific theories - huh?
Yes, I just was slow to understand that. I know several people have said that in several different ways. I just didn't see how it was possible previously.
"We all" also define what me mean by wind: it is the motion of air and a surface relative to each other. By this definition, the treadmill creates wind. You, on the other hand, are not able to define what you mean by wind. And not able to answer any other of the many simple questions posed on you. Pathetic.
This was so funny a had to respond to a troll. The variations in the wind, current and other circumstances are the very essance of sailboat racing. You could ofcourse organize races in gigantic swimming pools with fans, there you could control the circumstances.
Can you tsig please specify, how exactly in your world are the circumstances controlled when sailboats are racing? Or how do they need to be controlled= I'd love to hear this one.
I would suggest twoother reansons:
1) Because it has already been done and presented with a cart that was desinged to run on a street. This cart is designed only to demonstrate and validate the possibility of running faster than the wind. The cart is designed to run on a treadmill and has no steering and therefore cannot run on the road unassisted (or unmodified to facilitate steering).
2) Because the test provides nothing to add to the tests allready made and the result is obvious to the builders of the cart.
It's like you saying bees can't fly, why are you not providing me with a video were bees are flying!
BTW, I have also previously noticed, that among "skeptics and critical thinkers" there are always a few bad apples among the crowd that can't make a difference between skeptic arguing and plain idiotic insisting.
Actually, how "direct downwind" must the wind be? That is, what angles not directly in-line with the cart's movement are allowed to still have it work properly?
Based on experience on sailboat performance, I would say the cart will work fine as long as you at least attempt to go straight downwind in any practically possible way. If you deliberately run like 45 degrees to the wind it probably won't work. I doubt that anybody dares to say where the absolute limit would be. Anyway the normal "real-life" variations in windspeed and direction will not be a problem.
The situation is comparable to sailboat that is "oversheeted" or "streering a bit off the optimum". The performance will suffer, but not that dramatically if the errors are small. If we rig the cart to do say 1,5 times windspeed, and driving a bit off would result in say 20 % performance loss (a LOT in a sailboat) it would still do 1,2 times the windspeed, that would be quite enought to demonstrate over windspeed performance beyound doubt.
Another analogy, though not correct if you do the real physics and math, is that a turbines power is directly comparable to the "sweeping area" of the blades. I would assume this would in a sence be true for propeller also. Therefore if the angle of the prop is a bit of the change in "effective" area diminishes just by a fraction first. Just think of it as a simple trigonometry problem, calculate the "effective area" of the prop. And I stress, this is NOT correct physics, just a way to think of it, that should be analogious to some extent.
ETA: Also you could calculate the component of windspeed that is in the direction where the cart is moving. That would give you a rough idea. This is the same thing as above. An ofcourse not taking account that the propeller efficiency will also suffer when angled.
OK, I think I have my head wrapped around the cart in the open OK at this point (rolling ferris wheel was a good example), haven't translated that to the treadmill example to my satisfaction.
So in the open air case its all about air coming in from the back and hitting the prop (so to speak), as opposed to the prop spinning fast enough to suck air in from the front (to speak grossly).
I think then there's a simpler analogy to use for the cart in the open- that of a sail near the front of the cart, cart is going at just about windspeed, and then some mechanism on the cart just moves that sail towards the rear of the cart fast enough that the sail 'sees' some wind from behind the cart. The sail 'sees wind' from the rear, and the mechanism pushing the sail rearwards of course pushes the cart forwards. Get 2 of these sails on a moving belt driven by the wheels, fold 'em down or shield them from the air as they move forwards on the bottom part of the belt and I think the analogy holds nicely.
(I'm deliberately not phrasing this very scientifically because then it wouldn't help to explain it to someone else)
You can then think of the surface of the propeller (let the 'point' where an individual bit of wind hitting the propeller slide across the propeller, the wind doesn't care) of as a sail that's moving backwards. Look at it this way- if you spin the prop, and shine a laser pointer on the prop, it looks like the red dot is moving backwards relative to the cart.
Now hopefully I don't have that completely backwards.
You're thinking of the wind only pushing from behind. In fact the cart is always in the air, and it's working its way through that air. There's air behind the cart, but there's also air in front of it. The propeller of the cart is screwing its way though that air like a screw through a piece of wood.
You're right that the prop is like a sail moving backwards relative to the cart. A state of equilibrium will be reached when the pressure of the air behind that "sail" and the pressure in front of it are equal. At this point, the "sail" will be stationary with respect to the air and the cart will be moving forward with respect to the sail, so it'll be going faster than the wind.
The fixed-vane tumbleweed won't go forwards on a treadmill: JB posted a diagram somewhere (sorry I can't find the link now) which clearly shows that when the fixed-vane tumbleweed is going at the speed of the wind, the forces on it are already in equilibrium. A movable-vane tumbleweed could theoretically work, if it could be made efficient enough to overcome unwanted drag and friction.
The treadmill is worse than the fishtank. To talk of border conditions is pointless, as the entire edifice is flawed. Really.
Despite that, you can always start a discussion with "assume that X is sphere.." The infinite version would be indistinguishable from a larger, but equally flawed model.
I just posted a link to a site that very carefully shows how Newton's laws precisely falsify this. If what you said above is true, Newton's three laws are false. There is no point in anyone discussing this beyond that point.
The infinite treadmill is completely indistinguishable from a steady wind, down to the velocity distribution of air molecules.
You're thinking of the wind only pushing from behind. In fact the cart is always in the air, and it's working its way through that air. There's air behind the cart, but there's also air in front of it. The propeller of the cart is screwing its way though that air like a screw through a piece of wood.
You're right that the prop is like a sail moving backwards relative to the cart. A state of equilibrium will be reached when the pressure of the air behind that "sail" and the pressure in front of it are equal. At this point, the "sail" will be stationary with respect to the air and the cart will be moving forward with respect to the sail, so it'll be going faster than the wind.
The fixed-vane tumbleweed won't go forwards on a treadmill: JB posted a diagram somewhere (sorry I can't find the link now) which clearly shows that when the fixed-vane tumbleweed is going at the speed of the wind, the forces on it are already in equilibrium. A movable-vane tumbleweed could theoretically work, if it could be made efficient enough to overcome unwanted drag and friction.
Yes, I've left off talking about the air in front of the prop because I'm just trying to most clearly picture how energy is being added to the system, that's always the key to the whole thing.
And yes, it was the moveable-vane tumbleweed I was thinking of. Pretty good for a thought-experiment, a bit trickier to build and test with.
W.r.t. my other questions, I'm hoping to see if someone has run the treadmill over a range of speeds to see what the lowest treadmill speed is that the cart will advance at, and the highest speed. Just for curiosity's sake, obviously there's some speed below which it'll fall back (low prop efficiency), and above some speed it'll fall back (tip drag and turbulence on the prop).
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