The Real Bozo Attempts to Atone: Why the DDWFTW Car Works

Technorati Tags: , ,

So, as I said in the edit to my previous post about the wind-driven cart, I
seriously blew it. The folks who pointed out the similarity of the cart to a tacking
sailboat were absolutely correct. The guys who built this cart, and recorded the demo
were absolutely right, and I was stupidly wrong, in multiple ways. First of
all, I thought this was a really simple system. I couldn't possibly be more wrong
about that - this is anything but simple; in fact, it's a remarkably
interesting and elegant demonstration of how complicated and counterintuitive fluid
dynamics can be. Second, I completely misunderstood the simple mechanics of the
device; I originally thought that the propellor was spinning in the opposite
direction - and I completely missed it when people repeatedly tried to explain that
error to me. And third, I completely screwed up my own mathematical model of how
something like this works.

So - to repeat: the guys who did the demo of this are clearly not bozos; the only bozo in this situation is me, for screwing it up so badly, on so many levels. I sincerely apologize for calling them bozos and mocking them. I made a whole series of really stupid errors, and took an unreasonably long time to recognize that fact.

It should be obvious that there's some way to go downwind faster than the
wind, because as so many people pointed out, sailboats do it. It was frankly
stupid of me to even argue about this - it's really pretty boneheadedly obvious. The question never should have been "can it be done?", but rather just "does this device do it?"

And the answer to that is "Yes". This thing does do it. It's not magic, it's not perpetual motion. In fact, it's really astonishingly simple, once you realize that the behavior of things moving through air is quite different from the simple rigid system that it appears to be equivalent to.

In this post, I'm going to try to do two things:

  1. Explain the faulty reasoning that led me to think it couldn't work,
    and why it's wrong.
  2. Explain why the thing really works.

In another post later this week, I'm going to try to explain why I think the
mathematical element is so important. There's a ton of people who've got devices that
really look convincing, and that have really convincing arguments for why
they should work; only they don't, because they've missed something.

The explanation that got me started on really understanding this
was based on a rigid geared cart, which had one wheel on the ground below,
and one wheel touching a moving belt above. While this is really what twigged me to how things could work, I also realized that it's a good demonstration of
why I thought it wouldn't work. Here's the diagram:

i-4e6a54cca7460bc184f722d5def7ad1c-rigid-wheels.png

We've got a rigid cart. It's help up by free wheels on either side, to make sure that it doesn't tip. It's got a belt on top, which is moving
at a velocity of vupper. The upper belt is touching the upper wheel, which makes it rotate. The middle wheel is touching a center wheel, whose radius is equal to the upper wheel. The middle wheel touches a bottom wheel, which has a different radius. The only purpose of the center wheel is to reverse the direction of rotation, so that the rotation of the top and bottom wheel are the same - so that the upper track is making the bottom wheels move the correct direction. Assume that the wheels are actually gears, and that the energy transfer between gears is lossless. The
upper and middle wheels have equal gearing. The bottom wheel is geared differently - one rotation of the middle wheel causes more than one rotation of the bottom wheel, and the bottom wheel is slightly larger than the other two.

If you look at this with a static analysis, you can work out what appears to be
an interesting result:

  1. The upper belt is moving at velocity vupper, which means that the rim of the upper wheel at the point of contact should move at a velocity of -vupper, which will give it a rate of rotation of vupper/2πrupper
  2. Because of equal gearing, the rotation rate of the middle wheel is the same.
  3. The bottom wheel is more complicated, since its gearing is different. Let's assume that it's turning K times for each turn of the middle wheel. So the bottom wheel should turn at Kvupper/2πrupper.
  4. The speed of the bottom wheel at its rim touching the ground is
    2πrlowerKvupper/2πrupper =
    rlowerKvupper/rupper.
  5. The forward speed of the cart is the same as the speed at the rim of the lower wheel.

So, this makes it look like if rlowerK > 1, then the maximum speed of the car should be greater than vupper.

Is this the end of the story? Nope. Because that's a static analysis of
something dynamic. It doesn't actually work out quite that smoothly, because
the rigidly connected moving parts that constrain each other.

What happens when Vcart = (1/2)vupper? The rim velocity of the upper wheel relative to the upper track is reduced by 1/2. So it's getting less push. But not only is it getting less acceleration, it's limiting the speed of the bottom wheel, because they're rigidly connected. If the top wheel slows down, the bottom wheel needs to slow down. If the cart is moving at a speed equal to vupper, then the upper wheel isn't turning at all. It's stationary relative to the upper track. Which means that the lower wheel can't be turning either! Because of the rigid gearing, you're creating a drag, because the upper wheel slows down relative to the upper track as the vehicle accelerates, which slows down the bottom wheel.

So there's an equilibrium point where the connection to the top switches from acceleration to drag; that equilibrium point is going to be determined by the ratio between the gears - and it's going to be less than the speed of the upper belt. So the static look at the gear system can give you a sense of how the wind powered vehicle might work, but its rigidity limits its speed to less than the speed of the belt providing the force that's pushing it.

So: I think that with the rigid gear system, it doesn't work. However, the
wind-based system isn't rigid, and that's the key. The propellor system is
similar (but not identical to) the rest-based analysis of the
geared system.

That's what I initially thought was happening with the wind. The wind was
behaving as the upper belt, and as the cart accelerated, the amount of
force that could be extracted from the wind reduced.

Another piece of my misunderstanding was the real nature of the drive mechanism - which again can be demonstrated by the geared system.

Suppose that the wind is spinning the propellor. Then the rotation of propellor can't also be providing a propulsive force. That would be like the geared cart working by having the upper wheel rotated by friction with upper belt pushing the heel, and also having the cart propelled by the rotating wheel pushing against the belt. That's a double-dipping explanation, where the same force is being counted twice, as if it's simultaneously pushing in opposite directions.

So that, in a nutshell, covers the errors I made in believing that the thing didn't work. Now, let's move on to why it does work.

Let's look at a new diagram.

i-d681cb47cd3619860d22cddfa22c56d3-propellor.png

This is the cart. There's a propellor the back. It's connected by a gearing mechanism to the wheels. In a somewhat simplified model, the wind provides a force by blowing against the propellor - not by rotating it, but by treating it as a dead sail.

So, initially, you get a forward accelerating force, which is proportional
to the wind velocity. As it accelerates, the rotation of the wheels starts to spin the propellor. The spinning of the propellor pushes air backwards. The force from the
spinning propellor is proportional to some properties of the propellor (generally summarized as an "advance ratio". We'll describe the propellor in terms of
its force ratio, which is proportional to the advance ratio; the force ratio of a propellor tell us how much force the propellor generates at a given rate of rotation. We'll call it "A") times the rotation rate of the wheels, which is proportional to the velocity of the cart. The propellor being moved by the wheels is really the key to this: what that's doing is providing a way of exploiting the connection to the ground, allowing the cart to (as so many people pointed out)
provide a way of extracting energy from the difference between the
motion of the ground and the motion of the wind.

Here's where it starts getting tricky. What's the total force provided by the wind? It's basically the forward thrust of the moving wind plus the backward thrust of wind moved by the propellor.

Suppose the cart is moving at velocity Vc. The wheels are
rotating at vc/2πr, where r is the radius of the wheel.
The rotation rate of the propellor is going to be the rotation rate of the
wheels, times the gear ratio. We'll call the gear ratio G. So, the
propellor is spinning at Gvc/2πr, and generating a force
GAvc/2rπ.

Now, suppose that the cart accelerates to windspeed. Then
the force from the propellor is GAvwind/2πr.

At this point, the pure wind force has fallen to 0, because the cart isn't
moving relative to the wind. But the propellor is still producing a
force dependent on G, A, and r.

So for the right values of G, A, and r, you'll still be accelerating.

What stops it from being perpetual motion? As you accelerate above windspeed, you'll start to suffer a vaccum effect - the wind is moving slower than
the vehicle, so it'll effectively be sucking away some of the force generated
by the propellor. So you'll need to start subtracting a force
proportional to the relative windspeed from the amount of force you can
generate from the propellor. Eventually, that vaccum force will equal GAvcart/2πr. As you get closer and closer, the amount of force that you'll be generating by spinning the propellor will be completely consumed - and you'll be at the maximum attainable speed in that amount of wind.

What this all means is that you've essentially gotten energy from the friction of the wheels against the ground, and turned it into propulsion. The ground friction
is providing a way to make the propellor "tack" against the wind. The nature of the mechanism means that the initial acceleration of the cart is slower than a pure sail-driven system, because the way the propeller spins adds resistance to the wheels via the gearing. But ignoring losses to friction, if the wind is constant, it won't stop it from accelerating - it'll just slow the rate of acceleration.

Once it's moving, what's going on can be described in a bunch of different ways. They're all equivalent, but the one that seems easiest to model to me is to think of the "sail" as being not just the propellor, but the cushion of moving air that it's pushing behind it. So it's very much as if the "sail" is moving backwards relative to the cart. (An equivalent view is that the angle of the propellor blades are tacking relative to the wind, and that tacking angle combined with the rigid connection to the propellor spindle translates into a forward force.) Either way, the rotation of the propellor provides a way of getting an accelerating force from the wind even when the forward velocity of the cart matches the velocity of the wind.

So the folks who keep comparing to tacking in a sailboat are right. This
is, essentially, the same effect.

More like this

(NOTE: It appears that I really blew it with this one. I'm the bozo in this story. After lots of discussion, a few equations, and a bunch of time scribbling on paper, I'm convinced that I got this one wrong in a big way. No excuses; I should have done the analysis much more carefully before posting…
I ride my bike and mostly the wind makes me unhappy. On a very few days the wind is with me on the way to work and then changes so that it is with me again. But most days the wind is fairly constant. So, if the wind is constant then shouldn't everything even out? (Even Stephen). Assumptions: Let…
Maybe this is a little old (in internet age), but it is a great example. Here is the Loop-the-loop stunt from the show Fifth Gear. I like this. First, it is a bold stunt. But also, there is some good physics here. Though, most importantly, the Fifth Gear producers were kind enough to include a…
The third of the great physics principles introduced in our introductory mechanics courses is the conservation of angular momentum, or the Angular Momentum Principle in the language of the Matter and Interactions curriculum we use. This tends to be one of the hardest topics to introduce, in no…

Maybe, when correcting others, if we don't do so through insulting them but rather just by pointing out the perceived mistakes, we don't have to apologize as much if we turn out to have made a mistake ourselves.

Good show on the correction!

It seems that the key here is when you assert that the resistance on the wheels will not prevent the cart from attaining wind speed, but merely slow the rate that it does so. Once the cart is at wind speed, we can confidently add the thrust of the propeller, and no matter how slight it is we have a net gain in velocity. Thanks for clarifying this.

You do yourself proud by admitting your wrong.

Everyone will be wrong some of the time. Many fail to stand up and admit it, and many of those fail to learn because they can't admit it to themselves.

A lot of people don't seem to realize that, downwind, a larger sail by itself won't make a sailboat go faster than the wind. Yet it still adds energy to the boat, which can be harnessed lots of ways.

For instance, you can increase the friction against the boat and have it not slow down, and then use that friction to generate extra propulsive force.

There are innumerable ways to end up going faster than the wind. Unfortunately, regular old tacking is still the most efficient and practical!

ps: People shouldn't get upset when people use strong language on the Internet. Read anything ever on the Internet? Everyone does. It's necessary to overcome the lack of non-verbal signals: In real life, Mark would have let you know he thought you were a bozo through tone of voice, etc.

Minor correction: In "So, this makes it look like if rlowerK > 1, then the maximum speed of the car should be greater than vupper", you're missing a factor of rupper.

Kyle:

Maybe, but I also think that there's a real benefit in calling a spade a spade.

There are a lot of idiots out there, promoting a lot of bullshit; and pulling punches just makes it easier for them to go around fooling people. And fooling people that way isn't harmless:

  1. A lot of people have been robbed of their savings by hucksters promoting perpetual motion machines.
  2. People have died because they got tricked by people pushing fake medicines on them (witness homeopathy; it's "magic water", but there are people who've been talked out of getting the chemotherapy that could save their lives in favor of magic water that does nothing.)

Just to show how personal it can get: my father died of an antibiotic resistant infection. One of the reasons that antibiotic resistance is so able to spread is because of idiots like Michael Egnor who keep telling people that evolution doesn't do anything, and so there's nothing to worry about. My father was given medications that a non-fundamentalist doctor who was up-to-date on his literature would know wouldn't work. But his doctor was a fundie who didn't read that stuff.

More on point for perpetual motion type stuff: a lot of "free energy" devices are used as arguments against conserving energy, or against investing in developing better, cleaner, safer power generation. After all - why invest billions of dollars in manufacturing clean-running hybrids, when the free-energy magnetic motor will be available by next year?

In the best case, idiots can distract people from what's important. In worse cases, they can cost people and even nations huge amounts of money. And in the worst cases, they can cost lives.

Mark, I think there's nothing wrong with *you* calling a spade a spade. Other people sling insults, but then don't apologize when they're wrong. A respect for truth that makes you unflinching in your assessments of others but also willing to admit when truth is on the other side is admirable. Most Internet talkers are only interested in when the other guy is wrong.

I look forward to your math post. Have you read "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"? I think what a lot of people in the other thread were rightly pointing out that mathematics can easily be misused to "prove" things which aren't true-- math BY ITSELF cannot predict anything about the world. Your models have to be tied to reality. But the mathematical side of things is simply indispensable.

(My opinion of math alternates between a neo-platonic reverence and a dismissal of it as nothing but complex tautologies.)

@boyo #8:

I had a really overbearing logic teacher. Now, even when I agree with the sentiment, I have an involuntary pedantigasm when people say things like that, and must respond: Every valid argument is a tautology.

You know, I think TSK is right. In the article he cited (http://scienceblogs.com/goodmath/2008/08/astrology_and_the_olympics.php) you said you'd expect a normal distribution when you plot medals versus astrological sign.

It seems pretty obvious that it should be nearly a uniform distribution though (an equal number of winners from each astrological sign). I can't imagine a normal distribution there ...

Of course, the statistician's errors were far, far more egregious than your typo. How can someone like that earn a PhD?

Mark, thanks for the great example of why to avoid making ad hominem attacks.

@chris #9

You're quite right!

Which is why deductive reasoning isn't useful in most fields.

I kind of get upset when people say that a scientific theory is "proved." Strongly corroborated as good as you can get, I'm afraid.

Re #11:

I didn't make an ad-hominem attack.

Ad-hominem is "this guy making this argument is stupid, therefore his argument must be garbage".

My arguments generally take the form "This argument is garbage, therefore the person who must be an idiot".

It's actually a common and annoying error on the internet, where if you dare to say anything against the person making an argument, you get slapped with "Ooh, ad hominem, your argument must be worthless", when it's not an ad-hominem at all. The argument is what matters. If you address the argument, and show why it's crap, the fact that you said something nasty about the jerk making the lousy argument doesn't make the argument any less lousy.

Take, for example, one of my favorite total idiots, a gent by the name of Ted Holden. I've said lots of really nasty things about Ted, because the guy makes some of the dumbest arguments that I've ever seen. He's a Velikovskian, who believes that the planet jupiter used to by a "hyper-intelligent electromagnetic star", that earth used to orbit jupiter in a tide-locked orbit, and that this resulted in a "reduced felt effect of gravity" around the pole of the earth facing Jupiter.

Ted's arguments are ridiculous. To merely call them stupid is incredibly generous. I've addressed them elsewhere; search the blog archives for "Holden", or go to the Google groups usenet archives, and search for "Mark Carroll" in the archives for talk.origins. (I was mainly active on talk.origins before my marriage.) If I say that Ted is a total damned moron because he believes in his nonsensical, ridiculous arguments, is that ad-hominem? No. I've addressed his arguments, repeatedly, and in great detail. I don't conclude that arguments are stupid because he's an idiot; I conclude that he's an idiot because he makes stupid arguments.

On the other hand, I've been attacked in the past by a couple of guys from the discovery institute blogs. Their critiques of me have been, roughly, "He's just a software engineer, how could he possibly make a valid critique against a genius like William Dembski?" That's ad-hominem: it ignores the content of the argument, in favor of focusing on the personal qualities (or lack thereof) of the person making it.

See the difference?

Re #12:

I don't actually know how a hydraulic transmission work, so I'm not sure. My best guess, from what little I know about how other hydraulic systems work, is that you probably could build a fluid-based linkage that would allow you to exploit the difference in speeds between the top and bottom tracks, but it wouldn't be exactly the mechanism illustrated above with them mechanical gearbox.

For example, to draw a metaphor with the wind vehicle: you could build a system where the top wheel started off stationary - so that the upper belt just dragged the cart, and then have the gearing from the bottom wheel spin the top wheel. I don't think you could do that with entirely rigid gearing; I think you need to have some give in the system.

Mark, if you make a mechanical cart like the one in your diagram, it will move at half the speed of the upper track. v_cart = v_upper/2. Here's why:

First look at the point of the bottom wheel in contact with the ground: its velocity is 0. Now look at the top point of the bottom wheel: its velocity is twice that of the cart. Moving up the wheels, the bottom point of the middle wheel also has a velocity twice that of the cart, being in contact with the top point of the bottom wheel. The top point of the middle wheel has a velocity of 0, the bottom point of the top wheel also has a velocity of 0 and the top point of the top wheel has a velocity of twice that of the cart. In fact the sizes of the wheels won't make any difference: you could make all three wheels the same size, or make the middle one twice as big: the relative velocities of the top and bottom points won't change.

There are indeed fixed-gear mechanical models which work. I made the simplest model I could think of: admittedly it doesn't used fixed gearing, since the reel could slip on the paper, but you could make a similar model with a gearwheel and geared tracks. Have a look:

http://www.youtube.com/watch?v=E7vcQcIaWSQ

By Michael C (not verified) on 07 Dec 2008 #permalink

Mark,

with rigid gearing like in your first diagram, then regardless of the various radii, vupper = vlower, what is different is angular velocity. In order to get different liner velocities you need to make the angular velocities equal, by putting a chain drive between them with equal sized sprockets.

@boyo:

You've hit my second reflexive quibble, and one that I think is actually pretty important. It's a real pity that there's so little patience for your last point among defenders of science. Saying otherwise 1) is lazy 2) is untrue/dishonest and 3) gives aid and comfort to malcontents by letting them feel they win the day if they can raise any doubts whatsoever.

Apologies to the rest of the thread for the tangent.

Mark,
I don't actually know how a hydraulic transmission work, so I'm not sure. My best guess, from what little I know about how other hydraulic systems work, is that you probably could build a fluid-based linkage that would allow you to exploit the difference in speeds between the top and bottom tracks, but it wouldn't be exactly the mechanism illustrated above with them mechanical gearbox.

I think #12 is essentially referring to a torque converter like in automatic transmissions. It is essentially two propellers in a fluid, one attached to the engine the other to the drive train. It allows the car to be stopped with the engine running without having to disengage a conventional friction clutch.

Laugh!!

It's pretty funny that gears example to 'explain' it is so wrong as well.

Hint: Any gear has same same tangential speed at the top and bottom of the gear relative to the mount (but with opposite sign obviously). The size of the gear doesn't matter..

So gearing ratio is irrelevant: relative to the cart, the tangential speed at the top and bottom of the cart will be the same, but opposite sign.

So you've cleverly built a cart that's guaranteed to travel at exactly 1/2 the belt speed. :)

Mark,

as others have pointed out, the first half of this article is still incorrect. There is no actual gearing in the "rigid geared cart". In order to do any gearing at all, you need to have things of various diameter on the same axle. If you just touch the outside of wheels, nothing is going to get transformed (except direction). Your rigid geared cart is equivalent to a simple wheel held between two surfaces, which will of course move at half the relative speed of the two surfaces.

If you, however, did some gearing, the thing could move at any chosen multiple of the relative speed of the two surfaces (from zero to infinity, or even backwards).

Mark, in spite of the debate regarding certain points of your writeup, I would like to say again how I appreciate both the apology and the effort you are taking to make it public.

Every third grade daughter should be so lucky to have a Dad set such an example. Props.

JB

By ThinAirDesigns (not verified) on 07 Dec 2008 #permalink

Hello Mark,

great to see that you come forward as you said. Kudo's for that since it is really rare on the net that people do this.

As for post #12, well, i think that there is a bigger idiot around: Ever heard of John R.R. Searl? That guy claims to have invented a over-unity machine (of course, out of magnets). Not only he says it producec energy, no, it can also fly "to teh moon" by defeating gravity, it cleans the air, etc. And what makes him really that big of an idiot is the fact that he claims that his "laws of the squares" describes the whole thing, and that this is law behind the thing that makes it work.

In case you haven't guessed, yes, it is plain old magic squares!

The really bad thing is that this scam is going on for over 60 years now. And people still fall for that.

Greetings,

Chris

The gearing makes no difference. The cart is driven by force from the rear. It is possible that gearing will mean that more can be taken from the wind, but the final speed will depend upon the power that is available to do work against the friction of travel, under the same conditions.

Changing the gearing may help match the load to the wind, like a car's gearbox matches the engine to the load and that may increase the speed over a wind-cart without gears, but that does not mean that it will then reach the speed of the wind.
The treadmill is a demonstration of how (some object) may travel up a belt. It has nothing in common with wind travel.
If the the criticisms made in the first article were not so childish, then such a grovelling apology may not have been needed.

By Mr Clovis (not verified) on 07 Dec 2008 #permalink

Mark,

you might want to take a look at this posting on the JREF forum. It shows a cart uding wheels/gears like yours do, just the propper way:

http://forums.randi.org/showpost.php?p=4252145&postcount=1645

Don't get confused by the top wheel's spinning direction wrt. to the drawn direction of travel for the belt. Just remember that the cart moves faster than that belt, so, relative to that belt it moves backwards.

Of course in #25 i meant that it moves forward relative to the belt.

Mark,

I have to admit when I first read your blog I was seething. In fact I called and left you a message saying that I'd like to talk. Many many people have taken a stance similar to your initial stance, and many have been eventually convinced of the truth. However, VERY few have been so up front with an apology and so eager to set the record straight. I was surprised, and am impressed that you did so.

Onto some minor nits:

For what it's worth, I've argued somewhat strenuously against the notion of a cushion of air being squeezed between the prop and the tailwind, but in the larger scheme of things that's something of a footnote. Intuitively that approach has a certain attraction.

Two other minor nits I'll point out...

What we normally refer to as the "advance ratio" isn't a property of the propeller, but rather the ratio of the distance the propeller would theoretically advance in a single rotation divided by the distance the wheels advance in that same single rotation of the prop. Advance ratios below 1.0 produce a cart that goes downwind faster than the wind, while ratios above 1.0 produce a cart that goes directly upwind.

Finally, with a fixed pitch and fixed gear ratio, one can design a cart that goes either upwind or downwind at any multiple of the true wind speed (with higher multiples as the advance ratio approaches 1.0 from either side). However, in the real world this will be limited by the practical efficiencies you can achieve. I'm not sure that your thinking differs from this, but thought I'd offer a possible clarification.

"The treadmill is a demonstration of how (some object) may travel up a belt. It has nothing in common with wind travel."

Mr Clovis,

Not only does the treadmill have something "in common with" wind travel - it IS wind travel. There is no such thing as an absolute reference frame. Any inertial reference frame is just as good (and indistinguishable from) another. I suggest you look into Gallilean Relativity (which explains the principle of equivalence of inertial reference frames).

Furthermore, if your analysis suggests this cart cannot go downwind faster than the wind, you need to carefully check your anaylsis, because it does just that.

spork, I think Mr Clovis means that a mechanically-linked belt pair illustration, whether you design one that works or not, doesn't prove anything about the original problem. If you have two belts moving at different speeds (or one moving and the other not, same difference) you can build a machine taps the speed differential to go faster than that differential. This can work because the thing driving the belt is arbitrarily powerful and we have no imposed limit to our ability to tap that power, and we can leverage it with gears to get any arbitrary speed out of it, limited only by the torque of the driving motor, which if left unspecfied must be regarded as unlimited. Wind is a rather subtler and more exacting problem.

"spork, I think Mr Clovis means that a mechanically-linked belt pair illustration, whether you design one that works or not, doesn't prove anything about the original problem"

Perhaps you're right. I assumed he was refering to our DDWFTTW video. I imagine he'll let us know which he was refering to.

Incidentally, I will agree that aero forces are not without infinite subtleties; but I'm actually inclined to say that the belt vehicles go a long way toward proving it can be done with a wind powered vehicle. It's mostly a matter of how you choose to propel yourself.

As with many such devices, it pays to take a step back from the details and just consider the basic conservation laws.

Case in point: the cart has accelerated to exactly wind speed. There is no force coming from the wind, at all. All forces on the cart are from the wheels-to-ground and propeller-to-air interactions.

To go faster than wind, those forces have to be net forward. At break-even, the power from the wheels is F*Vwind and the power applied to reverse airflow is F*Vblow, where Vblow is the velocity of air expelled from the propeller in still air. Assuming no losses, you can get net forward thrust at Vblow<Vwind.

In a headwind situation, the power extracted from the wind would be F*(Vwind+Vcart-Vblow) and the power to the ground would be F*(Vcart) so as long as Vwind>Vblow again, it would be possible to have net forward thrust.

Obviously the simplifying assumptions are pretty extreme: ignoring the hydrodynamics of the conversion and all losses. Still, it gets the point across that it's possible to extract useful power from the difference in motion between two media.

By D. C. Sessions (not verified) on 07 Dec 2008 #permalink

"the cart has accelerated to exactly wind speed. There is no force coming from the wind, at all. All forces on the cart are from the wheels-to-ground and propeller-to-air interactions"

In steady-state the force of the wind on the prop exactly equals the force of the wheels on the ground plus the aero drag forces on the frame. This is true below, at, or above wind speed. It's a mistake to think the prop isn't feeling wind just because the cart is going downwind at wind speed. At this point the prop is working purely on relative wind, just as the sail of an ice-boat that's making downwind VMG of exactly wind-speed.

It's also a mistake to think the energy comes either from the ground or the wind. Energy, like velocity, is purely relative to the frame in which you do the analysis. So it's easy to end up with all the energy coming from the ground, all coming from the wind, or anything in between.

Okay. So now how do we make a car out of this?

Seriously, could something like this be used as part of a propulsion system for a vehicle that does something useful. Not neccessarily the whole job, but as an aid?

It's particulary good for starting internet pissing matches. Beyond that I haven't been able to figure out a practical use for it. Although I was contacted today by the free energy people. Try explaining to them it's not perpetual motion.

It's a mistake to think the prop isn't feeling wind just because the cart is going downwind at wind speed.

Say what?

Help me here -- how is this different from the case where the cart is stopped in still air? Does the propeller also "feeling wind speed" then?

By D. C. Sessions (not verified) on 07 Dec 2008 #permalink

It's also a mistake to think the energy comes either from the ground or the wind. Energy, like velocity, is purely relative to the frame in which you do the analysis. So it's easy to end up with all the energy coming from the ground, all coming from the wind, or anything in between.

Ummm -- if you say so. Me, I just add up the power balances at each interface. If the dot product of the thrust at the wheels and the cart ground velocity is positive, then the power is "going to" the wheels. If the dot product of the airspeed and the thrust from the propeller is positive, then the power is "going to" the propeller. Not at all dependent on the reference frame, conveniently, and (neglecting frame drag and losses) the two have to add up to zero.

By D. C. Sessions (not verified) on 07 Dec 2008 #permalink

"Help me here -- how is this different from the case where the cart is stopped in still air?"

It is different in that the propeller rotates, whereas in the case where the cart is stopped in still air, it doesn't.

The propeller is feeling no force from the wind only if air passes through it at the same speed as the "thread of the airscrew" is moving. This is true when the cart is stopped in still air, and it would also be true if you had a non-rotating propeller moving at the windspeed, but it is not true when the cart is going downwind at non-zero windspeed.

"Help me here -- how is this different from the case where the cart is stopped in still air? Does the propeller also "feeling wind speed" then?"

It does if it has a road rolling beneath its tires. Because that causes that prop to spin. When the prop is spinning in still air there is interaction (i.e. thrust).

"If the dot product of the thrust at the wheels and the cart ground velocity is positive, then the power is "going to" the wheels."

Yes - and that depends entirely what frame you're doing the analysis in. Velocities are all relative - as is kinetic energy. Every single experimental result will be invariant. But energy and work-done are not experimental results. As bizarre as it seems these things are bookkeeping.

Mark, the geared cart (your first example) is all messed up, as several others have pointed out. The picture is just all wrong.

But on the larger point. Yes, its clear that the cart works. This one stumped me for pretty much a whole day of thinking about it. I figured it out thinking about tacking boats as well.

And also, I think your admission of error here is, ironically, really what gives credibility to this blog.

-kevin

Seriously, could something like this be used as part of a propulsion system for a vehicle that does something useful. Not neccessarily the whole job, but as an aid?

As I noted above, you can go downwind at greater than wind speed if Vwind>Vblow assuming no losses or drag. At that point you can get an idea of the maximum thrust available by figuring the cross-sectional area of the vehicle and the wind speeds you're willing to assume.

If you assume a cross-section of four square meters, an air density of 1 kg/m^3, and a wind speed of 3 m/s, your exhaust flow in still air is at most 12 m^3/s for a thrust of about 36 newtons. So you're going downwind at about 11 kph and have surplus thrust for drag, losses, and acceleration of 36 newtons. Neglecting losses and assuming your vehicle has a net mass of 180 kg, that's enough to get you an acceleration of 0.2 m/s^2. If you have losses or other power demands, you get as much as 108 watts from it.

On a less blustery day, everything scales back.

By D. C. Sessions (not verified) on 07 Dec 2008 #permalink

"If the dot product of the thrust at the wheels and the cart ground velocity is positive, then the power is "going to" the wheels."

Yes - and that depends entirely what frame you're doing the analysis in. Velocities are all relative - as is kinetic energy.

As long as we're in a Newtonian system, the frame is totally irrelevant to the energy economy. F dot delta-V is not dependent on any of the references used.

The key to examples like this is to not overthink them.

By D. C. Sessions (not verified) on 07 Dec 2008 #permalink

I followed this discussion with much interest and am firmly in the "it works" camp. In the hopes that it might help convince some of the remaining non-believers I have posted 2 videos:

http://www.grogware.com/ddwfftw/

The first video shows a much simplified version of Mark's belt driven device. I used a chain and a set of nested gears; pulling the chain to the right causes the device to travel much faster than the chain is being pulled.

The second video is much more analogous to the cart that JB and Spork built. Like their cart my device has wheels which turn an aft facing shaft. However instead of a propellor, I have a threaded rod with a nut on it. Instead of the wind pushing the cart, you use the nut and simply pushing on the nut causes the cart to travel faster than the nut moves.

I suspect that some people who have trouble understanding how the wind driven cart works will easily see how these two devices work. Hopefully it will then help them understand the wind driven versions.

Please let me know if any of this is unclear, David

David G @42,

nice work! Is there any chance that you could put direct links to the .mov videos there as well, for the people who don't have the Quicktime plugins, or who can't have them because of a different OS they use?

Greetings,

Chris

"one rotation of the middle wheel causes more than one rotation of the bottom wheel, and the bottom wheel is slightly larger than the other two."

No, bozo. Hehe, this is fun.

"As long as we're in a Newtonian system, the frame is totally irrelevant to the energy economy. F dot delta-V is not dependent on any of the references used."

We're not talking about "energy economy"; we're talking about energy. And if you do the analysis in the frame of the road, the road can't do any work on the wheels because there is no V for the F dot V. Energy is relative to the frame in which it's measured - just like velocity.

Consider a bullet... from the frame of the earth it's got a pile of kinetic energy. But from a frame that's moving at the same speed as the bullet it has none - even in a Newtonian system.

"The key to examples like this is to not overthink them."

Or under-think them.

To never make a mistake to to never push the boundary of that we know and what we can do. I'd be happy to make a few mistakes half as good as Marks.

Cheers for intellectual integrity.

Well done Mark.

Sincere suggestion: don't use the word "obvious" so much. You initially claimed it was obvious that you can't go faster than the wind, and now you say it's obvious that you can.

Nothing is obvious at first, and everything is obvious in retrospect. Claiming that something is obvious once we are convinced of it makes it tempting to call the other person an idiot, which we may regret later even if we are right. More importantly, it makes it hard to see that we're wrong when it is pointed out, because having called something obvious, the instinct is to defend it at all costs.

In order to construct a mechanical model that illustrates the principle of the DDWFTTW cart, it is important to understand this essential point:

Whatever is pushing or pulling the machine (conveyer belt, chain, strip of paper...) must be acting on a point on the machine that moves along the ground slower than the machine as a whole.

How do we make a machine with a part that moves forward slower than the rest of it? In fact it's surprisingly easy. Consider a wheel rolling along the ground. If the wheel is moving forward at speed v, any point below the centre of the wheel is moving forward as less than v and any point above the centre is moving forward at more than v. If we keep pushing (or pulling) at a point directly below the centre of the wheel, we can make the wheel move forward faster than the speed at which we are pulling/pushing.

Using this principle, you can create all sorts of machines that will run faster than whatever is pushing/pulling them. Not only in your imagination: you can build ones that really work.

And once you've done that, the way is clear for a DDWFTTW machine. You just have to find a way of making sure that the part of the machine in contact with the moving air is moving slower than the part that is in contact with the ground...

By Michael C (not verified) on 08 Dec 2008 #permalink

Nice post.

You didn't have to beat yourself up THAT much ... this is the blogosphere. The benefits of immediacy come along with the risk of jumping the gun now and then.

Now I'm not sure if I screwed up the diagram. I think that there's some confusion because of my limited artistic abilities.

The diagram shows everything as smooth wheels - because I have no idea of how to draw a gear.

With gearing, you can set up a system where the rotation rate of one gear is different than the rotation rate of another coupled gear. The easiest way to see that is via a chained gear (like a bicycle), but planetary gearing systems are doing the same basic trick. (Just for an example, I've got a tuner on my banjo where one turn of the actual tuning peg requires three turns of the tuning grip.)

Assuming that you've got the correct gearing, so that one turn of the wheel against the upper belt corresponds to N turns of the wheel against the ground, you can arrive at different equilibrium speeds - or am I, once again, missing something?

Re #33:

I don't think that you'll get much real use out of this as a propulsion enhancer. You're doing a slightly better job of extracting energy from the wind than a simple sail, but not in a particularly dramatic way. I don't think that in any real vehicle, this effect is going to be particularly useful.

The best example I can come up with to illustrate would be braking on a jet plane. You've got a plane coming in for a landing at 100mph. Suppose you could use the rotation of the wheels against the ground to increase the rate of spin of the thrust reversers. How much more spin is going to be generated? Back of the envelope says it's completely lost in the noise - well, well under 1%, and thrust reversers variability of performance due to wind conditions is already more than that.

[...]I sincerely apologize for calling them bozos and mocking them. I made a whole series of really stupid errors, and took an unreasonably long time to recognize that fact.

I saw only two errors in the whole fiasco that I would characterize as stupid: saying "impossible" and being really rude.

I guess you're most always rude in your badmath posts. The name-calling, the exaggeration of how stupid a mistake is--it seems inappropriate to me every single time.

I can't find the comment, but someone pointed out that you can, indeed, accelerate a sailboat using a fan mounted on the sailboat blowing air at the sail.

Yup, you sure can. That's one of my favorite physical pseudo-paradoxes. The key to it is recognizing that you're getting energy from an external source - that is, a battery or spring or flywheel which has stored energy. So there's energy added into the system, which has to go someplace. And if you work out the actual forces, as long as you set things up at the correct relative angles, it works beautifully.

Yet another reason that I shouldn't have had the knee-jerk "this can't work" reaction.

"or am I, once again, missing something?"

Mark, I think you are still making a mistake with your mechanical example. If you consider the tangential velocity at the surface of any of your rollers (or gears) it will be the same on each. True that they will have different rotational rates, but they will both present the same tangential velocity at their point of contact with the ground or the plane above. This can easily be solved by using a concentric gear pair in the middle. One of the concentric gears would mesh with the lower gear, while the other rigidly attached concentric gear of a different diameter meshes with the upper gear.

... it occurs to me however, that you should probably one use an upper and a lower gear (no middle gear) so the cart moves the same direction relative to each. It simply moves faster relative to one surface than it does relative to the other. Again, one should incorporate the concentric gear idea. It could simply be a smaller gear with a larger concentric tire that rolls on the upper surface for example.

In another post later this week, I'm going to try to explain why I think the mathematical element is so important. There's a ton of people who've got devices that really look convincing, and that have really convincing arguments for why they should work; only they don't, because they've missed something.

I'm curious to see this. I tend to think the opposite. There are a lot of mathematical arguments that seem convincing--like your previous explanation! A working device is proof.

To my mind, all the math did in this case was convince you.

Maybe part of what duped you here is that the video has all the hallmarks of crankery. It set off your Internet Bullshit Detector. I think the Web teaches people to rely far too heavily on that device. Fortunately, you have the math, logic, time, and inclination to right yourself after a false alarm! Not everyone does.

>Again, one should incorporate the concentric gear idea.

The first of my two videos demonstrates exactly this idea. I can't claim that my models are even half as elegant as those built by Spork and JB but they do illustrate the principals. As an aside my wife was slightly bemused to find that her freshly gift wrapped package was exactly the right height for my experimentation.

Videos and pictures here: http://www.grogware.com/ddwfftw/

# 51 (Mark C. Chu-Carroll): "Now I'm not sure if I screwed up the diagram. I think that there's some confusion because of my limited artistic abilities."

Mark, I think you should make a mechanical cart and try it out. If you make one just like your diagram, with gears that mesh together on the wheels and on the tracks, you will find that it moves at half the speed of the upper track, as many have already said. It really will. I guarantee that. I'd happily place a bet on it. If you don't believe us, please make one and try it out for yourself.

On the other hand, if you make a mechanical cart where the point that is acted on by the moving track is moving forward slower than the rest of the cart, the cart will move forward faster than the moving track that is giving it propulsion.

And that is exactly how the DDWFTTW vehicle moves forward faster than the stream of moving air that is giving it propulsion.

By Michael C (not verified) on 08 Dec 2008 #permalink

"With gearing, you can set up a system where the rotation rate of one gear is different than the rotation rate of another coupled gear. The easiest way to see that is via a chained gear (like a bicycle)..."

Rotation rate is irrelevant here: if you have two wheels, one large and one small, rolling on the ground, then the small one's rotation rate will be greater than the large one's, but both will advance at the same speed.

What matters is tangential velocity, and correspondingly, force. In your bicycle, the chain keeps tangential velocity and force constant - that's its purpose. The actual change in tangential velocity/force comes from the differences in diameter between the pedals and the front gear (which are on the same axle), and between the rear gear and the rear wheel (which are on the same axle).

"Gearing" that only consists of gears touching each other does no gearing at all. You need to have gears of different diameter on the same axle.

Re #61:

I am suggesting two gears of different diameter on the same axle. The middle wheel in the diagram is using one gearing for its coupling to the upper wheel, and a different gearing for the lower wheel.

But I haven't done a full analysis of this - as I said in the post, I did the analysis up to the point where I convinced myself that the direct rigid gearing as illustrated wouldn't get the thing above the speed of the upper track.

I don't have access to the stuff I'd need to build a physical model, so that approach is out. I could do a full analysis and work it out, but at this point, I just don't care that much about the rigid-geared cart. To me, it was just a stepping stone on the way to understanding the prop-vehicle, and unless my incomplete analysis of it means that the analysis of the prop-cart that it led to is also incorrect, then the incomplete understanding is good enough for me, and I'll take the word of folks who've considered it in more detail.

In response to the various people congratulating me for admitting that I'm wrong:

One of the best teachers that I ever had was my high school AP physics teacher. One thing that he taught me that I've tried to take to heart is: there's nothing wrong with ignorance, so long as you admit it, and work to correct it.

That's a damned good guide for how to conduct yourself, and I really try hard to live up to it. When I'm faced with a situation where it's apparent that I'm missing something, I try to sit down and start studying.

That's all that I did here. I was wrong about the mechanics of the machine, because I didn't really understand it. So I learned.

To me, that's what any honest person should do. And I'm frankly arrogant enough to believe that my honesty and integrity really matter - they're more important than just being right about some individual point of argument.

So ultimately, it's my own arrogance that both gets me into trouble, and back out of it. Not quite so deserving of praise as it sounds initially, but there it is.

"Maybe part of what duped you here is that the video has all the hallmarks of crankery"

The irony is that, while you may be exactly right, the whole point of our video was to put this question to rest. We tried to address the criticisms that were levied against Goodman's video, and even made a number of videos at the direct request of our critics. Our intention was never to confuse or deceive. We were truly naive enough to think we could produce a video that presented the evidence clearly enough to answer the critics concerns.

We've learned the hard way that no evidence will ever be sufficient for the most ardent of critics.

And I don't mean this in any negative way. I accept that a video on YouTube will always invite scepticism. I only offer this as an honest insight into our thinking.

"I am suggesting two gears of different diameter on the same axle. The middle wheel in the diagram is using one gearing for its coupling to the upper wheel, and a different gearing for the lower wheel."

I see... so what you're saying is that the rims of the middle wheel and the bottom wheel are not touching each other, but they are connected in some other way, not drawn in the picture, which increases the tangential velocity from the middle wheel to the bottom wheel. Do I understand you correctly?

"I did the analysis up to the point where I convinced myself that the direct rigid gearing as illustrated wouldn't get the thing above the speed of the upper track."

Well, a direct rigid gearing actually can get the thing above the speed of the upper track. So the question is whether you convincing yourself incorrectly played a major role in your understanding, or not.

"... at this point, I just don't care that much about the rigid-geared cart. To me, it was just a stepping stone on the way to understanding the prop-vehicle, and unless my incomplete analysis of it means that the analysis of the prop-cart that it led to is also incorrect, then the incomplete understanding is good enough for me ..."

I guess that's fair enough, as long as only you and your understanding are concerned. But if you intend this article as an explanation to others, then the incorrect conclusion that "with the rigid gear system, it doesn't work" will be confusing at best.

I understand that you don't want to spend time rewriting the article if the rigid-geared cart isn't of much importance to you, but even just a short note inserted at the relevant point (such as: "It has been pointed out that even rigid-geared carts can exceed the speed of the upper track; see comments") would help those who try to understand.

If you intend this as an explanation, that is.

Damn, should have asked for ketchup

Mark, you blog is named Good Math, Bad Math. Your analysis of the mechanical cart is Bad Math: it simply isn't correct.

"1. The upper belt is moving at velocity vupper, which means that the rim of the upper wheel at the point of contact should move at a velocity of -vupper, which will give it a rate of rotation of vupper/2Ïrupper"

The minus sign before vupper is incorrect. The point of a wheel in contact with the belt will be at rest with respect to the belt, so the top point of the top wheel moves at the same speed as the belt, in the same direction. Furthermore, the speed of rotation of the wheel cannot be inferred from from the speed of the upper track only; it depends on how fast the wheel is moving along the track. For example, if the centre of the wheel is moving along at the same speed as the track, the velocity of the top point is indeed the same speed as the track, but the speed of rotation of the wheel is zero.

You introduce a number K, which is the number of times the bottom wheel turns for each turn of the middle wheel. This number can be expressed simply in terms of the radii of the two wheels. Since the radius of the middle wheel is rupper, K = rupper/rlower.

"4. The speed of the bottom wheel at its rim touching the ground is 2ÏrlowerKvupper/2Ïrupper = rlowerKvupper/rupper."

If we replace K with the known value rupper/rlower, we see that the value you calculate for the speed of the bottom wheel at its rim turns out to be vupper. However, this cannot be the case: the speed of the point on the rim touching the ground is zero!

"5. The forward speed of the cart is the same as the speed at the rim of the lower wheel."

No, the speed at the rim on the lower wheel is zero. The forward speed of the cart is that of the centre of the wheel. A correct analysis of this cart will show that it moves forward at vupper/2, whatever relative sizes are chosen for the three gearwheels.

It is worth analysing the mechanical models that do go faster than the conveyor belt, since they help in analysing the DDWFTTW.

By Michael C (not verified) on 08 Dec 2008 #permalink

Ur statement (for the example system);

The bottom wheel is geared differently - one rotation of the middle wheel causes more than one rotation of the bottom wheel, and the bottom wheel is slightly larger than the other two.

Seemed dodgy to me. As I understand mechanics, the gears on each wheel must be the same pitch, in order to mesh, so the number of teeth around each wheel is proportional to the circumference. If the teeth meet rim-to-rim then one rotation of the smaller will equal less than one of the larger.

Of course, you could use composite wheels, with one rim connected to the other wheel while another connects to the ground. Or you can use belts, and not need the middle wheel at all.

As for the actual system; It's not just a prop, it's a sail too so the energy from the wind, via the sail feeds to the wheels which then feed back to the prop. Downwind this feedback is positive while upwind it'd be negative.

I have to second (or third or fourth or whatever) the comments about the mechanical cart. It moves at half the speed of the upper track.

Imagine it this way, using a somewhat informal intuitional approach...

First, as others have pointed out, the outer rims of each gear is moving at the same speed, necessarily because they're touching. Their angular velocities are different, but that matters little, as nothing is taking advantage of that.

Second, when considering the cart and the upper track only, it's clear that the upper track surface is passing the cart by at Vtrack if you hold the cart still ("still" meaning Vground, or 0 in the reference frame of the ground).

Third, when considering the cart and the ground only (and assuming the outer gear surfaces are moving at Vtrack, which we know to be true by our first point), the cart is passing by the ground at Vtrack.

Fourth, when considering collectively the ground, track, and cart, we know that the cart is passing the ground at the same speed the track is passing the cart, again by our first observation. So if the track is passing the cart at the same speed the cart is passing by the ground, then Vcart - Vground = Vtrack - Vcart ==> 2 Vcart = Vtrack + Vground. Vground is zero, so Vcart = Vtrack / 2.

I know it's been explained to death above, and I'm not trying to be condescending or anything, but it's interesting and bears correction. Your blog is fantasic, by the way, and thanks for the correction with this post. It's been fantastic just studying this problem.

re 69:

The problem is that what Mark describes mathematically is not what is drawn in the diagram. Although he shows three wheels touching at their rims, his intent is to couple the angular velocity of the upper wheel to the negative angular velocity of the lower wheel. So forget the diagram and equate the angular velocities and the cart will go faster than the upper belt.

Lol, this is ridiculous. I stopped reading this blog a while ago because of all the math errors and I find this when I check back.
Of course Mark was wrong, but he doesn't deserve a pat on the back for admitting it.
Mark has said that mean-spirited commentary is just the nature of the Internet and everyone else needs to get use to it. He 'doesn't owe anyone anything.' That's his character, and we've seen his math.

Haha, I like how this physiscs and diagramming is now "complex" and "fascenating." We should all thank Mark for his explaination of this difficult subject. Only certain people can still condescend to their readers after being so arrogant, and I say "arrogant" because this was never about math. Mark never used mathematics to illustrate his criticism, although he does demand it from those he criticizes.

What's left to say?

Back to using Mathematics to point out fools!
At least he still has his pride. Good for Mark.

One thing I'd like spork and the gang to bear in mind, in terms of the video and convincing people, is that it would be good to have one, clear, concise explanation of the physics; the explanation given on several blogs by AirShowFan is the clearest I've seen and is the one that convinced me.

Something that confused me during the Great Schism :) was that a lot of people insisted the device worked but posted unworkable explanations as to why.

By Stephen Wells (not verified) on 09 Dec 2008 #permalink

"Something that confused me during the Great Schism :) was that a lot of people insisted the device worked but posted unworkable explanations as to why."

It would be nice to have all the info available in one place, clear and accurate. In fact I have all of that in one folder on my laptop, along with diagrams and motion-GIF's. I've posted most if not all of it on various forums. I have not posted it to a website that I can link to.

Too often when I'm directed to a new forum, I'm literally too busy responding to crticisms and attacks on that new forum to go through the entire list of analyses and examples yet again.

Also, bear in mind that JB and I were naive enough to think that if we built a working model, and documented it carefully enough, that would simply convince the sceptics. We chose to use a treadmill to answer the question of gusts, wind direction, etc. We show that it can't be tied to a string. We show a level so you know it's always either on dead level ground or going uphill. We pan around the room to show there is no fan, etc. We have come to the realization that absolutely no amount or form of evidence will be sufficient for some.

We even posted the parts list and build notes. I agreed to build several of these carts for those that asked. JB agreed to send his cart to sceptics free of cost (his is current on loan as we speak).

Are there proponents that explain it incorrectly? Yes. But I assure you I've explained it MANY times in MANY ways, perfectly accurately. I can point you to relevant posts on other forums where I've done so. However, in almost every case the discussion grows into a 50 page sh!t fight with those that are CERTAIN it can't be done.

Mark,

the gear analysis in your post is wrong. the speed of the belt and the speed of the center of mass of the bottom wheel will be equal, no matter what the radii of the three wheels.

the definition of angular speed in terms of tangential speed is:

v=rw

where r is the radius of the wheel.

in this example we say that the wheels are in contact with one another and roll without slipping. (equivalently,we can say the gears turn without teeth skipping.)

this means that the tangential speed of each wheel at the rim where they contact is the same.

so v_upper=v_middle
and v_middle=v_lower

where upper, middle and lower refer to the three wheels.

from this you can see that v_upper=v_lower

the center of mass motion of the bottom wheel is what you can identify with the cart motion, since they move together. the bottom wheel has tangential speed of v_upper, so the cart will move with the same speed.

if you change the radii of the wheels, the cart velocity will not change. what will change is the angular speed of the wheels.

v=rw

so v_upper=r_upper * w_upper
v_lower=r_lower * w_lower

since v_upper=v_lower

r_upper * w_upper = r_lower * w_lower

or, solving for w_lower and substituting r_lower = R, r_upper = r

w_lower = (r/R) * w_upper

this shows that the angular speeds of the wheel will be different, unless r=R. however, no matter what the radii of the wheels, the cart will move with the same speed as the belt.

Rob:
>...no matter what the radii of the
>wheels, the cart will move with the
>ame speed as the belt.

More bad math (or at least bad conclusion).

As mentioned above by countless posters, the cart as shown will travel at 1/2 the upper belt speed. In Mark's posted design, there is no need whatsoever for the lower two wheel -- one gets the exact same cart result by placing one large wheel between the two surfaces. Try rolling a pencil between your palms if you have doubts.

JB

By Anonymous (not verified) on 09 Dec 2008 #permalink

May I pause here to place an explanation point on the value of physical experiments rather than relying on math alone to "prove" the behavior of a mechanical device?

Just as with the cart, on a simple belt and roller example, posters from the OP on down continue to throw "math" around and come up with results different from that which the physical world dictates.

As spork is fond of saying "If you're gonna use math to 'prove' your point, you better damn sure not forget to carry the two."

I present that few of us are sharp enough to carry the two without fail and some of us are failing at that quite often.

JB

By Anonymous (not verified) on 09 Dec 2008 #permalink

to all the down-wind people:

the treadmill experiment and the outdoor runs are NOT equivalent reference frames.

to see this, lets do a thought experiment. pretend we are in a car. if we drive the car at 55 mph outsdoor in still air and stick our head out the window, we will see the ground going by at 55 mph and feel a 55 mph wind mussing up our hair.

now put the car on a treadmill and move the tread mill belt at the right speed so the car stays motionless relative to the floor that the treadmill sits on, while the speedometer says 55 mph. in this case, if we stick our head out the window and look down we will also see the belt going by at 55 mph, but we will NOT feel a wind mussing our hair.

the treadmill/outdoor reference frames are NOT equivalent, because even though the ground/belt is moving by in the same way, you can tell if your on a treadmill or not by the lack of wind.

since you can tell one reference frame from another, you are NOT in equivalent frames.

in order to mimic the outdoors you would have to add a very large fan in front of the treadmill in order to add the wind. since the down-wind cart people did not include a giant fan in the video, comparison between the outdoor cart motion and treadmill cart motion is invalid.

the treadmill experiment does not show that the cart is going faster than the wind. THERE IS NO WIND.

however, i still have doubts as to whether or not the outdoor videos show faster-than-wind (FTW) travel.

i will follow up with a post explaining why.

Rob. The question if if you are treavelling downwind outside not in still air. So in your car example you are going 55mph with a 55mph tail wind. It will feel just like still air. As anyone who has ever sailed directly down wind can attest.

Re Rob #77:

For goodness sake, do we really need to go through the elementary physics part of this?

The treadmill simulates going N miles per hour with an N mile per hour tailwind

If there's a five mph wind, and you drive with the wind at 10mph, then if you stick your head out the window, you'll feel a 5 mile per hour forewind.

If there's a 10 mph wind, and you drive with the wind at exactly 10mph, then if you stick your head out the window, you won't feel any wind.

If there's a 20mph wind, and you drive 10mph with the wind, then if you stick your head out the window, you'll feel a 10mph tailwind.

The treadmill demonstration is simulating: the point at which forward velocity is exactly the same as the wind.

As others have pointed out repeatedly, this is a very elementary application of the idea of equivalent frames of reference. On the treadmill, the speed of the vehicle relative to the "ground" beneath it, and the speed of the air relative to ground, are both exact matches for the corresponding relative speeds in the outdoor wind scenario. They are equivalent frames of reference.

JB,

oops. i goofed. i didn't do the analysis from the same reference frame. i biffed the translation from center of mass motion to a frame based on the ground.

my analysis is from the rest frame for the wheels. if they see the top going by at v_upper, then they see the ground go by at v_upper also. so my math is correct.

however, Mark's analysis if from the point of view of the ground.

so, if you change frames from the rest frame of the wheels, to the ground, you need to add v_upper vectorially to the center of mass for the wheels and to the belt on top. this makes the wheels go by the ground at speed v_upper, but the belt is going by the ground at 2*v_upper, (according to my def of v_upper.)

that is where the factor of 2 comes in.

so the final corrected analysis is that if a belt rotates wheels which move relative to the stationary ground, the wheels will move at v_upper/2.

"the treadmill experiment and the outdoor runs are NOT equivalent reference frames."

"the treadmill/outdoor reference frames are NOT equivalent, because even though..."

"since you can tell one reference frame from another, you are NOT in equivalent frames."

"since the down-wind cart people did not include a giant fan in the video, comparison between the outdoor cart motion and treadmill cart motion is invalid."

"the treadmill experiment does not show that the cart is going faster than the wind. THERE IS NO WIND."

You almost had me. Maybe one more time and a few caps and you'd be there.

"i will follow up with a post explaining why."

I look forward to it.

Mark,

(banging my head on the table)

ahh! tailwind. for all the discussions about this, i was failing to put in the tailwind.

i agree then, the treadmill does seem to be a valid setting to mimic the cart moving outdoors in a tail wind.

(but something seems wrong about it still. i need to think more.)

one of the things bothering me is that the treadmill is at an angle, while the ground outside is flat.

at first thought, since it is on an incline, it seems that the component of gravity against the cart down the incline must be needed to counter balance the thrust of the carts propeller, which implies that if it were on level ground, it would in fact acclerate, reaching some terminal speed which is faster than the wind.

this calls for an analysis of the forces on the cart while on the treadmill.

what will also be useful is doing an energy analysis using the work-energy theorem.

it will be useful to analyze a couple similar situations which should shed some light on the cart dynamics.

first i want to look at a cart with a sail on it, since the cart begins motion purely by sail action where the area of the blades wrt to the wind give arise to the force. it seems to me that we can use the sail cart to find an upper limit to the speed attainable.

second, i want to look at how a wind turbine operates to see what sort of power we can expect to get, as well as see what role the wind velocity plays in determining the power. i want to do this because one way of looking at the cart is a wind turbine powered car. the only energy input into the cart is from the wind. this energy gets converted by the gearing into kinetic energy of motion.

also, anyone who has done the experiments, do you have actual average wind speed measurements for the outdoor, as well as the speed the cart attained? i have a print from the Journal of Amateur Yacht Research Society which describes the cart.

afterall, the proof is in the experimental results, not the theoretical calculations. at least not the theoretical calculations i am going to do, since i have no access to a super computer running fluid dynamics software that can more accurately model reality.

So, for the mechanical cart (between two treadmills) the carts forward velocity is given as:

Vc = (Rlower*Vupper - Rupper*Vlower)/(Rlower-Rupper)

What happens if Rupper = Rlower?

No, not really. just no solution except for Vupper=Vlower and Vc unconstrained. If Vupper.ne.Vlower then the cart breaks or one of the wheels slips.

SteveM: I point out, once more, that the mechanical cart in Mark's picture moves at half the speed of the upper track, whatever the sizes of the wheels are. Mark's supposedly mathematical analysis is complete nonsense.

By Anonymous (not verified) on 09 Dec 2008 #permalink

rob:
>one of the things bothering me is that
>the treadmill is at an angle, while the
>ground outside is flat.

Rob, we have posted plenty video footage with both a flat treadmill and an inclined treadmill. Search YouTube for "Spork33".

Any conclusion you base on the assumption that the treadmill must be angled will be flawed from the start.

We can control the forward progress of the device through three methods:

A: slow down the belt until the internal mechanical friction of the device balances with the thrust of the prop

B: incline the treadmill so we can run a faster belt speed and still control progress.

C: physically stop the device from running off the front of the treadmill.

In our videos, we show many combinations of all three.

JB

By Anonymous (not verified) on 09 Dec 2008 #permalink

Rob, I did the math for you; no supercomputer required for the first pass. And yes, the small cart requires the treadmill to be tilted to simulate a 4.4 degree incline to prevent the cart from accelerating forward when the treadmill is at 10 mph.

The source of the energy needed to propel the cart to a specific speed is the momentum of the air mass in relation to the ground that the cart is rolling on. One thing to remember, the propeller is always trying to slow down the speed of the air mass around it in order to harness that energy. A wind turbine slows the air to generate electricity and the amount of power from that momentum change is well documented. The cart also harnesses that energy but in a slightly different way.

Here's a link to the article published about a DDWFTTW prop cart that was tested outdoors and on a treadmill. In the article, data is provided that can be analyzed.

http://www.ayrs.org/DWFTTW_from_Catalyst_N23_Jan_2006.pdf

The method used for measuring the thrust and drag is listed in the article.

The amount of forward thrust was taken directly from the scale which was attached behind the cart to restrain the cart from moving forward off the treadmill. That showed the force directly at various speeds. The readings were taken at 1 mph intervals between 4 and 10 mph.

The next phase of the test was conducted with two changes: the belt was repositioned so that the propeller turned the opposite direction from the wheels, and the scale and tether repositioned to restrain the cart from moving backwards off the treadmill. The reading from the first test was subtracted from the readings from the second test to remove the imbalance, then that result was divided by two to show the total drag of the cart during operation.

By adding the thrust measured at each point to the drag measured and calculated at each point, the difference between the drag that the cart produced was compared against the thrust for each interval.

The reading at 4 mph was zero and the drag part of the test showed 185 grams. Since the drag part showed the sum of the drag in two directions, the drag in one direction with all systems functioning and accounted for was 92 grams. A thrust of 92 grams balances the drag at that point for a lift to drag ratio of 1:1.

At 10 mph, the measured imbalance was 150 grams and the calculated drag was 402 grams, giving a thrust of 552 grams or a L/D ratio of 1.37:1.

I checked a wind energy calculator to see if the energy needed to provide the thrust measured could be captured from a wind moving at 4 mph given the size of the prop on the cart (40" in diameter). After doing the conversions and using Betz' law as a guideline for the max efficiency, the amount of power available to a wind turbine of the same diameter as the prop is 1.63 watts. That translates to 93.37 grams of thrust at 1.78 m/s, quite close to the test figure of 92.5 grams. For 10 mph, the numbers work out to 25 watts or 585 grams thrust at 4.44 m/s, again within experimental error of 552 grams as indicated by the treadmill test.

The small cart in spork and JB's video tends to back those numbers up, with the 169 gram cart "climbing" a 4.4 degree incline at 10 mph, indicating an imbalance of 13 grams force in the forward direction. That would give it an acceleration rate of 2.47 ft/sec2 on level ground in a 10 mph wind when the cart is at 10 mph. The large cart would have an acceleration rate of 2.12 ft/sec2 based on a weight of about 2300 grams (five pounds). The break even speed on the little cart is 2.7 mph vs the large cart's 4 mph, so a little better performance could be expected from the small cart.

So it appears that the energy available from the different wind speeds correlate quite well to the treadmill test. There is no mystery force needed to accomplish this, no violation of any physics, in fact pretty normal physics, just applied in a unique way.

JB: i will have to look at the all the videos. i have only seen a couple.

for now:

here is the sail car force analysis.

take a cart and attach a sail on it that has the same area, A, as the blades on the FTW cart. the wheels are friction less and massless etc, to make analysis a bit simpler.

(this should actually be a good approximation to the propeller cart, in the first moments it moves before the propeller is rotating too fast)

definition of force is F=dp/dt, by newton's second law.

or F=m dv/dt = m/dt dv, which says the force is equal to the mass flow rate times the change in velocity.

the wind blows at speed u. in time dt the wind will blow a volume of air into the sail v=udtA. the total mass is m=pudtA where p in this case is the density of the air.

therefore the mass flow rate is m/dt = puA.

now we need to find the change in velocity of the wind as it hits the sail.

realistically, the air will get deflected by the sail and continue around on the other side with a slightly lower speed, so dv

SteveM: I point out, once more, that the mechanical cart in Mark's picture moves at half the speed of the upper track, whatever the sizes of the wheels are. Mark's supposedly mathematical analysis is complete nonsense.

read my #70, his picture is misleading and doesn't represent the actual physical arrangement he wants to achieve. My equation in #84 is based on the correct mechanical configuration of making the upper wheel spin at the same angular velocity as the lower wheel but in the opposite direction. This will indeed propel the cart forward faster than either of the belts.

Hi Mark. One problem with your analysis:

the wind provides a force by blowing against the propellor - not by rotating it, but by treating it as a dead sail.

Trouble is, it -does- rotate it. Because in addition to being a prop, it can also server
as a windmill. And that rotation results in a force, thought the wheels, towards the
wind / against the intended direction of motion of the cart.

Beever@90

No Beever, the wind does not rotate the prop as a turbine under any operational circumstances. If this were the case, it would force the wheels to rotate the wrong direction against the rolling surface and the vehicle would be in one constant skid.

No, the wheels roll forward against the ground as one would expect any normal vehicle to do. The prop always acts as a simple propeller, generating thrust by acclerating air relative to the cart and slowing it down relative to the ground.

JB

By Anonymous (not verified) on 09 Dec 2008 #permalink

The tailwind does produce a force which tries to rotate the propellor in the "wrong" direction when the cart is starting. But it's outweighed by the sail effect; the main force on the cart is forwards - and that produces a rotational force in the opposite direction, which outweighs the original rotational force from direct wind on the propellor.

I'm pretty sure you could work out a version of the cart with the right propellor and the right gearing to make it move into the wind - harnessing that rotational to move the cart in the other direction. But it would be a very different setup - different prop ratio, etc.

Mark is right on both points:

A: the tailwind does *try* initially to rotate the prop as a turbine when starting but with the cart geared properly the wind fails to win that battle operationally.

B: A simple change in gearing will in fact change the behavior of the cart to an 'upwind' vehicle. If you reduce the size of the front wheels by say 50%, and set it down in the same tailwind in the same orientation, it happily backs up directly into the wind.

JB

By Anonymous (not verified) on 09 Dec 2008 #permalink

Well, I believe it works, but I'm having a dickens of a time figuring out where my analysis goes wrong. Any help is appreciated.

I start with imagining a cart with a sail. It travels downwind slightly slower than the wind. The wind pushes on the cart just hard enough to counteract F_roll, the rolling friction.

We start drawing power off of the axle. Now there is another retarding force on the cart, F_load. The cart slows down slightly, so that the force of the wind on it equals F_roll + F_load.

According to the experiment, we can use the power drawn off the axle to generate thrust (F_thrust) greater than F_roll + F_load and get us above windspeed.

Obviously, the work done by the thrust of the fan cannot be greater than the work done by the axle, but if they are both acting on the cart in the direction of motion (opposite signs) then it seems like we would integrate them the same way in order to calculate work, and find that the fan does more work than the axle.

Where am I going wrong?

-Charles

By chasmotron (not verified) on 09 Dec 2008 #permalink

The wheels are absorbing force at 10 mph. The prop is dissipating force at a lower speed into the air because of the gearing (advance ratio is less than 1:1).

"Well, I believe it works, but I'm having a dickens of a time figuring out where my analysis goes wrong. Any help is appreciated.

I start with imagining a cart with a sail...."

From that perspective, the best place to start is with a land-yacht on a 45 degree downwind tack. Let's start with the assumption that the cart's speed on that tack is 2X the wind speed. That will give it a downwind velocity component greater than the true wind speed. This vector analysis shows that from this assumed condition, the land-yacht can continue to accelerate (the net force vector has a forward component when projected on the vehicle's velocity vector. If/when you accept this, we can move on to how the vehicle first achieve's that condition. We can also work toward how this vehicle is exactly analagous to the prop-cart (though it may not be immediately evident).

http://www.putfile.com/pic/8419299

I would like to suggest to spork and the others who have already created and published the various treadmill videos that one more clip showing the final steady state situation with the cart going into an actual (relative to the cart) headwind might be helpful. A suitable fan placed at an appropriate distance in front of the cart on the treadmill and facing towards it would seem to be "all" that is required. Unfortunately this simple approach may also be likely to produce a somewhat turbulent, narrow and even variable speed airflow (varying with distance from the fan) rather than the completely uniform flow we'd really like to have, but perhaps a second fan pointing in the same direction again but this time at the other end of the treadmill could help generate a more uniform flow over the working area? Anyway, to stop the cart wandering off to one side or the other in this imperfect head wind, how about also adding a "guide wire" stretched in the direction we want to the cart to maintain, and threaded through a couple of "eyelets" in some suitable location(s) near the head (and tail?) of the cart.

I do understand how carefully viewing the longer term behaviour of the cart in the various existing treadmill videos does appear to more or less prove the point, but (to me at least) there still seems to be at least one way to get confused over what is shown. For one thing, you *could* have a cart with a propeller so highly geared that it generates enough thrust to guarantee more or less arbitrary forward acceleration initially (perhaps even with skidding wheels) after being released on a treadmill in still air, etc., as per the set-up in most of the current videos. It seems pretty clear to me that this initial forward movement could occur even if that particular cart configuration had no chance of actually starting from rest and eventually accelerating to "faster than the wind" (with the "windspeed" given in this case by the speed of the treadmill instead).

Whilst adding the guide line could obviously open the door to suggestions that the cart was being pulled or held in some way, it should at least (I think) enable a video to be made showing the cart in a stable state going "faster than the wind" and with no manual adjusting of direction, etc., being required. Put some coloured sections on the guide line so it can be moved forward or backward relative to the cart so to show it isn't doing anything more than essentially maintaining the direction. Release puffs of smoke or similar into the airflow to show it is there, etc.

Or is it just me that thinks this rather more complicated set-up would still be worth trying to achieve? :-)

So here's a plan B! Just tether the tail of the cart in a set-up otherwise identical to that in most of the existing videos, and also use a simple spring scale or similar to show the constant "pulling force" being generated while it is in that state (going "downwind at the speed of the wind").

In fact this kind of set-up could possibly also be used fairly easily to show the cart at various stages throughout the whole process if the speed of the treadmill can be varied more or less at will and a reasonably steady relative tailwind or headwind can also be created at around the desired speed (with fan(s) again as above). I.e. fan(s) plus treadmill plus tether and scale to measure force on cart for a range of different speeds from being at rest on the ground all the way through to the holy grail of DDFTTW!

Yeah, yeah. I know... it's a lot harder to actually make this all work than it is to just imagine it, and I'm sure you've almost certainly already thought of something like this anyway, but I (for one) would still like to see it if it was possible! Dreams are free after all... :-)

Re #97:

I don't think that there's any way of doing a video that's going to convince doubters. I'm speaking from experience here, both my own experience with respect to this vehicle and other things, and just general experience dealing with people on the internet.

The problem is, there are so many crackpots out there. YouTube currently has over 10,000 videos purporting to demonstrate free energy generators. And every single one of the crackpots pushing them has an elaborate explanation for why it works, video clips purporting to show why critics arguments are all wrong, etc.

Unfortunately, this means that when you're trying to demonstrate something which is really counterintuitive, you're stuck trying to distinguish yourself from the gigantic swarm of crackpots. The overwhelming preponderance of the evidence, when faced with yet another claim of what appears to be a violation of physical laws, is that it's just another crackpot.

I've been writing this blog for about three years now. I've been peppered with claims and videos from people about all sorts of scams - hydrogen augmentation in automobile engines, magnetic free energy, magnetic wind power, plasma energy, Brown's gas, and more than I can name. Every one of them has been utter garbage.

If you look at the videos from the crackpots, the majority of them are obvious crap. But there's a sizeable minority - probably around 10% - which do videos of a quality comparable to the videos that started this whole discussion.

If you listen to Spork in the video, he sounds reasonable. But if you listen to Tom Bearden (one of the magnetic energy cranks) in a video, he sounds reasonable too. Spork tries to counter the basic arguments against the vehicle by showing it working under a variety of conditions, and trying to show that most of the basic ways of cheating aren't being used. But if you look at one of Bearden, he does the same thing: he shows his magnetic generator working under various conditions, and shows various things which are supposed to prove that his generator isn't cheating. In fact, Bearden's explanation of why his generator works even sounds a lot like Spork's explanation of the cart! (Bearden claims that his device is extracting energy from the difference in electrical potential between the magnetosphere and the earths surface.)

The difference is, Bearden's thing doesn't really work. But can you tell that from a video demonstration? No. It's just too easy to cheat in a video. No matter what you do in a low-quality internet video, there's just no way to prove that you're not cheating. Spork could spend the rest of his life producing more and more videos demonstrating how the thing works under various conditions, but people aren't going to believe it without either seeing it live, in person; or seeing a real careful analysis of it to show where the energy is coming from.

Spork can film it with a fan in front. He could film it in a wind tunnel. He could film it on a treadmill in a wind tunnel. Internet videos just aren't going to convince skeptics; we've seen far too many compelling looking demos that have been faked for the internet.

Re #97:

I don't think that there's any way of doing a video that's going to convince doubters. I'm speaking from experience here, both my own experience with respect to this vehicle and other things, and just general experience dealing with people on the internet.

The problem is, there are so many crackpots out there. YouTube currently has over 10,000 videos purporting to demonstrate free energy generators. And every single one of the crackpots pushing them has an elaborate explanation for why it works, video clips purporting to show why critics arguments are all wrong, etc.

Unfortunately, this means that when you're trying to demonstrate something which is really counterintuitive, you're stuck trying to distinguish yourself from the gigantic swarm of crackpots. The overwhelming preponderance of the evidence, when faced with yet another claim of what appears to be a violation of physical laws, is that it's just another crackpot.

I've been writing this blog for about three years now. I've been peppered with claims and videos from people about all sorts of scams - hydrogen augmentation in automobile engines, magnetic free energy, magnetic wind power, plasma energy, Brown's gas, and more than I can name. Every one of them has been utter garbage.

If you look at the videos from the crackpots, the majority of them are obvious crap. But there's a sizeable minority - probably around 10% - which do videos of a quality comparable to the videos that started this whole discussion.

If you listen to Spork in the video, he sounds reasonable. But if you listen to Tom Bearden (one of the magnetic energy cranks) in a video, he sounds reasonable too. Spork tries to counter the basic arguments against the vehicle by showing it working under a variety of conditions, and trying to show that most of the basic ways of cheating aren't being used. But if you look at one of Bearden, he does the same thing: he shows his magnetic generator working under various conditions, and shows various things which are supposed to prove that his generator isn't cheating. In fact, Bearden's explanation of why his generator works even sounds a lot like Spork's explanation of the cart! (Bearden claims that his device is extracting energy from the difference in electrical potential between the magnetosphere and the earths surface.)

The difference is, Bearden's thing doesn't really work. But can you tell that from a video demonstration? No. It's just too easy to cheat in a video. No matter what you do in a low-quality internet video, there's just no way to prove that you're not cheating. Spork could spend the rest of his life producing more and more videos demonstrating how the thing works under various conditions, but people aren't going to believe it without either seeing it live, in person; or seeing a real careful analysis of it to show where the energy is coming from.

Spork can film it with a fan in front. He could film it in a wind tunnel. He could film it on a treadmill in a wind tunnel. Internet videos just aren't going to convince skeptics; we've seen far too many compelling looking demos that have been faked for the internet.

Re #94:

"Where am I going wrong?"

All right.

"Obviously, the work done by the thrust of the fan cannot be greater than the work done by the axle, but if they are both acting on the cart in the direction of motion (opposite signs) ..."

Work is not acting. Force is acting. Work is done (over time).

"... then it seems like we would integrate them the same way in order to calculate work, and find that the fan does more work than the axle."

That "seems" is where you go wrong. The thrust is created by moving the sail backwards using a lever. You use "power" of the axle to move a long arm of the lever forward, and the short arm of the lever will move the sail backward. The force exerted by the air on the sail (F_thrust) and the resistant force exerted by the long arm as you move it (F_load) will be related in this way: F_thrust/F_load = l_long_arm/l_short_arm. On the other hand, the distances travelled by the ends of the lever, over any given period of time, will be related in this way: d_short_arm/d_long_arm = l_short_arm/l_long_arm.

Work is force times distance. Work done by/on the sail, over a given period of time, is W_sail = F_thrust*d_short_arm, and work done by moving the long arm is W_axle = F_load*d_long_arm. From the equations above, it follows that W_sail = W_axle, over any given period of time. Even though F_thrust > F_load.

In the practical implementation, you don't use a lever which can only move once, but gearing which can move and transform force constantly, and you don't move the sail backward once, but you use a propeller which can move the air-pushing surface (the "thread of the airscrew") backward constantly.

(P.S.: You chose a rather awkward way of modelling the device by "drawing power off of the axle". Although the math will still work out, such model is quite impractical if you try to understand how it works. Rather than having a hard time understanding the intricacies of this model, it would be wiser choosing a simpler one.)

my next step in analyzing the FTW cart was to pretend the propeller is a wind turbine whose power is then converted into kinetic energy. this isn't strictly true. the wheels and prop are mechanically linked, and the prop is supposed to be turning the opposite way that it would if it were operating as a turbine.

however, the physics involved should be applicable to the actual cart, since the cart and a wind turbine extract energy from moving air.

here are assumption i make: smooth air flow through propeller. no energy lost except that removed by the propeller as work. prop spins around with area A. use a stream tube for the analysis.

(see http://www.windpower.org/en/tour/wres/tube.htm for a picture of what i mean by a stream tube)

the wind has speed u moving towards the prop. at the prop the speed will be u1 and on the other side of the propeller it is u2. u2 < u1 since kinetic energy was lost to the prop/cart.

the power available in the wind is what will be available as kinetic energy to the cart. the power is the rate of change of kinetic energy. let's calculate this total wind power:

the total power of a mass of moving air with speed u, density p and cross sectional area A is the rate of change of kinetic energy:

Power=d(KE)/dt=d(1/2mu^2)=1/2 u^2 dm/dt = 1/2 Apu^3

where the mass flow dm/dt=Apu (from previous comment)

we see the total power available in wind is proportional to the speed cubed.

now lets look at the work that is extracted by the propeller.

the wind has some initial momentum at speed u. it passes through the propeller, losing momentum, and later it has less momentum at speed u2.

the force on the propeller is by newton's second law:

F=dP/dt=dPi/dt - dPf/dt (Pi and Pf are initial and final momenta, P=mv, mass m, velocity v)

F=dm/dt(vi-vf) =pAu1 (u-u2) (where initial and final velocity are u and u2)

we can calculate the power extracted by the propeller using Power=Fv (force times velocity)

the power extracted by the propeller from the wind is:

Power=F*u1=pAu1^2(u-u2)

we can also calculate the power by considering conservation of energy. the inital kinetic energy is equal to the work extracted plus the final kinetic energy:

Power extracted = d(KE)/dt = d(1/2 m u^2 -1/2 m u2^2)
= 1/2 dm/dt (u^2-u2^2)= 1/2pAu1(u^2-u2^2)

now we have two equivalent expressions for the power extracted by the propeller, one derived by force and momentum considerations, the other by energy considerations:

power=pAu1^2(u-u2)
power=1/2 pAu1(u^2-u2^2)

set these equal and you can solve for the speed of air at the prop u1 = 1/2 (u + u2)

this says that the speed of air moving through the propeller is the average of the initial and final wind speeds. intuitively this makes sense.

using u1=1/2(u+u2) to substitue u1 into power=1/2 pAu1(u^2-u2^2) and doing some algebra, you can show:

power= 1/4 pAu^3(1+a-a^2-a^3)

where i have substituted the dimensionless constant a=u2/u.

this is the total power that the propeller, acting as a turbine, can extract from the wind. the constant a is the ratio of the final wind velocity to the initial wind velocity. the design of the propeller will determine the actual initial and final wind speeds, which determines the value of the dimensionless constant a. for some optimum design, and corresponding value of a, you will get the maximum power extracted by the propeller. to find the value for a, take the derivative of the power wrt a and set it equal to zero. solving for a yield a=1/3 for the maximum power.

to find the efficiency at maximum power, take the ratio of the (power available in wind) / (max power extracted by prop) when setting a=1/3:

Pw/Pp=(1/4*pAu^3*(32/27))/(1/2 pAu^3) =(16/27) = 0.59

this shows that the maximum efficiency for a wind turbine is about 60%. if you are sufficiently clever in your turbine design you can approach, but never surpass this efficiency value.

my next task is to use these results and apply them to a cart moving at speed v in a steady wind u. this ought to give the maximum speed attainable by the cart.

"my next step in analyzing the FTW cart was to pretend the propeller is a wind turbine whose power is then converted into kinetic energy. this isn't strictly true. the wheels and prop are mechanically linked, and the prop is supposed to be turning the opposite way that it would if it were operating as a turbine.

however, the physics involved should be applicable to the actual cart, since the cart and a wind turbine extract energy from moving air."

I don't think this will work. While it's true that one could look at the cart as a whole as a turbine, the propeller clearly operates as a prop and not a turbing. The flow through the prop-disk is from front to back; from low pressure to high. As such it is not subject to the Betz efficiency limit.

spork:

yeah, i know it is not a turbine. it is like a turbine in reverse. however, the same momentum and energy analysis should apply, but with the flow reversed, providing thrust.
once i have the proper power relations, i should be able to find the relative car and wind speeds.

Rob:
>this shows that the maximum efficiency for
>a wind turbine is about 60%. if you are
>sufficiently clever in your turbine design
>you can approach, but never surpass this
>efficiency value.

As spork points out Rob, your 60% number is not applicable in this situation as our spinny pinwheel thingy on the back is a simple prop and not a turbine.

If you garbage in it will just be garbage out.

JB

By Anonymous (not verified) on 10 Dec 2008 #permalink

When I did the numbers from Jack's treadmill tests (rob, did you look at post #87?), the measured drag at both 4 mph and 10 mph seemed to correlate quite closely to the energy available when using Betz' law, i.e., the equivalent to 59% of the total energy available. I assume that is because of the actual prop efficiency. This may show a relationship between the reasoning behind Betz' law and propeller stall. Just a thought.

Using Jack's road test numbers of 9 mph wind speed and 13 mph cart speed and his advance ratio of .75, the prop is trying to push air back at 9.75 mph. For Betz' law to work, the air has to be slowed to 1/3 of the original speed or down to 3 mph. That would seem to point to a propeller efficiency (speed-wise at least) of about 70% ((9.75 mph - 3 mph)/ 9.75 mph). That appears to me to be within the expected range.

I guess a test that demonstrates that the tailwind momentum (and speed) is completely canceled by the prop wash would answer the question. But I think I remember someone indicating that the best results were achieved with an advance ratio of .2 to .4 rather than close to 1.

Delete the sentence containing "propeller stall". I had another thought going and didn't edit before posting.

Is there any way to edit after posting here?

Mender, I did not mean to imply that just because Betz law does not apply that one cannot happen to be using a propeller that is 59% (or even less) efficient.

I mean only to say that Betz law (which states a *maximum* of 59% available) itself doesn't apply in this case at all as the spinny pinwheel thingy functions as a prop and not a turbine.

Even a finding of fact that the prop was exactly 59% efficient wouldn't add any support to the Betz claim being applicable.

JB

By ThinAirDesigns (not verified) on 11 Dec 2008 #permalink

JB, I understand that, was just commenting that so far the trend seems to support the use of Betz'law as a guideline. The only hard data so far seems to point to that.

However, since Betz' law is stated as the maximum under ideal conditions, I'd have to say that achieving 59% under quite a bit less than ideal conditions firmly indicates to me that the cart isn't conforming to that restriction. I don't believe it is subject to Betz' law but haven't ruled anything out at this point.

In order for the prop to "stall" the tailwind completely, the advance ratio would have to be 1. I "know" the cart won't self-start with that but will it be able to maintain speed (or gain more) when conducting a treadmill test, i.e., brought up to speed and released?

"I don't believe it is subject to Betz' law but haven't ruled anything out at this point."

The way we know it isn't subject to Betz' law is simply due to the direction of the flow through the prop-disk - from low to high pressure. If you think about the implication of Betz' law, it involves a reduced capture area, and this results from the high pressure ahead of the disk. We don't have this situation.

"In order for the prop to "stall" the tailwind completely, the advance ratio would have to be 1. I "know" the cart won't self-start with that but will it be able to maintain speed (or gain more) when conducting a treadmill test, i.e., brought up to speed and released?"

Nope. At 1.0 the cart won't operate. You can relate it directly to a yo-yo in which the hub has exactly the same diameter as the yo-yo itself. Greater than 1.0 gives a cart that goes upwind. Less than 1.0 gives a downwind cart. The theoretical speed of the cart speeds up as you approach 1.0 from either side, but is eventually overtaken by internal losses. As such there is an optimal ratio for the cart for a given wind speed and rate of internal loss.

By Anonymous (not verified) on 11 Dec 2008 #permalink

Sorry, forgot to "log in". That last post is me.

Thanks, spork, I didn't go into enough depth on the Betz' law reasoning.

I was thinking that given a less than perfect prop, the advance ratio of 1 would have some slippage (10%?), so might still be possible - maybe.

"Thanks, spork, I didn't go into enough depth on the Betz' law reasoning."

Hey, we've all had our mind twisted by this thing at one time or another. It can seem simple as pie, and then some other aspect jumps out and has you guessing again.

"I was thinking that given a less than perfect prop, the advance ratio of 1 would have some slippage (10%?), so might still be possible - maybe."

Hmmmm... now you've got me thinking. I think any prop inefficiency gets lumped in with other real-world losses and simply increases the margin around 1.0 where the cart does nothing. But admittedly, that's off the cuff and not yet fully noodled.

I've just put a demonstration of a mechanical "faster than the track that's pushing it" machine. See http://www.youtube.com/watch?v=k-trDF8Yldc
It should be easy to see the anolgy between this machine and the DDWFTTW cart. Look at how the big wheel turns against the direction of movement of the ruler, just as the propeller of the wind-propelled cart turns against the direction of the wind.

By Michael C (not verified) on 12 Dec 2008 #permalink

Spork, if Betz' law applies to wind turbines because of the wind essentially flowing around the high pressure or the air restriction of the wind turbine, wouldn't it also flow around the backwash (high pressure) from the prop? We have a high pressure area behind the disc, which is the direction that the wind is acting from. Betz' law, yes?

"if Betz' law applies to wind turbines because of the wind essentially flowing around the high pressure or the air restriction of the wind turbine, wouldn't it also flow around the backwash (high pressure) from the prop? We have a high pressure area behind the disc, which is the direction that the wind is acting from. Betz' law, yes?"

The wind is blowing from behind, but at a speed slower than the cart is moving downwind. So the flow through the disk is still low-pressure to high pressure. One innaccurate concept a lot of people have about this is the notion that the tailwind and the prop-wash essentially "collide" behind the cart - that the thrust from the prop forms some sort of extension of the cart that the tailwind pushes against. But this simply isn't the case. The prop behaves exactly the way a prop behaves on a plane that is taxiing in still air. The prop is moving through that air-mass, but at less than the theoretical design speed of the prop. Any tell-tails you put in the vicinity of the prop will tell you the two situations are identical. There is no convergence of flow behind the prop of the cart.

Yeah, I backslid on that one. Must be tired!

Sailboats can exceed the wind velocity by sailing *across* the wind, but not by sailing *downwind*.

Once a vehicle going downwind reaches the wind velocity, it "sees" *no* apparent wind. If a vehicle goes down wind faster than the wind velocity, it "sees" an apparent headwind.

The bottom line is *you cannot capture wind energy if your velocity is the same or greater than the wind*.

By LightningRose (not verified) on 13 Dec 2008 #permalink

LightningRose,

and how exactly do you think do the propeller's blades move through the air? Has the air to move initially to make a fan work? No, a fan works in still air just fine. So does a propeller.

You seem to think that the prop spins the wheels, but this is not true. It is the other way round. When the cart is at windspeed, the ground below it is moving at the same speed, but opposite direction. That can be used to draw energy from to spin the prop, which then pushes the cart above windspeed.

It has been said a thousand times and more that this device draws its energy from the difference between air and ground, and not the air alone.

For LightningRose, I'll say this once more: the relevant law is "Conservation of Energy". There is no law of "Conservation of Velocity"!

By Michael C (not verified) on 13 Dec 2008 #permalink

"The bottom line is *you cannot capture wind energy if your velocity is the same or greater than the wind*."

This is what we call proof by absolute assertion. Nicely done.

I forgot to mention one of the most basic principles of "proof by absolute assertion". The more times you assert your belief, the truer it becomes.

LightningRose,

This isn't rigorous (far from...) but maybe it will help.

In an iceboat I can make a downwind Velocity Made Good (dVMG) substantially faster than the true wind speed, by tacking downwind. 15 mph wind, I sail at an angle about 30o above dead downwind, and my iceboat will go 50-60 mph or better, making it easy to maintain a dead down wind velocity vector of 40 mph or better. If I zigzag, I can make good 40mph on a line straight downwind - always, as you say, sailing across the wind, but going so fast that my dead downwind vector is faster than true wind speed. Tacking at an angle down wind allows me to maintain a dead down wind velocity vector that is faster than the true wind speed.

The propeller on this cart is not going dead down wind. The prop is being spun by the wheels, and each propeller blade is going across the wind at an angle one way at the top of the spin, and across the wind the other way at the bottom of the spin. In effect, the propeller blades are tacking downwind, 'jibing' to a different direction or 'tack' across the wind, twice for each full revolution of the propeller.

Mark, if you want to read about a "good math, bad math" example dealing with the DDWFTTW cart, have a look here:

http://forums.randi.org/showthread.php?t=128483&page=59

Read Christian's summary of the bizarre statements that Humber has been making in this thread. I find it quite fascinating!

Yea, and keep in mind that i only highlighted a very few of his, uhm, strange assumptions how physics work.

The really best thing, imho, was when he said:
"The other problem is that there is no load for the propellor because the cart is stationary. The propellor cannot be forced to do work."

Thats not only a bad/good thing, it is just pure fantasy.

Greetings,

Chris

been thinking and calculating on this again. not as much as i wanted to, but anyway:

if you do streamline analysis of a propeller, you find that instead of a betz's law you can define a propeller efficiency.

the ideal efficiency of a propeller can be calculated as:

e= 2/(1+v_out/v_in)

where v_in is the speed of the air going into the prop and v_out is the speed of the air coming out.

the maximum efficiency is when v_out=v_in. in this case the efficiency is 1, but in general, a real prop will have v_out>v_in and e<1.

if i understand the argument correctly, FTW proponents say that since the hanging airspeed indicator flag behind the prop on the cart in the video is angled against the wind, that this means the cart is going faster than the wind. that is not necessarily true.

a real prop with e<1 and v_out>v_in. i suspect that for a real value for efficiency, the v_out speed can be greater than the wind speed, making the flag airspeed indicator point into the wind, only making it look like the cart is going faster than the wind.

has anyone actually gotten accurate measurements of the outside wind speed and the cart outside speed simultaneously, showing that v_cart > v_wind? or is all the evidence for FTW the treadmill data and the flag on the cart on the video?

Hello Rob,

if you watch the Goodman video closely, you will notice that the indicator is not behind the prop, but on the left side of it (if you would look directly at the back of the cart from behind). You can clearly see that at the beginning, the indicator seems to go "through" the prop, even when it is spinning. Which, of course, cant be. So, it must be on the side.

Greetings,

Chris

Rob, you're absolutely right that the stream directly behind the prop would not necessarily indicate FTTW travel. A perfect example would be our cart on the treadmill. When we're going exactly wind speed the prop is producing thrust, and that thrust would definitely deflect a tell-tale (because of course the prop is of finite size and has to create a finite delta-V). However, Chris is right in pointing out that Goodman's indicator is well off to the left and out of the way of the prop stream.

Moreover, our cart is operating on a treadmill under very controlled conditions. It's quite easy to tell whether it is going faster or slower than the wind. If it advances on the treadmill it's going faster than the wind. If it retreats it's going slower.

For anyone that might be interested in trying this at home I just posted a set of build videos:

Build video 1 of 3:
http://www.youtube.com/watch?v=T-ArigMKhi4&fmt=18

Build video 2 of 3:
http://www.youtube.com/watch?v=p0rhgop5wEM&fmt=18

Build video 3 of 3:
http://www.youtube.com/watch?v=gSHNqrF93MU&fmt=18

It is quit pathetic to me to 1st dismiss the dilemma as silly perpetual nonsense and later to admit that is not - with the caveat that its actually really complicated fluid dynamics!!

That is a lame excuse. Complicated fluid dynamics or not this is clearly perceivable dilemma. The delicate and detailed ways the air flows over the wing of the propeller... all that is secondary.
This really stinks as a way to justify being blatantly wrong - and mind you, calling other people names while being wrong.

By Hank Antler (not verified) on 23 Dec 2008 #permalink

i would like to revisit the equivalent frames discussion. at first glance, it may seem like the treadmill and outside are equivalent frames of reference. but they are not.

outside, the force of gravity is perpendicular to the relative motion of the cart on the road. since it is perpendicular to the cart, it cannot do any work on the cart.

on the treadmill, which is at an angle to the floor, there is a component of gravity parallel to the motion of the cart. thus, gravity will be doing work on the cart.

this means that the two situations are *not* equivalent, so you cannot use the treadmill experiment to naively conclude the cart outside is moving faster than the wind.

Rob,

what if the cart outside travels uphill a small inclination? Also note that usually the treadmill is not inclined. It is only for a few tests to avoid the cart moving along the belt until it reaches the end. With the small inclination the gravity "pulls" on it to make it stay in place instead.

You might want to read the several discussions on the net to find out what the test with an inclined treadmill is meant to be, instead of jumping to conclusions that are wrong.

Greetings,

Chris

I just came across this blog by accident, and I am quite astonished to see even elementary Physics being cast aside when discussing this ridiculous subject.

This is a classic case of someone who was initially correct in his understanding, being confused by the browbeating of others who choose to include in their arguments only those elements which fit their theories while discarding all others (such as that inconvenient annoyance called mass).

Most of the discussion I have seen here is just so ridiculous I am now suffering from severe abdominal pain caused by laughing so much. I have not read all of the thread as my doctor advises against it.

Mark, you were right in the first place. Go back and think about it, then ask your daughter!

<131 I agree with Greg 101%, also together with abdominal side pain, and additional headache. In spite of my abdominal and head aches, you may enjoy Pseudo-Science, or Miss-Science, or any.

Interesting how so many can be so confused. Go back to very basic physics and you might begin to understand why over unity devices in general do not work. I will not imply that the commentators here are all idiots. They might be lacking the clarity of sight to see that what they believe is possible is actually not.

You don't get anything for nothing, period. The sooner you all accept this fact the better as far as I am concerned. In every case there is two guiding forces. False authority syndrome where people confidently assert incorrect "facts", and "gull ability" where the believer thinks they can fly with a few feathers stuck on despite the effects of gravity and any other sense that what they think they can do is not possible.

Do the planet a favour and turn off the computer, take a walk to the plant nursery and buy some trees to plant. Spend some time with your family and take pleasure in your otherwise meaningless life. If you feel you must make comment on anything, make sure it is worthwhile.

I could go on and on but from here I would only begin to upset delicate egos who will no doubt disagree with common-sense and take ridiculous amounts of time to point out why my viewpoint is not correct.

By Rob (a serious… (not verified) on 06 Sep 2009 #permalink

Re #133:

The key to being a serious skeptic is to rely on evidence, not "common sense".

If you follow through, and work out the math - fairly simple math, ultimately - this isn't something from nothing. That's where I went wrong in the initial post on this topic.

As lots of people pointed out: sailboats can achieve speeds higher than windspeed using tacking.

This isn't all that different.

The catch is that the wind is carrying a lot of energy, and you're able to "harvest" that energy using mechanisms based on collisions of the molecules of air with the vehicle. As long as you can devise a method by which you can continue to get meaningful interactions between the air and some mechanism on the vehicle, you can continue to get energy from the air.

In a tacking sailboat, you use something related to an elastic effect - the keel of the boat in the water provides a counterforce that pushes the boat on an angle relative to the wind. You're able to continue to harvest energy from the wind, until you achieve a maximum speed which is dependent on a combination of the structure of your boat and the windspeed.

In the case of this wheeled vehicle, you're basically exploiting the difference between the stationary ground and the moving wind: the stationary propellor is initially acting as a dead sail. It is not being spun by the wind. The wind pushes the vehicle, which makes the wheels move, which makes the propellor spin. How can it get the "better than windspeed"? It's basically the same as the tacking effect: tacking exploits the friction from the boats keel in the water to continue to harvest energy from the wind. This uses the friction between the wheels and the ground.

You can build a model yourself, and test it. You can do the mathematical analysis. This isn't perpetual motion. It's not free energy. And it's not super-unity. That's where I went wrong - I thought that this was a super-unity/perpetual motion claim. It's not. It's just a counter-intuitive application of basic mechanics, combined with some really clever engineering.

If you're seriously a real skeptic, then do the analysis. Run the tests. Form a conclusion based on real evidence, not "common sense".

What an entertaining thread!

Particularly the "it's just perpetual motion" yelping. Perpetual motion is not about velocity -- it's about energy. If you make an energetic claim, then you need to back it up.

I mean -- really! If you've ever played with marbles, you know that a lower velocity motion can create a higher velocity motion in another body -- that's not perpetual energy. That's just momentum.

This question is only secondarily about velocity -- it's primarily about whether you can extract momentum from wind that leads to a velocity above that of wind. So do the integration -- see if it leads to a larger output energy than input. But velocity, per se, tells you nothing!

I also just stumbled upon this page.

At first I firmly put them (spork + friend), and then put you in the "perpetual motion looneys" bin, but after some thought, it became clear that the machine can definitely work.

To help convince those that don't believe it can work, somebody posted this video, which demonstrates the unintuitive part of the puzzle quite straightforwardly by replacing the "wind", which is hard to visualize, with a ruler: http://www.youtube.com/watch?v=k-trDF8Yldc .

Through clever gearing he's made a vehicle which goes twice as fast as the pushing medium (the ruler). It is clear that it is not a "perpetual motion machine" - it is generating speed by trading out mechanical advantage (if I were to stop the car with my other hand, the car would be pushing my hand with 1/2 the force as I am pushing the ruler with). The downwind-fast-than-the-wind cart is exactly the same thing (the propeller is pushing back on the wind exactly like the large wheel is pushing back on the ruler in the video). To better represent the imperfect propeller/wind interface, you could make the ruler or big wheel slippery, so that when you slide the ruler, the vehicle speeds up slowly, but it should be obvious that there is no weird inflection point when the vehicle is moving exactly rulerspeed.

Good lawd.

Look at it this way. What happens when the vehicle is going the same speed as the wind? What is driving the prop? Nothing. In a perfect world, this cart would reach a relative wind speed of zero and keep going at that speed. Any faster and the prop turns into drag. Anyone claiming that the inertia of the cart is driving the prop through gearing from the wheels so it goes faster is fooling himself.

I do not see how people get sucked into this nonsense about gearing and whatnot. That stuff is just obfuscation - a distraction away from the vectors.

Vectors in the setup:

Wind - a forward vector
Atmospheric resistance from the cart body, wheels, prop - negative vector
Friction of wheel bearings, gearing - negative vector.

This really is seventh grade physics. I'm surprised at you all buying into this.

I am betting myself a cheese sandwich that this fails any real peer review.

You have all been trolled. It is a masterful troll, but a troll nevertheless.

bmo - the voice of reason!

This whole thing is a set-up right?!

If this is legit (which I don't believe it is)why does it not start accelerating exponentially as soon as the apparent wind moves forward of the beam?

Doesn't Newtonian physics require that the propulsion generated by the propeller be counterbalanced by an opposing force resisting movement of the wheels (which drive the propeller)? The cart's own motion cannot itself provide energy to accelerate the vehicle. Period. To the contrary, since the vehicle exists in a fluid, the net effect of the vehicle's movement in that fluid has to be to slow it down.

Assume that the wind speed relative to ground is zero - no wind - and also assume no friction. If I push start this gizmo with an impulse, does that mean that the propellor will accellerate the vehicle to a steady state velocity? Of course not. That would violate the law of thermodynamics.

Mark. You let yourself get confused. Let's talk briefly about the sailboat example.

Sure, sailboats can travel faster than the wind, when they have a tangential velocity vector. But their downwind (ie, normal) velocity vector is limited to the wind velocity. Got it? It's a simple rule. If you take a moment to visualize it, it makes perfect sense.

Now let's talk about the silly car. It's pointed straight downwind. There's no tangential component to the velocity. As the silly car accelerates, the difference between its velocity and the wind velocity gets smaller and smaller. This is akin to a stationary windmill, mounted on the ground, that experiences lighter and lighter winds. As the wind speed approaches zero, the windmill loses the ability to generate power. In the same fashion, as the car approaches wind speed, its windmill ceases to generate significant power.

The car does not work.

Mark, you were right in your first analysis; the cart cannot and does not work. What pressured you into this silly apology? I see you work for Google and Google is a co-sponsor of this nonsense, any possible connection there? Stick to computer programming and forget about physics, please for your sake!

By physicist (not verified) on 09 Jul 2010 #permalink