## Downwind faster than the wind

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Goemon
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### Re: Downwind faster than the wind

Very cool. My train of thought on how this works:

1. Review video demonstrating small buggy, ruler and paper
2. Imagine ruler is dragged rightward by a couple of hot air balloons. Clearly, the cart can move faster than the balloons. Concept must be feasible! In this case, balloons are slowed somewhat by drag of ruler and buggy; pushing back on air; wind is slowed somewhat. KE of wind is ultimately used to push buggy.
3. See Rohit's diagram of turbine powered cart, but add the purple arrow showing which direction the "turbine" turns. "Turbine's" gearing makes it turn OPPOSITE direction of what one would otherwise expect; it's constantly fighting against the wind.
4. Replace simple turbine with propeller.
5. Suppose propeller is geared such that the air pushed by the propeller moves twice as fast as the wheels turn; e.g. when wheels are turning for 1 m/s, the propeller pushes air BACKWARDS at 2m/s RELATIVE TO THE CART.
6. Imagine the cart is moving at say, 8m/s rightward (relative to the ground) in a 10m/s wind (relative to the ground).
7. The cart is moving only 2m/s relative to the wind. But the air thrust backward by the propeller is moving 16m/s backward relative to the cart = 8m/s relative to the ground. The relative speed between the wind and the air pushed backward by the propeller is 18m/s !!! Thus, the propeller exerts a thrust which INCREASES as the cart goes faster, and continues to increase even when the cart is moving faster than the wind!!
8. Of course, the drag that the propeller exerts on the wheels also increases as the cart goes faster. Eventually, when combined with the frictional drag of the wheels and gears, the speed will reach equilibrium. If the friction of the wheels and gears is relatively low, the equilibrium speed could easily be higher than the wind speed.

The thrust exerted by the wind on the cart does NOT drop to zero as the cart approaches wind speed, it INCREASES.

As the cart passes a stationary observer, she will see air molecules pushed BACKWARD by the action of the rapidly spinning propeller. The air's momentum is changed and KE is lost; the energy is used to overcome friction of the moving cart (or even accelerate it if it hasn't reached equilibrium).
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Tass
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### Re: Downwind faster than the wind

Okay. To bad I was unable to get in here in the weekend to be a part of this debate. Now, having read at least most of the thread without having seen any really good explanation of this, I will give my own attept of an explanation.

First asume we have a car moving at roughly the velocity of the wind. The wheels of corse have friction (traction) with the ground, but since they are rotating so that the relative velocity at the ground is zero, no energy is lost there. The loss that exists comes from the friction in the bearings, but it can be made arbitrarily small (although not disapear) by good engineering.

Now mount a big frigging propeller on the car. Since the relative velocity of the air and the car is almost zero, the propeller doesn't rotate and doesn't really change anything yet.

Now if we were too drive the propeller with just a tiny power source it would be able to push some of the air backwards generating thrust. As the relative velocity is small it can get a lot of momentum out of a little amount of energy. E=p*v/2 >=> P = F*v/2 (p is momentum, P is power)

Now the wheels are spinning fast, so by putting a small load on them we can extract a good deal of energy, without costing the cart much momentum. This energy as we have seen can be fed into the propeller giving more momentum than was lost.

Conservation of energy you say? No problem, is was the difference in velocities (i.e. the wind) that made it possible to extract a net energy surplus. We pushed back on the wind wich lost thereby lost kinetic energy.

Mathematical explanation:

A car moving at velocity Vcar has wheels of radius R rotating at angular velcocity ww
Vcar = Ww * R

A propeller rotating at angular velocity wp has a certain prefered relative airflow speed Vp at which the propeller does not alter the speed of the air flowing by.
Vprop = k1 * Wprop

The relative angular velocities of the wheels and the propeller is coupled geometrically through gears.
wprop = k2 * ww =>
Vprop = k1 * Wprop = k1k2 * ww = k1k2R Vcar

Now if we have a wind of speed Vwind then we have a flow of air through the proppeller Vrel = Vcar - Vwind

If every thing was frictionless then we would need to have Vrel = Vprop = k1k2R Vcar => Vwind/Vcar = 1-k1k2R

In other words the ratio of the windspeed and the car speed is a constant depending on the geometric design of the vehicle, it can take any value, positive and negative, bigger or smaller than one. This is the case demonstrated in the ruler video, since disipative friction does not matter there, speed is determined solely by geometry.

In the real case with disipative frictions it will of course go slower, but if it is well designed not slower than the wind.

Edit: Goemon posted while I was writing. Very nice explanation.

gmalivuk
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### Re: Downwind faster than the wind

Charlie! wrote:
gmalivuk wrote:
This guy wrote:[et cetera, et cetera, et cetera]
Note that if our [other] losses are small relative to our drag, the lift to drag ratio need only be greater than 1--an easy task. Either the losses must be minimized (good bearings, low rolling friction, etc.) or the drag on the propeller must be increased. As bad as that sounds, what this really says is "or the propeller must be made bigger", or "the propeller must be made to generate more thrust", keeping a constant lift to drag ratio, of course.

Interesting. Except the "other losses" include the force against the ground that provides enough power to spin the propeller. I'm annoyed that people keep neglecting this. His assumption about "small relative to drag" is therefore false, and his conclusion is invalid.

He doesn't assume it's small, though. He just says that if it is, the Lift:Drag ratio need only be greater than 1. But it's not difficult to make it several times larger than that, I believe (though it was difficult to find actual practical values of propeller lift to drag ratios). So even if other losses are two or three times larger than drag, I'm pretty sure a propeller with a big enough Lift:Drag ratio is still pretty feasible.
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frezik
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### Re: Downwind faster than the wind

If you are incredulous, replicate the experiment- I sure want to. That's how science works.

Not quite. Scientists usually don't spend their time and resources on experiments that they know are doomed to fail because they violate half a dozen laws of nature. But you can try it if you insist.

Intutively, I agree that this cannot work. Intutively, I also agree that light should always behave as a particle. Or a wave. Uh . . .

Here's the YouTube vids I could find where the experiment is done by different people working (seemingly) independently (some of these are duplicated elsewhere in the thread):

This is enough to make me lean towards the idea that the intutive explaination is simply wrong and the device is possible as stated. However, I'll have to do the experiment myself to be certain, since it's possible that all the above are hoaxes. Since repeating the experiment should only take a few hours and less than \$20 worth of parts that I can obtain from most hobby stores, I'm willing to give it a shot.
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spork33
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### Re: Downwind faster than the wind

Howdy guys. spork33 here. As Thinair said, he and I are the perpetrators of the 3rd video linked. A few facts:

- It's quite definitely real - no hoax
- It's NOT perpetual motion (or anything else useful)
- We do know exactly how it works and have explained it many times - happy to do so again.
- I've posted the parts and build notes in several places, and happy to do that here as well.
- It's plenty easy to try it yourself ad remove all doubt.

Since repeating the experiment should only take a few hours and less than \$20 worth of parts that I can obtain from most hobby stores, I'm willing to give it a shot

You may be able to do it for \$20 in parts. We managed to get it down to \$40 in parts, but it would cost \$80 for quantity 1. I've bought enough parts for 10 of them and will be sending them to several people that requested them.

Charlie! said: Man, that was so much easier than that ruler and wheels analogy. And more, er, correct. I'm not convinced that the math is right, but I'll go over it again next wednsday to be sure.

The math is no more or less correct than the ruler analogy. I'm surprised you call it "more correct" and the IMMEDIATELY say "I'm not convinced that the math is right". Do you see any contradiction there?

BlackSails said: We now have a machine, that from nothing, powers itself and does work.

We built a machine that's powered by the wind and starts internet pissing matches. If you've built a machine that provides useful power from nothing, that would arguably be much better than ours.

hideki101
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### Re: Downwind faster than the wind

It seems you don't even need a propeller to go faster than the wind; sailboats do it all the time.
Gliding high: Flitting across the water on a moth boat is 'very pure sailing'
How fast? The record is 27 knots. Hydrofoil moth boats don't just go faster than other small sailboats. They go faster than the wind. In a 10-knot breeze, one can skim along at 20 knots. And it can lift off in winds as light as 6 knots.
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ThinkerEmeritus
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### Re: Downwind faster than the wind

While trying last night to persuade my body that it was time to get some sleep, I constructed the following Gedanken-experiment: Put a windmill on a cart with locked wheels that is facing into the wind. Use the windmill to charge a set of batteries; take as long as necessary. Unlock the wheels and use electric motors to move upwind. Repeat as necessary until you get where you want to be. Net, you have an average upwind velocity.

There is nothing fundamentally wrong with this scenario, and I'm sure a good experimentalist or engineer could build the gadget without trouble. So it is possible to move a cart-and-windmill upwind. We are not even surprised, since we are used to sailboats going up wind. A purely mechanical example is extremely plausible.

However, if there is nothing fundamentally wrong with a cart-and-windmill moving upwind, there is nothing fundamentally wrong with going downwind faster than the wind. Unlike the sailboat, there is nothing that changes fundamentally, except that you may have to change the gearing when you go through the point where you are going the same speed as the wind.

Gedanken experiments don't necessarily prove much, but in this case I find it good enough to accept the statements that others have in fact accomplished the feat. Nice gadget.
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spork33
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### Re: Downwind faster than the wind

It's true of course that sailboats can tack upwind. It's also true that high performance sailboats can tack downwind faster than the wind. In fact ice boats can maintain a downwind velocity component of 3X to 4X the true wind speed on a 45 degree downwind tack. This is documented by GPS data and plenty of experience.

However - even when a sailboat tacks upwind, we know that it's demonstrating exactly the same principle as the sailboat that tacks downwind faster than the wind. The sailboat is a sort of "wedge" that works between the wind and water. When we see it tack upwind, the fish see it tacking down-current - faster than the current.

Unlike the sailboat, there is nothing that changes fundamentally, except that you may have to change the gearing when you go through the point where you are going the same speed as the wind.

On our prop-cart the gearing is fixed. The advance ratio (the distance the prop would theoretically advance in a given time divided by the distance the wheels would advance in that same time) is a fixed number less than 1.0 (we've used various ratios from about .65 to about .85)

frezik
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### Re: Downwind faster than the wind

spork33 wrote:
Since repeating the experiment should only take a few hours and less than \$20 worth of parts that I can obtain from most hobby stores, I'm willing to give it a shot

You may be able to do it for \$20 in parts. We managed to get it down to \$40 in parts, but it would cost \$80 for quantity 1. I've bought enough parts for 10 of them and will be sending them to several people that requested them.

How about almost free? I threw together a version with Legos, though I don't have a prop or a connecting belt to go on it yet. Until then, here's some grainy cameraphone pics for your amusement:

Spoiler:

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spork33
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### Re: Downwind faster than the wind

frezik wrote:How about almost free? I threw together a version with Legos, though I don't have a prop or a connecting belt to go on it yet.

I think it will be a challenge to make it work with a Lego version and belt drive. We built a much larger cart and used a timing belt drive. The belt has to be run as loose as possible, and the tight side has to be perfectly aligned with both upper and lower gears. The loose side of the belt can tolerate the misalignment. Also, the prop has to be respectable and the bearings nearly perfect.

I hope it does work for you. You'll have to post some vids.

ThinAirDesigns
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### Re: Downwind faster than the wind

frezik wrote:How about almost free? I threw together a version with Legos, though I don't have a prop or a connecting belt to go on it yet. Until then, here's some grainy cameraphone pics for your amusement:

Creative work. Let us know how the testing goes when you get the prop and belt. I'm going to go out on a limb and say there's too much friction in your system -- but that's just a guess. Might work fine.

We even go to the trouble to remove many of the dust covers on our high quality bearings and then solvent out the grease to reduce friction. There are many, many ways to build one of these devices and have it *not* work.

JB

EDIT: darnit -- spork beat me to it.

Baza210
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### Re: Downwind faster than the wind

With apparent wind it's possible to sail faster than the wind upwind.. not so sure about downwind, seeing as you can't create apparent wind unless you are going faster than the wind, and you can't go faster than the wind unless you're creating apparent wind..
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Technical Ben
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### Re: Downwind faster than the wind

Is it just me or is this device moving "towards" the energy source (IE towards the wind)?

That is an interesting concept. I always thought friction would overcome such a design before it reached wind speed or gained enough energy from the wind.

1) The wind pushing the propeller
to power the card forwards.
2) The ground resisting the movement of the car by friction, and also the wind pushing the car backwards.

 Guess I was wrong.
This link has the math for the sailing into the wind thing. It is possible to go faster than the wind this way by producing LIFT. I think I get it now.

Can anyone do the math to figure out what kind of speed you could get? As this wind only increases your speed to a certain degree and does not continually accelerate your wind powered car.
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ThinAirDesigns
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### Re: Downwind faster than the wind

Baza210 wrote:With apparent wind it's possible to sail faster than the wind upwind.. not so sure about downwind,

Interestingly enough, that's the opposite of the current state of the art. I know of no sailing vehicle that can achieve an upwind VMG greater than 1.0 (not saying it's not possible, just that I don't believe it's been done yet) but it only costs ~\$40 to own one that can achieve VMG greater than 1.0 downwind.[/quote]

JB

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### Re: Downwind faster than the wind

I've given this problem a lot of thought the past day. It just flat our refused to leave my head. There seem to be lots of different reports of people who have succesfully build a car that can move forward on a threadmill (as in the 3rd video in the first post). Too many to dismiss out of hand as forgery. I've only seen one video however of a real-life model (the 1st video posted in the first post), and that video is very dubious. Many people have already pointed out telltail signs that it could be faked. I'd like to add another: The car moves in a perfect straight line, never deviating from its course. How is this possible with an air-powered vehicle? Shouldn't there be wind gusts? And doesn't the propeller produce a sideway force? It's very dubious.

But if one is possible, so is the other, right? Well, maybe not. I'm no longer convinced that the situations are similar. The threadmill is an active component in the setup. It does work. It can actively resist forces working against it. The earth does not. It provides merely a resistive force. If you push against the earth, it moves. If you push against the threadmill, it will keep moving at the same speed, the engine can and provide energy to counter your pushing force. So I think the problems are not comparable.

Bottomline: The threadmill setup might work even if the real-life setup is impossible. 'Might' and 'if' are the keywords here. It's still possible that both are impossible I guess, I haven't really looked into the threadmill scenario. Or that both are possible, if there's some horrible flaw in my previous proofs of why the real-life setup could not work.

Let's look closer at the real-life setup. So no more threadmills.

All those explanations with gear ratios and stories about the direction of movement of the propeller and how it affects the apparent air motion are interesting, but they do not solve the basic problem I have with the whole setup.

Any mechanics problem is a problem of both momentum and energy. None of you have even discussed momentum yet. How can you give a comprehensive explanation of the problem without even looking at momentum?

Look at the frame of reference of the car. The momentum of the air is now negative. Any collision of an air molecule with the car will either increase the momentum of the air molecule, or decrease it. If it increases the momentum, it decreases the momentum of the car, which means the car speeds down. If it however decreases the momentum, that means making it more negative, thus increasing its energy. Thus decreasing the energy of the car, which means slowing it down. Either way the car slows down.

Noone has even addressed this issue yet. So how can you claim to have explained this problem? The remark gmalivuk made that it's about the speed difference of ground and air is interesting, but doesn't really explain anything. It does however raise lots of interesting new questions.

I'm trying to calculate a complete three-particle collision now (car, air, ground). But my mechanics is rusty, and three-particle collisions are notorious for being hellish. So wish me luck
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gmalivuk
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### Re: Downwind faster than the wind

Sanity check: Airplanes work, right?

Every air molecule hitting one starts with negative momentum mv, and either decreases that negative momentum (thus decreasing the positive momentum of the plane) or increases it (thus increasing its energy, and decreasing that of the plane). Is this not your argument for why the car can't work? How come it doesn't apply to the plane? Keep in mind that the only thing that can possibly be increasing (or holding constant) the kinetic energy of the plane is its propulsion system, which works entirely by moving air.
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### Re: Downwind faster than the wind

gmalivuk wrote:Sanity check: Airplanes work, right?

Every air molecule hitting one starts with negative momentum mv, and either decreases that negative momentum (thus decreasing the positive momentum of the plane) or increases it (thus increasing its energy, and decreasing that of the plane). Is this not your argument for why the car can't work? How come it doesn't apply to the plane? Keep in mind that the only thing that can possibly be increasing (or holding constant) the kinetic energy of the plane is its propulsion system, which works entirely by moving air.

The difference is indeed that airplanes have engines. Engines can't generate momentum, but they can generate energy. Or more accurately, they can transfer one form on energy (the chemical energy stored in jet fuel) into another kind (kinetic energy).

So we have an air molecule hitting the engine of the airplane, and being *pushed* away. The air molecule's momentum becomes more negative, so it decreases, so the airplane's momentum increases. Meanwhile the molecules kinetic energy increases. But this energy doesn't have to come from the kinetic energy of the airplane, because we have a second source of energy. The jet fuel.

Our wind-powered car unfortunately has no engine. The only kind of energy available is it's kinetic energy.
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mamalala
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### Re: Downwind faster than the wind

About your observation that the original Goodman cart looks suspicious because it stays straight on the street: The guy equipped it with a small radio control to operate a brake and steering the front wheel. That's why it stays "on track", and also that is why it slows down at the end of the video.

Greetings,

Chris

Baza210
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### Re: Downwind faster than the wind

ThinAirDesigns wrote:
Baza210 wrote:With apparent wind it's possible to sail faster than the wind upwind.. not so sure about downwind,

Interestingly enough, that's the opposite of the current state of the art. I know of no sailing vehicle that can achieve an upwind VMG greater than 1.0 (not saying it's not possible, just that I don't believe it's been done yet) but it only costs ~\$40 to own one that can achieve VMG greater than 1.0 downwind.

JB[/quote]
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spork33
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### Re: Downwind faster than the wind

Diadem wrote:But if one is possible, so is the other, right? Well, maybe not. I'm no longer convinced that the situations are similar. The threadmill is an active component in the setup. It does work. It can actively resist forces working against it. The earth does not.

The situations are identical almost by definition (well at least by well established physical law). Galileo, Newton, and Einstein tell us that a road moving at 10 mph beneath still air is identical to a 10 mph breeze over a stationary road. Technically, "still" and "stationary" are only concepts. But both road and treadmill act as perfectly valid inertial reference frames. So any experiment done in one MUST give the exact same results if done in the other.

Any mechanics problem is a problem of both momentum and energy. None of you have even discussed momentum yet. How can you give a comprehensive explanation of the problem without even looking at momentum?

Fortunately, our cart doesn't break any physical laws. The cart goes steady state faster than the wind. The wind left in its wake is going slower (relative to the ground) than it was before the cart passed. The earth is made to spin a little faster as a result. This is because the wheels of the cart push on the road in the direction the cart is moving. But our cart only weighs 5.7 oz, so you probably won't notice the change in rate of earth rotation (at least not without a very keen eye). This covers momentum.

Now let's look at energy. The wheels move along the road at 15 mph while the cart operates in a 10 mph tailwind. The drag force on the wheels must equal the thrust on the prop disk for us to maintain steady speed. So the wheels feel N lbs of force at 15 mph. Because of the tailwind, the prop disk feels N lbs of force at only 5 mph. The wheels are able to provide far more energy than is needed by the prop to produce the necessary thrust. The excess energy is lost to friction and aero drag.

lightvector
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### Re: Downwind faster than the wind

Diadem wrote:Look at the frame of reference of the car. The momentum of the air is now negative. Any collision of an air molecule with the car will either increase the momentum of the air molecule, or decrease it. If it increases the momentum, it decreases the momentum of the car, which means the car speeds down. If it however decreases the momentum, that means making it more negative, thus increasing its energy. Thus decreasing the energy of the car, which means slowing it down. Either way the car slows down.

Disclaimer: I do not have any significant formal physics background - (just some high-school physics and a decent grasp on mechanics)

However, I do not think the above argument is valid. If the car is cruising at a speed greater than the wind, then in the frame of reference of the car, the car has no energy, because in that frame, it is not moving! It also has no momentum! You are conflating values in two different reference frames (positive energy and rightward momentum of car in ground frame, with the negative momentum of the wind in the car frame) without making the proper transforms between the two frames.

Here is my best attempt to see what happens in each reference frame. For simplicity, assume that the car has such a slim profile that it experiences no air resistance on its frame - the only interaction of the air with the car is with the propeller. We look at the case where the car is at an equilibrium cruising speed above wind speed.

Reference frame of car: (+ to the right, - to the left)
Car is moving at 0 m/s.
Wind is moving -5 m/s. Wind, after hitting propeller moves at -6 m/s (gains energy and loses positive momentum)
Car gains positive momentum that the wind lost, and in order to stay at equilibrium 0 m/s, transfers all of this positive momentum to the ground.
Ground is moving -10 m/s. Ground gains positive momentum, and changes velocity extremely slightly (-9.99999 m/s), and loses energy due to this extremely slight change. If we do the calculations, (dE = m(v+dv)^2 - mv^2) we find that the ground releases somewhat more energy than is needed to power the wind, but roughly on the same order of magnitude. Some is transferred to the wind above, the rest disappated in turbulence and the car's internal friction.

As you can see, this is a very unnatural frame to be working in when considering energy and momentum calculations.

Let's try a different frame.

Reference frame of ground**: (+ to the right, - to the left)
Ground is moving at 0 m/s.
Wind is moving 5 m/s. Wind, after hitting propeller, moves at 4 m/s (loses energy and positive momentum)
Car is moving at 10 m/s. Car gains positive momentum and energy. Car transfers all of this positive momentum to the ground. The ground's velocity changes extremely slightly (0.000001 m/s). However, since the ground is extremely massive, it only gains infinitesimally in energy. We therefore have excess energy, which is disappated in air turbulence and the car's internal friction.

(**Technically, not the reference frame of the ground, but the inertial reference frame with the same velocity as the ground to begin with - the ground will change velocity slightly as time passes if it is of finite mass, and our reference frame will depart from this)

If I didn't mix something up above, you can see that the existence of a faster-than-wind car is not precluded by momentum and energy considerations. You can argue that the specific mechanisms for the cars constructed do not perform the above momentum and energy transfers, but an ideal car that makes the above momentum/energy transfers between particles would perfectly well maintain an above-wind speed.

If we assume the mass of the Earth is HUGE (because, well, it is), then we will observe no perceptible velocity change in the Earth over any reasonable timescales. So we are left with a car that goes faster than the wind.
Last edited by lightvector on Tue Dec 16, 2008 8:59 am UTC, edited 4 times in total.

4=5
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### Re: Downwind faster than the wind

You cannot go faster than the wind in the same direction as it is going, you can however go faster than the wind in the opposite direction.

ThinAirDesigns
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### Re: Downwind faster than the wind

4=5 wrote:You cannot go faster than the wind in the same direction as it is going,

Woops -- spork, I guess we should have checked with "4=5" before we went and just did it.

Now that we know we "cannot" what will happen to the fact that we did, and do, and help others do?

JB

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### Re: Downwind faster than the wind

It is important to be very careful about which frame of reference you are in.

Also, you seem to be disregarding contributions to kinetic energy and momentum from the ground.

In the ground frame, the propeller takes energy from the air, and gives it to the vehicle. In the air speed frame, the vehicle takes energy from the ground and gives it to the air. In the vehicle frame, the vehicle also takes energy from the ground and gives it to the air.

If this still bothers you, does a car break conservation of momentum when it accelerates? The engine provides energy only, not momentum.
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gmalivuk
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### Re: Downwind faster than the wind

Oh, right, sorry. I forgot to mention that 4=5 makes the rules around here. Like the completely sensical one that is his username in the first place...

Another thing to note with Diadem's previous argument about the momentum and energy in different frames: It's entirely possible for something with a negative velocity relative to the car's frame to still impart energy to that car. This is what's happening with the ruler in the wheeled contraption demonstration. So again, the fact that the velocity of both the wind and the road is negative relative to the car's frame is not enough to show that the car must slow down, unless it's also enough to "proove" that the wheeled thing doesn't move the way it's obviously seen to (and which it can be expected to by anyone who runs through the mathematics). This is, once again, because of the *difference* in velocity between the air/ruler and the ground. That difference is absolutely relevant and any explanation that doesn't take it into account isn't possibly going to include all the relevant features of this problem.
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4=5
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### Re: Downwind faster than the wind

oh I see the error in my thinking, you can have the device that is drawing power from the wind be moving slower than the wind while the vehicle is geared to move faster. When I saw the thread I neglected to check for pages and forgot about gearboxes.

spork33
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### Re: Downwind faster than the wind

lightvector wrote:Disclaimer: I do not have any significant formal physics background....

It's always the guys with the disclaimer that get things 100% right. Even the subtleties of energies measured in different frames and the business about the inertial ground frame being the inertial frame attached to the ground prior to any slight acceleration of the earth itself.

On the other hand, it's always the guys that tell me they know every darn thing there is to know about physics that can't even get their head wrapped around the most basic idea of an inertial reference frame. Go figure.

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### Re: Downwind faster than the wind

Hmm, this is interesting. I have not yet convinced myself that it's impossible. Here's a more simple, though perhaps less realizable apparatus, that might illustrate how it could be possible.

Picture an water wheel, but with the paddles about halfway between the center and the edge. There are pivots on the paddles, so they can be rotated arbitrarily instead of always being oriented radially. Now, set this wheel on the ground, and arrange it so that bottom paddle is vertical, and all the other paddles are horizontal. As the wheel turns, turn the paddles so that the one nearest the bottom is always vertical, and the other paddles are always parallel with whatever wind they feel.

The only aerodynamic force to consider is the bottom paddle, since the other paddles are oriented to have negligible resistance. We've formed a lever, with the contact point with the ground as its fulcrum, the paddle in the middle, and the axle (center of mass of the wheel) on the far side. So if the paddle gets pushed forward at a speed aproaching the speed of the wind, then the whole wheel will move twice as fast. (You could vary the ratio by changing the radius at which you mount the paddles.)

I'm assuming that the other paddles, which we keep aligned with the wind, and the rest of the wheel, have negligible air resistance. I'm assuming I can move the paddles quickly while expending negligible energy and not disturbing the airflow much. I'm assuming the one paddle doesn't affect the airflow for another. And I'm ignoring forces in the Y direction, so hopefully I have enough paddles that the one on the bottom is vertical enough that this is OK. These factors keep the wheel from going arbitrarily fast by moving the paddles arbitrarily close to the edge. But I don't see any fundamental reason why this wheel would be constrained to the wind speed.

Random thought: what I described is similar to what happens when you put a half-wound yo-yo on the floor, with the string below the axle, and pull on the string - the yo-yo comes towards you faster than you are pulling the string.

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### Re: Downwind faster than the wind

TomBot wrote:Random thought: what I described is similar to what happens when you put a half-wound yo-yo on the floor, with the string below the axle, and pull on the string - the yo-yo comes towards you faster than you are pulling the string.

Indeed. And completely similar to this model explanation http://www.youtube.com/watch?v=E7vcQcIaWSQ

This is an in theory copletely workable aproach, although rather impractical. Using a propeller to do the same is easier.

TomBot wrote:Hmm, this is interesting. I have not yet convinced myself that it's impossible.

Good idea, since it is not.

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### Re: Downwind faster than the wind

I finally solved the problem yesterday. But i forgot to post it *whoops*. Here it is.

Look at the reference frame of the car (that is, the inertial frame in which the car's velocity is zero at a specific time. Of course if the car accelerates it's speed won't be zero anymore some time later). The momentum of both air and ground is now negative. BUT the former is much less negative than the latter.

So: An air molecule hits the propeller of the car. The propellor accelerates it. The molecule's energy increases, and its momentum decreases (it becomes more negative).
At the same time the ground hits the car. This is a passive collision, so the ground looses energy. It's momentum thus increases (it becomes less negative).

We want the car to gain both energy and momentum. If it only gains energy while loosing momentum, it's accelerating in the wrong direction. If it gains energy without changing momentum or changes momentum without gaining energy, then we've broken the laws of physics.

The car gaining both energy and momentum is possible if:
1) air energy increase < ground energy decrease
2) air momentum decrease > ground momentum increase

We know that ground velocity < air velocity (the ground speed is more negative!). Energy goes with the square of velocity, while momentum is linear with it. Changing a number by a small amount changes its square by a relatively larger amount. (11 is 10% bigger than 10, but 11^2 is 21% bigger than 10^2).

So if the ground energy decreases => ground momentum changes relatively small amount
an if air energy increases => air momentum decreases relatively large amount.

Ergo we can meet both requirements 1 and 2 simultaniously

SOLVED

This is really a very interesting application of physics. It's a very subtle interaction between car, air and ground. In physics you usually ignore all three-particle collisions because they are hell to calculate, and you assume the system can be treated as several 2-particle collisions. That's what I did earlier. And if you do this you see that the car must always loose either momentum or energy. Both in a collision with the ground, and one with the air. It's only the fact that both collisions happen at once that allows you to take energy from one and momentum from another, gaining something in the difference. Awesome.

One tiny note: I've proved that this contraption doesn't violate conservation of energy or momentum. That doesn't automatically make it possible of course. But i guess it is, since there are videos of it.
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### Re: Downwind faster than the wind

spork33 wrote:
Diadem wrote:But if one is possible, so is the other, right? Well, maybe not. I'm no longer convinced that the situations are similar. The threadmill is an active component in the setup. It does work. It can actively resist forces working against it. The earth does not.

The situations are identical almost by definition (well at least by well established physical law). Galileo, Newton, and Einstein tell us that a road moving at 10 mph beneath still air is identical to a 10 mph breeze over a stationary road. Technically, "still" and "stationary" are only concepts. But both road and treadmill act as perfectly valid inertial reference frames. So any experiment done in one MUST give the exact same results if done in the other.

Yes of course a road moving at 10 kmh beneath still air is identical to a 10 kmh breeze over a stationary road. I agree. But a road moving at 10 kmh beneath still air is NOT identical to a threadmill moving with 10 kmh beneath still air. That's my point. Because a trapmill does work, a road does not. If you push against the road (the earth) it slows down. If you push against the threadmill, its engine will do more work, and its speed remains unchanged. That's a fundamental difference.

The question of course is if this difference is relevant. At first I thought it wasn't. But since people were building succesful faster-than-wind contraptions on threadmills, but I'd only seen one dubious video of the real thing, I started to wonder if it might be relevant. I guess it isn't though, after all.

But there is a difference. It's worth realizing this. Might be relevant for other problems.
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### Re: Downwind faster than the wind

lightvector wrote:However, I do not think the above argument is valid. If the car is cruising at a speed greater than the wind, then in the frame of reference of the car, the car has no energy, because in that frame, it is not moving! It also has no momentum!

My apologies, I should have been clearer about what I meant. I meant the inertial frame initially tied to the car. Not a reference frame that you keep tied to the car all the time. In such a frame the momentum and energy of the car will always be zero, but such a frame isn't an intertial frame (the car is accelerating, so in this scenario your frame will be as well). You can't do physics in a non-intertial frame. At least not without giving you horrible headaches trying to comprehend all the ghost-forces appearing.

The reference frame I meant is the reference frame in which the car is initially moving (initially meaning at the time you start looking. It's already moving faster than the wind). As the car accelerates it is no longer stationary with respect to this reference frame of course. But that can't be helped.

Here is my best attempt to see what happens in each reference frame.

Your calculations are mostly okay, but you make the mistake I explained above. Since the car is accelerating, you can't take a reference frame where it is at rest both before and. Such a reference frame won't be intertial. You do seem to keep this in mind in the ground-reference frame case though. So that's good
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gmalivuk
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### Re: Downwind faster than the wind

Please don't triple post. There's no reason for it at all. Just edit your previous post to include additional things you want to say.

Also, I'm glad Diadem finally solved this for us. It means I no longer have to keep "trolling" every time I don't buy overly simplified explanations that ignore the ground...
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spork33
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### Re: Downwind faster than the wind

couldn't you just view the cart-on-a-treadmill situation as an elaborate fan? Energy > treadmill > car > air simplifies to Energy > air.

You could if you want, but then you'd have to look at the cart on the road in the same way - since the situations are identical.

But I don't see any fundamental reason why this wheel would be constrained to the wind speed.

Random thought: what I described is similar to what happens when you put a half-wound yo-yo on the floor, with the string below the axle, and pull on the string - the yo-yo comes towards you faster than you are pulling the string.

Your theoretical paddle wheel would work just fine. We use that and the yo-yo as examples frequently. Here is a cart I propose based on that approach:
http://www.putfile.com/pic/2794071

Diadem said: Yes of course a road moving at 10 kmh beneath still air is identical to a 10 kmh breeze over a stationary road. I agree. But a road moving at 10 kmh beneath still air is NOT identical to a threadmill moving with 10 kmh beneath still air.

Do you read what you type here!?

Because a trapmill does work, a road does not. If you push against the road (the earth) it slows down. If you push against the threadmill, its engine will do more work, and its speed remains unchanged. That's a fundamental difference.

Wrong, if you're going to worry about the earth slowing down, it will slow down just as much even if there's a treadmill between you and the earth when you do your pushing. Besides it will have done work on you in either case.

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### Re: Downwind faster than the wind

gmalivuk wrote:Also, I'm glad Diadem finally solved this for us. It means I no longer have to keep "trolling" every time I don't buy overly simplified explanations that ignore the ground...

What do you mean Diadem solved it? The energy and momentum considerations? Is that not pretty much what you yourself has been trying to say all the time?

spork33
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### Re: Downwind faster than the wind

Yes, it's good that he discovered the error in his own analysis, and now agrees with what we've been saying for three years.

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### Re: Downwind faster than the wind

Tass wrote:
gmalivuk wrote:Also, I'm glad Diadem finally solved this for us. It means I no longer have to keep "trolling" every time I don't buy overly simplified explanations that ignore the ground...

What do you mean Diadem solved it? The energy and momentum considerations? Is that not pretty much what you yourself has been trying to say all the time?

Well, yeah. That statement is what we in the business like to call "sarcasm".
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### Re: Downwind faster than the wind

Also, I'm glad Diadem finally solved this for us. It means I no longer have to keep "trolling" every time I don't buy overly simplified explanations that ignore the ground...

You want to turn this into a pissing contest?! Well so be it!

My initial assessement that this contraption violated conservation of momentum was indeed wrong. What can I say? That is how science works, you start with one model and improve it as understanding increases. I did finally arrive at the right model (or at least a better one). Meanwhile all you have done is selectively quote my text, leaving out all the important bits, and then attack is with cheap points. It's easy to point at others for being wrong when you haven't given a single explanation yourself. You were in fact so consistent in completey ignoring any momentum considerations that at one point i was wondering if you perhaps simply didn't know the word.

Personally, I prefer trying to understand a problem and arriving at a wrong conclusion over not making the attempt at all.

Oh and, no, I didn't solve the problem,that's too much honour. The guy that wrote the explanation ThinAirDesigns linked to did. Though he didn't look at energy/momentum balance. That part of the puzzle I did solve.
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spork33
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### Re: Downwind faster than the wind

Diadem wrote:Oh and, no, I didn't solve the problem,that's too much honour. The guy that wrote the explanation ThinAirDesigns linked to did. Though he didn't look at energy/momentum balance. That part of the puzzle I did solve.

Actually, Tad wasn't the first to solve this. I posed this as a brainteaser three years ago on another forum. I posted solutions back then that included energy and momentum solutions (as well as a number of other proofs). Upon further investigation, it turns out I wasn't the first to conceive of it or solve it either. We found Jack Goodman's video (that came out around the same time I first posed the problem). We then learned that an engineer by the name of Andrew Bauer built a full sized cart he could ride back in the 1960's. I spoke to Bauer's wife and some of his colleagues recently, and learned that he wasn't the first either (though he may have been the first to build one). Bauer learned of it in a paper written by a student (whose name I've not yet found), and built his cart to settle a debate between himself and A.M.O. Smith.

But if you want to be indignant about your own revelation of the truth - feel free. But you might expect folks to take it poorly when you attack our results, conclusions, integrity, and even intelligence, and then pronounce the problem "SOLVED" when you find your own error.

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### Re: Downwind faster than the wind

I don't like the sound of all this talk of these contraptions whizzing around, causing the world to slow down... Al Gore's next film?
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