Let's see, where do I start?
If you're reading this, chances are you remember the whole "airplane on a conveyor belt" madness. Many web forums, blogs, email lists, and other forms of communication on teh interwebs, were filled with arguments by people who clearly saw what the answer was, and who disagreed with each other. Eventually, people realized that the airplane-on-a-treadmill question is asked in an ambiguous way, and that depending on your interpretation of the situation being set up, you might reasonably reach one conclusion or another. A thorough analyses of this whole thing, by Randall "XKCD" Munroe, is here. It is one of only two or three webpages that go over each possible interpretation of the question and the ways in which the followers of each interpretation argue against the other ones.
A new issue is causing similar debate right now, and it regards these little propeller-powered carts that supposedly can go downwind faster than the wind:
Can a cart, with a propeller attached to its wheels via gears and/or belts, use aerodynamics and gearing in a clever enough way to go downwind faster than the wind (DWFTTW), i.e. to outrun the wind? This question has caused discussion on many online forums, such as on the JREF's site, the Mythbusters Fans' forum, the Discovery Channel, a Physics website, ScienceBlogs, MAKE magazine, the Amateur Yacht Research Society, random blogs, and BoingBoing not once not twice but three times. (No, wait, FOUR times!)
What I aim to do with this page is create a thorough analysis of the DWFTTW issue, similar to what Randall Munroe did for the plane on a conveyor belt. (Mark Chu-Carroll has also tried a thorough analysis but I think he leaves out a lot).
It is different from the airplane/treadmill issue in that there is one definitive answer. But it is similar to the airplane/treadmill issue in that it is very easy to listen to DWFTTW claims and mistake the statement for something it is not claiming: perpetual motion, or a machine that is both a propeller and a turbine, or other things that are impossible. So let me clear up just what the DWFTTW claims are, and show some math and some analogies and a few thought experiments to try and explain why I think they are possible.
This page will be divided into seven parts:
6) Is a treadmill really equivalent to being outside in the wind? In the treadmill, the energy comes from the treadmill, but where does the energy come from outside when you're going at wing speed? How can you have a wind-powered vehicle that is not moving relative to the wind? (There are good answers to these questions, they are not rhetorical).
Hopefully, by the end of this page, you will agree with me that DWFTTW is not perpetual motion, that it is at least theoretically possible, that some vehicles already do it, and that the Youtube videos (by which I mainly mean Spork33's) are probably not faked and show a cart that can go DWFTTW steadily in a steady wind.
Let's get started.
1) The Claims
The claim is the following:
- A cart can harness the energy that is available from the difference in velocity between the air and the ground (i.e. "powered by the wind") and use it to move directly downwind, at a speed (from the point of view of the ground) that is greater than wind speed. The cart can out-run the wind. It can go downwind faster than the wind. Steadily. On nothing but wind power. There is no energy stored in rubber bands, batteries, or in the motion of the parts themselves (i.e. no flywheel effect). It works by having the wheels be turned by the ground as the ground goes by, and this causes a propeller to turn, which pushes against the air much like an airplane propeller and pushes the cart forward. All this can be seen in numerous videos like this one and this one and this one and, most famously, this one. (As for whether a treadmill test is truly equivalent to a test outside in the wind... I will address that in part six, below. But in short... Yes, it is).
The claim is NOT any of the following:
- A cart with a wind turbine on top of it. A cart that when the wind blows across it, the wind causes a propeller-like turbine to turn, and this causes the wheels to spin. (Such carts do exist, but they are not the ones in question here. They cannot go downwind faster than the wind. They CAN go upwind, though, which is kinda neat). The carts analyzed on this page have a PROPELLER on top, which PUSHES against the air, like a FAN, even when the vehicle is moving at the same speed as the air. A turbine can't work if there is no wind around it; A propeller can.
- A cart that can accelerate itself up to wind speed without assistance and without gusts. That is, a cart that starts out at rest relative to the ground, and when the wind blows the cart can accelerate itself up to wind speed, and from there go DWFTTW. Well, ok, to be perfectly honest, most DWFTTW proponents do claim that their carts are self-starting. However, in this discussion I would like to ignore this issue (and simply say "forget for a minute how the cart goes from "at rest relative to the ground" to "at rest relative to the air") for two reasons: 1) A big enough sail should be able to bring just about anything to almost wind speed, so when you think about it, the question of whether something can get UP to wind speed is not that interesting. And 2) to convince DWFTTW skeptics, the most important thing is to focus on the steady-state mechanisms and forces and energy transfers that happen during DWFTTW travel, NOT on the transient phenomena of how you get there. No one is skeptical of a vehicle's ability to reach wind speed. The only skepticism worth addressing is the ability to maintain DWFTTW speeds without using stored energy, gusts, or other non-steady-state processes. So let's just focus on the steady-state part, the actual sustained DWFTTW travels.
- Perpetual motion. On a day without wind, if you pushed this cart and let go, it would slow down and stop. We are not saying "Pushing the cart spins the wheels which makes the prop turn, which pulls the cart and makes it go faster, which turns the wheels faster, which spins the prop even faster, which pulls the cart even harder, making it go even faster, which spins the wheels even faster...". As you will see in the "math" part of this page, unless the wind is blowing, this cart will not work. It relies on decreasing wind speed (similar, in that sense, to a wind turbine) in order to get energy. (Actually, from the point of view of the air, the cart relies on slowing down its PLATFORM - the treadmill, or the Earth, depending on how you look at it - in order to get energy).
Now you know what the claims are, and what the claims aren't.
2) Non-Fluid Analogues
To start wrapping your head around DWFTTW, it's probably helpful to imagine mechanisms where pretty much the same thing happens, but instead of a propeller and some air we have TWO sets of wheeled or geared mechanical connections. In other words, if we have two large solid objects, one stationary and one moving at a steady speed to one side, is there a way to make some contraption that connects to both large objects and moves itself off to that side FASTER than the large object, steadily?
BoingBoing reader IDONTCOMMENT had the following comment, which provides one good answer to this puzzle:
You have a robot on an airport style people-mover which moves at 10mph. The robot can use 1 watt to move forward at 2mph on the mover, making a total ground speed of 12mph. To keep this up, it puts out a generator wheel to contact the ground. This wheel sees a total speed of robot_speed + mover_speed. The extra force of this generator rolling along the ground is going to make it harder for the robot to crawl forward, which is going to slow its crawl. What makes this work out is that the generator is using the total_speed, but the robot only needs to produce robot_speed. So they will come to an equilibrium where the robot slows down until the energy its using to move forward is equal to the energy produced by the wheel. Even in a very inefficient setup, the wheel will be producing some power since its moving at at least 10mph, and the robot can use that to make some forward progress.
If the people-mover stops, then you're back to the standard perpetual-motion situation where you're trying to power a car from a generator based on the wheel speed of the car - doesn't work. When the people-mover is going, however, you have a base wheel speed that's powered externally, and that's what makes it work.
Now on to the wind. The people-mover is the wind, the robot is the vehicle. The robot's wheels are the propeller, worming its way slowly along the wind (i think worming slowly through the wind as a worm gear would is easier to picture than the aerodynamics). The propeller is powered off the vehicle's wheels (as the robot was powered off its ground-touching generator).
With the wind situation it is very similar, only it is easier to imagine losses and inefficiencies (for the robot it is easy to stick to and crawl along the people-mover, far easier than to grab onto the wind!).
How will the power we take from the wheels increase our speed past the speed we would have been without taking that power, you ask?! Go back to the people-mover example! We're taking power from the sum of the wind just regularly pushing us along, plus the extra speed we get by clawing our way forward through the wind with the prop, but we only have to put that power back into the extra bit of speed from the prop.
Not bad, huh? And as you will see in Section 5 of this page, the difference between the small "extra little bit of speed" (robot speed relative to the mover it's on) and the large speed of being "pushed along" (robot_speed + mover_speed) is key for making the math work out, to making sure this is not a perpetual motion machine and gives plenty of thrust.
But let's go back to the basics and do some even simpler examples. Forget all this energy flow stuff. It is possible at all to move faster than the platform you are moving on, without stored energy, just from mechanical advantages and the difference in speed between the two platforms?
Imagine a board of wood, that is sitting on the ground. Over it, imagine another board of wood, or maybe a cable, that is parallel to it (also horizontal) and moving steadily to one side, say to the right. Can a mechanism connect itself (by gears or wheels or something) to the board of wood on the ground AND to the moving board or string, and then move to the right at a faster speed than the board or string that is moving to the right?
The answer is yes.
When the board goes left, the cart goes left even faster. When the board goes right, the cart goes right even faster. Here's another one, arguably the best of the mechanical analogues. It's the "sequel" to the spool-and-paper video that's coming up.
There is an even simpler way of doing it, which is the following: Put a yo-yo on the table, standing it up on its cylindrical side so it can roll. Have the string partly wound around it, and sticking out the bottom. Now pull the string. The yo-yo goes in the direction you are pulling, FASTER than the string, i.e. it winds itself. Don't believe me? try it.
Or try the following: Go outside and get a bicycle. Now push forward on the lowest spoke, i.e. the one that is connecting one wheel axle to the ground. The bike will move in the direction you are pushing, FASTER than your hand. In this case it is clear to see why: Every point on a rolling wheel is moving forward. From someone riding the wheel, it looks like the points below the axle are moving backwards, and relative to someone moving along with the wheel (say, riding a car or a bake), this is true. But relative to the ground, every point is moving forwards, except the very bottom, which is in contact with the ground. In fact, it's a really easy linear relationship: The axle (halfway up the wheel) moves forward at 1x the wheel's overall forward-moving speed. The very bottom goes at 0x the axle speed (but soon gets lifted up and moved faster), and the very top is going forwards at 2x the axle speed. A point halfway between the ground and the axle (where I told you to push the bike wheel) moves forward at 0.5x axle speed, and a point halfway between the axle and the top moves forward at 1.5x axle speed. So if you pull or push a point that is between a wheel's axle and the ground, the whole wheel moves faster than that. In a sense (and this is obvious if you push on the vertical spoke on a bicycle wheel), a wheel can be a lever. Push on the lower part (closer to the pivot point, which in the case of a rolling wheel is the point where it touches the ground at each instant), and the upper part is moved faster and farther than the lower part where you are pushing. Push below the axle, and the axle (and thus the wheel overall) goes faster than your push.
I know that I need to draw images of this, and I will when I have the time. But even better, here's a video example (the "prequel" of the video shown above).
More nice mechanical analogues can be seen here.
What's the point of all this? The point is to show that, if you have two platforms moving relative to each other, it is easy to build a machine that grips them and harnesses that difference in velocity to propell itself in one direction even FASTER than either of the platforms. This is what a DWFTTW cart does. The only difference is that, in a DWFTTW cart, the propeller cannot push on the air as efficiently as the mechanical surfaces that are in contact in the two videos above.
But there is a point to all this talk of mechanical analogues, and a reason why I went into detail about how fast each point on a wheel moves. It is the following:
3) The Sail-Based DWFTTW Ferris Wheel
Imagine a big Ferris Wheel rolling down a huge flat surface. Imagine that the Ferris Wheel is being blown by the wind, and is rolling downwind, parallel to the wind.
Now imagine that this Ferris Wheel has sails where the seats usually go. The sails are movable: They can be turned vertically so that they are perpendicular to the wind, or laid down horizontally so that they offer almost no wind resistance.
Imagine that, as the Ferris Wheel rolls, the sails go into the horizontal (almost no wind resistance) position when they are on the top half of their rotation around the axle. And imagine that they are set to the maximum-draggy position only when they are below the axle.
From the push-a-bicycle-wheel thought experiment, you know where this is going: If the sails are very draggy, and the whole thing is very lightweight, then the sails will be pushed to ALMOST wind speed. And since the sails are below the axle of the Ferris Wheel, the whole wheel will travel faster than wind speed, because points between the axle and the ground will be forced by the sails to travel at almost wind speed. This is equivalent to the yo-yo winding itself, or to the "Spool rolling faster than the paper" video. There will be some "slippage" between the sails and the wind, but if the fraction of wind speed picked up by the sails is higher than their distance up the lever (i.e. if the sails are blown to 1/2 of wind speed, but are located only 1/3 of the way from the outer circumference of the wheel to the axle), then the wheel will roll faster than the wind.
A similar idea is illustrated here...
... and is the basis of Greg London's attempt at a DWFTTW design, the "Tumbleweed".
The problem with the device shown on this video, and with Greg London's Tumbleweed, is that once the thing is rolling at wind speed, the top will be hitting the air in the same way as the bottom, so the push on the bottom will no longer overcome the push on the top. The solution: The vanes must be movable - like the sails on my Ferris Wheel - so that when rolling at wind speed (i.e. when the axle is travelling at the same speed as the wind), the vanes on the bottom get pushed downwind with greater force than the vanes on the top get pushed upwind. It can't be symmetric, otherwise it won't get past wind speed. In other words, from the point of view of a balloon, such a rolling vehicle going at wind speed is just spinning in place (with the ground moving by underneath it), and the bottom of the vehicle (which is moving backwards relative to the air) must be draggier than the top of the vehicle (which is moving forwards relative to the air) so that the vehicle, overall, gets a net forwards push (from the air onto the backwards-moving lower vanes).
4) The DWFTTW Cart
Here's where we start talking about the specific controversial example, the carts made by Spork33 and others. Spork has put build plans here so you can make your own cart and run your own experiments.
The basics of how the cart works are as follows:
First, the cart is pushed to wind speed. (Again, while some may claim that the cart is self-starting, I am not convinced that it is, but this doesn't matter in a discussion of whether the cart can sustain DWFTTW speeds or not. So let's just assume a non-self-starting cart). That means that it is pushed, with some external assistance, until it is not moving relative to the air, until someone riding the cart would not feel any kind of wind.
At this point, there is a propeller spinning on top of the cart. The propeller, like the propeller of an airplane sitting at the end of a runway and beginning a takeoff run, is pulling the cart forward.
The wheels on the bottom of the cart are rolling along the ground at some speed (the speed of the wind as measured from the ground). There are gears that power the propeller, and they are attached to the wheels. They are powered by the wheels. It takes some work to move the propeller (even if the propeller were not pulling on the cart, it takes some work to swish two big blades around the air at high speed). So the wheels actually resist their motion. The wheels are pulling on the ground, trying to hold the cart back. If brakes were activated on the wheels, they would undergo similar forces as they do when they pull the cart back and resist the ground's motion in order to power the propeller. In a sense, the wheels are generators, and anyone who has tried to bike with a generator attached to the wheel (drawing power from the ground going by) knows that they resist that motion.
So the wheel traction (the wheel's resistance to the motion of the ground past the cart, a resistance caused by the fact that when you spin the wheels you're also spinning the prop and some gears and axles, and that takes work) is pulling the cart backwards. The propeller thrust is pulling the cart forwards.
Now, the question is: When the cart is released, which pulls harder? The prop thrust or the wheel traction?
The cart is released. If the cart is well-made, the propeller's forwards thrust will be greater than the wheel's backwards pull, and do the cart will accelerate forward. This is what the controversial Youtube videos show.
But wait!, you say. Isn't that perpetual motion? If I just pushed this cart forward on the ground, are you telling me that when I let go, the propeller force would be greater than the force necessary to spin it up, and that the cart would then just keep going faster and faster? No, I am not saying that. As you will soon understand, the mechanism above will only work if there is wind (and, after the cart goes through, the wind speed is decreased by it). In an odd way, the cart is wind-powered, even if its speed relative to the wind is very very small. First, in Section 5, let me explain the physics behind the cart, which should indicate why it cannot be a perpetual motion machine (i.e. why it would not work if there is no wind). Then, in Section 6, let me go through some thought experiments that explain where the energy is coming from, and how something can be "wind powered" when it barely feels a breeze. (The answer, basically, is that it steals KE from the EARTH; That is, our whole planet will spin just a tad bit slower (relative to the air around it) if one of these carts is running around. But I'm getting ahead of myself again).
5) The Physics
Our model of the physics of the situation involves balancing the work done on the cart, and balancing the forces acting on the cart.
From the point of view of the cart (imagine you are riding the cart), you have the ground going by under you at a good speed, and a slight breeze blowing in your face. The ground pulls back on the wheels, trying to slow the cart down, while the propeller pushes the whole thing forwards, trying to speed it up. As long as the forwards thrust of the propeller is greater than the backwards pull on the wheels, the cart will not slow down. And because the air and the ground are going by at different speeds, this is not perpetual motion. Since the ground is going by very fast, the wheel can produce a lot of power without a big slowing-down force. And because the air is going by very slowly, the propeller does not need a lot of power to generate a big thrust force. If you had no wind (air moving relative to the ground), then this would be impossible.
Six parameters are key to understanding what's going on:
- The force exherted by the prop pulling the cart forwards (Prop Thrust);
- The force exherted by the wheels pulling the cart backwards (Wheel Resistance);
- The work done (energy per second) by the prop to pull the cart (Prop Power);
- The work received (energy per second) by the wheels as they are spun by the ground (Wheel Power);
- The speed of the ground going by, which is high (Ground Speed); and
- The speed of the air going by, which is low (AirSpeed).
(And yes, there are two different AirSpeeds; the one in the air overall, and the one in the air being affected by the prop, which is pushed back a little faster than the general slipstream. You can use either one. For the purposes of this analysis, that doesn't really matter).
Power (energy per second) is force times speed. (For example, if an F-22 requires 320 kiloNewtons of thrust to go at MACH 2 (about 650 meters per second), then this requires just over 200 megaWatts of power (energy expended per second), since in this case "force times speed" is 320,000 times 650, giving a power of 208,000,000, give or take).
In order for this to be a DWFTTW craft, the Prop Thrust must be greater than the Wheel Resistance (at least when going at wind speed, maybe not when going significantly faster).
In order for this to NOT be a perpetual motion machine, the Prop Power must be lower than the Wheel Power, since some of the energy provided by the wheels is lost to friction in the gears and other inefficiencies.
Prop Power = AirSpeed x Prop Thrust
Wheel Power = Ground Speed x Wheel Resistance
So how can Prop Power be less than Wheel Power even though Prop Thrust is more than Wheel Resistance?
Simple! AirSpeed must be smaller than Ground Speed.
Think about it.
Say Ground Speed is a huge number (i.e. strong wind) and AirSpeed is a tiny number (i.e. the cart is going barely faster than the wind). This means that Wheel Power can be quite large, and Prop Power can be quite small, with Prop Thrust still being a little greater than Wheel Resistance.
This means that you don't need to make energy out of nowhere in order to get a cart to propell itself faster than the wind.
It DOES mean that you need SOME wind. If AirSpeed equals Ground Speed (and if Wheel Power is greater than Prop Power, i.e. no perpetual motion), there's no way to make Prop Thrust bigger than Wheel Force.
The faster the wind, the better. The more wind you have, the more different AirSpeed and Ground Speed will be. And the more different they are, the bigger Wheel Power can be relative to Prop Power while still allowing Prop Thrust to be bigger than Wheel Resistance. If power is force times speed, then the greater speed difference you have (between the air and the ground, i.e. the cart's Ground Speed), the easier it will be to multiply a low Wheel Resistance by a big number and get lots of power which can then give lots of thrust given the low AirSpeed relative to the cart.
It may not be easy to juggle six variables at once. But try it for a little while. Remember, the Prop Thrust has to be greater than the Wheel Resistance (so that the cart can accelerate past wind speed) and the Wheel Power has to be greater than the Prop Power (otherwise it's a perpetual motion machine). How can that be done? The answer is, with a low AirSpeed (which means the cart is moving barely faster than the wind) and a high Ground Speed (which means a strong wind, so the cart is going fast to keep up with it).
If you would actually like the real-life numbers behind these variables, I recommend a great BoingBoing comment by MENDER, which goes on from here to also talk about gear ratios and about how steep a slope could be climbed by one of these little carts. I want to keep things as simple as possible here, so I'll skip those details. But the math does add up.
Or does it? Right now you may be asking yourself: "This cart is supposed to be wind-powered. Yet it moves along at basically the same speed as the wind. It has no way of interacting with the wind, other than a very thin structure that does not provide much drag at all, and a spinny thing that is not being used as a turbine (something that the wind blows on and spins, such as a windmill) but instead as a propeller. How can this thing be wind-powered? It can't. And how could it be powered by anything BUT the wind?". I'll explain in just a second.
You may also be asking: "The videos only show these carts running on treadmills. It is clear where the power is coming from: The treadmill motor. But when you're outside going through the wind, there is no such source of power. Right? How can a treadmill test be equivalent to an outdoors wind test? The treadmill test proves nothing!" That, too, is a mistake that is easy to make.
Let me explain:
6) Where Is The Energy Coming From?
In the online debates about DWFTTW around these cart-on-a-treadmill videos, a lot of people trouble seeing the equivalency between a treadmill test and an outdoor wind test. The problem is that they can see energy flowing "from the treadmill" and see this as being significantly different from energy flowing "not from the ground, but from the wind".
The technically correct thing to say is not "The cart is wind-powered". A more strictly correct statement would be "The cart draws its power from the energy that is inherently available given the difference in speed between the air and the ground", or, in short, the energy comes from "the air-ground interface".
This did not make sense to a lot of people, which is understandable:
Imagine a balloon floating in the air, and it's a windy day so the balloon gets pushed along, but since it's floating in air the balloonist feels no wind. Then say that a DWFTTW cart comes along and overtakes the balloon. The balloonist's point of view is analogous to the person standing in a room full of still air, with a treadmill running, and a DWFTTW cart on it. From the point of view of a balloon, the air has no kinetic energy. From the point of view of the treadmill experimenter, the air has no kinetic energy. But the treadmill does take power, and pass it on to the cart. What passes power on to the cart in the outdoors test?
The answer, from the point of view of the balloonist seeing a DWFTTW cart go by: The EARTH supplies power to the cart.
Let me try to explain this. Let me demonstrate it via a three-step thought experiment. (Well, only the third step is really a thought experiment, since the first two parts happen around the world every day in real life).
1) Imagine you have a wind turbine, like the kind that generates electricity out in the hills. You could say "The wind slows down and some of that kinetic energy becomes electricity", but that's not the only way of looking at it. There is an equal and opposite force: In order for something anchored to the ground to pull on the wind, the wind pulls on that something too. So not only is the wind noticeable slowed down relative to the Earth, the Earth is imperceptibly pulled along with the wind. A wind turbine is like a giant air brake, that makes the whole earth more closely match the local wind speed (by just a teeny tiny bit). With me so far?
2) Imagine you have a Prius driving down the highway at some steady speed. At some point the driver touches the brakes, not too heavily. This will turn on generators (not friction-based brakes) that will convert some of the car's kinetic energy into electricity. From the point of view of the Earth: The Prius slows down, its KE becomes electricity (stored in a capacitor or as chemical energy in the battery or whatever). BUT NOW imagine the same thing, except YOU start out in an inertial reference frame that is flying in formation with the Prius. You see the Prius as stationary and the Earth as moving. The Prius is stationary next to you, and the Earth is going by below you. When the Prius hits the brakes (turns on the generators) and thus becomes somewhat connected with the earth, it shoots off in one direction (towards its back). The Earth, meanwhile, slows down just a teeny tiny bit, since it must share its Kinetic Energy and its Momentum with the Prius. When the Prius connected itself with the Earth, some of the Earth's Kinetic Energy went into accelerating the Prius backwards, and some KE went into the Prius's battery. So from an inertial reference frame going at the Prius's original speed, the Earth lost KE, and the Prius got some KE and some electricity. (The Earth only loses a tiny fraction of its KE, though, since it has so much. So it would be pretty much impossible to measure the change in the Earth's speed caused by one small car hitting the brakes. But you can see that this does happen).
3) Here's where it gets a little crazy, and more directly applicable to DWFTTW. Say you have wind blowing steadily and perfectly parallel to a road. Say you have a Prius driving at wind speed (so the driver feels no airflow) and a manned balloon above the Prius (the balloonist feels no airflow). Now say the balloonist drops a rope that hooks onto something in the car. And say the Prius now lightly hits the brakes (the generators). The rope becomes taut, and the balloon and the Prius pull each other. The Prius slows down, but not quite to rest since the wind is blowing the balloon and the balloon is attached to the Prius. So the balloon and the Prius reach some terminal velocity, and keep generating energy! NOW HERE'S THE IMPORTANT PART: What would a second balloon (or an astronaut overhead in an almost-geostationary orbit, which originally was in formation with the balloon) observe? They would observe the Prius shooting off in one direction, dragging the first balloon away with it... and the Earth moving by at a slightly slower rate, like we said before. This is like the car hitting the brakes, but it's also like the wind turbine: The Prius and balloon act like a big air-brake slowing down the earth as it moves through the air: As the Prius (which pulls on the earth) drags the balloon around, it slowly slows down the Earth. The Prius is being pulled by the Earth through its wheels and by the balloon through the rope and hook. So it is the RELATIVE MOTION between the air and the ground that is allowing for energy to be generated. And meanwhile, the Earth is slowly being slowed down. If the Prius did this for millions of years, the Earth would eventually come to rest relative to the air. (The air is also being pushed around to more closely match the Earth's movement, andt that is why I suggested that an almost-geostationary astronaut is the one with the best perspective, not the second balloonist).
If the balloon then had an electric engine attached to a prop, and could run it off the Prius's battery, this would be just like the DWFTTW cart, but with an electrical (not mechanical) connection between the wheels and the prop.
If you doubt that this Prius-plus-powered-balloon contraption could go DWFTTW, please ignore that for a second to take in my main point, about where the energy comes from.
From a truly inertial reference frame, the Earth supplies some KE. When the DWFTTW is dragged along the earth being pulled by its propeller (or even if it only had a sail and weren't a DWFTTW cart at all), it pulls on the earth, and the earth ends up moving just a tad more slowly than it did initially.
To really appreciate this, you have to be in a TRULY inertial reference frame. The balloon is not one (since all the air, through viscosity and separation effects, gets slowed down relative to the Earth), and the ground is not one (since it is pulled to the side by the vehicle). You'd have to be an astronaut in deep space observing through a huge telescope, or an astronaut in an almost-geostationary orbit that is going at the same angular velocity around the earth as the ballonist was at the beginning of the experiment (and even that is not truly inertial).
So the Earth supplies some energy. So it's the same as the treadmill. The difference is that the Earth supplies kinetic energy out of a huge reservoir (so you don't notice that any of the Earth's KE has gone missing, but some of it has), while the treadmill keeps making it from electricity and only holds a little at any given time.
That is why a treadmill test indoors really is equivalent to a wind test outdoors.
And that is where the energy is coming from. Not so much "from the wind", but from the fact that the wind and the Earth ar emoving at different speeds, and if you try to hang on to one, you can get some energy by pulling on the other. Like that robot in the people mover that I mentioned near the top of the page.
7) Ice Boats and VMGs
Sorry, but this page is still under construction. For now I'll just give a brief summary, to be better-written later:
Check out the many discussions online to find out about sail-powered ice vehicles that can travel at an angle to the wind but with the downwind component of their velocity vector (the VMG, or Velocity Made Good) greater than the wind speed. In other words, they can beat a balloon in a race to a spot downwind of the starting point. Two of these ice boats zig-zagging down the ice in a symmetrical way (away from each other, towards each other, away from each other, towards each other) and connected by a thin telescoping rod would essentially be one big DWFTTW vehicle.
Or imagine a cylinder of ice, with gravity pulling towards the centerline. And imagine wind blowing along the long axis. An ice boat moving at some angle relative to the wind, going downwind, would trace a helix along that cylinder. By carefully setting up the angle of the sail (and changing it depending on speed and heading) and the angle of the ice skates underneath, the vehicle would go down the cylinder faster than the wind, making a spring-shaped helix. That's similar to what the prop does in the DWFTTW cart.
You can get more info on REAL and MANNED vehicles that go DWFTTW here. You can see a vector analysis of sustained DWFTTW sailing here. (Soon I will make one that is just like that but shows the vectors around a DWFTTW cart's prop blades).
Ok. Enough for now. This page will be updated again in a day or two. I need some sleep. This debate has taken way too much of my time over the past few days...
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