DWFTTW – The saga continues.

Wow. I wrote a post about Directly Down Wind Faster Than The Wind (DWFTTW) vehicles. At the time of this post, there are 37 comments for the original post. That is way more than I expected. This is very popular topic. Clearly, it brings a lot attention to Dot Physics. The first question – is this the kind of attention a naked person running through campus gets or is it a different kind of attention? I really don’t mind either way.

I am going to try to look through all the posted material and see if I can add or subtract anything for the discussion.

First – the parameters of the discussion

The discussion should be about directly down wind faster than the wind vehicles. Yes, an ice sail boat goes faster than the wind. I think sail boats can do this also. However, they go this speed when they are NOT going in the same direction as the wind but perpendicular to it or something. This discussion is for a vehicle that is going say 15 mph in the same direction as a wind that is maybe 8 mph.

Ok – let the discussion begin.

Friction

In my original post, I said that I would ignore friction between the wheels and the ground. If indeed there can be a DWFTTW vehicle, it would likely need friction. My argument was based on vehicles that used things like jet engines.

Work and Energy

Let me start off by re-emphasizing some fundamental principles. In particular, the work-energy principle. This says that the total work done on a system is equal to its change in energy. Let me take the vehicle as the system (but not the air). Also, let me assume that it is moving at a constant speed faster than the wind (directly down wind). Here is a diagram:

If the vehicle is traveling at a constant speed, the net force on it must be zero. In this case, I included everything acting on the vehicle (which I model as just a point so that friction can make it change momentum and it doesn’t matter where the forces are applied). Note that there is the gravitational force and the force from the ground. These two forces are the same magnitude but opposite directions. Thus, they do not change the vertical momentum of the vehicle. Also, since these forces are perpendicular to the direction of travel, they do no work. Really, I could leave these out, but I want to be complete.

Now for the important forces. The force from the air and the force from the ground in the direction of motion (friction). Did I leave out any forces? I don’t think so. In terms of work-energy, the air does negative work on the vehicle (because it is in the opposite direction as the motion). Friction does positive work. Where does the energy come from for friction to do positive work? That is the key question. If this were an automobile, that energy would come from burning gasoline. In the DWFTTW, I am not sure where this energy comes from. Not saying it doesn’t really work, but for me – this is the key question.

Moving against the wind

One point that was brought up was that boats can said into the wind (in a manner). From what I understand (which clearly isn’t everything) this has a lot to do with aerodynamic lift from the sails. Anyway, if a boat can do it, why not a DWFTTW vehicle? But remember, this is a discussion about faster than the wind, not against the wind.

I bring up moving against the wind because I can think of one case that might work moving against the wind (and I think this was mentioned in the forum). Suppose I had a wind generator that charged a battery or capacitor. After a while, the generator should be able to build up enough energy to get the vehicle moving some. However, this would not be a constant self-sustaining vehicle. It would need to stop and recharge. Also, it would not be moving faster than the wind, but against the wind.

Other stuff from the comments

Chris posted this http://home.san.rr.com/tadhurst/DWFTTW.htm. It seems like a discussion about the forces on the prop.

JB posted this link http://www.nextenergynews.com/news08/next-energy-news8.29.08b.html. Clearly there is some evidence of wind powered cars that can go directly into the wind. But the article does not say anything about going down wind faster than the wind

Jason posted this link to the Brennan torpedo http://en.wikipedia.org/wiki/Brennan_torpedo. I don’t think it really applies to this situation since it clearly has an external power source.

Final stuff

Is there a conclusion? I am still not clear. If you have a car moving faster than the wind, into the wind, powered by the wind – where is the energy coming from? If it is moving with the wind and then reaches the wind speed and then moves faster than the wind, how does it make this transition? There seems to be a lot of stuff out there that says this can happen, but you can’t get something for nothing. I am sure I will get just as many comments on this saying all sorts of things. I really appreciate all the feed back and the civil discussions that have followed.

Hey look! A naked guy running across campus.

1. #1 meichenl
December 16, 2008

Rhett,

I intend this response to show that a DWFTTW vehicle is compatible with the basic physical principles you consider in your post. I will not describe the mechanism, but I will quantitatively address the particular points you make regarding free body diagrams, work, force, and energy.

In a DWFTTW vehicle, the friction will do negative work while the wind does positive work. This is opposite as you have drawn it. You could build a vehicle that works either way. You get to choose which force points which way based on how you construct the thing.

Friction will push to oppose you, whichever way you want to slide one surface over another. So you can make friction push forward or backward, which is why a car can either accelerate when the driver hits the gas, or decelerate when he/she hits the brakes. The fact that the car in my example is powered by gasoline is irrelevant, because I am only making the point that friction itself can indeed point either direction. I’ll get to energy in a moment.

Friction points backwards on the vehicle, so the wind must push forwards on the vehicle. In your example of zero acceleration, the wind and friction forces have the same magnitude, but I intend to analyze an ideal example where the force of the wind is actually greater, and the car accelerates. It may seem ridiculous to say the wind pushes the car forward when the wind is actually blowing straight into the car. But consider a very streamlined car. In that case, the force of the wind blowing directly into the car becomes very small. Now take the streamlined car and attach a windmill-type thing that pushes air backwards. The wind isn’t powering the windmill. In that case the force of the air would push backwards as you suggest. Instead, the windmill draws whatever power it needs from a direct connection to the wheels – from the kinetic energy of the cart. It then uses this energy to push backwards on the air, jet-engine style. It pushes the wind in the same direction is was already going, from its own point of view. From the point of view of the ground, however, the windmill pushes the air in the opposite direction it was already going. This is possible because the windmill thinks the wind is blowing backwards, while the ground thinks the wind is blowing forwards, but just doing it slower than the vehicle.

From the car’s point of view, such a windmill is drawing power. It’s taking wind already moving towards it, and pushing it even faster in that same direction. It’s adding to the kinetic energy of the wind (from its reference frame, of course. From the ground’s reference frame the windmill is extracting energy from the air.) We will have to worry about where the windmill gets this energy.

Because the windmill pushes the air backwards (again in the car’s frame), the air pushes the windmill forwards in a third-law pair. I intend to show that the force of the friction slowing the car down is less than the force of the air speeding the car up. I will do this by assuming that no energy is lost to heat, and then explicitly calculating the forces.

The windmill pushes back on the air with force F. The windmill is putting out energy into the air. The rate it is putting out that energy, its power, is the force times the relative velocity of the air and the windmill. This relative velocity is v_vehicle – v_air. The power output by the windmill is therefore

P_out = F_air*(v_vehicle – v_wind)

This isn’t free energy. The windmill has to draw this energy. It draws the energy from the wheels. There must be a force of friction slowing the vehicle down as it delivers power to the windmill. This power, P_lost, is the same as the power output, P_out (under ideal conditions). But the power lost is drawn from the force of friction slowing the car down. By allowing friction to do negative work, the car is losing kinetic energy, and converting that kinetic energy into the energy needed to power the windmill. This power is the force of friction times the relative velocity of the ground and vehicle, v_vehicle. So the power lost can be written as

P_lost = F_frictionv_vehicle = P_out = F_air(v_vehicle – v_air)

Solve this for F_air to obtain

F_air = F_friction * v_vehicle/(v_vehicle – v_air)

Thus, the force of the air on the vehicle is greater than the force of friction on the vehicle. There is a net force forward, and so the vehicle accelerates forward, going even faster into the wind.

Finally, we can analyze this scenario from the point of view of the ground to make sure we didn’t somehow cheat the first law (of thermo). From the ground’s point of view, the car is gaining energy as it moves forward, while the air is losing energy because the windmill is pushing it opposite its direction of motion.

The power the wind delivers to the windmill is

F_airv_wind
= F_friction
v_vehicle*v_wind/(v_vehicle – v_wind)

and the power the car picks up is

(F_air – F_friction) * v_vehicle
= (F_frictionv_vehicle/(v_vehicle – v_wind) – F_friction)v_vehicle
= F_frictionv_windv_vehicle/(v_vehicle – v_wind)

The power in and the power out are identical in this frame, just as we set them up to be (P_lost = P_out) in the car frame.

So there is no fundamental physics problem with the DWFTTW vehicle. I think the tricky part is that going DWFFTW you need friction to slow you down, and force of air to speed out up. This is opposite from going down wind slower than the wind, and opposite of what a sail does. So the vehicle can’t be a sail. And if it’s going to go from slower than the wind to faster than the wind, it needs to be able to make friction go from pointing one direction to pointing the other, and from being pushed by the wind to pushing on the wind.

However, these are practical problems of engineering, and I do not believe physics prevents such a design.

2. #2 Tom
December 17, 2008

The concept I missed in my fist few passes at this was that the propeller is always pushing air out the back — it’s not acting as a turbine to turn the wheels. This means that the air can exert a force on the vehicle even when moving downwind at wind speed. I don’t think there’s a question that the air contains enough energy to propel the cart, as long as the cart’s mass is appropriate to the situation.

3. #3 ThinAirDesigns
December 17, 2008

Rhett:
“JB posted this link http://www.nextenergynews.com/news08/next-energy-news8.29.08b.html. Clearly there is some evidence of wind powered cars that can go directly into the wind. But the article does not say anything about going down wind faster than the wind”

Rhett, the only reason I addressed the “upwind” issue is because you argued that DDWFTTW couldn’t be done because upwind directly into the wind couldn’t be done.

I address whatever arguments are presented and it was you who chose the ‘upwind can’t be done” argument.

I’ll work in some of your questions a bit later.

JB

4. #4 spork
December 17, 2008

Without putting too fine a point on this, I consider the real world physical proof to be pretty good evidence that DDWFTTW can be done (and we can assume it doesn’t violate any of the laws of nature). JB and I have such vehicles and a pile of videos that attempt to document as clearly as possible exactly what they’re doing.

As a good friend said – “sure it’s possible in practice – but can you prove it can be done in theory?”

And the answer is yes. Just tell me what form you’d like the proof to take. We have all flavors.

5. #5 spork
December 17, 2008

“Yes, an ice sail boat goes faster than the wind. I think sail boats can do this also. However, they go this speed when they are NOT going in the same direction as the wind but perpendicular to it or something. “

It’s true that a traditional sailing vessel can’t go directly downwind faster than the wind, but they can do a darn site better than beating it on a perpendicular course. In fact ice boats can maintain a downwind velocity component of 3X to 4X the true wind speed. There’s plenty of rock solid evidence of this, not to mention very simple analyses that show how this can easily be done.

So they can’t go straight downwind faster than the wind, but they can tack downwind, and beat the wind by a very wide margin. Just connect two of them with a telescoping pole so they stay on mirror tacks as the whole contraption goes downwind at 3X true wind speed, and the discussion is over.

6. #6 spork
December 17, 2008

Rhett, I think there are a couple of very critical errors in your diagram if I’m reading it correctly. First you have the force from friction (aerodynamic drag?) acting in the same direction as the vehicle’s velocity even though the vehicle is presumed to be moving faster than the wind. Similarly you have the force from the air (the tailwind that’s doing the work to make the vehicle go faster than the wind?) acting opposite the vehicle’s velocity. If I’m understanding what you mean for these vectors to represent, they’re both backward.

Finally, you’re only interaction with the ground is a normal force. This thing can only work by using the tangential force of the ground on the tires to turn the propeller. So that’s a pretty important force to include as well.

My apologies if I’ve misinterpreted the diagram.

7. #7 Matthew
December 18, 2008

spork, I’ve been following these discussions for the last few weeks, and have been convinced (after initial skepticism) that your cart works. I think you are misinterpreting the diagram, but the diagram does not correctly correspond to your cart. The friction vector, as I interpret it, refers to the force of static friction between the ground the cart. This doesn’t really make sense for your cart because the cart isn’t sliding; it’s rolling and the force of static friction is actually applying torque to the wheels (which drive the propeller, so I guess in a way, the friction vector is pointing in the right direction), and the point of contact on the wheel is actually moving opposite the direction of motion. The direction of the force of air resistance on the cart is correct because the diagram represents the cart moving faster than the wind. The diagram is missing the force vector for the thrust from the propeller (unless that is what the friction vector is supposed to represent).

8. #8 Anonymous Coward
December 18, 2008

DWFTTW for physicists.

Or: an attempt to answer the somewhat ill-posed question “Where is the energy coming from?” using nothing more than 1st semester freshman physics.

Assume:

Car with wheels and a propellor on top.

Car’s wheels do not slip on the ground, and their bearings turn with no friction.

Propellor is much larger than rest of car, so interaction with the wind dominated by propellor.

Any batteries, motors, or generators mentioned are 100% efficient. I am using motors and generators because they make calculations easy. Gears are hard.

1-D problem
Velocity of wind relative to ground: Vw
Velocity of car relative to ground: Vc

I’m gonna start with two trivial examples to warm up, then get to the real deal.

1) Wheels free-spinning. Propellor free-spinning.

Equilibrium solution: Vc = Vw

2) Wheels free-spinning. Propellor driven by motor to push against wind, with energy supplied by MAGIC!

Equilibrium solution: Vc > Vw

3) Propellor driven by motor to push against wind, with energy supplied by car’s battery. Generator connected to wheels to charge car’s battery.

Equilibrium (i.e. constant velocity, net power into battery = 0) solution? Let’s work it out!

For convenience, we’ll work in the intertial frame of the car (with the positive direction defined as being opposite the direction the ground is moving):

The propellor encounters some mass of wind per unit time dMdt, and changes its velocity by some amount -D.

The resulting force on the car (equal and opposite, and all that) is +D*dMdt.

From the change in the wind’s kinetic energy, we calculate the power supplied to the wind is
Power = (1/2) * dMdt * ( ((vw-vc)-D)^2 – (vw-vc)^2 ).
You should draw yourself a picture to convince yourself my sign convention is correct.

(In the above, we have neglected any sort of turbulence, etc by assuming the only energy imparted to the air is that associated with the change in its net momentum. Those neglected effects will degrade the performance of the system, and this is a very idealized model of air, but hey – we’re physicists here. And remember – rest frame of the car.)

Now, what is the available power supplied to the battery from the generator? In equilibrium the force on the car is zero, so we have a force -DdMdt and a velocity of the road of -Vc (again – car’s inertial frame), and a resulting
Power = force
velocity = DdMdtVc.

In equilibrium, the power from the generator must equal the power driving the propellor, so
(1/2) * dMdt * ( ((vw-vc)-D)^2 – (vw-vc)^2 ) = DdMdtVc
work through algebra to find
D = 2 * Vw

Holy cow! There’s no condition on Vc! You can go as fast as you damn please directly downwind! (In this overidealized physics version). To get a finite velocity, we will have to introduce a bit of loss into our system, which we will model as a power loss which is linear in the difference in the velocity between the car and the wind. To make the equations work out nicely I’ll take this power to be LDdMdt(vc-vw). This leads to a revised energy equation:
(1/2) * dMdt * ( ((vw-vc)-D)^2 – (vw-vc)^2 ) = D
dMdtVc – LDdMdt(vc-vw)
which we solve to find
Vc = Vw*(1+L)/L – D/2L

Clearly, to get large velocities, we need L small (pushing the air without stirring it up, for example) and D small – the propellor causes a small change in the air velocity.

At large L we have the expected limit Vc -> Vw.
As L -> 0, we have Vc -> (Vw – D/2) / L.

Counterintuitive? Certainly. C’est la vie.

Exercises for the reader:

Check my math. I ran through this pretty quickly.
Calculate in your favorite reference frame.
Generalize to 2-D.
Calculate the relativistic version.
Develop a better model of the losses in the system than the ad-hoc method employed above.

9. #9 Anonymous Coward
December 18, 2008

Hmm. Now that I read the previous comments more carefully, I suspect my preceding analysis is redundant with meichenl’s above. Well, double your pleasure, double your fun and all that.

10. #10 Uncle Al
December 18, 2008

That a solely wind-propelled vehicle can move faster versus the ground than the wind is empirical fact. Ice boats can do 5X windspeed vs. ground. Theory that predicts otherwise is wrong.

A middle ground would be Subtle Transaction Regarding Inviolate Noreaster Groundspeed theory that has 10^(10^5) solutions and no predictions. More studies are then needed.

11. #11 ThinAirDesigns
December 18, 2008

Uncle Al @ #10

What you state is a fact, though what you state isn’t directly relevant.

What’s important in its relation to DDWFTTW, is whether an ice boat VMG (velocity made good, or it’s downwind component) is greater than TWS. In other words, just because an ice-boats velocity is 5x TWS over the ground, wouldn’t necessarily mean that it’s downwind VMG is greater than 1.0 of TWS.

Now, as it turns out, that an ice-boat can also achieve a downwind VMG of greater (far greater) than 1.0 of TWS is also an empirical fact and any theory that predicts otherwise is also wrong.

JB

12. #12 spork
December 18, 2008

Question: Is Rhett a troll on his own blog? He’s now had two blogs where he posed questions, made some wrong conclusions, and claimed he wanted a discussion. Where has he gone?

13. #13 ThinAirDesigns
December 18, 2008

spork, I’m beginning to agree with you.

In response to my request for a friendly back and forth Rhett said:

“I of course would be happy to discuss this further.”

As of yet, no real discussion — only a ‘I’ll grok it” and then another blog entry where he gets it wrong, essentially ignores all the excellent comments from the previous bog and essentially blames the participants for discussing “upwind” carts when he himself definitively started that discussion.

It’s looking more and more like Rhett’s kids are gonna have to witness the carnage.

JB

14. #14 Rhett
December 18, 2008

Spork,

I am a naked man running across campus. Sorry, it is difficult to keep up with all the other activities going around here. I really have not had to time to think about these things. You guys are just way too fast for me.

Rhett

15. #15 Chris
December 18, 2008

Hello Rhett,

while i have nothing substantial to contribute, i’ll just dropped by to say some kind of thanks for reconsidering the whole thing.

Also, the link to the DWFTTW math i gave is now defunct, and so far i was unable to find a mirror of it. I should have saved it locally and put it my site just for backup purposes. Let’s hope it will reappear some day. In the meanwhile you might want to put something like “(link now defunct)” next to it.

Greetings,

Chris

16. #16 Chris
December 18, 2008

Spork,

while i agree that Rhett could give that impression, we all should be aware that people actually have a life to take care of and thus can’t be posting all the time as we do. Give him a few days to response. 2 days is really nothing if people have to do work, care for the family, etc.

Said that, i’m way more curious what happened to Mark CC at good math/bad math. Much longer time of silence and no response to the issues raised in the comments to his second blog entry on the topic.

Don’t let the “bad experiences” that we clearly have with other people on this topic taint our overall stance on it. Let’s play nice to the people who try at least, only that way we can expect some meaningful progress and sane behavior on the other side.

Let’s all have a break, sip some nice beer (or whatever beverage you prefer) and let time work out things. Cheers!

Greetings,

Chris

17. #17 Rhett
December 18, 2008

Ok – some comments. Numbered for your convenience.

1) Thanks for your contribution to this discussion.

2) The force diagram above should be ok. If the object is traveling at a constant speed, the net force is zero. The F-air is the total force from the air. The friction is the frictional force from wheels, which I assumed where “driving” the thing by not slipping just like an automobile. In my first treatment of this device, I (for some reason) assumed the propulsion was coming from the air, like some type of jet engine.

3) Note that I try to approach this whole situation from a fundamental perspective such as: Where does the energy come from? Where are the forces from? It should be possible to talk about these things without going into too much detail about the actual device.

4) Someone previously mentioned that if two mediums are traveling at different speeds, you could get energy out of it. I am not sure I understand this. Is the air moving slower afterwards?

5) Forgive my skepticism, I can’t help myself. I saw the video that was posted on Tom’s site, but I couldn’t really see any details. Is this device something that someone could build themselves?

18. #18 spork
December 18, 2008

“4) Someone previously mentioned that if two mediums are traveling at different speeds, you could get energy out of it. I am not sure I understand this. Is the air moving slower afterwards?”

Yes, the air in its wake is moving slower relative to the ground after the cart passes.

“5) Forgive my skepticism, I can’t help myself. I saw the video that was posted on Tom’s site, but I couldn’t really see any details. Is this device something that someone could build themselves?”

Yes, I’ve posted parts lists and build notes. In the next few days I will have a comprehensive video posted on YouTube that takes you through the complete build.

19. #19 Rhett
December 18, 2008

Well Spork, when you have the instructions up (and it is not too complicated) I will have to try to build this device and maybe take some data on it.

Rhett

20. #20 Chris
December 18, 2008

Hello Rhett,

you can find plans here:

Ah, finally i could contribute something here, even if it’s only two links 😉

Greetings,

Chris

21. #21 spork
December 19, 2008

And I now have the videos posted:

Build video 1 of 3:

Build video 2 of 3:

Build video 3 of 3:

So easy even a physicist could do it 🙂

22. #22 Rhett
December 19, 2008

Spork and Chris,

Thanks for the links. Someday I will try to get around to building and testing one of these suckers. Doesn’t look too complicated.

Although, now I will be the physicist that goes around and sees DDWFTTW signs all over the place with the slogan “so easy a physicist could do it” and then they will make a terrible TV show about physicists that nearly as funny as the commercials.

23. #23 Anonymous Coward
December 19, 2008

To Rhett (#17)

2) The total force from the air should be in the same direction that the vehicle is moving. For your diagram to be correct, F_air would have a negative value.

3) See posts #1 and #8

4) Of course.

5) As David Mermin would say (and has often been attributed to Feynman), sometimes the right thing to do is “shut up and calculate.” Balance the powers and forces to work out the equilibrium velocity of the system. If you’ve taught freshman physics, it should take about 10 minutes. If you don’t have the time to do that, I’ve done it for you in #8.

24. #24 Anonymous #2
December 20, 2008

Rhett: I’m a bit shocked by how cavalierly you’ve treated this topic. Not to be rude, but your first post on the subject was riddled with basic errors, and your second was sloppy to the point of being almost as wrong. After reading the comments on the first post, it should be totally obvious to you that there is no problem with conservation of energy. The force balance in question here is really quite trivial (determining whether the prop generates enough force to overcome friction is a little harder, but that’s an engineering detail). As for moving into the wind, just think for a second – it’s absurdly simple to mentally design something that will roll into the wind. And if you can move into the wind, you can move DWFFTW if losses due to friction are small enough.

To pick on one example from your second post: you said “However, they go this speed when they are NOT going in the same direction as the wind but perpendicular to it or something.” It’s true that no sailboat can sail directly upwind (or directly downwind faster than the wind, for exactly the same reason). But to say “perpendicular to it or something” is just inexcusably lazy. 5 minutes of googling would show you that ice boats can sail at an angle and with a speed such that the downwind component of their velocity is MUCH faster than the wind. To sail (not-quite-directly) DWFTTW, they can tack into the apparent headwind they see from their motion. That alone proves immediately that there is no problem with any law of physics here.

As for where the energy comes from, it comes from the relative motion of air and ground in almost exactly the same fashion the power of a sailboat comes from the relative motion of air and water.

Bluntly: I’d be embarrassed if I were you. Is this not supposed to be an educational blog? Don’t you owe it to your readers, and to the field and institution you represent, to get this right? It’s really not that hard, especially considering it’s been explained to you quite carefully multiple times over. I hope for your sake you have tenure.

Again, sorry if that seems harsh, but I’d hate to see someone confused by these posts of yours.

25. #25 spork
December 20, 2008

This was my favorite part:

“Dear MythBusters. When you do an episode on this topic, please mention my blog. It will make my kids think I am cool.”

This after explaining how DDWFTTW is impossible. I hope the Mythbusters does mention this blog.

26. #26 zeynel
December 20, 2008

Anonymous #2 writes:

“. . . I’d hate to see someone confused by these posts of yours.”

What if I am confused by this post? Knowledge arises from errors and mistakes. Please, be simple and direct but wrong. The method of physics in general is the opposite of what is being done in this blog. In their professional work physicists try to be as obscure as possible in order not to be wrong. Instead, try your best but if it is wrong, it is not the end of the world. No one reading this blog will be harmed by anything wrong here. I believe that readers will learn more by errors. Let them think for themselves and correct and learn.

27. #27 spork
December 20, 2008

“In their professional work physicists try to be as obscure as possible in order not to be wrong…. I believe that readers will learn more by errors.”

WOW!

“Let them think for themselves and correct and learn.”

People will learn by making errors, not by reading others’ incorrect explanations. And even then, they only learn from their errors if they keep at it until they get it right.

28. #28 spork
December 20, 2008

By this theory it seems physics texts should just print misinformation so the readers will learn the most.

29. #29 Michael C
December 20, 2008

“If you have a car moving faster than the wind, into the wind, powered by the wind – where is the energy coming from?”

From the relative movement between the air and the ground. This energy is always available, no matter at what speed and in what direction the cart is going, as long as it has contact with both air and ground. Think of the cart as a system of leverage between air and ground. Did you look at my mechanical analogy: http://www.youtube.com/watch?v=k-trDF8Yldc ? My cart uses the relative movement between ruler and ground as its source of power, enabling it to go faster than the ruler that pushes it.

“If it is moving with the wind and then reaches the wind speed and then moves faster than the wind, how does it make this transition?”

When the machine is travelling at below wind speed, the gearing between wheels and propeller is making the propeller turn at a speed that would propel the cart faster through the air than its actual speed (which at this point is negative through the air). The net force on the cart is a forward, accelerating force. When the cart reaches wind speed, this is still the case (the speed of the cart is now zero through the air, but the prop is turning, still creating a net thrust forwards). The cart continues to accelerate until the forces acting on it are in equilibrium, at which point it maintains a steady speed. The theoretical speed of the prop through the air is now equal to its actual speed. Note that the forces acting on the cart include the thrust from the propeller: this essential force is missing in your diagram.

“There seems to be a lot of stuff out there that says this can happen, but you can’t get something for nothing.”

You’re not getting something for nothing. Energy is conserved. Just like any system of gearing, the cart trades force for speed.

30. #30 Rhett
December 20, 2008

Michael,

I did see your mechanical analogy for the energy from two different speed mediums, but it looked unnecessarily complicated. Really, I think the next step is for me the build the thing and test it. Might take a while though.

31. #31 spork
December 21, 2008

Rhett,

If you think Michael’s example was too complicated, there’s no chance that building the prop cart is going to shed any light – it is far more subtle and complex. I’m not sure if you saw this video that Michael did, but this is just as simple as it gets:

32. #32 Michael C
December 21, 2008

I’m flabbergasted. Unnecessarily complicated? The first machine “Along the paper” is just an empty cotton reel, no more, no less. The second machine “Under the ruler” consists of two parallel cotton reels with a third wheel that rotates against them. What’s complicated about that?

33. #33 Anonymous #2
December 21, 2008

Not only is it not “complicated”, it’s so simple and explained so slowly and clearly that a small child can understand it (I know, I checked). As for “unnecessary”, it reduces the DDWFTTW cart precisely to the minimum set of elements required to model the principles at stake. Which was more or less the ideal in physics education last time I checked.

34. #34 Clive
December 21, 2008

In #17, Rhett said:

“2) The force diagram above should be ok. If the object is traveling at a constant speed, the net force is zero. The F-air is the total force from the air. The friction is the frictional force from wheels, which I assumed where “driving” the thing by not slipping just like an automobile. In my first treatment of this device, I (for some reason) assumed the propulsion was coming from the air, like some type of jet engine.”

Just in case you’re still missing this key point, please note that the wheels are actually driving a propeller which in turn is basically accelerating air from the front towards the rear of the cart, thereby generating thrust. (When I read your comment above it sounds to me like you are perhaps still thinking the “propeller” is actually a turbine powering the which are then propelling the cart – like a car. That is not correct.)

Hopefully I am not just simply misunderstanding what you have written, but there are a couple of typos in your comment, plus (to me) some ambiguity, especially in that last statement about jet engines.

So, at the risk of repeating what others may already have said or what you already know, you should note that the wind initially moves the cart forward (from rest) simply because there is enough overall surface area and so on presented to the wind to enable the “sail effect” of the cart as a whole to overcome the tendency of the propeller blades to make it back up into the wind at that point. But once it starts moving downwind, the propeller is also forced by the turning wheels to turn in the desired direction for it to start generating thrust just like a propeller on an aircraft. As the cart gains speed, the propeller spins faster and the thrust also increases further. (The “apparent wind” seen by the propeller blades changes as this happens also.) With a properly designed cart, once it is nearing (or at) wind speed, the propeller is generating most (all) of the force required to keep the cart accelerating to a point where it exceeds the wind speed. Finally, some time after doing that, the increasing friction from the relative headwind now “seen” by the cart plus other factors such as the increasing losses due to friction in the ever faster rotating gearing and so on means there is no net force on the cart and it now travels at a constant speed (but still “faster than the wind”).

Hopefully that is reasonably accurate description, but I’m sure I’ll be corrected by others if it’s not. 🙂

35. #35 ThinAirDesigns
December 21, 2008

Rhett:

… looked unnecessarily complicated.

I’ll bet your kids could explain it to you — talk about them thinking something is “cool”.

JB

36. #36 spork
December 21, 2008

I don’t think this blog is going the direction Rhett expected it to go.

37. #37 Rhett
December 21, 2008

I don’t really have any expectations.

38. #38 spork
December 21, 2008

To quote a friend from another forum:

“There was a study a while back that showed that junior faculty with blogs were far less likely to get tenure than those without. Junior faculty with really bad blogs are probably in even more trouble…”

39. #39 Anonymous Coward
December 21, 2008

Rhett: (#30)

Really, I think the next step is for me the build the thing and test it.

As one (anonymous) physics instructor to another: what a self-defeating thing to say! One of the beautiful things about physics is that, by constructing simple physical models, we can predict the behavior of a wide variety of physical systems. There are obviously certain complex phenomena that cannot be understood through such simple models, but this problem is not one of them. A simple balancing of forces and powers can get you an equilibrium velocity DWFTTW or, for a different “gearing”, into the wind.

I understand that this blog is not one of your primary (or probably even secondary) priorities, and that posting controversial material increases traffic and participation, but it’s a bit frustrating that you’ve posted multiple times on this topic without attempting a quantitative analysis (it’s not a hard problem), or checking the comments to see where you might have made an error.

40. #40 Rhett
December 21, 2008

AC,

The plan of the two DWFTTW posts was not to explicitly solve the problem. What I hoped to bring to the table was a fundamental perspective on the problem (work-energy and momentum). I would like to build the device, and perhaps I will do so. I wonder if it could be built with Lego. As for the expectations (I was really talking about myself).

41. #41 spork
December 21, 2008

“The plan of the two DWFTTW posts was not to explicitly solve the problem.”

There is no problem to solve. Several people have built working models and have both understood and explained quite exhaustively how and why they work.

“What I hoped to bring to the table was a fundamental perspective on the problem (work-energy and momentum).”

Again, it’s been analyzed from force, momentum, and energy perspectives. There are interesting aspects worth discussing to be sure, but if you’re hoping to unravel the mystery of the DDWFTTW cart you’re a bit late to the party.

“I wonder if it could be built with Lego.”

NO. I fear that yet another person will do as Charles Platt did in his now infamous article. It would be a real mistake to make a poor attempt at building one just so it fails and you then claim it’s theoretically impossible. That definitely does not serve anyone. If you actually want to build one I strongly recommend you carefully follow the instructions in the videos I posted. You would be hard pressed to build a working model with less time or money than that – and certainly won’t do so on your first attempt. Once you’ve built a working model by all means experiment with any parameter or hardware you like. But there’s no reason to start with a very significant disadvantage.

42. #42 Michael C
December 22, 2008

“I wonder if it could be built with Lego.”

Mechanical analogies such as mine: yes. A wind-powered cart: I doubt it. You need a pretty efficient prop and very smooth-running bearings, together with a lightweight, low-drag frame. You’d do better to spend a bit more time on understanding how the wind-powered cart works before trying to build one.

I’m still completely perplexed by your reaction to my videos. Your profile page at your university says that you’re doing research in the field of Physics Education and that you are”interested in physics for elementary teachers”. Doesn’t the educational aspect of my demonstrations interest you? How can you call them “unnecessarily complicated”? How can you miss the connexion with DDWFTTW?

43. #43 Rhett
December 22, 2008

Michael,

I am sorry – my comment on “unnecessarily complicated” was referring to the diagram on one of the sites that showed a mechanical device that that got energy from two different moving surfaces. Not saying it can’t happen, just saying one should be able to explain it without something that complicated.

44. #44 Michael C
December 22, 2008

Rhett, did you actually look at the videos? I tried to make them as simple as possible: they’ve been understood by children and by adults with no training in maths or physics. There is an essential point: there’s no way of extracting kinetic energy from one thing moving at a constant speed in a straight line on its own; you can only extract kinetic energy from relative motion, by slowing down this motion.

The whole point of extracting energy from the wind is that you are using the relative motion between the air and the ground. A mass of air is moving across the surface of the Earth at a certain speed: if you have contact with both ground and air (like a wind generator, or the DDWFTTW cart) or water and air (like a boat), you can extract energy from this relative motion by locally slowing it down. If you only have contact with the air (like a balloon), you won’t gain any energy, you’ll just float with the wind.

The bottom line: you can only understand the DDWFTTW cart if you understand that the energy is being extracted from the relative motion of two things, air and ground. If you consider that idea to be unnecessarily complicated, you won’t understand the cart.

45. #45 joerenes
December 30, 2008

I think it can be understood by considering both the force of the wind on the prop/cart and the torque of the wind on the prop. See here

46. #46 DavidGlover
December 30, 2008

Ahhh, the Pied Pipers of DWFTTW strike again, leading another expert down the primrose path… instead of big game animals on their wall … they have have the virtual heads of math and physics experts. Happy Hunting – the grounds here on the interweb are fertile. “sure it works in practice, but prove it works in the theory”

47. #47 spork
December 31, 2008

“…instead of big game animals on their wall … they have have the virtual heads of math and physics experts. Happy Hunting…”

But sometimes it’s like hunting cows – and that makes me sad.

48. #48 Harvey C.
January 13, 2009

If I were to design something that could be powered by the wind and travel as fast as possible, directly down wind,the best I could do is to design an air molecule! I cannot imagine anything that could be more efficiently powered by the wind and travel any faster. But the max velocity of the air molecule would be exactly the same as the wind velocity. If I were to add any other appendages, gears, wheels, propellers etc etc it would only make my basic device more massive and only serve to slow it down! This is a question of the answer being so simple that people overlook it and make it overly complicated. Nothing at all can go directly down wind, faster than the wind, powered only by the wind. Nothing!

49. #49 Robin
January 13, 2009

@Harvey
Proof by lack of imagination… brilliant!

Notwithstanding your incredulity, the thing exists and works. Look on Youtube for videos by “spork33”.

50. #50 Harvey C.
January 14, 2009

The videos prove nothing about a device going faster than the wind. They do prove that a treadmill can power a cart. What is so amazing about that? A big, powerful treadmill acting as a drive system for a little flimsy cart. I can also use a treadmill to power a garbage disposal, or an electric shaver, a lawn mower, in fact any small device that requires mechanical energy. This has absolutely nothing at all to do with going faster than the wind. Nothing!

51. #51 Robin
January 14, 2009

Harvey, you might want to read up on a topic called “Frames of Reference”, and possibly “Galilean invariance” too. This is basic physics.

From the point of view of the cart, a moving treadmill surface under a body of still air is EXACTLY equivalent to a stationary surface with a moving body of air above it, i.e. the Earth with wind blowing over it.

If you can disprove the equivalency, you will overturn conventional physics, win a Nobel and date supermodels.

Try reading this thread on the James Randi forums: http://forums.randi.org/showthread.php?p=4342871

52. #52 Harvey C.
January 14, 2009

Yes, the frames are equivalent. What of it? Is the cart going faster than the treadmill? No it is not! It is just moving in the opposite direction to the treadmill. Has anyone measured the actual speed of the cart relative to some stationary reference and the absolute speed of the tread relative to the same reference? If you do that, I am sure you will find that the cart is running at a much lower speed than the treadmill! If I run at 5 mph from North to South and you run at 6 mph South to North, our relative speed is 11 mph. But obviously neither of us is running at 11 mph. You are saying the cart is outpacing the treadmill simply because it is going in the opposite direction and from that you are saying it will outpace the wind. That is ridiculous!

53. #53 Robin
January 14, 2009

Is the cart going faster than the treadmill?

Yes it is, because it’s moving AGAINST the treadmill. If it was to go slower, it would move with the treadmill surface. At windspeed it goes the same speed in the opposite direction and remains stationary in the ground’s frame of reference.

This is very simple stuff.

54. #54 Harvey C.
January 14, 2009

55. #55 Robin
January 15, 2009

“Turn off the treadmill and the cart stops.”

Turn off the wind and the cart stops. Big deal, nobody claims differently.

These two are exactly identical in the reference frame of the cart. Your problem is that you cannot separate yourself from your own reference frame and imagine this from the point of view of the cart.

56. #56 Kasper Feld
January 15, 2009

Harvey.

Imagine that the earth was rotating insanely fast – say once every 24 hours – but that the atmosphere was standing still relative to the sun. Then when if you went outside you would agree it was quite windy.

Now if you put up a sail (well even if you didn’t I guess) you would end up moving at some intermeadiate speed (slower than the earth, faster than the (still) atmosphere). As you tumble across the ground (or the ground tumble under you) you wonder, where is the energy for my motion coming from, the earth or the wind? -well that depends on the frame of refference.

A ballon would move at pretty much excactly the speed of the air, which means that people on the ground would see it moving very fast past them, while the sun would see it standing still, rigth? If something was going even a little bit faster yet then the sun would see it moving slowly backwards the opposite direction of what the earth was turning.

Now replace the earth with the treadmill. The ballon still hangs motionless in the air. The cart is going slowly in the opposite direction of the treadmill, utilising the only energy source there is: the relative motion of the air and the surface. A small guy standing on the treadmill would see the ballon rush past following the air, and the cart going sligthly faster yet.

Your evaluation of what the cart does on the treadmill seems correct enough, you just need to see that the same thing aplies if the road is stationary and the air is moving.

57. #57 Kasper Feld
January 15, 2009

“If I run at 5 mph from North to South and you run at 6 mph South to North, our relative speed is 11 mph. But obviously neither of us is running at 11 mph.”

No relative to the rest of the galaxy we are moving at several miles per second.

“Has anyone measured the actual speed of the cart relative to some stationary reference and the absolute speed of the tread relative to the same reference?”

In this case we are using the treadmill surface as refference, because it is the only ground that the cart has contact with. There is no such thing as a “stationary refference” or “absolute speed”.

Principle of relativity, dates back to Gallileo.

58. #58 Harvey C.
January 16, 2009

The floor is a stationary reference “relative” to both the cart and the treadmill which is allowed in relativity. All you need to do here is widen the reference frame to include the floor. There is no reason to limit the frame to only the cart and the treadmill. You can include as much frame as is relevant to the solution to the problem and no more than that. I consider the relatively sationary floor as relevant to solving the question of which is going faster, the cart or the treadmill. In fact, in the limited frame which does not include the floor, no positive determination can be made, so you can claim anything you want. Once you iclude the floor in the frame, the additional information obtained clearly will show the treadmill is going faster than the cart. The claim of the cart going faster is based on excluding relevant information and it is false. My claim that the treadmill is going faster is based on a greater amount of relevant information and is therefore the correct claim.

59. #59 Robin
January 17, 2009

No, the floor is stationary only relative to the “body” of the treadmill and the cart.
The part of the treadmill that the cart actually touches and interacts with is the belt surface, which is most certainly moving wrt both the cart, the body of the treadmill AND the floor. If the floor is relevant, then the surface of the treadmill belt must be too, and yet you have ignored it completely.

60. #60 Harvey C.
January 17, 2009

The floor is relatively stationary to both the cart and the moving tread. Are you seriously saying the tread is not moving relative to the floor?
When I said “The floor is a stationary reference “relative” to both the cart and the treadmill which is allowed in relativity.” I meant the moving tread. Obviously the floor and the body of the treadmill are not moving relative to each other so I ignore the body completely and only refer to the moving tread and the moving cart as the moving components in the frame of the floor. I hope that is now clear.

61. #61 Robin
January 18, 2009

You said:
When I said “The floor is a stationary reference “relative” to both the cart and the treadmill which is allowed in relativity.” I meant the moving tread.

That is just wrong. It is clear you don’t understand the meaning of relative motion, because those two sentences conflict. If something is stationary relative to something else, that means that if you take the part of EITHER object, the OTHER seems not to move.

If you take the part of the floor, the treadmill surface is obviously in motion, and vice versa.

62. #62 spork
January 19, 2009

Harvey said the following entertaining things:

“This is a question of the answer being so simple that people overlook it and make it overly complicated. Nothing at all can go directly down wind, faster than the wind, powered only by the wind. Nothing!”

“How so many people have been taken in by this nonsense is the only thing that amazes me.”

“My claim that the treadmill is going faster is based on a greater amount of relevant information and is therefore the correct claim.”

63. #63 spork
January 19, 2009

Well Harvey, you sound like you’re pretty darn sure of this. We’re not going to change your mind or teach you anything. So I’ll offer you the option I offer everyone who’s SURE DDWFTTW is impossible – wanna bet?

Seriously. You name the amount. No point arguing back and forth here when you can just name your price and take my money – right?

64. #64 Michael C
January 19, 2009

Interesting developments here. I wonder if Rhett Allain is going to intervene? It’s his blog, after all.

I’m looking again at his “work and energy” diagram near the top of this page. It’s just as if he decided to analyse the forces on a sailing boat, without taking into account the sail and the keel. You could make a diagram like that of a sailing boat seen from above. If you represented the boat by a blob like the one in Rhett’s diagram, you’d come to the following conclusion: since the only forces acting on the boat are the wind in one direction and the reaction of the water in the other, the boat can only move exactly in the direction of the wind.

Whoops, that can’t be right: we’ve all seen that boats can move in all sorts of directions relative to the wind. By representing the DDWFTTW cart as a blob, not taking into account the train of force going through the propeller and the wheels, Rhett comes to a similarly erroneous conclusion regarding DDWFTTW.

65. #65 Harvey C.
January 26, 2009

Well Harvey, you sound like you’re pretty darn sure of this. We’re not going to change your mind or teach you anything. So I’ll offer you the option I offer everyone who’s SURE DDWFTTW is impossible – wanna bet?

Seriously. You name the amount. No point arguing back and forth here when you can just name your price and take my money – right?–Spork

Whooo! Real fine scientific argument there sport! Would you be willing to race your cart down wind against a styrofoam whiffleball? Make the video and post it! Oh, and don’t put any lead weights in the ball! I guaranteee your cart will be left in the dust, and remember that whiffleballs do not even approach actual wind velocity. Yes, Spork, I am Damn sure of myself
Note to Rhett: I like your illustrations and I have an idea for one which will clearly establish that the cart on the treadmill is actually moving slower than the treadmill, even while “advancing against” the treadmill. Let me know if you are interested in making this animation and I will work with you. It should put this story to rest once and for all.–Harvey C.–

66. #66 Robin
January 26, 2009

It’s very telling that after slinking away for over a week you come back and completely ignore all the errors you made, and yet take spork to task for bad science!

He’s the one who’s actually done some science here… a hypothesis, experiment and theory. All we have from you is an argument from personal incrdedulity and a demonstrated lack of understanding of relative velocities.

67. #67 spork
January 26, 2009

Whooo! Real fine scientific argument there sport!

I would hope you’d understand the difference between a bet and a scientific argument. You’ve pointed out that you have no interest in the science. You’re already 100% sure of your answer. That’s why I offer you the bet. This way you can simply take my money and shut me up. You are 100% sure of your position – right?

Would you be willing to race your cart down wind against a styrofoam whiffleball?

Absolutely! How much are we betting on the result?

Yes, Spork, I am Damn sure of myself

I don’t know how to interpret that. What does “damn sure” mean in dollars and cents?

>
Note to Rhett: I like your illustrations and I have an idea for one which will clearly establish that the cart on the treadmill is actually moving slower than the treadmill…
<<

You’re going down a blind ally here. Rhett has either been let go, or he’s learned how incredibly wrong he is, or perhaps he’s finally realized what a career limiting move it is to post unbelievably bad physics on a public forum when you teach physics for a living.

But I’m DYING to see your proof that the cart is going slower than the belt when it’s plain for everyone to see that it’s going faster.

68. #68 ThinAirDesigns
February 2, 2009

Harvey C:

Yes, Spork, I am Damn sure of myself.

Spork:

What does “damn sure” mean in dollars and cents?

Apparently ‘Harvey C’ isn’t as sure as he would like for us to believe.

JB

69. #69 LURK
February 4, 2009

“Jason posted this link to the Brennan torpedo http://en.wikipedia.org/wiki/Brennan_torpedo. I don’t think it really applies to this situation since it clearly has an external power source.”

Of course the torpedo has an external power source, just like the DDWFTTW has one: the wind.

Jason also explained to you how to drive the torpedo without motors: Fix cables to the ground, and let the torpedo go downstream in a river. It will go down the river faster then the river. If you don’t know why read your own blog:
http://blog.dotphys.net/2008/09/basics-relative-velocity/

70. #70 spork
February 5, 2009

“If you don’t know why read your own blog: http://blog.dotphys.net/2008/09/basics-relative-velocity/

I hesitate to recommend his blogs for anyone (including himself) that wishes to enhance their understanding of physics.

71. #71 skepsci
September 8, 2009

Well, I’m coming late to this discussion, so maybe nobody will ever notice this post.

Can we agree that it is possible for a wind-powered vehicle to move directly upwind, steady-state (at some nonzero speed – not necessarily faster than the wind)? One idea for doing so has already been presented. Now look at what happens in the reference frame of the wind – the air is stationary, and the ground is moving. Additionally, the vehicle is also moving, in the same direction as the ground, faster than the ground. So in this reference frame, we essentially have a vehicle, powered by the motion of the ground, that moves in the direction of the ground faster than the ground. If this is possible, there’s no reason why moving directly downwind faster than the wind shouldn’t be possible. There is plentiful energy from the relative motion of the ground and air – the only tricky part is building a vehicle which can extract this energy and convert it into useful work.

72. #72 spork
September 25, 2009

@Harvey C.:

>
The videos prove nothing about a device going faster than the wind. They do prove that a treadmill can power a cart.
<<

Not true. It seems they also prove that you aren’t familiar with one of the most basic principles of physics – the equivalency of inertial frames.

What is so amazing about that? A big, powerful treadmill acting as a drive system for a little flimsy cart.

True. That’s no more amazing than all the power of the wind powering a little flimsy cart.

This has absolutely nothing at all to do with going faster than the wind. Nothing!

You almost have me. Add one more exclamation point and I think I’ll be convinced.

73. #73 spork
September 25, 2009

Here’s a guy that refuses to believe a physicist could ever doubt something so simple and obvious:
http://forums.sailinganarchy.com/index.php?s=0878c87d82107f63136f3700a51efd25&showtopic=82175&pid=2471145&st=2450&#entry2471145

74. #74 seebs
October 3, 2009

At this point, I’m quite sure it’s possible.

Where’s the energy coming from? The wind. Why? For the same reason that some sailing vessels (especially land or ice ones, but some water boats can do it too) can beat the wind by tacking. The propeller on the cart is just tacking in a spiral.

Question: You have an object moving north at 2m/s, in air moving north at 1m/s. Can the air possibly be pushing the object to the north rather than to the south?

Answer: possibly, yes. Imagine that the object has length and is angled, and is moving also to the east. For a simple case, imagine that the object is aligned precisely northeast, has a length of 2*sqrt(2), and is moving east at 2m/s also.

Now, the object’s northward motion is still 2m/s. However, take the point where the object’s northeastern-most point is at any given time t. At t+1, the objects southwestern-most point is still there. Any air south of that point had a full second to move northwards and push on the object, which was obligingly remaining in front of it.

That’s the trick; while the object as a whole is “moving north”, there is always a part of it at that particular point for a period of time, so the air can run into it anyway. Repeat over the whole range of the leading edge of the prop, etcetera, and you find that there’s plenty of air pushing on the prop blade.

And that’s for a hypothetical case where the “prop blade” is moving north at 2x the speed of the air.

75. #75 wither
July 19, 2010

This is plain scary. It’s just not this hard…really.

It’s *really* simple math, including some *really* simple trig, and little else aside from confidence in your basic math skills. I got done letting some high school physics students figure it out for themselves in less than a single 50-minute period (hard to do, but they did it!). They successfully replicated a published sailing race table for a downwind race as a function of the most windward point of sail a boat can make. All by themselves. A race boat *can* beat the balloon on the downwind course, but most boats are not efficient enough. And so can the cart. They “got” it, and proceeded to scheme how to do this on a skateboard…lol.

76. #76 Ruy Exel
March 2, 2011

Sorry for entering this discussion so late but I hope to have an elementary thought experiment which proves the possibility of DWFTTW.

Quoting Rhett: “Suppose I had a wind generator that charged a battery or capacitor. After a while, the generator should be able to build up enough energy to get the vehicle moving [upwind] some. However, this would not be a constant self-sustaining vehicle. It would need to stop and recharge.”

Although Rhett intended to prove the possibility of moving upwind, his argument can easily be modified to go fast downwind: wait until your batteries have a lot of charge and use it to accelerate downwind as fast as you like.

As Rhet said, the batteries will eventually run dead, but here is a way around it: get yourself a huge propeller (think of an Everest sized one if you wish) made of very light material. When you need recharging, step on the brakes and, if there is any wind at all, your monster propeller will quickly generate a lot of energy, say, in a few seconds. Release the brakes, step on the gas and accelerate downwind at blazing speed! If your vehicle is very light, the energy stored will certainly get you going for a long time compared to the few seconds lost recharging. When you run out of energy, just repeat the above procedure for as long as the wind is blowing!

Of course this might be a little unpleasant, given the constant stop and go, but it proves the concept. Maybe what Cavallaro’s Blackbird is doing is simply making the charge/go interval time tend to zero (mathematically speaking), thus providing for a smooth run.

Incidentally, I believe the above argument also shows the possibility of moving directly upwind in a sustainable way!

A final comment: Daniel Kammen, the head of Berkley’s Renewable and Appropriate Energy Laboratory, has argued that that DDWFTTW was not possible “due to conservation of energy.” I wonder if he’s ever been in a sail boat! His mistake was to think that wind should be treated as a conservative vector field. His argument does prove that you cannot play the same game, say, with the force of gravity! However, wind is a completely different ball game!

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