Dot Physics

A commenter (Joe) suggested I look at vehicles powered by the wind that can move faster than the wind. This also came up on Swans on Tea. One of Joe’s points was that I should do this BEFORE MythBuster’s gets to it. And so I shall. I know this is one of those topics that can never really be won – like “the moon landings were fake” or “you can run your car on water”. I will try anyway. If you are not sure what this “faster than wind” thing is all about, check the Swans on Tea link or this boing boing link.

There has been a ton of stuff posted about DWFTTW vehicles. Literally a ton. If you took all the electrons used to transmit data regarding DWFTTW over the internet, it would add up to one ton. So, what I am going to say may have already been said (I can’t look through the whole internet). But you know me, I like to give my own spin on stuff. This one was difficult to start because I wasn’t sure what “angle” to take. Clearly, there is a problem if a vehicle is wind powered and travels faster than the wind. You see it, I see it. But there are many that do not see this as a problem. Really, the reasoning in this area is the same as for most perpetual motion machines. Energy for nothing. Free energy – it’s not the 70′s. Stuff isn’t free.

So, where to start? Start with the basics. There are two important ideas that are useful in this discussion. The momentum principle and the work-energy principle. Both of these ideas are very solid. If someone found a situation where these were violated, it would be a pretty big deal (so, basically we can take them as true).


I talked about the work-energy principle before. Check it out if you want a more in depth tutorial. The basic idea is that we (you and I both) can define work as:


The energy part of the work-energy principle says that the work done on an object changes its energy


At the most fundamental level, energy is either particle energy or field energy. When looking at macroscopic things (like cars) we can make up other energies – like chemical potential energy, thermal energy, electric energy and stuff. Again, this work energy idea is very successful.

Momentum principle

The most basic form of this is the same as Newton’s third law. It says:


In this situation, the most useful way to use this is to say that if the net force is zero(vector) on a system (whatever that system may be) then the total change in momentum of that system is zero(vector). Or, if there is a net force, there will be a change in momentum. So, back to the first case of no change in momentum of the system. If there are two particles in the system, and initially both objects have an x-momentum of 5 kg m/s, then after something happens one could have 8 kg m/s and the other could have 2 kg m/s.

Happy? Ok, I am not going to start with a DWFTTW vehicle. Are you disappointed? Instead, I am going to start with a wind generator (is that the correct term?). Here is a simple diagram:


First, in terms of work and energy, the air coming into the generator has a greater kinetic energy than the air leaving. This means that the air decreases in kinetic energy. Where does this energy go? Well, the moving air pushes on the blades of the generator and do work. This increases the “electric energy” of the generator (yes, electric energy is very vague, but it serves the purpose). So, in short the generator gets energy by slowing down the air. It’s not free energy.

In terms of momentum, the air has a change in momentum to the right in the picture above. If I think of the generator plus air as the system, then it also has a change in momentum to the right. This means there must be a force exerted on the system to the right. This force is the force from the ground holding the generator in place. If you want to think about just the air, it has a force exerted on it from the blades of the generator.

Wait. You thought I was going to talk about wind powered vehicles. Well, I am. I think the above case is a great place to start because it uses some of the same ideas as a wind powered vehicle. After all, that is a wind powered device. It just isn’t a vehicle.

Next, some type of sail powered vehicle thingy

I know sail boats are complicated, but I am going to pretend they are simple. Imagine an ice-car sail boat. There is no friction and it has a plain flat sail. The wind is blowing directly behind the ice-car. Here is a picture.


Again, this is simplified. However, in this case the air both changes direction and decreases in speed (and kinetic energy). The car increases in momentum and kinetic energy. I left off the air in front of the car that also collides with it (air resistance), but hopefully you get the idea. The car “gets” energy from the air, which loses energy. Will this car keep speeding up forever? No. If there were no air in front of the car (and no friction from the ice), the car would speed up until it reached the speed of the air. At that point, the air from behind would not hit the sail and interact with it. Obviously, a real ice-car in this case would not even get that fast because of air resistance and ground friction. I have ignored the cases where the wind is coming from the side (because that is more complicated).

How about a jet engine? Or something like that.

Here is a diagram of a jet engine initially at rest (maybe on the runway or something):


So, air comes in from the left. Stuff happens (like a turbine or fuel burning stuff – not really sure). Then air leaves going faster than it was initially. Clearly the air increased in momentum to the right. If I take the air plus engine as my system (ignoring gravity and the force of something holding it up) then the engine must increase in momentum to the left in order for the total momentum to stay the same. What about energy? Well, the air leaving the engine is moving faster than the entering air (increases in kinetic energy). Also, the engine will increase in kinetic energy. Where did this energy come from? It can from burning fuel. Even if the engine is moving, basically, the same thing happens.

Are we ready for the DWFTTW vehicle?

Using the ideas above, couldn’t I put a wind generator on a cart and attach that to an electric motor? Then I could push the cart to get it moving, the wind would turn the generator and power the electric motor. If this was true, then the vehicle should be able to move without any wind at all – or into the wind (whichever you like). I am sure some people will say driving into the wind is different than faster than the wind, but for the purposes of this argument it is not.

One simplification is the wheels. If this is a wind-powered vehicle, you would like the wheels to be as low friction as possible. I am going to go all the way and say that (for this argument) the wheels have ZERO friction. This will make things easier in that I can just talk about the air and the car as the system with no net external forces. Yes, there will be the force of gravity pulling it down, but there will also be the force of the ground pushing up. These forces are equal and thus do not contribute to any change in momentum. Ignoring the friction of the wheels also lets me choose any frame of reference I want. A car moving into a wind is equivalent to a car moving with the wind, but faster than the wind.

Now for my diagram of the DWFTTW car (but I will start with it going INTO the wind):


In this case, I put the wind leaving the “car” going slower than it was before. I did this to match the generator from before. Also, if the air slows down, it can “give” some energy to the car by decreasing its kinetic energy. Why is this a problem? Well, compare this to the jet engine. In the engine, the air was going FASTER afterwards. This resulted in a change in momentum in the direction of desired travel. For this car, the change in momentum of the air is to the left. This would mean (with no external forces) that the car would have to change momentum to the right (oops – that would be the wrong way to go).

Ok – what if I made the air going FASTER after it goes through the wind generator? Well, then momentum would be ok – but not energy. The air would gain energy, where did it come from? Magic? Do you see why this is a problem?

This is the same situation as people trying to make energy from nothing. Clearly the ideas of momentum and energy are very well tested. Still some people think that if just maybe something was different…. Well, I don’t know what else to say. If some supporter of DWFTTW vehicles wanted to reply, he or she would probably make some claim about going faster than the wind is different than going into the wind. If the wheels do not matter, then neither does that. A DWFTTWer may also say something about a purely mechanical means to power the vehicle. Although I discussed a wind generator hooked to a motor, I will still considering the system of the car plus air. So, there you go. That is my take on this subject.

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


  1. #1 Uncle Al
    December 10, 2008
    Modern iceboats can do five times wind speed

    Is 5X windspeed vs. ground approximately slower?

  2. #2 meichenl
    December 10, 2008

    DotPhys guy,

    Your analysis assumes the wheels have no friction. But the claims of DWFTTW are for cars whose wheels DO have friction. I ride a bike to work every day. If its wheels had no friction, I would spin the pedals hard all day and get nowhere, except that I would fall over. Yet, I get to work day after day with no problems except the occasional flat tire. It simply does not make sense to analyze a ground-based vehicle while ignoring friction.

    Claiming that a wind-powered vehicle can go directly into the wind is not a claim of free energy. Imagine that I have a little car whose wheels work like a ratchet. The axle is only allowed to spin forward. Then if I set it up down “forward” is upwind and give it a sail, it will go nowhere at all. If its axle spun freely, it would go backwards, but the ratchet won’t let it.

    Now I replace the sail with a windmill that stores energy in a battery. The car goes absolutely nowhere, but is constantly storing energy in a battery due to the wind flying over it and spinning the windmill.

    Then, I use the battery to drive the car forward, since a battery-powered car can undoubtedly go into the wind – they do it all the time. Now I have a car traveling directly into the wind, using power that came from that wind. In fact, it can do so continuously, because the windmill can continuously recharge the battery.

    This does not violate conservation of energy because the energy comes from the wind, which decreases in kinetic energy as it passes through the windmill. It also does not violate conservation of momentum, because the car and wind both gain forward momentum, but the car pushes on the Earth, which pains momentum in the opposite direction. That’s why you need to include friction – so that momentum can be transferred to the Earth.

  3. #3 meichenl
    December 10, 2008

    in the second paragraph, that should say, “Then if I set it down so that “forward is upwind…”

  4. #4 meichenl
    December 10, 2008

    also, the last paragraph should say the Earth “gains” momentum, not “pains” it

  5. #5 Tom
    December 10, 2008

    meichenl, the objection I have to your model with the windmill and cart is that when the cart moves at the same speed as the wind there is no force on the blades that would cause them to turn. If you are claiming you can move forward faster that the wind and still generate energy, as you appear to be claiming, how is that different than moving into the wind and generating propulsion? Or no wind at all, relative to the ground, and having a wind relative to the cart because you are moving forward?

    If you can do that, then we can start this with the tiniest nudge. Shouldn’t you generate more propulsion the faster you go? Isn’t that perpetual motion?

  6. #6 Dan Riley
    December 10, 2008

    In addition to the (actually relevant!!) links Uncle Al posted, I’d also recommend an article Physics Today ran on the physics of sailing:

    Sailboats go fastest when reaching, with the wind from the side, and really can go much faster than the wind speed.

  7. #7 meichenl
    December 10, 2008


    My post was intended to describe a vehicle that drives directly into the wind, not a vehicle that achieves DWFTTW. The original article claimed both were impossible, and I was just responding to one claim (that you can’t go straight into the wind.)

    In answer to your point about the apparent free energy when there is no wind at all, the cart I described would not accelerate if the speed of the wind relative to the ground were zero and the cart was given a nudge. In that case, there would be wind relative to the cart, which would generate energy. The maximum power generated would be F*v_w, where “F” is the backwards force of the wind on the car, and “v_w” is the velocity of the wind as seen by the car. That power generated by the windmill would have to go towards overcoming the force of the wind pushing back in the opposite direction of the car’s motion. The power it would need to expend to continue moving with the same velocity is F*v_g, where “F” is the same as before, and “v_g” is the velocity of the car relative to the ground. In this case, where the air is not moving at all relative to the ground, v_w = -v_g, so the power in and the power out would be exactly the same. The best the car could theoretically do is keep moving at the same speed it was originally pushed. In reality it would slow down because it could not capture 100% of the possible available energy with the windmill, especially considering that some of the force on the car is applied to the body of the car, not the blades of the windmill.

    The situation is different if the wind is blowing. In that case v_w > v_g. Therefore, the car can generate more power than it needs just to keep going the same pace. It can use that extra power to accelerate.

    Although I did not intend to demonstrate DWFTTW in my previous post, the device is possible. I recommend the link from Uncle Al for a more detailed description. There, Mark Chu-Carroll describes someone else’s device that does actually accomplish DWFTTW using only a simple mechanical car, with a windmill whose blades and wheels are directly linked so that turning one will necessarily turn the other. I won’t recapitulate the entire argument, but the thing really does work.

  8. #8 meichenl
    December 10, 2008

    ah, hell. i can’t help but go on.

    Consider the moment when a potential DWFTTW vehicle is comoving with the wind. Then the relative velocity of the vehicle and the wind is zero, meaning that the power necessary for the car to exert some force “F” on the wind is F*v_w = F*0 = 0. When something isn’t moving, you can push on it as hard as you like without using energy, just as when a bully decides to sit on me, he can do it indefinitely, even if he dies up there, exerting great force on me despite spending no energy.

    On the other hand, the wheels are moving relative to the ground, and can deliver a power as great as F*v_g, where F is whatever force you want the windmill to exert. But we know that to exert that force NO power at all is strictly required. So the cart can use a very small amount of power from the wheels to exert a large force on the air. The air will push back on the cart with an equal and opposite force F. So now there are two forces on the cart. One is the reaction to the cart pushing on the air, and one is a force pushing in such a way as to slow the wheels. They push in opposite directions, but for the reasons described above, the force pushing backwards on the wheels can in theory drop to zero, and can in reality be made significantly smaller than the force the cart exerts on the air. That way, the cart accelerates forwards.

  9. #9 Henry
    December 11, 2008

    Imagine the inclined plane of the propeller as a surface that moves BACKWARDS though the air, much like the paddle wheel of a river boat re the river. An air particle on the inclined plane of the propeller actually moves backward relative to the cart, and slower than the wind. This allows the wind to push on the propeller and thus do work on the blade surface. The car moves faster than the wind creating drag, but the power the wind exerts on the propeller may make up for it and then some. HenryB

  10. #10 magetoo
    December 11, 2008

    I’ll third the recommendation to read the threads posted over at Good Math … . At the beginning Mark dismisses the whole idea as “free energy” and the people behind as “bozos”. Then it turns out that the whole problem is much more complicated than everyone thinks, and that faulty assumptions prevent nearly everyone from getting what is actually happening, until a few hundred comments in.

  11. #11 peter
    December 11, 2008

    Fourth, the one mistake that you are making, that good math, bad math also made, is in your thinking about which way the propellor is turning. The vehicle in question is not a wind powered vehicle in the sense you mean, the wheels are not powered by the prop, the prop is powered by the wheels. In the example above, imagine that the vehicle (with no prop) has been pushed to near wind speed. Now imagine that attached to the wheels is a pusher propellor geared to turn fast enough to provide meaningful thrust. Now the vehicle can propel itself to somthing greater than the wind speed. Not excessively more, but more just the same.

  12. #12 kevin
    December 11, 2008

    Yup. Go read good math/bad math. He gets his followup wrong in lots of details, especially the mechanical geared cart. But he gets the big picture right. The stupid damn hoax-looking free-energy-seeming thing does actually work. It ain’t free energy, just counterintuitive.

    Here is the model I played with to finally figure it out. Everyone claims ice boats can go really fast, faster than wind, but nobody explains why, or gives much evidence at all. Here is a similar situation that will get you to the answer: imagine two tracks on the xy plane. One is rigidly fixed to the plane on the y=x line. The other track sits on the y=k line, with k variable. The track is sliding downwards (k goes to -inf) at some constant rate, say 1 unit/sec. Now put a cart at the intersection of the two tracks and rigidly fix it to both tracks. How fast does the cart go. Clearly, it goes downward at a rate of 1 unit/sec, and leftward at a rate of 1 unit/sec. Still not faster than wind in the downwind direction (where I’m imagining the moving track to be “wind”. Change the sliding track to sit on the line y=x/2+k, with k still variable. Now how fast does it go? Obviously faster. After 1 second, the cart will have moved 2 units down and 2 units leftward. This is your faster-than-wind cart.

    From here you can figure out why an ice-boat can go downwind faster than wind, then figure out how a properly propeller-geared-to-wheels can do exactly the same.


  13. #13 Uncle Al
    December 11, 2008

    If Mr. Riley pursues something original Mr. Riley begins with an original thought or observation. The APS alone has some 60,000 members. Physics is nanoscopically picked over (untenured faculty!). Three choices: Be an SOP hack (bold route to grant funding). Be a mathematician oozing physics, albeit trailing a length (or at least string) of non-empirical toilet paper. Think outside the toroid.

    Founding postulates are indefensible. It is the place to look. Covariance with respect to reflection in space and time is not required by the Poincaré group of Special Relativity or the Einstein group of General Relativity. Noether’s theorem fails for discontinuous symmetries. Metric gravitation can fall to parity violation re teleparallelism. It is an act of cowardice not to perform a parity Eötvös experiment opposing chemically identical single crystals of right- and left-handed quartz (cinnabar for heavier atoms, also in space groups P3(1)21 and P3(2)21).

    Theory predicts what it is told to predict. Yang and Lee were heretics, but in a receptive milieu. Ice boats easily exceed windspeed, bumblebees fly, Bernolli’s Principle does not lift 3-D wings (stunt planes with symmetric profile wings). Get over it.

  14. #14 Henry
    December 11, 2008


    I like your track example in you post above. Here is a mechanism by which the wind can do work (add power) to a machine moving downwind faster than the wind. Consider this example first to understand JBs prop cart:

    A paddle wheel, with sails instead of paddles, is attached to a car such that paddle wheel is driven backwards by the wheels of the car much faster than the wheel turn forward. The sails on the paddle wheel protrude through the roof of the car so that only the backward moving sails are in the outside air. The air in the car is frictionless.

    Even when the car is moving faster than the wind down wind, there will be a range of car speed for which the sails outside the car will move backwards relative to the car, but forward relative to the wind and less than the wind speed, and thus allow the wind to push on them in the direction of the applied force and do positive work on the system.

    Power into the system = Force of wind on sail surface X sail speed in the direction of the wind force.

    In other words, when the wind speed is be greater than the sail speed, the wind can do work on the sails by pushing on the sails in the direction of travel. This force F times the velocity of the sail Vs is the power added to the paddle wheel which can be used to power the car through the wind. The paddle wheel must move backward relative to the car so that it will reduce its speed relative to the wind so that the wind can push on it in while it moves in the down wind direction.

    If the sail moves faster that the wind then the sail will do work on the wind and the car will lose power, so the sail can not go faster than the wind downwind. When the power dissipated in drag equals the power applied by the wind the car will reach a stead velocity going down wind faster than the wind.

    If we replace the paddle wheel with a propeller we can imagine the inclined plane of the propeller as a surface that moves BACKWARDS though the air, much like the paddle wheel example above. The inclined plane of the propeller does not move faster than the wind, it moves slower, and allows the wind to push on the propeller surface and do work on the blade surface as the wind moves PAST the blade in the down wind direction. The car move faster than the wind creating drag, but if the drag is small enough, the power that the wind exerts on the propeller will make up for it and then some, as we see in JB and Ricks video.

    Im I getting close?

    Now regarding the cart on the tread mill in the reference frame of the still air, I am still working on that. Any insight from anyone using work and power in the manner of the above example?
    Henry B
    Funston SF CA

  15. #15 ThinAirDesigns
    December 11, 2008

    Hi Rhett. I am the individual in the BoingBoing video and the co-designer/builder of the downwind cart in question.

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

    We are in direct contact with the Executive Producers of MythBuster’s regarding the potential for an episode on this topic. I will do my absolute best to get them to mention your blog on the show — but if they were to do so, currently it could only be in the context of “Physics professor gets it all wrong”. I’m not sure how cool your kids will think that is in the end.

    You might wish to engage us on this topic and have a friendly back and forth. I’m convinced that with your knowledge of physics it would be an interesting and informative exchange for you.

    What do you say? — shall we give it a go?

    Thanks Rhett.


  16. #16 ThinAirDesigns
    December 11, 2008

    And to Henry B. After all these years, how the heck do we run into each other in a place like this? LOL I think the last place I saw you may have been the hospital in Greece at the World Championships 2001. PM me on OZ and we’ll get together sometime.


  17. #17 Rhett
    December 11, 2008


    I of course would be happy to discuss this further. But, did I at least get the momentum principle right? Please say yes.


  18. #18 ThinAirDesigns
    December 11, 2008

    Hi Rhett

    >But, did I at least get the momentum
    >principle right? Please say yes

    Much of what you wrote was excellent, and I actually like your writing style — it’s all quite good until partway through the first paragraph of the section titled: Are we ready for the DWFTTW vehicle?

    The third sentence reads:
    >If this was true, then the vehicle should be able to
    >move without any wind at all – or into the wind
    >(whichever you like).

    A: I agree with your point regarding the “no wind” scenario. Any ability for your described cart to move in any direction without any wind would require an over-unity component.

    B: It appears however from the above that you do hold the the following position:
    A wind turbine powered device cannot drive itself directly upwind into the wind that is powering it. You’re case appears to be based on the fact that the change in momentum is in the wrong direction.

    Have I accurately described your position?



    PS: I really love the drawings you do. Would mind telling me what software application you use for them.

  19. #19 kevin
    December 11, 2008

    JB says: “You might wish to engage us on this topic and have a friendly back and forth.”


    Rhett: I’m glad you seem to be leaning towards taking JB up on this offer. Because it won’t be pretty otherwise.

  20. #20 Rhett
    December 11, 2008


    First, the easy question: I use Apple’s Keynote software to make my drawings. I found that hint somewhere online and it really suits me. Long ago, I used to use MS Word to make drawings. I got used to the group function and stuff like that. Keynote does this, but makes things much prettier. Alas, it does not do any 3D objects.

    As for the article, I made the point using a wind generator but I neglected any forces from friction. Obviously, this is a mistake. My main points are that energy has to come from somewhere. I will need to think about this some more. I know that fluid dynamics gets very messy, but I will try to grok the whole thing.

    Thanks for your feedback.


  21. #21 ThinAirDesigns
    December 11, 2008

    >I use Apple’s Keynote software to
    >make my drawings.

    Of course, I should have known it was Apple software. Why do apple people always get to use the cool stuff? Ok, I’m stuck with the Windows crap. Moving on.

    >I will need to think about this some more.
    >I know that fluid dynamics gets very messy,
    >but I will try to grok the whole thing

    If I accuratly described your position, I don’t even think we would need to get into fluid dynamics to find the flaw in that position. For example, If I had cool software like Keynote, I could draw scores of variations of a purely linkage based mechanical device that would have you merely throwing a baseball at a target — and each time you hit the target, the vehicle is driven just a bit closer to you. Clearly though, if we isolate the ball and the target in the same manner you did the air and the turbine in your demonstration cart, we would see the same momentum change you described. If you truly do believe I’m wrong on this I’ll be happy to use my crappy Windows software and draw you up a crude version of such a device.

    Certainly when we get into the fluid dynamics side, there are numerous examples which conflict with that ‘momentum change in the wrong direction’ position as well.

    A sailboat sailing up wind is one of the more obvious ones. Replace the turbine in your drawing with a traditional sailing rig and the air after the sail will be slower than the air before and will have gone through the same noted momentum change. Even after all that however, no one will rationally argue that the sailboat can’t make progress upwind.

    One more thought for you:
    Let’s take that fan on your cart and turn it into one of the biggest, baddest wind turbines available today, the Enercon E-126. This puppy produces enough power to run a ~10,000hp motor. Let’s take that 10,000hp motor and hook a 1,000,000:1 gear reducer on the output shaft (yeah, imagine the torque) Let’s hook the output of the gear reducer to the wheels of our car in such a manner as to move the cart 1mm per day.

    Just as a real world example, do you really think that a turbine like that (or any other for that matter) can’t generate enough electricity in one day to move itself only 1mm into the wind? Obviously, not a proof — but something just to think about in context.



  22. #22 ThinAirDesigns
    December 12, 2008

    Rhett, something else for you to think about:

    They actually just recently finished a race in which the challenge was to build wind powered ‘cars’ that would drive directly into the wind on a 5.3km course.

    Excerpt from the above link:
    “In this first time ever race the participating teams were challenged to drive directly into the wind, without tacking. During the preliminary races, the Stuttgart Ventomobile had already proven to be the most lightweight and most efficient vehicle among the contestants when, with its 130 kg, it succeeded in racing at 64% of the wind speed directly against the wind.”

    More on the race:

    The car that won:

    Somehow they’ve managed to get that momentum turned around and used it to go upwind at a pace of greater than 50% of the wind speed.


  23. #23 sol invictus
    December 12, 2008

    As long as the air is moving relative to the ground there is a source of energy and momentum that can (at least in principle) be tapped. For all practical purposes the energy available that way is infinite, so there is nothing “over-unity” about the claim that a wind-powered vehicle can travel in any direction at any speed.

    Building such a thing is a matter of engineering, not physics. It easy to make wind-powered devices that travel directly into the wind, with an arbitrarily high top speed (the speed is limited only by non-ideal resistive losses). Once you have that in mind, invert air and ground and you have a device that, when the ground is moving and the air is at rest, can travel “up-ground”. But that’s something that goes downwind faster than the wind.

    Hope that helps!

  24. #24 Michael C
    December 12, 2008

    The funny thing is, you don’t need to get stuck in the “messy” parts of fluid dynamics to analyse how a machine can go faster than the wind. Start with a purely mechanical analogy:

    The working principle is this: when a cotton reel rolls along a table, there are always points on the cotton reel moving slower than its centre of gravity. If we can push (or pull) with a constant speed against a point that moves slower than the cotton reel as a whole, the cotton reel will advance faster than the thing that is pushing/pulling it. It’s easy to see in the video that this is the case, and indeed anybody can make their own version of this little device to see how it works.

    Here’s another mechanical version, that comes a bit closer to the down wind cart:

    In both cases, the machine moves faster than the thing that is pushing it. In both cases this is possible because the machine takes its power from the relative motion between the moving surface and the surface on which the machine is running. Similarly, the energy for the DDWFTTW cart comes from the relative motion between the air and the ground. As long as the machine is in contact with both air and ground, this energy is always available, independent of the speed or direction of travel of the vehicle. As a friend of mine remarked, the the relevant law is “Conservation of Energy”. There is no law of “Conservation of Velocity”!

    To directly compare the last machine with the propeller driven cart, imagine that the propeller “screwing its way” through the air replaces the big wheel “working its way” along the ruler. The way the big wheel is geared to the other wheels forces it to turn against the direction of travel of the ruler, so it ends up moving faster than the ruler. Similarly, in the DDWFTTW cart, the way the prop is geared to the ground wheels forces the prop to turn against the direction of the wind, so it will screw its way though the mass of air and therefore move forward faster than that mass of air.

  25. #25 Henry
    December 14, 2008

    Howdy Physics Buffs,

    As I think all of us see now, with two media moving relative to eachother there is energy available. The hard part for mechanical engineer like myself, or a Physics proff like Rhett, is that we want to see the mechanism by which energy can be addedd to a system that is moving faster than the thing pushing it. Wind turbines produce power because they are anchored to the ground and then the wind flows over the blades creating forces the produce power pushing, our pulling, on a surface in THE SAME DIRECTION as that surface is moving. Force times Velocity time Cos(angle between the two vectors) = power produce by pushing on the surface. Knowing this, HOW DOES THE WIND DO WORK ON THE CART?!! IThe surface that is moving slower than the wind
    In the example of the cotton spool moving down the paper faster than the paper and in the cart moving down wind faster than the wind, he medium doing the work to push the system down wind or down paper, need something to push on that is moving

  26. #26 Chris
    December 14, 2008

    Hello Henry,

    keep in mind that in this cart the prop does not work as a turbine, but always works as a prop when it is spinning. So you have indeed a part that is moving slower than the cart’s center of gravity, namely, the prop blades surfaces. Another way to see it is that the prop generates thrust that works on the wind or still air (the latter in case the cart is at wind speed).

    Some math is here:

    Hope that helps,


  27. #27 Henry
    December 14, 2008

    Howdy Physics Buffs, ***this is copy of the above post, I hit the submit key before I was done editing sorry! Please read, Id like to see if this point resonates with you all as it did with me-

    As I think all of us see now, with two media moving relative to each other there is energy available. The hard part for a mechanical engineer like myself, or a Physics Prof like Rhett, is that we want to see the mechanism by which energy can be added to a system that is moving faster than the thing pushing it.

    Wind turbines produce power because they are anchored to the ground (i.e. move slower than the wind) and then the wind flows over the blades creating forces that produce power pushing, our pulling, on a surface in the SAME DIRECTION as that surface is moving.

    Eq1) Force X Velocity X Cos(angle between the two vectors) = power produce by pushing on the surface.

    Knowing this, HOW DOES THE WIND DO WORK ON THE CART that is moving faster than the wind?!!

    As Michael C points out above regarding the cotton spool moving down the paper faster than the paper that is pushing it, the part of the spool in contact with the pushing paper is actually MOVING BACKWARDS with respect to the CG of the spool and is moving slower than the paper pushing it!!.(note that the pushing paper in under the center of the spool, not over it) thus the frictional force provided by the pushing paper is pointed in the direction of the absolute velocity of the point on the spool that is being pushed allowing work to be done on the spool by the paper! This is the mechanism by which work is done on the spool. How so with the cart?

    The interaction of the prop on the cart with the wind is harder to see because every bit of the prop is moving faster that the wind down wind. How can the wind push on it? I would like to say that the inclined surface of the prop is MOVING BACKWARDS with respect to the cart, and thus has a velocity LESS than the wind in the direction of the wind. This surface moving slower than the wind allows the wind to do work on the cart while it is moving down wind faster than the wind………

    But this is not quite right, because every point on the prop is actually moving with the cart down wind faster than the wind. It is a point in space directly next to the prop blade that is pushed backwards by the inclined plane so as to move slower that the wind, not the blade itself.

    So I don’t have a physical surface moving slower than the wind in the direction of the wind as I require in EQ1) above. I am left with the explanation that the wind does work on the air directly behind the prop by compressing it against the backwards moving inclined plane of the prop creating a static increase. It is this pressure which pushes on the surface of the prop (not to spin it, but to translate it forward) doing work on the cart and increasing its energy in the form of velocity (velocity is limited only by the energy balance of power added and drag created). Im not totally satisfied with this explanation and would love some help and insight into the specific “Mechanism by which the wind can do work on the cart”. (see my backwards moving paddle wheel example two posts above). I realize that a sail boat moves into the wind because the wind creates lift forces that act on the surface of the sail in the direction the boat is moving. The surface integral of lift (dot) velocity = power into the sail boat. I assume there is something to be taken form this but I cant quite connect the dots to the prop and wind…any help?


    To JB!

    I was totally surprised to see your face holding this CONFOUDING prop cart!!! Yet I was also totally enthused because I know you are always at the center of the most interesting situations, ones with a good measure of controversy! Its funny that like minds seem to cross paths..only your mind always seem to inject some extra energy into the mix to get the dialog flowing. Your arguments are a pleasure to follow because you have the ability to be clear about what you saying. Good to hear form you. Id like to get together with you and Rick sometime. Perhaps for some of that indoor sky diving!!.

  28. #28 David G
    December 14, 2008

    Hi Henry -

    Perhaps this model will help you understand what’s happening:

    The quality of the video is not as good as what others have done but I was working with the equipment I had and hopefully it is good enough to be instructive.

    As the nut is being pushed, the threaded bolt twists itself forward and the cart ends up moving faster than the nut is moving. The propellor driven cart works the same way but in moving air rather than a moving nut. Of course “moving” is relative to the surface and a stationary nut (or air) above a treadmill will give similar results.

    • David
  29. #29 Jason Rogers
    December 14, 2008

    DotPys guy said “I know this is one of those topics that can never really be won”. Sorry, it can be won, it was won over a century ago… Just think about nailing the wires to a tree and then throwing the torpedo into a river, and what will happen… I’m just completely astounded that you still think it’s perpetual motion… He also said “Dear MythBusters. When you do an episode on this topic, please mention my blog. It will make my kids think I am cool.” which is just as funny! I wouldn’t be wanting my kid to see this…

  30. #30 spork
    December 15, 2008

    Henry, you’re onto it quite well actually. There are a couple of items that might still help though.

    One important but subtle point is that there is no convergence of air masses behind the prop. Some people like to think of the tail wind colliding with the aft thrust of the prop to produce the resultant force on the prop disk – but this isn’t really accurate. If we consider the situation when the cart is going exactly the speed of the wind, there is no wind over the cart. In this case the prop behaves exactly like the prop of a airplane sitting on the runway, revving the engine with the brakes on. The prop produces plenty of thrust working on an airmass that’s otherwise stationary relative to the plane.

    If we consider the cart going faster than the wind, the prop behaves like the prop on a plane that is taxiing or accelerating for take-off. It’s important to remember that the flow of air through the prop disk is from front to back. The prop doesn’t have to “push against a cushion of air that the tailwind places behind it”. Instead, the prop is immersed in this fluid. Becuase it’s moving much more slowly through this fluid than the wheels are moving against the ground the wheels can provide more energy than the prop needs to provide the thrust that matches the wheels’ load on the road.

    If you want to understand the actual nature of the flow around the prop blades, and what’s happening there, you have to realize that even though the air flows through the disk from front to back, the relative wind hitting the prop hits the backside of the prop (from a very oblique angle). To understand this we “unwind” the props path and look at it like the sail of an ice boat on a 45 degree downwind course. The airflow and the work done by the air on the sail is particularly interesting in the case of an ice boat whose downwind velocity vector is faster than the wind.

    Here’s a little vector analysis I did for the sail of an ice-boat on a 45 degree downwind tack with downwind VMG greater than 1.0:

    It’s interesting to note that the relative wind angle on the sail rotates forward as the boat’s speed increases, but always strikes the back surface of the sail. There is really no magic moment where the flow over the sail changes in a drastic way. In this diagram I simply assume the ice-boat is going at twice the wind speed on a 45 degree downwind tack, and show the resultant force vector still has a component on the positive trajectory vector for the boat. This tells us that the boat can continue to accelerate beyond the assumed case.

    I didn’t get to do the indoor skydiving this weekend because the wife was outta town. I’d like to get there in the next couple of nights. I’ll check the availability.

  31. #31 Henry
    December 15, 2008

    Thank you Spork and Chirs!

    Spork, I look at your vector diagram and there I saw that the wind speed causes the apparent wind to keep a POSITIVE angle of attack (for us flying guys). If I take it on faith (at this point) that boats sail up wind and the wind does the work..and I’ve sailed a lot.. then I must conclude that the wind can do work on this sail (via Bernoulli) while it is moving down wind as well…

    Chris, your drawing and explanation are excellent. I read through the math and geometry quickly but need to study it to really understand. Ill be sure to have some questions for you and Spork in about a week. Funny, that Im so compelled to think about this problem of “How the wind does work on the cart, or sail, going down wind”.. We must all share a common Obsesive Compulsive Geek gene..

    Thanks so much for you time laying this all out!!

    are you and Hang/Para Glider pilot Chris?

  32. #32 Henry
    December 15, 2008

    Chris, you say that

    “So you have indeed a part that is moving slower than the cart’s center of gravity, namely, the prop blades surfaces.”

    My whole confounding problem is that I see now that the blade surfaces do NOT move slower than the CG of the cart, the blade velocity in the direction of the cart equals the cart velocity because that prop is rigid with the cart in the horizontal axis. Thus there is no surface on the prop cart ON Which the wind can DRAG across as that surface moved to do positive work, i.e. to input power through DRAG..
    ……. but for LIFT!!! the answer is YESSS!!!!..

    My take on your drawings in the link from you Post #26 (yours I assumed?).. is that the prop can be though of like sails moving into an APPARENT wind. In this case the wind PULLS the sail forward, due to the lift generated. These PULLING forces are those described by Bernoulli equations and it is in these equations that the work is done on the boat or prop cart.. these equations are not as accessible to me in a satisfying way like Newtons laws.. I know the two are equivalent if you can do the differential calc and solve the Cauchy equations.. Anyway.. long story short..there is NOT a surface moving less than the wind speed that the wind can flow over (DRAG over) and do work on the system in the simple Force X Distance = Work done manner I would have liked..

    I cant see the energy transfer clearly at work here..but then again I cant see it in the boat moving up wind either, unless Im to be satisfied with the surface integal of Lift X Sail Velocity = Power into the boat… I suppose this should be enough.. I will study your drawings in the link in Post#26 more.. thanks again

  33. #33 Chris
    December 15, 2008

    Hello Henry,

    note that the drawings and math is not mine, someone else did it.

    Yes, my explanation of the surface moving slower isn’t really correct, it is just a imaginary thing to help me understand it. However, if you draw a line parallel to the ground, from the back of the cart to the front, then you can see that while that cart is moving and the prop crosses that line, the point where the line and prop surface meet does indeed move slower than a point on a line drawn through the cart’s center of gravity. Now one could say that the tailwind is indeed blowing straight along that line, thus seeing a smaller moving surface relative to the cart’s COG.

    Bear with me since i am not a physicist. So i need to refer to these thought-constructs to get myself thinking about it. I know it isn’t the 100% correct way to explain it, but i think it is some way that is not utterly wrong, but can help all the layman’s out there to grasp the concept on the real cart. The other mechanical explanations are quite good as well, and Michael C. did a great job with his videos, but still they are quite abstract compared to the real cart. If in doubt, go along with Spork’s and TAD’s explanation, since they know much more about the topic than i do.



  34. #34 Henry
    December 15, 2008


    Yes I see exactly what you saying with this surface “of the blade” moving backward relative to the cart. Read my Post #14 above.. I had exactly this thought that made me realize the wind could “Push” on the cart. In my Post#27 I realize, however, that the surfaces on the prop do NOT move backwards relative to the cart. However, if we could build a paddle wheel where the paddle moves backwards relative to the cart but less than the wind speed (and where the forward moving paddles were enclosed in a friction less gas so as not to add to the drag) then I think we could build a cart that used the wind DRAG on these surfaces to power the cart to move faster than the wind.

    A paddle wheel is a lot higher loss than a well designed prop which using LIFT..

    Prop pitch must be less than the gear ratio… a really cool conclusion of the equations from the link you posted for me..who is a author of that explanation?


  35. #35 Henry
    December 15, 2008

    To David G re Post #28

    Brovo, I do finally see what you were trying to show in the video.. the nut is that “winged” drywall camp thing and you push with your hand. The car screws itself forward relative to the nut, thus moving faster than your hand that is doing the pushing!.. I like this because the prop is like a bolt threading through the “NUT of the air”..

    The problem is the wind does not “PUSH” on a surface that is moving at its speed or slower (suface moving slow would mean the wind would DRAG over that surface).. all surfaces have the same speed component IN the direction of the cart. The Wind in reality must use a different mechanism to do work on the cart instead of a PUSH or DRAG.. I am beginning to understand that this mechanism uses LIFT on the blade, like a sail..
    Chris posted this link to an excellent explanation using LIFT

    I looked at the link and I see the name Tad Hurst.. Tad if your the author, much Thanks,


  36. #36 Chris
    December 15, 2008

    Hello Henry,

    sorry, i don’t know the exact name of the author. I suspect some Mr. or Mrs. Tadhurst, or someone called Tad Hurst (is Tad a valid name?). Unfortunately there is no mention of the name on the main page either.



  37. #37 spork
    December 15, 2008

    Henry, Tad is an old (ex) HG and PG pilot in San Diego. Also a sailor – and a pretty sharp guy.

    If I may offer some bizarre observations…

    “These PULLING forces are those described by Bernoulli equations and it is in these equations that the work is done on the boat or prop cart”

    In point of fact, even when we use Bernoulli, lift is entirely due to the air pushing on the wing. Primarily for accounting purposes we think of the wing being pulled from above due to the lower pressure, but as you know lower pressure ain’t negative pressure. Lower pressure is just that – it’s a smaller downward force on the wing. The pressure on the bottom of the wing must account for all lift PLUS the pressure on the top. This isn’t terribly relevant, but it’s an interesting clarification – at least to me.

    As to whether we have anything moving backward on the prop cart, that gets into a matter of philosophy and definition (which happens a LOT on this silly toy). Imagine an infinite line at a 45 degree angle to the horizon (top to the right, bottom to the left). Now start that line moving to the right. Is the line moving to the right or is it moving down? It’s an infinite line – you can’t say – the two options are identical.

    We have a similar situation with our prop surface. Without question we cannot identify a point on the surface of the prop and say that point is moving backward. The surface itself however can be said to be moving backward. Look at a barber pole. Doesn’t it look like that stripe is moving down continuously? Our prop does the same thing.

    Now, for what it’s worth, that’s not the most compelling approach to me (but that’s why they make menus). I really think the best way to get your head around the interaction of prop and wind is to look at the sail of the ice-boat on the 45 degree downwind course in 2D.

  38. #38 Tad Hurst
    January 3, 2009

    Roadrunner changed their setup. My page is now at:


  39. #39 Mr. Moonlight
    January 13, 2009

    Sir…you led us into logical error with your ice boat in the section: “some type of sail powered vehicle thingy”…”I have ignored the cases where the wind is coming from the side (because that is more complicated).”

    You are obviously not a sailor, and me either, since sailing vehicles rarely can sail due downwind. Here’s the question though for a wind directly at your back…if the wind is constant and unvarying at 30 mph, and we hoist the sail, you are correct to say the minute we do 31 mph the sail collapses and inverts!

    But to reach 30 mph and then 31, we have to have a big enough sail. We have to count the units of energy in our collection device vs the inertia of our rig. If we hoist a hankie, chances are, even if just me on ice skates, I’ll never get up to 30 mph. However, If I hoist a blanky, stretched tight like a kite, I might get to 30 mph. If I could hoist multiple blankies, betcha I’d got faster than 30 mph, until inversion point. OR ELSE WHY WOULD SAILING VESSELS THROUGH THE YEARS BOTHER WITH MULTIPLE SAILS? if there wasn’t some gain. Have people throughout history been idiots? Multiple sails collect more energy units (ergs, I guess…)

    Now you say there is no free lunch. Well let’s say that’s true…but:

    Can a fire burn hotter than the match that starts it? Yes sir, if the fuel has an ignition temperature as low as the match’s temp, and if the fuel has plenty of energy units (BTUs), and oxygen…that’s how a welding torch works!

    Can a solar collector get hotter than the ambient (air) temperature? Yes sir, it can. That’s WHY there is a solar industry. A batch solar collector gets about 20 degrees over ambient, a glazed collector can get up to about 400 degrees and a concentrating solar collector can get white hot and melt stuff. Like a parabolic mirror…

    Can a baseball pitcher throw a pitch faster than his shoulder moves? Yes sir, it’s the principle of the lever. At the end of his arm, the ball is moving in the same time frame a much greater arc than his shoulder. Therefore the speed of the ball when released is much greater than the speed of his shoulder movement. A lever, as we know, can magnify force. It doesn’t create free energy, but the force of the end of a lever moving, say, one inch, could easily be as great as that of me the energy supplier moving my end 5 feet; it depends on the length of the lever. “Given me a lever, and a place to stand, and I can move the earth.” Didn’t Archimedes say that? As my brother the Masters in Physics pointed out, he needs a fulcrum, though, the pivot point.

    So back to the wind-driven vehicle…If it ratchets down the wind, with a collecting surface somewhat crossways to its forward motion, it can collect (and shed) energy units depending on its collection surface area and these can greatly exceed the resistance of the wind created by the vehicle moving forward, because the cross surface the forward air sees, of the sail, is not what the driving wind sees. There’s an upper limit, or NASA could launch satellites at 19,000 mph from a dingy starting off from fisherman’s wharf. But–that wasn’t so complicated, now, was it?

    The driving wind sees a big surface area collection surface. The forward profile of this surface is slight, and the oncoming air streams around it and does not impede it, so a 10 mph driving wind might propel a craft, I dunno…more than 10 mph for sure. Because, bottom line is: It happens.

    You really are a professor? And not a devil’s advocate. I’m a nobody.

  40. #40 dp
    September 4, 2009

    It’s actually very simple.
    It is possible to go faster than the wind (in absolute speed terms), but not directly downwind.

    Suppose you are at point A. Put the point B directly downwind, say, 30km from A. Suppose the wind speed is 30km/h.
    It is theoretically not possible to get to the point B in less than an hour (faster than the wind).
    Let’s draw a line through point B perpendicular to AB. It is not possible to get to any point of this line in less than an hour.
    However, it is possible to get, in ideal circumstances, (close) to the point C on this line, standing, say, 40 km apart of point B. Doing so, the vessel will travel with the speed approaching 50 km/h, i.e. faster than the wind’s absolute speed. There is no paradox here. Ice boats can travel 5 times faster than the absolute speed of the wind but still cannot cross the line described above.

    All the references of “travelling faster than the wind” actually talk NOT about direct downwind motion.

    DWFTTW vehicles are as impossible as the perpetuum mobile.

  41. #41 Michael C
    September 17, 2009

    dp: look up the figures for ice boats. You’ll see that not only can they go faster than the absolute speed of the wind, they can get to a point directly downwind faster than the wind itself, that is to say that the downwind component of the ice boat’s velocity vector is greater than the speed of the wind. See the Wikipedia article on ice boats, for instance. Or see

  42. #42 SarahB
    October 3, 2009

    DotPhysics guy – Rhett, is it? – I’m sorry, but I have to tell you that your analysis of DDWFTTW is appalling. You make wrong assumptions about how it functions, presumably from thinking how you would go about it starting with a turbine to collect wind energy. You make stupid mistakes like temporarily analysing it with zero friction at the wheels and then not realising that the wheels are geared to a prop – NB, NOT a turbine – and you then draw your conclusion on the basis of those wrong assumptions and faulty temporary propositions. The wheels must have friction. The wind is slowed in its motion relative to the ground, both when the cart is going slower than the wind and when it is going faster than the wind. It is that change in momentum of air relative to ground which powers the cart. Unless you actually ask people who know how these things work to explain them to you, you’re likely to analyse the wrong thing, aren’t you? Then you run the risk of not having the balls to say you were wrong when the penny drops later. That would be a shame. Have you ever seen a mechanism of any kind where input at a low velocity causes an output at a higher velocity? Do such things always break the law of conservation of momentum or energy? A lever. That’s all it is. Here’s a challenge for you. Put a wineglass on its side on a flat table and push it across the table with your finger in contact with the stem under the stem. Then post a correct analysis of DDWFTTW if you can explain how you didn’t just break the law of conservation of energy.

  43. #43 spork
    October 3, 2009

    You aren’t really understanding Rhett Sarah. He’s far more interested in explaining physics than he is in understanding it. He and I exchanged a few emails in which I offered to speak with him on the phone and describe how it works. I offered what seemed like sufficient evidence that I’m not some crank. What I got back was essentially a condescending response that amounted to “no thanks”.

  44. #44 Gilligan
    December 9, 2009

    Sorry Doc, you fail.

    I am going to start with a wind generator

    Bad idea, Doc. There’s no wind generator on a DDW vehicle.

    couldn’t I put a wind generator on a cart and attach that to an electric motor?

    Only if you want people to make fun of you. The way you go faster than the wind is to put a small generator in the water, with a large air propeller to push the boat forward. The boat itself transfers energy from the air to the generator, which converts the linear motion into rotation that drives the air propeller. In the boat’s reference frame, the water generator pulls energy directly from the water.

    Thanks for trying, Doc. Let us know if there’s anything else you don’t understand.

  45. #45 David Walley
    May 5, 2010

    Dear Doc

    You are wrong, and a couple of kids proved you wrong at a science fair. If you had any integrity you would resign.

  46. #46 NJ
    May 5, 2010

    Oh, look! Random nuts on the Internet disputing physics with someone who understands it at a fundamental level!

    Never seen that before…

  47. #47 David Walley
    May 15, 2010

    He’s not a random nut. He’s a professor at Southeastern Louisiana University!

  48. #48 Paul Hofmann
    June 9, 2010

    Well, Rhett you were wrong check this out; the proof of the pudding is in the eating. For a physics professor you made a big mistake. Its rather simple, one can transform the kinetic energy of the wind into propulsion with a momentum opposite to the driving direction. If the sail is big enough there is enough energy left to accelerate the vehicle in addition to the velocity of the wind. Part of your error in all your blabbing is, you assumed that the wheels have no friction; the gist is, to use the friction of wheels (on the ground) to generate a momentum opposite to the driving direction (via e.g. a propeller); the engineering art here is to find the right trade off between sale surface, weight and friction (on the ground) paired with a light weight propeller. Read the article and admit that you were wrong.

  49. #49 S.K.Graham
    August 30, 2010

    Hello, I’m late to the party on this controversy. Cavallero and Bolton have built their machine and broken the downwind world record, with an official record of nearly 3x windspeed. See this article:

    I’ve written my own blog post about this, directed at a lay audience. But you may find particularly my 2nd “vector cartoon” enlightening.

    Specifically it shows how a sailboat at about 45 degrees from downwind can still get a forward thrust from the induced wind, even if the downwind component of velocity is already equal or exceeding the windspeed. All that is required is that this forward thrust exceeds the drag.

    If this is possible then a boat can “zig zag” to outrace the wind to a point directly downwind from the start.

    If that is possible, you can imagine (engineering nightmare) a boat that allows its sail, mast, and keel to make tight zig-zags with lateral motion independent of the hull, while the hull itself moves in a straight line. This is of course not practical.

    The final solution is using a propeller. The propeller’s 3-dimensional path is a helix like a coil spring, and this path is a spiral version of the sailboat’s motion at an angle to downwind. But to make the propeller work, you need something analogous to a keel in the sailboat — the keel prevents the lateral component of force on the sail from moving the boat sideways, or in other words, the keel *constrains* the motion of the sailboat to a linear path at the desired angle off downwind. By locking the propeller to the wheels with a transmission, the blades are *constrained* to move in the helix path — this actually means that much of the force (including forward force) on the prop blade is wasted against the restraining forces. Only the component of force in the direction of the helical path is used, because that is the only path along which the blades can move (assuming that the wheels do not slip on the ground).

    I cannot emphasize enough that the true importance of the transmission between prop and wheels is to *constrain* the motion of the system.

    Doc, maybe now is a good time to revive this topic and recant?