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Sailing Directly Downwind… Faster Than the Wind

by Brian Dunning, May 27 2010

It’s one of those annoying brain teasers that turns half the people in the room against the other half, a simple engineering riddle that even professional aeronautical engineers get wrong.

It’s well known that racing boats can travel faster than the wind when traveling to windward. The fastest boats, and especially ice boats and land yachts, can even beat the wind downwind by sailing off the wind at an angle. This is because a boat is not driven by the true wind, but by the apparent wind. When you move at some angle relative to the wind, the apparent wind changes its speed and direction. Lift and drag (including friction) all factor into the equation.

But sailing directly downwind poses a different challenge. The apparent wind’s angle never changes, and the apparent windspeed approaches zero the faster you go. And so, from a superficial examination, this proposition should be impossible. And, using a conventional sail, it is indeed impossible.

However, when you change things up by replacing the sail with a windmill that drives wheels, it is possible to go directly downwind faster than the wind. Since the windmill’s blades are spinning, there is always apparent wind that can be used to generate lift. Moreover, the tips of the windmill blades are moving much faster than the wind, so the true wind speed is actually not all that big a factor.

Foul, you may cry. Once the vehicle is traveling directly downwind at exactly the same speed as the wind, there is zero apparent wind. Thus, there’s no impetus for it to accelerate any faster. If the apparent wind on the spinning windmill blades caused the vehicle to accelerate, it would have to be an impossible perpetual motion machine. Right? Hmmm… Well, don’t worry. Internet forums where this problem has been discussed run thousands of posts long. Even professional aeronautical engineers can’t agree.

The Douglas Aircraft model

People have been testing this for a long time. The latest is a group working with the San Jose State University aeronautical department, Dead Downwind Faster Than The Wind (DDWFTTW, lots of stuff on their web site), with corporate sponsorship from Google and wind energy company Joby Energy. A video of one of their prototype’s vehicle’s test runs is posted here. They cite a test cart built in the 1960′s, as a result of such a disagreement between two engineers at Douglas Aircraft. Reportedly, it managed to travel downwind at 1.2x true wind speed. The DDWFTTW has traveled at more than 2x true wind, and is aiming for 3x.

The rules are simple. No stored energy can be used. The vehicle must travel directly downwind, not at some offwind angle. The only power allowed to drive the wheels is the windmill.

The hardest thing about this is to get your mind away from the concept of apparent wind on the vehicle, and think instead about apparent wind on the windmill blades. It’s way too easy to get stuck on this point, but you have to remember that apparent wind on the vehicle is not relevant to the blades’ lift, even though it’s coming from what intuitively seems like the “wrong” direction. It is relevant to the drag, and as such, it is still a variable in the equation. Friction, weight, and wind resistance must be minimized, because once you exceed the true windspeed, these all work against you.

But watch the video. Yes, it’s possible that SJSU, Google, and Joby Energy are all being hoaxed here. What do you think?

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Sailing Directly Downwind… Faster Than the Wind, 4.3 out of 5 based on 18 ratings

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91 Responses to “Sailing Directly Downwind… Faster Than the Wind”

  1. Lukas says:

    I guess it’s possible to go faster than the wind for a time, but once you exceed wind speed, aren’t you just using energy stored in the motion of the blades themselves? At some point, you’ll fall back to below-wind speeds.

    Once the vehicle overtakes the speed of wind, the wind direction on the blades changes; this can still be used to turn the blades, but the drag will also slow down the vehicle. And it’ll slow down the vehicle faster than it’ll increase the speed of the blades. If not, that would be like saying that these blades can accelerate a vehicle if there is no wind once you give it a good shove.

    • Andy Clitheroe says:

      “saying that this is enough to keep the speed of the vehicle above the speed of the wind is akin to saying that the vehicle is capable of driving when there is *no* wind.”

      Ah, but it isn’t. They’re not claiming ‘wind speed PLUS X’ they’re claiming ‘wind speed TIMES X’. X times zero is still zero.

      • Andy Clitheroe says:

        Let me put it another way: assume a 9knot wind relative to the ground. We put a car with a sail (Sailcar) and a car with this funky geared propeller on it (Propcar) next to one another.

        When stationary, all the surfaces of both cars ‘feel’ to the wind like they’re moving at -9knots.

        So it blows them forward. Let’s say each reaches 3 knots groundspeed.

        To the wind, all surfaces of the sailcar now feel like they’re doing -6knots. But with the propcar, friction with the ground is spinning the wheels and turning the propeller in such a way that – from the wind’s perspective – the blade surfaces ‘feel’ like they’re doing -8 knots, not -6.

        So the wind pushes both faster. Let’s assume both cars are ‘perfect’ so they can hit 9knots groundspeed.

        At this point, all the surfaces of the sailcar ‘feel’ motionless relative to the wind. So it stops accelerating. But the propcar’s blades still feel, to the wind, like they’re doing -6knots. So it can push them faster, right up to the point where they feel like they’re doing 0 knots, which occurs when the car is doing 27knots groundspeed.

    • Fred Nurk says:

      Here’s my guess:

      Three phases:
      1. Slower than wind speed (relative wind coming from behind)
      2. At wind speed (no relative wind)
      3. Faster than wind speed (relative wind from in front)

      1. At first, the prop is acting like a sail on a boat running downwind – the wind pushes on it, and moves the vehicle forward. Because the vehicle moves forward, the wheels turn the prop, actually increasing forward speed a fraction. As the cart gets faster, the prop moves faster, and is actually beginning to propel the cart. The faster the cart goes, the greater effect the prop has as a propelling force.
      So to start with, the wind pushes the cart forward, but then the turning wheels drive the prop, which then pulls the cart forward. The wind is needed here to offset the inefficiency. At this stage the wheels are driving the prop, which then pulls the cart forward, helped by a pushing wind, until it reaches wind speed.

      2. When the cart is going the same speed as the wind, then the wind is no longer pushing. However, the wheels are spinning at say 15mph. This drives the prop. The prop is then like an aircraft standing still, and it will pull the cart forward through the apparently still air – just like an aircraft can move forward from rest. The propulsion is supplied by the momentum of the wheels only at this point. If the cart is light enough, and the ratio worked out nicely, then the cart continues to accelerate. This is only possible because of the wind – creating a no airspeed yet fast groundspeed situation that allows the wheels to drive the prop.
      In this stage, the wheels are driving the prop, and it is the prop that is providing the forward acceleration. This phase only lasts a short while until…

      3. Once there is a headwind, then the prop stops acting as the propulsion, and instead acts as a windmill. The wind moves the prop, which then turns the wheels. More forward speed = more apparent wind to windmill the prop to drive the wheels = more forward speed. And the whole thing happily accelerates until it reaches its efficiency limits.

      The cool thing about this is how the prop and wheels interact. At first the prop is being pushed, then it’s the wheels driving the prop, then the wind driving the prop that then drives the wheels.

      The amazing thing is they got the ratio, efficiency, and managed to get it rolling in the first place.

      Well done!

  2. MadScientist says:

    This is reminiscent of Feynman’s dilemma about which way a sprinkler would spin if you forced water into the spout and out the base – but in that case I can work out that the sprinkler will still spin in the same direction as it would when operated in the usual fashion. I’m afraid I’d have to see this wind thing to believe it – and of course I’d want my own instrumentation on the ground as well as on the vehicle as part of testing the claim.

    • MadScientist says:

      OK, I get it. In the case of a propeller (as opposed to a yacht’s mainsail) the implication is that the blades will spin faster when the pitch is not 90 degrees to the wind – which does seem kind of obvious. The spinning propeller can then be used to provide the energy to give the gizmo a little boost in addition to the push of the wind.

      I suspect an equally tough question for many (except for sailing folk) would be how a sail boat can move upwind.

      • Lukas says:

        While it is true that the blades can spin faster than the wind, once the vehicle equals wind speed, there is no wind to spin the blades anymore. When the vehicle overtakes wind speed, there will be wind to spin the blades again; however, saying that this is enough to keep the speed of the vehicle above the speed of the wind is akin to saying that the vehicle is capable of driving when there is *no* wind.

      • MadScientist says:

        That’s not quite right; the craft has to travel some speed above that of the wind before there is no longer a force to spin the propellers (the prop stalls). As you exceed the wind speed the propellers will spin slower and at some point (your top speed) the propellers will continue to spin and push you along although it doesn’t have enough power to push you faster. The propellers will only stop spinning when you reach the wind speed if you have symmetry between the fore and aft surfaces of your propellers – except of course when your actual wind speed is 0.

      • Brian M says:

        The short answer to moving upwind is that it can’t, only from a few degrees off (45 degrees, usually).

        I think you hit the nail on the head. The blades are at an angle off the wind, whereas the craft is not.

        I often wish I knew more about apparent wind, etc. :(

  3. Ken Baker says:

    Think of this gizmo standing still in an absolutely calm. Isn’t that situation aerodynamically the same as the gizmo travelling directly down wind at X knots in an X knots true wind?

    • DarthCaitSith says:

      Not quite. At windspeed the cart is not stationary wrt the ground. And something that seems to have been skipped over in the blog post is the fact that the wheels are geared and dirrectly connected to the prop.

      Now i have never figured out this thing for myself yet, though i have spent a bit of time trying to think it through. I just don’t have the physics for it.

  4. Ellindsey says:

    A slight error in your explanation. You state that the cart works by “replacing the sail with a windmill that drives wheels”. In fact this is not the case. The propeller is not driving the wheels, it is actually geared the opposite way that it would be if that were the case. The wind pushes on the propeller, which forces the car to accelerate forward. The wheels turn from the force of the car being pushed by the wind. The propeller is turned by the wheels, and pushes back against the wind. The blades of the propeller are acting just like the sail on an ice boat, hitting the wind at an angle that causes the sail to feel an apparent wind pushing it forward even though the vehicle is traveling faster than the actual wind speed.

    • Lukas says:

      Okay, that makes a little bit more sense.

    • Jim Shaver says:

      I mostly agree with Ellindsey’s statement, that the wheels drive the propeller. For the first half of the run, that is definitely what is happening. However, it also appears to me that the propeller is linked to the wheels without a clutch mechanism, so that in theory whichever is generating the most torque will drive the other.

      When the vehicle’s land speed is initially zero, and the wind pushes on the car with just enough force to overcome friction and start the car rolling forward, the wheels transfer more torque to the propeller than the counter-torque imparted on the propeller by the wind. The result is that the propeller starts to spin counter-clockwise when viewed from behind.

      By the time the vehicle reaches the forward wind speed, the wind is pushing forward on the vehicle with an average force of zero, so the wind is no longer able to accelerate the vehicle forward. But by this time, the forward force provided by the propeller against the air is enough to cause the vehicle to continue accelerating.

      At faster-than-wind speed, the relative wind speed at the vehicle is backwards, and the resulting friction produces a negative force. When the vehicle reaches its top speed, the backward drag and other frictional forces on the vehicle exactly cancel the forward thrust from the propeller, and the vehicle can theoretically continue to move at that maximum speed indefinitely.

      Say that the vehicle is running at maximum speed, when the wind suddenly dies down to zero. Now, the backward drag force on the vehicle has suddenly increased substantially, unbalancing the force equation and slowing the vehicle’s speed. At this moment, I believe the momentum of the propeller would impart a forward force to the wheels, although this forward force would still be insufficient to overcome the drag force, and the vehicle would continue to slow down and eventually stop.

      Anyway, I hope this thing isn’t a hoax; it’s way too cool to end up being a fake!

      • Jim Shaver says:

        Oops! I should have said that the propeller spins clockwise when viewed from behind.

  5. Andy says:

    Why do they tow it back into position (according to their annotated telemetry)? Couldn’t they just turn it around and sail directly upwind? Which would also be another traditional-sailing impossibility…

    • Sean says:

      If the propeller were engineered to work as a turbine, it would be able to sail straight upwind – and there are carts that do this. There’s even a racing league for them.

      Technically, I don’t think it would be impossible to create a cart that’s able to go both directly downwind faster than the wind and one that’s able to go directly into the wind. The way you’d gear it to the wheels is identical. But the pitch of the propeller blades will impact which way the propeller wants to spin when the device is starting from a dead stop, which determines which way the cart wants to go. Ultimately, the more you engineer it to be able to travel into the wind the worse it will perform at traveling downwind, and vice versa. Since this vehicle is being engineered to achieve a record multiple of windspeed traveling downwind, it may not even be feasible for it to travel upwind, not even if you give it a good push to get it started going the right way.

      • PuddleDuck says:

        If the theory holds water, that it is the prop that is turning the wheels, then you should be able to reverse the gearing and it should go upwind as fast as the wind is blowing (less the wind resistance on the vehicle). But this will not be as spectacular as the claim that when the wind is from behind, the vehicle will travel faster than the wind.

    • Max says:

      Maybe they don’t have a reverse gear. If the windmill spins clockwise downwind, and counterclockwise upwind, then a reverse gear is needed to spin the wheels forward in both cases. Either that, or they need to turn the windmill 180 degrees, but it looks fixed in the video above.

  6. Brandon says:

    You mis-represented a large part of the vehicle, which is where a lot of the confusion comes from. The prop does not drive the wheels, it is in fact the other way around.

    If you watch any of the carts closely you will see that the prop is turning in the “wrong” direction and acts like an upwind cart. Slower than windspeed the prop acts like a sail and the wind pushes the cart in a similar manner to if the prop didn’t spin. After that it is the speed it is the wheels that spin the prop causing the cart to act like an airboat.

    • Max says:

      Now THAT sounds like a perpetual motion machine. The wheels power the prop, which pulls the vehicle and powers the wheels. Where does wind even enter the equation?

      • Jim Shaver says:

        It’s not perpetual motion, Max. Wind — an external source of energy — is required to keep the vehicle moving.

        Yes, you could lift the rear end of the vehicle, spin the wheels with an external motor to get the propeller moving fast enough to provide forward thrust, drop the rear end, and watch the vehicle move forward. But without a tail wind, friction and drag will slow the vehicle to a stop. With a strong enough tail wind, the vehicle can theoretically travel perpetually, faster than the wind speed; but you’d need an endless, straight road and an unrealistically cooperative wind.

    • PuddleDuck says:

      If the prop is turning the wrong way, then by merely facing the vehicle upwind, the prop should turn the wheels, and when facing downwind the wheels turn the prop. Gee, it seems so simple on paper.

      • PuddleDuck says:

        The wind is pushing the prop, which is not acting as a prop, but a sail, initially. As the vehicle begins to move forward, the prop is forcing air backwards, partially counteracting the air coming from behind. In theory, the vehicle will always go slower than the wind, as the wind from behind is trying to turn the prop in the opposite direction from the wheels.

        Even if you used a power source, other than the wheels to turn the prop, the wind would tend to slow the prop down, as it is trying to get it to turn in the opposite direction of the way it is being powered.

  7. jrpowell says:

    Um, because the they are twisted, some portion of the blades are ALWAYS at an angle to the wind, so this is NOT the same as sailing directly downwind, and is in fact a more complicated case of holding the sail at an angle to the wind. Paradox resolved.

    • Tane says:

      That’s probably the simplest and easiest way to explain this phenomenon.

    • dsquared says:

      You’re right that a big part of seeing the non-paradox is to realise that the rotation of the propellor is perpendicular to the wind, not parallel, but this isn’t a complicated case of holding a sail at an angle. The propellor is a propellor, not a turbine; it’s driven by the wheels and pushes air backwards, not driven by the wind pushing it (the way in which it is wind powered is that when the wind is directly behind it, the “apparent propellor draft” is bigger than the actual amount of air displaced, which is how the system keeps moving forward when the only thing turning the propellor is the friction of the wheels on the ground).

      The trick here is in using the word “sailing” for something that doesn’t have a sail and which isn’t propelled in a fashion remotely analogous to sailing. The optical illusion of the plane of rotation of the propellor makes you want to think that the boat has something a bit like a sail on it – from there, you fall into the error of thinking that the propellor is a turbine, and then you move on to establishing (correctly) that the machine you have in your mind wouldn’t work. It’s notable that the “Ride like the wind” website scrupulously avoids using the word “sailing”, but obviously everyone who has written an article about this thing has done, hence the confusion.

  8. Brian van Doren says:

    If you watch the videos closely at http://vimeo.com/10476216 you can see the prop is mounted such that the *wheels* drive the *prop*. It was clear during video DDWFTTW #3 when they had a mechanical failure. The blades started to turn the opposite direction once the vehicle nearly stopped.

    With this in mind, consider a simplified situation where the vehicle is moving downwind AT wind speed (something we can agree can happen – almost). In this situation, there is no wind drag on the vehicle only small drag in wheel bearings. The situation is thus: F_net = F_prop – F_wheels_turning_prop. Can F_net > 0 and thus propel the vehicle past wind speed?

    Since we are stationary with respect to the air, the question is: can we turn a propeller using the wheels that will generate more force than the wheels are taking away?

    Visiting various web sources, I can up with the following relationships:

    T = torque
    D = diameter of blades
    k_t = thrust coeff
    k_q = torque coeff
    l = effective lever arm between ground and propeller via wheels, gears, etc..

    F_prop = k_t * T / (k_q * D)
    T = F_wheels * l
    so…
    F_prop = (k_t F_d l) / (k_q D)
    and thus ratio
    F_prop/F_wheels = (k_t l) / (D k_q)

    This only needs to be greater than 1 to push us beyond wind speed (assuming negligible friction in gearing, etc..). Beyond that, it is a game of decreasing your overall wind drag.

    k_t seems approx 6 k_q so it’s a matter of gearing to get l > D/6 (and reduce losses due to friction and such).

    I imagine the real game is overcoming losses and air friction. Anyone see any glaring mistakes?

    Sources:
    http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html
    http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-154Fall-2004/E10E4FCB-7962-4A89-8DD4-9EDF0A563E8D/0/lec12.pdf

    + others that spam filter didn’t like…

  9. gwen says:

    My brain is hurting, and I was not a physics major, but it would seem to me that the propeller would continue to spin and that the actual wind speed is a red herring.

  10. Robo Sapien says:

    It seems the obvious has escaped us all. This is a manned vehicle, as long as the driver maintains a steady diet of baked beans, the resulting flatulence could easily give it that extra boost.

  11. Zenn says:

    Oh no, I can see this going on forever here too. There is a very long thread at http://www.randi.org site on this matter.

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

  12. Beatrice Honningforth says:

    Rating 3 instead of 5 since it’s low on math. Yes, he replied with some math, but he should have worked out the problem mathematically when he wrote the article. The only reason I won’t do it here, is that it’s been done to death on the rest of the Internet.

  13. rob says:

    i wasnt able to watch the video yet but one small caution on deciding rotational direction off video.
    i presume u have all seen a cars wheels spinning the wrong way on tv, as the wheels rotational speed does not match the frame rate of the camera.

  14. Max says:

    Physics class should teach these kinds of brain teasers and experimentally test them. The ping pong ball demo of the Bernoulli principle is a classic example of something that’s counterintuitive. Even without math, it corrects students’ intuition. Wrong intuition makes people fall for scams and conspiracy theories. I think a top educational goal should be to first make students realize that their intuition can be wrong, and then try to correct it.

  15. spork says:

    Howdy all. I’m one of the builders, and the pilot of this thing. It’s a bit too late at night for me to go into great detail, but I’ll hit a few high points…

    - It’s no hoax. But it’s a great brainteaser. I’ve posted a set of detailed build videos for anyone that wants to build a small working model for themselves. It will go forward against the treadmill belt, and even climb the treadmill.

    - The wheels turn the prop – at all phases. The prop never turns the wheels.

    - Yes we could make it go directly upwind by simply changing the gearing (or using smaller wheels).

    - No – it won’t work at all with no wind.

    The prop pushes the cart forward, causing the wheels to turn, which in turn causes the prop to turn – which pushes it forward. Sounds like perpetual motion, but it’s more like an typical feedback loop – with external power supply (i.e. the wind). The reason we can generate more thrust at the prop than is needed at the wheels is precisely because of the tailwind. With the tailwind, the cart moves through the air more slowly than it moves over the ground. So the thrust from the prop acting on the air expends less power than we can harness with the wheels moving over the ground.

    Make sense? Don’t be surprised if it doesn’t yet. But if you keep an open mind, and ask questions, I’m nearly certain I can get you over the hump.

  16. gwen says:

    This is a job for MYTHBUSTERS!!!

  17. Zenn says:

    No myth to bust! It is real.

  18. spork says:

    >> This is a job for MYTHBUSTERS!!!

    We tried everything we know for more than a year to get the Mythbusters to tackle this. I think the lack of explosion potential worked against us. In the end I like to think we busted this particular myth.

    • Max says:

      Can you make a normal website instead of a blog? With a “How it works” page, and a video page, and a link to the San Jose State University aeronautical department.

  19. Glenn B says:

    An interesting clue in understanding what is driving what is to consider the drive chain.

    When actively cycling, the top of the chain is under tension, showing that the crank is driving the back wheel.

    On the wind cart the chain tension is on ‘the wheels are driving the prop’ side at all times (though what happens at max speed I’m not sure).

    • spork says:

      At max speed the wheels are still providing the torque that turns the prop – and the prop is still producing the thrust that turns the wheels. I’m always a bit hesitant to say the wheels “power” the prop, but it’s certainly true that they provide the torque that turns it. If we say the wheels “power” the prop it can get into some subtle semantics.

  20. Michael Kingsford Gray says:

    I say ‘bollocks’.
    It is no more than previously stored** excess energy being released to gain a temporary*** exceeding of wind-speed.
    _____________
    ** In the form of the vehicle momentum.
    *** I am willing to wager that this apparent phenomenon is not sustainable.

    • Zenn says:

      Michael, you obviously haven’t seen all the videos, threads and tests. Have you seen the treadmill videos that demonstrates that the treadmill energy on a horizontal plane can propel the cart forward. That alone is proof.

      It just doesn’t appear logical but because the wheels are driving the prop, it is. It isn’t a sail.

  21. Martin says:

    Are you really prepared to wager, Michael Kingsford Gray, because if you are the people building the cart will happily take you up on it.

    Also, if you have a think about it, and how the system works, you’ll figure out your hypothesis is wrong.

  22. Max says:

    Can we turn this into an equivalent problem without the complexities of propellers?
    Instead of a land yacht with a tailwind, we have a wheelchair on a moving walkway. Can the wheelchair move faster than the moving walkway by driving its wheels with the rotation of an extra wheel that’s extended to the stationary ground?

  23. spork says:

    >> Are you really prepared to wager, Michael Kingsford Gray, because if you are the people building the cart will happily take you up on it.

    I would most definitely take that bet. We’ve found that most people that are “SURE” it’s a hoax aren’t sure enough to bet.

    >>
    Can we turn this into an equivalent problem without the complexities of propellers?
    Instead of a land yacht with a tailwind, we have a wheelchair on a moving walkway. Can the wheelchair move faster than the moving walkway by driving its wheels with the rotation of an extra wheel that’s extended to the stationary ground?
    <<

    You sure can. Here are some nifty videos one of our on-line friends put together.

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

    Under the ruler faster than the ruler:
    http://www.youtube.com/watch?v=k-trDF8Yldc

    Equivalence of reference frames:
    http://www.youtube.com/watch?v=9Yt4zxYuPzI

    • Max says:

      Cool videos. I did something similar to the spool experiment with a yo-yo when I was a kid. Simply unwind the yo-yo and drag it by the string across the floor. It’ll roll faster than the string is moving, and wind itself up.

    • Max says:

      It’s easy to calculate the spool’s speed relative to the moving paper.
      The spool’s outer wheels with radius Rout touch the ground, so the spool’s speed is 2pi*Rout per cycle, relative to the ground.
      The spool’s smaller inner wheel touches the moving paper, so it travels 2pi*Rin per cycle relative to the paper.
      For the inner wheel to keep up with the outer wheel relative to the ground, the paper must move at a speed of 2pi*(Rout-Rin) per cycle relative to the ground.
      Therefore, the ratio of the spool’s speed to the paper’s speed relative to the ground is: Rout/(Rout-Rin)
      When Rin=0, the ratio is 1 because the paper is basically pulling on the axle, so the spool moves at the speed of the paper.

      • Max says:

        When winding a yo-yo by dragging it across the floor, as I described above, the inner radius, Rin, grows so the yo-yo accelerates.

  24. Joe Lewis says:

    The problem is that when you exceed the wind speed, the backward “wind” is only due to the existing kinetic energy of the car, this is NOT an external energy supply! So all the windmill is doing is taking energy from the car and feeding it back in. To accelerate under these conditions you would need to give the car extra kinetic energy thus you would require an efficiency of greater than 100%. It is impossible to generate at even 100% (wich would only keep you going at the same speed). Thus it is energetically impossible to exceed the speed of the wind (in the same direction). At best you could exceed it for brief periods but your average speed will always be less than that of the wind!

    Believe me, I haven studied physics for 4 years for nothing!

  25. Zenn says:

    Michael Kingsford Gray, how would you like to place your bet because I will wager you. This is real!

  26. Joe Lewis says:

    Actually…… I’ve been thinking about this overnight and it does work! I never realised but the backward wind inst driving anything. And it can accelerate to any velocity (theoretically but not practically).

    Heres how it works.

    1 imagine the cart has somehow gotten to velocity W. The wheels are also turning from running along the floor at speed W. Ignoring air friction then the vehicle is going at a constant velocity, this is because the windmill is blowing air from the vehicle backwards at velocity -W. (Think of it as the air stopping relative to the windmill and the windmill spitting it back out at the speed of the vehicle. Because outside the air is stationary there has been a change in the air speed of W – W = 0, so the vehicle is neither accelerating or decellerating.

    2 Now is there is a wind to the vehicles back of W and the vehicle is traveling at the same speed W. If the vehicle isnt sliding then the wheels must also be rolling such that the bottom of the wheel is not moving relative to the ground (no sliding). And we all agree the vehicle can reach this speed! So there is an extra force from the fan, this is now blowing air relative to the vehicle backwards at speed W, this means the wind from the fan is moving: (backward in the frame of reference of the wind or: Stationary in the grounds frame of reference or: backwards in the cars frame of reference) This is similar to when there was no wind BUT, the air in this situation has changed direction. Newton says that if you move something in one direction you yourself travel in the opposite direction. So the fan here is actually doing work and accelerating the car. The change in the wind velocity is is 0-W.

    Now at this point you may think ok it will accelerate but then slow down but this isn’t true. If you keep thinking that at this increased velocity of (W+bit) where bit is the small amount of extra speed, then the fan will be blowing wind in the opposite direction at the same speed as the car is going forwards. If we still have a wind (in the reference frame of the ground) of W (still ignoring the backward wind resistance on the car). Then there is still a change in wind speed in the frame of the car of: the backward wind -(W-W+bit=bit)- the velocity of the wind from the fan (-(W+bit)) giving a total change in wind speed of -bit – (-W-bit) = W!

    From this we can see that the car will continue accelerating but can only ever change the wind speed by W the original wind speed. If the tailwind stops then the car will be changing the wind speed by 0. and Newtons says we don’t get any acceleration.

    So question 1, what stops the car from continuous acceleration? The answer is wind resistance, this increases with velocity so the more the car travels faster than the wind, the greater the backwards drag it sees from the air moving backwards relatively. At a certain speed this backwards drag will equal the forward force the car gets from changing the air speed by W. At this point the car has reached its peak velocity, and will maintain it as long as the actual wind is blowing.

    2, why cant we put them on cars? We can, If you expect to be driving constantly with some wind from the rear (excuse me) at very low speeds such that the overall drag is is small. But this is unlikely. You will be going at 60mph down the motorway with a windmill on top of your car! The drag from the backward wind will be tremendous, not exactly fuel economy.

    It helps if you keep in mind that the backward wind isn’t turning the mill, the backward wind is ALWAYS bad and acts to slow down the car.
    Sorry about the long reply, hopefully this helps, for me it is the best way of thinking about it!

    • Joe Lewis says:

      In the above model I’m assuming the windmill is 100 % efficient. I know this is far from true in reality, the only thing that matters conceptually is that there is a net forwards force on the car. I don’t care what the force actually is, it doesn’t matter! And always make sure its not creating energy from nothing, the acceleration of the car and maintaining it at the peak velocity always depends on a good backwards wind.

      Did any of that make sense? I think its a bit more satisfying an explanation than anywhere else. The clincher came from spork, I realised what was driving what.

  27. spork says:

    I think MKG has made it clear just how certain he is afterall.

    • tmac57 says:

      I think he just got a kick out of using the word “bollocks”. Really enjoyed the videos BTW (though they made my brain hurt).Thanks spork.

  28. spork says:

    This thing just got picked up by WIRED and Popular Science today.

    http://www.wired.com/autopia/2010/06/downwind-faster-than-the-wind

    http://www.popsci.com/cars/article/2010-06/wind-powered-car-looks-odd-answers-tricky-physics-question

    Not completely accurate; but it’s a tricky topic. That’s the point.

    • tmac57 says:

      Hey,that’s great press! I was struck by the idea that so many physicists were so adamant that this COULDN’T work.It reminded me of the PhD mathematicians that could not accept the solution to the Monty Hall problem.

  29. Mikkel says:

    The clue to understanding the riddle is not in the “apparent wind on the windmill blades” as written in this article, but in a quote from one of the designers on wired.com:

    “Skeptics think that the wind is turning the prop, and the car is turning the wheels, and that’s what makes the car go,” Cavallaro said. “That’s not the case. The wheels are turning the prop. What happens is the prop thrust pushes the vehicle.”

    The blades are not windmill blades, but *propeller* blades. Driven by the wheels they are pushing back on the wind coming from behind.

    • Adam says:

      Mikkel is right. There are several articles that get this windmill/propeller thing backwards. It makes these arguments that much longer because people are arguing that it’s impossible based on false assumptions.

  30. Marc says:

    Hello,

    I think if you take the example of a sailboat sailing into the wind (or sideways with respect to it), you may have your answer.
    The boat is propelled like a “wedge’ in-between the ocean and the rudder.
    Whatever circular motion the propellors derive from the wind-power is motion sacrificed from thrust which could have gone toward the motion of the vehicle. I’m gusessing that any additional motion comes from a sideways wind movement, and that if you combine the lateral and vertical wind-power vectors you would find that they add up to more than the wind-velocity (no perpetual-motion machine).

  31. Max says:

    The spool rolling on a moving ribbon is not a perfect analogy because there’s no drag when the spool moves faster than the ribbon, yet there is drag when the prop moves faster than the wind.

    I like the treadmill videos, but I’d like to see less pushing and pulling, which may add energy. Just anchor the cart with a string so it doesn’t go too fast, let it run for a minute, and then release the string without pulling the cart, and see if the cart accelerates.

  32. Tim says:

    LOL @ skeptics.

    This works. It’s just a way to get leverage and multiply speed, as is sailing faster than the wind.

    Ph.D. in Mechanical Engineering here, and I assure you this is sound.

  33. ThinAirDesigns says:

    @Max “Just anchor the cart with a string …”

    Like this? … http://www.youtube.com/watch?v=oTMRviy-5zY

  34. spork says:

    You’ll have to check out our “physics on a shoestring” video (search the “spork33″ videos).

  35. mike says:

    “With the tailwind, the cart moves through the air more slowly than it moves over the ground. So the thrust from the prop acting on the air expends less power than we can harness with the wheels moving over the ground.”

    NOW I understand !!!! this is the crux.

  36. GregW says:

    My question is: How do you REALLY know which direction the wind is going, at any given time??? I mean that the actual wind direction can vary a few degrees over a short period of time. It must be really hard to figure out which way is downwind when you’re driving.

    A related question is what about turbulence? Unless you’re in some near-perfect wind tunnel with laminar flow, you’re going to get some level of turbulence.

    Both the wind direction variance and the turbulence would give you a slight angle to downwind at any given time.

    It would be interesting to put the machine in a good wind tunnel and test it’s performance directly downwind and at slight (2-5 degree) variances from downwind. That would help to determine whether these small variances from downwind have any significant effect on the vehicle’s ability to truly go DDWFTTW.

    • Subduction Zone says:

      Greg, for the NALSA tests they did several runs. Some of them were slightly off of directly downwind to show that the cart performed not as well when it was going at an angle to the wind. Their indoor treadmill tests of their small scale carts proves that it goes directly downwind to anyone who has had enough physics to understand the concept of a Galilean Transformation. I am sure that NALSA will be publishing an article after they have thoroughly analyzed the data. And there is quite a bit of it. This was not your usual measure how fast or how far the vehicle goes test. They had to continually, and carefully measure the wind velocity. They had checked the performance of the cart both directly downwind, as best as you could go directly downwind, and at various angles to the wind. But the simplest test was that of the BUFC when they were doing practice runs and you could see the cart zip through the cloud of dust generated by the pickup truck that started off being a chase vehicle. How fast does a cloud of dust go compared to the speed of the wind?

  37. Mel Holloway says:

    Something for the sailors among you to try. Once, sailing a downwind course in light wind, I put an extendable spinnaker pole (maybe a gennaker pole) between the forestay and the clew of a large genoa to push the clew out, steered the boat so the wind was coming over the stern quarter, not full astern, then let the clew of the genoa forward, the sail filled and there was a noticeable increase in speed. Try it, but be conscious of the load the pole puts on the forestay.

  38. From an old physical chemist,
    A simple solution:

    The vehicle with its propeller, transmission
    and wheels tracking the ground
    provide a mechanism
    for translating all three gaseous air molecule
    translational degrees of freedom
    (with velocity v = sqrt(vx^2 + vy^2 + vz^2) and
    air molecular N2, O2 mass m)

    3 degrees of freedom 3 * (1/2)*k*T = 3 * (1/2)*m*v^2 = 3*p^2/(2*m)

    into energy momentum transfer to the vehicle one degree of freedom ‘x’
    picked up by the
    vehicle with Mass M, momentum P_x and velocity V_x

    from air three degrees of freedom within the propeller influence
    with air mass within propellers Ma
    and air volume within propellers Va
    and molecular weight of air MW

    and energy momentum transfer being:

    air 3 degrees of freedom * (Ma/Va)*(1/MW)*(1/2)*R*T
    = vehicle 1 degree of freedom * (1/2)*M*V_x^2 = 1*P_x^2/(2*M)

    The ground, wheel, transmission, propeller linkage
    provide the inertial_x reference for this process.
    Conservation of energy and momentum is maintained
    before, during and after vehicle passage
    through a block of air.

    During vehicular air block passage,
    the block of air energy within the propeller space
    has only one degree of freedom in the vehicular travel ‘x’ direction containing the other two y,z transformed degrees of freedom made available due to propeller/air dynamics.

    On this basis, the vehicle will never exceed 3*wind speed.

    Best,
    Richard D. Saam

  39. Max says:

    http://www.wired.com/autopia/2010/07/its-settled-downwind-faster-than-the-wind-officially-possible/
    July 29, 2010

    “The results are in and a new record has been set in a new category after a wind-powered vehicle officially traveled downwind faster than the wind…
    The North American Land Sailing Association (NALSA) made it official when it ratified the results: The DWFTTW cart traveled directly downwind at 2.8 times the wind speed.”

  40. Timmy says:

    Richard D. Saam says: “On this basis, the vehicle will never exceed 3*wind speed.”

    Well, they already went 3.5 x wind speed. But numerology is always fun :-)

    For physics see this paper
    http://orbit.dtu.dk/getResource?recordId=241183&objectId=2&versionId=1
    Quote: “There does not exist a definitive upper limit for vehicles of this kind. As long as efficiencies are improved, the velocities will increase unasymptotically”

  41. Arak says:

    I suspect it has built-up a volume of pressurized air behind the prop. The combination of votex and wind holds it there for only a few seconds while the prop-and momentum runs down.

    The flag doesn’t actually see the relative wind on the prop because it not inside the vortex area, where the pressure exists.

    If that is right, it’s impossible to keep the speed up for more than a few moments, as this craft did.

    • Timmy says:

      Arak: [crazy vortex theory]

      Why don’t you try to understand the actual physics involved. I posted a link to a paper in my previous comment.

      Arak: “it’s impossible to keep the speed up for more than a few moments,”

      Wrong, they go faster than wind until they hit the brake. See other videos for longer runs.

  42. Mike says:

    OK, think of it like this. you have a sail machine. The wind pushes you and you start moving. It will push you up until you are the speed of the wind.
    Now hook a generator to the wheels and you generate power. Now use that power, to push back against the wind. You have the wind pushing you, and you are pushing back against it using the power generated by turning the wheels.
    And this is not a perpetual motion machine because, power from the wheel is linear, but speed generated from it is not so you can go the speed of the wind-loss for friction + speed from wheel power.

  43. Super Peter says:

    Hello is this on? Good explanation(s) and so many post(s).

    The answer is gear ratio between propeller and wheels, meaning they’re trading torque (weight of the car) for velocity.

    Yes, thank you, I now, I’m exceptional.

  44. HaHaHa says:

    Very nice hoax. Seems like a lot of work for a laugh.

    So, if you can go faster than the wind then this should operate just fine on a calm day. Just give it a push and start the propeller, from then on you have a head wind just like your faster than the wind situation.

    Again, what are you getting out of all this work?

    Very lame.

  45. Timmy says:

    HaHaHa says: “So, if you can go faster than the wind then this should operate just fine on a calm day.”

    No

    HaHaHa says: “Just give it a push and start the propeller, from then on you have a head wind just like your faster than the wind situation.”

    No true wind -> apparent headwind = ground speed at the wheels.

    This not same as downwind faster than the wind where

    apparent headwind < ground speed at the wheels.

    HaHaHa says: "Very lame"

    Actually it is very cool, because it makes overzealous skeptics who argue against it look foolish. It demonstrates that many of the internet skeptics are not much better at physics than actual crackpots, and argue from pure intuition.

  46. spork says:

    >> Very nice hoax.

    Yes, kind of like the moon landing hoax. What a hoot!

    >>So, if you can go faster than the wind then this should operate just fine on a calm day.

    I have no doubt that wind powered vehicles work just fine on calm days – in your world. In ours – not so much.

    >> what are you getting out of all this work? Very lame.

    Ahhh – you’re worried we’re working to hard for nothing. That’s sweet.

  47. Alex says:

    I had the pleasure of meeting Rick and Rob at an AIAA presentation in Mountain View California last Thursday.

    You can see a review of the event at http://open4energy.com

    Look to the right – article is titled Downwind Faster Than the Wind

    Not only is it possible, but I had my hands on a model of the principle – working on a treadmill – actually going faster than the belt.

    As I wrote: I began to understand better – how something could go directly downwind faster than the wind – when I realized that the question was not about wind speed, but rather one of conversion of kinetic energy potential. In this case using a propeller to convert the energy potential in a volume of air moving at a speed (wind) into a force that could be applied to wheels.

    I do hope that some of our readers will look further and see the potential for energy efficiency – and think about energy saving.

  48. Timo says:

    Could this work on a sailboat or is friction caused by water too high? Instead of wheels have propellers at the water and instead of sail a propeller. How about using induction AC engine and generator so no direct connection between the two? Too much losses?

  49. Anon. says:

    I feel like there have to be practical marine applications for this. But the physics of marine vehicles is complicated….

  50. Aircargk says:

    If you understand sailing, than you know that you can sail cross wind faster than the wind speed. If you understand sails than you understand that a wind, a sail and a prop blade are conceptually the same for the purpose of sailing (and efficient propeller blade in simple terms is a wid, A wing is a more efficient sail (the advent and of wingsail for high performance sailing is ample evidence of this.) The vehicle is traveling downwind, but the sail is traveling crosswind at a near 45 degree ang to the wind direction (given the blade andle and the speed of the vehicle. The blade (sail!!!) is thus traveling in what sailors call apparent wind, and thus can travel many times faster than the wind. The only necessary element is for the wind to spin the prop with enough torque to overcome drag. Yes it will go much faster than the wind.

  51. John says:

    Simple explanation,
    the “fan” is blowing backwards against the wind, which pushes the cart faster than the wind.
    Initial acceleration is poor as the wind is only pushing against the frame of the cart, and a stationary fan – any downwind movement starts turning the fan via the wheels, which starts to blow against the wind.

    Perhaps a flap to start it moving would help, which could fold down when the cart speeds exceeds the wind speed ?

  52. Tad Hurst says:

    Besides the fact that it has been physically demonstrated, here is the definitive analysis using math and science:

    http://www.tadhurst.com/personal/DWFTTW.htm

    Sorry for the late entry here.

  53. frenk says:

    Ok, so the easiest explanation with the least variables possible I thought of :

    In an ideal scenario comparisons, no losses :

    Windspeed = W
    Force applied to the vehicule = F

    A conventional downwind pushed vehicle would be pushed by a wind until its speed = W thus nothing pushing in the back.

    This DWFTTW machine takes the wind force and throws back the difference between F from the real W and the cart’s speed through wheel and prop , ideally keeping the same wind force on the vehicle at all times/ vehicle speeds.

    Ideal example without loss :

    -At speed 0, wind blows a force F the back structure of vehicle, no force from the wheels, creating initial movement.

    -At car speed (W / 3), the vehicle is blown by 2F/3, + blows back the current inertia power which comes from actual car and prop movement through wheel and prop, which would be the other F/3, the two drafts colide, making the total 3F/3. Nothing gained, nothing lost, just the same windforce redirected on itself.

    -At W, the vehicle is blown by 0*F (no apparent wind), but the inertia of vehicle now sends back a total F, hence same acceleration.

    -At 3W vehicle speed, the vehicle is blown by -2F on its structure (front wind opposite to back wind) , and throws back 3F (from wheel power), still a total F (-2F + 3F) pushing.

    IMPORTANT key here : a positive F means acceleration, so not all of the wind force needs to be thrown back to push the vehicle. The vehicle DECELERATES or stalls when force F – friction reaches 0.

    Cut some F from basic friction and you have a car that accelerates less, then cut the progressive wind friction and you get a max speed at some point.

    So bring all kinds of resistance that grow or not with speed and cut it off F, plus check gear ratio VS torque and you get your max speed and project feasability.

    At no wind speed, you have nothing to throw back.

    Hope this helps, I made it as simple as possible.