Tuesday, June 08, 2010

Flying Before (and Faster than) the Wind

Sometimes you just have to say "sorry." It appears that it's my turn.

Yesterday, I saw a story on Wired touting the first full-scale demonstration of a wind powered machine that can move faster directly downwind than the wind itself is moving. The piece instantly got my perpetual motion scam meter ringing. So I did what any well-meaning physics fan would do -- I flamed the shysters in the comments section of the article.

I now know I was wrong. I spent most of last night a drawing up page after page of force diagrams and pouring over videos like this . . .



. . . in an attempt to figure out how they managed what was clearly a deception. Instead, I have seen the light. I'm convinced that Rick Cavallaro and his buddies at Thin Air Designs and San Jose State University deserve a hearty pat on their collective backs for sticking with their convictions.

My belief that outrunning the wind is impossible stemmed from hours on sailboats as a kid. You can build up a lot speed while tacking across the wind, as these folks demonstrate.



But running with the wind always seemed so dull and slow. I tried endlessly to think of some way to speed up my downwind motion. I talked to countless sailors and physics profs, and ultimately came to terms with the inevitable fact that there's no way to sail faster than, or even at, wind speed if it's blowing straight at your back. That fact still holds true for sail-powered vehicles. Cavallaro, as it happens, didn't build a sail boat, or sail car, or sail anything. I'm not really sure what to call it other than a faster-than-the-wind vehicle.

The problem with the new vehicle is at least in part the challenge of explaining the physics of the thing. In short, it exploits the difference in the motion between the air and the ground. There's absolutely nothing wrong with that. There's no perpetual motion or free energy involved. Once you take energy out of the system, you're free to use it anyway you like, including outrunning the wind. If you can use a windmill to collect energy when your sitting still, then you should be able to continue collecting energy when you're moving. You just have to be clever about how you do it.

The key to the new vehicle is that part of it has to be connected to the ground and part has to be immersed in the air, and that there has to be relative motion between the two. In other words, you can't have a a propeller scavenge energy from the wind in order to turn a propeller that moves you along. Nor can you have a wheel that steals energy from your forward motion over the ground in order to turn drive wheels that move you forward. Those would be examples of perpetual motion machines. I could, however, build a machine that has a paddle wheel immersed in a running river and wheels on the adjoining shore that could outrun the river that powers it (maybe Rick Cavallaro could make one of those next). It would be a tricky thing to design, but it should work just fine.

I freely admit that my 180 degree conversion from yesterday to today has me a little nervous. If I could be so convinced that outrunning the wind was impossible at one moment, and then convinced that it's entirely possible only 24 hours later, then what's to guarantee that I'm right now? Epiphanies are like that I guess. But just to make sure, I'm going to build a model myself. Once it's done, I'll show it to my friends and colleagues here at the American Physical Society to see what they have to say about it. I'll report back as things progress.

-Buzz

8 comments:

  1. You rock Buzz -- we appreciate folks who aren't satisfied with only intuition. Good luck on the build and please keep us posted on your expoits.

    Thin Air Designs (JB)

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  2. Care to post your calculations and such? I am skeptical of this, but open to the possibility if the free body diagrams and math can be provided. As it sits, I can not see how this is possible.

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  3. Calculations:

    http://forum.woodenboat.com/showpost.php?p=2062356&postcount=34

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  4. Buzz, Rick Cavallaro here. Nicely done! Very few people seem to be able to come back and admit they got it wrong initially. But that's the whole point of this thing. It's a brainteaser. That's literally why I conceived of this vehicle (and later learned that I wasn't the first to have done so).

    I love the fact that you're going to build one. If you check out my build videos on YouTube (search spork33) you should be able to knock one out pretty quickly. I provide all the part numbers and where to buy them. Please let us know how it goes.

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  5. Let me try to figure this out:
    Sails make use of the relative velocity between the sail and the air to extract energy. Hence sail-powered vehicles do not move faster than wind.
    If the first video is an accurate representation of vehicle operation, then it must be that the propellers are doing the work (converting rotational kinetic energy to translational kinetic energy, eventually). But to get the vehicle to start from rest is slightly different from what is shown.
    There is no free energy since it comes from moving air anyway. Another way to see it is that the machine will never acquire infinite energy, since the air resistance will eventually overcome the driving force.
    What this machine does is to allow energy conversion/extraction to take place at a higher velocity than the wind speed. The moving air should actually lose energy, but I don't see any way to measure that.
    That brings us back to the first video, where the air can be regarded as still. So where does the energy come from? My solution: if you regard the air as still, then the treadmill is moving, and it is providing the energy. On the other hand if you regard the treadmill as 'still', then the air must be moving. By Galilean relativity there shouldn't be a difference in these two cases, so we now have two ways of thinking about the problem.

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  6. Anonymous, that sounds about right, the energy comes from the difference in the speed of the air and the ground (or treadmill). So Galilean transformations to the case with the wind sitting still make analysis of the problem of moving at wind speed clearer. It's still a bit tricky when you try to understand what's going on when it travels FASTER than the wind, though. @Rick, thanks! I was a little grumpy there for a while as I tried to figure it out. But it's very satisfying to see the answer. I'm glad to have heard about it as a result of your vehicle. Thanks also for the information about the parts list -- it will make building one a lot easier. I hope to demonstrate it on our treadmill in the office gym and see what a bunch of physicists think about it. Should be fun!

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  7. On another note, you should also consider some other things you wrote a few years ago in haste; being wrong about people is no smaller of a deal than getting physics wrong.

    sister

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  8. Anonymous CowardJune 15, 2010 at 7:54 PM

    >The problem with the new vehicle is at least in part the challenge of explaining the physics of the thing.

    It's easy to calculate; it's just freshman physics. And I occasionally teach freshman physics. Here's something I posted on another doubter's site.


    Assume:

    Car with wheels and a propellor on top.

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

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

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

    1-D problem

    Velocity of wind relative to ground: Vw

    Velocity of car relative to ground: Vc

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


    1) Wheels free-spinning. Propellor locked in place.

    By inspection, the equilibrium solution is Vc = Vw



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

    By inspection, the equilibrium solution is Vc > Vw



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

    What's the equilibrium (net power into battery = 0) solution for Vc? Let's work it out!

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

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

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

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

    (In the above, we have neglected any sort of turbulence, etc by assuming the only energy imparted to the air is that associated with the change in its net momentum. Those neglected effects will degrade the performance of the system.)

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

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

    Holy cow! There's no condition on Vc! You can go as fast as you damn please directly downwind! (In this overidealized frictionless, turbulence-free version).

    To get a finite velocity, we will have to introduce a bit of loss into our system, which we will model as a power loss which is linear in the difference in the velocity between the car and the wind. To make the equations work out nicely I'll take this power to be L * D * dMdt * (vc-vw). This leads to a revised energy equation:
    (1/2) * dMdt * ( ((vw-vc)-D)^2 - (vw-vc)^2 ) = D * dMdt * Vc - L * D * dMdt * (vc-vw)
    which we solve to find
    Vc = Vw * (1+L)/L - D/2L

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

    Examining the limits, we see that at large L (where most of the work we do stirs the air without getting a propelling force) we have the expected limit Vc -> Vw. As L -> 0, we have Vc -> (Vw - D/2) / L.

    That's the energy conservation version of directly-downwind-faster-than-the-wind. Counterintuitive? Certainly. C'est la vie.

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