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Own the Controversy! Blackbird DDWFTTW Up For Auction!
Alsee writes "Center of flaming controversy across the Internet and here on Slashdot for claiming to travel 'Directly Downwind Faster Than The Wind, Powered Only By The Wind, Steady State' (DDWFTTW), the Blackbird is now up for auction on Ebay. It has been certified by the North American Land Sailing Association and Guinness World Records to have reached 2.8 times wind speed directly downwind and was subsequently modded to also achieve more than double windspeed directly upwind. It has been the subject of an MIT physics paper and was included as a model problem in the International Physics Olympiad, yet many still argue it would violate the laws of physics. Let the bidding (and debate) commence!"
Seems like a simple conservation of energy problem to me. Why compare wind speed to a vessel's speed? Wind would be better measured in terms of flux. If it can impart enough energy on the vessel, of course the vessel could go faster than the wind.
DDWFTTW? WTF? UUDDLRLRBA?
A squid eating dough in a polyethylene bag is fast and bulbous, got me?
...please check out the jet plane on a treadmill that I'm auctioning off - free shipping if it gets airborne!
I love the DDWFTTW controversy because I initially was convinced it had to be rubbish then revised my opinion as I convinced myself it was possible. As you note from an energy conservation argument it isn't that bothersome. TO see this just imagine the following. Stop the vehicle. Let it suck up some energy. Then let it power itself downwind. It's easily possible that the net downwind speed averaged over the stops could be faster than the wind. Now you just have to extend that to the infinitesimal limit. Thus energetically no problem.
The problem is that it's mind bending to figure out the forces involved. How can wind push anything faster than the wind? Even if you rationalize that with the angle of attack on the proellor or something, you then have to ask, well then doesn't the apparent wind (the wind as seen by the moving cart) lead to a positive feedback loop (faster than the wind --> more power to go faster than the wind --> increased speed faster then wind --> .... ). Like wise how come a cart that is not moving at all, could not be pushed to create some apparent wind, then propel itself using that? Clearly, the gain on that feedback loop has not only to be less than unity, but it has to have a very special curve that leads to net integral such that a cart that is shoved on a windless day cannot go faster (on average) than the shove would provide. Otherwise I think you have a paradox.
It's this latter subtely that I can't connect all thr way through all the complicated force arguments.
Now when the wind is blowing, we know the force arguments have to be valid for a very simple reason. We already know that sailboats not heading directly downwind can go faster than the wind in the net downwind direction. They do this by jibing (i.e tacking down wind) in a zig zag path. If you were to drop a large black box over such a sailboat then you would not be able to see the actual motion of the boat, but you would see a black box going directly downwind faster than the wind. thus we know this happens empirically. It's not some werid stored energy issue. the forces directly allow this. but it's hard to figure. Even the apparent wind effect of increasing the effective windspeed on a sailboat is real.
So it's only truly mindbending at the second order level of how somehow the force argument still has to conserve energy.
Some drink at the fountain of knowledge. Others just gargle.
You might be careful using the word stupid. It is likely that everybody occupies both sides of the effect in different areas of knowledge. Skilled versus unskilled is not the same as smart vs stupid. ;)
...violate the laws of physics, too. Because that's really all that this is: a form of leverage that multiplies speed while decreasing force.
"How to Do Nothing," kids activities, back in print!
The story is quite simple. The propeller pushes against the air, its positive effect is affected by the difference in speed between the craft and the air. The propeller is driven by the wheels, so its negative effect on the craft is due the the difference in speed between the craft and the ground.
If you have a wind, the craft-to-ground speed is different from the craft-to-air speed. The vehicle can extract energy from this difference - like any sailboat, really - and pull ahead of the wind.
1. Force equations? The force backwards on the wheels is proportional to the groundspeed, the force forwards on the propeller is proportional to the airspeed. If groundspeed exceeds airspeed, as it does travelling downwind, there is an unbalanced force. If losses could be eliminated, the craft could travel at infinite speed (until relativism takes effect!)
2. If you give it a shove, without wind, airspeed == groundspeed, so there is no unbalanced force. Losses are all there is, so it slows down.
Prediction for end of Universe #42: Fencepost error in Quantum_bogosort.cpp
Arggghhh. the slashdot formatter ate my less than sigh. I meant to write "consider the case V_land LESSTHAN V_wind.
Is that the one of resignation when trying to write formulae on slashdot?
If you want a vision of the future, imagine a youtube comments section scrolling - forever.
The shortest answer, the key insight is that the wheels drive the propeller.
Therefore, it isn't the wind speed relative to the vehicle that matters. It's the wind speed relative to the ground. Energy is extracted from the vehicles ground speed, producing a backward force X. That energy is transferred to the surrounding air producing a forward force Y. Since the surrounding air is moving more slowly than the ground relative to the vehicle, so long as your propeller is sufficiently efficient, Y will be larger than X.
To answer your second question, in that situation the air and the ground will be moving at the same speed. No matter how efficient your system is, there's no speed differential to extract energy from.
It's a thing that has to do with where the wind interacts to provide power to this particular vehicle. Although the wind is hitting the vehicle flat on (dead downwind), it's not doing that relative to the actual blades of the wind turbine powering the vehicle. When you look at where the wind is hitting the blade surface, it's still deflecting off at an angle. And considering that the blades are rotating, the effect is the same as having a regular sail which is moving at some angle to the wind. (It's all relative to how you look at it. And most people think the principles of relativity is just a nuclear physics kind of thing.)
Also the power here comes from the airspeed difference relative to the ground, and the same concept also works on water. (Because like the ground, the water isn't going to be moving at the same speed as air.) Interestingly enough, if you can exploit the airspeed difference over a wind-shear boundary the same concept may even work for aircraft. Something that may work is using tractor kite or turbine on a tether at a different altitude where winds are much higher, or perhaps flying at the very boundary of a strong wind shear and using the mechanics of that to gain momentum.
In this case, it's wheels driving a propeller, but I think the other way could work too. See this animation for a good intuitive reason as to why it works
http://sifter.org/~simon/journal/20101107.h.html
It's the movement of the wind relative to the ground that's important (to avoid the perpetual motion stuff), and the relative forces required in air vs on-ground. The animation clearly shows how a simple geared machine can move in the opposite direction to the motive force (and faster), aor move in the same direction. In this case, the prop is the inneficient mechanical interface to the wind,
Like wise you you put in that magic moment when V_land-V_wind = 0, for another silly result.
V_land-V_wind = 0 is saying V_land=V_wind. If the velocity of the air equals the velocity of the ground, then someone standing on the ground sees zero_velocity_air. So what you're looking at is the case where there's no wind blowing. No wind means no power source, which means zero force generated. The "silly result" equation was:
F * v_land = (1-alpha) * F * (v_land - v_wind)
Filling in the zeros gives:
0* v_land = (1-alpha) * 0 * (0).
Getting a force of zero and "zero equals zero" isn't unusual when you're looking at the zero power case. The only possibly odd detail is that v_land is free to take on any value. That simply reflects the law of inertia and the fact that you could start the cart at any speed. Zero power provides zero generated force, yielding an any-speed cart in an inertial coast.
P_wheel = F * v_land
P_air = F * (v_land - v_wind)
The person who wrote that equation was sloppy. The F on the first line is NOT the same as the F on the second line. This should clarify things:
Power_extracted_at_wheel = force_of_ground_against_wheel * velocity_of_ground_against_wheel
Power_spent_at_prop = force_of_prop_against_air * velocity_of_air_through_prop
(For clarity: The wheel and prop are attached to the cart, so ground velocity and air velocity both being measured from the cart frame of reference.)
F * v_land = (1-alpha) * F * (v_land - v_wind)
positive number = negative number
That's the equation for finding the steady-state (peak) speed of the cart. That is a cart experiencing zero acceleration. This means the multiple forces on the cart sum to zero. Prop_Force + Wheel_Force = 0, and of course Prop_Force = -Wheel_Force. It's saying the forwards thrust of the prop equals the backwards drag of the wheels.
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- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
I would like to thank the original poster, this is one of the best story I've read for weeks. I should have known this earlier but I didn't... Thanks again for pointing out this enlightening discovery.
First I really doubt it was real, then I wondered how it could be possible, now I understand how it works !
My short explaination: the propeller harvests the wind energy (relative to ground) that was in front of the vehicle. The more it moves forward, the more it stops different masses of air, accumulating wind's forward momentum.