Weeble ([info]clockworksaint) wrote,
@ 2008-12-04 00:50:00
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Question for the physics experts
Is it possible to build a mechanical vehicle, powered solely by the wind, that travels directly downwind faster than the wind? It seems there are some big arguments on the internet over this and some Youtube videos claiming to show such vehicles. Here's one that looks cool, but it's not entirely clear what's keeping it steered onto the road, suggesting that the video might be faked, possibly by just towing the thing:

http://www.youtube.com/watch?v=aJpdWHFqHm0

Here's another video of a little contraption of a similar design that is demonstrating the same feat in a difference frame of reference: rather than travelling faster than the wind over a static ground, it travels against the motion of a treadmill in static air:

http://www.youtube.com/watch?v=1pSYALWQ-nI

Now, whether or not these videos are fake, is such a thing possible? We're not talking about breaking conservation of energy or momentum: there's lots and lots of moving air, so we only need to decelerate some of it to speed up our hypothetical cart. It seems unintuitive, but it's not immediately clear that it should be impossible. Pulleys and levers can seem unintuitive the first time you encounter them.

I'm actually inclined to say it's possible. Am I wrong?

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[info]_sideshow
2008-12-04 10:29 am UTC (link)
As a non physics expert, I'm inclined to say you are wrong. If your cart is moving faster than the wind, then relative to the cart the air will be moving in the opposite direction (i.e. the wind powered cart will be moving upwind).

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[info]clockworksaint
2008-12-04 01:37 pm UTC (link)
Yes, that is the case. The cart itself will perceive a head-wind. Crazy as it sounds, I don't think this alone stops it from working. Regular sailing boats can sail up-wind, they just can't sail directly upwind.

Want to build one to find out?

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[info]_sideshow
2008-12-04 01:59 pm UTC (link)
searched for it on sci.physics
The prop acting as a store, saving up energy from strung gusts and then emitting it during relative calm seems plausible, the crux being that the mean vehicle speed is not greater than the mean wind speed. Picture this: you're pelting along heading directly downwind in your yacht, and you hit an area of dead calm. You are now moving faster than the wind in a sailboat.

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[info]clockworksaint
2008-12-04 07:22 pm UTC (link)
That's not what's claimed, and is certainly not what the treadmill test shows. By advancing against the treadmill the cart clearly can attain a mean vehicle speed faster than the mean wind speed.

Another question: suppose you have two long wooden planks, placed alongside each other with space in between. We hold one steady and move the other along its length. Can we construct a machine in the space between them that, using only the planks for motive power, can move itself faster than the moving plank?

====PLANK=A=======================
         *MACHINE*
====PLANK=B=======================


-> ====PLANK=A=======================
         ---> *MACHINE* ?
====PLANK=B=======================


Is this the same problem as the faster-than-the-wind problem?

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[info]_sideshow
2008-12-04 07:40 pm UTC (link)
It's not what's claimed because what's claimed is claimed by a crank.

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[info]clockworksaint
2008-12-04 10:10 pm UTC (link)
But surely you don't consider me a crank (yet)? If it is impossible, I am interested in finding out exactly what makes it impossible. I propose the planks problem because it seems like it may be equivalent, and yet it does not seem so clearly crazy. Plenty of machines move some of their parts faster than the thing propelling them (e.g. a pulley), so what is it that makes the wind-driven machine special? Is it that the entire machine moves? Is it specifically that the mean velocity of the whole machine cannot exceed the speed of the thing pushing it? I believe there is a machine you could place between these planks that does move right faster than the top plank.

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[info]_sideshow
2008-12-04 10:24 pm UTC (link)
Go on then, demonstrate

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[info]clockworksaint
2008-12-04 10:47 pm UTC (link)
Okay, I made a diagram:



You place this between the two planks. The white red peg you fix to the lower, static plank. The redwhite peg you fix to the upper, moving plank. After a short period of time, it has extended. Detach the pegs and fix the pegs at the opposite end:



Again, the white peg is fixed to the lower plank, the red peg to the upper one. After waiting another period of time we have the machine back in its initial state, but it has moved right, and it is further right than the upper plank has moved in the same time.

Of course for this version we have to attach and detach the pegs for it. However, we can observe that this step doesn't involve any work in the sense that it doesn't actually move the machine. It should in principle be possible to contrive a mechanism to automate this, and it wouldn't require any significant quantity of energy.

EDIT - I screwed up the colours in the first diagram.

Edited at 2008-12-04 11:17 pm UTC

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[info]_sideshow
2008-12-04 11:50 pm UTC (link)
Take your basic idea, but change it so that the bottom rests on the ground, and instead of fixing pegs, the peg you are attaching to the bottom creates a firm attachment to the ground, while the other connections to the ground are wheeled. The peg you would be attaching to the top raises a sail, while the other top sail is furled. Once the device extends, furl the open sail, unfurl the other one, wheel the firm attachment and affirm the other. Oscillate.

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[info]biggingerdave
2008-12-06 12:07 am UTC (link)
Having consulted with my beautiful wife, the wind power expert, I now believe it is not possible to travel faster than the wind.

Leaving aside the bizarre scenario where you go faster than the wind is pushing, common sense and energy laws say it's just not possible. Explaining why is a different matter entirely.

OK diagram time:
http://www.flickr.com/photos/crackshot1980/3085078757/
http://www.flickr.com/photos/crackshot1980/3085078741/
http://www.flickr.com/photos/crackshot1980/3085083139/

The first one is a diagram of the relative wind speed of the rotor compared to the relative velocity of the kart. If the kart ever goes faster than the wind speed, then the rotor will be in a region of negative velocity, and try to brake the kart (slowly), making sure the kart is not sucking energy out of the ether.

The 2nd diagram is a quick simulation I knocked up in Matlab trying to see if the kart would go faster than the wind if pushed (or if gearing makes a difference [it doesn't]). The blue is the kart velocity, the red is the wind velocity at a constant. Note that the power available to the kart is the difference between the wind and the kart velocity.

I suspect that the wind is a bit variable in the clips, and it has gusted to faster than the mean wind velocity and has found itself in the 3rd diagram - where the kart is outrunning the wind. It speeds along quite nicely until a faster gust of wind (than the mean wind) pushes it again, and seems to always be faster than the wind.

Word of warning, those diagrams don't include anything like friction, road friction or wind drag, and assume perfect conversion from wind power to wheel rotation, which Jo assures me is impossible due (see Betz' law) .

conclusion:
It is probably going faster than the wind, but that's only because the wind is non-linear. There's no fancy energy storage or breaking laws of physics, it's just a bit of an illusion - it's a bit like riding a bike over a sine wave.

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[info]clockworksaint
2008-12-06 03:25 am UTC (link)
Could you clarify what equations you're using to draw the graphs?

As I understand it, when the postulated cart is travelling faster than the wind, the propeller is turning at such a rate as to slow the wind down, but not so much as to force it backwards. Whether or not you believe it got to this speed under its own power, consider the forces acting upon it. Since the fan is turning fast enough to slow the wind down, there is a forward force on the kart and a backward force on the air. There is also a torque applied to slow down the propeller, which is transmitted to the wheels and transformed into a backward force on the kart and a forward force on the ground. Both of these forces are proportionate to the difference between the speed of the wind and the speed* of the propeller. Their size in relation to each other is determined by the gearing, wheel size and blade pitch, and I do not think it varies with the speed of the cart. We're ignoring friction and drag right now, but are there any other forces I have omitted? Or am I wrong in my analysis?

If the propeller is locked in place and disengaged from the wheels, it acts like a sail and the cart will tend towards the speed of the wind.

If the propeller is geared to blow forward with forward motion, the cart will stabilise in forward motion slower than the speed of the wind. This seems reasonable, no?

If the propeller is geared to blow weakly backwards with forward motion, the cart will stabilise in forward motion faster than the speed of the wind.

If the propeller is geared to blow strongly backwards with forward motion, the cart will advance backwards into the wind.

Of course, drag and friction will spoil all our fun. It's possible that it's just not practical to build such a machine that isn't overcome by these forces.

Does Betz' law matter? Does it matter how efficient the propeller is? I'm not sure.

* - I'm not sure what is the right name for this. Determined by the pitch of the blades, for a given rotation speed of a propeller, there's a linear (axial) speed of wind that will pass through the propeller without exerting a force on it. Blow the wind a bit faster and it will exert a force to both speed up the propeller and to push it forward. Reduce the wind a little and it will exert a force to both slow down the propeller and to pull it backward. Right?

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