h a l f b a k e r yRecalculations place it at 0.4999.
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If you don't know about vortex rings, what follows will be
gibberish.
Vortex rings are surprisingly stable, and can propagate
over long distances. They have even been investigated as
non-lethal weapons. However, eventually the ring
dissipates. The dissipation must (more or less by
definition)
arise from the interaction between the
boundaries of the vortex ring and the surrounding, still air.
What I propose is a set of concentric vortices, forming a
complete disc (apart from a small hole in the middle).
In a single vortex ring, the air rotates around the large
circle of the torus (ie, the torus is constantly turning itself
'inside out'). The overall movement of the ring is such that
the air on the outside of the torus is turning "backwards",
while the air in the middle is turning "forwards".
If you make two concentric vortex rings, one just inside
the other and travelling in the same direction, it won't
work very well: to travel in the same direction, they have
to rotate in the same direction, which means that where
they meet, the two lots of air are moving in opposite
directions. This means that two concentric vortex rings
will dissipate very quickly by the friction between them.
However, suppose we make *three* concentric vortex
rings, with the middle of the three rotating in the opposite
direction to the inner and outer rings.
Now, the three vortex rings will "mesh", a little like gears:
where two rings touch, the air in them is moving in the
same direction.
Moreover, this triplet of rings should propagate in the
direction determined by the inner and outer rings (think
about the forces).
The idea can be extended to create multiple concentric
vortex rings, as long as they are an odd number.
Why?
Well, a "wall" of 3 (or 5, or 7...) vortex rings stores the
same amount of angular momentum as 3 (or 5, or 7...)
individual vortex rings. But only the first and last ring
experience full contact with the surrounding still air.
Therefore, a circular wall made of concentric, contra-
rotating vortex rings should propagate further and deliver
much more punch.
The secret life of vortices.
http://www.youtube....07M&feature=related
ssshhhhhhh, it's a secret. [2 fries shy of a happy meal, Feb 21 2012]
Just a cool link on vortices
http://www.youtube....watch?v=mHyTOcfF99o
Dolphins and stuff show how it is done. [AusCan531, Feb 21 2012]
Airzooka
http://en.wikipedia...i/Air_vortex_cannon
The "Airzooka" is probably the best-known commercially available vortex generator. [hippo, Feb 21 2012]
Hippo beat me to it, but here's another one anyway.
http://www.thinkgee...warfare/60b6/?srp=1
(Very easy to build on your own too.) [swimswim, Feb 21 2012]
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Annotation:
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Please allow me to be the first to say "If you do know about vortex rings, what follows may still be gibberish anyway". |
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Not that it's true, but I wanted to be the first to say it. |
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And since I was expecting an interesting read about how to construct a tortoise wall, or a walrus / tortoise hybrid, I had to do something to assuage my grief (+). |
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Instructions on tortoise-based walling, and on how
to create your own tortoise/walrus hybrid, will
follow. |
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(+) Not sure why but my gut says; negatory.
You may however be able to turn that negative space vortex ring in the center into your stable vortex ring as the linked rings break apart but it would be inverting in the opposite direction to continue moving forward.
Mind you, seeing a wall'o'toruses spit a tiny vortex ring backwards as they dissipate would be something to see. |
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There is a very cool video simulation of dissipating vortex rings that took some pretty serious computation, I'll see if I can find it. |
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Found it. [link]
Very worth watching. |
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//my gut says; negatory.// |
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Suppose you're looking at the wall'o'vortexes from
the side (ie, all the rings are edge-on to you).
Suppose also that it's moving from left to right. |
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Now take a vertical section. You will see: |
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Now concentrate on the topmost 3 'o's: |
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the top and bottom ones are rotating
anticlockwise, the middle one is rotating
clockwise. |
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How will this system fall apart? |
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No no, I think you got it right. They'll mesh together like gears, I just don't think that they will reinforce one another, it'll just add another factor of instability. (this is strictly a hunch, I have no reason to think it's wrong... it just doesn't feel right)
Where the rings touch each other, the negative-space vortex will not be rotating, but inverting, opposite to the direction of travel. It might be this instability niggling at me. |
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When I run it in my head I see them dissipate slightly faster than normal and then puff a little smoke ring backwards after they do.
<shrugs>
I just calls'm like I sees'm. Don't always know 'why' I sees'm that way.
It's downright frustratin at times I tell ya. |
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I can understand why a single vortex moves forward as the outer wall, possessing more surface area than the inner wall, "pushes" against the surrounding medium which, combined with vortex's initial momentum, helps keep moving it forward. In your posting with an odd number of vortices you will indeed always have a net force of 1 vortex but it is trying to propel a much larger surface area of vortices through the medium which, incidently, has less opportunity to 'get out of the way'. |
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Just as 3 people on one end of a tug-of-war will overcome 2 people on the other end of the rope but the entire system won't move nearly as fast as 1 person dragging the rope on his own. Add in all the extra stresses of trying to move that much surface area through the surrounding medium and I believe the whole system of joined vortices will come apart rapidly and will provide 'less' punch rather than the 'more punch' sought. |
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// If you don't know about vortex rings, what follows will
be gibberish // |
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(Although wallotori sounds like some kinda Anglo-
Italian dish.) |
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First Read: Wall of Trousers. Deeply disturbing. Note To Self: Make Appointment with Optometrist. And Bartender. And Haberdasher. Not necessarily in that order. |
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I reckon if you have 2, same rotation, then the third in the
center (I mean between them) will naturally form. |
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Apologies if I've misunderstood, but when two vortex rings are generated, each ring continually rotates/braids itself around the other one - from inside to outside and back again. Is that because the circulation of each ring pushes against the other? |
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If 3 such rings were generated, would, or would they not intertwine in this way? |
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Can these tori be filled with different coloured smoke? |
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//with an odd number of vortices you will indeed
always have a net force of 1 vortex but it is trying
to propel a much larger surface area of vortices// |
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Yes, but the vortices are maintained by the
angular momentum of the air. With nested
vortices, you have more air spinning. |
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Consider the analogue with solid wheels. A single
vortex is analogous to a single wheel which is set
spinning, then allowed to roll along the ground. A
multiple vortex is like a series of 3 (or 5, 7...)
connected wheels. It takes more energy to get
them all spinning but, once they are spinning,
their greater net angular momentum should keep
them going for longer. |
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On the other hand, your point about the greater
frontal area of the wall'o'vortices is well taken. |
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By jingo, [bigsleep], I think you're right. I take back
all those things I wrote; had printed and distributed;
or said on radio and television. |
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Yes, you are indeed right. A pair of concentric tori
will have only "rolling resistance" against the
surrounding air, and no resistance at the point
where they touch. |
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// First Read: Wall of Trousers. Deeply disturbing. Note To Self: Make Appointment with Optometrist. And Bartender. And Haberdasher. Not necessarily in that order. // |
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First Read: Wall of Tortoises. Deeply disturbing. Note To Selves: Schedul;e urgent replacement of optical scanner systems. And visit to Bartender. And Haberdasher. And Herpetologist. Not necessarily in that order. |
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I think I figured out what is bugging me about this. Please correct me if I am mistaken. |
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While it's true that the meshing of the vortices will cause no disruption to the coherence of the linked shapes, this new linked shape is also travelling through the air, and that air must part to allow passage of the points of contact of each ring. As the parted air re-combines I think that Karman votices will be formed and trail along behind each contact point causing premature vorticulation.
The linked video shows diapoles created at the outer edges of the ring begin destabilizing the vortex.
These linked rings you propose would have a new clover shaped periphery rather than a single round one.
As it destabilizes there will come a point where the inner ring created from the points of contact will become more coherent than the rings themselves and at this point the inverse rotation of this new vortex ring will cause it to break away, shrink a bit, and travel back in the opposite direction. |
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I am tempted to duct tape five air-zookas together and try this out. |
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I think the plural of torus is torum. |
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Since they look like a sphincter, I nominate my fellow American
Rick for Sainthood. Saint Torum. |
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