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roy
Social climber
New Zealand -> Santa Barbara
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Mar 21, 2007 - 01:09pm PT
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A specific case: rapping on the Leaning Tower and at the top of pitch 2 pulling the rope down from the station on Guano ledge. As it fell below me into space it was in a perfect "U" shape with the free end falling absolutely vertically. The crack was probably heard across the valley and the last inch of the rope (10.5mm dynamic) was turned to fuzz.
Cheers,
Roy
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Ed Hartouni
Trad climber
Livermore, CA
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Mar 25, 2007 - 03:21pm PT
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ok, I am descending from the most general theory of rods to a theory of motion in 2 dimensions of a classical, uniform, hyperelastic isotropic strings...
for those interested, I am working through the paper by
J.H. Maddocks and D.J. Dichmann, J. Elasticity, 34, 83-96 (1994)
which is pretty cool.
I'm hoping to be able to write out the dynamical equations sometime today, and then work on a solution to the problem, which simply stated is:
If I drop one end of the rope does that end reach the speed of sound?
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 25, 2007 - 03:33pm PT
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Thanks, Ed! Somehow I suspect the problem is simple to state, difficult to solve. Perhaps ropes sometimes make a "crack" noise - we've all experienced that. I doubt that a rope-end can reach the speed of sound, but think it an interesting question. Hence my suggestion for some empirical measurements, simply to get an idea if it was even in the ball park.
The phenomena of rope ends bursting open is quite mysterious - the forces involved, even if quite focussed on deceleration of the very end, can't be all that great, and must be much less than those generated in even a modest fall. If rope ends do burst open, and it's not simply because a) they're already quite worn, or b) they hit something just as they reach peak (sub-sound) velocity, the physics may be very complex.
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hobo
climber
PDX
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Mar 25, 2007 - 04:52pm PT
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Ed, could you post a pdf or a scanned slide of your analysis? Or email them to me?
Thanks
Alex
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Ed Hartouni
Trad climber
Livermore, CA
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Mar 25, 2007 - 06:43pm PT
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Anders - if the tip hits the speed of sound it is possible that the shock launched in the air is accompanied by a shock launched into the rope. If that is so, the rope response might be to blow apart at the tip. It is hard to see how anything else could cause the "blown tip" phenomena... anyway, I think the correct thing to do is to get the analysis done on the speed of sound and see what the possibilities are.
Alex, once I get the analysis done I'll post a link here.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 25, 2007 - 07:26pm PT
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Thanks, and looking forward to more.
Does a snap/crack noise necessarily imply super-sonic tip velocity? When I shake out my throw rug (about 1 x 2 m, fairly heavy material), it makes a very satisfactory snapping noise. (It helps if the wave from shaking travels parallel to the edge.) Bits of stuff come whizzing off the far edge. As with towels, I somehow doubt it's moving faster than sound. Moving reasonably quickly. Displacing some air, so making a very nice thwack noise. But I'd be surprised if a shaken rug or towel exceeds the speed of sound. Possibly a rope tip, given energy from both falling and from wave motion. We'll see.
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cintune
climber
Penn's Woods
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Mar 25, 2007 - 08:36pm PT
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Just a thought, but blown-out rope tips proably have less to do with the exact sub- or supersonic speed than with the nature of kernmantle construction. As all those little bundles of spiral braids fall, friction along the strands is going to take the form of untwisting that passes down the line, and when the end snaps and recoils, poof.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 26, 2007 - 12:34am PT
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Wow, that was a snappy answer! I still don't believe my rug breaks the sound barrier, but maybe it does.
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 26, 2007 - 12:05pm PT
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I'm hoping to be able to write out the dynamical equations sometime today, and then work on a solution to the problem, which simply stated is:
If I drop one end of the rope does that end reach the speed of sound?
Hmm. This sounds like it is perhaps too simply stated.
For example, if you drop the end of the rope allowing the rest to fall following it, the end of the rope will not likely exceed (or even reach) the terminal velocity of a body in free fall in the air.
In fact, the geometry of the rope when dropped will necessarily be a boundary condition playing a role in the solution. Consider, for example, one end at same height as tied end and the middle of the rope one half rope length (plus a stretch factor) above; or just dropping a coiled rope - imagine what the equation of motion of the tip is in that case!
Or perhaps you hold both ends and drop the rest of the rope, then drop one end. Reverse of the first example above (with respect to the initial location of the middle and which part of the rope is actually dropped).
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 26, 2007 - 06:12pm PT
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I suppose the limiting case would be that you tie one end of the rope to the current rap station and pull the rope such that the end falls from 1/2 ropelength above (with some initial velocity governed by friction of the previous station and the force of the final tug which causes it to come free) and the bottom of the rope is 1/4 rope length below the current rap station.
Or the two rope version of above with previous rap nearly 1 rope length above.
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CAMNOTCLIMB
Trad climber
novato ca
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Mar 26, 2007 - 07:16pm PT
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The only thing I hope for when I toss a rope is that it reaches the ground.
The only snap I hope for is a cold one headed for my thirsty lips.
Brian
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Jun 27, 2007 - 12:53am PT
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bump.
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Ed Hartouni
Trad climber
Livermore, CA
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Jun 27, 2007 - 01:01am PT
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geeze... here's the problem (besides not having time to work on this lately)..
As the rope falls, a wave is launched down its length. So the calculation of the conditions under which the tip exceeds the speed of sound is complicated by the combined rope kinematics and the wave dynamics.
It will be simple once I derive the special case for the rope... but I haven't gotten there yet.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Jun 27, 2007 - 01:04am PT
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Thank you! I was just curious, and suspected it was more complex than it seemed at first blush.
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Tom
Big Wall climber
San Luis Obispo CA
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Jun 27, 2007 - 11:49pm PT
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From way back when, the tip speed of the 78-inch propeller turning at 2500 RPM is only 850 FPS, not 1700. The radius of the prop is only 39 inches, not 78. 850 FPS is about 260 meters per second, which is less than the speed of sound at standard sea level conditions. Sometimes you can hear the rotor of a helicopter cracking, because the air flowing over the tip exceeds the speed of sound. This is typically during high-angle maneuvering at speed.
Supersonic flow at propeller and rotor tips is undesirable, and is what limits the speed of prop airplanes and helicopters. The military has spent $$$$$$ and decades trying to make a V-22 Osprey-type tilt rotor aircraft practical, to get vertical take-off and high speed capability in the same machine.
The solution to the rope whipping problem lies with considering the conservation of angular momentum. The product of the velocity and the radius of the loop must be a constant. When the falling loop reaches the end, the radius is rapidly reduced to near zero, and the velocity increases dramatically. For a reasonably large initial loop radius, the tip goes supersonic - POP!
If you drop the rope so it doesn't form a large loop, you won't get the supersonic afro poof-pop.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Jul 2, 2008 - 05:05pm PT
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Recent speedy ascents of the Nose of El Capitan bring this question to the forefront again. Did Hans' and Yuji's rope exceed the speed of sound?
I don't imagine that relativistic or quantum tunnelling effects were observed, though Doppler shift doesn't seem out of the question.
Afterthought: I wonder if the snapping effect is from deceleration, rather than acceleration? That is, the tip of the rope is going at a reasonable speed, say 100 metres per second. It decelerates pretty quickly.
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sawin
climber
So., CA.
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Interesting Ed,
My nunchuks traveled at over 90 mph however my
hands were not moving that fast. My chain nunchuks
were not as fast.
I'm wondering if the ascension or opposite reaction
from a broken rope could exceed the sound barrier
otherwise I have doubt?
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