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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Original Post - Mar 6, 2007 - 10:38pm PT
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The current Rock & Ice (#157) has an article in the "Ask Gear Guy" section (page 82), which says that the tip of a falling rope may exceed Mach 1. The question was posed by someone who pulled rappel ropes on a near-vertical wall. The rope end went by, and they heard a loud crack. When they got to it, the end had "exploded into tatters".
The reply says "When you pulled your cord, the tail of your new rope cascaded down in a loop, rather than falling straight. When the loop straightened as a result of the rope coming taut on the anchor, the tail accelerated at such a speed it created a vacuum in space. The cracking sound you heard was made by air rushing back into the vacuum, creating a mini sonic boom... The cracking of a bullwhip is identical to what your rope experienced.."
Is this possible? How fast can the end of a falling rope go?
Edit: Wikipedia says "At sea level, at a temperature of 21 °C (70 °F) and under normal atmospheric conditions, the speed of sound is 344 m/s (770 mph or 1238 km/h)."
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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I am guessing (a little bit).
The end of the rope could go the speed of sound in nylon, which is probably higher than the speed of sound in air.
BTW. The same is true and is well known for hemp, leather, and the various materials that one can make bullwhips from.
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Ed Hartouni
Trad climber
Livermore, CA
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http://www.npr.org/programs/wesat/features/2002/june/whip/index.html
Phys. Rev. Lett. 88, 244301 (2002)
Shape of a Cracking Whip
Alain Goriely2,1* and Tyler McMillen2§
1Department of Mathematics, University of Arizona, Tucson, Arizona 85721
2Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721
Received 4 March 2002; published 3 June 2002
The crack of a whip is produced by a shock wave created by the supersonic motion of the tip of the whip in the air. A simple dynamical model for the propagation and acceleration of waves in the motion of whips is presented. The respective contributions of tension, tapering, and boundary conditions in the acceleration of an initial impulse are studied theoretically and numerically.
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JuanDeFuca
Big Wall climber
Stoney Point
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It is impossible for a climbing rope to go supersonic.
Its to limp.
JDF
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Landgolier
climber
the flatness
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Possible but kind of weird -- taper is a big part of what makes a bullwhip work. Also, the mag explanation of sonic booms is not quite right (gasp!), by that explanation fastballs and corner kicks would go boom as well.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 7, 2007 - 12:34am PT
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I guess it may be possible for a cracking whip to be supersonic - perhaps a radar gun could be used to measure the tip speed, as empirical proof of the model.
It sounds like it's not the rope's falling that gets it going so fast, but a wave propagating along its length. I still wonder if a rope tip can be supersonic - the tip damage referred to in R&I could have been caused by impact at fairly high but sub-sonic speed, but with a rough surface. An interesting challenge, to design a valid model, or experiments.
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Ed Hartouni
Trad climber
Livermore, CA
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I'll download the paper tomorrow and take a look...
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 7, 2007 - 01:31am PT
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Thanks, Ed. It doesn't help that the terminology used in the R&I article is less than precise. An interesting question, anyway. It's a bit like "does a snapped towel break the sound barrier?" It makes a nice cracking noise, maybe from displaced air, but is far slower than 344 mps. My guess is that it's the same with ropes. They're also fairly thick and don't flex all that fast.
Looking at it another way, if even the tip of a rope - say the last few metres - was going the speed of sound or anything even close to it, that implies a fair amount of force when it hits something. Ropes damaged by being "whipped" open, and rope-concussed climbers, are rare.
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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More likely the last (few?) millimeters.
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wootles
climber
Gamma Quadrant
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I made static ropes that routinely go supersonic...
behind an F-16.
Way cool rig. The F-16 tows a target practice drone at supersonic speed while dudes shoot at it with a .50 cal.
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Euroford
Trad climber
chicago
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while bigwalling on the diamond last year i just loved the mid afternoon when everybody began bailing off the free routes. crack crack crack over and over as each party tossed there coils down the face.
cool stuff!
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Mr.T
Big Wall climber
topanga
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While dealing with ropes on overhanging wall routes I have the whip-cracking happen all the time. The ends of these ropes frequently burst open, creating a cool afro-like tip. Whatever the explanation, it happens all the time.
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Landgolier
climber
the flatness
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I'd forgotten about it, but the same thing can happen with a fly rod if you practice casting without a leader. BANG!!! and then you have to cut off a couple of inches of line.
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Kevster
Trad climber
Evergreen, CO
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Well just thinking out loud, but it seems that the cracking action is due to doubling the speed of the object as it passes some radial point and slingshots past. So if the length of the rope is falling at x speed, the end of the rope could potentially double this speed by picking up momentum around the radial point. Am I smoking crack?>
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G_Gnome
Boulder climber
Sick Midget Land
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I think you would have to add in the change in momentum caused by the bulk of the rope actually ceasing to fall too.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 9, 2007 - 06:34pm PT
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bump, for the Friday-afternoon physicists.
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Ed Hartouni
Trad climber
Livermore, CA
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I have the paper today, looks approachable... stay tuned....
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HighDesertDJ
Trad climber
Arid-zona
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So Ed are you saying that a whip crack is essentially a little sonic boom?
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JuanDeFuca
Big Wall climber
Stoney Point
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Ropes are to limp to make Shock Waves?
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G_Gnome
Boulder climber
Sick Midget Land
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Ho man, I am feeling saucy today. If you only knew what I almost posted in response to Juan there.
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Ed Hartouni
Trad climber
Livermore, CA
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Mar 10, 2007 - 12:37am PT
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A progress report on the paper...
...it probably does have all the ingredients for determining the velocity of the rope, and whether or not it is possible for the rope to exceed the speed of sound and emit a shock wave we hear as a crack.
The ingredient is a loop. In a wip this is a distinctive feature of making the crack. It turns out that in the case of the wip, the tapering of the wip from the handle to the tip is an important part of the explanation. Of course, ropes don't taper.
Another difference is that the loop "falls," it's accelerated by the earth's gravity, and that same gravity puts a tension gradient in the rope, the tension is higher near the top of the rope than at the bottom. However, it still seems somewhat difficult to understand how the rope loops get to such high velocities, even in the wip scenarios.
More later
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 14, 2007 - 10:12pm PT
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Bump. In case any of the resident physicists, and would-be physicists, haven't seen it already.
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Ed Hartouni
Trad climber
Livermore, CA
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Mar 15, 2007 - 12:44am PT
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I'm still working on it...
...here's how it might work.
Tie the rope end to an anchor and through the coiled loops over the edge. Let's not get complicated, the rope free falls, never in contact with the wall.
The loops accelerate as they fall, uncoiling along the way. My first estimate of the speed at which the rope falls is just the free fall velocity at the end of a rope of length L:
v = sqrt(2gL)
where g is the acceleration of gravity, roughly 10 m/s/s.
For a L = 60 m of rope, this is 35 m/s (about 78 mph).
The top of the loop actually travels at twice the speed of the loop, or 70 m/s... but the speed of sound at sea level is something like 330 m/s, the velocity is off by an order of magnitude.
Based on the cheesy kinematic estimate I'd say a rope can't crack like a wip.
However, the wip is more complicated and a proper dynamical analysis has to be done. Basically, the acceleration of the loops has to be taken into account properly. The tip of the rope as it wips through the air can be accelerated by factors of 10 or more then the loop velocity. If this were so, then the rope could crack, it's tip exceeding the speed of sound.
But the analysis has to be done.
So far, I'm looking at the following references:
A. Goriely and T. McMillen, Phys. Rev. Lett. 88 2443011 (2002)
R.S. Falk and J.-M. Xu, SIAM, J. Numer. Anal. 32 1185 (1995)
B.D. Coleman and J.-M. Xu, Acta Mechanica 110 173 (1995)
and I haven't quit my day jobs yet.
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Ed Hartouni
Trad climber
Livermore, CA
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Mar 15, 2007 - 12:50am PT
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the speed of sound changes with altitude:
340 m/s at sea level
334 m/s at 5,000 ft
328 m/s at 10,000 ft
322 m/s at 15,000 ft
it looses 6 m/s for every 5,000 ft elevation gain, or 1.2 m/s every 1,000 ft... so at altitude in the mountains it might be more likely to happen than at sea level...
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 15, 2007 - 11:01am PT
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My memory of this is that the swing of the whip imparts a certain kinetic energy to essentially the entire rope. So the energy is approximately 1/2 mvv where m is mass of rope and v is the velocity of the hand (rope) while the rope is essentially in a straight line behind the whipper.
Then the hand stops. So the rope held in the hand stops, but most of the kinetic energy has not yet been converted to heat. As a result some of the rope must be accelerated (conservation of energy).
As the mass of the moving part of the rope declines, the velocity (squared) must increase. So the key is to have a small tip, giving low mass and smaller turning radius. It is the turning radius that allows for the mass to reduce more than linearly with the amount of "uncracked" rope.
Of course, this unquantitative analysis does not address the question of whether it would be easy to reproduce in a climbing rope. But it does seem, at least qualitatively, to me that it would be more likely in a static rope than a dynamic one.
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G_Gnome
Boulder climber
Sick Midget Land
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Mar 15, 2007 - 01:06pm PT
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Are you sure you are going down the right path here? Seems to me the most relevant piece of data to look at is the unrolling of the end loop once the rest of the rope ceases to fall. And I just don't see how a static rope is going to be substantially different than a dynamic rope given the small loads (ie. it's own weight) on the rope.
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 15, 2007 - 01:34pm PT
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g-gnome.
Pretty sure the analysis of the whip and falling (whipping) rope is the same.
As far as the static vs dynamic...
Static rope would exert higher force regardless of the load, so higher acceleration and resulting higher velocity.
Another way of looking at it is that the kinetic energy of the rope is reduced by the work done stretching the rope (Force times distance). Hmm, maybe that explanation is not so clear.
In fact, I guess I could find a way to question both of the above qualitative arguments. The acceleration is surely higher with the static, but it is accelerated for a shorter time (less stretch).
Kinetic energy argument is also less clear. If static will, in fact, retain more kinetic energy for the whipping action, then it stands to reason that it is heated less.
Ok. rambling over. Static rope stretches less (by definition). So the potential energy of the dynamic rope is lower at the end of the fall. Since it is lower, the dynamic rope must have heated more than the static, since they both have zero kinetic energy at the end.
So less heating means the final kinetic energy of the tip was larger. (I think - anybody disagree?) :-)
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 15, 2007 - 01:50pm PT
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hmm - are densities of static and dynamic rope the same? arg.
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G_Gnome
Boulder climber
Sick Midget Land
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Mar 15, 2007 - 02:31pm PT
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I just meant that I suspect that the actual velocity from falling is a small part of the whole, it is probably the whip (which I know gets it's momentum from the fall) that accounts for 90% of the total. Also, I can get a 'not very tapered' fly line to snap even without a tapered leader on the end by casting too fast. It is pretty hard to get a snap unless you actually change direction of the line before the line has straightened out that enables the tip to whip fast enough to actually crack, yet that change in direction is not going to happen with a falling climbing rope.
Good luck with the math on this one!
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 20, 2007 - 05:45pm PT
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Ed, here is another reference. I do not have easy access, but found this in "The Physics of Golf".
B. Bernstein, D. A. Hall, and H. M. Trent, "On the dynamics of a bull whip," J. Acoust. Soc. Am. 30, 1112 (1958).
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 20, 2007 - 06:45pm PT
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I wonder if this is one of those deceptively simple seeming problems, that in fact is more complicated than it seems.
There are some variables - rope stiffness, elasticity, diameter, length, and wear, whether it is in contact with itself or the rock as it falls, what kinds of wave patterns it makes. (Presumably a fuzzier rope has more air resistance.) Leaving those aside, it would be interesting to do some empirical tests, on an overhanging wall, and use a radar gun to see what kinds of velocities are attained. There'd have to be lots of repeats, measuring from different angles and so on, but it might fairly quickly give an approximation of the possible velocity.
Looking forward to more on this, though I know Ed's quite busy right now.
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ChrisW
Trad climber
boulder, co
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Mar 20, 2007 - 07:10pm PT
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The article also said there's noway to advoid the crack. With a little practice there is a technique to advoid it. Can't really explain it very well. But i will try. I guess all u do is keep a few feet of rope in your hand and release right when the end of your rope is going to crack. Some how this works.
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Klimmer
Mountain climber
San Diego
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Mar 20, 2007 - 07:12pm PT
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Yes, it is very possible to make something go faster than the speed of sound which is appox. = 340m/s at normal room temperatures (speed of sound also varies with temperature).
When a Bull-whip is used properly, the tip goes faster than the speed of sound and the crack you hear is a mini "Sonic Boom."
Ever use a wet towel to slap your friend on the bum? Have you ever made the same towel crack sharply in sound? If you have, then my friend you made a small sonic-boom. The towel went faster than the speed of sound.
When a car backfires, the exhaust is expelled faster than the speed of sound and you get a large "Sonic Boom." Ever wonder why the tail-pipe doesn't explode when you hear that backfire? Because the gases travelling faster than the speed of sound through the tail pipe, don't make the "Boom" until the gases hit the atmosphere right at the opening. Some back-fire sonic booms can be unbelievably loud, but no damage.
Google, "Sonic Boom in a Bottle" for a great experiment to do. I do this demo for my Physics students, and we get gases to go faster than the speed of sound coming out of a 1 liter bottle and it makes a great big sonic boom, but the plastic bottle is left intact. I 've been using the same bottle for about 7 years, doing this demo for my students.
Bullets flying over head make a sharp crack sound. It's a mini sonic boom! Etc, etc.
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 20, 2007 - 08:48pm PT
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Can we assume that because the tip of the whip exceeds the speed of sound that any air does?
For example, the diameter of a Cessna 177 propeller is 78 inches. At 2500 rpm the tip travels at a speed of 1700 feet per second or over 1.5 times the speed of sound.
But what does the air do? Does any air move at the speed of the tip? The plane only cruises at that rpm at about 140 knots.
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scuffy b
climber
The town that Nature forgot to hate
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Mar 20, 2007 - 09:06pm PT
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The propellor is designed to minimize the speed of the air. It's
just supposed to part and rejoin at the trailing edge.
Maybe a chewed-up prop could make booms.
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TradIsGood
Happy and Healthy climber
the Gunks end of the country
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Mar 20, 2007 - 09:17pm PT
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That is my point. And it also rolls over at the tip in a vortex, which may be turbulent, but I do not expect air velocity would be supersonic. (But I am not aerodynamicist.)
But one could imagine that the air simply flows around the tip of a whip or rope and never reaches the speed of either.
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Kevster
Trad climber
Evergreen, CO
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Mar 21, 2007 - 01:12am PT
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Thought I would add on the static vs dynamic that I have had both types of ropes go "Boom" and blow apart their ends when dropped on an overhanging face.
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gunsmoke
Trad climber
Clackamas, Oregon
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Mar 21, 2007 - 10:55am PT
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I watched my rope end crack on a drop from an overhanging route. Blew out the last inch into a fray. The end didn't make contact with the wall at the point of the crack. ChrisW is right about being able to prevent it. When I chuck a rope I give a slight upward tug just before the tip reaches its bottom point.
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scuffy b
climber
The town that Nature forgot to hate
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Mar 21, 2007 - 11:09am PT
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Maybe the tip of the propellor on that Cessna is actually
creating sonic booms. The task is not to get air moving along
with the prop tip, rather to get the tip moving fast enough
(there's all that power) to "outrun" the rejoining air at the
trailing edge. That might create a tiny moving, ever-collapsing
vacuum continually booming upon collapse.
When accelerating a propellor, is there a speed where the noise
level increases suddenly?
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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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Ed Hartouni
Trad climber
Livermore, CA
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I have a mechanical model of a rope that I have to bust out on your guys...
...later tonight
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Jul 2, 2008 - 06:08pm PT
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If you want, I have a REAL rope that you can use for experiments. 60 m x 10.5 mm, somewhat used.
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tolman_paul
Trad climber
Anchorage, AK
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I'm glad to have had my last physics class 20 years ago. Just thinking about what would be needed to model this makes my head hurt.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Feb 25, 2009 - 03:37pm PT
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Then there's this one - outstanding business.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Mar 20, 2009 - 02:13am PT
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Still interested in the answer. There's a readable summary of the Goriely paper that Ed refers to near the start of the thread at http://www.spacemart.com/reports/Whip_Cracking_Mystery_Explained.html
Analyzing whips, concluding that a main factor allowing them to go supersonic at the tip is that they're tapered. Although unlike climbing ropes, which passively fall, whips are also given energy by hand motions.
Anyway, it does seem an interesting question. I wonder if it may take both theory and empirical results to determine the answer?
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Brock
Trad climber
RENO, NV
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Mar 20, 2009 - 10:43am PT
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I was repelling from Dolt once and I think it was my static line (could have been my lead line too though) but I remember it making a super loud "crack!" It does and can happen. So, if I am farting and it is loud, is it supersonic or is it just my butt cheeks are that tight???
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Greg Barnes
climber
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Jul 15, 2009 - 07:03pm PT
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When we were replacing bolts on Rock Warrior on the Velvet Wall after finishing up Dream of Wild Turkeys and Prince of Darkness, I would rap down a 100m 11m static, replace an anchor, rap to the next anchor, replace and fix the line, then they'd drop the rope and the other 3 guys would replace the pro bolts on the way down. The Chief was down at the base warning people off of the routes (good thing since we dropped a few hangers). One team decided to ignore The Chief and go up anyway on Prince of Darkness.
The guys 2 anchors up dropped the rope (I had a backpack to cover myself with as I hugged the rock), and the 100m static went zipping by, then made a louder-than-a-high-powered-rifle "crack" that echoed up and down Black Velvet Canyon. The core popped out as well.
But that was only a few feet away from the leader on Prince - I wonder if he actually crapped his pants or not...
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Mighty Hiker
Social climber
Vancouver, B.C.
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Topic Author's Reply - Jul 16, 2009 - 03:23pm PT
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The phenomena that wes mentions is interesting - it suggests that one possibility is the core of a kernmantle rope separating from the sheath, perhaps due to mass, density and other considerations, and literally 'popping' off the melted end. The cores of ropes do shift within the sheath, and they have different characteristics. Greater density suggests greater energy, which if directed along the axis of the rope could explain it. The core essentially blows the end off the rope.
I suspect a theoretical analysis of this problem may be complicated by the rope not being a single uniform body.
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Ed Hartouni
Trad climber
Livermore, CA
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OK, Anders really really wants an answer to this... so I've been thinking a bit about it for a while and will try (really try it is not so easy to do) to come up with an answer... but just to wet your appetites here is a picture of a rope at the bottom of the drop:
the numbers are the "strobe" flash, this was set up to be 24 flashes, each 1/30 of a second apart. This was set up pretty quickly just to see what I could do with my SB-28 Speedlight and the Fujifilm S5-Pro... came out ok...
what you see is that the distance from strobe 3 to 4 and strobe 4 to 5 is very big compared with the other inter strobe distances, which is the rope end accelerating.
Given a rope constituent model it may be possible to calculate the equation of motions and see just how fast the rope end can go under various drop conditions. It is possible that the rope acts like a whip, and the crack is the rope end exceeding the speed of sound. That shock wave could put forces on the rope tip that exceed the strength of the material...
...but I don't know yet. Anyway, there seems to be a hint of a path in getting to a reasonable solution.
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 4, 2010 - 12:13am PT
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Thanks, Ed! A blast from the past, as it were. Although combined with yesterday's reapparance of the "History of Tube Chocks" thread, it may cause people to start thinking I'm some sort of geek wannabe.
It looks like you've set up an experiment, with falling ropes and strobe photography and so on. Thanks - a lot of effort. It may still be fun to do some empirical testing with a radar gun, to see what happens. Get some old ropes, someone a couple pitches up something quite overhanging, and let fly.
Nice to see that Juan was interested in this one, too.
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Shack
Big Wall climber
Reno NV
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That's cool Ed!
So what is the formula?
Terminal velocity + acceleration calculation = tip speed?
I'm sure it is waay more complex but just wondering the general idea.
I'm thinking that since I can easily make a towel tip break the sound barrier with very little energy input by me (I only have to flick my wrist), that the speed of the rope as it falls is only a small part of the equation, and that the way the end section of rope acts, as it reaches the bottom, is a far greater factor. The more rope that falls will affect the speed at which it falls which helps set up the needed conditions for the whip crack to occur and probably can't happen with a short rope. Rope diameter could be a factor as well.
My $.02
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Ed Hartouni
Trad climber
Livermore, CA
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the way to do the calculation is to have a model of how the rope acts as a solid, I have a model, it's pretty interesting and I'll write it up for this thread...
then you consider the rope as composed as segments that are attached like the model says they should be
constraining one end of the rope to a point in space let the other end fall in a uniform gravitational field in a fluid with finite viscosity, etc, etc... (the "fluid" is the atmosphere)
the trajectory for every point on the rope can be calculated, and the velocity of the rope's tip determined
but I'm a bit of a ways from that right now...
...probably no need for a "supercomputer" as the iBook I'm typing this message out on is a pretty good supercomputer by the standards of my graduate student experience (I think the microwave in the kitchen has a more powerful CPU then the one I used to do the data analysis for my thesis)...
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Shack
Big Wall climber
Reno NV
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Would you do different models with different weight per meter, maybe change diameters and see how it changes the outcome?
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Ed Hartouni
Trad climber
Livermore, CA
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once I get there different things can change to see what the effect of the differences would be...
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Paul_in_Van
Trad climber
Near Squampton
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MH,
Deceleration is the same as negative acceleration. Both positive and negative accelerations are just changes in velocity over time, but in different directions, either faster or slower.
P
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 4, 2010 - 01:41am PT
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Physicists might not use the terms "deceleration" or "negative acceleration" at all. You simply state the acceleration, the vector of acceleration, the time, and the initial velocity (speed + direction), and that's all that's needed. (At least in Newtonian mechanics.)
Popular usage, trained by a century of motor vehicles, is acceleration and deceleration. It may not be precise in the terms of physicists, but is comprehensible.
I'll just go out to the car now, and negatively accelerate it.
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Shack
Big Wall climber
Reno NV
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First you must drive a negative distance.
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Ed Hartouni
Trad climber
Livermore, CA
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we're all Bozos on this bus [squeek, squeek]
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 4, 2010 - 01:59am PT
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Hmmm, two climbing-geek related threads attributable to me on the front page. Things may be a bit anti-positive. Bwahahaha!
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bmacd
climber
Relic Hominid
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We can't be certain the rope cracking in this part of the universe is the same as in remote regions of space, If the fine-structure constant really does vary through space, it may provide a way of studying the elusive higher dimensions that many theories of bigfoot predict, but which are beyond the reach of particle accelerators on Earth.
http://economist.com/node/16930866?fsrc=scn%2Ffb%2Fwl%2Far%2Flawsofphysics
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Ed Hartouni
Trad climber
Livermore, CA
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for the purposes of this thread we can assume that alpha is constant...
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 4, 2010 - 02:38am PT
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Bruce may have been alluding to dark energy and dark matter - or is that Dark Energy and Dark Matter?
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Dr.Sprock
Boulder climber
I'm James Brown, Bi-atch!
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The high speed of the tip is explained by the law of the conservation of momentum. The initial motion is applied to the handle, and the initial wave along the whip's thong has a much larger mass than the end wave at the whip's tip or popper (a thin flexible piece of material tied at the end of the whip). Since the momentum is the product of the mass and speed of the moving object, the smaller the mass, the higher the speed, hence the light popper moves extremely fast. Also, the more flexible the popper, the shorter (and lighter) the last moving wave, hence an even higher speed. Many popular science explanations published capitalize on the fact that the general shape of a whip is tapered: thick at the handle and very narrow at the tip, hence the decrease of the mass. While tapering does contribute to the quality of the crack, it is not a deciding factor. Even "flat" whips can crack: the actual decrease of the mass of the moving part occurs simply because the whip ends: the closer the moving loop to the tip, the shorter the moving part. In this respect the whip crack resembles the "shoaling" action of a tsunami: a deep-water ocean wave piles up tremendously when entering into shallow waters. Recently, an additional, purely geometrical factor was recognized: the tip of the whip moves twice as fast at the loop of the whip, just like the top of a car's wheel moves twice as fast as the car itself.
quiz after lunch,
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Ed Hartouni
Trad climber
Livermore, CA
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Dr. Sprock, you haven't done the reading, look above, check out the references (they're not "popular science") and report back
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Dr.Sprock
Boulder climber
I'm James Brown, Bi-atch!
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i need diff equations,
i'm just not satisfied,
he ed, how is your math?
do you use it in heavy amounts at work everyday,
or is it sporadic calculus, used once a year?
i got a problem i need help with,
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Ed Hartouni
Trad climber
Livermore, CA
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everyday....
unless I'm catching up on my training...
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Dr.Sprock
Boulder climber
I'm James Brown, Bi-atch!
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ok Ed, i have been working on this seeming simple but yet, difficult problem.
if i want to wind a transformer, i usually use a square or rect bobbin.
if i wind on a circular bobbin, the wire velocity at the wire feeder will be constant.
but with a squate bobbin, there are accelerations from a dead stop to whatever,
4 times per revolution of the bobbin.
i want to program the stepper motor driving the bobbin to take out the x axis accelerations out of the wire, so that i can get a better wound coil.
the problem is to develop a set of functions that will describe the x velocity for given distance and set bobbin size.
i have tried setting it up in a number of ways, here are a few ideas,
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Ed Hartouni
Trad climber
Livermore, CA
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if you want a "constant tension" wind,
try this:
you set the feed motor velocity up so that it increases with an increased angle (as shown) and decreases with negative angle
This will keep the wire at a constant tension as it winds around your square bobbin
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Banquo
Trad climber
Morgan Hill, CA (Mo' Hill)
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Search google scholar for: folded free falling chain
Seems to be an old and difficult problem.
http://arxiv.org/PS_cache/physics/pdf/0510/0510060v1.pdf
I haven't been following this thread and apologize if I missed something. My thought problem goes something like this...
A tightly coiled rope sits on a ledge and one end is dropped. Ignore friction and air resistance. After some time, the rope reaches a point where it has just about reached straight in free fall. The CG of the rope has fallen half it's length (solve potential energy for 60m rope and I think this is about 24 m/s). The last tip of the rope has to accelerate from rest very suddenly putting the rope in tension and stretching it. As the tension pulls the tip of the rope off, it over accelerates as the stretch releases. If the last foot of the rope has a fold in it, it seems reasonable that it might snap as it pulls off.
Another model is holdong the two ends with the rope folded in half and hanging free, then drop one end.
Also:
"Falling Chains" Chun Wa Wong and Kosuke Yasui, American Journal of Physics -- June 2006 Volume 74, Issue 6, pp. 490-496
These guys actually did experiemnts:
"The motion of a freely falling chain tip" Tomaszewskia, Pieranskib & GeminardAmerican Journal of Physics -- September 2006 -- Volume 74, Issue 9, pp. 776-783
In the folded chain model, you can see the end whip depends on how close the ends are when it is dropped:
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Banquo
Trad climber
Morgan Hill, CA (Mo' Hill)
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With a tightly folded 1 meter chain they got peak velocity at the tip of almost 20 m/s and peak acceleration of 50g!
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Dr.Sprock
Boulder climber
I'm James Brown, Bi-atch!
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he Ed, i figured it out, you just find an equation for position, then integrate to get the total velocity equation.
but the integration is a pain, see here>
so i just need your help now in integrating:
Z= Root (D^2 -2D*cos t + 1)
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Ed Hartouni
Trad climber
Livermore, CA
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I'll check it out Dr. Sprock, you can always integrate it numerically....
Banquo - good reference, the rope is a bit different than a chain, but they share behavior in some regimes... I think that in the "whip crack" regime they are very different...
Look at my strobe picture up thread and see similarities to the figure you posted....
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Ed Hartouni
Trad climber
Livermore, CA
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to the paper by Tomaszewski, Pieranski and Geminard is a good one, and anticipates some problems with the rope.
Their Equation 10 has an analytic expression for the velocity of the chain tip as a function of how far the tip has fallen:
v(h) = √[gh(2L-h)/(L-h)]
as h → L, v(h) → ∞
this is good news for the OP as it indicates that the chain tip considered in the paper gets going very fast.
The analytic approximation does not correctly predict the maximum velocity of the tip...
their final sentence is my excuse for not getting to the solution yet:
Dynamics of the falling chain hides certainly a few more interesting details. The same, even to a larger extent, concerns the dynamics of the falling rope. In the latter case the dissipation plays a much more important role and elasticity becomes a crucial factor. Laboratory and numerical experiments are waiting to be carried out.
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Ed Hartouni
Trad climber
Livermore, CA
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looking at that paper, let's scale to a 100 m chain.
dropping the chain with the ends at the same height, and separated by 25m, would give a peak velocity of something like 320 m/s
This assumes that the peak velocity is well approximated by the analytic result but at the observed height of the maximum velocity in the experiments and numerical experiments, roughly 0.99 of the length of the rope...
This is close to the 343 m/s speed of sound... so that's quite good!
But the details of the constituent model of the rope will matter...
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Ed Hartouni
Trad climber
Livermore, CA
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here's another good article:
The weight of a falling chain, revisited by Hamm and Géminard
which concludes that the minimum radius of curvature (which is a part of the constitutive model of the real chain) is an important factor in the analysis of the dynamics...
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 4, 2010 - 11:30pm PT
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Another aspect of this, raised by Ed's recent remarks, is that the science may show that it's possible for the tip to exceed the speed of sound. However, possible doesn't necessarily equal likely. It may be a rare event. If the math shows that it's just possible, then it may be time for some empirical tests, to see what actually happens. If you get ten different 50 - 60 m ropes, and drop each ten times from different positions (always dropping it the maximum twice the length of the rope), then it should become evident fairly quickly what actually happens.
If someone can borrow a radar gun, we could spend an afternoon at the FaceLift doing this, maybe at the base of the crazy wall.
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bmacd
climber
Relic Hominid
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The sound is just the tip of the rope flopping the full 360 degrees and hitting the other side of the rope.
The sound is not caused by breaking the sound barrier but by the rope tip smacking against the rope itself.
Problem Solved, Next question please ....
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Peter Haan
Trad climber
San Francisco, CA
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This is when MIghty Anders has to mooch up to Fattrad as Fatty can get his gun.
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 5, 2010 - 01:27am PT
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Maybe I can outrun FatTrad, or grab his radar gun when he's busy during the BBQ. Hopefully he won't tase me.
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Chinchen
climber
Way out there....
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MythBusters.
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Ed Hartouni
Trad climber
Livermore, CA
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unlikely that a radar gun will do the trick...
here are some more studies... with a 9.2 mm Sterling Fusion
1.42 meters, with reflector tape in the middle of the free length, and at the end, strobe is 1/30 s and there are 23 strobes seen
I've numbered them in the following image strobe 1 to 23
and they correspond to the measured positions represented on this plot of the trajectory
from this we can get the velocity magnitudes for strobe 2 through 22:
where the red line shows the "free fall" velocity
and the acceleration for strobe 2 through 22:
where the red line is the acceleration of gravity.
The peak occurs at strobe 14, which is when the rope is extended to 0.977 of it's total length, the acceleration is quite large at that point, roughly 30g's. This launches a wave back up the rope and throws the tip to the right in the image quite far.
The important characteristic of the rope at this length is the fact that it resists bending at some angle (it has a minimum bend radius) so it is acting like a spring in the transverse direction. This is what limits the acceleration at the whip point to something finite (but large!).
For a much longer rope, the elastic properties along the axis of the rope will be important. As the rope drops and bends, the stretch will provide another energy dissipation mechanism and change the trajectory somewhat.
If I used the Tomaszewski, Pieranski and Geminard paper equation (10) to calculate the velocity at the point of the maximum measured velocity, using the length of the rope that is out h=1.088m, I would calculate v=7.484 m/s where I measure 6.284 m/s.
The figures above for velocity and acceleration are comparable to their Fig. (10) also...
So if I were to drop the rope with one end connected, the rope length is 80 m assuming that the minimum radius sets the scale for the point of maximum velocity, that is L-h = 1.422-1.088 m = 0.335 meters from the end...
v = 433 m/s
which is quite a bit larger than the speed of sound, 344 ms
the acceleration I estimate is huge, about 46,500 m/s^2 or 4700 g's that's going to do some damage to the rope.
Of course the velocities won't be so large because the air resistance in the 4 s drop will be significant. There is also the dissipative stretching that hasn't been considered in the calculations. But it would seem that it is possible that the end of the rope could exceed the speed-of-sound, and probably have the tip damaged in some significant way.
This can be tested by starting short and working up in length and then checking with the expectation from the calculations. I doubt we could capture the actual act in normal video... things are moving way to fast.
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Dr.Sprock
Boulder climber
I'm James Brown, Bi-atch!
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nice work Ed!
do they make a small acceleration recorder that you could attach to the tip of the rope?
a little ram memory to record the event on a flash chip,
download on the usb,
little lthium powered jobbie,
i bet they have one you could "borrow" over at lawrence labs?
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dipper
climber
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Ed,
Your contributions to this site are fantastic.
Thank you.
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Shack
Big Wall climber
Reno NV
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It will be known as the Hartouni Effect.
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 7, 2010 - 01:18pm PT
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Thanks, Ed! Excellent work, and most interesting.
I still think it would be fun to to some experiments, dropping ropes. I guess a problem is that the terminal velocity of the end won't necessarily be straight down, and the measurement needs to be parallel with it. When the rope end is moving fastest, it might well be off to a side as viewed from below.
Still, isn't constructing experiments part of physics?
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Banquo
Trad climber
Morgan Hill, CA (Mo' Hill)
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Awesome Ed, I'll buy you a beer any day.
"One test is worth a thousand expert opinions"
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MH2
climber
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Of course the velocities won't be so large because the air resistance in the 4 s drop will be significant. There is also the dissipative stretching that hasn't been considered in the calculations. But it would seem that it is possible that the end of the rope could exceed the speed-of-sound, and probably have the tip damaged in some significant way.
Whew!
I will definitely try to keep my eyes out of the way if this comes up in real life.
Very satisfying treatment, Ed.
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Mighty Hiker
climber
Vancouver, B.C.
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Topic Author's Reply - Sep 9, 2010 - 03:10am PT
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I'm very amused to note that the first post to the thread was March 6th, 2007. Good things are worth waiting for!
Bump, to recognize all Ed's hard work on this one.
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Mighty Hiker
climber
Outside the Asylum
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Topic Author's Reply - Sep 16, 2017 - 12:31pm PT
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Anybody want to spend some time with ropes and a radar gun at the Facelift, testing this out? A little experimental physics could be an entertaining diversion.
Maybe there's an I-phone radar app?
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timy
Sport climber
Durango
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Sep 16, 2017 - 05:48pm PT
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Most of the routes on this crag start off of the ledge halfway up. Many a rope end has been exploded into fray when pulled from 30m above and CRACK!! popping way below. Interesting
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Ed Hartouni
Trad climber
Livermore, CA
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Sep 17, 2017 - 07:12pm PT
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Missing images from above post...
1.42 meters, with reflector tape in the middle of the free length, and at the end, strobe is 1/30 s and there are 23 strobes seen
I've numbered them in the following image strobe 1 to 23
and they correspond to the measured positions represented on this plot of the trajectory
from this we can get the velocity magnitudes for strobe 2 through 22:
where the red line shows the "free fall" velocity
and the acceleration for strobe 2 through 22:
where the red line is the acceleration of gravity.
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EdBannister
Mountain climber
13,000 feet
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Sep 17, 2017 - 11:59pm PT
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Ed Hartouni if you ever do really need a fast camera, Cal Tech has two different cameras developed to photograph high speed materials failure. but both are set up in labs, where the falling rope scenario would not be repeatable. and thanks for all your contribution here.
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Ed Hartouni
Trad climber
Livermore, CA
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Sep 18, 2017 - 09:06am PT
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high speed photography is something I am very familiar with, and my work at the lab in the mid 1990s actually provide some inspiration to my interest in my amateur photography efforts becoming more serious. There we were capturing movement with velocities of 10s km/s to 100s km/s (1 km/s = 1 micrometer/nanosecond).
but even more, I thought in this particular topic, that using commonly available tools would best, since anyone one of you photogs could do the same... and I suspect that most of the camera gear out there could be used in some way similar to get the "strobe" shots of the rope.
to capture the actual failure of a rope end would be a really big challenge, as it takes place over a rather large rope motion at high speed, and probably is difficult to predict in time well enough to take advantage of high frame rate, you have to have the camera pointed at the right place at the right time...
but it might be possible to explore all these aspects (given enough rope) to see if the theoretical calculations are at least close, and to see what the range of rope constitutive models make sense.
maybe we could all collaborate on a paper (or at least a submission to arXiv!)
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Mighty Hiker
climber
Outside the Asylum
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Topic Author's Reply - Sep 18, 2017 - 09:26am PT
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Naah, we should just get a bunch of ropes, take them up to the alcove, and measure how fast we can get them to fall, whether we can get the ends to explode, and if so whether that correlates with velocity or audible clues. What could be more fun that busting some ropes, playing with gadgets, and maybe doing a few swings? All in the public service, of course.
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