Ropes @ Speed of Sound (physics question)

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Mighty Hiker

Social climber
Vancouver, B.C.
Topic Author's Original Post - Mar 6, 2007 - 07:38pm PT
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)."
TradIsGood

Happy and Healthy climber
the Gunks end of the country
Mar 6, 2007 - 07:43pm PT
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.
Ed Hartouni

Trad climber
Livermore, CA
Mar 6, 2007 - 09:15pm PT
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.
JuanDeFuca

Big Wall climber
Stoney Point
Mar 6, 2007 - 09:21pm PT
It is impossible for a climbing rope to go supersonic.

Its to limp.

JDF
Landgolier

climber
the flatness
Mar 6, 2007 - 09:29pm PT
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.
Mighty Hiker

Social climber
Vancouver, B.C.
Topic Author's Reply - Mar 6, 2007 - 09:34pm PT
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.
Ed Hartouni

Trad climber
Livermore, CA
Mar 6, 2007 - 09:56pm PT
I'll download the paper tomorrow and take a look...
Mighty Hiker

Social climber
Vancouver, B.C.
Topic Author's Reply - Mar 6, 2007 - 10:31pm PT
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.
TradIsGood

Happy and Healthy climber
the Gunks end of the country
Mar 7, 2007 - 05:20am PT
More likely the last (few?) millimeters.
wootles

climber
Gamma Quadrant
Mar 7, 2007 - 05:41am PT
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.
Euroford

Trad climber
chicago
Mar 7, 2007 - 07:23am PT
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!
Mr.T

Big Wall climber
topanga
Mar 7, 2007 - 07:23am PT
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.
Landgolier

climber
the flatness
Mar 7, 2007 - 12:32pm PT
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.
Kevster

Trad climber
Evergreen, CO
Mar 7, 2007 - 12:46pm PT
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?>
G_Gnome

Boulder climber
Sick Midget Land
Mar 7, 2007 - 01:50pm PT
I think you would have to add in the change in momentum caused by the bulk of the rope actually ceasing to fall too.
Mighty Hiker

Social climber
Vancouver, B.C.
Topic Author's Reply - Mar 9, 2007 - 03:34pm PT
bump, for the Friday-afternoon physicists.
cintune

climber
Penn's Woods
Mar 9, 2007 - 03:49pm PT
This discussion needs sound effects.

http://www.sounddogs.com/previews/25/mp3/329363_SOUNDDOGS_Wh.mp3

http://www.sounddogs.com/previews/25/mp3/329375_SOUNDDOGS_Wh.mp3

http://www.sounddogs.com/previews/2721/mp3/466197_SOUNDDOGS_Si.mp3

Dozens more here:
http://www.sounddogs.com/results.asp?Type=&CategoryID=1059&SubcategoryID=30

It's like a Chinese restaurant menu. I particularly like the Single Close Up Reverberant Whip Swish With Crack And Hit.
Ed Hartouni

Trad climber
Livermore, CA
Mar 9, 2007 - 03:50pm PT
I have the paper today, looks approachable... stay tuned....
HighDesertDJ

Trad climber
Arid-zona
Mar 9, 2007 - 03:59pm PT
So Ed are you saying that a whip crack is essentially a little sonic boom?
JuanDeFuca

Big Wall climber
Stoney Point
Mar 9, 2007 - 04:32pm PT
Ropes are to limp to make Shock Waves?
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