Discussion Topic |
|
This thread has been locked |
Mighty Hiker
Social climber
Vancouver, B.C.
|
|
|
Topic Author's Original Post - Mar 6, 2007 - 10:38pm 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
|
|
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
|
|
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
|
|
It is impossible for a climbing rope to go supersonic.
Its to limp.
JDF
|
|
Landgolier
climber
the flatness
|
|
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 7, 2007 - 12:34am 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
|
|
I'll download the paper tomorrow and take a look...
|
|
Mighty Hiker
Social climber
Vancouver, B.C.
|
|
|
Topic Author's Reply - Mar 7, 2007 - 01:31am 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
|
|
More likely the last (few?) millimeters.
|
|
wootles
climber
Gamma Quadrant
|
|
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
|
|
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
|
|
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
|
|
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
|
|
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
|
|
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 - 06:34pm PT
|
bump, for the Friday-afternoon physicists.
|
|
Ed Hartouni
Trad climber
Livermore, CA
|
|
I have the paper today, looks approachable... stay tuned....
|
|
HighDesertDJ
Trad climber
Arid-zona
|
|
So Ed are you saying that a whip crack is essentially a little sonic boom?
|
|
JuanDeFuca
Big Wall climber
Stoney Point
|
|
Ropes are to limp to make Shock Waves?
|
|
|
SuperTopo on the Web
|
Let us know!