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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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