Pendulum swings?
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So, I was contemplating pendulum falls the other night, belaying a top roper in the gym. He was way off to one side, fixing something on an adjacent route, but very close to the top (short amount of rope on his side). We were both aware of the fall potential, and he was very cautious. But, he was close to horizontal, so that set me pondering. |
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Let out more rope. Makes belay safer in most situations. In this one specifically it decreases the angle of the rope when it will come tight on the climber during a fall in relationshion to the direction of gravity. |
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Old lady H wrote:The angle part I get, the farther from vertical the worse the fall will be when/if you whack something, but does the rope length make a pendulum fall worse? Falls seem faster on the shorter length.Assuming:
Rope length can help or make things worse. As stated by Medic741, introducing extra slack pre-fall so the rope droops between the climber and the anchor reduces the effective angle during the fall and so reduces the horizontal speed at the bottom of the fall - a good thing in the above circumstances unless the extra slack causes the climber to instead vertically impact, say, on a ledge or on the floor. But when the rope is essentially horizontal between the climber and the anchor, the farther the climber is out from the anchor (e.g., the more rope) the faster the horizontal speed the climber will have when swinging into something - probably (?) not what you meant. Anyway, in this case, the horizontal striking force is essentially the same as the vertical striking force if the climber had simply fallen straight down a distance of that length of rope onto the floor. Not good. |
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Old lady H wrote: I know it is probably very simple math, but geometry was about 45 years ago!Actually that's dynamics, and nothing much is simple about it. But in a nutshell, if I remember correctly, the shorter rope creates faster ACCELERATION. This is different than VELOCITY. This is because with the shorter rope, the radius you are swinging through is much smaller. Think of it as taking a tighter corner. |
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Potential Energy is being converted to Kinetic - no energy dissipation of any form is assumed. |
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amarius wrote:Potential Energy is being converted to Kinetic - no energy dissipation of any form is assumed. If H is the height of a drop, velocity at the bottom is going to be V=sqrt( 2*g*H) g- free fall acceleration sqrt - square root When climber is swinging around the pivot point we, usually, notice change in the angle, hence it is worth looking at the angular acceleration Diff equation of motion for angle - angular acceleration = -g/L *sin( angle) When the climber is at the bottom of the swing, angle =0 degrees, when to the side of swing point, it is 90. sin( angle) is decreasing function of angle - sin( 90 ) > sin( 45) > sin(0). With larger angle deflection, initial angular acceleration is going to be larger. L, distance from the swing point is in the denominator - hence the closer you are to swing point, the larger your initial angular acceleration is. OK, so, what the heck does it all mean? Here are some numbers - I am going with meters, numbers are smaller Short Rope - 1 meter (~3ft), directly to the side of anchor, initial angle 90deg, drop 1 meter; Long Rope - 4 meters (~12ft), angle to give 1 meter drop is 41deg. Velocity going through the bottom in both cases is going to be ~4.4 m/s Just looking at it - short rope will start the swing with angular accel of ~560 deg/s/s, while the long one will swing at ~90 deg/s/s, roughly 6 times slower. To recap - the long one will appear to be slower, while max velocity will be the same in both cases.+1 Thanks for saving me from having to pull out some old text books. |
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One of the nasty things about pendulums is that the body isn't really designed to smack sideways into things. |
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Medic741 wrote:Let out more rope. Makes belay safer in most situations. In this one specifically it decreases the angle of the rope when it will come tight on the climber during a fall in relationshion to the direction of gravity. The smaller this angle is the less lateral force that will be generated which causes a climber to swing. Systems are very good at safely managing load in the y direction, swings can rip gear and snap ankles. Let out slack, idecrease 'theta' and you'll be safer. Good on you for taking interest in being a good belayer. It's something like Force magnitude * sin(theta) I forgetThanks, Medic! As it happens it wasn't a big deal, and I left the climber to manage himself (although I handed him his helmet), but I do have a habit of thinking when belaying. Outside climber, I guess. The angle makes total sense, I already knew that, hadn't heard it suggested to get some slack out to chase it. Yet another argument for belay gloves, if you are going to go from one to the other really quickly. And swings kill people. Early lesson, will never be ignored. |
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Everyone else, just to make it clear to my addled old head: |
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Yes, assuming climber is in line horizontally with top pro, the further out the climber is from the vertical impact area, the harder it is going to hurt. Less far, he may accelerate faster, but impact speed will be less. Introducing slack will let him fall further vertically and reduce sideways motion. |
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Got it! Thanks, all |
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So basically, the distance you fall vertically is simply translated into lateral speed, meaning you hit sideways just as fast/hard as if you'd fallen straight to the ground. Right? |
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Without getting technical - yes. |
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johnnyrig wrote:So basically, the distance you fall vertically is simply translated into lateral speed, meaning you hit sideways just as fast/hard as if you'd fallen straight to the ground. Right?Take a look at my web page: people.bath.ac.uk/dac33/hig… the stuff on pendulum falls is after the stuff on anchors and angles |
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johnnyrig wrote:So basically, the distance you fall vertically is simply translated into lateral speed, meaning you hit sideways just as fast/hard as if you'd fallen straight to the ground. Right?This is a point not realized by many ... worth re-quoting for emphasis. |
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Bill Lawry wrote: This is a point not realized by many ... worth re-quoting for emphasis.But, also the post above about bodies not doing so well hitting sideways. Ten, fifteen, even twenty foot ground fall is maybe just broken bones. Twenty, fifteen, even ten sideways slam into a dihedral from straight out? |
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Old lady H wrote: But, also the post above about bodies not doing so well hitting sideways.Agree - although you can "hit sideways" in a vertical fall if you don't land upside right. |
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Bill Lawry wrote: Agree - although you can "hit sideways" in a vertical fall if you don't land upside right.Ah, but if you flip over, your body has just done a 180° pendulum. |
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Old lady H wrote: Ah, but if you flip over, your body has just done a 180° pendulum.Yes - at least feet and head were in some kind of pendi-spiral whack-a-mole. ;-) |
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The observation that bodies don't react well to sideways impacts is essentially correct. |
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Healyje wrote:The observation that bodies don't react well to sideways impacts is essentially correct. It should be further noted that even in a vertical fall on a face with shallow overlap / roof features of - say 12-18 inches - there's still potential for dangerous side impacts to the head if the rope comes taut with your body and shoulder under the lap/roof and your head remains above it. About 20 years ago such a seemingly innocuous 15' fall happened to a friend who ended up severely and permanently disabled as a result.Sorry to hear that! For your friend, but you too. I think of it a bit like a car: arms and legs are our first line of defense crush zone, then hips, shoulders. Hopefully never head, neck, or front/side torso, if you can avoid it at all. There's good reason why we put our arms out if we stumble, and curl up and turn sideways if that softball is headed below the belt! Day to day, this works pretty well, so long as we are within the millenia designed parameters of a human body. But climbing throws it out the window. Stuff happens so fast, so suddenly, and with much, much greater forces. But I still consider my bike commute more dangerous! H. |