SLIDING DOWN A LONG ROPE.
Posted: 23 Apr 2012, 07:42
SLIDING DOWN A LONG ROPE.
Martha, here is a quick reply on the speed business. Maybe you could forward it to Stanley...
The rope is AWFULLY long in comparison with the height of the stack. We can't really be sure what happened
without knowing the tension and elasticity of the rope, the weight of the man, the loss in the pulley, and of
course everything having to do with drag such as the speed profile of the bloke and his cross-section and the
velocity of the prevailing winds. But we can say a few things that must be mostly right:
1. If he reached 100 miles per hour he was almost certainly not the first person to do so. Neglecting drag, the first person who fell or was pushed over a cliff about 330 ft high would have reached about 100 miles per
hour when he hit. I have read somewhere that terminal velocity in still air near sea level is about 140 miles per hour, so that would be no limit to reaching 100. A somewhat higher cliff would compensate for the
probable losses.
2. If the rope were stretched very tightly out to 1500 feet, it would form an angle of less than 8 degrees to the horizontal. If the bloke were to slide from the top of the tower to the ground, constantly at this angle (i.e. more
like on a rigid track, than on a rope), the component of the force of gravity would be only 200/1500 of the maximum and this would accelerate him to the ground in about 27 seconds, but he would hit the ground at about 77 miles
per hour (which he certainly did NOT do in real life). But even in that case, he would only have averaged half the 77 miles per hour, besides taking all the time.
3. So we conclude that the rope was tied at the top and tied at the bottom so that it formed a catenary, which allowed him to drop almost straight down (i.e. in free-fall) at the beginning, but then slowed him down so that at the end he could hit something soft without being injured. This ought to work. Neglecting losses, you could fall 200 ft in only 3.5 seconds. But you would again end up at about 77 miles per hour (gravity does enough work
on you to get you up to this speed no matter HOW you descend, if losses are neglected!). So you need to fall far enough to accelerate up to a good speed and to fall fast, and THEN to decelerate at as high a rate as you could tolerate..
what? several g's ?? ...until you got to the ground at a running speed.
The problem of course is the rope and the effect of his weight on it, etc. etc. No way of knowing....How do you suppose he knew how long to make the rope and where to fix the lower end? The only way I can think of to do it is to START WITH A LOW POSITION and to try various things without getting badly hurt. Then to work your way up to the top of the tower. Maybe there were rules-of-thumb about this sort of thing, developed through hard-won
experience, if not prior calculation!
Best Wishes, Tom.
Martha, here is a quick reply on the speed business. Maybe you could forward it to Stanley...
The rope is AWFULLY long in comparison with the height of the stack. We can't really be sure what happened
without knowing the tension and elasticity of the rope, the weight of the man, the loss in the pulley, and of
course everything having to do with drag such as the speed profile of the bloke and his cross-section and the
velocity of the prevailing winds. But we can say a few things that must be mostly right:
1. If he reached 100 miles per hour he was almost certainly not the first person to do so. Neglecting drag, the first person who fell or was pushed over a cliff about 330 ft high would have reached about 100 miles per
hour when he hit. I have read somewhere that terminal velocity in still air near sea level is about 140 miles per hour, so that would be no limit to reaching 100. A somewhat higher cliff would compensate for the
probable losses.
2. If the rope were stretched very tightly out to 1500 feet, it would form an angle of less than 8 degrees to the horizontal. If the bloke were to slide from the top of the tower to the ground, constantly at this angle (i.e. more
like on a rigid track, than on a rope), the component of the force of gravity would be only 200/1500 of the maximum and this would accelerate him to the ground in about 27 seconds, but he would hit the ground at about 77 miles
per hour (which he certainly did NOT do in real life). But even in that case, he would only have averaged half the 77 miles per hour, besides taking all the time.
3. So we conclude that the rope was tied at the top and tied at the bottom so that it formed a catenary, which allowed him to drop almost straight down (i.e. in free-fall) at the beginning, but then slowed him down so that at the end he could hit something soft without being injured. This ought to work. Neglecting losses, you could fall 200 ft in only 3.5 seconds. But you would again end up at about 77 miles per hour (gravity does enough work
on you to get you up to this speed no matter HOW you descend, if losses are neglected!). So you need to fall far enough to accelerate up to a good speed and to fall fast, and THEN to decelerate at as high a rate as you could tolerate..
what? several g's ?? ...until you got to the ground at a running speed.
The problem of course is the rope and the effect of his weight on it, etc. etc. No way of knowing....How do you suppose he knew how long to make the rope and where to fix the lower end? The only way I can think of to do it is to START WITH A LOW POSITION and to try various things without getting badly hurt. Then to work your way up to the top of the tower. Maybe there were rules-of-thumb about this sort of thing, developed through hard-won
experience, if not prior calculation!
Best Wishes, Tom.