how to calculate fall forces in relation to rock climbing?

Question

so you got wieght of climber @ 185 lbs falling from a height of 16 ft
with a attachment point @ 8 ft (this is where the rope is attached )
here's the senerio i'm 8 ft above the attachment point with 8 ft of rope played out which mena i'll fall the 8 ft to the attachment point and then proceed to fall another 8ft un till the rope becomes tuant on the attachment and let's also assume that the rope has infinte strenght and ridgity when i come to a stop and start the penglim effect towards the wall how fast will i be traveling and how much force is exerted on to my body?

Answer 1

Let's use some loose and rough figures. Acceleration due to gravity is about 32 feet per second per second, so that after 1 second of free fall, you've falled 16 feet (D = 1/2 g t²). This means that you are falling at 32 ft / sec after 1 second, in which an apparently STEEL wire yanks your motion to a dead stop. This is exactly like hitting a concrete floor, so I don't know why you'd even talk about "force" of the stop! The only thing elastic in this impact scenario is your own body, and so, how much shall we stretch the body to determine the force on it, since F = m a, where m = 185 lbs, and a = v² / 2d, where v = 32 ft /sec, and d is the stretch of the poor body? The forces can be enormous. This is why climbing ropes are deliberately designed to be very stretchy, much more than conventional ropes that you buy at the hardware store.

Let's say that we're using a proper climbing rope, and it stretches a foot (remember, it's the total length of the rope from the belayer to the top anchor to the bottom of the fall that's stretched, so a foot is very little stretching). Then we have F = (185 lbs) ( 32² ft² / sec² ) / (2 ft) = (185 lbs) (16) (32 ft / sec²) = 185 pounds at 16 g's, which is a lot of force, equivalent to weighing 2,960 pounds on the rope, which is why rope has to be very strong, and why stretchy rope is always better.

Now, let's get to the next part of the question. If a person falls, and the rope prevents further downward traveling, and converts it into a sideway motion, because of conservation of energy, this sideway motion has the same speed as the climber had at the bottom of his fall, or 32 ft / sec², in which case he still has a problem with the rock face he's about to slam into. It's over 20 mph, or like a very fast sprint towards a brick wall. Fortunately, stretchy rope again saves the day, because it can soak up a lot of kinetic energy as the climber bounces up and down, so that if the climber has planned his climb carefully, he does not end up in a careening arcing free-fall towards a rock face that he'd rather not meet.