Time for rope to stop a person in freefall

[jondoty]

How long does it take typical inelastic rope to stop a person in freefall?

I'm taking a gun-safety course and the instructor claims that for a 200lb person falling 1 meter out of a tree stand before their safety harness halts their fall, it applies a force of 1700 pounds to the body. I feel that that estimate is a bit high, but it all comes down to the length of time the stop is spread out over.

I calculate that for a rope to apply 1700 pounds of force on the body after a 1 meter fall, the stop must last only 0.053s. If you increase that time to just 0.1s, the force drops significantly to 903lbs, or 4018.2Newtons. What is a good estimate? Any thoughts?

 

[Gokul43201]

A lot depends on the kind of rope being used. If it is a bungee cord, the force would be a lot less.

Your calculations so far look correct to a first order approximation - the stretch time for the rope is about 0.05 seconds. This assumes that the force exerted by the rope is uniform during this stretch time. This is not usually true, and a better model is to assume a damped harmonic response. The problem here, is that this is a little harder to calculate and needs knowledge of the stiffness and damping coefficients of the rope. If you neglect damping, and calculate the time period for a half inch thick nylon rope (k is about 160kN/m), you get about 0.15 sec. But the real stretch time is closer to half or quarter of this number (for an undamped oscillator this is a quarter), OR about 0.05 seconds.

I have no idea if the rope I described falls under "typical inleastic rope", but it probably is close, since I got that info from a website that calculates stuff for climbing ropes. You could check that out too. It's
http://www.materials.ac.uk/resources/casestudies/ropes.asp

 

[Gokul43201]

A quick way to check is to find a thin enough rope whose breaking strength is say, 1000lbs. The breaking strength is roughly proportional to the square of the thickness, so you can shave a section to make it thinner, if needed.Then you drop a 200 lb weight attached to the rope and see if it breaks.