# Practical Problem (debate between friends)

1. Dec 14, 2008

### X_Art_X

Hi Guys,
First post here.
I'm in a debate with my friend who happens to be a climbing buddy.
Dynamic ropes for climbing & abseiling come in two standard sizes, 50 and 60 Meters.

The point being debated is weather or not the 60 meter rope has to be stronger than it's
50 meter counterpart in order to hold the same weight at the end.
These ropes (being dynamic) have a little stretch like a bungee cord so you can fall with them.
I assume that they are a little thinner when stretched.

I know the difference between 50 & 60 M isn't great, but let's assume the difference is 5 Kilometers,
and the rope itself weighs nothing.
Thanks, Art.

2. Dec 14, 2008

### vanesch

Staff Emeritus
I would say that the only difference could be the weight of the rope, and if you specify that that doesn't matter, then there is no difference. You can see this as follows: consider with your mind's eye that the 60 m rope consists of a 50 m rope plus a 10 m rope ; and that you have next to that a 50 m rope. Now, the weight attached to the 50m part of the 60 m rope is the same as the weight attached to the 50 m rope. So the 50 m piece of the 60 m rope, and the real 50 m rope, see the same weight, have to have the same mechanical strength, and will stretch the same. However, the 10 m part will also stretch a bit, so the total stretch of the 60 m rope will be more than that of the 50 m rope of course. But the mechanical strength will be the same.

3. Dec 15, 2008

### timmay

Just clarifying the previous poster's message with a little bit of engineering theory:

Compare this to two tensile test samples such as http://web.mit.edu/course/3/3.042/team1_06/solidworks files/3-15 tensile-solidsmall printedunits.jpg. Both of the samples are made from the same material, with the same (dynamic) elastic modulus (E) and (dynamic) tensile yield stress / ultimate tensile strength, with the same cross sectional area. The only difference between the two samples is their length (L).

The ropes (or samples) will be safely rated to a load within the elastic region, with a safety factor included. If the initial cross sectional areas of the samples are the same, and the samples are loaded to the same load (and therefore the same stress) within this region, we can see the difference in extensions between the two ropes. Using the relationship:

E = $$\frac{\sigma}{\epsilon}$$

and rearranging and expressing in terms of original length ($$L$$) and extension ($$\Delta L$$):

E = $$\frac{\sigma L}{\Delta L}$$

It can be seen that for two samples of the same cross section and elastic modulus, loaded to the same stress, the longer sample will show a greater extension than the shorter one, although both samples will have been subjected to the same strain.

As for the question of strength, as I mentioned, the ropes will be rated to a load (and hence stress) within the elastic region, including a safety factor. If both ropes are identical in all but length (i.e. same material, same number of cores and hence cross sectional area) then their strength will be identical. The only difference will be the amount they extend under loading - although expressed in terms of strain (or percentage elongation) this would be equal.

Hope this helps.

Last edited by a moderator: Apr 24, 2017 at 9:28 AM
4. Dec 15, 2008

### Ranger Mike

i can assure you there is absolutely no differnece in the specification of the rope. Comes off the same roll. having had to hump a ruck sack and standard issue rapelling rope thru swamps, desert, jungle..the weight is the difference. work load not tensile strength typically is the key. btw, UVs and sand reduce life of these.
Polyester Dacron Static Kernmantle with a work load of 540 lb. Very low stretch for easy descent. Tensile strength: 5,400 lb.
7/16" diameter. Length: 150'. Wt: 9.5 lb
10 pounds don't seem like a lot ...it is

Last edited: Dec 15, 2008
5. Dec 15, 2008

### vanesch

Staff Emeritus
I come to think of something which might affect the "needed strength" for a 60 meter rope to be higher than that of a 50 meter rope ; I don't know if it is meaningful (I don't do mountain climbing at all). It might be that one considers the necessity to resist a falling of 50 meters or 60 meters, and given that the shock is larger after falling 60 meters, maybe these ropes have to be stronger ?

6. Dec 16, 2008

### kenewbie

According to the Guinness Book of Records (!) a falling human reaches terminal velocity after approximately 560m of free fall, so the shock needed to be absorbed at 50 meters is indeed less that at 60.

Being practical though, you have the exact same distance between your safety-plugs regardless of the length of the rope. It is not like you will fall the entire length of the rope. This also eliminates the "weight of the rope" argument, as you always have a segment of x size when you fall, regardless of the total length of the rope.

k