Physics of SRT tie off

In Jepson's book, he states that when you rig a single rope running over a branch, then tie off the rope at the base of the tree, the downward force on the branch while you're climbing is equal to double your weight. Can anyone explain why the weight is doubled, and do it in understandable terms? I searched the treebuzz.com boards and didn't get a clear answer.
Thanks!

Patrick,

When my 200 pound body weight is connected to a double rope over a limb, a load of 100 pounds is placed on each rope. The limb has 200 pounds. 100+100=200.

When a static rope runs over a limb and is anchored to the base of a separate tree, a 200 pound load is on the rope holding me. I don't fall down because there's a 200 pound resisting force to the tie-in on the second tree trunk. Each side of the rope carries 200 pounds. The limb takes both loads. 200+200=400.

Jepson's depiction of the resulting loads is accurate to establish the concept. However the angle of the rope over the limb changes the actual loading. At the end of the day, you climb with a rope, not a calculator. Though, it's good to realize how the load on the limb holding you can double.

I felt the need to experience this for myself, because actions speak louder than words. I held a carabiner in my hand as the tree limb. Taking the Statue of Liberty pose, I found a maximum weight that I could hold. Using a cord attached to this weight, I connected the remaining length to my carabiner with a clove hitch. At this point in the Statue of Liberty pose, I'm ok with holding the weight. Then I untied my clove hitch and ran the cord through the carabiner, using a door knob as the anchor point. This created the inverted V where the side with the weight represents the climber, the carabiner is the limb and the door knob anchor is a separate tree trunk. In this configuration, I couldn't hold the weight up in the Statue of Liberty pose. I could feel the dramatic increase in weight.

You should be able to recreate this, using cord and a fish-scale holding the carabiner. I didn't have a fish-scale to measure the actual weight change, so I did the above description, which relied upon the "feel" and the physical failure of my arm to suspend the weight.

Regards,
JimK

Wow, that was a good description. If anyone doubts that it's double a load, they can try that test! Nice.

love
nick

I too, had trouble with visualizing this double load when I first started climbing. Only my problem was when I tried to assist another person in advancing their rope. I could'nt figure out why it was so hard to pull on the standing end of another persons climbing rope when it was so easy to pull the standing end when I was climbing myself. Of course, it was because I was only pulling half my weight. When attempting to help another person climb, I was pulling all their weight. If I weighed less than the other person, it would be immpossible to lift them at all. I could hang on the rope all day and not go anywhere.

It was also easy in this position to see that the branch was now carrying both people's weight.

Hey, it's all just physics!

As long as you're talking physics, don't forget the frictional force at the branch. The load on the branch due to a ground tie-off is only double your weight when the friction is zero. As the friction becomes large, the branch only supports one times your weight, since large friction (a sticky branch) approximates a tie-off at the branch.
Then remember the difference between static and dynamic friction. If the rope is not sliding over the branch, the friction is of the static variety, which tends to be large, especially if the bark is rough. If the rope happens to slip, even a tiny bit due to the swaying of the tree, for example, the friction can change dramatically, as dynamic friction (rope moving over branch) tends to be much less.
The result in the real world is that the force on the branch would generally be somewhere between one and two times your weight.
This question calls for a fish scale and two carabiners!

Originally posted by JimK
You should be able to recreate this, using cord and a fish-scale holding the carabiner.

Great description!
I tried this out using an ankle weight and a measurement tool we use to see how strong someone's grip is. The weight hanging from a tied off SRT setup was twice as heavy than when the weight was hanging straight down (like a DRT setup). It was also very easy to see that the weight dropped significantly as the tie off angle was changed to be more horizontal:



more wt. on limb

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> less wt. on limb