# Back-tie rigging – tension and compression forces

## Back-tie rigging – tension and compression forces

The other day I had a question come through about how I worked out the tension and compression forces for a post, pole or tree when you back-tie for support.

### The context?

Before I get to the question, we need to set the context:

1. The front anchor is in the right location; however, it needs a back anchor to make it acceptable with sufficient margin.
2. The back anchor is some distance from the front anchor.
3. Multiple strands are tensioned to reduce stretch in the rope or cord over the back-tie distance.
4. The front anchor can sustain any forces applied in compression, but the post needs support for a bending (moment) force as the rigging is off the ground.
5. Having the anchor rigging higher is to get it off the ground, so it’s easier and safer to operate. For example, it has less friction for a rescue raise, or if you are abseiling/rappelling over an edge, it makes the transition easier.

### Now to the Question

I wondered what trig functions you are using on page 194 of the guide (Rope Rescue and Rigging Field Guide)? I understand the “factors”, I’d like to run the numbers to better my understanding.

Good question. I had my workings scribbled on a bit of paper. I have put it into a 2-page summary for you to work through (see the download at the end of this post). The following is the process I used to work out the factors in the book.

#### Notes

• Orientating the drawing vertically made it easier to see what’s happening. Imagine having the load hanging on the end of the post. But it can be in any orientation.
• C1 is a solid object subject to (and can handle) compression such as a post (tree, pole or similar).
• T1 is the rigging that supports the post and subject to tension such as a rope (wire, cable or equivalent).
• It’s a 2 stage process. First, work out the tension (T1), then the compression (C1).
• Use the three basic trig ratios – SOH CAH TOA – to solve a missing side in a right-angled triangle.
• Check out this link if you need a reminder of how it works. (https://calcworkshop.com/triangle-trig/sohcahtoa/).

#### Stage 1

• Start with the tension on the rigging T1. Break this down into x and y vectors T1x and T1y.
• For every action, there is an equal and opposite reaction. Whatever the load is also on the T1y vector.
• The angle formed by T1x-T1 is the same as the angle formed by T1-C1 (alternate angles inside a transversal). I have put an equal sign on the drawing.
• Now use SOH (Sin angle = Opposite/Hypotenuse) with the formed right-angle triangle (Tx-Ty) to work out the tension on T1 (which is the hypotenuse).
• Manipulate the equation to get T1 = L/Sin angle.
• Plugin the values you know (the load(L) and the angle) to determine the answer.

Check out the download worksheet below for the workings and examples.

#### Stage 2

• Now use CAH (Cos angle = Adjacent/Hypotenuse) with the formed right-angle triangle (C1-T1) to work out the compression force on C1 (which is the adjacent).
• Manipulate the equation to get C1 = T1 x Cos angle.
• Plugin the values you know (which is T1 from stage 1 and the angle) to determine the answer.

Check out the download worksheet below for the workings and examples.

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