Tying Up Small Loose Ends
We were at the Whangie, when the inevitable happened. Giuliana had mistaken the route next to the descent route for the descent route itself, and was perched just above an overhang. The sun had long since set, and we were trying to swing a rope to her through the gloom when a small voice came up from the darkness: "Daddy, look where I've got to!" He was going to have to be looked after properly. Besides, I would need someone to lead the hard bits when I was too old for them.
Now, the problem with protecting a small child climbing is the difficulty of fixing a rope to it. A climbing rope is too stiff to tie to a small person directly, and adult harnesses or waist belts are just too big. I decided to make something.
The something had to be simple and secure. The obvious first idea, a waist belt, didn't work - small children don't have waists - so a chest harness seemed the best idea. The stress-carrying member of a chest harness is the belt; the shoulder straps merely hold the belt in place, so an old camera strap was good enough for them. The belt was the interesting part. 25mm tape as used for slings seemed ideal (and a rainbow-coloured sample appealed to the intended victim), but no-one made an adequately strong buckle.
The design of a buckle is not simple, as the forces on it are complicated. A one-ton minimum breaking strain seemed a good design aim. The conventional buckle is two holes joined together with metal, like this:
The belt passes through the buckle like this:
The three verticals are heavily loaded in shear, and the horizontals have a combination of compressive and bending stresses. A design with equal cross-sections in every member looked aesthetically right, and with this configuration the most significant stress is the bending of the horizontal member. For a 25mm belt and a high strength stainless steel (321 S12, 33 tons/square inch) the dimensions ended up as:
Hacking this out of a lump of stainless steel was not easy. Ordinary non-stainless steel would have been easier to cut, but is less decorative and would have gone rusty. I was careful to put large blend radii on the internal corners to avoid stress concentrators, and I rounded the sharp edges externally for comfort and internally to avoid cutting the belt material.
Analysing the strength of a piece of metal is a straightforward engineering problem with textbook solutions. However, I couldn't find any books about the strength of sewn joints. The sewing books in the library were more concerned with neat pleats and stylish buttonholes than about whether the clothes would stay together. Eventually, I decided to experiment. Stitches made by a sewing machine look like this:
I simulated one stitch with two interlinked loops of strong button thread and hung a small plastic bucket from the lower loop. I poured water into the bucket until the thread broke. This happened when the water and bucket weight about 9kg. Repeating this gave quite consistent results; the variation was only about +-20%. This suggested that 110 stitches were needed to meet the one ton breaking strain requirement. To give a safety margin and to allow for uneven stress distribution, I used 1000 stitches, which sounds a lot but is only a few minutes work with a sewing machine.
Although I was confident with the design, it seemed wise to test it. At the time, I had access to an industrial sewing machine, but I could have tested the belt by hanging it from the garage roof and lowering a car onto it from a jack. For the test, I made up a sample using the real buckle and real stitches and, for economy, some tape from an abandoned abseil sling. The test set-up was cruder than it should have been, and the belt was tensioned between sharp-edged bars rather than round bars. The old tape tore at one of the sharp edges at 1100 kg load, which seemed an adequate vindication of the design. There was no slip in the lacing of the tape through the buckle, nor any damage to the stitching, though the arms of the buckle bent by about 5ø.
How did the real belt work in use? The victim (and his mother) seemed happy with it, and I was a lot happier when he used it rather than scrambling about unroped. It was important to tie the rope on directly rather than using a karibiner, to avoid a smack in the face from the Krab when tension came suddenly on the rope.
Anyone copying this should be aware that, although what I have described was intended to be an honest piece of mechanical engineering, it comes with a "big boy guarantee" - you're a big boy now; don't come back and complain if it doesn't work. You should also remember that a light weight falling on an adult climbing rope stops in a shorter distance and therefore with a bigger jerk than a heavy weight, as the rope stretches less.
TAC 23 Index