04-06-2018, 12:02 PM
7138
Re: Leisurely Scribbles (part 5)
Good moaning all and one. 'Tiz a lovely day by here on the Riviera. I have just ordered a load of brass chain to string (or should that be to chain) across my pond in my eternal fight against the fish stealing heron wot keeps a-visiting.
Pond life is an oft used derogatory expression, but the lives of the things wot inhabit my pond are to me a thing of beauty, and fighting for their lives is something I take seriously.
In the early days of stringing chains, ropes, and cables, a new mathematical formula had to be invented to calculate the correct length. Previously it had been assumed that a chain, rope, or kay-bell would describe a parabola when hung.
However, every time this was done, the chain rope or cable length came out wrongly, lengthwise. It was eventually realised that the shape described was different to the parabola theory and thus a formula was developed, called a catenary.
y = a cosh(x/a)−a.
When calculating the length of chain needed for my garden pond, I pace it out, convert paces to metres, and then guess how much extra I need for the amount dropped over the length or width. It are very compilcated, I assure you.