# Thread: Origins of 83.333% [5/6?] guide

1. Wow after all that math, I'm worn out, going to take a nap in my hammock!

Cat curves are mathematically much messier than parabolas, and yet there is very little quantitative difference between them. I thought that if I considered the question using parabolas and found an answer quite a bit different than 5/6, that would be strong evidence that the answer to the question is "no".

So. y = a*x^2 + b is a parabola. The derivative is
dy/dx = 2*a*x. The question asks about the curve where the angle of the hammock at the ridge-line is 30 degrees. In geek-speak that is PI/6.
x of interest here is half the ridge-line length, because the parabola's minimum is at the center of the ridge-line. So fixing x at whatever, say 108/2, we can set up
dy/dx = 2*a*x = PI/6
and solve for a
a = PI/(12*x)
and this characterizes the parabola of interest.

Now there is some formula for the arc-length of a parabola over a range but it too is nasty. I've got code I've cooked up for bridge hammock designs that numerically computes this quantity, and so here I can empirically compute the ratio of ridge-line to hammock-length for a variety of hammock lengths to see what I can see.

What I see (accepting of course the possibility of some blunder-headed mistake along the way), is a ratio that over a wide range of ridge-line lengths is 0.957 with any differences in digits beyond that.

In particular, no-where close to 0.833333

suggesting to me that wherever 83% comes from, it ain't from a cat curve's slope when that slope is 30 degrees.

here ended the first lesson
This is why Grizz is known as Professor Hammock!

3. Originally Posted by FLRider
Yep, but the SRL shortens the hammock to about 83% of its length as a starting point (which makes the hammock hang as close to a 30 degree angle as possible with the materials involved). It doesn't do it perfectly, since--even with dyneema line as the SRL--it's a dynamically changing surface with different load points. It's elastic to a certain extent, which is why hanging the hammock looser feels better (if my high-school-level understanding of the physics involved is right).

If my own experience is any guide, the center of the hammock still remains at that 30 degree sag when strung tight. However, the edges of the hammock try to meet each other to take up the rest of the slack--I think this might be due to the way the hammock is whipped--causing shoulder squeeze. Of course, that could just be a body issue on my part; not everyone is built the same way, after all.

Bolded for emphasis. That's the worst pun I've read all month. By rights, I should flee screaming into the night, holding my nose...
Plus one on that, Bravo!

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