Origins of 83.333% [5/6?] guide

[DivaB]

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

KAPOW!!! Spontaneous brain explosion.

[ernesthemmingway]

I wont claim to understand all of this, but it is a very intersting thread. Keep it coming mathematical hammockers!! We need to figure this thing out.

[Murl]

KAPOW!!! Spontaneous brain explosion.

Me, too!
Definitely time for some field testing, but I think I'll go with 80.7%
I'm starting to think that the hammocks aren't all that's strung too tight around here.

...just kidding, guys. I actually find this pretty interesting.

[DemostiX]

Grizz might be laughing at the amount of fuss he avoids with the feel engineered into his bridge hammocks, instead of it having to be calibrated into the hammock in the field.

The difference between 83.6% and 86.6% inches of ridgeline on a (short) 8 foot hammock barely squeezed between two trees is about FIVE inches of hammock bed height, an irrelevent difference we notice, though, from our dailiy lives sitting down on chairs. That's also a large difference even for a short man on a short hammock.

Put that short hammock between trees twice as far apart, 15', and the difference in seated height -- or adjustment in straps on the trees is doubled to 10 inches.

I still want to know when and where the creed of 83.3% was written, even if there are so many many casual followers. Maybe because Hennessy has a patent on the adjustable ridgeline, and that the Warbonnet BB fixed ridgeline came to be a standard prescription(as a %)?

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I'm just reading differences off a cosine table here. For rule of thumb:
Within the 25 - 40 degree range of hang angle, there's a 1 to 1 correspondence in % of ridgeline and degrees of hang. eg: shorten the ridgeline by 1%, and flatten the angle by 1%.

[oldgringo]

Why don't you ask Hennessy?

[Trooper]

I quit reading after a few posts--math confuses me. But, as mentioned, Hennessy originally proscribed a tight suspension, and my stuff sack from 2007-2008 shows that any change is fairly recent. Also, as Red pointed out, the 83% and the 30° suspension may be completely independent.

I know the 30° is what Brandon suggests on his setup video for a Warbonnet hammock, and I assumed we just adopted it from there. I also thought the 83% is what Brandon used, and that number was derived from reverse engineering the Warbonnet hammocks.

I know that my Hennessy feels more comfortable with a tighter suspension than hanging at 30°, so I don't think that number is relevant to comfort for any given hammock. However, the stresses created by the angles do increase quickly at angles less than 30°.

[Adarack]

This is a very interesting thread. I wont pretend to understand all the math used but the principals involved are coming through loud and clear.

I have to wonder if the source of this is less about semi-complex mathematics and more about trial and error. Perhaps whomever first created the 83.3% rule simply kept trying different lengths till one worked and that happened to be 83.3%. Could it also have been from observation of what length people tended to use with a given length of hammock on their DIY builds?

[mophead]

I am very interested to know if the ~83% was calculated out and if so how.

But I had never heard of the figure. I just set up my hammock afew times until I got it comfortable and locked it in. It's now at a little over 82% From what I've read here same happened to others.

This makes me wonder if it was not discovered empirically. Like a bunch of hangers got together averaged their lengths and got 83. The repeating decimal also makes me wonder though...

[DemostiX]

I've just started hanging a Clark with a much smaller fractional ridgeline. I'm very familiar with the hammock from over 100 nights in it. I can tell you that it is a very different hammock at 83-85% ridgeline than at 87-89%. For the first time, I am thinking of Knotty's stretch-side, so loose are the sides and so broad is the hammock starting to become.

So, just a few % difference in ridgeline length makes a large difference, as many have attested. "Dialing in" around 88% is much different than dialing in around 83%.

That said, I'll suggest that nobody does well in estimating 30 degrees from horizontal within just a few % by eye, so a ridgeline is informative.

Now, the easiest way to get the information with a string and without a ruler is to measure off some distance between ends of the hammock (or between attachment points beyond ends of the hammock.) Fold the string over to exact thirds. Fold in half. Mark off the last crease from one end. You've got 5/6 or 83.33% of the hammock length left in your hand, the often-recommended ridgeline length. Add a few inches, and if you ridgeline is now just barely tight with you sitting in the hammock, then you are hanging at 30 degrees, too.

[ezadventurer]

I find all of the formulas quite impressive and would be wont to actually have to work out all of the necessary mathematics to determine whether this 83 percent in some way correlates to the 30 degree angle. With that said, however, I am a little confused on the initial assumptions that are made and then used in the formulas. I understand the 83 percent since this is just the supporting ridgeline length as a percentage of the hammock length from the gathered ends. The 30 percent is what throws me. I have viewed the video on the warbonnet hammock and clearly see where he talks about the 30 degrees, but this 30 degrees is the measured angle of the supports and not the angle of the hammock. If you look at the ridgeline and assume that is 0 degrees, then look at the support lines you can see a 30 degree angle from that 0 degree angle; however, if you extend that 30 degree angle towards the ground, the hammock does not form a 30 degree angle down from the ridgeline. It is closer to a 50 or 60 degree angle. This is of course due to the greater weight of the hammock fabric in comparison to the support lines but I believe it is enough to throw off the calculations.

Then again, I may be wrong.

ez