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  1. #1
    Senior Member DemostiX's Avatar
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    Origins of 83.333% [5/6?] guide

    Will an old coot, hammock bee, or geek of any age point to a source or two on the 83.33% guidance for estimated ideal ridgeline length in ratio to gathered hammock total length? Do hexagons, optimal packing, and 5/6 come in somewhere?

    I'm sure it is back there, somewhere, but this gospel hasn't been indexed, yet.

  2. #2
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    I figure it is because the early hangers new they would need an easy way to check their angle of hang and needed to utilize something they always had available. Thus the 83% rule was born to fit the 30* rule and the Materials At Hand.

  3. #3
    Knotty's Avatar
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    Only thing I know is that Hennessy hammocks used that ratio and they're the ones who popularized hammock camping.
    Knotty
    "Don't speak unless it improves the silence." -proverb
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  4. #4

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    while I like my Hennessy I also went through a couple of periods of of playing with DIY hammocks to get a feel for different things. I think that is as good a standard as one can ask for but it is a general number. Folks who want to play can change that and *may* get an improvement in how they fit their hammock the way they lay in it.

  5. #5
    Senior Member DemostiX's Avatar
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    So this is a Grizz question

    Is the number really 5/6?

    And if so, where do I find the proof that the when a catenary curve is hung such that the limiting angle is 30 degrees, that the horizontal line between the two legs of the curve will be 5/6 the length of the curve?

    I'm not doubting its true. I'm just fascinated -- those were the references to bees, optimal packing and hexagons in my question.

    Is there something behind Tom Hennessy's 30 degrees, in engineering? Maybe something about the distortion of the surface of the sling when a horizontal rod / body is placed diagonally across it?

  6. #6
    Prefers life at 12 MPH. FLRider's Avatar
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    Can't answer the geometry questions; my math peters out towards the end of high school. However, yes, 83.3 (repeating) is 5/6 of 100.

  7. #7
    Moderator raiffnuke's Avatar
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    Quote Originally Posted by DemostiX View Post
    Is the number really 5/6?

    And if so, where do I find the proof that the when a catenary curve is hung such that the limiting angle is 30 degrees, that the horizontal line between the two legs of the curve will be 5/6 the length of the curve?

    I'm not doubting its true. I'm just fascinated -- those were the references to bees, optimal packing and hexagons in my question.

    Is there something behind Tom Hennessy's 30 degrees, in engineering? Maybe something about the distortion of the surface of the sling when a horizontal rod / body is placed diagonally across it?
    The Catenary curve can be any angle. Not just the comfortable 30 degee angle.


  8. #8
    Senior Member DemostiX's Avatar
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    Yes, I know that well. The question is whether when the angle is 30 degrees the horizontal distance between the legs is exactly 5/6 the length of the catenary.

    This is of no consequence whatever, except as a matter of trigonometric relations.

    Well, actually it is convenient, because without a ruler, you can easily find exactly 5/6 of a line: By repeated approximation, fold it into exact thirds. Then fold it in half.)

    But, I'm interested in geometry / trig.

  9. #9
    GrizzlyAdams's Avatar
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    Quote Originally Posted by DemostiX View Post
    Yes, I know that well. The question is whether when the angle is 30 degrees the horizontal distance between the legs is exactly 5/6 the length of the catenary.

    This is of no consequence whatever, except as a matter of trigonometric relations.

    Well, actually it is convenient, because without a ruler, you can easily find exactly 5/6 of a line: By repeated approximation, fold it into exact thirds. Then fold it in half.)

    But, I'm interested in geometry / trig.
    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
    Grizz
    (alias ProfessorHammock on youtube)

  10. #10
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    *brain hurts....brain hurts....brain hurts*

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