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  1. #1
    Senior Member fugalster's Avatar
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    Single Point Suspension (an engineer's approach)

    I've been toying with the idea of tree camping for a little while now (shout-out to www.treefool.com). But I want to do it with my existing hammock gear. Turns out finding some anchor points far enough apart in the canopy can be kinda difficult. Wouldn't it be nice to only need one tie off point?

    The ridgeline's job is to keep the hammock ends the correct distance apart, but it only works in tension. If I swap out the ridgeline for a rigid spreader bar it should work in compression, too, which means the ropes can come back toward the center of the hammock and join ends, which then can rise vertically to tie off on a branch.

    The concept is simple enough, but the problem is the potential for the spreader bar to buckle under load. The bar can have plenty of compressive strength but if it's able to bend to the side it could collapse on itself.

    WARNING: Nerdy math follows.

    I looked up Euler's column formula, which deals with buckling, and determined n=1 (ends allowed to pivot). Then, using the free body diagram below, I calculated the compressive force in the spreader bar. From there the required EI (modulus of elasticity (material) * area moment of inertia (shape)) of the spreader bar can be calculated. I made a list of the EU of easily obtainable bars and tried each of them until I found a bar that offered a reasonable safety factor.

    single_point_hammock.jpg

    All these calculations I built into this spreadsheet so I could play with different values. Some things to note:
    • The force to buckle is inversely proportional to the (length of the bar)^2. That means increasing the length of the bar by 10% will decrease the force to buckle to 1/(1.1^2)=0.83 , or 83% of the force of the unlengthened bar.
    • The height above the bar where the lines join together will influence how much force is on the bar. Increasing the height will decrease the force on the bar.
    • A larger diameter hollow bar is much lighter than a solid, smaller diameter bar with the same EI.


    END OF NERDY MATH

    For my setup I didn't want a huge height between the spreader bar and where the ropes tied together so that I could hang high up more easily. With my weight and preferred ridge line length a 3/4" steel conduit pipe turned out to be strong enough and very cheap ($3.40 at Lowe's!).

    Currently this is not a backpacking friendly setup. The bar weighs just under 4 pounds and is one continuous piece that's hard to fit anywhere. But I've got some ideas of how to use multiple tent poles attached together in a way to reduce their effective buckling length (remember that L^2 from Euler?). I'll come back with more details once I try it out.

    IMG_20160605_121754.jpg
    IMG_20160605_121908.jpg
    IMG_20160605_121726.jpg
    IMG_20160605_121656.jpg
    Last edited by fugalster; 06-05-2016 at 14:33. Reason: Corrected Math

  2. #2
    Senior Member Ratdog's Avatar
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    Excellent.

    Any studies on the strength of limbs, limb type, limb to tree joint type and the type of wood for a given tree?

    The manmade stuff, I figure we have a handle on that, but hanging 14' out on a 12" diameter limb for say a poplar tree with a 24" diameter, assuming no carpenter ant damage, given the single point of failure at the limb and downside risk, I'd be interested in that stuff as well.

    EDIT: tracked down some info, not a bunch but there's more out there.

    Branch to stem diameter ratio affects strength of attachment. Turns out how the branch attaches to the tree doesn't matter as much as one might have thought.

    http://hort.ufl.edu/woody/documents/...es/EFG0301.pdf

    Mechanical stability of trees under dynamic loads. References to Euler and several others. Mostly concerned with the impact of wind and storms but the swaying information and loads seem to be relevant.
    http://www.amjbot.org/content/93/10/1522.full

    Structural features related to tree crotch strength. Given that you have to hang out on the limb, not as relevant but still interesting.
    https://theses.lib.vt.edu/theses/ava...thesis0610.pdf

    Each of these papers references source material in addition to the independent studies, so there's more to dig into.
    Last edited by Ratdog; 06-05-2016 at 15:04.
    Have sherpas, will travel...
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  3. #3
    Senior Member fugalster's Avatar
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    Thanks for the info! I'm new to the sport, so I err on the side of too strong of a limb.

    And always follow a basic climbing rule: never trust your life on one anchor point. In addition to the hammock tie off, you should sleep in your harness tied off to the main trunk in case the branch does break.

  4. #4
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    I've used a length of 2x4 as spreader bar in my back yard but used 2 closely spaced attachment points instead of one.

  5. #5
    Senior Member Tacblades's Avatar
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    How do you fit the tarp?
    ..........................................
    Tacblades

  6. #6
    Senior Member fugalster's Avatar
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    Exact tarp setup us TBD. It will be custom, for sure. I'll probably be stealing some ideas from the portaledge crowd.

  7. #7
    Senior Member GadgetUK437's Avatar
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    Sounds like you need to talk to Refreshing (Treefool).
    I've used a ridge pole for years on my lounger.


    --
    Gadget.

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