For those who love the power of calculus I've attached a PDF of the Mathematica notebook I used.
Oh God, not again...
Before you posted this I found formulas for the arclength and tangent angle of the cat curve, which let me gin up something in Perl to solve numerically for the ratio of interest....and it was close to 95%.
On seeing this I went back to my equations and see the problem,
a = tan(PI/6)/L, not a = 2*tan(PI/6)/L. With that fix the parabolic approximation comes in with an answer at 95% too. So...the mystery of the origin of 83% remains.
NCPatrick---that is an EXCELLENT cartoon. A number of fundamental equations in there I recognize, and a bunch that I don't. This is T-shirt material....!
(alias ProfessorHammock on youtube)
I did not think that the 30° angle was specifically related to the 83% rule. I thought the 30° bit came from the force on the suspension, once you get much past 40-sum degrees the load almost exponentially increases. I of course can't find any chart to back that up, and I'm no mathlete so I can't prove it out mathematically either.
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Any chance it's just empirical knowledge. As people hung the hammocks they noticed were it was most comfortable and so came up with the ridge line. After the fact somebody decided to build a new hammock of different length, measured the ridge line, measured the hammock length, bam found a ratio and that ratio worked as hammock length changed.
I'm from the TLAR school "That looks about right" although it's probably the TFAR "That feels about right" school which created this rule.
I may be slow... But I sure am gimpy.
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Patrick - I too like the graphic. May have to make it part of one of my class websites. Students just love it when I bring up a graphic they've been doing their best to ignore and show them that its an integral (sorry - pun NOT intended) part of the course.
Won't any old coot sure he's as smart as back then check the records on this?
Is Hennessy really the originator of the guidance? Or is that a just so story,too.
Are you sure that 83.33% is not a mis-transcription, a copy error of 86.6%, .866 being the cosine of a 30 degree angle. (Sit in the center of a 100" hammock stretching between trees 86.6" apart and the hang angle will be 30 degrees) and the ridgeline barely taut.)
[A big BTW is that much as folks like to refer to cat cuts and the bridge hammock (BH) as being catenary curve based, according to references in raifenuke's comment, a suspension bridge is better modeled as a simpler parabola, what with its very heavy deck, and so certainly for the same reasons --negligible weight of the bridge hammock compared to even Grizz's lightest beneficiaries -- should bridge hammocks. All well covered in prior notes here?]
Last edited by DemostiX; 04-11-2012 at 19:05. Reason: cat vs parabola
In the military, no one knows WHY we are told we have 9 seconds to put our gas mask on, WE JUST DO IT...
Could the same simple solution apply here as well? It's 83% just 'cause?
I'm dropping this class, sorry guys...
A very confused Shnick