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

1. Originally Posted by FLRider

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...
Thank you. Thank you very much. I'm here all night...

someone 'round here good at Mathematica?
You rang?

which the quick-witted but never-the-less kind among the gentle readership here have not pointed out. The blunder-headed mistake.

For you see, the slope of the line at 30 degrees is not PI/6, it is of course the length of the opposite side of the triangle over the length of the adjacent side, known in the biz as "tangent". Substituting tan(PI/6) in the equations where once PI/6 stood as an object lesson in the wisdom of not posting hastily, and re-doing the calculations gives the ratio of interest as....wait for it....
0.83 with some other digits that aren't 33333, but I'm doing numerical integration here, and probably more to the point, the parabola ain't a catenary curve.
Hmm.. I worked this out for both the catenary and the parabola and am getting no where near 83% - closer to 95%. In fact Tan[Pi/6] is very close to Pi/6, so I don't see why your result would change so much. But maybe I've made a blunder somewhere?

For those who love the power of calculus I've attached a PDF of the Mathematica notebook I used.

3. Oh God, not again...

Shnick

4. Originally Posted by krugd
You rang?

Hmm.. I worked this out for both the catenary and the parabola and am getting no where near 83% - closer to 95%. In fact Tan[Pi/6] is very close to Pi/6, so I don't see why your result would change so much. But maybe I've made a blunder somewhere?

For those who love the power of calculus I've attached a PDF of the Mathematica notebook I used.
Hi Don! The more the merrier...

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....!

5. 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.

6. 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.

7. Originally Posted by Shnick
Oh God, not again...

Shnick
It's been a while since we've had a good mathlete Olympics....

8. Originally Posted by Shnick
Oh God, not again...

Shnick
You sound like some of my students. Don't worry, no quiz this week.

Originally Posted by BBenski
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 think that's probably it. Someone dialed in their own hammock and then started passing around the number. Though 83% sounds a bit too exact for anything empirical.

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.

9. 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?]

10. 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

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•