Catenary / Parabola Curve Calculator

[TinCanFury]

I recently wanted to make a tarp with catenary cut so I downloaded your spreadsheet to get the curve values. Before building I plotted the curve in a CAD program I use. I also compared it to a pure arc as drawn in the cad program. Much to my surprise the straight arc and the catenary curve varied by only hundreths of an inch when plotted in CAD. The reason the two are so closely matched is the relatively shallow cut used when making tarps. A much deeper cut would then have the catenary curve and arc significantly deviate.

I'll go one blasphemy further. I don't think the catenary shape is any better than any other even shallow curve for non-ridgeline cuts, and for the ridgeline I think the catenary cut is actually a detriment.

There's a lot of pseudo science/engineering in backpacking DIY, and the strict adherence to the catenary curve is one of the most egregious. That said, for those making tarps that don't have access to CAD, the hang a rope and trace the curve method is the easiest way to get a shallow even curve, so it's a wash at the end of the day. When I design my tarps and tents in CAD, I don't bother with a catenary formula, I just do what you did.

[XTrekker]

The curve generator is for those who wish to just plot the marks on fabric and cut. There alot of methods that lead to the same end. None are necessarily wrong. Even if you just eyeball it, your tarp will be just fine.

Sent from my SM-G900V using Tapatalk

[GadgetUK437]

Are you happy to share the unlock sheet password?

I want to add a "X inches per foot" input that will generate the depth of curve input, based on the length and the inches per foot requested.
Like this,
Depth of curve = ((inches per foot)/12)*(length of curve)

[blackbishop351]

Just FYI.

There's no such thing as a printable "perfect catenary curve," since the functional form is analytically intractable. All that can be done is exactly what you did, provide point-specific values (coordinates).

I'm glad someone else made one of these. People were having strange issues with the one I provided with my BlackCat tarp instructions.

Also - what do you mean by "parabola?" Afaik, a parabolic curve won't provide the same stress dispersal as a catenary.

Thanks!

[kitsapcowboy]

Afaik, a parabolic curve won't provide the same stress dispersal as a catenary.

With your legendary reputation, I have no doubt that you understand these engineering points better than I do, but I was under the impression that while a true catenary curve used in typical hammock applications will outperform a parabola, for certain common aspect ratios in those same applications a parabola is usually a sufficient approximation to the appropriate catenary curve to provide some of the same engineering benefits and has the virtue of being easier to describe and compute mathematically. My $0.02...

[blackbishop351]

for certain common aspect ratios in those same application a parabola is usually a sufficient approximation to the appropriate catenary curve to provide some of the same engineering benefits and has the virtue of being easier to describe and compute mathematically. My $0.02...

If your goal is to simply remove some material to avoid sag, then yes the parabola is an acceptable substitute. If you're after actual stress dispersal, the catenary is the way to go.

For example, a parabola on a tarp isn't going to get the job done due to the large surface areas and types of stress you encounter. But for a hammock maybe (I have zero experience using a curved cut on a hammock btw), the parabola might work fine.

[kitsapcowboy]

If your goal is to simply remove some material to avoid sag, then yes the parabola is an acceptable substitute. If you're after actual stress dispersal, the catenary is the way to go.

For example, a parabola on a tarp isn't going to get the job done due to the large surface areas and types of stress you encounter. But for a hammock maybe (I have zero experience using a curved cut on a hammock btw), the parabola might work fine.

I stand schooled; like I said, you are the expert.

One must conclude that your construction skills and standards are indeed as refined as your knowledge with regard to tarps -- you yourself having invented a particular kind of tarp that has been widely copied -- because when I compute a true catenary curve 72" long by 5" deep -- which would be a relatively common shape for a cat-cut on the side of a hammock tarp -- and compare that to a parabola of the same depth and span -- specifically y=(5x^2)/1296, intersecting the points (-36, 5), (0,0), and (36, 5) -- it looks to me like the catenary and parabolic curves are approximately congruent to a precision of about +/- 1/16 of an inch. That is to say, if you draw the two computed curves -- catenary and parabolic -- on the same paper template, the two respective lines stay within about 1/16" of each other along the entire curve.

I know for a fact when I sew complex curves or hems on the bias, my sewing skills admit variation of at least that magnitude. If I had known beforehand that variances of +/- 1/16" would mean the difference between a tarp that hangs and a tarp that fails or between a hammock that holds its rated weight and one that blows up under load, I would probably never have attempted any of my DIY shelter system projects to date. I guess I have been lucky so far.

[blackbishop351]

I'm no expert, I just took some math in college and played around with some tarps. Obviously I don't have a Master's in sarcasm like you do.

Do whatever floats your boat.

[kitsapcowboy]

I'm no expert, I just took some math in college and played around with some tarps. Obviously I don't have a Master's in sarcasm like you do. Do whatever floats your boat.

No sarcasm (or offense) intended -- although the degree I hold in sarcasm is technically doctorate-level...

My operational definition of "hammock legend" is anybody who has entire categories of hammock gear named after her/him. That's you on at least a couple of counts.

Your reputation on HF is beyond reproach, and it is a fact that you are an old guard pioneer in DIY hammock tarps.

I really do want to understand the physics as you do that explain how variances that seem so minor to a layperson like myself, i.e., presumably beyond the limits of precision for at least some segment of the DIY community here, actually lead to meaningful differences in performance on a tarp build. You pointed out that you have the technical background that afforded you this understanding; in truth and in deference, I am just hoping you can explain it to the rest of us who have been taking a short cut in error.

(PS:

"Physics is the only true science. All else is stamp collecting." - J. J. Thompson

I had always thought that your signature line quote was attributable to Rutherford, not Thomson, under whom Rutherford worked. Learn something new every day...)

[Kroma]

Does this have anything to do with the parable of the cat and the canary?