True Catenary Curve

[kitsapcowboy]

The ancient one is to fix a weighted chain on two ends and let the weighted length hang down. You can do this by taping heavy string to silnylon and then hanging the fabric on a vertical wall. Trace the curve with a pen or chalk.

I have used this method many times in the past to achieve a satisfactory result with no calculations (only two measurements), except I have usually traced the shape of the suspended cord onto paper to make a template that would then be applied to the fabric as needed.

[jellyfish]

You can compare the True Catenary Curve with the Parabola here:

Catenary vs. Parabola Calculator

This is the version with the most extreme difference that I plotted, which is 12' rise over 12' or a 1:1 ratio.

12-12 catenary and parabola.JPG

You can play around with it, but you'll have to unhide some of the columns and rows.

[GrizzlyAdams]

I have used this method many times in the past to achieve a satisfactory result with no calculations (only two measurements), except I have usually traced the shape of the suspended cord onto paper to make a template that would then be applied to the fabric as needed.

Not to be pedantic (but being so anyway) the 'bent rod' method is a great and easy way to get a symmetric curve, but the curve you get will be neither parabolic nor catenary. I gather that the jellyfish's desire for a catenary curve has to do with the mathematical esthetics of the curve, because (as was already pointed out) for the purposes of an endcap there's no real load being carried. For me the endcap esthetics are practical. The parabola is an easier curve to manipulate mathematically (e.g., for a given width and arc length, what is the length) than the cat curve.

Let many curves blossom, or whatever it is that curves do to progenerate.

[jellyfish]

I gather that the jellyfish's desire for a catenary curve has to do with the mathematical esthetics of the curve...

Oh yes! Nailed it.

[jellyfish]

Phi is my new favorite number. Stay tuned for the golden ratio hammock. Lmao.

[FJRpilot]

The parabola is an easier curve to manipulate mathematically (e.g., for a given width and arc length, what is the length) than the cat curve.

Lol... Easier for some professor... then there are the rest of us.... I feel guilty preying on Jelly's kind nature. Thanks Jelly, I really do owe you. This is just what I needed.

[jellyfish]

Lol... Easier for some professor... then there are the rest of us.... I feel guilty preying on Jelly's kind nature. Thanks Jelly, I really do owe you. This is just what I needed.

I am getting a zen moment with the catenary. Less so with the parabola. It lacks the elegance of Phi. It is not divine.

[jellyfish]

I haven't done this much excel since graduate school. Hahahaha

[GreatBigDave]

I'm wondering. Is it the catenary curve (which describes an even pull perpendicular to a fixed horizon) or a hyperbola (which describes a curve that infinitely approaches intersecting asymptotes) that will render even, puckerless, stretch across the plane of a tarp?

[ACoffee]

I'm wondering. Is it the catenary curve (which describes an even pull perpendicular to a fixed horizon) or a hyperbola (which describes a curve that infinitely approaches intersecting asymptotes) that will render even, puckerless, stretch across the plane of a tarp?

The catenary curve is a hyperbola, just rotated 45%.