Calculus and caternary cuts/Hammocking...

[michgan241]

So i just took my final for Calc 2 and part of it involved conic sections specifically ellipses. Where you would/could essentially pin a string in two places along a line then a loop of string around the pins would form a perfect ellipse if you were to place a pen inside the string and keep tension on it and drew around in a circular motion. and then half of that ellipse would be a cat curve I've never done the sagged string but i suspect it is easier although not quite as interesting(for math geeks)

just something i thought of as I became a more interested in DIY projects for my hammock.

I'm sure there are a plethora of physics applications regarding loads, forces, and that sort of thing anyone else stumble across something like this?

This video gives the idea without the math behind getting the proper length/depth of the elipse

[nothermark]

Several to many of us probably did similar math problems sometime in the past. Since then I have run across the string method for making parabolic reflectors and oval picture frames among other uses. It is interesting but a skill one loses over time unless often dealing with it.

[e_2]

Actual catenary arcs are not parabolas or elliptical sections, though they are so similar as to not make much of a difference when making tarp cat-cuts. The easiest "real world" way to make a true catenary arc curve is by hanging a chain from two points and either you move the points closer/further apart... or you use longer/shorter lengths of chain. Gravity does the math for you.

[MAD777]

Actual catenary arcs are not parabolas or elliptical sections, though they are so similar as to not make much of a difference when making tarp cat-cuts.

I agree, a catenary curve is a hyperbolic cosine function. I also agree that a cat curve, or parabola, or ellipse, or even a circular arc won't make any difference on our tarp curve layouts. The differences in these shoes is less than the accuracy of your cut.

[WV]

After all, catena is the Latin word for "chain". (But the quant apostle, Grizz, speaks in parabolas. )

[aclawrence]

Here is a formula I use when figuring the radius for arches when framing a house. You take the width of the opening times itself. Then times .25. Then plus the height squared. Then divide that by the height times two. I'm sure it would work the same for a catenary cut. Width squared x .25 + height squared / 2(height). Will give you a perfect arch.

[nothermark]

At one point I thought I would point out how to calculate a catenary curve then I thought better of it. If anyone wants to know more here is a reasonable place to start:

http://en.wikipedia.org/wiki/Catenary