# Formula to calculate arch length

• 02-01-2013, 20:20
packeagle
Formula to calculate arch length
I'm looking for the formula to calculate the arch length. I need the "cat cuts" length to match the hammock body length for a tarp. I've tried for a few days and no luck. Any Calculous savvy hangers care to lend a hand?
• 02-01-2013, 20:29
the_gr8t_waldo
i don't have a mathematical formula for ya but..you COULD hang a string from two level points. the string will take the needed shape- then all that remains is to trace the shape of the string onto the project.
• 02-01-2013, 20:34
packeagle
Quote:

Originally Posted by the_gr8t_waldo
i don't have a mathematical formula for ya but..you COULD hang a string from two level points. the string will take the needed shape- then al that remins is to trace the shape of the string onto the project.

K I S S. Something even I can figure out.
• 02-01-2013, 21:36
gmcttr
I agree with the string method. It's what I use.

However, if you want a bunch of dimensions (and one time I did), go to the Black Cat Tarp Tutorial, scroll down to "Step 1", download the "Calculation File" and play with it until you get the length and depth of cat cut you desire.
• 02-01-2013, 22:07
Tijereyes
Math *sigh*
Quote:

Originally Posted by packeagle
I'm looking for the formula to calculate the arch length. I need the "cat cuts" length to match the hammock body length for a tarp. I've tried for a few days and no luck. Any Calculous savvy hangers care to lend a hand?

Ooh calculus. My old enemy, we meet again.

So if we assume that the cat cuts are going to be on a parabola (not strictly the case, but close enough that your cutting errors will make up the difference), we can calculate the arc length.

The arc length for a parabola leaving the origin and ending at a point X is given by http://images.planetmath.org/cache/o...12/js/img2.png. That is to say, it gives you half of the arc length of the whole cat curve -- you need to double it to find the total length.

This is a big nasty equation. (note that I skipped all the line integrals). So how do we apply it?

First, we need to define X. Set your origin at the center of your arc cut -- so if for example you want an arc cut that's 20" long, your origin would be at the midpoint, and then the max/min values that X can have would be 10 and -10.

Second, we need to define A. If you want a cat cut with a max depth of 1.75", for example, then you want to find the value of A that satisfies

1.75 in. = A * X^2

or, in this case, A = 1.75 / (10^2) = 0.0175

Then you can plug your values for A and X into the equation to find the length of your caternary curve.

For these values of X and A, I come up with a total distance of 20.4" -- not a whole lot of difference from if you'd just guessed 20". If you tried a deeper cat cut, though, you'd come up with a bigger difference.

PS -- I used Wolfram Alpha (www.wolframalpha.com) to perform the calculation - if you're careful with your parentheses and whatnot when you're typing it in, it'll work fine for you.
• 02-01-2013, 22:09
Tijereyes
Of course, in practice the string method is probably far easier. Especially since (for me, at least) the "on-paper" calculated lengths go out the window the instant the scissors touch fabric :D
• 02-01-2013, 23:49
packeagle
... Or I could use Google Sketch Up! Woot that process was kinda cool and i got a better model to print.
• 02-02-2013, 07:03
fortran42
Arc lengths for tarp
I just finished a hex tarp and used the string method....4mm climbing cord is quite rigid and has enough weight for this task...i cut a contactor trash bag into a long rectangle and taped it to the wall level w/floor. mark endponts & midpoint and select desired (arc depth)...approx 1" per linear foot is good. Pin ends and adjust sag from one end to get drop..pin in place at midpoint. Add pins along arc formed every 6" or so. Trace arc with bright sharpie pen. Since i used silver silnylon the arc trace was visible thru the material when laid underneath...simply retrace the arc onto the fabric after lining up the endpoints and pinning them. Attached are pics of arc guide, cat cuts & finished tarp..it came out quite nice...No Calculus is necessary for this project...just a steady hand!
• 02-04-2013, 09:55
jordo_99
Quote:

Originally Posted by packeagle
... Or I could use Google Sketch Up! Woot that process was kinda cool and i got a better model to print.

I've found this to be the easiest...after you make the arc you can even go into "Entity Info" and change the number of segments.

At that point...you have the arc broken into X pieces and can do the same with the straight line to help plot your arc. For instance, at 32" in the offset is 2 5/8", at 40" offset is 3"...etc