1. ## Catenary Curve - Easy spreadsheet

I posted this as a response to a question on another thread, but thought I should post it as a separate thread. Perhaps that would make it easier to find when searching.

The attached spreadsheet is based on the classic cat curve formula of
Y = a * cosh (x/a) but some simplifications have been made that match the conditions where we use cat curves in tarps.

The assumptions are that the cat curve is symmetrical and the simplification is that a unit curve is used. In other words the distance from the center of the curve to the end is 1. It really doesn't matter what the unit is; feet, inches, etc. An offset is calculated based on a proportion of length. This means it can work on any curve given just the length and amount of cut.

After simplification, the formula transforms to y = cosh(x) - cosh(1)

Here is the attached spreadsheet that includes simple instructions.

2. I'll just assume that was all in the English language and trust that the spreadsheet works. Seriously, those are some math skills that I just don't comprehend but I see the value of the spreadsheet for figuring out the cat cut. Nicely done, thanks so much MAD.

3. Why not combine the ball chain method with a strip of brown wrapping paper. Pin it up to the wall and then mist it with rattle can paint. Don't go wild with the paint :-( Take down the paper and cut out the template for the edge cut. While the paper is still on the wall you might lay out another line of a shorter length but same percentage of drop per length to see how much different the curves are. If they are close, you could cut out the larger curve and mark it's center, then use the center portion of the curve for the shorter sides. The ends of a parabola are flatter than the center, so cutting a small amount of the ends does not change much. Roll up the pattern when done and put in patterns.

Not speaking from experience here, but can see the process in my mind :-)

I posted this as a response to a question on another thread, but thought I should post it as a separate thread. Perhaps that would make it easier to find when searching.

The attached spreadsheet is based on the classic cat curve formula of
Y = a * cosh (x/a) but some simplifications have been made that match the conditions where we use cat curves in tarps.

The assumptions are that the cat curve is symmetrical and the simplification is that a unit curve is used. In other words the distance from the center of the curve to the end is 1. It really doesn't matter what the unit is; feet, inches, etc. An offset is calculated based on a proportion of length. This means it can work on any curve given just the length and amount of cut.

After simplification, the formula transforms to y = cosh(x) - cosh(1)

Here is the attached spreadsheet that includes simple instructions.
I used this formula in laying out my first tarp ... and my personal preference was the "true" cat was too steep ... so I halved the value of the depth of the cut ... once again proving there's more then one way to skin a cat ...
What do think ?? ...

PS... this is after pitching it last night in the rain with 15 mph winds & no further adjustments ... ridge-line is 11' max width 10'

6. Originally Posted by Syb
I used a "combo" of Mad's spread sheet and Old Gringo's "bendy" baton ... a few yard sticks duct taped together ... I'm finding the key is accurate, asymmetrical, points as well as consistent curves ... and the lay-out is the easy part ... cutting and sewing that shizzle is the hard part ...if you see my seams ... there's no doubt this is a DIY ...