I am planning my next tarp (Black Cat), so I made (or rather I got my sister Sally to make) a new calculator for a true catenary curve. I was visiting her over the weekend in North Carolina, and I convinced her to do some math for me while I entertained my 7 yrs old niece.
I will make this available to everyone, if you'd like to download the spreadsheet:
Dr. Sally's True 1:12 Catenary Curve Calculator
It seems as though while they are similar, a true catenary curve differs from a parabola. Parabolas are cool, but if I'm making a Black Cat tarp, it has to be an actual Cat Curve, right?
The Xtrekker calculator that I used for my winter tarp is a great calculator, and I really love it (thank you XTrekker), but it doesn't do something that I need: It lists the inches as decimals, not as fractions. My ruler is in fractions (to 1/16"), so converting decimals to fractions makes my head hurt (dividing the decimal by 0.0625). XTrekker locked his spreadsheet, so I can't easily make that adjustment for the auto-conversion to fractions in the spreadsheet itself. (Unfortunately, Excel is not smart enough to recalculate fractions from 1/16 to 1/4 or 8/16 to 1/2 in my calculator, so I don't quite have everything I want out of this.... why can't I get everything I want???)
If you want a calculator for a true 1:12 Catenary Curve for cutting out your tarps (etc. etc.), you are welcome to use Dr. Sally's. For every foot of length, the curve will be 1" deep, which is what I am going to use on my Black Cat tarp, which is the minimum according to Black Bishop's instructions. I am going for greater coverage, which is why I chose the BB recommended minimum of 1:12.
There are 2 sheets in the file. One is the calculation, and the other is a larger graph of the plotted curve (for the curious and visual learners like myself).
If you want to edit the spreadsheet, you can download it and it is unlocked. Notice that I "hid" columns C through F to clean it up and prevent typing somewhere where typing shouldn't occur, so if you want to play around with it, you'll have to "unhide" the hidden columns.
If you want to fiddle with the scaling factor (so that your cat curve depth is greater than or less than 1"), you'll have to unhide the columns C trough F. You could try various numbers into the scaling factor and see how the curve responds just for fun.
This calculator will plot up to 144" (12 feet). If you feel the need to go greater than that, you'll need to drag down the columns at the bottom (unhide and drag down column F too).
For the mathematically inclined, or those who want to just play around with the calculations, they are as follows:
Cantenary Curve =[a*cosh(x/a)]-a
1:12 Scaling Factor a = x+(x/2)+((x/2)*0.03)
I plan to make a scale version of the curve for my Black Cat Tarp that I can simply print out and then cut out with scissors. If you are interested in a pdf of this, let me know.
Many thanks to my little sister Sally for doing the math and plotting this in Excel. I know I'm lucky to have her.
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