True Catenary Curve

[jellyfish]

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.

[FJRpilot]

Very nice! Thanks Jellyfish. Any chance you could convince Dr. Sally to make a "Parabola" calculator too?

[jellyfish]

Very nice! Thanks Jellyfish. Any chance you could convince Dr. Sally to make a "Parabola" calculator too?

I think she already did while I was teaching my niece how to latch hook. We are making an owl.

They looked amazingly close. I didn't realize how close. She wanted to compare the two curves.

I'll get it from her.

[onesojourner]

Very cool. I love spreadsheets.

[ACoffee]

Hey Jellyfish, I fixed your spreadsheet, so now you CAN have everything you want.

Dr. Sally's True 1:12 Catenary Curve Calculator (v2)

[kitsapcowboy]

Very nice! Thanks Jellyfish. Any chance you could convince Dr. Sally to make a "Parabola" calculator too?

...They looked amazingly close. I didn't realize how close. She wanted to compare the two curves.

Black Bishop and I fell on opposite sides of this catenary/parabolic curve argument recently in another thread. He argued correctly that the true catenary curve is really the more appropriate one in most hammock-related applications, and also that they just felt "right". I pointed out that, while this is true, for curves with aspect ratios (i.e., the ratio of length to depth) typical in hammock-related applications the differences between the two curves are proportionately very small, and also that there is some practical utility (for DIYers) in being able to describe the required curve with sufficient precision and accuracy using a single, much simpler equation that can supply values (if necessary) by elementary hand calculation without the absolute requirement of a spreadsheet and without reference to trigonometric tables, etc. For example, on a 72" cat-cut curve with a 7" deflection, I think the parabolic approximation never varied more than 1/16 of an inch, which is beyond my personal limits for precision in sewing a complex curve on the bias using slippery waterproof fabrics. If the curve had a drastically different aspect ratio, such as being as deep as it were wide, the parabolic approximation would have more significant discrepancies, with the biggest differences being out at the very ends. A master seamstress like JF may indeed eek out a little extra benefit from following the correct catenary curve, but in truth I don't think either method will lead anyone terribly astray on a hammock project, at least in practical terms.

Thank you, Jellyfish, for your time and contribution!! You rock.

[jellyfish]

Hey Jellyfish, I fixed your spreadsheet, so now you CAN have everything you want.

Dr. Sally's True 1:12 Catenary Curve Calculator (v2)

Omg omg omg

[jellyfish]

Black Bishop and I fell on opposite sides of this catenary/parabolic curve argument recently in another thread. He argued correctly that the true catenary curve is really the more appropriate one in most hammock-related applications, and also that they just felt "right". I pointed out that, while this is true, for curves with aspect ratios (i.e., the ratio of length to depth) typical in hammock-related applications the differences between the two curves are proportionately very small, and also that there is some practical utility (for DIYers) in being able to describe the required curve with sufficient precision and accuracy using a single, much simpler equation that can supply values (if necessary) by elementary hand calculation without the absolute requirement of a spreadsheet and without reference to trigonometric tables, etc. For example, on a 72" cat-cut curve with a 7" deflection, I think the parabolic approximation never varied more than 1/16 of an inch, which is beyond my personal limits for precision in sewing a complex curve on the bias using slippery waterproof fabrics. If the curve had a drastically different aspect ratio, such as being as deep as it were wide, the parabolic approximation would have more significant discrepancies, with the biggest differences being out at the very ends. A master seamstress like JF may indeed eek out a little extra benefit from following the correct catenary curve, but in truth I don't think either method will lead anyone terribly astray on a hammock project, at least in practical terms.

Thank you, Jellyfish, for your time and contribution!! You rock.

I don't know if I am going to get extra benefit from this, but I hold certain beliefs in the harmony of certain things.

For example, I am now planning to reconfigure my ridgeline length according to the golden ratio.

I also worship the teachings of Lucretius and believe that there is harmony in the "nature of things".

And there is something poetic about it all. I may write a few limericks to describe how it makes me feel. Or haikus. It all depends on whether it makes me laugh or feel zen.

[kitsapcowboy]

...And there is something poetic about it all. I may write a few limericks to describe how it makes me feel. Or haikus. It all depends on whether it makes me laugh or feel zen.

And THIS just one reason why you are appreciated by so many here. I may be at the top of that list

[BigE94]

Awesome Jellyfish! Great contribution. Your projects never cease to amaze and the videos have been great too.

While I fully appreciate the discussions and the brain power required to make all this happen, I just need a piece of tarp material with a line that says "cut here". RBTR are you listening?? I actually ordered one of their precut tarp kits and it turned out great.