Two minor corrections to the measurements in the original post may help anyone wishing to replicate this design...
1) The finished width of the hammock at its midpoint was listed as 34"; in actuality, the width of the trimmed hammock body when laid flat was 34" at the midpoint (the narrowest part of the hammock, NOT 36" as quoted in construction step 1 of the OP), so after some allowances are taken up wrapping the Amsteel suspension the hanging arc length of the fabric at the midpoint of the hammock is closer to 32" and the edge-to-edge measurement across -- its true width as measured parallel to the spreader bars at each end -- is a couple of inches narrower than that. The actual deflection of the long edge curves was, in application, closer to 8" than 7", giving it am arc length of 82" over the 80" finished length if the hammock body.
2) The parabolae describing the end caps were listed as being approximately 14" deep including allowances, but, in fact, the parabola describing the correct size of the finished end cap without allowances, i.e., the path where the seam runs joining the end cap to the hammock body is 14-3/8" deep by 36" wide with a 48" arc length, so I sketched out a pattern with that finished shape and then added a generous 1" seam allowance along the curve for sewing the standing seam, as well as along the flat edge for a roll hem. The method I used created end caps with an arc length slightly greater than the width of the hammock body at the ends with allowances included, and I had a deeper depth and extra fabric to fold over for the top edge of the end cap pockets. Using an an alternative method, one could compute a parabola that is 15" deep and 37-1/2" wide to describe a parabola with an arc length exactly matched to the 50" width of the hammock end with its allowances included and then add a 1" seam allowance to the flat top edge of the end cap with no fabric flap left to fold over. Ultimately, either method should work adequately, but the choice will dictate both the necessary finishing steps and the aesthetics of the final result. (Regardless of which method you choose, I recommend stitching the two layers of the pocket together first before joining them to the hammock body, and I recommend starting at the centerline of the endcap curve, matching it to the midpoint of the end of the hammock body, and sewing your seam outward in each direction from that point, in order to ensure evenness.)
[Links below reposted for the sake of convenience]
Here is a link to a handy online calculator for arc lengths based on parabolic height and width dimensions...
http://www.had2know.com/academics/pa...ngth-area.html
Here is a calculator that finds values for an equation, y=(a*x*x)/b, that describes your chosen parabola...
http://www.emathhelp.net/calculators...la-calculator/
And this link will plot a graph of your parabolic curve based upon the equation that describes it...
http://www.meta-calculator.com/online/
Using these three resources, one should be able to decide on dimensions for a required edge and then plot reasonable "quick and dirty" parabolic approximations of the necessry catenary curves for bridge hammocks.
Ball park, anyway...
Originally Posted by B_rizzle
Alternative Online Parabolic Calculators
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