Thank you, Kroma.Originally Posted by Kroma
The less-than-satisfying truth is "yes and no", because although we like to think of gathered-end hammocks as simple rectangular shapes and model them with equal simplicity in our hammock design plans, the fact that hammocks are made of soft, foldable (and in some cases slightly stretchy) fabric makes their real-world geometry in actual application and use extremely complex.
In this case, while it is the length of the hammock body that determines the total perimeter measurement of the folded parallelogram-shaped net/cover, the specific angles of the parallelogram net/cover in turn dictate how (and to what degree) the body of the hammock is constrained when an occupant of a given size is inside, because the acute and obtuse angles angles vary within a broad family of parallelograms that have the same total perimeter measurement, and it is the choice of angles, i.e., the ratio of the long sides to the short sides, that determines the placement of the obtuse vertices of the net, i.e., where the hammock will be tied out (at the corners of the net/cover). Hammocks of different widths, partially constrained by the net depending on the location of its lateral corners, will still behave differently depending upon the width of the body and the size of the occupant, yielding the aforementioned complexity.
Consider two netless hammocks of the same length but different widths. Imagine you hook your index finger over the rolled hem of one long edge just a couple of inches from one gathered end and pull the edge taut, and then you have a friend do the same on the other side at the other gathered end; if you consider the SRL of the hammock to be its long diagonal the two of you have formed a really long, really skinny folded parallelogram shape defined by the perimeter of the hammock body. You would note that your action has barely constrained the hammock at all, and the behavior of the hammock body would be almost the same as if you were not touching it, since your pull-out points are so close to the gathered ends.
If each of you were to then move in concert, sliding your fingers toward the midpoints of the long edges of the hammock body on your respective sides, eventually you would create a folded rhombus (diamond) shape, and in between you would have formed all the possible folded parallelogram shapes with the same total perimeter measurement for a diagonal lay in one direction; if you were to continue sliding past the midpoints to the opposite gathered ends, you would form all of the possible parallelograms for the opposite lay direction. At every point along the edge, if the hammock were to be tie out congruently along a particular vector in 3D space, the hammock body would be constrained slightly differently, with its behavior further modified by it width. Ergo, "yes and no"...
HTH...
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