There's the rub, isn't it. You'll have one angle when the hammock is empty, and another when it is loaded. And you want the one when it is loaded.Originally Posted by Sailor
Here then is an approximation. If you ASSUME that under load the angle of the hammock suspension line with respect to the horizontal is 30 degrees, which makes that angle with respect to the vertical 60 degrees.
if the pole is h' units of length high when set at its angle, and the length of cord from the top of that pole to the ground is L units of length, then the angle with respect to the vertical from pole top to ground is arccos(h'/L). But that's only part of the story isn't it, because h' is the pole height at the (unknown) angle . See diagram. We know p, the height of the pole, which makes h' = p x cos C, where angle C is yet unknown. But we know angle B is 60, and we know that angle C+B is the bisected angle, thus C+B = 0.5*(60 + arccos((p x cos C)/L), which is a trigonometric equation in one unknown, C. Solve for C, add to B, and there's the bisected angle.
On the off chance that you won't want to solve this equation, you could figure what length of cord L would allow the pole to be vertical when bisecting the angle. In that case B is 60 degrees, and L = p/(cos B). Luckily for us cos 60 = 0.5, so that means to make the cord length twice the height of the pole. You'll want it long like this anyway to cut down on the force the stake has to hold.
your backwoods trigonimetrarian, Grizz
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