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Topic Date User

SRENE anchors may go the way of the dinosaur 13-Mar-2006 At 9:31:59 AM uwhp510

Message

OK,

The crux of the matter lies in the fact that stuff (nylon webbing, cord, spectra, steel cable...) stretches, and provided we don't exceed the elastic limit of our material, stretches in the manner;

F = kx (where k is the spring constant, and x is the extension resulting from force F)

If we ascribe a length of cord (equating to one of the arms of the cordalette) the spring constant k1, then the spring constant of the other arm (which is twice as long) is k2 = k1/2 (which can be determined by treating the arm as two equal springs, of the length of the shorter arm, in series ie. 1/keq = 1/k1 + 1/k2).

So now we have two springs in parallel, being the two arms of the cordalette, one with a spring constant k1 and the other with a spring constant k1/2. Springs in parallel add, so keq = k1 + k2 = 3/2k. So the extension in the whole system, x, is due to the load F, which is the load on the belay and F = 3/2k1x

But the tension in each arm, which is each also extended by x, is given by T1 = k1x and T2 = k2x = k1/2x. Thus substituting for k1x, F = 3/2T1 = 3T2, ie T1 = 2T2.

The assumptions i've made are that
a) the two arms are directly in line, so that once loaded the system can't swing to the side to compensate, but since we are talking about the most ideal case (with no angle between the anchors, and a perfect loading direction, I think this is unimportant)
b) that we can treat nylon cord/webbing as a perfect spring. I think that this is at least a good approximation for my purposes.

If it all doesn't make sense I can draw a picture I guess.