On 12/15/18 7:01 AM, Hans Hammarquist via TowerTalk wrote:
No, I did not include the catenary curve in my calculation. actually, the
spring coefficient doesn't come into the calculation at all.
I figure the effect of the curve would act similar to the stretch movement. Maybe that
was to oversimplify the whole thing. I would like to see how the "spring"
coefficient looks for the curve. I just assumed that Hooks law is valid there too.
No, Hooke's law is not valid for the tension on a catenary. Simple
non-catenary example: you have a massless cable with a weight in the
center and two supports that are at the same height (the classic sagging
wire).
When the supports are zero distance apart, the tension is Weight/2.
When the supports are .707 the cable length apart, the cable hangs at 45
degrees, so the tension is 1.4* weight/2. it's that 1/sin(sag angle)
thing - when the cable is horizontal, the tension is infinite.
So the force is highly nonlinear as a function of the distance. Over a
"small" range, it might be close to linear. Out of a 100ft run, the
delta between 99 and 100, and 100 and 101 is probably about the same.
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