OK Jim,
I disagree as the Hooks law is still valid. It's just that the Hooks "spring
coefficient" will vary with the distance. A fast calculation in my head reveals
that it will move the optimal point closer to the tower as the closer to the
tower, the less influence from the catenary curve.
Just wondering if I can substitute the catenary curve with a weight in the
center of a weightless guy wire or maybe a few weights evenly distributed along
the wire. I'll check it out.
Hans - N2JFS
-----Original Message-----
From: jimlux <jimlux@earthlink.net>
To: towertalk <towertalk@contesting.com>
Sent: Sat, Dec 15, 2018 1:48 pm
Subject: Re: [TowerTalk] Fwd: Fwd: guying distance
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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