[TowerTalk] Fwd: Fwd: guying distance

[jimlux]

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.