What I really just want to know is the equation and basic concept on how to determine the optimal length of power cable needed to connect two poles while knowing only the linear density of the cable.It does not matter how much sag is produced because of limitations due to the strength of the power cable.
The web page provides very thorough information and rigorous mathematical treatment relevant to the answer you seek. But it is just too much all at once to digest. So take it piecemeal, one bit at a time! First, you must realize that the sag of the cable is the single most important design parameter and strict attention to cable weight determines the optimal length. The equation of the catenary is the precise model but a parabolic approximation may work. (parabolic approx.) ymax = (3wl?) / ?√(64EA) P = wl?/(8ymax) Where ymax is the maximum sag l is the unstretched length w is the weight/unit length E Youngs modulus A Wire area P axial tension the curve is a parabola, which is a good approximation if the depth of sag is no greater than 1/8th of the span. Use the second equation to derive the induced tension P. H:=WL?/8S S:=WL?/8H L: distance between support S: Sag at mid-span H: tension (horizontal component of tension) The tension depends purely on the loaded geometry and the weight per unit length.
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