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Antenna Sag Curve

February 8th Fact-of-the-Day

A flexible antenna wire supported from two end points forms a catenary curve due to the pull of gravity if no other weight, such as a feed-line, is attached. The name 'catenary' comes from 'catena,' which is Latin for 'chain.' Galileo claimed a parabola was formed by a hanging chain. However, Jungius disproved Galileo's claim in 1669. Sometime later Gottfried Leibniz challenged geometers to submit geometric methods for construction of a catenary curve by mid-1691. After making that challenge he submitted his own solution. His solution was followed by other solutions from Jean Bernoulli and Christian Huygens. The catenary curve equation is now known to be precisely the hyperbolic cosine function y = a cosh (bx). ©2005 Martek International All rights reserved.

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