Wednesday, August 30, 2017

Balance points and congruent wires in square compound 2-ply

For a cut length of square, compound, 2-ply to be composed of two congruent wires, the midpoint of the length must lie at what I call a balance point. Any length will do, so long as the midpoint is at a balance point.

At a balance point in a square 2-ply compound helix, the line joining the centers of the two plies is perpendicular to a radius of the major helix. For example, this 2-ply has been cut exactly at a balance point
For comparison, this 2-ply has been cut just short of a balance point.
When a length of 2-ply is centered on a balance point, diagonally opposite half segments are congruent, and therefore also, the two wires are congruent over their entire length.
As these end-views show, at a balance point the two cut faces of the wires lie parallel to a side of the 'square'. There are four balance points per wavelength.

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