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@trickyK3C2L wrote:
.... Can you help me please with maybe drawing it for me and sending a file ....
See the attached, without the vertical exaggeration of @richard_387 's images, and ignoring the fact that the Earth is not actually spherical. A drawing unit is an inch.
The red is my suggested [in Message 2] initial Line from the top quadrant point downward, the yellow are the 1-mile offsets to each side, the green is the chord over that 2-mile distance, and the white are the quarter-mile-interval drops [you'll need to Zoom way in, and maybe REGEN].
You talk of a string with no stretch, but even if that could possibly be true, that doesn't mean it has no sag over a spanned distance. To actually get zero sag would require infinite tension, no matter what the material. And of course, at this degree of curvature over this kind of distance, any little ripples / waves in the water will spoil your test.