My precursor formula would give the radius of an arc section when the width and depth of that arc are known. I used a formula to make a formula to find the radius of the long-arc on either side of the gore. A gore is an "eye-shape" that is two arcs meeting at points, glue them up and you get a sphere. Years ago I made a paper globe (because it was fun) - this is done by making gores. Working on 0.020" mirror-polish aluminum sheet requires as little touch as possible - bending and scribing and cutting and repeating will ruin the final product - it's a one-and-done proposition. I do not know how to derive or determine the necessary curve on the aluminum strips, such that the seams line up when lain down. I can use this to make the curve of the spars, so that when I assemble the grid it has a parabola on the two axes, whose focal length is equal - that will give me the skeleton of a 1945 Navy RADAR dish. SVG parabola based on width and depth - and will give the focal-distance as well. I have a little Python utility that will output a. I intend first to use my little 6040T CNC router, or maybe my K40 Laser, to cut skeletal sections of Baltic-Birch that half-lap connect into the shape, then I will lay on strips of aluminum as the mirror - these strips will need a strange flat-pattern, with some kind of curve on the long edges such that they nestle down into the paraboloid and the seams between the strips meet (like the gores on a paper-globe but a parabola, not a sphere) Its purpose is to make stuff hot - specifically "stuff" being a circle of approximately 7/8" in diameter - concentrated from a rectangular section of 1 square meter (mixing Imperial and Metric is fine in my shop - the meter is for ease of future calculations, the 7/8" is for ease of machining and visualization.) I intend to use paraffin wax actuators and some "by guess and by-golly" machining to make it follow the sun. The goal is concentrated solar power applications (CSP) - Solar Thermal. On the horizon is the parabolic dish this is not a round-plan section, but rather quadrilateroidal - think 1945 battleship RADAR dish, and you'll have the image.
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