- Joined
- Oct 15, 2020
- Messages
- 208
Gentlemen (and the Lady who machines),
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.
The goal is concentrated solar power applications (CSP) - Solar Thermal. I intend to use paraffin wax actuators and some "by guess and by-golly" machining to make it follow the sun. 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 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)
I have a little Python utility that will output a .SVG parabola based on width and depth - and will give the focal-distance as well. 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.
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. 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.
Years ago I made a paper globe (because it was fun) - this is done by making gores. A gore is an "eye-shape" that is two arcs meeting at points, glue them up and you get a sphere. I used a formula to make a formula to find the radius of the long-arc on either side of the gore. My precursor formula would give the radius of an arc section when the width and depth of that arc are known. My formula to make the gores consisted of dividing the sphere's circumference by 24 (the number of gores X 2, to render half the depth of that arc) then using 1/2 the sphere's circumference (from north pole to south pole) as the width of the gore-arc. Striking a line the length of half the sphere's circumference, then placing a pivot 90 degrees from that line, at the midpoint of that line, at a distance of the radius of the gore-arc. I did that on either side of the line, then the two gore-arcs met at a point at the top and bottom of the line. I cut out the resulting "eye-shape", made 12 of them, and glued them together at the seams. TADA! A 3-D shape from a flat pattern - and because I derived the gore-arc from the globe, when the seams lined up (arc to arc), the shape was a sphere....
I don't know how to do that with a parabola....
SO!
I have LibreCAD and Inkscape (also Sketchup Make and FreeCAD) so I can work in 2D SVG or DXF. AutoDesk (Fusion 360) and SolidWorks are not worthy of my time - not really personal, but for me, a "Subscription Model" for software (not $1500, but rather $1500 PER YEAR) is enough reason for me to refuse to use them.....
If you aren't put off by my attitude towards the CAD-CAM Duopoly, and if you're interested in the project...
Is there anyone who can help derive a geometric method of making the flat-plan for these paraboloidal-strips?
Honestly, a plug-in for Inkscape or LibreCAD - or a little Python utility - would be the awesomest of awesome - for the days when I can afford a CrossFire plasma table, and I build the full-size skeleton out of 1/4" aluminum plate, rather than 1/8" baltic birch....
But, I am pretty handy with a steel-scale and a set of dividers (and a scroll-saw or band-saw) as well...
SVG or DXF for the ultimate NC file would be the goal...
Any CAM Masters or Mathematical weirdos out there interested in helping me to derive a method to make the flat-pattern of a paraboloid - when depth and width of the resultant dish are known? The reflective strips would run along the long dimension....
I hope someone is interested, and my personality hasn't gotten in the way of this post.
Thank you for reading!
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.
The goal is concentrated solar power applications (CSP) - Solar Thermal. I intend to use paraffin wax actuators and some "by guess and by-golly" machining to make it follow the sun. 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 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)
I have a little Python utility that will output a .SVG parabola based on width and depth - and will give the focal-distance as well. 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.
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. 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.
Years ago I made a paper globe (because it was fun) - this is done by making gores. A gore is an "eye-shape" that is two arcs meeting at points, glue them up and you get a sphere. I used a formula to make a formula to find the radius of the long-arc on either side of the gore. My precursor formula would give the radius of an arc section when the width and depth of that arc are known. My formula to make the gores consisted of dividing the sphere's circumference by 24 (the number of gores X 2, to render half the depth of that arc) then using 1/2 the sphere's circumference (from north pole to south pole) as the width of the gore-arc. Striking a line the length of half the sphere's circumference, then placing a pivot 90 degrees from that line, at the midpoint of that line, at a distance of the radius of the gore-arc. I did that on either side of the line, then the two gore-arcs met at a point at the top and bottom of the line. I cut out the resulting "eye-shape", made 12 of them, and glued them together at the seams. TADA! A 3-D shape from a flat pattern - and because I derived the gore-arc from the globe, when the seams lined up (arc to arc), the shape was a sphere....
I don't know how to do that with a parabola....
SO!
I have LibreCAD and Inkscape (also Sketchup Make and FreeCAD) so I can work in 2D SVG or DXF. AutoDesk (Fusion 360) and SolidWorks are not worthy of my time - not really personal, but for me, a "Subscription Model" for software (not $1500, but rather $1500 PER YEAR) is enough reason for me to refuse to use them.....
If you aren't put off by my attitude towards the CAD-CAM Duopoly, and if you're interested in the project...
Is there anyone who can help derive a geometric method of making the flat-plan for these paraboloidal-strips?
Honestly, a plug-in for Inkscape or LibreCAD - or a little Python utility - would be the awesomest of awesome - for the days when I can afford a CrossFire plasma table, and I build the full-size skeleton out of 1/4" aluminum plate, rather than 1/8" baltic birch....
But, I am pretty handy with a steel-scale and a set of dividers (and a scroll-saw or band-saw) as well...
SVG or DXF for the ultimate NC file would be the goal...
Any CAM Masters or Mathematical weirdos out there interested in helping me to derive a method to make the flat-pattern of a paraboloid - when depth and width of the resultant dish are known? The reflective strips would run along the long dimension....
I hope someone is interested, and my personality hasn't gotten in the way of this post.
Thank you for reading!