Parabola! (Do doo do do do) Parabola? (do doo doo do)... Hoping for a CAD Master's Interest

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MERLIncMan

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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. :laughing:

Thank you for reading!
 
A few thoughts.
1. Will you be pressing this into a mold to give the final shape?
2. Just how accurate does the focal point need to be?
3. Is the focal point a line or a single point?

When laying this out, assume it is a full round parabola the final shape does not matter. you just trim off the parts of the full parabola that you do not want, the parabolic shape stays the same.
 
What is the size of your target? What is your design focal length and size for the mirror?
I suspect tha you could get by nicely with a spherical mirror. In that case. the radius of curvature will be equal to twice the focal length. All your segments would be identical, simplifying fabrication. If the segments are small enough, they can actually be flat and still focus enough sunlight to your target.
To make the segments, I would suggest a vacuum forming process where the blank is pulled into shape from the back side, eliminating any tooling marks on the reflective surface.
Way back in the 1980's, the wild west days of satellite television, a local entrepreneur was making 9' steel dishes by hydroforming them. The blank was placed in a mold and the edges sealed and water pressure was used to press the blank into the mold
 
Flyinfool said:
A few thoughts.
1. Will you be pressing this into a mold to give the final shape?
2. Just how accurate does the focal point need to be?
3. Is the focal point a line or a single point?

When laying this out, assume it is a full round parabola the final shape does not matter. you just trim off the parts of the full parabola that you do not want, the parabolic shape stays the same.
Click to expand...

There will be no mold but the grid-skeleton - I'd love to spin form or press-form this, but too far beyond reality. Strips riveted to grid.

Focal Point: It's actually reflected twice: once off the main mirror, then off a secondary mirror into the target that will not be mounted out on an arm, but rather in the larger (primary) mirror itself - the primary mirror is less important than the secondary in this arrangement (and the secondary is available retail as a fish-eye for a bus or semi-truck). BUT The target is roughly 7/8" - so it's all got to go into that space. Not optical quality, but not "crumpled aluminum foil" either.

Single point - The target is actually a cavity with an aperture - as long as the collected sun can make it through that aperture, it's all good!

I had actually considered trimming a round into a rectangle - it's possible I suppose, but not scalable. The design must be scalable for the future.
 
RJSakowski said:
What is the size of your target? What is your design focal length and size for the mirror?
I suspect tha you could get by nicely with a spherical mirror. In that case. the radius of curvature will be equal to twice the focal length. All your segments would be identical, simplifying fabrication. If the segments are small enough, they can actually be flat and still focus enough sunlight to your target.
To make the segments, I would suggest a vacuum forming process where the blank is pulled into shape from the back side, eliminating any tooling marks on the reflective surface.
Way back in the 1980's, the wild west days of satellite television, a local entrepreneur was making 9' steel dishes by hydroforming them. The blank was placed in a mold and the edges sealed and water pressure was used to press the blank into the mold
Click to expand...

I'm actually thinking about spherical - or just catenary cross-sections. I said to Flyin' that it needs to be scalable for future builds of the same gizmo, so I need to be able to index it to desired variables. Also, it is double reflected - the target is mounted in the primary dish, and is a cavity with an aperture, so it doesn't have to be full-optical-quality point, but just make it through the aperture (7/8") in a semi-orderly way - once inside the cavity, the light can do as it pleases, it ain't getting out!

I would very much love to form it in such a manner as you suggest! I had considered vacuum, or pressure, or even centrifugal (liquid mirror in super-high-end telescopes) - but for feasibility and scalability (and reality of my resources), the strips on grid seems the best way.
 
It is easy to draw the round in CAD and then trim to final size in CAD and add the needed structure to hold it together. CAD does not care if you need to start with a planet sized sphere and only use a 1 meter square chunk.
 
Flyinfool said:
It is easy to draw the round in CAD and then trim to final size in CAD and add the needed structure to hold it together. CAD does not care if you need to start with a planet sized sphere and only use a 1 meter square chunk.
Click to expand...

Will CAD give me a flat pattern for strips that bend to connect into a paraboloid?
 
Some can, I am not familiar with your software. But you can do it by manual methods in most any software. You only have to lay out one edge of one strip and then can use mirror and rotate commands to generate the full flat pattern.

You can get that initial curve by calculating points along the curve, the more points the more accurate the curve, you have to decide just how much accuracy you need. You should be able to create a spreadsheet to all the math. Depending on your CAD you may be able to just import that to create the curve. Then just draw a splined curve to hit all the dots. Mirror it and you now have one pedal, do a polar array and you have your flat pattern.
 
Fair enough, I'll give it a spin.

I need to get better with LibreCAD anyways - it's a fork of QCAD (of which I know nothing).

I like the idea of FreeCAD, but the curve is too damned steep at the moment (no pun intended!)
 
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