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View Full Version : Constructing a parabolic dish (for the mathematically inept/lazy)

Mangetout
04-21-2008, 10:04 AM
I want to make a parabolic dish out of plywood or thin MDF - I think it should be easy enough to construct in approximately the right shape by cutting out a big circle, dividing it into segments, then making each of those segment lines as the centre line of a tapered segment such that when gathered together, the edges join to make a big dish.

Oh dear, that wasn't very clear.... OK... I want to cut out a big plywood flower and join the edges of adjacent petals together to make a big plywood dish that is approximately parabolic

What I think I need to do is to be able to calculate the diameter of the dish at any point in its depth measured around the profile circumference from the centre - (unless there's a simpler way) - so that at intervals along the length of the petals, I can calculate their proper width at that point

masterofnone
04-21-2008, 10:10 AM
I'm not exactly clear what you're trying to do, but would any of the designs under the parabolic cookers section here help?

http://solarcooking.org/plans/default.htm

Mangetout
04-21-2008, 10:24 AM
I'm not exactly clear what you're trying to do, but would any of the designs under the parabolic cookers section here help?

http://solarcooking.org/plans/default.htm
Thanks - yes, well, sort of.

this one:
http://solarcooking.org/plans/DATS.htm
is sort of similar to the shape I'm imagining, except that it consists of tapered sections gathered at the centre. I want to make a shallower dish from sections joined at the middle. (Shallower means it will focus at a point outside its own volume - like a radio telescope dish)

I'm hoping to do a couple of different experiments with it - firstly to try to use it as a sound collector, and after that, to line it with foil or mylar and use it to make things really hot. (Obviously I'm aware that doing these experiments in the other order might result in me cooking my own head).

Squink
04-21-2008, 10:25 AM
A Simple Technique of Fabrication of Paraboloidal Concentrators (http://ashokk_3.tripod.com/srinivasan.htm) Principle of Fabrication

Figures 1 and 2 illustrate the principle of construction of a paraboloid starting from a plane sheet of material. Figure 1 is a plot of the parabola Y=X2/4f representing a vertical section through a paraboloid having a focal length of f cm. If the paraboloid is slit symmetrically along eight radial directions and flattened out, then it would appear like an eight petalled flower as in Fig. 2. the non-shaded portion in Fig. 2 represents the reflector part, and the shaded portion that part of the plane sheet which has to be cut out and removed.

Mangetout
04-21-2008, 10:35 AM
A Simple Technique of Fabrication of Paraboloidal Concentrators (http://ashokk_3.tripod.com/srinivasan.htm)
Thanks - that's exactly the sort of thing I'm trying to do. I was planning to do it with more sections than that example, but the formula given has that as a variable.

The Them
04-21-2008, 11:05 AM
Took some thought...

So, you want this parabola to focus, i.e., have a focal point. Choose one; above the center point (think locating a point 10 cm directly over the center of a dinner plate with a pencil). Doesn't matter where so much as long as you stick with it. Now, work out some oven-tongs-shaped device with a roller at the apex. Here's the fun: keeping one end of the tongs pointed at your focus (kitestring should help with that), and the other end straight up (I'm assuming you're building this on a flat surface), the roller on the tongs will be exactly where your parabolic curve should be. IMPORTANT: you'll need to keep all your lines straight while doing this, so no slack on that kitestring, or letting your chosen focal point move from however you've anchored it. Then, it should be completely no hassle to manipulate your ever-so-easy-to-work-with surface to follow where roller on the tongs is, and parabola away!
The reason for the tongs is that it will need to bend a bit to maintain these specified directions for the pointy ends. It will work in 3 dimensions, so once you've made it, you can use it for the whole thing.

butler1850
04-21-2008, 11:53 AM
This guy that runs cockeyed.com (http://cockeyed.com/incredible/solardish/dish01.shtml) may give you some hints. He ended up making a HUGE one out of an old satellite dish, which may or may not be too big for your uses.

(He had WAY too much fun... I want one of my own! :D)

Mangetout
04-21-2008, 01:31 PM
Took some thought...

So, you want this parabola to focus, i.e., have a focal point. Choose one; above the center point (think locating a point 10 cm directly over the center of a dinner plate with a pencil). Doesn't matter where so much as long as you stick with it. Now, work out some oven-tongs-shaped device with a roller at the apex. Here's the fun: keeping one end of the tongs pointed at your focus (kitestring should help with that), and the other end straight up (I'm assuming you're building this on a flat surface), the roller on the tongs will be exactly where your parabolic curve should be. IMPORTANT: you'll need to keep all your lines straight while doing this, so no slack on that kitestring, or letting your chosen focal point move from however you've anchored it. Then, it should be completely no hassle to manipulate your ever-so-easy-to-work-with surface to follow where roller on the tongs is, and parabola away!
The reason for the tongs is that it will need to bend a bit to maintain these specified directions for the pointy ends. It will work in 3 dimensions, so once you've made it, you can use it for the whole thing.
That would work well if I was trying to create a form, but what I'm attempting to do is to make a bunch of panels that pull themselves into a parabola shape, when joined along their edges, by virtue of their geometry - sort of like creating a hot air balloon, only not out of fabric.

Seems to me that if one of these little 18 inch jobs can cook things, a 4 foot diameter one should be capable of more impressive feats.

Oslo Ostragoth
04-21-2008, 06:41 PM
This guy that runs cockeyed.com (http://cockeyed.com/incredible/solardish/dish01.shtml) may give you some hints. He ended up making a HUGE one out of an old satellite dish, which may or may not be too big for your uses.

(He had WAY too much fun... I want one of my own! :D)I would love to have this guy in my neighborhood. Not so sure about right next door, though.

butler1850
04-22-2008, 09:03 AM
I would love to have this guy in my neighborhood. Not so sure about right next door, though.

He really has a fun site. I love his "how much is in..." series... and I'd like to play with his solar collector. And beat the guy that destroyed an Action Comics #1.

Sage Rat
04-23-2008, 12:46 AM
That would work well if I was trying to create a form, but what I'm attempting to do is to make a bunch of panels that pull themselves into a parabola shape, when joined along their edges, by virtue of their geometry - sort of like creating a hot air balloon, only not out of fabric.

Seems to me that if one of these little 18 inch jobs can cook things, a 4 foot diameter one should be capable of more impressive feats.
Going through the cockeye stuff, it looks like it might be an idea to build a rotisserie in previous to laying down the reflective surface.

Mangetout
04-23-2008, 02:25 AM
I definitely need to try cooking something, if I get around to completing this project.

I seem to recall seeing big sheets of dense foam with a silvered side at a materials bank I sometimes visit - I'm thinking that might be a better material for my experiment (I had been planning to use MDF or thin ply and attach silvered mylar, but gluing that stuff to anything isn't all that easy)

I love the cockeyed.com site - I'm sure I've stumbled across isolated pages from it in the past, but this is the first time I've deliberately browsed it - it's exactly my cup of tea - and I love the style of writing.

Sage Rat
04-23-2008, 03:23 AM
I seem to recall seeing big sheets of dense foam with a silvered side at a materials bank I sometimes visit - I'm thinking that might be a better material for my experiment (I had been planning to use MDF or thin ply and attach silvered mylar, but gluing that stuff to anything isn't all that easy)
Professional photographers often have reflective flexible things (so that they can be compacted down for easy carry.) I'm not personally a photographer, so I don't know nor recall specifically what all offerings there are, but you might try googling along those lines for a good material.

I love the cockeyed.com site - I'm sure I've stumbled across isolated pages from it in the past, but this is the first time I've deliberately browsed it - it's exactly my cup of tea - and I love the style of writing.
If you're taking any suggestions, I'll just note that I'd like to see some different marble computers like the adding (http://www.youtube.com/watch?v=GcDshWmhF4A) machine (http://www.youtube.com/watch?v=md0TlSjIags).

Mangetout
04-23-2008, 03:31 AM
If you're taking any suggestions, I'll just note that I'd like to see some different marble computers like the adding (http://www.youtube.com/watch?v=GcDshWmhF4A) machine (http://www.youtube.com/watch?v=md0TlSjIags).
Thanks - yeah, I've had my eye on that for a while - and on the other stuff that guy does - with wooden gears.

si_blakely
04-23-2008, 06:41 AM
Going back a long time ago, I tried to build a parabolic reflector for a school science project (we were building a photophone (http://en.wikipedia.org/wiki/Photophone)). We started with an accurate parabola in card, and had the woodcraft teacher turn it using the card as a guide. We probably got a good parabola, but could not make it reflective enough for a decent focus.

Rather than trying to grind a glass mirror, we shifted to using the fresnel from an overhead projector - worked a treat up to about 100m, but not big enough for what you want to try.

Good luck

Si

Mangetout
04-23-2008, 01:10 PM
A Simple Technique of Fabrication of Paraboloidal Concentrators (http://ashokk_3.tripod.com/srinivasan.htm)
Just trying to actually implement my master plan and the old mathematical ineptitude kicked in again. I can't make sense of the maths in that document and the author skips right through it like a breeze. But I need the 'for dummies' version. (It isn't helped by the diagram being tiny and fuzzy).

um.... Help!

si_blakely
04-23-2008, 02:41 PM
Just trying to actually implement my master plan and the old mathematical ineptitude kicked in again. I can't make sense of the maths in that document and the author skips right through it like a breeze. But I need the 'for dummies' version. (It isn't helped by the diagram being tiny and fuzzy).

um.... Help!OK. Here goes. Not easy without diagrams, but I'll try...

In the equations, f is the focal length of the final parabola, and is a constant.

The author works on the principle that a parabola of radius X becomes the petal shaped flattened figure with a radius R (where R is greater than X). You will only need the shallow parabola equation, and he gives the relationship between R and X. To be honest, you don't really need this.

What you do need to know is how much material to remove between the petals. There is a difference between the circumference of circle R and circle X (X is smaller).So you draw your final circle of radius R. Divide it into 16 equal sectors. Then draw concentric circles at regular intervals. Where each circle crosses the sector line, calculate delta W, the difference between circ(R) and circ(X) divided by the number of petals - this formula is given in the text (the last one, and only one you need to know).

In practical terms, for each subcircle of radius R, calculate delta W. Set a compass to delta W, put the point on the intersection of the sector line and the circle, and mark the circle on both sides. The area between these two marks can be removed. As R gets smaller, delta W gets smaller quick, until the practical limit is reached about 2/3rds in.

I hope this is clear. Set up a spreadsheet, set your focal length and number of petals, then calculate deltaW in increasing steps up to your final size.

Si

si_blakely
04-23-2008, 02:50 PM
Bollocks - just noticed that deltaW is calculated in terms of X, the radius of the parabolic object, not R, the plane object. Thats daft - I'll rework it into something easier.

Si

si_blakely
04-23-2008, 03:38 PM
Just an example , for a focal length of 10 units, 8 petals you get, and R is a circle on the plane
R deltaW
0____0
1____ 0
2____ 0
3____ 0
4____ 0.01
5____ 0.02
6____ 0.03
7____ 0.05
8____ 0.08
9____ 0.11
10___ 0.15
11___ 0.19
12___ 0.24
13___ 0.3
14___ 0.36
15___ 0.44

This was just cobbled up in openoffice, and I massaged the X values to give integer R values. My MathsFu is not strong tonight - if R = X + (X3/24f2), what is X in terms of R :- too hard

Si

Mangetout
04-23-2008, 03:38 PM
Thanks - I really came unstuck. I mean, it may be the case that crude methods of construction, disobedient materials etc will make it all moot anyway, but I ought to start from something that should at least theoretically work (if I've learned anything at all from the boat project).

El Cid Viscoso
04-23-2008, 05:32 PM
Speaking of the boat, if you build the dish will you please post Mangetout-style instructions on the proper construction of said foiliferous flower? I would very much appreciate it. Thanks!

Mangetout
04-23-2008, 05:49 PM
Speaking of the boat, if you build the dish will you please post Mangetout-style instructions on the proper construction of said foiliferous flower? I would very much appreciate it. Thanks!
I'm planning to. It won't be updated on the site while it's in progress because of issues too silly and subtle to properly explain, but when it's all done, it will be fully documented.

si_blakely
04-24-2008, 01:49 AM
The main issue that I see is the fact that 2/3rds of the parabola ends up basically being a flat sheet - that means a pretty poor focal point - maybe not an issue for a solar heater.

Also, I would be tempted to make the cutouts asymmetric - one side with an extra unit to under-lap and tape behind. Another better design (maybe) would not use straight sectors but curved ones (so the cutout looks like a submarine propellor) - the maths remains the same, but it may be easier to pull into shape, and if you make the cuts to near the center, get a bit more curvature into the center of the parabola. Using overlaps only works if the material you are working with is not too thick - 1 or 2 mm rigid plastic (pvc or similar) sheet would be ideal.

Si

Mangetout
04-24-2008, 02:29 AM
Thanks - I have some ideas for the construction - it won't be all that dissimilar to the stitch and tape method I used for the boat - it's true that the centre of the dish will be flattish if the petals are cut so as to be naturally joined to a central disc, but I plan to cut the kerfs between the petals longer than the layout dictates, so there shouldn't be a sharp corner where the flat part turns into the curve.

My plane shape is almost exactly a metre in diameter, and will have 16 petals - these will be narrower and thus easier to bend than 8 would be - but it also means any errors will be magnified more. I'm looking for a focal length of somewhere around 500mm - I don't want it to be too deep, as that will limit the usefulness of the final object.

I'm planning to attach small blocks on the back of the petals at intervals along their radius - they will be drilled and a cord threaded through the holes - around the diameter of that sub-circle will be wound tight (Spanish windlass) so as to pull the dish into shape (then I'll glue it).

Tristan
04-24-2008, 02:37 AM
You know there are easier ways to make a 1920's Style Death Ray, right?

CalMeacham
04-24-2008, 07:08 AM
You could always do what physicist R.W. Wood did (and the Martia n named Number 774 in Raymond Z. Gallun's "Old Faithful") and fill a bowl with mercury and spin it. The surface will form a perfect parabola, as long as the rotation is smooth, and the bowl is pointing straight up.

(The idea has since been takemn up by lots of others:

http://www.sciencemag.org/cgi/content/summary/299/5613/1650

http://en.wikipedia.org/wiki/Liquid_mirror

It has been used also to manufacture disposable contact lenses.)

Mangetout
04-24-2008, 07:56 AM
That's a great idea, but would limit the portability of my device - also, it would make it difficult to use for solar experiments - in its raw state, the device would only work as a solar concentrator at midday, when used near the equator. The angle of incoming light could be adjusted for by means of a large plane mirror, but it would be difficult to manipulate the focused rays (it could be done by making the focal length quite long, and diverting it with another plane mirror, but that would get in the way of the first one directing the incoming rays.

Also, juices from my solar-roasted meat would drip into the mercury - leaving me with the dilemma of whether or not to sop them up with my bread - on the one hand, it's gravy - on the other, it's toxic metal. Hey! you got your gravy in my toxic metal!

WarmNPrickly
04-24-2008, 09:20 AM
I sure wish Squinks link worked for me. All I get is "DNS lookup error". My new internet service gives me all sorts of weird errors from time to time, but they usually resolve when I reload.

CalMeacham
04-24-2008, 09:25 AM
That's a great idea, but would limit the portability of my device - also, it would make it difficult to use for solar experiments - in its raw state, the device would only work as a solar concentrator at midday, when used near the equator. The angle of incoming light could be adjusted for by means of a large plane mirror, but it would be difficult to manipulate the focused rays (it could be done by making the focal length quite long, and diverting it with another plane mirror, but that would get in the way of the first one directing the incoming rays.

Also, juices from my solar-roasted meat would drip into the mercury - leaving me with the dilemma of whether or not to sop them up with my bread - on the one hand, it's gravy - on the other, it's toxic metal. Hey! you got your gravy in my toxic metal!

Well, the toxic mercury fumes are admittedly a deal-breaker for most people. You could use Wood's metal or some low melting point eutectic, or gallium, I suppose. But you're still limited in most cases to relatively long focal lengths and not a huge collection area.

Projammer
04-25-2008, 10:04 AM
Back in the 80's one of my classmates built a parabolic reflector by spiral cutting his flat sheet of reflective material and then mounting it so that it was wound tighter thus pulling the outer edges up.

Something like this (http://www.ae-zone.org/Designs/altNRG/Parab_reflect.html).

I don't have time now to find a technical link for this but I'll check back in later.

What you wind up with is something similar to a fresnel lens (http://en.wikipedia.org/wiki/Fresnel_lens), just as a reflector rather than a lens.

Mangetout
04-25-2008, 10:17 AM
That's a seriously cool idea, but I think it's probably beyond the scope of my materials (and I don't want to buy too much for this - my substrate is a sheet of recycled ply).

Mangetout
04-25-2008, 10:22 AM
One other idea I'm toying with though: Build a large shallow, sealed box, cut a big circular window in one of the flat faces, glaze it with mylar and apply a gentle vacuum to the inside of the box - it should stretch the mylar sheet into a bowl shape, although I don't know how close to parabolic this would be.

I'm still struggling on the dimensions for my segmented paraboloid though. Si - are you there?

si_blakely
04-25-2008, 02:15 PM
One other idea I'm toying with though: Build a large shallow, sealed box, cut a big circular window in one of the flat faces, glaze it with mylar and apply a gentle vacuum to the inside of the box - it should stretch the mylar sheet into a bowl shape, although I don't know how close to parabolic this would be.

I'm still struggling on the dimensions for my segmented paraboloid though. Si - are you there?yep.

Here are the relevant elements of my spreadsheet - have a go at recreating it
Cell A2 - focal length (same units as C2)
Cell B2 - number of petals
Cells C2-C27 0 to 50 (in steps of 2) (these are X values, the radius of the Parabola - tweak these so that the R values are integers)
Cells D2-D27 =C2+(C2^3/(24*\$A\$2^2)) (these are the R values, the plane radii)
Cells E2-E27 =(PI()/\$B\$2)*(C2^3/(24*\$A\$2^2)) (these are the deltaW values, marked either side of the sector line on the R values)

hope this helps. PM If not, I'll email you the spreadsheet.

Rather than making it too awkward, create a template, marking the curve using R and deltaW, cut it out, lay it on the sector lines and draw the line, then invert it and draw the other line.

Si

Mangetout
04-25-2008, 06:08 PM
yep.

Here are the relevant elements of my spreadsheet - have a go at recreating it
Cell A2 - focal length (same units as C2)
Cell B2 - number of petals
Cells C2-C27 0 to 50 (in steps of 2) (these are X values, the radius of the Parabola - tweak these so that the R values are integers)
Cells D2-D27 =C2+(C2^3/(24*\$A\$2^2)) (these are the R values, the plane radii)
Cells E2-E27 =(PI()/\$B\$2)*(C2^3/(24*\$A\$2^2)) (these are the deltaW values, marked either side of the sector line on the R values)

hope this helps. PM If not, I'll email you the spreadsheet.

Rather than making it too awkward, create a template, marking the curve using R and deltaW, cut it out, lay it on the sector lines and draw the line, then invert it and draw the other line.

SiExcellent - I think I can do it now. Cheers.