Forming Acrylic Mirror

I think all this information exists in previous entries, but it's nice to have all my knowledge, however little that is, dumped into one spot.

Heat forming acrylic (aka plexiglass) is pretty simple. Just get the temperature up around 220°F and it's pliable. I put it into the kitchen oven. Don't rely on the oven temperature, though, use something with a probe to tell if you've got the real temp. For one thing, you can put the probe right down where the mirror is, not just floating around in the air inside the oven. Also, when I was researching this I found some warnings about fumes. I think that's only if you overheat because I never smelled or sensed anything. Maybe I've silently shortened my life by 20 years.

I tried a couple different methods of using a form. The first couple tries were "open-faced," meaning I laid the acrylic on top of something and counted on the weight of the material itself to cause it to sag into the form. It isn't really heavy enough for that, so I moved to a two-part form. It takes longer to heat that way because of the mass of the form itself. Another disadvantage of this method is that you have to be able to force the mirror into shape before you heat it, which means no 2D curves (like a bowl, if you see what I mean). Actually, you probably could do that by putting the acrylic sheet between the halves of the form and then weighing the top part down. Like the open-faced method, but with extra weight. Drill a hole in the form so the temp probe can sit right on the acrylic.

The above should give pretty nicely formed acrylic sheet even in complex shapes. Unfortunately it's totally unworkable for acrylic mirror. I'm not sure if it's the acrylic or the mirror backing, but the heat stresses the material such that you don't get a smooth reflection anymore. For a while I thought it was imperfections in the form, but various experiments ruled that out. (You can get bumps and ridges from a rough form, though, which can be eliminated by loosening the form a little or by lining the form with some kind of bumper material. I used a sliced up silicone baking sheet.)

Also: I never got far enough to have this problem, but eventually you'll run out of space in the oven. Multi-part forms? Some other heating method?

The curve I wanted wasn't 2D, so how about cold forming (aka "bending")? I have not yet determined the point at which the acrylic cracks or deforms. I haven't even determined if there's some point short of complete destruction where the mirror breaks down, a la the heat deformation. It seems to be pretty sturdy and stable, but then I'm not making tiny radius curves. If you imagine bending a yard stick, that's about what it seems like, or maybe a little stiffer. Put another way: I have a square of acrylic mirror that's 2'x2' bent into a curve about the same as the side of a 55 gallon drum and I haven't see any problems with it. (This is the 1/8" thick stuff. There's also a 1/4" thick stuff that I've never tried.)

The trick with cold forming is that you have to hold it in place somehow. Even drilling a hole through the acrylic will deform it, although only in the immediate area surrounding the hole. I started with a sandwich method--cutting two parts and then cramming the mirror between. That works, but you have to have some method of securing the bread of the sandwich that doesn't involve drilling through the mirror. Also, you cover up some portion of the mirror surface.

Of course, you can drill through the mirror, but in that case why even have the top piece of bread? That's what I switched to: Put the mirror on an open-faced form and drill a few well-placed holes to secure it down. Don't overtighten, because the force isn't distributed over a wide area like with the sandwich, so the local area can get quite deformed. Maybe a reason to have the top piece of bread after all. Or maybe just some rubber washers or silicone baking sheet for padding.

You can't get too fancy with this method, but for a single, relatively gentle curve it works great.

New Results

Latest solar trough configuration:

A few details:

1. Those are just simple, band-sawn parabolic arches. The mirror is attached with velcro. Works awesome. Ly.
2. I suspended the mirror from the pipe thinking that would keep the focal length constant while allowing simples changes of elevation. Why do I always go straight for the complicatedest solution in the universe?

And data from same:

The highest temp on there is almost 140°C. That's over 280°F. According to my rough calculations, the four steepest upward slopes indicate powers in the range of 20-25 watts. (Some of those dropouts are me messing around with the setup, some are cloud cover. Also, I later discovered that true solar south is like 15 or 20° east of where I've been pointing.)

Two big changes from the last run, other than the already-mentioned one of shortening the excess pipe.

1. Painted the pipe flat black.
2. Used a laser pointer to adjust the focus. I mounted a frosted glass square (I happen to have a bunch I bought for just such a use as this) at what I thought would be the focal length. Then I stood back and aimed the laser pointer in a roughly perpendicular way and looked where the point fell. This really needs a System to keep it perpendicular, but anyway I was able to determine that my focus was off by over an inch.

I'm thinking the Mark III will be the last iteration. Pointing in the right direction, and simplifying the pointing a little, may let me add another 10-20 degrees to the peak but that will be about as far as I can go with these simple materials and using an open-air design.

Belated Mirror Squeezer Results

I did one "live" run of data collection from the parabolic mirror squeezer, but after I did it I realized there was a major problem. The pipe was much longer than the mirror width, so it overhung. Too late, I realized that this meant there was unheated oil in there, making the temperature measurement invalid. And I don't even know what direction the error was worse in, since the overhang could also act as cooling fins. Anyway, here's the graph of the results:

It looks very similar to the original run in a hotbox:

One major difference: Check the x-axis. The parabola run is at least 4x steeper.

Anyway, if I get some sun this weekend I should be able to re-run with more accurate results.

Potpourri

• The diet hit a plateau. I'm down by 43 lbs from when I started, but in the last 30 days it's only changed by .5 lb. Looking at the chart from a year ago, I think I see a pattern. It was going down very slowly in May/June 2007, too. Looks like maybe 3 lbs in 60 days.

  There's probably two things going on. First, every year I imagine early summer weight loss should be easy. "Winter hibernation pounds just melt away naturally!" Second, a lot of good, fresh food shows up at the store.



• I used to listen to Pandora at work. The advertised feature, discovery and laser(ish) targetting of your tastes, worked great. The problem was that the selection wasn't so great. I was down to about 30 songs that they just endlessly looped for me. Then I switched to Last.fm. The targetting isn't very good, but the selection is pretty huge. Exhibit A probably says more about how out of the loop I am for just now finding this, but still: Pretty hilarious (Lyrics)


• And speaking of nerds: Do you like math? Do you also like mechanical devices? Then you will probably love How Round Is Your Circle. It's filled with mechanical ways to make, or approximate, mathematical functions, such as for linkages. The main problem with the book is that it's too short. It should really be a set of volumes so he can better explain each item. (Video teasers).


• I have dismantled and cannibalized the Squeezer for a much simpler version of a parabolic trough now in production. Stay tuned!

Ta-Da!

Once I abandoned the dead end of heat-formed acrylic, the ideas for cold-forming have been coming thick and fast. Here's the result of the squeezer configuration.

First, the squeezer itself:

Closeup of squeezing mechanism:

Result:

Closeup of accuracy:

Soo....yeah. That works. The squeezer is a bit overbuilt. I could go with 2x2s or even smaller next time. And one bolt every couple feet instead of every 6 inches. Other minor improvements. Those may never be made, though, since I had a real brainstorm on an extremely simple way to accomplish the same thing. More on that another time, though. I'm going to use this for my next experiment.

Duh.

Last you heard I'd come up with an incredibly complex system for getting a perfect parabolic wood form that still failed to make a good parabolic mirror. I actually tried tweaking a couple variables after that. The main thing I realized was that the mating surfaces of the form don't press perpendicularly, which means there's a shear force on the mirror between them. As a padding and semi-lubrication, I put in some strips of silicone baking sheet but to no avail.

So I decided to abandon the heat-forming idea altogether. At this point, even if it worked I'd still have major problems implementing anything at a larger scale. Instead, I'm going with a cold, mechanical system based on the working-extremely-well nail system.

The first stab at a mechanical forming system looked like this:

The idea is that you just wind on some wingnuts to raise the tension and adjust the shape. And that actually worked pretty well to get the shape, modulo this being a first stab prototype. But the focus wasn't all that much better.

Finally, one might even say AT LONG LAST, the light dawned. I turned the mirror around and actually looked at it, searching for the distortions. Huh, they are right around those big holes I drill...OMG. The plexiglass just can't take the stress of the drill! I'm distorting the area around the hole! The oven is probably distorting the whole schmiel! That's why the nail version works so well. I'm just bending, not drilling or melting. What I need is some way of shaping into a parabola as non-destructively as possible. (I realize how obvious this sounds, but I didn't hear any Internet Geniuses suggesting it to me at the time, so bite me.)

Kind of fiddling around with it, I found that I didn't really need to shape the main body, so to speak, of the curve. Just pressing on the ends gave me a pretty good parabola. So, Mechanical Parabolic Mirror System Mark II:

Now winding on the wingnuts transmits compression to make the shape you want. I'm pretty sure that doesn't make a perfect parabola (I think it's actually a cubic curve, based on my skimming of some beam bending equations) but it's pretty damn close. Maybe not so close at full size, we'll see. If it needs more adjustment at larger sizes, I can add some tension non-destructively.

And how does it work, doctor?

Parabolae Foci

I keep having to solve this problem. It's not hard, but to "save time" I usually google it and find too much information and not enough explanation. Then I end up solving it myself. And it's so easy that each time I figure it out I'm like "there's no need to write this down--it's obvious BY INSPECTION". And then I forget it. So here it is:

Where is the focus of a parabola? Alternatively, what formula should I use to create a parabola with a given focus?

Take the equation y = ax². Obviously the focus will be on the y-axis, but how far up? We know all the incoming rays will meet there, so let's choose a convenient one. A great choice is a ray that is turned by 90°. That is, it comes in vertically, hits the parabola, and heads towards the focus horizontally.

Since the angle of incidence equals the angle of reflection, the slope of the parabola at the point the ray hits is going to be 45°. (I spent like 20 minutes using gnuplot and the gimp trying to illustrate this before giving up. Just visualize it.) Where on a parabola is the slope 45°? Slope is also rise/run, so the the slope in the y = mx + b sense is 1. Where is the slope 1?

The equation was y = ax². The instantaneous slope is the derivative, y' = 2ax. We want that to be 1.

2ax = 1
x = 1/2a

Substitute in to find out where on the y-axis this is.

y = ax²
y = a(1/2a)²
y = 1/4a

Now let's say I want to make a parabola with a focus that is 6 inches from the bottom of the curve.

1/4a = 6 inches
a = 1/24 inches

Therefore my equation in inches should be: y = .0416x². (I think. Contradicting my claim about how easy this is is the fact that I actually got this wrong on paper, TWICE, before posting this.)

SUCCESS!

A non-blurry, curved mirror.

In my last post, I hypothesized the problem might be too much time spent in the oven, causing some kind of degradation. That prompted epicanis to wonder if the acrylic was oxidizing. That in turn made me actually take a close look at the failed samples (why I didn't already do this is a mystery).

The acrylic is actually fine in those failures. It's the mirror backing that cheesed out on me. What is the backing made of? Who knows! What do I do about it? I dunno!

Then I was coincidentally reading a book about polymer clay and it had a tip for firing: Put it in at a sub-firing temperature to evenly heat the item, then turn it up to actually harden it. And I was all: whoa. I know that the softening point for acrylic is around 230°F, but I've had to turn the oven up to 250°F to get the samples to bend. I've been chalking it up to oven imprecision and chemical composition variation. But I think the real issue is that the core of the mirror doesn't get hot enough until the outside is too hot.

So this time I put the whole apparatus (which I should have taken a pic of, sorry) inside the oven at 200°F until a probe told me it was more or less up to temp. Then I just cranked it up to 215°F and voila, it worked.

Now I need to do a bunch of these at once (or one large sheet)...

Acrylic Mirror Failures Learning Opportunities

The acrylic mirror samples arrived. I got 3 mirrors about the size of a credit card, but thicker, like a piece of glass.

OBJECTIVE: Create a "trough mirror" that focuses onto a line.

KEY FACT #1: Acrylic mirror softens and bends at around 230-250°F.

KEY FACT #2: A parabola is a mathematically perfect focusing shape, but (a small section of) a circle is plenty fine for my needs.

FIRST ATTEMPT:

I got a big, glass jar with smooth sides. I put it lying down inside the oven. I balanced the mirror on top, shiny side pointing down (and with the protective plastic sheet still on it). I had to tape the mirror in place.

Starting at around 215°F, I slowly heated the oven up until the mirror ends started drooping. After probably an hour of watching it slooooooowly bend, I just reached in with an oven mitt and press-formed it to the glass.

RESULT: Meh. The shape is great and the focusing is accurate but the mirror got all foggy. It looks more like polished metal now. Also the spots where the tape was touching are distorted.

SECOND ATTEMPT:

My theory was that I should have the mirror pointing up, which might make the cloudiness go away and would make using tape unnecessary.

This time I used a regular soup pan tipped on its side. I put the mirror inside so it could form to the inside curve of the pan. Left the protective plastic on. Set the oven to 250°F (that's what I had worked up to from the first attempt) and waited. And waited. And waited.

Once again, I eventually just reached in and press formed it. When I removed the sheet....still cloudy.

THIRD ATTEMPT:

I watched the video again. Oh, I'm supposed to remove the protective plastic. Replay the second attempt, but this time remove the thing first.

After waiting the requisite Long Time, I could see the mirror was already foggy even before I press forming it. Aha! Not the plastic or the form!

WHAT'S PROBABLY GOING ON:

I have small samples, so gravity isn't enough to bend them until they are very soft from being in the oven for 45 minutes or more. In that amount of time, some chemical degradation (or something) is causing the cloudiness. If I rig up some way to put a weight on top of the sample, maybe I could speed that up. Or I could just reach in there earlier and do it by hand.

But now I'm out of samples. I can bend and rebend the cloudy ones just to test out some weighting system and/or get my timing right. But I'll only be able to check if the cloudiness disappears if I buy more mirror. Which I can do, but I hate the shipping charges. Ah well.

Miscellaneous

1. I had a long, long thing here about how following my plan was so easy, but it kept reading like Tighter Buns in 30 Days While Eating Pizza, so let's leave it at this: Down by almost 27 pounds.
2. Way back when, I did some solar experiments. I said I'd come back to that. I'm still working on that. The problem is, the design I came up with is kind of crappy.

   What I want is a parabolic trough mirror focused on a central pipe. I've tried using mylar sheets on various surfaces before, but it didn't come out too well. This time I tried strips of mirror laid in a wooden parabolic form. I haven't tested it yet, but it doesn't look too convincing on the workbench. Lots of gaps, not much total area, not well focused, etc. (No picture, because seriously.)

   While I was wondering what to do about all this, I came across this video. The guy comes across as a little infomercially, but his ideas look pretty good. In particular, I didn't know you could "drape form" plexiglass (aka "acrylic") mirror. That changes everything! Almost zero work and much higher efficiency.

3. Which brings me to the third misc item. WhereTF do you find acrylic mirror at a reasonable price? I've found it as low as $4.50/sqft, but you have to buy at least $50, not to mention shipping. Plenty of ebayers, but the price with shipping never comes out lower than ~$12/sqft and you have to buy several sqft to get that. Lowe's can special order it, but you have to buy 5 48"x96" sheets and it's still $8/sqft. McMaster-Carr, despite their awesome website, doesn't reveal shipping information even if you ask a live human being, which, HELLO.

   This kind of mirror is used in a lot of children's products because it's shatterproof, so I've considered repurposing a baby mirror, but the cost is still pretty high there due to packaging, frames, etc. I've even wandered around Home Depot and Lowe's to see if I could find a bathroom/decorative/whatever acrylic mirror on some other product. The sole success was a really, really crappy medicine cabinet with attached acrylic mirror. The whole unit was $12 and the mirror was 2 sqft.

   I would just go with that, but the fact that it's attached to something else only proves that I should be able to get the mirror alone for cheaper. Also, I hate to buy something specifically so I can throw it away. In the mean time, I ordered a set of these to experiment with. With the shipping, even amortized over several other items in my order, the price per sqft comes out at lalalaicanthearyou.