Ray Menke is building a Helios in Texas (see blog) and had some questions on the focal drift and mirror calibrating process that are not well explained in the existing material so I wrote back a fairly long diatribe about the issues, and in case others have the same questions I’m posting the response here.

I also drew up an image explaining focal "cross over" which happens with the spiders: the light from one corner will cross the reflection and hit the other corner but the focal point size stays exactly the same. What does change however is that the internal stresses in the mirror increase leading to breakage. I think most of the mirror breaking is caused by this sort of thing as shown bellow.

Response to Mr Ray Menke 25 Mar 10:

The best explanation on-line of the focal drift as yet is found in the Prometheus-System-Calculator readme (the Calculator can calculate the drift; or miss as it becomes mysteriously called there which is explained at the very end of the readme). But it is not a very good explanation, since the reason is not so intuitive (especially in 3 dimensions)... so here goes.

Basically, for the mirrors to reflect the sunlight onto the target they must be exactly at half the angle between the suns rays (to the mirror) and the line from the mirror to the target (which is why your laser idea won’t work, no matter how nifty an idea it is). So if the sun was directly overhead and the target was horizontal to the mirror, then the mirror must be at 45 degrees. This is easy to see in 2 dimensions, which is why we would expect the Helios to function perfectly when considered only from the side. But this is in fact only true for the mirrors in the centre of each row (on the 2-dimensional plain with the sun and the target), where if the sun changes 5 degrees, each mirror must change 5 degrees and so tilting all the mirrors at the same rate produces no focal drift and everyone is happy.

However, in 3 dimensions what’s true for all the central mirrors, is not true for all the other mirrors on the rows. The outer mirrors must not only reflect up to down (virtical to horizontal) but also from left to right reflect the light towards the centre. This lateral reflection part isn’t covered by our 2 dimensional proof above, and it results in an slightly angle angle change rate between the suns rays-to-outer-mirror and the outer-mirror-to-target, compared to the angle change rate for the mirrors in the centre of the row.

But since all the mirrors must be fixed on their rows for the Helios to be practical to use (changing all the mirrors individually all the time is no an option), there’s no way to correct for this difference in angle change. Fortunately, it’s not a big difference, 1-3 degrees, and so either a moving oven can be constructed or just a wider door.

Calibrating the spiders

As mentioned above the mirrors must be at the half angle between the sun-to-mirror and the mirror-to-target (so the laser idea can’t work, but it’s worth a try).

Basically this part of the Helios construction is really, really annoying at first (takes about two days in the blistering sun, so cover all your skin in white, and wear good sun glasses), but you quickly get the hang of it and the end result is worth it I assure you.

What we do is set up a a piece of tin where the oven will be, and then draw a box for the precise target. As you discovered all the focal points make it difficult to work, so first it’s necessary to work row by row. To distinguish between the reflection on each row we move the reflection we’re working on off-target and focus it 15 cm away on the tin, then we place it back on the target and move to the next mirror.

For each mirror, I’ve never seen one break while being focused (if two concave they’ll break afterwards a bit spontaneously) so don’t worry about achieving the best focal point. However, "too concave" usually doesn’t result in a better focus; rather the light from one corner will cross the centre and hit the opposite corner of the focal point, but bizarly the mirror always (for me at least) doesn’t focus more, but because it’s more concave due to this crossing businesses has more internal stress and is more likely to break. So, when you feel you’ve "overworked" (even one corner of) the mirror in this way it’s usually faster to unscrew all the bolts and restart rather than try to correct the problem (lot’s of bizarre things start to happen with the focal point and it’s essentially impossible to understand what’s happening with the mirror).

So, the fastest way is to work out a method that’s always the same for each mirror: screw all the bolts so they just touch the mirror, then focus the mirror onto the tin (and tighten the attachment bolts so the mirror doesn’t move), then turn the top centre bolt once, then the bottom centre (always one then it’s opposite, starting with the centre bolts), then the side centres (the reflection should start to be come a cross), then the corners (should bring in the arms of the cross), and observe all the while, then repeat until the focal point is tight. At some point you should feel that one more turn makes the light cross the focal point, so turn back. On this first mirror you should get a good idea of how many turns each bolt takes (the centre bolts and corners will usually be different), so can speed up the process for the next mirror. After a few you should just sense by observing the affect on the focal point that you’ve turned correctly. But always keep in mind that once wonkiness sets in it’s more trouble than it’s worth to try to unwonk; once you lose the feeling it’s gone and correcting one corner mess up another corner.

After a while it should start to go really smoothly, and over a couple of days should get done.

IMPORTANT: for this calibration of each mirror the focal drift phenomenon doesn’t matter, so you can just set you your tin at 3.5 meters and go (can at least light wood on fire by the end of this process and feel really good). You can also go all day, regardless of the position of the sun. Don’t worry about the overall focal point during the spider calibration, just that each individual spider.

Oven and focal drift

For the focal drift the distances are small enough that it doesn’t really affect the focus of each mirror (maybe a few milimeters), so in focusing each mirror the drift doesn’t have to be taken into account and can be solved later, which is fortunate since otherwise calibration would be a pain.

Rather the drift is caused because the outer mirrors are fixed on their rows and need to correct more than the central mirrors. So, once all your spiders are good, it’s time to sync them all to a specific moment in the day, when the sun is 45-55 degrees, between 9 and 11 (depending on when solar noon is). This way the machine will be optimum at around solar 9, then "focal drift" a bit to a maximum drift at solar noon, and then drift back to optimum at solar 3. This minimizes the consequence of the solar drift and makes the machine optimum at the start of peak sun hours, then at noon there’s usually too much power anyway, and then goes back to optimum for the end of peak sun hours (there’s only 5 or 6 peak sun hours in a day).

This doesn’t really require any maticulous process, but rather when you start using your oven (or burning wood in the focal point) just keep an eye out for any "stray focal points" at around 9-10 o clock, then by standing in front of the mirrors (closer the mirrors than the focal point so you don’t get burned) and sort of waving your arms you should be able to zone in on the stray mirror. Keeping this in mind over a few days should result with a fairly tight focal point. A loose focal point will usually still heat the oven, just slower than a tight focal point, so a few stray reflections is nothing really to worry about and can be corrected casually with the use of the machine.

If you don’t intend to use you oven more than 6 hours a day, then correcting for the drift with a moving oven may not be necessary. (by placing the oven 20-30 cm above the chaser, easy to work it out so that you can add a track if necessary)

Your design for a light cone will probably be enough (it also block wind cooling as a bonus), and of course using a lot of insulation is a critical factor as well.

For the focal length, we’ve always used 3.5 meters, but if you shorten that to 3 m, it will only really affect the bottom mirrors (the top mirrors are farther away due to the slant), so one solution is to just be careful not to focus too much for the bottom mirrors. But again, in my experience the mirrors tend to have a natural limit to focal tightness and it’s usually due to this "crossing the focal point" which produces the same sized focal point, and so impossible to distinguish visually after focusing, that results in breaking. About 5 % of our mirrors usually break spontaneously, but often still work (just have a crack in them), and of course all the mirrors aren’t necessary for the Helios to function. At noon (on a hot day with no wind) our ovens usually stay at 250-300 degrees with only 2 rows.