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Introduction and explanation
The following is the text of an article I wrote for a magazine last year. After thinking about it for several months, the editors finally decided not to publish it. I have no great desire to spend a lot of time and effort on a search for another publisher for this article, so I am releasing it into the public domain via computer bulletin boards and networks.
Anyone is welcome to copy and/or re-distribute this piece on any BBS or network, or in any other form, providing this is not done for monetary profit. You are also welcome to make any additions to it, either before the start of the "original file" or after its end. However, I would ask you to make the authorship of any additions clear. Please do not make it appear that I wrote anything that I did not, and please do not alter my "original file" in any way. If you add any interesting information that you think I might like to know, please tell me about it directly. My address is at the end of the article. This applies especially to any information about heliostats that is not included in the article.
The article I submitted to the magazine was accompanied by a few diagrams and pictures. These are not, I think, essential to its understanding, so I have made no effort to include them in this file. However, if you would like me to mail you copies of them, please send me a self-addressed envelope. Put a Canadian stamp on it, please, if you are in Canada. Otherwise don't bother. I am not setting a fixed price for this, but I would appreciate a donation of a couple of dollars, say, to cover the costs of copying, etc.
I hope this turns out to be useful for someone.
February 20, 1994
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Making the Sun Stand Still
By: David Williams
Nowadays, we all want to make optimal use of sunlight. Whether we employ it for indoor illumination, space heating, making hot water, or maybe for something more sophisticated such as generation of electricity, good use of solar energy is a major consideration. The reasons are obvious. Sunlight is free, and it produces no pollution. It is the most environmentally friendly of all sources of energy. And yet it has a significant drawback. The sun does not stand still in the sky. Unlike other sources of energy, it moves, uncontrollably but highly predictably. And this movement causes problems. At some times of day or seasons of the year, sunlight may shine into a window, or beat down directly on to a water heater. At other times, it does not.
We all know why this happens. The earth is spinning on its tilted axis, and is also moving in an elliptical orbit around the sun. The result is that, seen from the earth's surface, the sun appears to execute a complex dance. Every day, as seen from most latitudes, it rises in the east, crosses the sky and sets in the west. On top of this motion are some intricate oscillations. The largest of these carries the sun further north in June than in December, and is responsible for the seasonal variations of climate. Others cause sundials to keep poor time, relative to clocks. In mid-February and also around the beginning of November, for example, a sundial is about a quarter of an hour wrong, compared with a good clock set to local mean time. All this moving around in the sky by the sun poses a problem for users of solar energy.
There are three possible ways of coping with this problem. One is just to live with it. We may make our water-heating device so big that, even though it is usually working at much less than its peak efficiency, it can still produce as much hot water as we want. This approach often works, but it is wasteful and expensive. The second way is to make the energy collector move so as to follow the sun's motions in the sky. This can also work, but often involves complicated and costly mechanisms. The collector is usually big and heavy, and has to be connected to the rest of the world with water pipes, electric cables or similar things. If the collector is to move, these connections have to be able to accommodate the movement. And neither of these two approaches can easily be used, for example, to make the sun shine through a particular window.
The third approach is to make a stationary sun! Of course, there is no practical way to stop the real sun from moving in the sky. But it is possible to have a stationary reflected image of the sun, seen in a mirror. To make this happen, the mirror has to move. However, mirrors are much simpler and lighter than solar-energy collectors, and do not need any pipes or wires. A machine that moves a mirror can be much simpler and cheaper than one that moves a collector. And light that has bounced off a mirror is still light. It can be used to illuminate a room, for example.
The idea of using moving mirrors for this purpose goes back at least as early as the ancient Egyptians. They brought sunlight into their buildings by using mirrors that were kept aligned by servants or slaves. When mechanical clocks were invented, their mechanisms were soon used to drive mirrors that would track the sun reasonably well for considerable periods of time without human attention. These machines were called "heliostats", from the Greek words for "sun" and "stationary". By the time the great artists of the European renaissance were creating their masterpieces, many of them were using heliostats to cast continuous sunlight on to their works. However, as artificial light became cheaper and cleaner, heliostats were almost forgotten. Only recently, with the increasing interest in solar energy, have they been re-invented.
Most modern heliostats are high-tech, sophisticated machines. They can function for long periods of time, months or years, without attention. To do this, they must accurately take account of all the sun's complex movements in the sky. Usually, they use a computer to do this. Its program includes a mathematical description of the sun's motions, the latitude and longitude of the mirror on the earth's surface and the direction in which light is to be reflected. The computer must also have access to a clock that keeps track of the time and date. From all this information, the machine figures out the correct orientation of the mirror, and sends signals to motors to keep it properly aligned. Large installations have a single computer controlling many mirrors, keeping them all pointing so as to reflect sunlight on to a single target, which therefore receives a very large amount of solar power. The target can consist of a boiler, to produce steam to drive machinery or generate electricity, or it can contain an oven or furnace, for all kinds of possible purposes.
Computer-controlled heliostats do not have to be very large or prodigiously expensive. I have a single-mirror one that I built a few years ago to reflect light from a sunny porch into my living room, which would not otherwise receive much sunshine. It uses a small Commodore VIC 20 home computer which I bought, second-hand, for $25. It was one of the cheaper components of the heliostat. However, although the materials were all quite inexpensive, the tasks of designing, building and programming the machine were far more complex than most home-design energy-use projects. I happen to have a background in these kinds of things, so for me the project was a feasible one. Even so, I put enough work into it that it would have cost several thousand dollars if I had done it commercially. I would not recommend this task to most other people, nor can I write precise instructions on how to do it. Too much depends on what components and materials happen to be available. For example, I doubt that it would be easy nowadays to find a VIC 20. It has gone the way of the dodo.
Fortunately there is another type of heliostat that is much simpler. Its inspiration dates back to the clockwork-driven machines of centuries ago. Actually, most of those heliostats were not very effective. In order to reflect sunlight in a constant direction even for a period of a few hours, a mirror usually has to move in quite a complicated way. Early heliostats were not capable of this complexity, with the result that they needed to be readjusted by hand very frequently. However, it is now understood that most of the complexity can be avoided by using not one mirror but two. One of the mirrors is mounted on a spindle that is set up to be parallel with the earth's axis of rotation. It is turned by a clock-type mechanism so as to make one rotation every 24 hours, keeping pace with the daily motion of the sun in the sky. This first mirror is aligned so as to reflect sunlight in the direction of either one of the celestial poles: either towards the north Pole Star, or towards the point in the southern sky that corresponds to the South Pole. These special cases, of reflecting light towards the poles, are the only ones in which the moving mirror's motion is simple, a steady rotation about a fixed axis. It does not matter if the pole in question happens to be below the horizon at the place where the heliostat is located. In this case, sunlight is reflected somewhat downward by the rotating mirror. A second mirror is arranged so as to intercept the sunlight that has been reflected from the first mirror, and to send it in whatever final direction is desired. This second mirror does not have to move. This combination of two mirrors, one rotating and the other stationary, produces a heliostat that tracks the daily movement of the sun very accurately. However, it does not take into account the slower, seasonal movements, so the machine has to be readjusted by hand every few days. In this sense, it is not as good as a computer-controlled one, even though it is much better than the clockwork heliostats of long ago.
You might consider building and using a heliostat of this type. It is a project that many people could undertake. I have made one that is driven by the works of a cheap clockwork alarm clock. Parts of the clock, including the case, face and hands, were not needed. A gear wheel is glued to the hollow spindle that originally carried the hour hand, and drives a second gear wheel that is mounted on the shaft that carries the rotating mirror. Finding suitable gears can be a bit of a challenge. They have to have exactly a one-to-two ratio, so the wheel on the mirror shaft has twice the diameter and exactly twice as many teeth as the one on the clock. This makes the mirror rotate once every 24 hours, taking exactly twice as long as the hour hand of the clock, which turned once every 12 hours. My heliostat uses a couple of plastic gear wheels that came out of an unrecognizable bit of machinery from a surplus store.
Most of the components, the clock, the two mirrors and their mountings, are attached to a long bar that can be tilted at a variable angle. The clock mechanism and the rotating mirror are attached to one end of the bar, so that the shaft driving the mirror is parallel with the bar. The stationary mirror is attached to the other end so that the line joining the centres of the two mirrors is also parallel with the bar. In fact, it is the same line - extended - as the axis of the shaft that drives the rotating mirror. When the heliostat is in use, the bar has to be parallel to the earth's rotation axis, which means that the inclination of the bar from the horizontal has to equal the local geographical latitude. I wanted the machine to be usable almost anywhere, so I arranged for this tilt to be adjustable. If you don't want this feature, you could fix the bar at the correct tilt for your latitude. The base of my machine carries a small bubble-level and a magnetic compass to show north. These are useful in setting it up when I have carried the heliostat to a new site. If your machine will not be moved often, you could do without these components.
I have found that it is better to use mirrors that consist of silvered acrylic plastic ("plexiglass") than regular glass. The plastic is lighter, less fragile, and easier to attach to other components by gluing. The mirrors in my machine are square, about 15 centimetres (six inches) on each side. Although they are small, they reflect a surprisingly bright light. However, you may wish to use larger mirrors and build the whole machine proportionally bigger. Small paint marks are placed on the mirrors at their central points, on both sides of each mirror. (Strictly, the front of one mirror has to be marked, and the back of the other. However, since my mirrors are identical in all other ways, I decided to mark them on both sides.)
Each mirror is held between a pair of friction-fit pivots in the arms of an approximately Y-shaped metal mounting, and is able to swivel, when turned by hand, about the line between the two pivots. The stationary mirror's Y-mounting can also be swiveled about its stem, which is friction-fitted in a hole in the long, tilted bar. It is important that the mountings of the mirrors should be such that all rotations occur about axes that pass through the central points of the mirrors, and that the line joining the centres of the two mirrors should be the same line as the axis of rotation of the moving mirror and parallel with the tilted bar. The direction of rotation of the moving mirror should be the same as the direction of the sun's daily movement in the sky, i.e. clockwise as seen from the north. If you use the same arrangement as mine, with a single pair of gear wheels connecting the clock to the mirror shaft, and if you put the clock on the machine in the same kind of way as I did, with the drive spindle facing inward toward the centre of the heliostat, you will find that the direction of rotation is correct if the rotating mirror is at the northern end of the machine. In the northern hemisphere, this means it is at the upper end of the tilted bar, reflecting sunlight somewhat downward towards the south celestial pole.
Aligning and adjusting the heliostat is quite simple. First, set the long bar so its tilt equals your latitude, and set the base so it is level and aligned to north. Strictly, this should be "true" rather then "magnetic" north, so you may have to make a correction to the compass reading, depending on your location. Second, turn the non-rotating mirror so its back side faces the rotating one, and turn the rotating mirror in its Y-mounting so it is roughly in the same plane as the Y. Turn the "time" adjuster on the clock mechanism so as to make the rotating mirror approximately face the sun. Then turn the rotating mirror in its Y-mounting so as to reflect sunlight on to the back of the non-rotating mirror. In the middle of this reflected beam of sunlight you will see the shadow of the mark at the centre of the rotating mirror. What you must now do is to fine-tune the alignment of the rotating mirror, using the clock "time" adjuster and the Y-mounting pivots of the rotating mirror, so as to make this shadow fall exactly on the mark at the centre of the non-rotating mirror. (This sounds far more complicated than it really is.) When this adjustment is correct, the rotating mirror is properly aligned. Make sure that the clock mechanism is wound up and running. Now all you have to do is turn the non-rotating mirror, by trial and error, so it reflects sunlight into your house, or whatever direction you want. Make sure that it is reflecting the light it is receiving from the first mirror, rather than light directly from the sun! Now, the heliostat is fully adjusted. The beam of sunlight emerging from it should not move as the sun crosses the sky.
Since this type of heliostat does not follow the sun's seasonal movements, you will have to realign the mirrors every few days. With a bit of practice, you will be able to do this in a few seconds. It is not a major chore. Also, if you use a clockwork mechanism, it will have to be wound up daily, or maybe weekly. I have thought of trying to use one of the little quartz-oscillator electronic mechanisms that are now used for many clocks, but the shafts on the ones I have examined have been very thin and fragile. If I ever find a bigger, stronger one, it would eliminate the need for me to wind clockwork.
I have not attempted to make this machine weather-resistant. I use it outdoors only rarely, during very fine weather. Usually, it is in a glazed-in porch, where wind, rain, snow, etc., cannot get at it. I suppose the mechanism could be made weatherproof, but I suspect it would be easier just to enclose the whole machine with a little glass or plastic greenhouse. This could be put outdoors, from where sunlight could be reflected in to the house, or anywhere else.
If you make a heliostat like this, what might you use it for? The glib answer is, "practically anything to do with solar energy". If you use the sun's heat to make hot water, you could shine a steady, unmoving beam of sunlight on to the heat collector. If you use photovoltaic cells to make electricity, you could greatly increase their average output. But the application that is likely to be most useful to many people is illumination: shining sunlight into places which would otherwise be too dark. (Solar energy enthusiasts call this process "daylighting".) Maybe you have a room in your house that you would like to receive more sunshine. Maybe you grow vegetables hydroponically, and they would do better with some more light. Or maybe you would like to cast a beam of sunlight on to an architectural detail or on to a sign in front of a business. A heliostat could do any of these, and many more.
The author, David Williams, would welcome correspondence from readers about this article. Write to him by mail at:
P.O. Box 48512
3605 Lakeshore Blvd. West
or by fax at (416) 259-3247.
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