Strange Experiences with a Heliostat
I am posting the following true story here since it may be instructive for anyone who is contemplating building a heliostat.
Back in the 1980s, I designed, built and programmed a computer controlled heliostat to bring more sunlight into the living room of my house. It was a simple machine, with the mirror in an alt-azimuth mount, so the principal axis of rotation was vertical and the other horizontal. The program that ran in its computer - an ancient Commodore VIC 20 - was developed from an earlier program I had written that calculated the position of the sun in the sky from astronomical theory.
Describing the heliostat in detail would be pointless. It was built from components that are now long out of date. Nowadays, duplicating it would be almost impossible. Anyone who wants to design a heliostat should start from scratch.
However, something happened when I was testing the machine that might be worth sharing...
I live in Canada, about mid-way between the Equator and the North Pole. Seen from here, the sun always moves clockwise in the sky, rising in the east, passing to the south around noon, and setting in the west. Since the heliostat mirror moves to keep reflecting sunlight in a constant direction, it was obvious to me that the azimuth drive of the machine would always turn clockwise. In fact, I contemplated using a motor for that drive which would turn only in the clockwise direction. I changed my mind only because it was convenient to use identical motors in the two drives. Since the elevation (altitude) drive changes direction as the sun rises and sets, I used motors, actually steppers, that could turn either way.
When I first set up the machine and started testing it, I encountered a couple of simple problems that I easily fixed. The next time I tried it, I was happy to see that it initialized itself and moved its mirror so as to reflect sunlight in the correct direction. It seemed to be working properly. But, as I watched it for a while, I saw to my dismay that the azimuth drive was turning anticlockwise. Obviously, that was wrong. I stopped the machine and started hunting in the hardware and software for the cause of the problem. In that, I had no success. Everything seemed to be as it should be, but the azimuth drive kept turning the wrong way.
Then I made another puzzling observation. Although the mirror was turning anticlockwise, it was continuing to reflect sunlight in the correct direction! The thing seemed to be working properly, but wrongly at the same time.
After some bemusement, I realized what was going on. It was about noon on a summer day, so the sun was high in the southern sky. The window through which I wanted the heliostat to reflect sunlight was roughly to the north of the mirror, and not much higher than it. The mirror had to be aimed in the direction that bisected the angle between the directions of the sun and the window, as seen from the mirror. At that time, the aim direction was high to the *north*. As the sun moved from east to west, this aim direction also moved from east to west. But since it was to the north of the zenith, this motion was anticlockwise in azimuth. My heliostat was absolutely correctly performing this anticlockwise rotation.
It was startling to realize that this machine, which I had designed and programmed, was apparently smarter than I was. It had correctly figured out which way to move, although my expectations were wrong.
Another realization was that only sheer good luck had allowed the machine to work properly. If I had used a motor in the azimuth drive that would turn only clockwise, which I had been sure would work properly, the machine would have been incapable of turning in the correct direction. I wonder how long it would have taken me to figure out what was wrong!
A few months later, as the noon-day sun sank lower in the sky as winter approached, a situation arose where the aim direction of the mirror was almost vertically upward at some time near mid-day. The angles of elevation of the sun and the window, as seen from the mirror, were equal, and their azimuths were 180 degrees apart, so the angle-bisector pointed vertically up. In that situation, a tiny movement of the bisector, as the sun moved westward, caused a large change in the bisector's azimuth. This made the azimuth drive of the heliostat turn very rapidly, about 180 degrees in just a few seconds! I hadn't expected the machine to move rapidly like that, since the sun moves very slowly in the sky. On one day, the drive spun anticlockwise, since the bisector was passing just to the north of the zenith. On the next day, the bisector passed just to the south of the zenith, and the drive spun clockwise. The reverse happened in the spring, as the sun moved northward. Of course, since the mirror was lying on its back, pointing upward, the rapid rotation about the vertical axis did not cause much change to the aim direction.
Heliostats can be very counter-intuitive machines!
DOwenWilliams 17:23, 5 July 2010 (UTC) David Williams