Drawing/diagram of Suntrak
A Technical Description of Suntrak
by Elsa Garmire
On the plaza a 30' sculpture makes a 10' sunbeam and throws it through the fog to a fixed place on the Pavilion. The 5' x 8' elliptical mirror forms a circular sunbeam by rotating once a day to follow the sun; the mirror constantly reflects the sunbeam to a large, stationary 10' triangular mirror. This mirror deflects the circular sunbeam to a fixed place on the Pavilion. The technical concept of this device is called a polar heliostat (see Appendix C), and it works only if the axis between the two mirrors points toward the North Star.
As the earth rotates on its axis the stars and sun appear to move in the sky, revolving around Polaris, the North Star. This star is the only part of the sky which appears stationary during a day. The sun's angle from the North Star is always the same, so that a mirror which rotates about the North Star at the rate of the sun (once a day) can reflect a sunbeam in a fixed direction. This requires that the mirror be tilted from perpendicular to the North Star by half the sun's angle. The direction of the North Star changes a small amount from day to day, however, for the same reason that the sun is high in the sky in summer and low in winter. This is because the earth's rotational axis (North-South pole line) is tilted with respect to the plane that the earth moves in around the sun. The daily tilt is about one solar diameter which accumulates to 23° in a year.
The large stainless steel mirrors are held in an arc and attached to a conical base. Initial positioning of the device required two-stage adjustment. First the axis between the two mirrors was sighted to true north using Polaris, and secondly the stationary triangular mirror was adjusted in two directions to reflect the sunbeam to the exact desired position on the pavilion. The moving elliptical mirror of the Suntrak has been made to tilt its spin axis automatically by a preset amount each day so as to compensate for the motion of the North Star and remain tracking the sun.
The mechanical motion of the elliptical mirror has been devised so that one 5-watt, 1 rpm clock motor is all that is required to run the Suntrak. By gear reduction and by use of a connecting rod and eccentric, this device tracks the sun's rotation and also corrects daily for the polar axis tilt. The entire mechanism is located directly in the back of the moving mirror. Suntrak is never turned off, so that the elliptical mirror follows the sun around even at night, pointing down to the center of the earth.
To Aim a Sunbeam by Mirrors
by Niels O. Young
The sun seems to move in the sky because the earth spins on its axis once around daily, and also orbits the sun once around yearly. So, while the sun shines (only half the time on the average) a beam from it is ever moving. By a single mirror, such a beam could be directed in a desired direction - and kept pointing that way by means of a servomechanism, for example.
So Suntrak got its name from the notion that a man (as a servo), or a machine using photodetectors and set up to track or follow, could achieve the desired result. A servo-mechanism to track the sun needs at least two photodetectors whose output voltage, for example, is proportional to deviation from proper pointing. This voltage, amplified with the correct phase shifts, time constants, and gain, feeds two motors so that the deviation is reduced. It is not too difficult to make such a tracker function stably in steady-state conditions, (i.e. to avoid oscillation or other divergences). But it would be difficult to design such a tracker for the other necessary conditions: 1) to acquire the sun in the morning, 2) not to go wild with searching when a cloud obscures the sun, 3) not to be diverted into tracking a brilliantly lit cloud edge.
But the sun follows a known track like clockwork (or vice versa) so why indulge in the panoply of technological overkill when a specialized clock will do? Indeed, clock-like machines to follow the sun have been used for over a hundred years to divert a beam of light into a laboratory, for example, to illuminate a microscope specimen. For such purposes sunlight was esteemed as brighter than any artificial source, at least until the advent of high-pressure Xenon lamps about 1950.
These efforts resulted in philosophical apparatus such as the Heliostat (fixed sun), Siderostat (fixed star, often tied to Siderial time), Coelostat (fixed celestial sphere, on Siderial time), and Uranostat (fixed celestial object but only for short times). The Heliostat and Siderostat can give a beam of fixed direction, although the displayed image of the sun rotates about the sun's center. The Coelostat alone produces a truly stationary image of the sky-—and uses two mirrors. The Uranostat only approximately compensates for the Earth's motion over short times.
Of these systems, only two use a single mirror: Foucault's Siderostat of 1869, and the Uranostat. Foucault's machine uses a linkage with pivots and slides and seemed altogether too complicated to attempt :m a. scale of mirrors yards across. Therefore, a "classical" two-mirror form of polar heliostat seemed the best solution for Suntrak—even after many an hour looking for alternatives having one mirror, and finding none less complicated than Foucault's solution.
So how does a polar Heliostat work? The Earth's rotation is compensated by having a mirror rotate at the Earth's speed, one turn per day. So as far as the Sun is concerned, that mirror is fixed. But the only direction the beam can be reflected off this mirror, is along the polar axis. Either upward, or downward, but nonetheless parallel to the polar axis. This axis is in a North-South direction and elevated above the horizon in the North direction at an angle equal to the local latitude. In other words, the polar axis can be a line between your eyeball and the North Star. Having a beam fixed along a polar axis, it is now only necessary to deflect it where desired by a fixed, second mirror—thus completing the design of the polar Heliostat.
In practice, further details must be accounted for: the Sun's altitude varies axis as the Earth orbits the Sun. This is because the Earth's spin is tilted by 23.5° with respect to its orbital axis. Because of this inclination, the Sun's altitude at noon oscillates with a period of 365^ days ( a Solar year), and can be expressed by: Altitude = (90° - local latitude)-(23 .5°) cos 2Õ (N/365¼)
where N is the number of days since the last winter solstice. If this yearly motion were not accounted for in Suntrak, the polar axis mirror would have to be reset about once daily, the maximum daily altitude change being a large fraction of the angle subtended by the Sun itself. So to satisfactorily track the Sun, the polar axis mirror must be organized to tilt around an axis normal to the polar axis, at the same time it spins once per day. Only at the equinoxes (about March 20 and September 20) is the polar axis mirror oriented at 45° to the polar axis. Since a plane mirror tilted by some angle tilts the reflected beam by twice this angle, the polar axis mirror must tilt through an amplitude of 11 3/4° or 23 1/2° peak-peak once per solar year.
Description of Machinery Used
Suntrak consists of an elliptical mirror which turns about the polar axis, and a triangular mirror which subsequently deflects the beam from the polar direction to the wanted direction. The outline of the elliptical mirror looks circular on the triangular mirror because a foreshortened ellipse can look circular. Indeed, an ellipse which can be circumscribed in an equilateral triangle at one orientation can be circumscribed also at any other rotational position (Geometers take note).
The mirror spins about the polar axis daily and also tilts. A 5-watt, 1-rpm clock motor gives it life. This motor output shaft, rotating at 1 rpm, is reduced by gearing, to turn once per day; or, one per 1440 minutes: This (1440/1) gear reduction is accomplished by a (9/1) ratio of numbers of teeth on two meshed gears. The remaining (160/1) ratio is obtained by a lump of machinery called a harmonic drive, which has the virtue of giving such a high ratio in one step.
The input and output shafts are coaxial; the output shaft has strong bearings Cagainst wind loads, for example); and there is little backlash or springiness. Attached to the stumpy output shaft is an H-frame which carries the elliptical mirror. This frame is tiled to account for the daily change in the polar axis. A connecting rod goes to an eccentric with a cycle time of 365-5/8 days. This is a result of easily obtainable gearing and results in a 3/8 of a day a year discrepancy. So Suntrak may have to be reset every two years or so—as well as after each power failure; As far as tracking is concerned, the gearing should therefore be indistinguishable from perfect.