Abstract:
The most urgent need in the field of solar energy is to lower the final cost per watt of all involved components. Some of the most expensive components within a solar tracker go into the precision drive system which accurately follows the motion of the sun. This invention reduces the complexity and the required number of drive components in a tracker optimized for reflective dishes. With this invention a single drive motor can keep 20 or more large reflective dishes accurately tracking the sun, whereas 40 drive motors with more complex control systems would typically be required for the same number of dishes. In addition this invention allows for complete inversion of the dishes, which helps reduce dust accumulation on the optical surfaces and lowers wind resistance during storms.

Description:
PRIORITY CLAIM 
       [0001]    This application is a continuation-in-part of Indian patent application No. 2010/DEL/2007 filed on Sep. 24, 2007 and entitled “An Economical Solar Tracker for a Concentrating Reflective Dish”. 
       FIELD OF THE INVENTION 
       [0002]    The invention relates to solar energy, and more specifically to methods for tracking the motion of the sun as it moves through the sky, enabling more efficient concentration and utilization of the energy coming from the sun. 
       BACKGROUND OF THE INVENTION 
       [0003]    In order to accurately track the motion of the sun through the sky, it&#39;s necessary to somehow replicate that motion. The majority of solar trackers deal with the sun&#39;s motion as if it were an arbitrary series of azimuth-elevation (az-el) coordinates. They generally depend on complex computer software to predict those coordinates, and/or a sophisticated, closed-loop, two-axis control system to move the tracker so that it accurately follows the motion of the sun. Such solar trackers are called az-el trackers, and two examples of them are illustrated in  FIGS. 1   a  and  1   b . Note that the dish in  FIG. 1   a  is high above the ground, which is a distinct disadvantage during windstorms. A further disadvantage is that the torques required to properly orient such a tracker are significant, since the full weight of the dish plus the solar energy receiver must be lifted in order to aim the tracker properly.  FIG. 1   b  shows an az/el tracker which has its dish somewhat lower to the ground. The weight of the solar energy receiver (a Stirling engine, in that case) also balances the weight of the reflector dish, which is an advantage in that greatly reduced torques are required to maneuver the dish as it tracks the sun. U.S. Pat. No. 4,583,520 was awarded for this balanced weight az-el tracker on Apr. 22, 1986. 
         [0004]    One distinct disadvantage of az-el trackers is that difficulties arise when they are installed in tropical locations, that is, anywhere between the tropic of capricorn and the tropic of cancer; a huge belt around the planet from 23.5 degrees south to 23.5 degrees north. In this region, the sun can and will pass directly overhead, which means that the elevation at that moment will be 90 degrees and the azimuth will be briefly undefined. In this situation the best that an az-el tracker can do is a quick turn-around at noon, since there is a discontinuity of as much as 180 degrees between the data it was following as the sun rose in the east, in comparison to the data it must follow for the descent of the sun in the west. Simplistic tracking schemes could easily be confused to the point of no longer working when confronted with such an extreme discontinuity. 
         [0005]    The problem is considerably simplified with a polar-axis tracker. Such a tracker works because in truth the motion of the sun is not at all arbitrary, rather it is very simple and predictable. The apparent motion of the sun is better understood as the earth&#39;s motion relative to the sun. The primary apparent motion of the sun is due to a constant rate rotation of the earth about its polar (rotational) axis. In order to accurately account for this motion with a tracker, a stable rotational axis must be created in accurate alignment with the earth&#39;s polar axis. Rotating the tracker&#39;s rotational axis at a rate which is equal but opposite to the rotational rate of the earth allows anything attached to that axis to stay at a fixed orientation relative to the sun. Solar trackers which take this approach are generally called polar-axis solar trackers, to better distinguish them from the previously mentioned az-el solar trackers. 
         [0006]      FIGS. 2   a - 2   c  show an illustrative sampling of polar-axis solar trackers. The tracker in  FIG. 2   a  (from U.S. Pat. No. 6,284,968, granted Sep. 4, 2001) has many of the disadvantages of the tracker in  FIG. 1   a : the dish is high above the ground, and large torques are required in order to track the sun. 
         [0007]      FIG. 2   b  (from U.S. Pat. No. 4,368,962, granted Jan. 18, 1983) shows a system of trackers driven by a common set of drive motors. The shared motor concept has the potential to reduce costs, but that potential is not fully realized in this case. The imbalanced weight of the dishes would require large torques in order to track the sun, as mentioned with prior trackers. When the system of imbalanced dishes are connected together, the torques accumulate rather than canceling each other out, so that a drive motor handling four dishes must be at least four times as powerful as the single motor was, and thus significantly more expensive. Another drawback of this design is the cumulative backlash that will be involved in the system of all of bevel gears. At each 90 degree junction between drive shafts, a small amount of play will be introduced between one gear and the next. Since there are four such junctions between the control motors and the dishes, that play will be quadrupled, significantly lowering the precision of the tracking. 
         [0008]    Note also that in  FIGS. 1   a ,  2   a  and  2   b , the reflective dishes are all quite small relative to the size of the trackers. Since it is the dishes that are collecting the solar energy, and the trackers are only there to properly aim the dishes, it is desirable to have the largest possible dish size for a given tracker size. 
         [0009]      FIG. 2   c  shows a tracker that brings together many of the best ideas mentioned above into a single and practical design. It was jointly developed by Dr. Wolfgang Scheffler of Austria and Dr. Deepak Gadhia of India. This picture was taken at an installation Dr. Gadhia constructed near Delhi. The polar axis trackers greatly simplify the daily motion, reducing it to a simple rotation. The weights of the dishes are more or less evenly balanced about the axis of rotation, so that smaller torques could be involved in moving the trackers, although in this case weights have been added to each dish to apply torque and thus keep tension on the control cable. The trackers are interconnected in a simple, accurate and practical manner so that they can be driven by a single drive mechanism, which in this case is a gearmotor from an automotive windshield-wiper mechanism, connected to the dishes through a steel control cable and some pulleys. At this installation fourteen dishes are accurately controlled by a single drive motor. 
         [0010]    Note that the elliptical Scheffler reflective dishes in the tracker of  FIG. 2   c  are very different than the circular reflective dishes in all the preceding images: their outer contour is elliptical rather than circular, and they are designed to bring light to a focus at a point to the side of the dish, so that the light from the sun reflects at a 90 degree angle while simultaneously being concentrated. The focus of this document is to present a new invention designed for circular reflective dishes, which are more commonly used. For the purposes of this document, a circular reflective dish is one which is designed to directly face the sun, and bring light to a focal point that is nearly or directly between the center of said circular reflective dish and the sun. Generally the reflective surface of such a dish will follow a parabolic curve, but small deviations are sometimes encountered. An example of this is the dish shown in  FIG. 1   b , in which mirror segments were ground to circular contours to reduce manufacturing costs. Generally such a dish will take a circular shape, but again some variations may be encountered. The dish in  FIG. 1   b  is again an example, with square mirror segments assembled to roughly approximate a circle, and with a empty slot in the dish which accommodates the supporting means. The dish of the working prototype in  FIG. 3  is another example, in which triangular segments come together to approximate a circle, but in truth the shape is a multi-sided polygon with a large number of sides, and with two polygons missing to accommodate the supporting means. 
         [0011]    The elliptical Scheffler reflective dishes of  FIG. 2   c  were also developed by and named for Wolfgang Scheffler. They are valuable for concentrating sunlight on a stationary point throughout the day, despite the motion of the sun. This is particularly useful for solar cooking applications, such as in this case, in which stationary water boilers generate steam for later cooking. Any accurate solar tracker must also account for the seasonal motion of the sun. These trackers do not themselves account for that motion, rather the Scheffler dishes are manually flexed along their long axis so as to attain the tightest possible sun spot on the water boiler, and this accounts for the seasonal motion of the sun. Since the sun moves very slowly through the seasons, this manual adjustment can be done periodically rather than every day. The only disadvantage of this excellent design is that the dishes are highly exposed to winds, especially the dishes which are concentrating light onto the upper side of the boilers. This problem, which is relatively minor near Delhi, becomes progressively worse at higher latitudes, because the entire assembly must be rotated to stay in parallel with the earth&#39;s rotational axis, which at higher latitudes will put the upper dish higher and higher above the ground. 
         [0012]    It is an objective of this invention to bring together all of the best qualities of the Scheffler/Gadhia solar tracker, and improve on them where possible, for circular reflective dishes rather than for elliptic Scheffler reflective dishes. 
         [0013]    It is an objective of this invention to have the weights of the solar tracker balance each other out, minimizing the torques required to maneuver the reflective dish. 
         [0014]    It is an objective of this invention to have a single control motor drive multiple reflective dishes, thus reducing the cost of the system. 
         [0015]    It is an objective of this invention to minimize the size of the solar tracker relative to the size of the reflective dish, thus collecting the most possible sunlight with a minimum tracker cost. 
         [0016]    It is an objective of this invention for the solar tracker to accommodate the seasonal motion of the sun in a manner which can be either manual or automatic, to permit a further cost reduction (by omitting the automatic drive system) in cases where it is possible and appropriate. 
         [0017]    It is an objective of this invention to keep the reflective dish as close as possible to the ground, so as to improve the system&#39;s ability to withstand wind storms. 
         [0018]    It is an objective of this invention to enable the complete inversion of the reflective dish, since that will reduce the dust build-up on the reflective surfaces, and further improve the system&#39;s ability to withstand wind storms. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0019]      FIGS. 1   a  and  1   b  show two prior-art azimuth-elevation solar trackers. 
           [0020]      FIGS. 2   a ,  2   b , and  2   c  show three prior-art polar axis solar trackers. 
           [0021]      FIGS. 3   a  and  3   b  are photographs of a working prototype of an embodiment of this invention. 
           [0022]      FIG. 4  shows a detailed side view of the preferred embodiment of this tracker. 
           [0023]      FIGS. 5   a - 5   e  show the preferred embodiment in various positions and configurations. 
           [0024]      FIG. 6   a - 6   d  show embodiments of fine-tuning adjustment systems, and an automatic declination adjustment means. 
           [0025]      FIG. 7  shows embodiments of the drive components configured for driving multiple trackers  FIGS. 8   a  and  8   b  show top views of one embodiment of the tracker support base. 
       
    
    
       [0026]    Table 1 shows the declination of the sun for each day of the year. 
         [0027]    Table 2 shows the daily changes in the declination of the sun for each day of the year. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0028]    In  FIGS. 3   a  and  3   b , a working prototype of one embodiment of this invention is shown photographically from two different views. While this prototype has been useful in proving the essential concepts of this invention to be valid and workable, the preferred embodiment is described in the following text and figures, and not in these photographs. The photographs are provided because they help the reader to better visualize the 3-dimensional structure and shape of the preferred embodiment, which may be harder to grasp from the 2-dimensional drawings. 
         [0029]    The fundamental details of the preferred embodiment are shown schematically in  FIG. 4 . Support base  401  provides a stable platform for the tracker, the long axis of which should be accurately aligned in a true north-south direction.  FIG. 4  is drawn for a tracker at 28.46 degrees latitude, which would be appropriate for an installation near New Delhi, India.  FIG. 4  shows a West-looking view of that tracker, so that rightward on the drawing is North, while leftward is South. 
         [0030]    Leveling bolts  402  at each of the four corners help to bring the support base accurately into level. To better withstand high winds, these bolts can be made much longer and anchored firmly in cement. Clamping assembly  403  firmly grasps tracker frame  406  and holds it in place, pushing it against two fixed stops which form the other half of the clamping assembly, and which also hold the two halves of the support base together. These fixed stops are visible in  FIGS. 8   a  and  8   b.    
         [0031]    Tracker frame  406  is a novel and unique aspect of this invention. Because it is in the shape of a 180 degree arc, clamping assemblies  403  (and optionally  405 ) can hold it firm at virtually any angle. This allows polar axle  407 , supported by tracker frame  406 , to be held at an angle such that it will be in parallel with the earth&#39;s polar axis.  FIG. 4  shows the tracker frame tilted at an angle of 28.46 degrees. This angle is measured from the horizontal to match the angle formed by polar axle  407 , mounted to tracker frame  406 . The correct angle for a given installation site is the same as the geocentric or spherical latitude of that site, which is close to but not exactly the same as the site&#39;s geodetic latitude. For sites south of the equator, the tracker would be flipped around, with North on the left and South on the right, so that the lowest side of the axle is on the side of the tracker which is closest to the equator. 
         [0032]    For higher latitudes which will require the tracker frame to be further tilted, optional triangular supports  404  hold an additional clamping assembly  405  which provides additional stability to tracker frame  406 . 
         [0033]    Note that all other known polar-axis trackers require a base or support system which either pivots and lifts the dish high in the air, or else is custom-built according to the latitude of the installation site, which complicates keeping the parts in stock for those trackers. In contrast, tracker frame  406  keeps the dish quite low to the ground, reducing exposure to winds, while simultaneously allowing a single set of tracker parts to work well at almost any installation site on earth. 
         [0034]    In order to account for and follow the primary motion of the sun, the polar axle must be turned at a rate of 1 revolution per day by the polar axle rotation means. In this embodiment, the polar axle rotation means includes a gear motor connected through pulleys to polar axle drive pulley  408 , which in turn rotates the polar axle. Bearings  409  firmly hold the ends of the polar axle in place and minimize the rotational friction, thus minimizing the torques involved. The dish assembly consisting of reflective dish  412 , dish support member  411  and solar energy receiver  413  are very nearly balanced about pivot rod  410  and hence polar axle  407 , which also helps to minimize the torques involved in the polar axle rotation. Note that solar energy receiver  413  can take a number of forms, as there are several types of technologies for converting solar energy into other useful forms. If electricity is immediately desired, it could take the form of concentrating photovoltaic (CPV) cells. Or if there are price breakthroughs in heat engines such as Stirling Engines, that could be used to create electricity. Alternatively, the heat could be absorbed with some kind of thermal transfer fluid, and transported and/or stored for later use, or later conversion into electric energy. 
         [0035]    Besides the apparent daily motion of the sun, there is also a seasonal motion. In astronomical terms, the declination of the sun describes the apparent north-south motion of the sun as seen from the earth. A declination angle of zero means that the sun is in alignment with the equator, which occurs at particular times on March 21 st and September 23rd. The declination of the sun peaks on about June 22nd at an angle of 23.43 degrees north of the equator, and reaches its minimum on about December 22nd at an angle of 23.43 degrees south of the equator. 
         [0036]    Within this document, the term declination angle is used not only for the declination of the sun above or below the equator, but also for the angle formed by the dish assembly of this tracker, which mimics that celestial angle. In  FIG. 4 , the dish assembly is shown at an angle perpindicular to the polar axle, thus perpindicular to the earth&#39;s rotational polar axis, which aligns it with the earth&#39;s equator. This angle of the dish assembly therefore corresponds to a declination angle of zero, which would align the tracker with the sun&#39;s declination on March 21st and September 23rd. A declination adjustment means is used to adjust the tracker&#39;s declination angle, bringing the tracker components into alignment with the current declination angle of the sun. In this embodiment, the declination adjustment means takes the form of adjustable length turnbuckle  415 , which is shortened or lengthened so as to pivot the dish assembly to the correct angle. Pivot rod  410  defines the declination adjustment axis, which can be envisioned as coming out of the paper at the center of pivot rod  410 , about which the dish assembly is pivoted. Northern declination angles would be achieved by lengthening adjustable length turnbuckle  415 , so as to pivot the dish assembly clockwise. See also  FIG. 5   b . Southern declination angles would be achieved by shortening turnbuckle  415  so as to pivot the dish assembly counter-clockwise. See also  FIG. 5   a . There is very little torque involved in either pivoting motion, since the components of the dish assembly are very nearly in balance about pivot rod  410  as previously mentioned. 
         [0037]    Note that in this embodiment, all components of the dish assembly are constructed such that they cannot collide with tracker frame  406  at any angle of motion about polar axle  407 , nor at any declination angle between plus or minus 23.43 degrees. Circular reflective dish  412  is also illustrated in a side view,  414 , to better illustrate the split-dish construction, and the all-around clearance that is another result of having the tracker frame shaped as a circular arc. The split in the dish is required in order to allow room for the polar axle as the dish pivots for variations in the declination angle. 
         [0038]    Before moving on to other figures, note that  FIG. 4  illustrates this embodiment of the tracker as it would appear at local solar noon on about March 21st or September 23rd when installed at a site near New Delhi. Local solar noon is an astronomical term meaning the moment in the day when the sun is at its highest point at a particular site, which generally happens close to noon in any time zone, but is unaffected by legal definitions such as daylight savings time or time zone boundaries. The latitude of the site is determined, as mentioned before, by the angle of polar axle  407  relative to the horizontal, which in this case is about 28.5 degrees. The day of the year is determined by the declination angle, which is the angle of the dish assembly relative to the equator, or in other words relative to a line perpindicular to polar axle  407 , as is better illustrated in  FIGS. 5   a  and  5   b . The hour of the day is determined by the angle of the polar axle, which in its rotation mimics the rotation of the earth. 
         [0039]    In  FIGS. 5   a  and  5   b  this embodiment of the tracker is illustrated at the two seasonal extremes of motion.  FIG. 5   a  shows how it would appear at local solar noon at winter solstice, while  FIG. 5   b  shows it at the same hour of summer solstice. 
         [0040]      FIG. 5   c  illustrates this embodiment in an inverted storage position for the dish. Since dust settles downward 24 hours a day, some of that dust can be kept off the reflective side of the dish by inverting the dish during the night when it&#39;s not in use. In this way the required frequency of washings can be reduced for a given level of cleanliness. Another advantage of being able to invert the optics is to better protect them from damage caused by wind or hail storms. An incidental advantage has to do with the economics of scale, in that larger dishes are sometimes economically advantageous. If the reflective dish is to be used with a Stirling Engine, for example, then that dish must be sized to match the capacity of that engine. A 10 kw Stirling Engine will cost less than twice as much as a 5 kw Stirling Engine, so there is an economic advantage of using the largest possible engine, and hence the largest possible dish. The primary factor that limits the size of reflective dishes is their ability to withstand high winds, so being able to invert the dish incidentally allows larger dishes, which allows larger Stirling Engines, which can be economically advantageous. 
         [0041]      FIG. 5   d  illustrates an embodiment of the tracker base without the triangular supports for near-equatorial latitudes. In this case there is no need for them, as all portions of the tracker are quite near the ground. 
         [0042]      FIG. 5   e  illustrates an embodiment of the tracker assembled with the polar axle drive pulley on the top side, for extreme latitudes in which there&#39;s insufficient space to accommodate that on the lower side. This is a case in which the triangular supports play a much more important role in supporting the tracker against lateral winds. Here the tracker is configured for a latitude of 58.5°, which would correspond to parts of Canada, Alaska, Sweden and Russia. 
         [0043]    Note that all of the other illustrations (excepting  5   d  and  5   e ) show an embodiment of the tracker configured for a latitude of 28.5°, corresponding to parts of India, China, Northern Africa, Mexico, Australia and many other locations. All of the configurations shown assume the same basic set of parts. 
         [0044]      FIGS. 6   a  through  6   d  are primarily related to fine-tuning adjustments, which serve to improve the tracking accuracy. In the realm of solar energy it is extremely important to minimize the costs involved. Often the precision involved in making a given part will play a substantial role in the cost of that part, so it is helpful if the highest possible precision can somehow be attained from a system that is built with components of only moderate (rather than high) precision. All of the following fine-tuning adjustments have the purpose of getting an embodiment of the tracker to track the sun as accurately as possible. 
         [0045]      FIG. 6   a  shows the details of one embodiment of a polar axle rotational fine-tuning means. The assembly shown would alternately take the place of polar axle drive pulley  408 , serving the same function, but adding the ability to fine tune the rotational position of the tracker. When multiple trackers are all driven by the same polar axle rotation means, that rotation means will at best be able to consider the position of one solar tracker, and keep it in good alignment with the sun. In order to maintain a comparable level of accuracy in all the other trackers being driven, it is essential that each of those trackers be aligned as closely as possible with the first tracker. One part of that alignment is served by having a good common reference, which is the sun, but a practical means must also be available to measure any misalignment with the sun. That means of measurement is the shadow cast by the solar energy receiver on the dish-mounting components at the center of the reflective dish. Using that as a reference, any misalignment angle with the sun is easy to see. 
         [0046]    The second part of correcting that misalignment is having an easy method of making a fine-tuning adjustment, which is the purpose of the polar axle rotational fine-tuning means, one embodiment of which is shown in  FIG. 6   a . The left side of  6   a  is a front view of those components, with a side view on the right. Hub piece  601  is mounted onto the end of the polar axle in such a way that it is firmly attached and completely prevented from rotating relative to that axle, for example with a keyed shaft and a tapered key. Hub piece  602  is bolted to Hub piece  601  in such a way that the two together clamp down on outer ring  603  when bolts  604  are tightened. When the bolts are loosened, however, the two hub pieces  601  and  602  can be rotated relative to outer ring  603 . In order to make this adjustment with more precision, a long steel bar can be placed along the hub, below the level of the bolt heads, and then rotated slowly in the direction needed, while holding the outer ring fixed in place. The steel bar would thereby apply torque to the bolt heads, which would turn the hub pieces relative to the outer ring in a much more controlled and accurate manner. Although it is not again mentioned below, simple tools such as just mentioned can be used to similarly make adjustments on many of the following fine-tuning methods, with considerably greater precision than without such tools. Since the cost for such tools does not add in any way to the cost of the tracker, this is an effective method of increasing tracker accuracy without contributing to its price. 
         [0047]    In  FIG. 6   b  the details are shown for one embodiment of a fine-tuning system for the North-South direction of the polar axle. Two views are shown; the top view shows details of bearing pillow block  610 , while the bottom view shows that same pillow block in place, assembled with all the components around it. Pillow block  610  supports one end of the polar axis, which is not visible in this view, but which is  620  in  FIG. 6   d  on the same page. By making small left-right adjustments to the position of pillow block  610 , the angle of the polar axis relative to the north-south direction is thereby adjusted by very small angles. Extra-length slots  613  are provided in pillow block  610  for this purpose. Bolts  612  firmly hold pillow block  610  in position, clamping it to cross-beam  611 . These bolts can be loosened for the purpose of making this adjustment. 
         [0048]      FIG. 6   c  shows the details of one embodiment of a fine-tuning system for the vertical slant of the polar axle, which fine-tunes the selected latitude.  FIG. 6   c  is an enlarged section of  FIG. 6   d . Bearing pillow block  621  supports the other end of polar axle  620 , and is held in place by bolts  622 . Firm springs  623  are introduced between pillow block  621  and mounting cross-piece  624 . Mounting cross-piece  624  is welded to tracker frame  625 , which holds the whole assembly firmly in place. By tightening bolts  622 , firm springs  623  are further compressed and pillow block  621  is moved slightly downward, lowering this end of polar axle  620 . By loosening bolts  622 , the process is reversed: firm springs  623  extend, pillow block  621  is moved slightly upward, and this end of polar axle  620  is vertically raised. Raising and lowering this end of polar axle  620  slightly changes the vertical slant of the polar axle. 
         [0049]    Another fine-tuning adjustment is shown in  FIG. 6   d . Leveling bolts  627  allow tracker support base  626  to be brought to level. 
         [0050]    If an automated declination adjustment is desired, one embodiment of such an adjustment means is also shown in  FIG. 6   d . Some of these components replace other manual components which have been previously discussed. Instead of adjustable-length turnbuckle  415 , threaded rod  635  can be used for the same purpose, which would be driven by motor  637 . Pivoting mounts  636  would hold the motor in place at one end of the rod, as well as holding swiveling nut  638  in place on the rod. When motor  637  is activated to turn threaded rod  635 , swiveling nut  638  is brought closer or further according to the direction the rod is being turned. This will bring dish support member  631  closer or further to polar axle  620 , and hence pivot the dish assembly about pivot rod  630 , changing the tracker declination. 
         [0051]      FIG. 3   a  already showed a photograph of multiple dishes being driven by a single drive motor, while  FIG. 3   b  showed a photographic view of one embodiment of the drive elements involved.  FIG. 7  schematically illustrates a similar embodiment of the same drive components. Drive pulley  701  is attached to a gearmotor, not shown, driven by a control circuit. Pulley assemblies  702  guide cable  703  in the path shown around a plurality of polar axle drive pulleys  708 , which rotate the tracker axles (not visible here) which are supported by bearings  709 . Bearings  709  are bolted to cross beams  705 , which are in turn welded to tracker frames  706 . (Components  706 - 709  correspond to components  406 - 409  in  FIG. 4 ). Cross beams  705  further support pulley assemblies  702 , with a slightly lengthened cross-beam also supporting drive pulley  701  and the gear motor attached to it. Tension is maintained on cable  703  by means of tensioning springs  704 , and this tension can be adjusted by tension-adjusting turnbuckle  710 . 
         [0052]    In this illustration embodiments of three solar trackers are shown, each of which has been configured slightly differently as the system of trackers was installed. The leftmost tracker is configured to be at the end of a string of trackers, thus there&#39;s only need for one pulley assembly  702 . The middle tracker is configured to be in the middle of the string, with two pulley assemblies  702 . For a string of 12 trackers, there would be 10 middle trackers configured like this one. The tracker on the right, finally, is configured to be driven directly from the drive motor, and all the associated drive circuitry (including sensors indicating the position of the trackers relative to the sun&#39;s position) would be installed on this tracker. The cables would be connected together as shown, with tensioning springs between them, in order to get all of the trackers in a string to track the sun in unison. 
         [0053]    The configuration of optional tensioning springs shown here has two purposes. First, in locations where the system of trackers will undergo large deviations in temperature, the steel cables will alternately undergo thermal expansion and contraction. In the configuration shown, the thermal length shifting in the steel cables is balanced by compensating shifts in the lengths of the tensioning springs which are distributed throughout the length of the cable. This serves to minimize the net angular shifting of any tracker, insuring maximum tracking accuracy in every tracker. Second, in locations with high winds, a sudden gust of wind could act on one dish, or a few dishes, or all of the dishes nearly simultaneously. With the configuration of tensioning springs shown, some of the energy of such gusts is harmlessly absorbed and dissipated by the springs, which would then quickly bring the dishes back to their intended orientations. This energy might otherwise be absorbed by the reflective dish, causing distortions or greater damage. Thus the springs can help to minimize wind damage to the system, as well as reducing the possibility that such gusts would disorient any of the dishes due to cable slippage. 
         [0054]    The friction between the steel drive cable  703  and the pulleys it interfaces with ( 701  &amp;  708 ) must be sufficiently high to prevent slippage, so the tensioning springs must be adequately stretched via turnbuckle  710  to insure this, and a material with a high coefficient of friction should be used to cover the pulley surfaces. Exorbitant tension is not needed, since the design shown includes large angles of working contact on the drive pulleys, and friction increases exponentially with the coefficient of friction between the two materials and the angle through which there is working contact, in radians. 
         [0055]    In  FIGS. 8   a  and  8   b , a top view of one embodiment of the support base is shown, with and without the tracker frame in place. As described previously in  FIG. 4 , support base  801  provides a stable platform for the tracker, the long axis of which should be accurately aligned in a true north-south direction. Leveling bolts  802  at each of the four corners of the base are provided to help bring the support base accurately into level. The base firmly holds tracker frame  806  in place with top clamp  803  acting against fixed stops  807 . This is the same action as was described earlier with clamping assembly  403  in  FIG. 4 , but in this view additional details are visible. Fixed stops  807  also act to hold the two halves of the support base together. For higher latitudes which will require a greater angle of tilt, triangular supports  804  hold an additional clamping assembly  805  which also provides stability to C-piece  806 . 
         [0056]    While the tracker described herein is intended primarily for countries in which labor is inexpensive and materials are expensive, it can be readily adapted for other countries, with the simple addition of an automatic declination adjustment, as in  FIG. 6   d . However, even in well-developed countries it would be worth evaluating whether this is really needed. The fastest that the sun ever changes its declination is at a rate of only 0.4 degrees per day (in March and September, when the sun is near the equinoxes), and there are periods when the declination changes much slower than this. Since the declination is changing over a 24 hour day and the sun is only up for about 12 of those hours, the declination would change at most 0.2 degrees during those daylight hours. If that change were accurately anticipated, by knowing the data shown in table 2, then the tracker declination could be manually set each morning to be at the midpoint of the solar declination throughout that day, theoretically attaining 0.1 degree accuracy, or better, through at least a majority of the day. This is for a worst-case day; on the best case days the declination does not change at all! Adjusting the trackers by hand is a very fast process, taking as little as 10 seconds per tracker, so very little labor is involved. Ultimately the choice will depend on the economics of the situation, the economic conditions where the trackers are to be installed, and the accuracy requirements of the solar energy receiver and the circular reflective dish. 
         [0057]    To better understand and weigh this trade-off, tables 1 and 2 are included. Table 1 shows the declination angle of the sun for every day of the year, based on the data published online at: www.wsanford.com/˜wsanford/exo/sundials/DEC_Sun.html. Note that positive numbers indicate that the sun is above the Northern hemisphere, while negative numbers indicate that the sun is above the Southern hemisphere. Table 2 shows how the solar declination angle changes on each day of the year; it is based the data in Table 1. 
         [0058]    While one embodiment of this invention with several options has been presented above, many changes can be made without departing from the spirit and scope of the invention. For example, there is no need for the support base to be flat or level, rather it might make sense to incorporate elements of a support base into a new structure which is already under construction for different purposes, but which would be well served by having solar energy collectors mounted on it. Any suitable solar energy receiver may be utilized with this invention, including Stirling engines, concentrating photovoltaic cells, solar-thermal collectors, or others as may be introduced in the future. The shape and size of the dish support member would naturally change so as to better accommodate the needs of those solar energy receivers. The various insights embodied in this invention enable the production of solar trackers for circular reflective dishes at significantly reduced costs, while still attaining tracking accuracies within small fractions of a degree. The scope of this invention should be determined by the appended claims and their legal equivalents, rather than by the explanations or illustrations here presented. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Solar declination angles for each day of the year 
               
             
          
           
               
                   
                 JAN- 
                 FEB- 
                   
                   
                   
                   
                   
                   
                 SEP- 
                 OC- 
                 NO- 
                 DE- 
               
               
                 Day 
                 UARY 
                 RUARY 
                 MARCH 
                 APRIL 
                 MAY 
                 JUNE 
                 JULY 
                 AUGUST 
                 TEMBER 
                 TOBER 
                 VEMBER 
                 CEMBER 
               
               
                   
               
             
          
           
               
                 1 
                 −23.07 
                 −17.33 
                 −7.82 
                 4.30 
                 14.90 
                 21.97 
                 23.15 
                 18.17 
                 8.50 
                 −2.95 
                 −14.23 
                 −21.72 
               
               
                 2 
                 −22.98 
                 −17.05 
                 −7.43 
                 4.70 
                 15.20 
                 22.10 
                 23.08 
                 17.92 
                 8.15 
                 −3.33 
                 −14.57 
                 −21.87 
               
               
                 3 
                 −22.90 
                 −16.77 
                 −7.05 
                 5.08 
                 15.50 
                 22.23 
                 23.02 
                 17.67 
                 7.78 
                 −3.73 
                 −14.88 
                 −22.02 
               
               
                 4 
                 −22.80 
                 −16.47 
                 −6.67 
                 5.47 
                 15.78 
                 22.37 
                 22.93 
                 17.40 
                 7.42 
                 −4.12 
                 −15.18 
                 −22.17 
               
               
                 5 
                 −22.70 
                 −16.17 
                 −6.28 
                 5.85 
                 16.08 
                 22.48 
                 22.85 
                 17.13 
                 7.05 
                 −4.50 
                 −15.50 
                 −22.30 
               
               
                 6 
                 −22.60 
                 −15.87 
                 −5.90 
                 6.22 
                 16.37 
                 22.58 
                 22.75 
                 16.87 
                 6.67 
                 −4.88 
                 −15.80 
                 −22.42 
               
               
                 7 
                 −22.47 
                 −15.57 
                 −5.50 
                 6.60 
                 16.65 
                 22.70 
                 22.65 
                 16.60 
                 6.30 
                 −5.27 
                 −16.10 
                 −22.53 
               
               
                 8 
                 −22.35 
                 −15.25 
                 −5.12 
                 6.98 
                 16.92 
                 22.78 
                 22.55 
                 16.32 
                 5.93 
                 −5.65 
                 −16.40 
                 −22.65 
               
               
                 9 
                 −22.22 
                 −14.93 
                 −4.73 
                 7.35 
                 17.20 
                 22.88 
                 22.43 
                 16.03 
                 5.55 
                 −6.03 
                 −16.68 
                 −22.77 
               
               
                 10 
                 −22.08 
                 −14.62 
                 −4.33 
                 7.72 
                 17.45 
                 22.97 
                 22.32 
                 15.75 
                 5.17 
                 −6.42 
                 −16.97 
                 −22.87 
               
               
                 11 
                 −21.93 
                 −14.30 
                 −3.95 
                 8.12 
                 17.72 
                 23.03 
                 22.18 
                 15.45 
                 4.80 
                 −6.80 
                 −17.25 
                 −22.95 
               
               
                 12 
                 −21.78 
                 −13.97 
                 −3.55 
                 8.47 
                 17.98 
                 23.12 
                 22.07 
                 15.17 
                 4.42 
                 −7.17 
                 −17.53 
                 −23.03 
               
               
                 13 
                 −21.62 
                 −13.63 
                 −3.17 
                 8.83 
                 18.23 
                 23.18 
                 21.92 
                 14.87 
                 4.03 
                 −7.53 
                 −17.80 
                 −23.12 
               
               
                 14 
                 −21.45 
                 −13.30 
                 −2.77 
                 9.18 
                 18.48 
                 23.23 
                 21.77 
                 14.55 
                 3.65 
                 −7.92 
                 −18.07 
                 −23.18 
               
               
                 15 
                 −21.27 
                 −12.97 
                 −2.37 
                 9.55 
                 18.72 
                 23.28 
                 21.62 
                 14.25 
                 3.27 
                 −8.30 
                 −18.33 
                 −23.23 
               
               
                 16 
                 −21.10 
                 −12.62 
                 −1.98 
                 9.90 
                 18.97 
                 23.33 
                 21.47 
                 13.93 
                 2.88 
                 −8.67 
                 −18.58 
                 −23.28 
               
               
                 17 
                 −20.90 
                 −12.27 
                 −1.58 
                 10.27 
                 19.18 
                 23.37 
                 21.30 
                 13.62 
                 2.50 
                 −9.03 
                 −18.83 
                 −23.33 
               
               
                 18 
                 −20.70 
                 −11.92 
                 −1.18 
                 10.62 
                 19.42 
                 23.40 
                 21.13 
                 13.30 
                 2.10 
                 −9.40 
                 −19.08 
                 −23.37 
               
               
                 19 
                 −20.50 
                 −11.57 
                 −0.80 
                 10.97 
                 19.63 
                 23.42 
                 20.97 
                 12.98 
                 1.72 
                 −9.75 
                 −19.32 
                 −23.40 
               
               
                 20 
                 −20.30 
                 −11.22 
                 −0.40 
                 11.32 
                 19.85 
                 23.43 
                 20.78 
                 12.65 
                 1.33 
                 −10.12 
                 −19.55 
                 −23.42 
               
               
                 21 
                 −20.08 
                 −10.87 
                 0.00 
                 11.65 
                 20.07 
                 23.43 
                 20.60 
                 12.32 
                 0.95 
                 −10.48 
                 −19.78 
                 −23.43 
               
               
                 22 
                 −19.87 
                 −10.50 
                 0.40 
                 12.00 
                 20.27 
                 23.43 
                 20.40 
                 11.98 
                 0.55 
                 −10.83 
                 −20.00 
                 −23.43 
               
               
                 23 
                 −19.63 
                 −10.13 
                 0.78 
                 12.33 
                 20.47 
                 23.43 
                 20.20 
                 11.65 
                 0.17 
                 −11.20 
                 −20.22 
                 −23.43 
               
               
                 24 
                 −19.40 
                 −9.77 
                 1.18 
                 12.67 
                 20.65 
                 23.42 
                 20.00 
                 11.32 
                 −0.23 
                 −11.55 
                 −20.43 
                 −23.43 
               
               
                 25 
                 −19.17 
                 −9.40 
                 1.58 
                 13.00 
                 20.83 
                 23.40 
                 19.78 
                 10.97 
                 −0.62 
                 −11.90 
                 −20.63 
                 −23.42 
               
               
                 26 
                 −18.92 
                 −9.03 
                 1.97 
                 13.32 
                 21.02 
                 23.38 
                 19.57 
                 10.63 
                 −1.00 
                 −12.23 
                 −20.83 
                 −23.38 
               
               
                 27 
                 −18.67 
                 −8.65 
                 2.37 
                 13.63 
                 21.20 
                 23.35 
                 19.35 
                 10.28 
                 −1.40 
                 −12.58 
                 −21.02 
                 −23.35 
               
               
                 28 
                 −18.42 
                 −8.28 
                 2.75 
                 13.97 
                 21.37 
                 23.32 
                 19.13 
                 9.93 
                 −1.78 
                 −12.92 
                 −21.20 
                 −23.32 
               
               
                 29 
                 −18.15 
                 −8.05 
                 3.15 
                 14.27 
                 21.52 
                 23.27 
                 18.90 
                 9.58 
                 −2.17 
                 −13.25 
                 −21.38 
                 −23.27 
               
               
                 30 
                 −17.88 
                   
                 3.53 
                 14.58 
                 21.68 
                 23.22 
                 18.67 
                 9.22 
                 −2.57 
                 −13.58 
                 −21.55 
                 −23.20 
               
               
                 31 
                 −17.62 
                   
                 3.92 
                   
                 21.83 
                   
                 18.42 
                 8.87 
                   
                 −13.92 
                   
                 −23.13 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Changes in the Solar declination angle for each day of the year 
               
             
          
           
               
                   
                 JAN- 
                 FEB- 
                   
                   
                   
                   
                   
                   
                 SEP- 
                 OC- 
                 NO- 
                 DE- 
               
               
                 Day 
                 UARY 
                 RUARY 
                 MARCH 
                 APRIL 
                 MAY 
                 JUNE 
                 JULY 
                 AUGUST 
                 TEMBER 
                 TOBER 
                 VEMBER 
                 CEMBER 
               
               
                   
               
             
          
           
               
                 1 
                 0.07 
                 0.28 
                 0.23 
                 0.38 
                 0.32 
                 0.13 
                 −0.07 
                 −0.25 
                 −0.37 
                 −0.38 
                 −0.32 
                 −0.17 
               
               
                 2 
                 0.08 
                 0.28 
                 0.38 
                 0.40 
                 0.30 
                 0.13 
                 −0.07 
                 −0.25 
                 −0.35 
                 −0.38 
                 −0.33 
                 −0.15 
               
               
                 3 
                 0.08 
                 0.28 
                 0.38 
                 0.38 
                 0.30 
                 0.13 
                 −0.07 
                 −0.25 
                 −0.37 
                 −0.40 
                 −0.32 
                 −0.15 
               
               
                 4 
                 0.10 
                 0.30 
                 0.38 
                 0.38 
                 0.28 
                 0.13 
                 −0.08 
                 −0.27 
                 −0.37 
                 −0.38 
                 −0.30 
                 −0.15 
               
               
                 5 
                 0.10 
                 0.30 
                 0.38 
                 0.38 
                 0.30 
                 0.12 
                 −0.08 
                 −0.27 
                 −0.37 
                 −0.38 
                 −0.32 
                 −0.13 
               
               
                 6 
                 0.10 
                 0.30 
                 0.38 
                 0.37 
                 0.28 
                 0.10 
                 −0.10 
                 −0.27 
                 −0.38 
                 −0.38 
                 −0.30 
                 −0.12 
               
               
                 7 
                 0.13 
                 0.30 
                 0.40 
                 0.38 
                 0.28 
                 0.12 
                 −0.10 
                 −0.27 
                 −0.37 
                 −0.38 
                 −0.30 
                 −0.12 
               
               
                 8 
                 0.12 
                 0.32 
                 0.38 
                 0.38 
                 0.27 
                 0.08 
                 −0.10 
                 −0.28 
                 −0.37 
                 −0.38 
                 −0.30 
                 −0.12 
               
               
                 9 
                 0.13 
                 0.32 
                 0.38 
                 0.37 
                 0.28 
                 0.10 
                 −0.12 
                 −0.28 
                 −0.38 
                 −0.38 
                 −0.28 
                 −0.12 
               
               
                 10 
                 0.13 
                 0.32 
                 0.40 
                 0.37 
                 0.25 
                 0.08 
                 −0.12 
                 −0.28 
                 −0.38 
                 −0.38 
                 −0.28 
                 −0.10 
               
               
                 11 
                 0.15 
                 0.32 
                 0.38 
                 0.40 
                 0.27 
                 0.07 
                 −0.13 
                 −0.30 
                 −0.37 
                 −0.38 
                 −0.28 
                 −0.08 
               
               
                 12 
                 0.15 
                 0.33 
                 0.40 
                 0.35 
                 0.27 
                 0.08 
                 −0.12 
                 −0.28 
                 −0.38 
                 −0.37 
                 −0.28 
                 −0.08 
               
               
                 13 
                 0.17 
                 0.33 
                 0.38 
                 0.37 
                 0.25 
                 0.07 
                 −0.15 
                 −0.30 
                 −0.38 
                 −0.37 
                 −0.27 
                 −0.08 
               
               
                 14 
                 0.17 
                 0.33 
                 0.40 
                 0.35 
                 0.25 
                 0.05 
                 −0.15 
                 −0.32 
                 −0.38 
                 −0.38 
                 −0.27 
                 −0.07 
               
               
                 15 
                 0.18 
                 0.33 
                 0.40 
                 0.37 
                 0.23 
                 0.05 
                 −0.15 
                 −0.30 
                 −0.38 
                 −0.38 
                 −0.27 
                 −0.05 
               
               
                 16 
                 0.17 
                 0.35 
                 0.38 
                 0.35 
                 0.25 
                 0.05 
                 −0.15 
                 −0.32 
                 −0.38 
                 −0.37 
                 −0.25 
                 −0.05 
               
               
                 17 
                 0.20 
                 0.35 
                 0.40 
                 0.37 
                 0.22 
                 0.03 
                 −0.17 
                 −0.32 
                 −0.38 
                 −0.37 
                 −0.25 
                 −0.05 
               
               
                 18 
                 0.20 
                 0.35 
                 0.40 
                 0.35 
                 0.23 
                 0.03 
                 −0.17 
                 −0.32 
                 −0.40 
                 −0.37 
                 −0.25 
                 −0.03 
               
               
                 19 
                 0.20 
                 0.35 
                 0.38 
                 0.35 
                 0.22 
                 0.02 
                 −0.17 
                 −0.32 
                 −0.38 
                 −0.35 
                 −0.23 
                 −0.03 
               
               
                 20 
                 0.20 
                 0.35 
                 0.40 
                 0.35 
                 0.22 
                 0.02 
                 −0.18 
                 −0.33 
                 −0.38 
                 −0.37 
                 −0.23 
                 −0.02 
               
               
                 21 
                 0.22 
                 0.35 
                 0.40 
                 0.33 
                 0.22 
                 0.00 
                 −0.18 
                 −0.33 
                 −0.38 
                 −0.37 
                 −0.23 
                 −0.02 
               
               
                 22 
                 0.22 
                 0.37 
                 0.40 
                 0.35 
                 0.20 
                 0.00 
                 −0.20 
                 −0.33 
                 −0.40 
                 −0.35 
                 −0.22 
                 0.00 
               
               
                 23 
                 0.23 
                 0.37 
                 0.38 
                 0.33 
                 0.20 
                 0.00 
                 −0.20 
                 −0.33 
                 −0.38 
                 −0.37 
                 −0.22 
                 0.00 
               
               
                 24 
                 0.23 
                 0.37 
                 0.40 
                 0.33 
                 0.18 
                 −0.02 
                 −0.20 
                 −0.33 
                 −0.40 
                 −0.35 
                 −0.22 
                 0.00 
               
               
                 25 
                 0.23 
                 0.37 
                 0.40 
                 0.33 
                 0.18 
                 −0.02 
                 −0.22 
                 −0.35 
                 −0.38 
                 −0.35 
                 −0.20 
                 0.02 
               
               
                 26 
                 0.25 
                 0.37 
                 0.38 
                 0.32 
                 0.18 
                 −0.02 
                 −0.22 
                 −0.33 
                 −0.38 
                 −0.33 
                 −0.20 
                 0.03 
               
               
                 27 
                 0.25 
                 0.38 
                 0.40 
                 0.32 
                 0.18 
                 −0.03 
                 −0.22 
                 −0.35 
                 −0.40 
                 −0.35 
                 −0.18 
                 0.03 
               
               
                 28 
                 0.25 
                 0.37 
                 0.38 
                 0.33 
                 0.17 
                 −0.03 
                 −0.22 
                 −0.35 
                 −0.38 
                 −0.33 
                 −0.18 
                 0.03 
               
               
                 29 
                 0.27 
                 0.23 
                 0.40 
                 0.30 
                 0.15 
                 −0.05 
                 −0.23 
                 −0.35 
                 −0.38 
                 −0.33 
                 −0.18 
                 0.05 
               
               
                 30 
                 0.27 
                   
                 0.38 
                 0.32 
                 0.17 
                 −0.05 
                 −0.23 
                 −0.37 
                 −0.40 
                 −0.33 
                 −0.17 
                 0.07 
               
               
                 31 
                 0.27 
                   
                 0.38 
                   
                 0.15 
                   
                 −0.25 
                 −0.35 
                   
                 −0.33 
                   
                 0.07