Thanks to Tom Semadeni for his kind words: >Thanks to Chris, for the clever graphical explanation showing especially the >discontinuities which support his recommendation to look at John Shepherd's >work on the beautifully designed and executed Richard D. Swensen Sundial >at the >University of Wisconsin - River Falls. >http://www.uwrf.edu/sundial/ >Not only is the sundial elegant, the web pages are too! > >....
... > >Precision: >The close-up photographs clearly show the precision of this Sundial (or >heliochronometer [sun-time-measurer], I guess), indicating an optimized >diameter for the gnomon. >Perhaps Professor Shepherd would care to share his thinking on the topic of >precision with us. > With a vertical sundial at our latitude (45 degrees N) the shadow length varies considerably and therefore so does the distance moved by the shadow on the wall in a minute. So unless we were to vary the width of the bar making the annalemmas (very costly) we had to chose a compromise for this width and that of the pipes for the . The main factor turned out to be visibility of the shadow and the annalemmas. We hung bar stock on the wall and just looked at it from different distances:-) 1.25 by 0.75 inch turned out to be best. Similarly we tried various pipes for the gnomon with various terminations. When we viewed at the extreme hours we found the discs and cross pieces on the end were too blured to see, hence the double gnomon was born:-) >Analemmae: >It appears that the calculations were done in general; then the location, >scale >and orientation variables were set in; resulting in some sort of output that >was used as input into a CAD program; which in turn gave those beautiful >analemmae which were then "pasted" onto the wall using another scaling factor. >Perhaps Professor Shepherd would describe how he went from those terrible >recursive functions which produce the EoT to getting a template for those >analemmae. > Actually as a Physicist part Astronomer the calculations were done first using the Ephemeris Tables to calculate the Right Ascension/Declination of the Sun at each hour for each day from this the direction of the Sun was calculated for any latitude longitude and hence the intersection of the shadow with the plane was found. Later I used "Compact data for navigation & astronomy for the years 1991-1995" from the Royal Greenwich Observatory, a set of tables that contain the Altitude azimuth data for the sun as a function of time in polynomial form which is even easier to use for computation. Hence I could calculate the direction of the sun for any time on any date. I have since purchased the tables for 1996 - 2000. In plotting the annalemas for different years I realized that there shape was year independent which from our preceding discussion is not at first obvious:-) The next task was to decide the scale which is determined by the size of the gnomon. This is where the advantages of direct plotter output were realized as I could draw many designs and pick the one I thought was best for the size and shape of the wall. I also discovered that the previous program based on the Ephemeris was in error having corrected for Sidereal to solar time twice! This led to an error of 4 minutes at the end of the day:-( In numerical work such as this its nice to have at least two different ways of calculating something as an error check:-) Once the size was decided I generated a file of x-y coordinates in inches from the base of the Gnomon for every minute to generate a smooth curve. Gene Olson then took this into his CAD program an generated the full size drawings which he used as templates to bend the bar stock to. You can see a picture of Gene placing them on the wall at: http://www.concentric.net/~mettlewk/sundial.htm Thats probably more detail than most of you wanted. Cheers, John Professor John P.G.Shepherd Physics Department University of Wisconsin-River Falls 410 S. 3rd. St. River Falls,WI 54022 Phone (715)-425-3196, eve. (715)-425-6203 Fax (715)-425-0652 44.88 degrees N, 92.71 degrees W.
