"A craftsman is as only as good as his tools." I learned this on a recent holiday when I found myself on the other side of the world with no tools to help me design a sundial. The wall over the swimming pool at our exchange home on the Gold Coast of Australia seemed to me to be the ideal spot for a vertical declining sundial. The location is S 28, E 153.4 and the north facing wall declines 21 W. I had brought with me none of my usual library of reference books, computer programs, not even trig tables or a scientific calculator. The computer that I used for email did not allow the installation of executable programs so I could not download the "Dialists Companion", "Zonwvlak 2000" or "Shadows" What could I do? What would a novice do to design their first sundial?
I decided to use this as a opportunity to relearn the fundamentals of gnonomics and to study the path of sun and shadows in this new environment, a sub tropical location in the southern hemisphere where the sun is high in the sky and seems to go backwards. At the local library I found "Sundials Australia" which covered the design principles and had the formulae for substyle height, substyle distance, difference in longitude and hour lines. This allowed me to write a little spreadsheet in MS Works and calculate the gnomon and hour lines for the dial. A paper mock up pasted on the wall proved the design was correct. But what about the utility of this dial? When would it be in the sun? At this time of year this dial was in sunlight from dawn to dusk, but what about December when the sun is almost directly overhead? I added azimuth calculations to the spreadsheet and used this to roughly determine when sunlight came onto dial. The long shadows when the sun came onto the declining dial reminded me of sunrise shadows. Then it dawned on me. Every vertical declining dial is equivalent to a horizontal dial somewhere else in the world. The sun came onto the vertical declining dial at sunrise for the equivalent horizontal dial. The sun shone on the dial when the Double Daylight criteria was met: Daylight at the location and daylight at the equivalent horizontal location. Sunrise and set times are easy to calculate and add to the spreadsheet using the tee shirt equation Cos t = - Tan (Dec) x Tan (Lat). For the equivalent horizontal dial, the latitude is the substyle difference. The difference of latitude is the time offset is which has to be added to bring the equivalent horizontal time to the time at the location of the VD dial. The attached plot "NewDawn.pdf" shows sunrise and set times against solar declination, or Double Daylight when the sun shines on this vertical declining dial. The red lines are sunrise and set for the equivalent horizontal dial, the black lines rise and set for the location and the blue lines the hours of sunlight on the dial by the Double Daylight criteria. I now know that this dial will work well through the year. Even for the limiting case the sun is on the dial by noon and remains on the dial most of the afternoon, prime time for the use of the pool. This Double Daylight sketch shows very well when sun shines on the dial. When I got home and checked my tool kit, I found, as usual, the experts were well ahead of me on this Double Daylight concept. Fred Sawyer described the technique with complete math in early Compendium articles(1-4 and 2-1). Fer de Vries produced a very similar but better drawing of double daylight. This is now included in his Zonwvlak program. Click on the black/white button on his menu to call up the subroutine that calculates and plots daylight at the dial location and the equivalent horizontal dial. This holiday without tools got me out of a rut and caused me to think about the principles of sundial design. It is also great to see that the tool have been made available for all of us to use. Thanks Fred and Fer for providing the information and software. It is a feature that I had not seen and appreciated before. Roger Bailey Walking Shadow Designs Back at N 51 W 115 Attachment converted: Macintosh HD:NewDawn.pdf (PDF /CARO) (00048D56)
