Greetings Dialist I have been slugging away at the third or forth prototype Helio-chronometer and have a problem. It tells time remarkably well but, Am I wrong in expecting the bead of light emanating from the aperture on the alidade to walk horizontally across the anelamma over the course of the day. or does it cross the appropriate date mark on the anelamma at noon? Dave Scott
lat. 42:56 N long. 72:40 W Wendell,MA. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Roger Bailey Sent: Thursday, April 18, 2002 11:04 AM To: Sundial Mail List; DeAmicis-Roberts, Mike Subject: Correction Epicycle Hi Mike, I promised to get back to you with some suggestions on corrections for the Sunrise Seasonal Marker that you proposed for your analemmatic sundial. Since this is of general interest, I hope you don't mind me posting this note to the sundial mailing list as well. First let's review the idea. You proposed a marker along the east west axis that could be used to determine the position and time of sunrise and sunset. When I did the calculations to check this proposal, I was surprised to find that indeed there was such point. Lines through this marker and the dates on the zodiac table extended one way shows you the azimuths of theoretical sunrises or sunsets. Extending these lines the other way to the hour ellipse of the dial tells you the times of sunrises or sunsets. This seasonal sunrise marker is a brilliant idea, a great addition to analemmatic sundials. There is a problem. The marker is not a point. All the lines do not go the exact same point but were spread along the axis a short distance. In your case of a large 9 meter or 30 ft diameter dial at your latitude, there is a spread of 15 cm (6 "). The error grows with latitude, reaching unacceptable size at latitudes like mine (51). Helmut Sonderegger suggested minimizing the error by using 20.2 degrees as the reference base for calculations. This works but I preferred to use the solstice as the base as this gave a periodic error. The periodic nature of the error is natural. The straight line approximation of circle should result in circle generated sine type error curves. Then it struck me! Why not correct for this periodic error by using a small circle projected onto the axis? We are in good company here. When Ptolemy needed to correct for orbital anomalies, he used epicycles on his perfect spheres. These epicycles are smaller diameter, or higher frequency cycles on top of the main cycle, sort of like the harmonic terms in a Fourier Series. What I am suggesting is not a true epicycle, a circle on a circle generating "Spirograph" patterns, but it is close enough to use the term. I uses a small spreadsheet to calculate and plot the marker position of the for dates and declinations throughout the year. Have a look at the attachment "Epicycle.pdf". The graph shows as a function of the yearly cycle the usual declination, equation of time, and now the sunrise/set azimuth for your location. The black line on the expanded secondary axis is the position of the seasonal marker throughout the year. It seems to be a perfect sine curve. This is the curve that would be generated by the circle on the right as you go around two rotations per year. The equinoxes are on top, giving the maximum marker position. The solstices are on the bottom showing the minimum position. Your seasonal marker is now a simple circle, 15 cm in diameter with dates marks around the circumference. Estimate the date; drop a perpendicular from the circumference to the axis. This gives you the precise position for the seasonal marker on that date. For general observations you can just sight across the circle. For precise readings, establish a precise line from the zodiac table date to the date from the epicycle on the axis. What a great analogue computer! It is simple to construct and easy to use. The correction epicycle works very well to give you a precise answer for sunset time and location. Now all we have to deal with are those devilish mountains, the Diablo Range, polluting your eastern horizon. Roger Bailey Walking Shadow Designs N 51 W 115 This is the second attempt post this message. The original that had a second attachment of similar size that reviewed the seasonal marker concept must have been stopped by the file size filter. I hope this one gets through. It takes about 6 seconds to transmit on my dial up modem connection. -
