Hello Brian, Although our personal notes started this four part response, I decided to post it to the mailing list for general information.
1. Error Correction: Thanks for finding the error in our analemmatic spreadsheet. You are correct, the central analemma was plotted the wrong way around. At this time of the year the sun is fast. To use this analemma as an eqt corrector, the gnomon must be on the west side of the central axis to bring the sun back to clock time. The solution is quite simple. Just change the signs in appropriate cells of the spreadsheet. I would recommend this change to all users. Helmut has posted the corrected version on his website. http://webland.lion.cc/vorarlberg/280000/sun.htm 2. Analemma Correction: Your comments raise some interesting issues on this EQT correction analemma on analemmatic sundials. The EQT correction analemma was added as a revision to Lalande's original dial at Brou. Many followed this lead but now its use is discouraged. I included it on the spreadsheet chart as a noon mark and an indicator or the magnitude and direction of the equation of time but have discouraged its use on public dials. My logic was that it only works around mid day and is an unnecessary complication. The correction only applies to the E/W component so it diminishes to zero at the six o'clock positions. With the analemma, we have a lot of explaining to do. You have a more positive point of view, pointing out that the analemma is attractive, a useful teaching aid and more accurate than expected for much of the day. Specifically, you point out that the accuracy would be acceptable during the school day. Based on the results of the following two pin experiment, I now tend to agree. 3. Two Pin Experiment: Print the chart with the analemma from the spreadsheet. Paste it onto a piece of corrugated cardboard. Stick in two long pins as gnomon on today's date, one on the central axis, the other on the date point on the correction analemma. Around noon, observe the time according to both gnomons. The central axis pin gnomon will read noon solar time when the analemma pin will show 11:45 clock time. Today the sun is 15 minutes fast. Observe throughout the day and check the two time indications. If you are impatient like me, just rotate the dial at any time during the day to get all the hour readings required. You will see that the correction goes to zero as you approach six and then reverses before and after six to give quite an error. But observe how the two values hang together for quite a while, about three hours before and after noon. As the time shifts from noon, the curvature of the ellipse and the compression of the hour angles results in the solar and clock time readings being reasonably consistent through that period. This effect depends on latitude but works reasonably well even this far north. As you suggested, the correction is reasonable for most of the school day so an analemma would be useful on a school dial. The two pin experiment is also a good teaching aid. Some math would help but "Math is hard." 4. Split Analemma Design: To apply a better correction, accurate throughout the day, and not just around noon, the analemma pin has to be moved in the N/S direction as well. The difficulty here is that this correction on the N/S axis is different for morning and afternoon. Have another look at the pin board. Today you would have to move the morning pin south and the afternoon pin north to have it work correctly. This is the basis for the split analemma applied by K. Seildelman on the DuPont Longwood Garden analemmatic dial. Fred Sawyer describes this dial concept and develops the mathematics very well in his paper "On Analemmas, Mean Time and the Analemmatic Sundial" a BSS paper in his "Sciatheric Notes" on the NASS Repository CD, or see http://www.longwoodgardens.org/Sundial/Analemma.html This is a great idea that deserves more use. The dual analemma, split hour ellipse design is satisfying from a number of points of view. It is fairly accurate, has a theoretical basis and looks good. I am pleased to see that you are working on design methods for this concept and I would encourage you to continue. Regards, Roger Bailey Walking Shadow Designs N 51 W 115 -
