Pete Swanstrom <[EMAIL PROTECTED]> writes: > I do want to specifically respond to Dr. Carlson's reply... he is > absolutely correct in his statement that nearthe summer and winter > solstices you can not simultaneously determine both the date and the > time from this sundial, if both are unknown. ... > > However, I do disagree with his statement that you would be doing well > within these periods to determine the date with an accuracy of 1 week. > On the first and smaller brass sundial I built, with an 11.5" radius (an > equatorial scale of 20 minutes/inch) the date may be determined to > within +- 3 to 4 days during the summer solstice, to within +- 2 to 3 > days during the winter solstice, and to within 1 day most other months > of the year. On the much larger park sundial, with a 32.75" radius (an > equatorial scale of 7 minutes/inch) I can easily determine the date to > within 2 days around the summer solstice (if I know the correct time,) > to within 1 day around the winter solstice, and to within 1/4 day during > most other months of the year. Knowing the date within these two > solstice periods, on the park sundial I can still easily read the time > within 20 seconds (on my home sundial the time can be read to within the > minute.) Today for example, when I checked the park sundial, I could > still distinguish today's date exactly (June 7,) but I was a little > disappointed to note at 1:57 this nice sunny afternoon that it was 8 > seconds slow in indicating the correct time ;)
The one week accuracy refered to the case of trying to find the date from a dial without knowing the exact time. Since the rate of change of the Equation of Time at the solstice is 13 sec/dy in summer and 30 sec/dy in winter, if you know the exact time and can read the dial to +/- 20 sec, a realistic value if you have an excellent instrument and excellent eyes, then the error in determining the date should be no more than one day all year around, or possibly two days near the summer solstice. Even near the equinoxes, the error in determining the date will be greater than 1/4 day in leap years and the years preceding them. In principle, a larger device isn't any more accurate than a small one, though it is possibly easier to manufacture and read. Have you considered replacing your analemmic cut-out with a solid of revolution? It simplifies the manufacturing and operation of the dial, but it does introduce errors of up to 1 min 30 sec because the exact analemma is "tilted". This type of dial was apparently invented by a man named Bernhardt. I independently reinvented it, but that doesn't count. :( Near sunrise and sunset, atmospheric refraction displaces the image of the sun by about half a degree, which should show up as an error of nearly 1-1/2 min, dial fast at sunrise and slow at sunset. I would be interested in hearing if you can measure this effect. I suppose the 20 sec accuracy you reported was for measurements taken when the sun was reasonably high in the sky. > My appologies if I appeared to oversell the result on my web pages. As > an engineer, and not a mathematician or a physicist ;) I am usually > thrilled if I am able determine a solution to any problem within 40%, > and then I multiply the answer by a safety factor of 2x or more. In plasma physics, that's the sort of accuracy we usually have to be happy with, too. Art Carlson
