Re: Comments to Annalemic-Equatorial Sundial Page
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
Re: Comments to Annalemic-Equatorial Sundial Page
Wm. S. Maddux wrote: > > Dear Dr. Carlson, > > >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. :( > > It is possible to use two half figures of revolution, one for the vernal > half of the tropical year, the other for the autumnal. I.e., make two > lathe turnings, divide them bilaterally and reassort, pairing the > enantiomorphic halves. (You get material for two gnomons, one to > use, one to spoil.) You mount this "optical cam" with the division > plane declined from the vertical, and offset laterally according to which > side's shadow is to be used for reading. Rotate it 180 degrees > about the polar direction at each solstice. > > I don't know who first did this, but I've seen a published description > some years ago, perhaps in "SKY & TTELESCOPE." > > Bill Maddux > > P.s. I independently reinvented this asymmetric dodge, but I too was > anticipated, and my invention doesn't count either. : < Bill: Add me too, to the list of disappointed reinventors. My first design approach was to try to use a solid analemmic gnomon shape, but I couldn't think of an easy way to manufacture it or to support it. My big "AHA!" came when I realized that I could use a rotatable plate with an analemmic cutout. I felt this was easier and cheaper to mass produce, it required much simpler support, and it could easily be labeled and read to also indicate every day of the year. I built my first brass sundial, saw that it actually worked, and decided to do a patent search for any similar sundials. I then came across Samual W. Balch's Jan 19, 1926 U.S. Patent #1,570,029, which claims exactly the solid analemmic shape that you have described. I thought I still had his patent beat for the very reasons I stated above, until Fred Sawyer informed me that a sundial which looked almost exactly identical to (mine?) was invented by Mr. John Ryder Oliver in the UK in the 1890's. Sigh. Thanks. Pete.
Re: Comments to Annalemic-Equatorial Sundial Page
Arthur Carlson wrote: > > 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. > > Art Carlson I started to keep a log of dates and time readings taken from the analemmic-equatorial park sundial after it was installed. I watched the sundial until the most-sharply defined edge of the gnomon's shadow intersected exactly with a minute mark on the dial, and then checked the time reading against my watch to see how the sundial reading compared with the U.S. Naval Observatory Master Timeclock's time. All of the dates and time readings I recorded are shown below, along with how much the sundial was fast (+) or slow (-) compared to my watch, and any notes I made during the readings. 5/04/98 1:30 pm +- 0 secs (O.K., I got lucky once), date exact. 5/05/98 7:30 am + 60 secs (fast), date O.K. I was only able to take this one reading as the sun disappeared behind a bank of clouds. 5:50 pm +- 0 secs to +20 secs, date O.K. I watched the time indicated by the gnomon's shadow vary rapidly from 0 seconds under bright sun to +20 secs fast as thin clouds darted across the sun. Since this sundial uses an analemma opening, more clouds = wider gnomon shadow = smaller observed analemma shape = faster time observed (on this date from the left side of the analemma pattern.) 5/06/98 7:10 am +- 2 secs (I checked it twice!) Date exact. Clear sky. 5/07/98 12:45 pm - 10 secs, date exact. Clear sky. 5/15/98 10:53 am - 15 secs, date exact. Clear sky. 5/17/98 12:17 pm - 6 secs, date exact. Clear sky. 5/23/98 9:25 am - 30 secs, 3/4 day slow. Sun behind cloud fringe. 6/04/98 (Forgot to record time) -20 secs, date exact. Some thin cloud fringe. 6/07/98 1:47 pm - 8 secs, date exact. Clear sky. 6/09/98 5:44 pm - 6 secs, date exact. Clear sky. 6/14/98 7:52 am - 80 secs (slow), date exact. Clear sky with only a minimum of high light haze. What happened here? 2:30 pm - 8 secs, date exact. Light cloud wisps. So there were three different occasions when I observed time readings before 8:00 am... 5/05/98 @ 7:30 am, the sundial was 60 secs fast as the sun disappeared behind thick clouds; 5/06/98 @ 7:10 am, the sundial was within +- 2 secs under a clear sky; and 6/14/98 @ 7:52 am, the sundial was 80 secs slow under clear sky with only a minimum of high light haze. Bottom line, I have not yet been able to accurately see the atmospheric refraction effect you described, caused by sunlight traveling obliquely through an atmosphere of uniformly increasing density. However, I DID see some large time and/or date inaccuracies, which I could best explain by refraction of the sunlight through random cloud, temperature and humidity layers. I think Boise has too much weather! Pete Swanstrom.
Re: Comments to Annalemic-Equatorial Sundial Page
Dear Dr. Carlson, >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. :( It is possible to use two half figures of revolution, one for the vernal half of the tropical year, the other for the autumnal. I.e., make two lathe turnings, divide them bilaterally and reassort, pairing the enantiomorphic halves. (You get material for two gnomons, one to use, one to spoil.) You mount this "optical cam" with the division plane declined from the vertical, and offset laterally according to which side's shadow is to be used for reading. Rotate it 180 degrees about the polar direction at each solstice. I don't know who first did this, but I've seen a published description some years ago, perhaps in "SKY & TTELESCOPE." Bill Maddux P.s. I independently reinvented this asymmetric dodge, but I too was anticipated, and my invention doesn't count either. : <
