Hello Richard and all, Refraction would not be the cause of these "errors". Refraction only becomes prominent at low altitudes, close to sunrise and sunset. There errors are more likely due to the design latitude being wrong as this has the dominant effect mid morning and mid afternoon. At noon and 6 o'clock as the latitude error is zero or minimum. A slight tilt, wrong gnomon angle or wrong latitude for the hour angles would give the errors described. Bill Gottesman's "Sundial Align" program may be useful here. See http://www.precisionsundials.com/ In any case it is very difficult to achieve heliochronometer accuracies with this type of sundial due to the solar diameter and the penumbra fuzz factor.
I gave a presentation at the NASS conference in Banff in 2004 That may be useful. "Error Analysis of Garden Variety Sundials". I can send the slides as an email attachment, a 255 kb pdf file, on request. Regards, Roger Bailey Walking Shadow Designs N 48.6 W 123.4 -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Richard Mallett Sent: July 19, 2005 3:34 PM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [email protected] Subject: Sundial accuracy A fellow member of a Yahoo group, who lives in Chester, has asked about making his sundial as accurate as possible. Would the morning and evening errors that he mentions be due to refraction, or to one of the other factors that he mentions ? Here are some extracts from his emails :- Dear Richard, The hour lines are offset to allow for the difference between my longitude and that of Greenwich. The twelve-o'clock line therefore doesn't coincide with the local meridian. Local noon is marked by two lines exactly matching the thickness of the gnomon. This means that it is far easier to judge the moment of local noon than any other time. As you rightly point out, the fuzziness of the gnomon introduces a considerable degree of uncertainty into dial readings, because it is extremely difficult to judge when the ill-defined shadow is right on an hour line. However, it is far easier to judge when the shadow of the gnomon is exactly filling the space between the two lines marking local noon. By taking many observations, plotting the results on a graph and taking means, I think I've managed to get quite a good picture of the setting of the dial. It was commissioned for me by my wife as a present for my 50th birthday last year. As we were then in the process of house-hunting, she wisely deferred the purchase until we were certain of our new address. It was made by a chap from the Bristol area who trades as Merlin Sundials. It was delivered last September or October, but for various reasons I have only just got around to setting it up. It's a smallish horizontal dial of conventional design, eight inches or so in diameter. As I think I mentioned in an earlier message, the hour lines are offset so as to enable one to read Greenwich time direct from the dial (subject, of course, to the EOT). An attractive graphical representation of the EOT is reproduced on the dial plate, so that one can make a rough estimate for any day of the year to within a minute or so. I was also able to choose my own motto (and I believe I have an original one, in Latin, which I'm fairly confident has not been used on a sundial before - if you're interested, I'll tell you about it). It is chemically etched and is graduated at 1/4 hour intervals. Anyway, my sons and I have levelled the dial plate pretty accurately, if one can trust spirit levels, and I think we are probably within about 6 arc minutes (20 seconds of time) in azimuth. That's what I'd really like your advice about. Is that a good adjustment, or should I try to improve it? To be honest, I'd expected a larger error, because I'm pretty hamfisted at DIY, and I thought that errors would inevitably creep in with drilling holes in the top of the plinth and so on. If I got the holes even a small fraction of a millimetre out, it would obviously affect the accuracy of the dial. In fact, through luck more than design, I fixed the dial in azimuth in exactly the position I intended. The only slight problem was that I was using a not-very-accurate value (1 m 15 s) for the EOT when setting the dial in the meridian. I actually set it about 15 or 20 seconds 'fast' on the correct value, which was more like 1 m 34 s. The position seems to be that at local noon the dial is more or less bang-on the intended setting, except that I have a hunch that (fortunately) I may have set it a few seconds slower than I meant to do, thus fortuitously reducing the error with respect to the correct EOT value from 18 to about 15 seconds. I hope I've made this reasonably clear. What it all boils down to is whether an error of 15-20 seconds of time in azimuth at local noon is acceptable. What do you think? How does it compare with normal practice? This is the only sundial I've ever set up, so I don't really have anything to compare it with. There are other errors, which I imagine arise from slight errors in the construction of the dial - possibly in the angle of the gnomon, lack of parallelism of the two edges or 'styles', the etching of the hour lines and so on. The result is that when it first catches the sun (about 0830 near the summer solstice), it is about a minute fast. This diminishes quite quickly, so that from about 10 a.m. to 1 p.m. it is pretty much exactly right, within half a minute or less. After 1 p.m., it gradually gets fast again, until by about 5.15 p.m., when the sun leaves the dial in June, the error is of the order of 2.5 minutes. I don't find this a problem, but have no idea whether it represents acceptable performance to an experienced dialist. I know this error doesn't flow from an error in the azimuth setting, because the dial is bang-on at local noon and, indeed, for at least an hour either side. I believe I have now solved the problem of computing the EOT. I have a copy of Peter Duffett-Smith's 'Easy PC Astronomy', with its accompanying Astroscript software. I've used this to calculate the EOT and now get figures closely compatible with the predictions in Whitaker's Almanack and the NASA ephemeris generator, and reasonably close to those provided by the calculator on the BSS website. In other words, I was right to criticise the 'standard' tables, which on certain dates can differ from the true value by well over 20 seconds. Best wishes, Tommy - -
