I remember John Carmichael did some experiments on a truly monumental sundial, The McMath-Pierce Solar Observatory, Kitt Peak Arizona. I think he put the judgment point for the transition well towards the dark side at about 85% dark.
That was long ago and far away so I would appreciate any comments to refresh my memory. Regards, Roger Bailey ----- Original Message ----- From: "Frank King" <[EMAIL PROTECTED]> To: "Chris Lusby Taylor" <[EMAIL PROTECTED]> Cc: <[email protected]> Sent: Sunday, February 17, 2008 10:22 AM Subject: Re: Monumental Sundial; 14 missing seconds > Dear Chris, > > I am a bit behind with my reading and I have only > just read your comments, and corrected comments, > on the umbra discussion. > > Subject to your corrections, I concur with almost > all you say but I feel a little amplification of > one of your follow-up remarks is needed. You > say... > >> If the gnomon is ... a conventional wedge-shaped >> gnomon with two style edges, then you can adjust >> the hour lines, by a little under a minute. > > I am very nearly happy so far! > >> This adjustment is definitive, in the sense that >> it is irrespective of the time of day, time of year, >> size of sundial, type of sundial (horizontal or >> vertical) or latitude. > > Yes, I am still happy [subject to your qualification > later that "the sun moves faster across the sky at > the equinoxes than at the solstices"]. > > My need for amplification is confined to the > 50 seconds figure here... > >> It is an angular change (about 50 seconds of time), >> not a linear change. > > It is indeed an angular change; it's the 50 seconds > figure which I feel needs a bit of amplification... > > At the equinoxes the sun obligingly trundles along > the celestial equator (well close to it) at a rate > of 1 degree every 4 minutes of time or 1 arc-minute > every 4 seconds of time. > > Consider a bug, sitting on the 2pm hour-line (say), > looking at the sun (via special eye protection) as it > approaches the business edge of a fat wedge gnomon. > > There will be a period lasting just over two minutes > (to be justified below) of significant interest: > > 1. Since sunrise the bug has been able to see the > entire solar disc and has been basking in full > sunlight. Then, about 13:59 sun time, the sun > makes first contact with the edge of the gnomon > and, soon afterwards, the bug notices a drop in > light. > > 2. The solar disc steadily slips behind the edge > and, about 14:01 sun time, we have second contact. > Thereafter, the sun is wholly behind the edge and > the bug is in maximum shadow. > > Taking the angular diameter of the sun to be 32' the > time taken from first contact to last contact will > be 128 seconds. This, measured in time, is the full > width of the umbra. > > The time from 14:00 to second contact is 64 seconds > and I pondered how to reduce this to 50 seconds... > > [Aside: of course I agree that you divide by the > cosine of the declination if you are not at an > equinox and the angular diameter varies a little > from 32'. These, as you say, are minor matters > though the first INCREASES the 64 seconds.] > > You later say, and again I concur, that "most people > seem to judge the edge very close to the dark side." > > The key words here are "very close". > > To reduce the true 64 seconds to the apparent > 50 seconds you seem, implicitly, to be saying > that "very close" translates into 14 seconds of > time, or 3.5 arc-minutes, about 10% of the solar > diameter. > > This feels about right but I should love to see > the results of some properly set-up experiments. > > I can imagine that the results would be different > for going from shadow to light (morning times) > from going from light to shadow (afternoon times). > > Do you have some mathematical justification that > has escaped me for the missing 14 seconds or is > this just a sensible estimate? > > Best wishes > > Frank > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
