Hi Roger: That's about right if I recall. The shift towards the dark side seemed to be somewhere between 75% to 85%. We used a shadow sharpener to determine this. But it was a rough judgement call and not all that precise. To really get a value that is more precise, I think you would need to conduct a well-executed experiment.
I wondering where this great discussion will take us? Which leads me to ask a question for those of you who are mathematicians and those of you who make sundial generator programs: If we know the exact amount amount of shadow shortening that occurs on monumental sundials, then would it be possible to add this correction to a sundial generator program like ZW 2000 as a design option? The sundial generator program would then make drawing of the sundial face with built-in shadow shortening correction. Many of our popular sundial generator programs have design options that allow us to correct designs for such things as atmospheric refraction, longitude correction, EOT date, etc. This would just be another correction tool that an anal retentive dialist could use to make "the perfect sundial". Would it be worth all the trouble? I'm not sure. What do you guys think? John -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Roger Bailey Sent: Sunday, February 17, 2008 10:33 PM To: Chris Lusby Taylor; Frank King Cc: sundial@uni-koeln.de Subject: Re: Monumental Sundial; 14 missing seconds 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: <sundial@uni-koeln.de> 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 --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
