Re: Reverse Engineer Oldest SGS

[Fer J. de Vries]

Hi John,   Assuming the sundial is vertical (because the XII hourline is vertical) and assuming the sundial is well made, just measure two angles in the pattern and it is possible to recalculate the latitude and declination of the dial.   The angles you need are the hourlineangles for hour 6 and 9 for a morning dial or 15 and 18 for an afternoon dial.   The formulae: I name the houline angles for an afternoon dial z15 and z18. Calculate:   A = ( cot z15 - cot z18 ) ^ 2 B = ( cot z18 ) ^2 a = B b = A + B -1 c = -1   Calculate y1 and y2 from :   (-b +_ SQRROOT(b^2 -4ac)) / (2a)   (A well known formula I think so typing it like this you should understand it.) (Only the positive y is interesting for our problem))   Now calculte the latitude and declination from   cot lat = sqrroot y   sin decl = cot z18 . cot lat   I learned this in 1988 from Mr. Martin Bernhardt, Germany after I once made an iteration progam for a calculator to solve this question.   I hope I didn't made a typing error but try it.   Bernardt wrote more about these problems but for the problem you have the above solution will do for many examples I think.   Bet wishes, Fer.     Fer J. de Vries   De Zonnewijzerkring mailto:[EMAIL PROTECTED] http://www.de-zonnewijzerkring.nl   Home mailto:[EMAIL PROTECTED] http://www.iae.nl/users/ferdv/index-fer.htm Eindhoven, Netherlands lat.  51:30 N      long.  5:30 E -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of John Carmichael Sent: April 6, 2004 8:53 AM To: Sundial List Subject: Reverse Engineer Oldest SGS Hello All,   I'm trying to "reverse engineer" the oldest known stained glass sundial (made in 1529) so that I can determine the area in Germany for which it was designed and the window's declination.  All we know about the design location of this dial is that it came from "somewhere in Germany".  (I wonder what a map of Germany looked like in 1529?).   Claude Hartman just wrote an article in the new Compendium (march 04) comparing vertical sundials with drawings of dials at different latitudes and declinations.  His article gives many clues to the solution of this problem.  Just remember that his article is for normal vertical wall dials, not stained glass.  So to view his sundial face drawings as if they were stained glass, you have to view his article reflected from a mirror!   We should be able to determine the latitude and wall declination fairly easily since the dial has declination lines. Looking at the slope of the equinox line will tell us the wall's declination.  (To do this, I'm going to make a bmp. of the photograph and import it into Delta Cad, then I'll draw line on top of the equinox line and will measure it's exact angle)  I will retrace all the hour lines the same way until I get a complete Delta Cad drawing of the sundial face.   Now I'm stuck.  How do I determine longitude? If it were a modern sundial corrected for longitude, the answer would be simple.  I'm thinking that it's impossible to determine its longitude.   As for its latitude, I should be able to determine that from the hour angles of the hourlines. Right? The traced Delta Cad drawing with the angle dimension tool will tell me the precise hour angle of each line.   Now I'm stuck again and don't know a mathematical solution so instead of using math,  I'm wondering if I should just start feeding in different latitudes of Germany into Shadows Sundial Generator or Zonvwlak of vertical dials of this window's declination until I find, by trial and error, a drawing that best matches the sundial face and that would be its latitude.   This isn't a very scientific approach I know, but I'm not as smart as you guys.  Would one of you have a better way to reverse engineer this dial?     thanks   John     John L. Carmichael Jr. 925 E. Foothills Dr. Tucson Arizona, 85718 USA Tel: 520-696-1709 Email: [EMAIL PROTECTED] Sundial Sculptures Website: http://www.sundialsculptures.com Stained Glass Sundials Website: http://advanceassociates.com/Sundials/Stained_Glass