RE: Zarbula's Method for Wall Declination
Hi Mac, Chicago, 19-21 August 2005, NASS conference. Roger Hi Roger, Are you going to leave us dangling, or are you willing to tell us how Zarbula found SH with a stick, some string and the Sun? Best wishes, Mac Roger Bailey wrote: (snip) Similarly you can calculate the Sub-style Height, the angle of the gnomon to the wall, as Sin SH = Cos Dec x Cos Lat. But this is not how Zarbula did it. He only had available a stick, some string and the sun. I will leave that as a homework exercise. - -
Re: Zarbula's Method for Wall Declination
I am not sure to understand Zarbula and Indian circle methods but perhaps this can help for your last question. I know this relation is validated : sin (D) = tan (X) / tan (L) D = wall declination X = angle between the equinoctial line and an horizontal line L = Latitude But I am not sure of this other one: sin (D) = tan (Y)* tan (L) Y = angle between equinoctial line and the substyle line But it seems to works with your examples Example 2 : sin (D = 45) = 0,707 tan (Y = 48.2) = 1.118 tan ( L = 32.3) = 0.632 Example 3 sin (90) = 1 tan (Y = 57,7) = 1;581 tan ( L = 32.3) = 0.632 Perhaps can you test this with other angles Best regards Joël 48°01'20 N, 1°46' W (FRANCE) http://www.cadrans-solaires.fr/ - Original Message - From: John Carmichael [EMAIL PROTECTED] To: Roger Bailey [EMAIL PROTECTED] Cc: Sundial List sundial@rrz.uni-koeln.de Sent: Saturday, December 04, 2004 5:46 PM Subject: Re: Zarbula's Method for Wall Declination Hi Roger: I followed your whole letter with great interest, and understand it all, except for one thing. Is it possible to determine the wall's declination once I have drawn the equinoctial line and the substyle line using this method? At first I thought that if I drew a horizontal line on the paper and determined the angle of the sloping equinoctial line, that this angle would equal the wall's declination, but it doesn't in all the examples I've tested. For examples, I played around with a sundial drawing program and entered different wall declinations (0, 45 and 90 degrees East of South) for my latitude 32.3 deg N. and then I measured the sloping angle of the equinoctial lines. Here are the results: 1. If the wall is due south, then the equinoctial line is horizontal which means the declination is 0. so far so good. 2. But if the wall declines say 45 degrees to the East of South, and I draw a sundial face using Shadows or Zonwvlak, then I thought it's angle is should be 45 also, but it's not. It's 48.2 degrees. 3. If I draw a dial the declines 90 degrees East of South, then the angle of the equinoctial line should be 90, but it's not. It's 57.7 degrees. So obviously my supposition is wrong. The angle of the equinoctial line is NOT equal to the wall declination. How can I get the wall declination using your Indian Circle method? Thanks John - Original Message - From: Roger Bailey [EMAIL PROTECTED] To: Sundial Mail List sundial@rrz.uni-koeln.de Sent: Friday, December 03, 2004 9:42 PM Subject: Zarbula's Method for Wall Declination Hello Colleagues, The Piedmontese painter and sundial maker, Giovanni Francesco Zarbula left an amazing legacy in the villages of the French alps. Between 1832 and 1870 he crafted over 60 sundials in the area from Grenoble to Gap, near the Italian border. Over half of these flamboyant folk art masterpieces still survive; recently many have been expertly restored. I often wondered how Zarbula laid out these designs on vertical declining walls. As an itinerant craftsman, carrying all the tools of his trade on the back of a mule, he would not be able to utilize the methods summarized in Frank King's note following John Carmichael's good question. How did he do it? I am pleased to report that Google found the answer for me. Follow the link to: http://www.meridianeitaliane.it/Rivista%20Gnomonica/gnomonica6.pdf On pages 8- 10 of this 61 page edition of Gnomonica, there is a letter by Alessandro Gunella outlining Zarbula's method: L'orolgio Francese e il metodo DI ZARBULA per trovare la declinazione del muro. Thanks, Alessandro for answering the question. I guess that I am not the first to be impressed by Zarbula's dials and wonder about his techniques. As Alessandro reported, Zarbula didn't actually measure the declination of the wall. He didn't need to. Zarbula seems to have applied a variation of the Indian Circle technique (Cassini's Method on Frank King's list) to establish the equinoctial and sub-style line on the wall. From these he could lay out the hour lines using well known graphical gnomonic techniques. The Indian Circle method (cerchio indu in Italian) is a simple technique for finding north. All you need is a stick, a string and sunshine. Put the stick vertically into the flat level ground. Use the string to describe some circular arcs, using the stick as the center. Watch the shadow of the tip of the stick and note where the path of the shadow tip crosses the arc in the morning and then again in the afternoon on the other side of the circle. The line between the crossing points is due east - west. North - south is perpendicular to the east - west line. Zarbula's method is based on the fact that every vertical declining sundial has an analogous horizontal sundial somewhere else in the world. To apply this variation to a declining wall, all you have to do is mount a stick perpendicular to the wall, draw one or more concentric arcs, mark
RE: Zarbula's Method for Wall Declination
Hi John, It is back to the basics on this one: Waugh, Chapter 10, Page 79, Verse 1 to 4. The concepts of Sub-style Distance (SD), Sub-style Height (SH), Difference in Longitude (DL) and Angle with the Vertical (AV) so well developed in Waugh, are not evident in the computer programs that we now commonly use. You can determine the wall declination from the Sub-Style distance if you know the latitude as Tan SD = Sin Dec / Tan Lat. The Sub-style Distance is the angle from the sub-style line to the vertical. This is the same angle that the perpendicular to the sub-style, the equinoctial, line, makes with the horizontal. As wall declination increases from zero, the sub-style distance (and equinoctial angle) increase but at a reduced rate, reaching a maximum, equal to the co-latitude, when the declination is 90 degrees. Using your examples and your latitude of 32.3 degrees and Tan Lat = 0.632: Dec = 0, Sin Dec = 0, Tan SD = 0 Dec = 45, Sin Dec = 0.707, Tan SD = 0.707/.632 = 1.118, SD = 48.2 Dec = 90, Sin Dec = 1, Tan SD = 1 / 0.632 = 1.582, SD = 57.7, or your co-latitude. Zarbula had it easy as he worked at latitude 45 degrees where the Tan = 1. For him, Tan SD = Sin Dec. Similarly you can calculate the Sub-style Height, the angle of the gnomon to the wall, as Sin SH = Cos Dec x Cos Lat. But this is not how Zarbula did it. He only had available a stick, some string and the sun. I will leave that as a homework exercise. Regards, Roger Bailey Walking Shadow Designs N 48.6 W123.4 -Original Message- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: December 4, 2004 8:46 AM To: Roger Bailey Cc: Sundial List Subject: Re: Zarbula's Method for Wall Declination Hi Roger: I followed your whole letter with great interest, and understand it all, except for one thing. Is it possible to determine the wall's declination once I have drawn the equinoctial line and the substyle line using this method? At first I thought that if I drew a horizontal line on the paper and determined the angle of the sloping equinoctial line, that this angle would equal the wall's declination, but it doesn't in all the examples I've tested. For examples, I played around with a sundial drawing program and entered different wall declinations (0, 45 and 90 degrees East of South) for my latitude 32.3 deg N. and then I measured the sloping angle of the equinoctial lines. Here are the results: 1. If the wall is due south, then the equinoctial line is horizontal which means the declination is 0. so far so good. 2. But if the wall declines say 45 degrees to the East of South, and I draw a sundial face using Shadows or Zonwvlak, then I thought it's angle is should be 45 also, but it's not. It's 48.2 degrees. 3. If I draw a dial the declines 90 degrees East of South, then the angle of the equinoctial line should be 90, but it's not. It's 57.7 degrees. So obviously my supposition is wrong. The angle of the equinoctial line is NOT equal to the wall declination. How can I get the wall declination using your Indian Circle method? Thanks John -
