Hello Helmut, Attached are graphs showing the typical error with the seasonal sunrise marker. As noted before, the error is periodic, zero at the solstices and equinox and at a maximum in between. The symmetrical, sinusoidal nature of the curves is even more pronounced when more points are added to the graph. I chose to determine the marker point at the solstice, when the error is zero. On the equinox when the error is also zero, the marker distance cannot be determined as the azimuth is due east west like the axis. I believe that choosing some other date would just cause an offset and not reduce the error.
The two graphs show the effect of latitude. The shape of the curves is identical. The absolute error increases from 3.4 cm at 38.6 latitude to 8 cm at 51 Latitude while the zodiac dimension goes down from 156 cm to 123 cm. In my opinion, the error is acceptable at the lower latitudes typical of the USA but a problem for northern Europe and Canada. At your latitude, 47.24, the maximum error is 6.3 cm with a 123 cm zodiac dimension. This zodiac dimension that I have quoted is from the centre to the solstice, half the total. From solstice to solstice the zodiac is twice that or 2.46 meters on a 9 meter dial (4.5 m semi major axis). This error analysis is based on fixing the marker distance based on the solstice date and sunrise azimuth. With the marker distance fixed, the zodiac distance is calculated from the sunrise azimuth for other dates and solar declinations. Then the difference is determined between the zodiac distances calculated from the azimuth compared to those for the dial layout. The differences are plotted against the date as a percent of the zodiac distance from the centre to the solstice. This technique is arbitrary but it does give a good indication of how much error is introduced by the linear approximation of a fixed sunrise marker. Roger Bailey Walking Shadow Designs N 51 W 115 -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Sonderegger Helmut Sent: January 12, 2002 5:59 AM To: [email protected] Subject: Re: Seasonal Sunrise Marker Hello Fer, hello Roger, your ideas on seasonal sunrise markers are very interesting. After having compared your constructions I have 2 questions: 1. Fer, where can I find the proof, that your construction ist exact? 2. Roger, I think the maximal error in your "linear approximation" would be a bit smaller, if you don't use the summer solstice for fixing the intersection point (you called this point "Sunrise" in your attached pdf-file) on the horizontal axis, but a day with smaller declination, may be half a month later or so. Is that correct? It looks so, when the points of the dates in Fer's construction are conected with the corelating points of sunset. Does anybody know which day would be the best? I suppose it could depend on the latitude. Thanks Helmut Helmut Sonderegger, A-6800 Feldkirch Email: [EMAIL PROTECTED] URL: http://webland.lion.cc/vorarlberg/280000/sonne.htm - Attachment converted: Macintosh HD:Error.pdf (PDF /CARO) (0003A15F)
