Hi Bill and all, I am resending this note without the spreadsheet attachment. Yes, I am beating a dead horse but....I agree with your comments that my original answer was correct but my method was not well explained. I have improved the spreadsheet, outlining the method and adding a sketch. It is now better explained but it is still spherical trigonometry. I was not comfortable with the solution until I ran it through the NASS Dialists Companion. It essentially agrees although the date looks equally good for 3 August, depending on the year and where we are in the leap year cycle.
The method I used is based on spherical trigonometry solutions for the "Navigators Triangle". There are two unknowns, time and declination. (If you find the declination you know the possible dates). To solve, you need two equations involving the same known parameters. These are not linear equations so I chose an iterative graphical solution. I am an engineer seeking practical results. I will leave the analytical solution to those better skilled at mathematical abstraction. There are two general solutions for the Navigation Triangle, one based on the sine rule, the other the cosine rule for solving the spherical triangles. The sine rule to solve for the opposite side, knowing two angles and one side is: Sin t/Sin Z = Sin CoAlt/Sin CoDec or Sin t = Cos Alt/Sin Dec when Z = 90 and Sin Z = 1. Put in different values for declination and you get the corresponding time angles. Do the same with the other equation based on the cosine rule, knowing adjacent sides and the included angle. (This one is easy to remember as sin sin sin cos cos cos). Sin Alt = Sin Dec * Sin Lat + Cos Dec * Cos Lat * Cos t. Rearrange for Cos t = (Sin Alt - (Sin Dec * Sin Lat))/(Cos Dec * Cos Lat). Again plug in values of declination and you get corresponding time angles. Where these time angle values are equal, you have the solution that satisfies both equations. Plotting the results makes the solution more obvious as a graphical solution. This is all the spreadsheet does. The improved spreadsheet is likely too large for the size filter at 33 kb so I have posted it at one of my websites. Go to http://www3.telus.net/public/rtbailey/WalkingShadow/Dead%20Horse.xls What I have learned from this is that working for NASA as a photo interpreter on forensic genealogy does not make you a "rocket scientist". But then again, neither does designing sundials but we know our shadows. Regards, Roger Earlier note without attachment follows. I agree Bill, it cannot be the equinox. On that date with an altitude of the sun at about 25.5 degrees, the azimuth would not be 90 degrees. But it is determinant and solvable using the usual navigators equations for time vs altitude and azimuth for dates (declinations) for that location (Lat 44.77). I used an Excel graphical solution. See attached file "Dead Horse.xls". Assuming altitude 25.5 and azimuth 90, the date works out to be August 2 at 4:44 pm solar time. Regards, Roger Bailey -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Bill CS.Com Sent: April 9, 2007 10:20 AM To: Sundial-List Subject: Mistake in "Shadows in a Photograph" There is an error in this report--either by the reporter, or the photo analyst. The report states "Since South Eighth Street (then Griffith Street) runs north-south, the shadows point almost exactly east-west. There are only two days in the year when this occurs the spring equinox (March 19-20) and the fall equinox (Sept. 22-23). " This is not true. In the northern hemisphere, a shadow will fall along an exact east/west line every day between the spring and fall equinox (positive sun declination), but at a different time day-to-day. On the equinox a shadow falls exactly east/west only at sunrise or sunset, so in fact this photo could not possibly have been taken on an equinox. What the reporter or analyst may have meant to say was that the tip of a shadow will trace an east/west line over the course of the day on the equinox, but this would not help his photo interpretation. -Bill Gottesman ----- Original Message ----- From: Fred Sawyer To: Sundial List Sent: Monday, April 09, 2007 12:27 PM Subject: shadows in a photograph Another fascinating example of detective work using shadows in a photograph: http://www.sheboygan-press.com:80/apps/pbcs.dll/article?AID=/20070401/SHE04/ 704010376/1097/SHElife Fred Sawyer ---------------------------------------------------------------------------- --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
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