At 07:14 AM 9/1/99 -0400, Mac Oglesby wrote: > >I wonder what it would take to make it a sundial showing hours until dark. >That is, how would the time of "dark" (relative to sunset) be determined? Hi Mac,
This is an excellent challenge. First, we have to define "dark". Bowditch defines Civil Twilight as 0 to -6 degrees solar altitude, Nautical Twilight as 0 to -12 degrees and Astronomical Twilight as 0 to -18 degrees. This is why star gazing in the summer at my latitude (51) is so frustrating. We don't get the dark skies back until mid August. The limiting latitude for astronomical twilight on the solstice is 48.5 degrees. 90-23.5-18=48.5 I believe you could add horizontal lines to the virtual section of a sundial (when the sun is below the horizon) for -6, -12 and -18 degrees and see where the lines intersect the hour lines. Good programs like Zonwvlak trap these errors but my old spreadsheet programs were quite happy to calculate and plot these virtual lines. The brute force numerical solution would be to use the navigators' altitude equation and solve for the time angle t at altitudes of -6, -12 and -18 degrees. Sin Altitude = Sin Dec * Sin Lat - Cos Dec * Cos Lat * Cos t An approximation would be to estimate how long it takes for the sun to set to -6, -12 and -18 degrees based on psi,the angle of the setting sun with the horizon. When the altitude is zero, Cos psi = Sin Lat / Cos Dec. A useful approximation for the setting sun is psi is approximately equal to the co-latitude. The time for the sun to set is proportional to 1/Sin psi. This explains why tropical sunsets are so abrupt and northern sunsets are so mellow. It is not just the fact that time flies when you are having fun. I will be expanding on this theme at the NASS conference next month with a presentation on "Sunset Phenomena". Or you could say it is dark when the street lights come on. When I was growing up in Norman Rockwell Land, when the street lights came on, it was dark and we all had to go home. Roger Bailey Walking Shadow Designs N 51 W 115
