At 04:13 AM 9/6/99 -0400, Charles Gann wrote: > >Nice idea Mac! Perhaps Roger could design the dial to show time remaining >until > >(1) sunset >(2) civil twilight >(3) nautical twilight, and >(4) astronomical twilight
Hello Charlles the diallist, The design of such a dial is not as easy as I originally thought in my midnight lucubration. On the celestial sphere, these altitude lines are parallel to the horizon. As Daniel Wenger pointed out, it is possible to define these lines and tell twilight times on a spherical dial such as his. Projected onto the plane of a vertical dial, the altitude lines are the usual complex hyperbolic curves as typified by declination lines. It can be done but I do not see a simple general solution. Each site would be a unique design. By contrast, Italian hours have an elegant simplicity in showing the time until sunset. No longitude or Equation of Time corrections are required as the shadow tracks the actual path of the sun. The mathematical complexity remains hidden. > >I've always been confused about when the three twilights begin and end. My >best guess is that the order is: > >(1) Astronomical twilight begins (altitude = -18 deg) >(2) Nautical twilight begins (altitude = -12 deg) >(3) Civil twilight begins (altitude = -6 deg) >(4) Sunrise (altitude = 0 deg) >(5) Sunset (altitude = 0 deg) >(6) Civil twilight ends (altitude = -6 deg) >(7) Nautical twilight ends (altitude = -12 deg) >(8) Astronomical twilight ends (altitude = -18 deg) > The twilight definitions are as outlined in Bowditch "American Practical Navigator: An Epitome of Navigation". The "Explanatory Supplement to the Astronomical Almanac" uses the zenith rather than the horizon as the reference datum. The different definitions mean the same thing to me. "Civil twilight ends in the evening and begins in the morning when the center of the Sun reaches a zenith distance of 96 degrees. Nautical twilight begins or ends when the Sun reaches a zenith distance of 102 degrees. Astronomical twilight begins or ends when the Sun reaches a zenith distance of 108 degrees. Sunrise and set are generally defined as the instant of the first or last crack of sunlight at the horizon. According to ref #2, "The calculated times of sunrise and sunset are based on the Sun having a geocentric zenith distance of 90 degrees 50 minutes (34 minutes is allowed for horizontal refraction... and 16 minutes is allowed for semi-diameter). There is no dip correction included in these calculated times. The Italian hour sundial is based your definition with the center of the sun having a true altitude of zero. The times are generally not corrected for refraction or semi-diameter. The apparent sun at time will appear to be one full diameter above the horizon. The confusion based on different definitions offers an opportunity. Think of the bar bets that could be won by carefully choosing your reference. Personally I prefer the definition of twilight time made popular by the Platters in 1958. "Heavenly shades of night are falling, its twilight time.." Cheers, Roger Bailey Walking Shadow Designs N 51 W 115
