A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Feb 13, 18:50 -0800
John Howard, you asked:
"How can ZD ever be negative? If the horizon is 0° and overhead is 90° then ZD is the angle from overhead to the sun or star - positive."
Yes, naturally when you do the calculation for zenith distance which is 89°60'-corrected altitude (or nearly enough 89°48'-raw altitude under many circumstances), you will get a positive number. It's always positive. But you could be facing in either direction when you take the noon sight. South of the Tropic of Capricorn, you'll be facing north every day at noon. North of the Tropic of Cancer (like in waters offshore of New England, near me), you're facing south every day at noon. Between the tropics, the direction you're facing at noon depends on the date and you need to remember to take note of your shadow when you make your observation. In general with a noon Sun sight, or with any meridian observation for latitude, it's not enough to record the altitude and then calculate the zenith distance. You also need to take note of which way you're facing. And I recommend doing this by noting which way your shadow is pointing. Just look at the deck, and make a mental note: shadows point north, or shadows pointing south. Then the rule for the sign that you will affix to the zenith distance --it's a separate step! ...after the subtraction-- will obey the same rules as the signs for latitude and declination. If your shadow points north, your z.d. is a positive number (no change after doing the subtraction). If your shadow points south, you slap a minus sign on the z.d. because south is always negative. It's a separate step after the subtraction, as it must be, since it's a separate component of the observation itself. Then the calculation proceeds as it always does:
Lat = z.d. + Dec.
If you teach latitude by noon Sun to groups studying for USCG exams or any groups using the drudgery of the late 20th century catechism, you'll run into a potential communications barrier. There may be confusion between Z.D. for "Zone Descriptor" and Z.D. for "Zenith Distance". It should be obvious by context. How could you confuse them? But all students are different. Depending on the group, a simple solution is to write it out a bit longer using, e.g., "zen.d." for zenith distance. It's easy to say, and who doesn't like things that are "Zen"? That beautifully simple noon rule then read Lat = Zen.d. + Dec.