A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Jun 21, 15:26 -0700
David C, you wrote:
"My explanation is (dec ~ lat) = mod(dec - lat)"
Nearly so. Looks like you just typo-ed this. What you meant to write was:
(dec ~ lat) = abs(dec - lat).
The tilde notation in navigation math was created at a time when algebraic signs on numbers were still counted as too alien for mariners. They used rules based on the names of angles, north or south in this case. The meaning of the tilde operation was "subtract the smaller from the larger if of the same name and add if of different names". Today, you can assume algebraic signs are well-known and treat dec and lat as positive if north and negative if south. Then calculate the difference dec-lat always and take the absolute value (meaning, if the result is negative, you drop the sign).
PS: Tilda displaying meaning...