A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2014 Oct 22, 14:48 -0700
Greg, you wrote:
"I saw the formula: 0.565 X Height IN FT / MIN OF ARC = NM. It seems to work quite well."
Yes, it does. To remind you, the key relationship for small angles in minutes of arc is
(angular size in m.o.a.) = 3438·(actual size)/(distance off).
You can solve this for any of the three "unknowns" when the other two are given. For example, given that the angular size of the Sun is 32' and the distance to it is 93 million miles, you can solve for the Sun's actual size. What do you get? You never need anything else for angular sizes when the angle is smaller than a couple of degrees. That "magic number" 3438, as we've discussed before, is just 180·60/pi (and if you want more than four digits accuracy, you can just plug that factor (180·60/pi) into a calculator. The "actual size" and "distance off" in this relationship are in the same linear units, both in feet or both in meters or both in nautical miles, for example. The version you've listed here is adjusted for different units, specifically actual size in feet and distance off in nautical miles. You can verify that it's the same thing by dividing 3438 by the number of feet in one nautical mile. What do you get? The point of all this is that you do not need to collect every formula you see. In fact, even the 3438 is a bit of a crutch. The fundamental relationship is that an angle is just a ratio. The angular size of anything (in the small angle limit) is the distance across the line of sight divided by the distance out. Multiplying by 3438 simply converts that to familiar minutes of arc.
In your first message on this topic, you also compared the various tables for dip short to "opinions". I realize you were just kidding, but you should find that they do all actually agree on the numerical values and differ only in layout and maybe the number of digits after the decimal point. There is little ambiguity in this problem. If you find a table that really seems different, don't use it until you understand why it's different.