A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2013 Dec 29, 13:30 -0800
A good approximation, which has more accuracy than The estimate of The angle, ( unless you actually measure The angle with a sextant) is to use 3600 instead of 3438, it's easier to do The math in your head.
If you are using binoculars with a mil reticle The math is even easier. Just divide The kmown height of The object by The number of mils it subtends and then multiply by a thousand.
From: Frank Reed <FrankReed@HistoricalAtlas.com>;
Subject: [NavList] Re: Getting ready for a spring demo...
Sent: Sun, Dec 29, 2013 8:55:03 PM
Hi Greg, you wrote:
A little problem there! You calculated the tangent of 0.016666 "radians" which is equal to 57.3 minutes of arc. So the actual difference in height corresponding to a tilt of 1 minute of arc is 57.3 times smaller than that.
Also, you don't really need trig functions for this. Just remember the magic number: 3438. One minute of arc is a ratio of 1-to-3438 when comparing distance across the line of sight to distance out. So a one minute of arc tilt in a 72 inch board is 72/3438 or 0.02 inches.
Another 3438 example: Suppose you're looking at a little boat far in the distance that you know is 20 feet long, and if you measure its angular size to be 1.0 minutes of arc, then you know its distance away from you is 3438*20 or nearly 69000 feet or just about 13 miles. Anytime you're dealing with angles less than a degree (and even less than 10 degrees with increasing inaccuracy), you almost never need a trig function.
Of course, that's not really a magic number. That 3438 simply converts angles as pure ratios (also known as "radians") to minutes of arc and it is exactly equal to 180*60/pi. It's so handy for quick estimates of angles and distances that you really should just memorize 3438.
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