geographic range 1.144 vs 1.17
Posted by nireves@reddit | sailing | View on Reddit | 6 comments
What is the reason John Rousmaniere uses 1.144 as his multiplier for geographic range instead of 1.17? In The Annapolis Book of Seamanship, 4th ed, Rousmaniere uses 1.144 in his formula for finding the visible range of an object given a height of the object. Any ideas?
nireves@reddit (OP)
Thanks for the informative replies. Does the USCG use 1.17 in its exams? When I look at the Geo Range table at the front of the Light List the numbers seem to work out using 1.17, and when I look at YT videos that are about prepping for the USCG exams, they mostly use 1.17. I'd hate to make a simple error when I sit for the OUPV exam.
MissingGravitas@reddit
Bowditch uses 1.17, so I'd stick with that.
Ironically it also refers to the US survey mile which NIST and NOAA finally got around to retiring a few years back. (The difference compared to the US statute mile is only about 3mm, so only matters over significant distances.)
MissingGravitas@reddit
A purely geometric calculation would give "d ≈ 1.06√h" where h is the height in feet and d is the distance in nautical miles.
Derivation: (2 x 3444 NM) / 6076 ft = 1.336, the root of which is 1.064
However, since Earth has an atmosphere you apply an 8% correction for refraction, and 1.06 + 8% gets you 1.1448. The exact correction would vary based on atmospheric conditions, which is likely the reason for the variation.
nireves@reddit (OP)
Excellent analysis and explanation. Thanks!
Mythurin@reddit
Best answer. Always taught 1.06 for LOS, perfect flat world with no atmosphere distortions.
Radar horizon, 1.23 still works quite well also.
flyingron@reddit
Most people use 1.17 to go from square root of the observer height in feet or 2.08 in meters to convert to nautical miles of range. The discrepancy here is most likely due to using a different value for the diameter of the earth. This is always going to be an approximation because the earth is not a sphere. Even if you use one of the ellipsoid models, the diameter in the polar direction is different than in an equatorial one. And it still isn't right as the earth isn't even an ellipsoid but an oblate spherioid.