Mercator Sailing: Course and Distance
08-28-2018, 12:46 AM (This post was last modified: 08-28-2018 02:45 AM by Gene222.)
Post: #8
 Gene222 Member Posts: 125 Joined: Feb 2015
RE: Mercator Sailing: Course and Distance
Regarding the equation for meridional parts, I saw a August 2012 forum on gcaptain.com. Students were discussing how to solve a Mercator Sailing problem with the moderators in preparation for their maritime license exam. What was interesting was that they were calculating the merdional parts using table 6 in Bowditch. They said that in the explanation of the merdional parts tables in the 1975 edition of Bowditch, the meridional parts were based on the Clarke spheroid of 1866, while in the 2002 edition of Bowditch, the meridional parts were based on the WGS ellipsoid of 1972. What I got out of this was that Bowditch was an authoritative reference on determining the merdional parts for Mercator Sailing and it explains how the meridional parts are calculated.

Bowditch is short for American Practical Navigator, originally by Nathanial Bowditch and published by the National Geospatial-Intelligence Agency, Springfield, Virginia. Bowditch was first published in 1802. On page 2 of Volume 2 of the 2017 edition of Bowditch, the formula to calculate the merdional parts is

M = a ln(10) log tan (45 + L/2) - a (e^2 sin L + e^4 / 3 sin^3 L + e^6/5 sin^5 L ...

(You really need to see this in textbook mode to make sense of it)

a is the equitorial radius of the earth expressed in minutes of arc of the equator = 3437.74677078.

ln(10) is 2.3025851

L is the latitude

f is earth's flattening = 3.35281066475*10^(-3)

e^2 is 2f - f^2 = 6.694379990141*10^(-3)

where the constants are based upon the World Geodetic System 1984 (WGS84). Plugging in the constants, they show

M = 7915.7 log tan(45deg + L/2) - 23.01358319 sin L - 0.05135389 sin^3 L - 0.00020627 sin^5 L ...

For reasons unknown, they rounded the first constant. If you multiply a ln(10) using their numbers, you get

M = 7915.70446787 log tan(45deg + L/2) - 23.01358319 sin L - 0.05135389 sin^3 L - 0.00020627 sin^5 L ...

This is the formula that should be used to calculate the merdional parts for Mercator Sailing, and it is based on the WGS84 ellipsoid. I never seen the expression - 0.05135389 sin^3 L. Is that the same -0.05135389 sin (L)^3 or -(0.05135389 sin L)^3?
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 Messages In This Thread Mercator Sailing: Course and Distance - Eddie W. Shore - 08-10-2018, 03:08 AM RE: Mercator Sailing: Course and Distance - PedroLeiva - 08-10-2018, 11:23 AM RE: Mercator Sailing: Course and Distance - Dieter - 08-12-2018, 05:13 PM RE: Mercator Sailing: Course and Distance - Eddie W. Shore - 09-22-2018, 11:37 PM RE: Mercator Sailing: Course and Distance - Gene222 - 08-24-2018, 07:21 PM RE: Mercator Sailing: Course and Distance - Dieter - 08-25-2018, 06:08 AM RE: Mercator Sailing: Course and Distance - Eddie W. Shore - 09-22-2018, 11:39 PM RE: Mercator Sailing: Course and Distance - Gene222 - 08-26-2018, 12:30 AM RE: Mercator Sailing: Course and Distance - Dieter - 08-26-2018, 07:18 AM RE: Mercator Sailing: Course and Distance - Albert Chan - 09-10-2022, 03:17 PM RE: Mercator Sailing: Course and Distance - Gene222 - 08-28-2018 12:46 AM RE: Mercator Sailing: Course and Distance - Dieter - 08-28-2018, 08:53 AM RE: Mercator Sailing: Course and Distance - Dieter - 08-28-2018, 04:49 PM RE: Mercator Sailing: Course and Distance - Gene222 - 08-29-2018, 09:02 PM RE: Mercator Sailing: Course and Distance - Dieter - 08-30-2018, 05:49 AM RE: Mercator Sailing: Course and Distance - Gene222 - 08-30-2018, 11:59 PM RE: Mercator Sailing: Course and Distance - Gene222 - 08-31-2018, 02:15 AM RE: Mercator Sailing: Course and Distance - Dieter - 08-31-2018, 05:46 AM RE: Mercator Sailing: Course and Distance - Dieter - 09-01-2018, 05:51 AM RE: Mercator Sailing: Course and Distance - VadimV - 12-21-2022, 08:31 PM RE: Mercator Sailing: Course and Distance - Gene222 - 09-01-2018, 02:52 AM RE: Mercator Sailing: Course and Distance - Gene222 - 09-02-2018, 04:03 PM RE: Mercator Sailing: Course and Distance - Dieter - 09-02-2018, 06:27 PM RE: Mercator Sailing: Course and Distance - Gene222 - 09-03-2018, 10:10 PM RE: Mercator Sailing: Course and Distance - Dieter - 09-04-2018, 07:19 PM RE: Mercator Sailing: Course and Distance - Gene222 - 09-05-2018, 05:46 PM

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