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Mercator Sailing: Course and Distance
08-26-2018, 12:30 AM
Post: #6
RE: Mercator Sailing: Course and Distance
"a bit of calculus"??? Your math skills are far better than mine. It looks like you are calculating the distance directly from the ellipsoid and not from the map projection. I did remember of another way to solve the course and distance on an East-West line for pt 1 and pt 2. This was on a old forum. This person said to create a third point mid-longitude between the two points, but with a latitude well above the two points. Then calculate the course and distance from pt 1 to pt 3 and from pt 3 to pt 2. He then added the vectors to give him the course and distance from pt 1 to pt 2. I need to think about this East-West issue some more.

Regarding the WGS84 ellipsoid, it certainly makes sense to use a more modern ellipsoid that is used by GPS, but this is a Mercator Sailing program. The WGS84 ellipsoid seem more like Rhumb-line sailing. Regarding the accuracy of the author's equation, I did find a more accurate meridian part equation from an on-line Mercator calculator's site. I don't know if it is Clark's ellipsoid of 1866, but it closely resembles the author's equation.

Calculator Afloat equation
Meridinal Part 1 = 7915.7045*LOG(TAN(45+Lat1/2))-23.2689*SIN(Lat1);

Online Mercator equation
Meridinal Part 1 = 7915.704468*LOG(TAN(45+Lat1/2))-23.268932*SIN(Lat1)-0.052500*(sin(Lat1))^3-0.000213*(sin(Lat1))^5;

I think I need to keep this program simple and stick with the Mercator sailing equations. I can add a more user friendly input and provided a output that give some intermediate results in addition to the course and distance. I can also adjust the program to handle equatorial crossings (m=M1+M2, but adjusted for direction) and 180 deg meridian crossings. I not sure what I will do about East-West courses. But first, I will take a break from programming and maybe read more on Rhumb-line sailing.
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RE: Mercator Sailing: Course and Distance - Gene222 - 08-26-2018 12:30 AM

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