Mercator Sailing: Course and Distance

[Gene222]

"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.