Online rhumb line calculations using the RhumbSolve utility

Rhumb Line calculation:
    lat1 lon1 lat2 lon2 → azi12 s12
    lat1 lon1 azi12 s12 → lat2 lon2

Input (ex. «40.6 -73.8 49°01'N 2°33'E» [inverse], «40d38'23"N 073d46'44"W 53d30' 5850e3» [direct]):
   

Output format:    
Output precision:  
Equatorial radius: meters
Flattening:

Select action:
   

Rhumb Line (input in black, output in blue):

    ellipsoid (a f) = 6378137 1/298.257223563 (WGS84)
    status          = 

    lat1 lon1 (°)   = 
    lat2 lon2 (°)   = 
    azi12 (°)       = 
    s12 (m)         = 

    S12 (m^2)       =

RhumbSolve (version 2.4) performs rhumb line calculations for an arbitrary ellipsoid of revolution. The path with a constant heading between two points on the ellipsoid at (lat1, lon1) and (lat2, lon2) is called the rhumb line (or loxodrome); its length is s12 and the rhumb line has a forward azimuth azi12 along its length. NOTE: the rhumb line is not the shortest path between two points; that is the geodesic and it is calculated by GeodSolve.

There are two standard rhumb line problems:

Latitudes and longitudes can be given in various formats, for example (these all refer to the position of Timbuktu): 
        16.776 -3.009
        16d47' -3d1'
        W3°0'34" N16°46'33"
        3:0:34W 16:46:33N
Azimuths are given in degrees clockwise from north. The distance s12 is in meters.

The additional quantity computed is:

The ellipsoid is specified by its equatorial radius, a, and its flattening, f = (a − b)/a, where b is the polar semi-axis. The default values for these parameters correspond to the WGS84 ellipsoid. The method is accurate for −99 ≤ f ≤ 0.99 (corresponding to 0.01 ≤ b/a ≤ 100). Note that f is negative for a prolate ellipsoid (b > a) and that it can be entered as a fraction, e.g., 1/297.

RhumbSolve is accurate to about 15 nanometers (for the WGS84 ellipsoid) and gives solutions for the inverse problem for any pair of points. The longitude becomes indeterminate when a rhumb line passes through a pole, and this tool reports NaNs (not a number) for lon2 and S12 in this case.

RhumbSolve, which is a simple wrapper of the GeographicLib::Rhumb class, is one of the utilities provided with GeographicLib. This methods are described in C. F. F. Karney, The area of rhumb polygons, Stud. Geophys. Geod. (2024); DOI: 10.1007/s11200-024-0709-z.

Charles Karney <karney@alum.mit.edu> (2022-04-10)
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