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A1 - - - RHUMB LINE SAILING - - - 10/03/2004

A line which maintains the same angle with respect to true north, (it also maintains the same angle crossing all meridians) is called a rhumb line. When traveling along a rhumb line it would appear (over a short distance) that you were traveling in a straight line, but the path is actually a curve, and if extended it will eventually spiral in on the North or South pole. (Except for the case where the direction is exactly East or West.)

The graphical Mercator sailing involves plotting your location and destination on a Mercator chart or Mercator plotting sheet, drawing a line between the positions and then measuring with a protractor to determine the course angle. This is the easiest method but if the distance is large both points may not fit on the same chart or plotting sheet, so a calculated course will be required.

The length of a degree of longitude (approximately 60 nautical miles at the equator) is proportional to the cosine of the latitude on a spherical earth, but when traveling at an oblique course angle the latitude is continuously changing and the relationship between change of longitude and East-West distance is more complex. As an approximation, the middle latitude is used as follows.

When sailing from point 1 (L1, LO1) to point 2 (L2, LO2)

C   = course angle
D   = distance traveled along the course
Lm  = ((L1+L2) / 2) = mid latitude
Ld  = ( L2-L1 ) = difference in latitude   (degrees)
DLO = difference in longitude   (degrees)

      tan C = ( DLO * cos Lm ) / Ld

          D = 60 * ( Ld / cos C )    (nautical miles)

This method can only be used on one side of the equator. When crossing the equator the parts North and South of the equator are calculated separately and the middle latitude is replaced by the half latitude of each of the locations.

When L1 is greater than L2, then the angle C will be negative (fourth quadrant). To put the answer into the second quadrant add 180 degrees.

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