Middle-latitude sailing - mid-latitude sailing, combines plane sailing and parallel sailing. Plane sailing is used to find difference of latitude and departure when course and distance are known, or vice versa. Parallel sailing is used to interconvert departure and difference of longitude. The mean latitude (Lm) is normally used for want of a practicable means of determining the middle latitude, the latitude at which the arc length of the parallel separating the meridians passing through two specific points is exactly equal to the departure in proceeding from one point to the other. The formulas for these are:
DLo=p sec Lm p=DLo cos Lm.
The mean latitude (Lm) is half the arithmetical sum of the latitudes of two places on the same side of the equator. The mean latitude is labeled N or S to indicate whether it is north or south of the equator. If a course line crosses the equator, that part on each side (the north latitude and south latitude portions, should be solved separately.
This sailing, like most elements of navigation, contains certain simplifying approximations which produce answers somewhat less accurate than those by more rigorous solutions. For ordinary purposes, the results are more accurate than the navigation of the vessel using them. From time to time suggestions have been made that a correction be applied to eliminate the error introduced by assuming that the meridians of the point of departure and of the destination converge uniformly (as the two sides of a plane angle), rather than as the sine of the latitude. The proposed correction usually takes the form of some quantity to be added to or subtracted from the middle latitude to obtain a "corrected middle latitude" for use in the solution.
