Great circle sailing
A course represented by a straight line on a Mercator chart is called a rhumb line and for short voyages sailing along such a line between the port of departure and that of arrival makes a minimal difference.
In order to find the shorter route for a longer passage, the same straight line will have to be drawn on a gnomonic chart, which uses a different projection with meridians converging at the poles and parallels of latitude represented by curved lines. Any straight line on a gnomonic chart is part of a great circle and is the shortest distance between the two points joined by that line.
A Great Circle is a circle whose plain intersects with the centre of the Earth. So there already are two kinds of natural Great Circles drawn on all our maps: 1- the Equator 2- all Meridians of Longitude. A great circle would effectively cut the whole earth in half.
if you are sailing in North-South directions, a Great Circle route is not necessary to be calculated, as you follow it anyway when sailing along a meridian of Longitude. Same applies if you are sailing around the equator. The differences are biggest in long East/West passages in high latitudes
Because gnomonic charts can not be used for navigation, the great circle chart drawn on such a chart has to be transferred to a Mercator chart. This is done by making a note of the latitudes at which the great circle route intersects successive meridians which have been selected at convenient intervals, usually at 5 degrees.
These positions are transferred to the correponding Mercator chart and joined by straight lines. This succesion of rhumb lines approximates very closely the actual great circle track for that route.
When you plot your course on the chart as a rhumb or straight line – you must then also plot the great circle course and double check that there are no hazards along that track. The problem with hitting an iceberg is also a consideration.
To avoid the danger of sailing high latitude, which is normally associated with bad weather and icing, a careful navigator will normally set a latitude limit on his ocean passage plan. The ocean passage will thus consist of a first great circle track with vertex at the latitude limit then sailing along that latitude until meeting the vertex of a second great circle track leading to the destination. This type of route is named as composite great circle route.
The easiest method to outline a composite greate circle route is by plotting it on a Gnomonic chart.
All this is taken care now by GPS, which gives both the great circle course and distance to the next destination with the added advantage of these values being constantly updated. However ,GPS only does this when one is allready underway. Therefore, for planning purposes one should obtain either a gnomonic chart or a software programme for a computer.