On a plane surface, a straight line is defined as "the shortest distance between two points. The direction from one point to another may be measured by using an ordinary protractor to determine the angle which the line makes with the rectangular reference lines.
The shortest distance between any two points on the surface of the earth is always along the great circle between them. The more closely the plane of a small circle approaches the center of the earth, the more closely will distance measured it approach the shortest distance. It is also true course.
A great circle is the shortest distance between two points on the surface of a sphere, the practical objection to following a great-circle is that the direction of a great circle is constantly changing; it makes different angle with each meridian it crosses from starting point to destination. This means that the ship's heading on a great-circle would be subject to continuous alterations.
For practical purposes, a rhumb line can be defined as a line which crosses every meridian of the sphere at the same angle. A ship may maintain a true heading without change from starting point to destination if one disregards factors such as currents, wind, changing magnetic variation. A navigator is concerned with both great-circle distances and rhumb-line distances. Except for a few special cases where they are the same, great-circle distances are shorter than rhumb-line distances, the difference depends on various combinations of latitude and longitude.
The equator is also a rhumb line, with a constant direction of 090° or 270°. Along the equator, then, great-circle distance and rhumb-line distance are identical there is no difference at all.
As a ship moves farther from the equator toward either pole, the saving in distance by great circle becomes greater, and is always greatest for east-west courses (090° or 270°).
All meridians are great circles they are also rhumb lines of constant direction, 000° or 180°. The difference begins to increase as the great-circle direction moves away from the north-south direction, reaching a maximum in an east-west direction.
Near the equator the saving in distance by way of a great circle is negligible. For an east-west distance of 1,000 nautical miles, the saving is only about 1.5 miles at latitude 40°, and 10.5 miles at latitude 60°.
Great-circle distances are sometimes computed, rather than measured on the chart. In this case, they are obtained in degrees and minutes of arc. As is true of any great circle (such as a meridian), one degree of arc is equal, for practical navigational purposes, to 60 nautical miles, and 1 minute essentially equals 1 nautical mile.
There are two kinds of direction, both of which are of interest to the navigator:
Rhumb-line directions are most commonly used in determining the course to be followed, or the track made good.
Great-circle directions are used chiefly in connection with radio direction finding or star sights, and are generally referred to as bearings or azimuths.
In navigation, true direction is the direction from one point on the earth's surface to another, without regard for the distance between them; it is expressed as an angle in degrees from 000° to 360°, referenced to true north. Direction is always expressed in three digits; for example, a direction 8° east of north is expressed as 008°, and one 34° east of north as 034°. True north may be considered as either 000° or 360°, according to the problem at hand.
Certain terms are used in navigation. A few that have I have already mentioned, with several related ones, will be mention here, with commonly used abbreviations and symbols.
Azimuth (Zn). The great-circle direction of any place or object from a given point; used to designate the direction of a heavenly body in celestial navigation. When referred to true north, azimuth is written as Zn. Azimuth angle (Az or Z) is measured either east or west to 90° using either north or south as the reference direction.
Bearing (B). Same as azimuth, but used in radio direction finding, or in visual sights. Azimuths and bearings (or any other directional term) may be true, magnetic, compass, or relative, according to the reference line or point used.
Course (C). As applied to marine navigation, the direction in which a vessel is to be steered, or is being steered; the direction of travel through the water. Course may be designated as true, magnetic, compass. The course is measured from 000° clockwise from the reference direction to 360°.
Heading (Hdg.) The direction in which a ship points or heads at any instant, expressed in angular units, 000° clockwise through 360°, from a reference direction. The heading of a ship is also called ship's head. Heading is a constantly changing value as a ship oscillates or yaws across the course due to effects of the sea and of steering error.
Track (TR). The intended (anticipated, desired) direction of movement with respect to the earth.
Course Over Ground (COG). The actual path of a vessel with respect to the earth; this will not be a straight line if the vessel's heading varies as she yaws back and forth across the course.
Course Made Good (CMG). The single resultant direction from a given point of departure to a position. Mile. The unit of distance used in navigation at sea is the international nautical mile (n.mi.) of 6076.1 feet. In practical terms, it is equivalent to one minute of latitude, or one minute of arc of any great circle. The statute mile (st. mi.) of 5280 feet is used on land and some inland U.S. waters such as the Great Lakes and the Intracoastal Waterways. One nautical mile equals approximately 1.15 statute miles. A nautical mile and 2,000 yards are often used the error is only 1 1/4 percent.)
Knot (kn, or occasionally kt). The unit of speed; one knot equals one nautical mile per hour. It is incorrect to refer to speed as knots per hour.
Latitude, the arc distance of a point measured from the equator toward either pole. In problems involving latitude at two or more points, latitude of the first point is usually written as L1 second point L2, difference of latitude between two places is indicated by l, mid-latitude (the mean latitude) is indicated by Lm.
Longitude the angular distance along the equator or a parallel between the prime meridian at Greenwich and the meridian of a particular point. In problems involving the longitude of two or more points, the longitude of the first point is written as Lo1 the second point as L02. The east-west of two points is difference of londitude (DLo) or as departure (p) when in nautical miles.
