Long range segments are more difficult to measure than short ones. Long range navigation involves following a great circle which is not a straight line. This problem is solved by breaking the curved line into numerous straight segments. The following are the mathematical formulas for calculating great circle distance and direction. Since the lines of longitude are approximately parallel, a straight line would be a line that crosses all the lines of longitude at the same angle.
Straight lines make the plotting and tracking simple.
On a sphere, where the meridians are converging at the poles, a rhumb line will form a spiraling curve that eventually ends at either of the Earth's poles. The adjacent illustration demonstrates the spiral created by a rhumb line. The spiral that is created by a rhumb line is a Loxodromic Curve or a Loxodrome . Since a loxodrome is not a great circle , it follows that by tracking a loxodrome a longer distance must be traveled compared to a great circle line. A great circle is a circle on a sphere's surface whose plane is passing exactly through the center of the sphere.