Cartography Word of the Day: Loxodrome

Third in an irregular series

1320051029loxodrome.jpgA loxodrome, or line of constant bearing, between New York and London, plotted on a Mercator’s projection world map (base map courtesy Cartographic Research Lab, University of Alabama)

The word loxodrome is defined by the 3rd edition of Robinson, Sale, and Morrison’s Elements of Cartography as “a line of constant bearing”, bearing here meaning a compass direction. In the example above a mariner or pilot, setting their bearing at approximately 39.6 degrees north of true east and starting from New York should eventually reach some point near London weather and seas not withstanding.

The word itself stems from the Greek roots loxo (meaning slanting), and dromos (meaning course), which is certainly what our pilot is following when plotted on the map above. Consequently, latitude and longitude lines, while strictly speaking loxodromes, are not usually regarded as such, regarded as special cases.

Constand bearing means constant; referring to the illustration it can be seen that the loxodrome cuts all lines of latitude at the exact same angle. This is the principal benefit and use of the Mercator projection–it enables navigators to plot loxodromes as straight lines, simplifying course plotting. Naturally, since the plot is made on a flat distortion of a curved surface, while simple to plot it’s actually longer; the great circle (discussion to come) is actually the shortest course, and navigation for planes and ships is actually a combination of the two concepts.

Moreover, only on the Mercator does a loxodrome appear as a straight line; plot a loxodrome on any other projection and you have a curve. Plotting it on a globe renders a 3-dimensional spiral; plotting it on a polar projection gives a logarithmic spiral.

Loxodromes are also known as rhumb lines.

Sources:

  • Elements of Cartography, 3rd Ed., Robinson, Sale, Morrison; Wiley & Sons, New York-1978
  • http://www.thefreedictionary.com/loxodrome (The Free Dictionary)
  • http://mathworld.wolfram.com/Loxodrome.html (Mathworld)