NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
The pedant's rhumb-line.
From: George Huxtable
Date: 2002 Oct 10, 20:31 +0100
From: George Huxtable
Date: 2002 Oct 10, 20:31 +0100
Every now and again, rhumb-lines appear as a topic on this list. Most list-members are aware that wherever you start from on the Earth, with whatever course, if you keep following a rhumb line (constant course), you will end up spiralling into one or other of the poles. You will have made a number (perhaps an infinite number?) of turns, in longitude, to get there, but will have travelled (in general) a finite distance. Navigators frequently ask for the rhumb-line course from A to B. Here I wish to display my pedantry by insisting that there is not just one rhumb-line course between A and B, but many (perhaps an infinite number?). The one required by the navigator is the SHORTEST rhumb-line course. This can be illustrated by a simple example. Take a navigator on the equator at position A, long = 0 degrees. What is his rhumb-line course and distance to a destination B, lat 10 deg North, long 0 deg.? The obvious answer is a course of zero degrees, which happens to be identical with the great-circle in this case. But what if he sets off from A with a course of about 88.4 degrees, that is, slightly North of due East, and holds that course? Well, that's a rhumb line, also, which will also take him to B (or it would if no continents got in the way), but he has to go Eastwards, right round the world, to get there. Similarly, a course of about 271.6 degrees will also take him round the world to B, but Westwards. He could set off with a course even closer to due East, roughly 89.2 degrees, and if he sticks to that while making two whole circuits of the Earth it will take him to B. Again, there's another corresponding rhum line Westwards. Other courses, progessively closer still to due East or West, would take him to B after 3, 4, or more circuits of the Earth, right up to infinity. What's the practical importance of this? None whatsoever. I am just pointing out that these alternative, but quite impractical ways of getting from A to B are all genuine rhumb lines between A and B, and each fully meets the definition of a rhumb line. There is no unique rhumb line. The only rhumb line that's of any practical significance, however, is the shortest rhumb line. Just something to ponder over on a quiet watch. George Huxtable. ------------------------------ george@huxtable.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel. 01865 820222 or (int.) +44 1865 820222. ------------------------------