A great circle route to Cape VerdeJul 27, 2007
Nineteen-seventy-six was a good year. I had a wonderful girlfriend, a dog, a car, my own business, and if that wasn't enough, it was also the year I made my first of two trans-Atlantic passages.
The boat was a Rhodes 70-footer called Mockingbird, bound from City Island, N.Y., to Portland, Maine, and then on to Cape Verde in western Africa and eventually MÃ¡laga on the south coast of Spain. I was hired as deckhand for $35 cash a day and a plane ticket home. Not bad wages for adventuring. To be honest, I was being overpaid. I may have been enthusiastic, but I was as dumb as a post when it came to knowing my way around a sailboat. And by the time the passage was over (a month later), I found that all I really learned was that under no circumstances would I ever go offshore again with people I didn't know. But that is another story.
The navigation equipment aboard was state of the art for the time: a Loran C that never worked, an RDF and a sextant. Fortunately the navigator, a former Navy man, knew what he was doing. I still remember how fascinated I was when he pulled out a gnomonic chart of the North Atlantic and laid out the great circle route from Portland to Cape Verde. It was my first serious introduction to offshore navigation, and I spent most of that passage reading Bowditch, which I didn't understand, and pondering concepts like time zones and the celestial sphere.
Now, for many sailors calculating great-circle distance is moot. Most of us are sailing routes that are too short or in a northouth direction (each meridian is a great circle) so as to make the difference between a rhumb line and a great circle negligible. Not to mention the fact that one rarely is able to follow a projected course exactly, especially on a sailboat.
Those with celestial computers already know that they can compute great circle distance and an initial course, but that method is cold and leaves the user with no understanding of what is actually being computed.
First we need some definitions. A great circle is defined as a line whose plane passes through the center of the earth. It follows that every meridian (longitude) is a great circle, but that only the equator is a great circle of latitude.
To plot a great circle, a gnomonic projection is used. This converts a curved line on the earth's surface to a straight one. If one were to plot a great circle track on a mercator projection, it would consist of a curved line and would be very tiresome to plot. A great circle route in practice is a collection of rhumb lines between waypoints laid out on a mercator chart, which is why one needs to make frequent course changes to follow the course. The great circle chart enables the navigator to derive the first course to follow, which is updated as the voyage progresses.
In order to find out great circle distance, one can use the sight reduction tables in HO 249 or HO 229. This method requires that the latitude and longitude of the departure be called the assumed position. The latitude and longitude of the destination is labeled the geographical position. The difference in longitude is the LHA. The initial course becomes the Z or Zn, depending on the specific case, and the great circle distance is the zenith distance. The latitude of the destination becomes the declination.
As in all celestial navigation problems, we are solving for the distance and direction from the assumed position to the geographical position. All we are doing now is substituting terrestrial positions for celestial ones.
One note: Since HO 249 has declinations that only go to 29 , if the latitude of your destination is greater than that, you must use HO 229. Remember that in this method latitude of destination equals declination.
A: What is the great circle distance between Portland Head Light (43 37' N, 70 12' W) and the light at Cape Verde (14 43' N, 17 31' W)?