This article was published in the March 1988 issue of Cruising Helmsman.
With the advent of electronic gadgetry, which gives instant answers, the great circle is in vogue. Mike Pepperday shows that for the cruising yachtsman, the great circle is not appropriate.
Nowadays even ordinary people have heard about great circles. If you fly between North America and Europe chances are you'll be on the great circle route. This is the track near or over the arctic which is followed, not for the fine scenery, but because it's the shortest way.
Ships follow great circles too, saving time and fuel. They have been doing so for a hundred years. In the past the question of great circle sailing for yachts hardly arose because the calculations were too much trouble. Recently the complications have been taken care of by features on artificial positioning equipment and celestial navigation computers. Now, at the push of a button, anyone can compute great circles.
Instead of steering according to the straight line on the chart-the mercator route, or "rhumb line" - you tell the computer the latitude and longitude of the start point and of the destination and computer tells you the great circle course. Unlike the rhumb line, the great circle changes course continuously throughout its length. No problem: at any desired position the computer gives the great circle course at that point. A miracle of modern science.
Nobody wants to go the long way so great circles are in. A friend tells me he recently followed the great circle across the Tasman from New Zealand to Sydney. Instead of drawing the rhumb line on the chart and reading off the course, the computer gave him the great circle starting course and then, every day or whenever he had a new fix, the computer told him his new heading. On the 1000 mile voyage he saved 1.9 miles. Another chap I know was proud of diligently following the great circle for about 1000 miles of a trip from Perth to Bali. He shortened his trip by about a hundred metres.
Does that mean all great circles are nonsense? What about those dramatic differences in the problems you solved with so much sweat during that ocean navigation course? Let's see now... Yokohama to San Francisco: mercator 4570 miles, great circle 4330 miles. That's more like it: 240 miles to saved. Unfortunately it is no way to cross the Pacific. The shortest route for a sailing vessel is to stand ENE to about latitude 42°N, then sail nearly due east until about 1000 miles from North America. That's where the wind and current are favourable. The great circle takes you too far north.
And that is typical. For sailing vessels the route which is fastest depends mainly on wind and current. If that coincides with a great circle, fine - but in those cases where there is any meaningful difference from the mercator, it seldom does. The question is-before things get too confusing - in what circumstances, exactly, is great circle significantly shorter and how do those routes look for sailing vessels?
A great circle is the most direct line between two points on the surface of a sphere. If you stretch elastic between two points on a model globe the elastic will indicate the great circle track between them (given no friction). A great circle is that track which, if you extended it to encircle the globe completely, would cut the world in half - that is, into two equal hemispheres. The centre of the great circle is the centre of the globe.
Every meridian, looping from pole to pole, is a great circle. Thus a north-south rhumb line is at the same time a great circle course. This is why there was no difference on the Perth to Bali passage: it is nearly due north. The great circle is shorter than mercator only if there's east-west travel.
The equator goes east-west. But the equator divides the world into two hemispheres too. Other parallels of latitude are not great circles but the equator is, and if you sailed east or west along it you'd be sailing both mercator and great circle simultaneously. A great circle only starts to be significantly shorter than the rhumb line when you sail east or west in latitudes well away from the equator. Not only that: the voyage must also be a long one. The Tasman crossing was 1000 miles at 34° south-it would have to be longer or further south for great circle to matter.
As a generality, great circles start to be noticeably shorter than mercator on long routes in the roaring forties. I should think that will make about 99% of yachties lose interest in great circles. The enthusiastic 1% will appreciate that the great circle is of interest only for east-going voyages on account of all the roaring being in an easterly direction. By and large, if you are sailing westward you sail in the tropical and temperate latitudes. (The 99% will say that the sensible way to sail is to go west.)
Evidently, if you are keen on doing great circle it helps if you enjoy coolish air. Cooler than you think. Like aircraft on the polar route, your great circle always arcs into even colder latitudes. For example, consider a passage from Buenos Aires to Cape Town. You start and end about 34°S, like the abovementioned Tasman crossing. But this journey is longer: 3700 mercator, 3609 by great circle. That's 91 miles difference which, if it's a gift, you'll be pleased to accept. The square-riggers used to take this route and it is perhaps the one half-way plausible sailing great circle on the planet. However, as you doubtless suspect, it is no gift.
Firstly, it's dangerous for it takes you down to 40°S in a part of the Atlantic which is all-seasons iceberg territory. That wasn't so bad for the old sailing ships - time was money and they had plenty of lookouts to listen for waves breaking on bergs. Also sinking wasn't so serious for them since both cargo and vessel were usually insured.
If that doesn't frighten you away, perhaps you can be attracted away: Tristan da Cunha lies at about the middle of the trip. What sort of cruising sailor are you that you would pass this fabled outpost without stopping? You are going to stop? Well then, you've now got two short legs like the Tasman crossing. Might as well sail by mercator.
Of course the sailing ships weren't really taking the great circle form Buenos Aires to the Cape: they were catching the gales at 40°. The great circle is incidental. From the USA to Europe the great circle also corresponds roughly to the wind and current but in practice your route is determined by the Gulf Stream report, the iceberg report, fog conditions, the pressure system, and the weather prognosis.
There aren't all that many long-distance, high-latitude, east-bound routes on the planet, and the great circles aren't appropriate to any of them. In the Indian Ocean you hold the fortieth parallel for optimal wind and weather. The Great Australian Bight isn't great enough or south enough to matter. The bottom of the Pacific, should anyone be interested, is similar to the bottom of the Indian. The top of the Pacific has already been mentioned: a voyage of three legs, broadly: to 42°, along 42°, from 42°. The middle leg is not to be sailed great circle at all; the first and last legs could sailed great circle to save a theoretical total of 18 miles, which is rather a come-down from 240 miles.
Is there any use for that great circle facility? It was, after all, one of the beaut features which sold you the equipment in the first place. What about Narvik to Iceland? This is on the Arctic circle at 66½° north. To the average sunny Queenslander that probably sounds a little desperate but a thousand years ago this was a popular cruising area. The yachtsmen of the day had a reputation as a tough bunch, however in summer the trip is quite feasible even for a modern Queenslander. Yet it is to no avail: even at this extreme latitude it only saves 6 miles on the 660 mile trip.
If the great circle doesn't do any good, does it do any harm? It depends. If a voyage is east-west, out of the tropics and medium long then the path of the great circle is not the mercator path. For example that Tasman crossing (1000 miles) starts and ends at 34°S but arcs down near 34½° in the middle which is a fair way off the mercator. Although it doesn't make any difference to the distance, the great circle can be quite a different path on longer voyages.
If the passage is about north-south (any length), or if it's a short distance - say under 500 miles - in warmer latitudes, then the great circle is interchangeable with mercator and therefore harmless. If there is clear water between you and your destination and if the buttons are convenient, press them. Otherwise it probably best to steer clear of great circles.