On spherical navigation

Juhani Suntioinen was looking for a story about long-distance navigation, so here it comes.

Commercial aircraft are normally equipped with two GPS receivers, so on a long-distance flight we mainly navigate with the aid of GPS. Although we would able to fly the shortest and most direct route to the destination, the route still needs to be planned so that it follows airways. This is done mainly because of air traffic control reasons. Airways consist partly of navigation beacons, such as VOR- and ND- beacons. By beacon I refer to a group of antennas – not to a beacon of a traditional marine lighthouse. These ground-based navigation beacons ensure safety when a GPS signal is not available for one reason or another (that is: there is a malfunction in the GPS system or the aircraft).

Most of the waypoints are beaconless points, normally with a five-letter name. Typically they are located at the intersection of two airways or at the boundary of air traffic control areas. Consequently, it is possible to use names instead of coordinates. This makes planning and radio traffic faster and decreases the possibility of human error. While en route, we try to find short cuts from one waypoint to another in order to save time and fuel and reduce emissions.

GPS navigation devices always follow a great-circle route. For many of our readers, this concept may be a bit unfamiliar so a little summary is probably in order.

As we know, the Earth is a sphere. A spherical surface cannot be presented on a two-dimensional map without errors. Depending on the map projection, the map of the Earth distorts angles, shapes, distances or surfaces. The map that is perhaps most generally used at school and in press is based on the Mercator projection where all meridians and parallels are perpendicular to each other. However, this projection exaggerates the size of circumpolar areas: Finland is nearly the size of India and Antarctica is bigger than all the other continents combined. On a Mercator map, the shortest distance, i.e. the great circle line, becomes distorted and bends towards the poles as the spherical surface is “stretched” at the poles when drawing the map. For this reason, in aviation we use gnomonic maps in circumpolar areas and for other areas Lambert conformal conic projections where a great circle is nearly straight. If you have a round globe map at home, it is easy to determine a great circle between two points by using a piece of thread, for instance. So, the word “great circle” is not very descriptive as it refers to the shortest distance – not the greatest: if one were able to drive along it with a car, one would not need to turn the steering wheel. Consequently, it is not a circle (except when thinking of it as a circle around the centre of the sphere). I wonder who came up with such a monstrous word. I suggest that it be replaced with “shortline”!

As meridians converge at the poles and consequently are not parallel as in the Mercator projection, the direction in relation to the great circle changes accordingly. The closer to the poles one is flying, the greater the change in the actual direction. When flying to the north and the south, there naturally is no change – and the same applies to flying to the east or the west on the equator. When looking from Helsinki, the great circle network is rather surprising. For instance, the great-circle route from Frankfurt to Tokyo goes over Helsinki. Finnair’s long-haul traffic strategy is based on this fact. We hold a key position between Central Europe and Asia. You can draw different great circles here, for instance.

When measuring on a Mercator map, the first thought might be that the fastest route to Tokyo is to take the direction of St. Petersburg (108o) and then fly over Russia, northern Kazakhstan, Mongolia, north-eastern China and North Korea, altogether 8,782 kilometres to the destination. However, Finnair heads for Joensuu (051o ) and flies the entire route over Russia directly to Tokyo. The distance is “only” 7,849 kilometres. The difference is 933 kilometres! What do you think, which route gets you there fastest?

The longer the distance in the east-west direction, the more surprising the great circle. For instance, the great circle from Singapore to New York goes to the north (357o) over Cambodia towards Chongqing in China, from there through Mongolia and Russia, near the North Pole to Canada, arriving to New York from the north. A less knowledgeable person would head towards the southern tip of India, over Yemen, across Sahara and over the Canary Islands and the Atlantic Ocean to New York. Via this route the distance would be 3,160 kilometres longer. You can see the differences between routes for yourself here, for instance.

In reality, a flight is carried out along airways following a great-circle route as closely as possible and optimising the route and the en-route altitude according to winds and temperatures at that moment.

Wishing everyone short long-haul flights,

Jussi Ekman

Coordinates used:
HEL: N 60° 19.0′ E 024° 57.8′
NRT: N 35° 46.0′ E 140° 23.3′ (Tokyo)
NYC: N 40° 38.4′ W 073° 46.7′ (New York)
SIN: N 01° 21.6′ E 103° 59.4′ (Singapore)