Radio direction finding (DF) bearings.

Use may be made of radio transmissions to obtain a position line. It would necessitate either the ship having a radio direction finding capability or asking a shore radio station that is equipped to take DF bearings to take a bearing of the ship’s transmissions. Since radio waves follow great circle tracks, the plotting of such on a Mercator chart would produce lines curving towards the poles. Only if they coincided with the equator or a meridian would they be straight lines. Because meridians are represented by parallel straight lines on a Mercator chart, a great circle bearing would cross the successive meridians at varying angles. This difference is known as convergence. Convergence is the sum of the difference between the great-circle bearings and the rhumb line bearings at the transmitter station and the DF station.

Example of a radio DF bearing of a shore radio station.

Convergence depends on the differences of longitude and latitude and on the mid-latitude between the transmitter and the receiver. In order to plot a RDF bearing as a mercatorial bearing, it is necessary to apply only half of the convergence correction to the true bearing observed. No matter whether the bearing is obtained by the ship or the shore station or whether they are in the north or south latitudes, the half convergence correction is always applied to the great circle bearing towards the equator. Convergence is obtained by calculation from the approximate formula i.e.