Dead Reckoning Position

Dead reckoning is the oldest position-finding method there is and it has never stopped being useful. You know where you were, you know the course you steered and the speed you made and how long you did it for, so you know where you are. No satellites, no sights, no shore in view. Every other method on a ship or in an aircraft is checked against it, and when an instrument fails it is what you fall back to — which is why it is still taught, still plotted, and still on the licence exam.

The arithmetic splits the distance run, $S \times t$, into two components with a course angle. The northing — the difference of latitude, $D\cos C$ — is what this page returns, converted to degrees by dividing by the earth's radius. The easting is the DEPARTURE, $D\sin C$, and it is reported alongside the answer. The distinction between departure and difference of longitude is the trap on this page and it catches people every year: departure is a distance in miles, difference of longitude is an angle, and you get from one to the other by dividing by the cosine of the middle latitude. At the equator they are numerically the same and the error is invisible. At 60° north the cosine is 0.5, so a departure of 30 miles is a full degree of longitude, and treating them as equal halves your easting.

The word "dead" is not about danger. The best evidence is that it is short for "deduced" — a DED reckoning in old logbooks — although the derivation is argued about, and Bowditch is careful not to insist. What is not argued about is what the method assumes: that the course steered is the course made good and the speed through the water is the speed over the ground. Neither is ever quite true. A current sets you sideways, leeway from the wind adds to it, the log under-reads in a seaway, and a helmsman on a long watch has a personal bias of a degree or two that is remarkably consistent.

That is a feature, not a defect. The gap between a DR position and the next real fix is measurable, and it is exactly what the set and drift page turns into a current vector — information you would not have had if the DR had been perfect. A navigator who stops plotting DR because the plotter is working has thrown away both the backup and the diagnostic. Plot it anyway, and plot it honestly: a DR position adjusted after the fact to agree with the fix has told you nothing at all.