Dead Reckoning Calculator
Departure is not longitude until you divide by cos.
Work out Dead Reckoning. Departure is not longitude until you divide by cos. Shows the working, not just the answer.
Estimated position
50.2828° N, 0.9026° W
28.6 nm made good on 53.5° at 7.14 kt
A minute of latitude is always a nautical mile. A minute of longitude is only a nautical mile at the equator and shrinks to nothing at the pole, which is why departure — the east-west distance run — has to be divided by the cosine of the mean latitude to become a longitude difference. Skipping that division is the classic dead-reckoning error, and it grows fast. At 60° latitude the correction is a factor of two; at 70° it is nearly three. Set and drift are the water moving under you, and they combine vectorially with the course steered. A beam-on tidal stream both pushes you sideways and increases speed over the ground, which is why the course made good and the speed made good both change.
How the Dead Reckoning Calculator works
Estimated position from course, speed, time and a tidal set, with course and speed made good, drift angle, and the departure-to-longitude conversion done properly.
Also known as: estimated position from course and speed · set and drift calculation · course made good with tide · departure to difference of longitude
Frequently asked questions
How is a dead reckoning position calculated?
Resolve the run into northing and easting, add the tidal set as a vector, then convert: northing is latitude directly, easting needs dividing by the cosine of the mean latitude.
Why divide departure by the cosine of latitude?
Because a minute of longitude is only a nautical mile at the equator and shrinks to nothing at the pole. At 60° the correction is a factor of two; at 70° nearly three.
What are set and drift?
Set is the direction the tidal stream flows towards; drift is its speed. They combine vectorially with the course steered to give the course and speed made good.
How reliable is dead reckoning?
Its error grows with every hour run, because every input is an estimate. It is a check on the plotter and a fallback when the plotter fails — not a substitute for a fix.
Why is a beam-on tide faster over the ground?
Because the two velocities add as vectors, and the resultant of two perpendicular vectors is longer than either. You go sideways and slightly faster.
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