What Is Dead Reckoning? Knowing Where You Are by Adding Up Where You Went

The calculation combines a starting point with a vector for each leg of the journey, and the accuracy of the result depends entirely on how well each component was measured. Direction came from a magnetic compass, corrected for two separate errors: variation, meaning the local difference between magnetic and true north, which changes with position and over time and is printed on charts, and deviation, meaning the error introduced by the ship's own iron, which changes with the vessel's heading and is measured for each ship. Distance came from speed multiplied by time, with speed traditionally measured by the chip log, a weighted board thrown overboard on a line knotted at regular intervals and paid out for a measured period timed with a sandglass, counting how many knots ran out, which is where the unit comes from. Time came from a sandglass and later a clock. Each leg was plotted on a chart or worked out with tables, and the running total gave the estimated position.

The characteristic weakness is that every error accumulates and nothing corrects it:

• •A small compass error applied over a long distance displaces the position substantially, since the error is proportional to distance run
• •Speed measurement is approximate, and the log measures speed through the water rather than over the ground
• •Current moves the vessel with no indication at all on any instrument aboard, which is the largest single source of error and is why tidal streams and ocean currents had to be estimated and applied as a correction
• •Leeway, the sideways slip caused by wind on the hull and rigging, adds a further offset that must be estimated by eye from the angle of the wake
• •Steering is imperfect, so the course made good differs from the course ordered
• •Because errors accumulate rather than cancelling, uncertainty grows steadily with time since the last known fix, which is the defining property of the method

Dead reckoning was never used alone where anything better was available, and the history of navigation is largely the history of finding fixes to reset it. A landmark or a sounding gives a position directly near a coast. Celestial observation gives latitude readily from the noon sun or the pole star, and longitude was the hard problem, solvable only with an accurate time reference, which is why the marine chronometer mattered so much and why the lunar distance method was developed as an alternative. Each fix resets the accumulated error to zero and the reckoning continues from there. The practice was to run the dead reckoning continuously regardless, because it predicts where the vessel should be, which tells the navigator where to look for a landmark and warns of danger before it appears. Losing that discipline caused disasters, and the loss of a British fleet on the Scilly Isles in 1707 with over a thousand lives is the case usually cited as prompting the longitude prize.

The method never became obsolete and is now performed by machines. Inertial navigation systems in aircraft, submarines and spacecraft are dead reckoning implemented with gyroscopes and accelerometers, integrating measured rotation and acceleration to track position from a known start, and they share the same defining weakness of accumulating drift that must periodically be corrected against an external fix. Satellite navigation supplies that fix, and the combination is used precisely because the two fail differently: satellites can be blocked, jammed or spoofed and do not drift, while inertial systems cannot be jammed and do drift. Vehicles use wheel rotation and steering angle to continue navigating through tunnels. Phones combine step counting with compass heading for indoor positioning. Underwater vehicles, which have no satellite access at all, depend on inertial methods with occasional acoustic fixes. Several animals appear to use path integration, which is dead reckoning by another name, with desert ants demonstrating it convincingly by returning directly to a nest across featureless ground after a wandering outward journey.

Dead reckoning adds a vector for each leg of a journey to a known starting position, using compass heading corrected for variation and deviation, and distance from speed and time, with speed traditionally measured by counting knots running out on a log line. Errors accumulate rather than cancelling, and current and leeway move the vessel with no indication aboard, so the method requires periodic fixes to reset it. Inertial navigation is the same method mechanised and shares the same drift.