What Is Dead Reckoning in Maritime Navigation?
Dead reckoning was the basic technique of estimating a ship’s position at sea, and it was the working method of navigators from the Age of Exploration through the twentieth century. The technique is simple in principle, but it required skill, discipline, and constant correction, and it was the source of many famous errors in the history of exploration. Understanding dead reckoning is central to how the great voyages of discovery were actually navigated, and it complements the celestial navigation methods described in our page on navigational instruments. The standard references are David Waters’s The Art of Navigation in England and the Netherlands in the Sixteenth and Seventeenth Centuries (1958) and J.H. Parry’s The Age of Reconnaissance (1963).
The crucial thing to understand about dead reckoning is that it is not a measurement. It is an estimate, and the estimate drifts over time. A navigator who had been out of sight of land for three weeks might know his latitude to within a degree or two, but his longitude could be off by five degrees or more. Columbus, da Gama, Magellan, and Drake all relied on dead reckoning for most of their voyages, and all of them made significant errors that they worked around with sightings of land, soundings, and constant latitude observations. The technique is treated in greater detail in the portolan charts cluster page.
The Basic Idea of Dead Reckoning
The basic idea of dead reckoning is to estimate a ship’s position at any moment by adding up the courses steered and the distances run since the last known position. Starting from a known starting point — a port, an island, a noon observation of latitude — the navigator would record the course steered on the compass, the speed of the ship (measured by the chip log), and the time elapsed. By multiplying speed by time, the navigator would estimate the distance run on that leg of the voyage. By adding the new vector to the previous position, the navigator would estimate the new position. The technique was called “dead” reckoning because it depended only on the “deduced” reckoning of position, not on any external observation.
The procedure sounds straightforward, but in practice it was full of difficulties. Compasses were subject to errors of several degrees, the chip log was an approximate instrument, leeway (the sideways drift of the ship under wind pressure) was hard to estimate, and ocean currents were often unknown. As a result, a ship’s position estimated by dead reckoning could easily be off by tens or even hundreds of miles after a long ocean passage, and the navigator had to check his position by every available means. For the broader context of how dead reckoning fit into the navigator’s working methods, see our page on portolan charts, dead reckoning, and piloting techniques.
Tools Used in Dead Reckoning
Dead reckoning required three basic tools: a compass, a chip log, and a timekeeper. The compass, typically a mariner’s compass mounted in a binnacle, gave the course steered. The chip log, a wooden board attached to a line with regularly spaced knots, gave the speed of the ship. The timekeeper, typically a half-hour glass, gave the interval over which the speed was measured. Together, these three tools allowed the navigator to estimate his position by the simple procedure of “course times distance equals displacement.” These three instruments were, along with the astrolabe and other devices, the working tools of every navigator of the era, and they are described in more detail on our navigational instruments page.
The chip log was developed in the sixteenth century and quickly became standard. To use it, the navigator would throw the log overboard and allow the line to run out, counting the knots as they passed over the rail. After a fixed interval — typically 30 seconds, timed by a half-minute glass — the line was hauled in. The number of knots that had passed gave the speed in nautical miles per hour, the origin of the term “knot” as a unit of speed. The same procedure was used to estimate the distance run over a watch or a longer interval.
The Traverse Board and the Logbook
To keep track of the dead reckoning over a watch (typically four hours), the pilot or his mate would use a traverse board. The traverse board was a flat board with holes corresponding to the 16 or 32 compass points, and a series of holes representing the speed in knots. At the end of each half-hour glass, the mate would place a peg in the appropriate course hole and a peg in the speed holes. At the end of the watch, the pegs were read off and the cumulative course and distance were calculated, then entered in the ship’s logbook. The logbook was the master record of the voyage, and it was used by the pilot to keep the dead reckoning up to date. These records, in turn, fed back into European knowledge of winds and currents, and they were eventually incorporated into the cartography and maps of the era.
Sources of Error in Dead Reckoning
Dead reckoning was subject to many sources of error, and even the best navigators of the Age of Exploration were often far off in their estimates of position. The most important sources of error were:
Compass error: The mariner’s compass did not point exactly to true north, and the difference (called magnetic variation) changed with location. A navigator using a compass that was off by 5 degrees, over a 1,000-mile voyage, would be off by nearly 90 miles.
Leeway: A ship sailing with the wind on its beam would drift sideways through the water, and this sideways drift (called leeway) was not measured by the chip log. A navigator had to estimate leeway and add a correction to the course.
Current: Ocean currents, especially in regions like the Caribbean, the Indian Ocean, and the Agulhas Current off southeast Africa, could carry a ship many miles off course. A navigator who did not know the current would be off by a corresponding amount.
Wind and weather: The state of the wind and sea affected the speed of the ship in ways that the chip log could not capture. A following sea would push a ship faster than the log indicated; a head sea would slow it down.
Log error: The chip log was an approximate instrument, and its measurements could easily be off by 10 or 20 percent, especially in heavy weather.
Cumulatively, these errors could add up to large discrepancies over a long voyage. The errors were so large that a famous rule of thumb emerged among later navigators: after a long ocean passage, a navigator had no real idea where he was, east-to-west.
Checking Dead Reckoning
Because of the inherent inaccuracy of dead reckoning, navigators checked their estimated positions by every available means. The most important check was a noon observation of latitude. By measuring the altitude of the sun at noon, and referring to a table of solar declination, the navigator could determine his latitude to within a degree or two. This latitude was then used to update the dead reckoning — discarding the old estimate of latitude and substituting the new observation. The longitude component of the position, however, could not be checked without a chronometer, and longitude error accumulated over the voyage.
Other checks included sightings of land (mounds of clouds over an island, flocks of birds, drifting seaweeds, changes in water color), soundings of the seafloor in coastal waters, and observations of currents. Pilots made notes of every sign that might indicate proximity to land, and they often turned toward a sighting long before they had any clear evidence of where they were. The famous landfall of Columbus in 1492 was preceded by several days of “signs of land” — seaweeds, birds, a carved stick floating in the water — that Columbus interpreted (correctly) as evidence of nearby land, and which were also connected to his broader voyage as described in our page on Christopher Columbus and the voyages to the New World. The relationship between dead reckoning and the broader practice of navigation is treated in our ships, navigation, and technology pillar page.
Dead Reckoning in the Age of Exploration
Dead reckoning was the working method of every navigator of the Age of Exploration. Columbus, da Gama, Magellan, and Drake all relied on it for most of their voyages, and they supplemented it with latitude observations, lead soundings, and sightings of land. The technique was the only practical way to keep track of position on long ocean voyages before the development of accurate timekeeping, and it remained in use well into the twentieth century. The combination of dead reckoning and latitude sailing — sailing north or south to the latitude of the destination, then east or west — was the standard method of transatlantic navigation throughout the sixteenth and seventeenth centuries.
The Legacy of Dead Reckoning
The technique of dead reckoning evolved over the centuries. The chip log was supplemented by the patent log, a mechanical device that recorded speed and distance automatically. The traverse board gave way to the logbook, which in turn was eventually replaced by electronic chart systems. The basic principle — estimate position by integrating course and speed — remained the same, however, and it is still used in modern navigation as a backup to electronic systems. Dead reckoning is among the most enduring techniques in the history of seafaring, and it remains a fundamental skill for navigators today. For the broader story of how the navigator’s working methods were taught and transmitted, see our page on portolan charts, dead reckoning, and piloting techniques.