In Search For Dead Reckoning Data

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I am in search for hard data on the error of maritime dead reckoning (DR) navigation. Any ship but preferred sails and from older times even better. This data is of special importance for the history of portolan charts. (See The Problem of the Portolan Charts for more information.) These maritime charts from the Middle Ages have an accuracy of 1 % or better and are thought to be created by DR navigation. Unfortunately DR data I found so far indicate an average error for sails at least in the 20 to 30 % range.

The Sources:

1. The DR system on a modern motorboat around 1985 (gyro compass, electric log and integrator) had a 5 % error. [1]

2. The physicist and astronomer R.R. Newton considered for classical times a 25 % error for sailing distance estimates as a good result.[2]

3. A Royal Navy fleet under Commodore Anson in 1741 had at least 40 % average error in distance and at least +-16.6° average error in heading.

On 7th of March 1741 a British fleet under Commodore Anson passed Straits le Maire and began to sail in mostly poor weather around Cape Horn. Towards the end of March they thought to be 10° west of Cape Noir, well into the Pacific. According to Anson this 10° was

"being double what former navigators have thought necessary to be taken in order to compensate the drift of the eastern current, we esteemed ourselves to be well advanced within the limits of the southern ocean,"[3]

They thought it safe enough west to begin a northward course to warmer climate. But on 14th April:

"weather, which had till then been hazy, accidentally cleared up, the [ship] Pink made a signal for seeing land right ahead and it being but two miles distant, we were all under the most dreadful apprehensions of running on shore; which, had either the wind blown from its usual quarter with its wonted vigour, or had not the moon suddenly shone out, not a ship amongst us could possibly have avoided."

So instead of 10° west they almost hit ground near Cape Noir. Instead of 20° they had only made 10° longitude since the 7th of March. So within about 23 days of mostly bad weather they had a longitude error of 100 %.

By luck their last storm day was 7th of April. After the sight of land, they sailed south-west until they reached 60° S around 22nd of April. Anson wrote about the weather during this period:

"And in this run we had a series of as favourable weather as could well be expected in that part of the world, even in a better season; so that this interval, setting the inquietude of our thoughts aside, was by far the most eligible of any we enjoyed from Straits le Maire to the west coast of America. This moderate weather continued with little variation till the 24th;"

In 1953 Royal Navy Commander W. E. May, from the National Maritime Museum, published a paper "Navigational Accuracy in the Eighteenth Century". He investigated the navigational log books of Anson's fleet during this period of "favourable weather" from 9th to the 20th April 1741.[4]

He had the logs of noon positions of about 7 persons on 3 ships. They all differed so considerably in longitude that he put them on the same longitude for the 13th of April. May: "For the sake of convenience the longitudes have been adjusted so that they all agree on 13 April." About half of the positions were with latitude measurement. But: "The spread in observed latitudes will be noted. [May used a big circle for this positions in his diagram] On 16 April, for example, Lieutenant Foley and the master disagreed by as much as 29 miles." Which is almost half a degree.

May wanted to track the course of the fleet, but: "It was then realized that even among the officers of a single ship there might be considerable differences of opinion as to the observed latitude and the course and distance made good;"

So he published a plot of each person's log book but bunched those on the same ship together. He gave no absolute longitudes in his diagram because the ships were much closer together than the diagram may suggest.[5]

I first digitized the diagram of May and calculated the "Mean", the average course of the fleet. This is the upper part of my diagram. Then I calculated the deviations of each person's daily distance and course estimate to "Mean", which is below in my diagram. It is like unfolding the tracks. Next the deviations are considered as errors and a statistic plot for distance and course heading is given.

The navigation accuracy of Anson's fleet in April 1741. Dead reckoning navigation with latitude, compass and log.

The average error in distance was about 40 %. The average error in course was about +- 16.6°. What does this show? We don't know the real position of the fleet except around 13th of April. So this does not give us the error of dead reckoning navigation of Anson's fleet. But it is the smallest error to expect from dead reckoning navigation under good to fair weather conditions in 1741. May concluded his paper: "Navigation in those days was not at all an exact science."

The course error of +-16.6° may need some explanation. This is not the error of the helmsman; that still has to be added. It is mainly the different estimate of the ship's real course. The real course of a sail ship is not the direction of its bow but some angle between bow line and wind, the leeway. It depends on the direction of the wind relative to the ship, the aerodynamic and hydrodynamic shape of the ship and how loaded it is. The main way to measure it is to observe the angle of the waves behind the ship. That is not very accurate and worse at low speed and in bad weather or at night.

Anson and his navigators were well aware how crucial navigation accuracy was for their survival. They were members of the most advanced navy of its time and about the last generation before the invention of the marine chronometer. In 1761 Harrison submitted his H4 chronometer to the Board of Longitude. In the Middle Ages around 1300, when the first portolan charts appeared, there were no logs, no latitude measurements and only a crude compass. The navigational accuracy then had to be considerably worse than in 1741.


  1. Jump up Hoffmann, Gerhard: Navigationsprobleme - Lösungen aus biologischer und technischer Sicht, in: Physik in unserer Zeit, 1985, Volume 16, Issue 2, pp. 40 - 49
  2. Jump up Newton, R. R.: The Crime of Claudius Ptolemy, London 1977, p. 45
  3. Jump up Walter, Richard: Anson's Voyage Round the World, London 1901
  4. Jump up William E. May, Navigational Accuracy in the Eighteenth Century, Journal of the Institute of Navigation 6 (1953) 71-73.
  5. Jump up Because Anson wrote: "And as separation of the squadron might prove of the utmost prejudice to His Majesty's service, each captain was ordered to give it in charge to the respective officers of the watch not to keep their ship at a greater distance from the Centurion than two miles, as they would answer it at their peril; and if any captain should find his ship beyond the distance specified, he was to acquaint the Commodore with the name of the officer who had thus neglected his duty."