Suppose we are trying to navigate with just a compass and lag (dead reckoning, plus some latitude measurements), like people did before they started using chronometers and lunar distances method. What typical error can we expect? Does anybody have examples of illustrations with actual and perceived tracks?
So far, I found an article "The Empirical Reconstruction of Columbus' Navigational Log and Track of his 1492-1493 Discovery Voyage" of Colonel Peck that shows actual and perceived tracks in one of Columbus's voyages. (there is also one more map there)
Also, I found map in Steven Callahan book(sorry, legend is in Russian):
About as accurate as it was for Amelia Earhart - which was usually pretty good, but subject to limitations.
Accuracy in Latitude was far better than accuracy in Longitude because of the well known Longitude Problem. Latitude could be corrected at every sighting with the pilot's (marine) astrolabe, to within the accuracy of the device at some fraction of a degree. With one degree being about 112km, accuracy to within 1/4 degree (likely the best attainable in good conditions) was within 28km. That's almost within visibility from a tall crows' nest. Longitude was another issue entirely.
The main navigational hazard in unknown waters was reefs and shoals (and lee-shores). This was overcome by sailing North-and-South well out to sea to a desired Latitude, and then sailing East-West to a known landmark in safe waters. (This was how Brazil was discovered: Portuguese pilots sailing North-South well away from the African coast spotted another landmass to their West.) Then the vessel would run down the (well known) coast to a desired port. Identification of the trade winds, both easterlies and westerlies, in the times of Prince Henry the Navigator, allowed pilots to select specific Latitudes of particular efficiency for these east-west legs.
In less well known waters the standard practice was to aim to one side of the desired destination; then after the requisite distance make a known turn for the final leg. But Earhart liked to show off her considerable dead reckoning skills and land right on top of the destination. But on that final flight to Howland Island something went wrong; Erhardt arrived outside visual range of the destination; and likely made a wrong guess on the turn.
An earlier post by yours truly outlines some of the dead reckoning techniques and equipment used during the Age of Exploration, with links to Nick Szabo's excellent articles on sandglass and mechanical clock, traverse-board, and dead-reckoning maps and errors