From A Land So Strange: The Epic Journey of Cabeza de Vaca, by Andrés Reséndez (Basic Books, 2007), Kindle pp. 77-79:
In the sixteenth century, the basic method of ocean navigation was “dead reckoning.” Pilots steered ships from an origination point or “fix” to a new position by estimating the direction and distance traveled. Any point on the globe could be specified by means of only direction and distance. To keep track of direction, navigators used a thirty-two-point magnetic compass. To judge the distance traveled, pilots estimated the speed of the ship by simply looking at the passing bubbles on the sea. During the Age of Discovery this disarmingly simple system was used with accuracy to negotiate even long ocean passages. Dead-reckoning navigation, for instance, enabled Columbus to sail four times from Spain to the Caribbean and back.
Dead-reckoning navigation, in turn, was made possible by a new type of chart known as a portolan. Invented in the thirteenth century, the portolan chart caused a nautical revolution, first in the Mediterranean and later in the Atlantic. Unlike medieval mappaemundi with their fanciful renderings of land masses and distances, portolan charts are incredibly accurate. One can gain a sense of their accuracy by comparing conventional maps of the sixteenth century, which often exaggerate the length of the Mediterranean by nearly twenty degrees (a problem traceable to Ptolemy), with portolan charts, for which the comparable error seldom exceeds one degree.
Intended for real, working seamen, portolan charts include only relevant geographic details like coastlines, islands, rivers, and mountains. But their most visually striking and useful feature is the series of lines bisecting the charts. These lines were the lifeblood of sixteenth-century navigators. Each one represents what pilots called a rutter (derrotero in Spanish) or technically a rhumb line—a path defined by a fixed compass direction. These were the lines that pilots strove to follow as they steered the ships through the oceans. Portolan charts thus gave pilots information about the distance between point A and point B, the precise direction that they needed to follow, and indications about any prominent geographic features along the way; all they needed to know, nothing more and nothing less. Crucially, portolan charts do not depend on latitudes or longitudes. Indeed, virtually no portolan charts contained such measurements prior to 1500. Moreover, they do not require the use of declination tables or any additional conversions or calculations, as these charts were drawn on the basis of the magnetic, rather than the true, north. Simply by maintaining a course with a magnetic compass and keeping track of the distance traveled on a portolan chart, an illiterate pilot—and roughly one out of four pilots in the sixteenth century was still unable to write his own name—could steer an expedition skillfully and safely to its destination.