Improvements in Navigation and the Search for Longitude

How radical innovations in seafaring enabled a more globalized economy.

Prince Henry the Navigator
Nicolaus Copernicus
13th century
Hans Lippershey
Gerardus Mercator
15 degrees
Gemma Frisius
A Mathematical School at Christ’s Hospital in London
The Board of Longitude

Advances in Shipbuilding during the Renaissance


During the Renaissance, advances in shipbuilding paved the way for the Age of Exploration. One of the most important developments during this period was the construction of two types of ships, the carrack and the caravel.

The carrack was a large, square-rigged, versatile sailing vessel developed in 14th-15th century Europe, Stable in rough seas, it was suitable for long journeys and cargo.

The caravel was a smaller and faster ship that was based on the design of the carrack, often credited as the design of Prince Henry the Navigator.

Unlike the carrack, the caravel had triangular, lateen sails capable of sailing into the wind, and proved a popular choice for long-distance trade and exploration due to its speed and maneuverability.

These designs were later built upon to construct Galleon warships in the 17th century.

Astronomy and Navigation: A Historical Overview

Astronomy has a long and rich history that dates back to ancient civilizations such as Babylon. The Babylonians were among the first to develop a sophisticated system of astronomical observations and predictions, using these to develop a calendar and predict astronomical events such as eclipses.


The Romans also made significant contributions to astronomy, with figures such as Ptolemy, who lived between 100 – 170 AD. Ptolemy’s model, like his predecessors, placed the Earth at the center of the universe, with the other celestial bodies orbiting around it.

This would be later overturned by the heliocentric solar system proposed by Polish astronomer Nicolaus Copernicus in the 16th century.

Navigation was an important application of astronomy, particularly for seafarers who used the stars to determine their position and navigate across oceans. Techniques such as celestial navigation enabled sailors to accurately determine their latitude, making long-distance sea travel much safer and more efficient.

The Astrolabe: An Early Navigation Instrument


Early navigation relied upon instruments such as the astrolabe, used by the ancient Greeks and further developed in the Islamic Golden Age.

The astrolabe consists of a disk with a movable pointer (the alidade) which is used to measure the angle between the horizon and a celestial object, such as a star or planet. By rotating the disk and aligning the alidade with the celestial object, the user can determine the object’s altitude and its position in the sky.

To use the astrolabe for navigation, sailors would use the instrument to measure the altitude of the North Star, or Polaris, which is always located at the same position in the sky. By comparing the altitude of the North Star with the observer’s latitude, sailors could determine their position on the Earth’s surface.

The Vital Importance of the Compass in Navigation

An instrument of vital importance to navigation was the compass.

A compass is a tool used to determine “cardinal direction” relative to the Earth’s magnetic north pole, typically consisting of a magnetized needle suspended on a pivot point, which aligns itself with the Earth’s magnetic field and points towards magnetic north.

It was invented in ancient China during the Han dynasty as a device for divination. The earliest record of its use for navigation dates to an account of 1187 by Englishman Alexander Neckam, and was in use by the 13th century among Italian merchants.

Prior to this technology, methods of navigation relied upon landmarks, celestial observations, and “dead reckoning”, which estimated a ship’s position based on the distance traveled and direction taken since the last known position.

This method was unreliable and subject to cumulative error: ocean currents and unpredictable weather could throw off calculations.

Counter to these previous methods, the compass therefore allowed sea-farers to navigate accurately even in poor conditions and periods of darkness.

The Importance of the Telescope in Navigation


Another instrument of vital importance to navigation was the telescope, its invention often credited to Dutch eyeglass maker Hans Lippershey in 1608.

Before the telescope, sailors were limited in their ability to navigate by the naked eye alone. They could only estimate their position based on the stars and other natural landmarks, by which ships could easily go off course or run aground.

With a telescope, sailors see land masses and other ships on the horizon in much greater detail, allowing them to chart their course with accuracy, and avoiding hazards.

The telescope was later aided by the “reflecting quadrant”, also known as Octant, invented by John Hadley in the 1730s, used for accurately measuring the angle between the horizon and a celestial object such as the sun, moon, or stars.

Cartography and Technological Advancements in Navigation


Some of the most significant technological developments both leading up to and during the Age of Exploration occurred in cartography.

One such invention was the portolan chart (from the italian ‘portolano’ or ‘pilot’s book’), used by European sailors beginning in the thirteenth century.

These charts depicted coastlines, landmarks, and ports of call, along with rhumb lines, as lines corresponding to a constant compass direction, allowed navigation along coastlines and between ports with a degree of precision that was not previously possible.

Another significant development was the creation of the Mercator projection by Gerardus Mercator in the sixteenth century. The Mercator projection is a type of map that shows the world on a flat surface while preserving the shape and angle of lines of longitude and latitude.

This would allow sailors to plot a straight-line course between two points on the map, which was particularly useful for long-distance navigation.

The Challenge of Calculating Longitude at Sea

Although a major breakthrough in cartography, the Mercator Projection could not be used in practice for many years to come, due to the difficulties in calculating longitude at sea.


While latitude (ones’ position north or south) could be determined by measuring the angle of the sun or stars relative to the horizon, longitude (one’s position east or west) presented far more of a challenge, and finding an accurate method would take centuries.

This was in part due to limitations in time keeping, since longitude was eventually reliably established by comparing the time across distances.

For example, consider that the earth is divided into 24 time zones, each separated by 15 degrees of longitude. If it’s noon in London and the local time on a ship at sea is 1p.m. the ship is one hour ahead of London time, which corresponds to a difference in longitude of 15 degrees. Therefore, the ship’s longitude can be calculated as the longitude of London plus 15 degrees.

The Evolution of Timekeeping for Navigation at Sea

While the first to propose the method of comparing clocks at sea was Gemma Frisius in 1530, timekeeping technology was far too inaccurate to make this method practical – particularly true at sea, when the temperatures, salt, and motion of the ship easily interfered with mechanisms.

Christiaan Huygens patented the pendulum clock in 1657, which revolutionized timekeeping. However, the motion of the pendulum was still susceptible to interference from the motion of the ship, rendering it useless for timekeeping at sea.

As such, maps suitable for the “dead reckoning”, along with maps suitable to this technique, remained in use beyond the invention of the Mercator Projection.

So too did other methods of calculating longitude, such as the method of lunar measurement first proposed by Amerigo Vespucci in 1499 – a serviceable, though imperfect solution that required complex measurements and charts.

Mathematical Education for Navigation

With the complexity of calculations required for accurate navigation, the Age of Exploration gave rise to a practical interest in mathematical education.


For example, a Mathematical School at Christ’s Hospital in London was founded by King Edward VI in 1673 in order to teach potential sailors, selected around age 11, preparing them for careers in the Royal Navy.

To this end, the school provided instruction on topics such as geometry, trigonometry and astronomy – all essential skills for undertaking long voyages across unknown waters.

This was a savvy investment during a time of fierce competition in navigation. Many, including Isaac Newton, suspected that longitude would be solved through mathematics. And whichever state was to succeed in calculating longitude could expect a significant global advantage.

The Board of Longitude and John Harrison's Marine Chronometer

In 1714, the British government established the Board of Longitude, with the aim of encouraging invention and competition among scientists and navigators.

The board offered rewards for anyone who could devise an accurate method for determining longitude at sea, offering up to £20,000 – a huge sum at that time – as incentive.


The eventual victor was a humble carpenter named John Harrison. His 1759 marine chronometer – his fourth prototype – used a novel system of counterbalanced springs, rather than gravity, and was therefore unaffected by motion.

It was accepted as sufficiently accurate by the Board of Longitude in 1762 after rigorous testing. The Board, however, withheld the prize until 1773, offering less than half promised, and only two years prior to Harrison’s death.

Nevertheless, Harrison has been remembered in history for revolutionizing the art of navigation.

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