A Historical Perspective of Navigation
Terrestrial navigation has relied for millenniums on maps, signs, and the human sense of direction [1, 2]; it is only in recent times that radio signals have helped land navigation. The most important tools for navigation were created to ensure safety during maritime journeys.
The first infrastructure created as a navigational aid was the lighthouse. The world’s first lighthouses were erected about 2,000 years ago: the Colossus on the Rhodes Island in Greece and Pharos at Alexandria in Egypt. It was not until the nineteenth century that the Fresnel lens improved the performance of lighthouses by increasing their range significantly.
Sea travel was considered unsafe for a long time and the best-known explorers, such as Bartholomeu Diaz, Ferdinand Magellan, Sir Francis Drake, Amerigo Vespucci, and Christopher Columbus, were considered brave sea captains .
These men used primitive instruments to calculate the position and speed of their ships . The mind of any sailor was closed to the new (for that age) astronomical
studies for determining the latitude. Christopher Columbus crossed the Atlantic Ocean without any accurate measurement of the latitude. The main instruments used for calculating the latitude were the quadrant, astrolabe and nocturnal. Columbus tried to use these tools but their results were disappointing. All these devices aimed to measure the altitude of a celestial body above the horizon. The quadrant was the first instrument developed for celestial navigation, known back to the fifteenth century. It had the form of a quarter circle with degree graduations along the arc. The astrolabe was similar to the quadrant. This device was suspended from a cord to hang perpendicular to sea level, while the navigator sighted the sun or a star through two small holes in the plates on its moveable vane.
The nocturnal, or night disc, consisted of two concentric circles of different sizes, made of either wood or brass, and it was also used to calculate the time at night. All these instruments were influenced by the ship’s movement, which, in case of bad weather conditions, rendered measurements difficult. Columbus tried to use the quadrant latitude reading for the first voyage only on October 30, 1592, in Cuba, but the measurement showed him to be 42° north latitude instead of about 20°. He blamed the
quadrant for the bad result and remarked that he would not take any more readings until the quadrant was fixed. Recent studies have demonstrated that Columbus read the wrong scale of the instrument, which was actually performing quite satisfactorily!
This could be considered a prime example of useful service implemented into a user-unfriendly terminal. Recent history has confirmed that users need services while, at the same time, they indeed do not need complex or interfering technologies.
Columbus and most of the sailors of his era navigated by deduced (or dead) reckoning method. This method was based on the measurement of the course and the distance from some known points. The course was measured by a magnetic compass, which was used in Europe since at least the twelfth century. The distance was measured every hour through the measurement of the speed. This was measured by throwing a piece of flotsam over the side of the ship; there were two points of the ship rail marked (one near the prow and one near the stern).
The sailor started a quick chant (part of an ancient oral tradition of medieval navigation) when the flotsam passed the forward mark and stopped the chant when it passed the aft mark. Each syllable reached was equivalent to a speed in miles an hour. At the end of the day, the total distance and the course, calculated as the sum of the distance and course measured each hour, was written on the chart.
The dead reckoning method could be considered an ancestor of the modern inertial navigation systems (INS). INS works with instantaneous and continued measurement of speed, distance, time, and direction and it allows a user’s knowledge of a new position each time when starting from a known one. It was initially developed for submarine navigation but is used nowadays for surface water, air, and land navigation as well. Because dead reckoning navigation does not need any astronomical observation, inertial navigation does not need any radio navigational aid.
A quadrant, if well used, could measure the latitude with an accuracy of about one degree, but at that time no instruments were used to measure longitude in a Introduction consistent and sufficiently accurate way. The problem of the longitude was keenly felt in the United Kingdom and the most important scientists of the day started to meet in Grisham College (London) to “find out the longitude”:
The Colledge will the whole world measure, Which most impossible conclude,
And Navigators make a pleasure By finding out the longitude. Every Tarpalling shall then with ease Sayle any ships to th’Antipodes.
—Anonymous, about 1661
In 1662, the scientists previously mentioned found the Royal Society of London for the Promotion of Natural Knowledge, even if the problem was not solved immediately. Between 1690 and 1707, several ships were lost during sea navigation due to the wrong estimation of their position. In 1707, after a 12-day storm, Admiral Sir Cloudesley Shovel evaluated wrongly to be west of the French islands of Ouessant and, as a result, four war ships struck rocks near the Scilly Isles and more than 2,000 men were killed. In 1714, Queen Anne established the “Board of Longitude,” composed of scientists and admirals, to examine the proposals and check the results by accurate tests, by the Act of Parliament 12th, which declared as follows:
That the first author or authors, discover or discoveres of any such method … shall be entitled to, and have such reward as herein after is mentioned; that is to say, to a reward or sum of ten thousand pounds, if it determines the said longitude to one degree of a great circle, or sixty geographical miles; to fifteen thousand pounds if it determines the same to two thirds of that distance; and to twenty thousand pounds, if it determines the same to one half of that same distance… 
It is quite clear that such a vast amount of money (current value at more than $10 million) provoked the interest of scientists and alchemists in the longitude problem . It is beyond the scope of this book to list the scientific or imaginative methods proposed to win the prize .
However, while the board expected an astronomical solution to the problem, it was solved through different means: longitude can be computed measuring the difference in time between midnight (or local moon, the highest point of the sun) and the midnight (or the moon) of a known place (e.g., Greenwich). The earth performs one full rotation (360°) every 24 hours, thus it rotates 15° every hour. This means that if the local moon is one hour before the Greenwich moon, the place is sited 15°W. Local moon or midnight time could be determined, respectively, by sundial and nocturnal [8, 9].
This method was well known and proposed by Gemma Frisius in 1530; unfortunately time on board ships was measured in a very inaccurate way by a sandglass, and a member of the crew had the responsibility to turn the glass (about every half hour). Clock artists grew fully in that age, but as Isaac Newton stated:
One is, by a watch to keep time exactly: but by reason of the motion of the ship, the variation in heat and cold, wet and dry, and the difference in gravity at different latitudes, such a watch had not yet been made.
To win the full prize, the clock used (more specifically a chronometer) would have had to measure the absolute time to an accuracy of 2 minutes, all journey long.
I should then see the Discovery of the Longitude, the perpetual Motion, the Universal
Medicine, and many other great Inventions brought to the utmost Perfection.—Gulliver’s Travels, Jonathan Swift, 1726
William Whinston and Humphry Ditton proposed a sort of optical transoceanic telegraph : the method was to use a number of lightships anchored in the principal shipping lane at regular intervals. They would have transmitted the signal of the Greenwich midnight time by firing a star shell; these synchronization signals would then have propagated ship by ship. Although this method was impractical for several technical reasons, nowadays we can recognize a number of technologies that use this concept, starting from radio bridges and the frequency shortwave broadcast radio stations for radio clocks synchronization to very high frequency omni range (VOR) and distance measuring equipment (DME) stations for air navigation.
Where scientists, astronomers, and mathematicians failed, a carpenter’s son with no formal education and self-taught craftsmanship won the longitude prize .
Between 1730 and 1759, John Harrison (24 March 1693 – 24 March 1776) built four clocks that were the most accurate and precise timekeepers ever seen at that time. The last one, called H4, was a pocket-size watch, just 13 cm in diameter and weighing 1.45 kg. In a voyage to Barbados aboard the Tartar on March 28, 1764, the watch error was only 39.2 seconds over a journey of 47 days (about three times better than the standards required to win the full prize). John Harrison was a self-educated English clockmaker. He invented the marine chronometer, a long-sought and critically-needed key piece in solving the problem of accurately establishing the East-West position, or longitude, of a ship at sea, thus revolutionising and extending the possibility of safe long distance sea travel in the Age of Sail. The problem was considered so intractable that the British Parliament offered a prize of £20,000 (comparable to £2.77 million / €3.52 million / $4.56 million in modern currency) for the solution
It is amazing how history has repeated itself many times. There is no need to cite the relativistic theory to understand the strict connection between space and time.
The design of a global navigation system was conditioned by the availability of very accurate clocks, much more accurate than any common quartz clock. Nowadays everyone can know where he or she is to a few meters accuracy with the help of a GPS receiver. We take this for granted because atomic clocks that are precise to a billionth of a second are installed onboard the GPS satellites . The concept of navigation is based on the knowledge of reference points. Just as celestial navigation, based on triangulation method, used celestial bodies as known points, many centuries later GPS, based on the concept of trilateration, uses satellites as known points, whereas long range radio aid to navigation (LORAN) uses fixed stations as known points.
- Prasad and Ruggieri, Applied satellite navigation using GPS, GALILEO, and augmentation systems, London: Artech House mobile communications series, 2005
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 Howse, D., and N. Maskelyne, The Seaman’s Astronomer, New York: Cambridge University Press, 1989.
 Sobel, D., Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, New York: Penguin, 1996.
 Dash, J., and D. Petricic, The Longitude Prize: The Race Between the Moon and the Watch-Machine, New York: Frances Foster Books, 2000.
 Chapin, S., “A Survey of the Efforts to Determine Longitude at Sea,” Navigation, Vol. 3,1953, pp. 1660–1760.
 Forbes, E. G., “The Scientific and Technical Bases for Longitude Determination at Sea,” NTM Schr. Geschichte Natur. Tech. Medizin, Vol. 16, No. 1, 1979, pp.113–118.
 Howse, D., Greenwich Time and the Discovery of the Longitude, Oxford, England: Oxford University Press, Oxford, 1980.
 Il cielo dei navigatori (The Sky of Navigators), the Astronomy Disclosure Committee and the Italian Astronautical Society, Florence, CD-ROM, Vol. 27, No.9518, 1998.
 Taubes, G., The Global Positioning System: The Role of Atomic Clocks, Washington, D.C.: National Academy of Sciences, 2003.
 Bowditch, Nathaniel, The American Practical Navigator, Bethesda, MD: National Imagery and Mapping Agency. 2002.
Also available at http://garminxtgps.blogspot.com (my GPS blog in english)