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Foul Anchor


Milestones in celestial navigation



    Even before I was hooked on sailing, I was hooked on celestial navigation. To me it combined the practical side of science with the romance and adventure I associated with sailing in the days of old. I pursued it as an end in itself and not as a practical matter. Now, when I hear somebody say knowledge of celestial navigation is not needed in these days of GPS I cringe. It is not only a backup but a beautiful art in itself. Or is sailing also pointless since the marine engine was invented? Is fishing out of style since you can go to the fish market? Did photography make painting obsolete?
    The purpose of this article is to summarize and give an overview of the development of celestial navigation through the centuries and to point out the landmarks in this field so you might better appreciate the conditions under which navigators worked through the centuries and their resourcefulness.
    Literally hundreds of inventions and sight reduction methods have been proposed and there are many ways to skin this rabbit. Still, there are a few inventions which stand out and became more widespread because they filled a need, were truly ingenious, represented the state of the art or became classics in the field. We are not only talking the invention of objects like the sextant or the chronometer but also of elegant and useful methods of performing sight reduction and other calculations.
    I do not attempt to teach you celestial navigation here. If you already know celestial navigation I hope you will appreciate this brief history and if you don't, I hope this might serve as a primer to get you started in learning this art and science.



    For centuries the Europeans had sailed around their coasts by piloting with reference to landmarks and aided by the their knowledge of sea depths at different places. When in the late 15th century the Portuguese and the Castillians (Spanish) started their voyages of discovery their instruments of navigation were:

  • Chip log and hour glass to determine speed and dead reckoning
  • Sounding lead to determine depth and nature of bottom
  • Magnetic needles floating on bit of cork to determine orientation
  • Astrolabe to measure the height of a celestial body above the horizon (H).
    They knew the limitations and errors of dead reckoning. They also knew that magnetic variation was not constant but changed with geography and time. And they knew Polaris was not placed exactly at the pole and knew how to correct for this by noting the position of the stars around it.
    The Arabs are credited with inventing the astrolabe, which is quite a simple instrument, in the middles ages. It needed three men to take a sight and gave very low precision (about one degree). It was used to determine latitude by a sight of Polaris or the meridian passage of the Sun. The cross staff, also a product of the middle ages, was hardly an improvement over the astrolabe. Although one single person could use it, he had to align simultaneously (and therefore view simultaneously) one end of the cross-staff with the horizon and the other with the Sun or other celestial body. Highly impractical.
    In 1590 Davis invented the backstaff (also called Davis' octant) which allowed a single person to take a sight of the Sun with slightly more accuracy than with an astrolabe. The observer, with his back to the Sun, aligns the shadow of the Sun with the horizon therefore maintaining one single line of sight.
    So, until the middle of the 18th century, latitude was determined by Polaris or the 'noon sight' of the Sun using first the astrolabe and later the backstaff. Because the calculation of latitude from the noon sight is so simple and because it does not require keeping accurate time, it has remained a tradition with navigators to this day.
    At that time, there was no way of determining longitude so ships would sail to a point on the same latitude as their destination but well to the East or West of it and then sail along this parallel East or West to their destination. One would think this was a highly inefficient way of doing things but it was the best they could do and not so inefficient as it might seem at first sight. For Castillian ships sailing to the Caribbean this was in fact quite efficient given the clockwise movement of the currents and trade winds in the North Atlantic. They would leave Spain and, following the trades, sail South to the Canaries and then across to the Caribbean. On the return trip they would sail North close to Florida and then across. From the standpoint of winds and currents this was the most efficient way to do it and, coincidentally, also the best for the navigator. Unfortunately for them (and fortunately for treasure hunters today), the Spanish fleet returned from the Caribbean every year at the height of the hurricane season and many ships were lost off the coast of Florida.
    Around 1750 the sextant was invented. It allowed a more precise measurement of H and has remained basically unchanged to these days. Still navigators did not give up their backstaffs for quite a while.
    The invention of the telescope and subsequent astronomical research allowed accurate prediction of the position of celestial bodies and in the latter part of the 18th century the British Royal Observatory started publishing the Nautical Almanac. With the chronometer, the sextant and Nautical Almanac (NA) remain the basic tools of the trade to this day.
    During the 18th century all the theoretical study had been done that would allow the determination of longitude *provided* the navigator knew accurately GMT when he took the sight. Up to that point time was kept aboard ships with hourglasses which were turned every half hour. This system was, of course, inaccurate and totally unsuitable for celestial navigation.
    The first systems devised to determine GMT were by observing celestial movements which were quite fast and predicted in the almanac. One very widespread method was the 'lunar distance' method. The moon moves quite fast against the background of stars and this movement is predicted in the NA. Today, knowing GMT I can determine the Moon's GHA and, therefore its SHA. The lunar distance method does the reverse: by measuring the angular distance between the moon and a star near the ecliptic, one determines the Moon's SHA and, with that, GMT.
    Another method of determining GMT was by observing the fast movement of the four planets of Jupiter in their orbits and their eclipses. This, however, required the use of a telescope.
    Although they were an improvement over having no way to determine time or longitude, both methods were extremely complicated and inaccurate by today's standards. Clearly there was a need for a machine that would keep time at sea.
    Spain and other countries had offered rewards to the inventor and constructor of an accurate chronometer without success. In the early 18th century Britain also offered a large reward to anyone who could 'discover longitude at sea with a precision of 60 miles after a voyage of six weeks'. This precision might not sound like much today but, in effect, it meant keeping time with an accuracy of four minutes after those six weeks.
    Unlike other inventions of the modern age which made use of existing technology by putting it to new uses, the chronometer was indeed invented by necessity and the technology needed for it had to be developed.
    Since Galileo discovered the constant rate of a pendulum, inventors had been trying to build a timekeeping machine or chronometer based on this principle but results were less than perfect on land and those chronometers could not be taken to sea. The whole 18th century was devoted to the development of an accurate chronometer but navigators still had to do without it during this century.
    In response to the British offer, John Harrison coupled the pendulum with an escapement of his invention and produced the first useful chronometers during the 18th century. The first one weighed 65 pounds. Years of work and improvements finally produced mechanical chronometers which were practical and could be mass produced.
    It is only after the beginning of the 19th century that useful chronometers were being built and even then they were expensive and during the first half of the century many ships were still sailing without them. Once chronometers were available, the navigator had at his disposal the same tools he still uses today: sextant, chronometer and nautical almanac. From then onwards the major advances in celestial navigation have been, not in the physical tools, but in the theory of mathematical methods and calculations used in reducing the observations.
    With the advent of the chronometer, longitude could be determined. This was done in the following manner. The navigator would determine latitude by the same method he had used for the last few hundred years: the noon sight. He would later take a sight of a body, still generally the Sun, on or close to the prime vertical, that is to say, due East or West. This was called the 'time sight' because time had to be noted. With his dead reckoned latitude from the noon sight (today we would say 'advancing this LOP') he would then calculate longitude.
    The time sight was a complement to the noon sight and the next logical step. It was more easily accepted by navigators than a radically new system would have been and it became the standard of the day.
    Aside from the central topic of navigation at sea, it is interesting to note that land surveyors and map makers of the time had the same problem of determining their position from celestial observations but they came up with completely different solutions. The mariner has a clear view of the horizon and can measure H with his sextant, which is not the case on land. On the other hand the mariner has no means of measuring accurately the bearing (azimuth) of a body or the precise time of its meridian passage. An astronomical observatory on the contrary, has a meridian telescope which serves to time with great precision the meridian passage of stars and consequently determine longitude.
    In 1837 Capt. Sumner was getting close to the English coast and was concerned about his position after several days of fog and no sights. An opening in the clouds allowed him to take a 'time sight' but, as he was unsure of his latitude, he decided to resolve the longitude assuming several different latitudes. When he did this, he discovered that all the points he obtained were aligned. He is credited with inventing the line of position (LOP). The straight LOP is, of course, a short segment of a small circle (as opposed to a great circle and not small in size) called circle of equal altitude. His method of resolving the longitude for two different latitudes was also in line with what had been done up to that moment and was adopted without resistance. Still, the navigator's system was to continually cross LOPs from time sights with advanced noon (latitude) lines.
    The reduction of the time sight was still complicated (and had to be done twice) and it had to be of a body close to the prime vertical. As this LOP was obtained by plotting the longitude of two points of different latitudes if the azimuth of the body was too far from the prime vertical (and therefore too close to the prime meridian) the error grew and the points would be off the chart.
    In the later part of the 19th century, Capt. Marcq St. Hilaire invented the intercept method which resolves this problem and is also known by the name of its inventor. It involves assuming a position for the calculation which can be our DR position but in reality it is not important which one we choose (within certain limits) as the resulting LOP will always be the same.
    The navigator then calculates the theoretical H of that body from that assumed position (Hc) and the theoretical azimuth (Zn). The difference between Hc and the actual H observed Ho is called the intercept distance and indicates where our LOP lies with reference to the assumed position.
    As we have seen, both methods involve assuming as known something unknown, in one case the latitude and in the other both latitude and longitude. This is because a single observation yields not a fix but a LOP. The beauty of the intercept method is that it removes the azimuth constraint and will work equally well regardless of the azimuth of the body observed. A navigator can now make several observations of several celestial bodies with different azimuths or of the same one at different times and resolve them all by the same method. Each observation yields a LOP and two or more provide a fix.
    Still this method took longer to be accepted because it was so different from the noon and time sights it was replacing. It has remained the standard method to this day even though many navigators still like to use the noon and time sight method. With the intercept method the calculations for calculating Hc and Zn were still complicated and prone to error in spite of the use of logarithms and other simplifying tools.
    Around 1930, Ageton, then a student at the Naval Academy in Annapolis, invented the method that bears his name and which has later been known under other names such as HO211 and Bayless. This method uses a short table of logarithmic functions and is still useful today. It truly simplified the intercept method. Later, other similar methods have been proposed and one of them known as the Compact or Davies method is included in the Nautical Almanac but, in my view, none even comes close to the beauty and simplicity of Ageton's.
    Still it was slow and not quick enough for air navigators so in the early 40s and especially during WWII tables of precomputed resolutions for given arguments were published. The navigator was restricted to selecting an assumed position that would make latitude and local hour angle (LHA) a whole degree but gained speed in working out the solution to the problem. This system and tables evolved in the 50s into HO249 for air navigators and later HO229 for marine navigators. Both are essentially the same but HO229 give more precision, are bulkier and a bit slower to use.
    With the advent of pocket programmable calculators and computers in the last two decades the resolution of the intercept method became almost instantaneous and manual methods were relegated to backup status. More advanced pocket computers include the calculations needed to determine the coordinates of the body observed and therefore make the Nautical Almanac unnecessary.
    This is a very brief summary of the history and evolution of celestial navigation. I have not gone into the development of astronomy which of course is crucial and the basis of celestial navigation nor into other aspects like sight corrections, etc.
    With the recent development of GPS and GPS receivers costing about 1/10th of the price of a decent sextant, celestial navigation is rapidly being lost as an art. It is not only useful as a backup system but beautiful and worthwhile in its own right.



    To the student who is about to start learning celestial navigation by the intercept method I would say this: The problem is always the same. You get to a point where you have three numbers (LHA, Declination, Latitude) and you need to calculate Hc and Zn. To do this you have a variety of methods at your disposal.
    As a first method I would suggest a programmable calculator. Get a solar one (you can't run out to buy batteries in the middle of the ocean) and program it yourself. Understand the calculator and what you are doing thoroughly. If you let someone else program it for you, later in the middle of an ocean you will never know what went wrong when you hit the wrong key or how to fix it. This is the fastest method of reducing a sight and you can get plenty of practice. Almost any scientific calculator or computer can be used to reduce sights. A spreadsheet is also a very convenient way of reducing sights.
    Once you master your calculator, learn Ageton's method. It is the total opposite: slow and prone to making mistakes but requires no batteries, only a small booklet with tables which will fit in the case of the sextant. It is great mental exercise, especially if you interpolate mentally.
    In third place you can learn HO229 or HO249 (I personally prefer HO229). These are faster than Ageton's but require you to carry some weight (and capital) in tables and you are restricted in the choice of your assumed position. It is the method first taught to students today (and the first one I learnt) but I believe this is a carryover from the days after WWII when calculators weren't around yet, these were the fastest methods available and were taught to everybody in the armed forces. Just like the 18th century navigator stuck with his backstaff for decades after sextants were around, today we stick to these methods even though we have calculators.
    I would say: You want practical speed and efficiency? Use a calculator. You want a secondary backup method, which is useful, flexible, elegant and sanctioned by tradition? Use Ageton's. For everyday use, instead of a calculator you want a manual method which is faster than Ageton's? Use HO249 or HO229. You still want to know more? As I said, there are literally hundreds of methods invented. Try the haversine method in Reed's nautical almanac or the Davies method in the Nautical Almanac. I personally don't like them much but that doesn't mean you won't either.

      Related pages:

      Rounding Cape Horn in a Windjammer
      Great Circle Sailing
      Navigation Problem (How to compensate for the effects of current.)
      Astronomy Tidbits

      Bibliography and links:

      Evolution of the Sextant
      The Lore of Sail by Sam Svensson and others
      American Practical Navigator by Bowditch.