Techniques & Tactics
- Category: Techniques & Tactics
- Created: Tuesday, 25 May 2010 15:55
- Written by Charles Doane
You may recall I threatened to abuse you with knowledge of celestial navigation back when they shut down the Loran system in February. I have long preached the wisdom of learning and practicing a bit of celestial nav, and once upon a time I actually practiced what I preached (as you can see in the photo up top, which is of me shooting the sun on Crazy Horse while en route from the Cape Verdes to Antigua in 1997). I still keep a sextant onboard, but I realized when I sat down to compose a celestial diatribe to share with you that it actually has been many years since I ever used it. Before lecturing you, therefore, I figured I best brush up a bit and so liberated my old Plath Navistar Pro from its tomb aboard Lunacy while sailing from Tortola to Bermuda last week.
I was amazed at how much I had forgotten. Fortunately, too, I was amazed at how much I remembered again after I pondered over my sextant, my old celestial nav workbook, and the Nautical Almanac for a while. In the end, it was reassuring to know I could still more or less figure out where I was without any help from satellites.
Those who are truly expert at celestial navigation do seem to enjoy making it mysterious and incomprehensible to the rest of us. Joshua Slocum, for example, was extremely coy on the subject. Early on in his classic Sailing Alone Around the World he boasts of his five-and-dime alarm clock chronometer and lets us believe he was quite casual about his navigation. Only much later, in an arch aside, does he note he was in fact a "lunarian." That is, he solved for longitude using the impossibly arcane and esoteric lunar distance method, and so did not need an accurate chronometer.
In reality, however, locating yourself at sea with a sextant can be quite simple. You don't need to learn spherical trigonometry and differential calculus; you don't even really need to learn how to use sight reduction tables. With a sextant, an accurate quartz watch (I use a Casio G-Shock), and a current copy of the Nautical Almanac, you can always shoot the sun at noon and get a very good idea of your latitude and a rough idea of your longitude without having to do anything terribly complicated.
Solving for Latitude
Imagine the sun is aloft at the top a giant pole. You know the height of the pole and the location of the base of the pole (this is what the almanac is for). If you measure the angle between the ground and your line of sight to the sun (or, same difference, the altitude of the sun as it appears from your location), you can figure out how far you are from the base of the pole. All persons that distance from the pole will see the sun at the same angle or altitude, and they can be ranged around the pole in a perfect circle of 360 degrees. This circle is one line of position (LOP). You can get a second LOP simply by taking a straight compass bearing on the sun. It will intersect the first LOP at your location.
In reality, however, compasses are not nearly sensitive enough to take an accurate bearing on the sun (or any other celestial body). A compass bearing can in fact only provide a vague idea of where you are among the vast circle of observers surrounding the base of the sun's pole at any given time. The one time during the day when you can obtain a precise bearing on the sun is at local noon, when the sun as you see it is as high in the sky as it will get that day. At that moment the sun is either directly north or south of you and any LOP obtained from it by measuring its altitude will coincide exactly with your latitude. Finding latitude from a noon sight is the simplest celestial nav calculation there is and yields very accurate results. It runs as follows:
1. Subtract the sun's precise observed altitude (in degrees, minutes, and seconds) at local noon from 90 degrees (the total number of degrees of latitude within your hemisphere). The result is called your Zenith Distance (ZD).
2. Look in your Nautical Almanac to see what the declination of the sun was to the nearest hour of when noon occurred at your location. (Note that the sun's declination is the same as the latitude of the base of the pole we imagine it is sitting upon.)
3. Add the sun's declination to ZD if you and the sun are in the same hemisphere; subtract it from ZD if you are not. This result is your latitude. (If you're so clueless you're not sure what hemisphere the sun is in, don't worry. The almanac has the answer. If you're not sure what hemisphere you are in--i.e., you're very close to equator and could be on either side--just run the equation both ways. One answer will make perfect sense; the other will be nonsense.)
Obviously, if the sun is directly north or south of you at noon, you and the sun must be on the same line of longitude at that time. If you know exactly what time noon occurred at your location, you can simply look in the Nautical Almanac to find your longitude. This will be same as the sun's Greenwich Hour Angle (GHA), which is the equivalent to the longitude of the base of the sun's pole.
The tricky part is getting the exact time of the event. The sun moves quickly (or rather the earth turns quickly), and even a couple of seconds of timing error will throw your position fix off by several miles. Even if you have a perfectly accurate watch, getting an exact time for noon is problematic. The sun always seems to hang at its highest (or meridian) altitude each day for a couple of minutes or so, and to time noon precisely you need to figure out exactly when the middle of that "hang time" is.
The technique I use to do this is fairly straightforward. I get out my sextant 15 to 20 minutes before I expect noon to take place (you can easily get a rough estimate from the almanac) and take a leisurely series of sights as the sun climbs higher in the sky. The sights I feel particularly good about I mark with an asterisk. After the sun reaches its meridian altitude, I preset the sextant to the altitudes for the three or four sights I felt were my best when the sun was going up and carefully record the time when the sun again hits those altitudes going back down. I then calculate the time spreads between each set of matched sights and figure out the time of the mid-point of each spread. These times I average together to arrive at a best estimate of when precisely noon took place.
Correcting Sextant Sights
There are various corrections you need to make to any raw sextant sight, and this does slightly complicate the business of taking noon sights. Remembering what corrections to make was in fact what slowed me down most when I first starting playing with my sextant again on my most recent passage.
Really, though, it's not a big deal. You may need to make corrections first for watch error, which means adding or subtracting a few seconds from your observation times if your watch tends to run a little fast or slow. To do this, you must know the rate at which your watch loses or gains time. You may also need to correct for what is called "index error," which relates to small flaws in sextants, usually having to do with the mirrors, that cause altitude readings to be off slightly.
There are two other corrections you always have to make to any sight you take with a sextant, even if your watch and sextant are perfect. The first is for dip, which relates to the height of your eye above the water when you take a sight. The second is called an altitude or diameter correction. This compensates for the fact that you are measuring the distance between the horizon and the bottom of the sun (or "lower limb," as it is called), rather than the center of the sun. The correction varies depending on the sun's altitude, as the apparent diameter of the sun varies depending on how much atmosphere you see it through. (The closer to the horizon, the more atmospheric refraction there is, and hence the sun looks fatter.) Tables for both dip and altitude corrections appear in the Nautical Almanac.
Quick & Dirty Noon Sights in Practice
Classically trained celestial navigators usually take a series of three sun sights over the course of a day. The morning and noon sights are advanced according to the course and distance traversed in the interim and are merged with an afternoon sight to create three different LOPs that criss-cross to offer what should be a very accurate fix of the boat's position at the time of the last sun sight each day. Said navigator also takes sights of various stars at sunrise and sunset, and thus, you can see, is busy for much of the day. This is why navigators were treated as minor deities on sailing vessels of old and never had to stand any watches.
Such a regimen obviously makes no sense for a modern navigator (particularly a singlehander) who merely wants to use celestial as a back-up to electronic navigation. After I first took a formal celestial nav course in the early '90s, I quickly deduced for myself the longitude-finding method described above and resolved only to take noon sights on a regular basis. A couple of hoary old salts I knew assured me that my quick-and-dirty longitude method was a travesty and insult to the art of celestial navigation. But I was very gratified when I later learned that Bernard Moitessier in fact used the very same method on his various voyages.
I was also gratified when I found it in fact works pretty well. While crossing the Atlantic for the first time aboard the schooner Constellation in 1992 I took quick-and-dirty noon sights every day. Once I really got the hang of swinging a sextant and parking the sun's butt on the horizon, my noon fixes routinely were accurate within less than one mile on latitude and within five miles on longitude. In the age of GPS I realize this sounds grossly inaccurate. But in reality, if you're making a landfall after many days at sea, it should be more than good enough to put you where you want to be.
My most recent foray into the sky with my sextant was rather sobering. In a sense it accurately simulated the predicament I might find myself in if, after many years of not practicing, I had to break out a sextant after losing GPS service while at sea. My results were very good as to latitude (again, within one nautical mile), but very poor as to longitude (within 16 to 25 miles, over three days of sights). I am confident, however, given several days of practice, I could achieve my old level of accuracy. By far the most difficult part of celestial navigation is handling a sextant and taking good sights on a moving boat with waves obstructing the horizon. The only way to get proficient at it is to do it repeatedly. Which is why it isn't a bad idea to break out the sextant for a little while on every passage you take.
Still, the sloppy sights I was taking approaching Bermuda were not without value. With accurate latitude lines and fuzzy longitude data you can still make very safe landfalls using the old "running down your latitude" method of navigation. In this case, for example, coming at Bermuda from the south, if I had lost GPS service, all I had do to was sail well east of Bermuda, then approach it on the latitude of St. George's, my destination.
Selecting and Learning to Use a Sextant
No matter how many GPS receivers you have on board, you should still carry a sextant as a back-up if you plan to do much offshore sailing. You should also learn to use it. If you're truly dedicated you can learn from a book (I'd recommend trying Celestial Navigation Step by Step, by Warren Norville, or the classic Celestial Navigation for Yachtsmen, by Mary Blewitt), but it's much easier to have someone else show you. Get a friend who knows celestial to teach you or take a class. Also, start by taking sights on shore before trying it at sea.
If you really want to learn sextants, it's also best to start out with a plastic one. The mirrors on these need tuning each time you use them, and this forces you to get good at it. They're also cheap and reasonably accurate. I used a plastic Davis Mark 15 (they sell new now for around $170) during my transatlantic aboard Constellation and had good results, as described above. One big advantage to using a plastic sextant is that they are very light and easy to handle. They do not last forever, however, as eventually the plastic female threads for the metal tuning screws on the mirrors wear out. Nor can they be used in high winds, as they tend to vibrate.
When you're ready to move to a more durable metal sextant, you'll find there are still three or four manufacturers to choose from. The most popular is the Astra IIIB, from China, which costs about $600 new. They are a great value and definitely give you the most bang for your buck. A very fine sextant, such as a top-of-the-line Cassens & Plath model, can cost over $2,000. Used sextants in good condition normally sell for about half the price of a new one and are also often a good value. Good sources for these are Robert White Instruments and maritime academies, where students will be looking to sell sextants they were forced to buy for their celestial classes.
When selecting a sextant, you should be most interested in the mirrors. Large mirrors are easier to work with than small ones, as they capture more light and it is easier to keep errant celestial bodies within their boundaries. Full-horizon coated mirrors are easiest to use when shooting the sun, but the coating absorbs a fair amount of light and can make it difficult to shoot planets and stars. If you plan to shoot more than just noon sites you should opt for traditional split-horizon mirrors (or look for a sextant that allows you to change the mirrors).
If you want to shoot stars and planets (including the moon), you should also invest in a celestial nav calculator, as this will save you from tearing your hair out over sight reduction tables. A good nav calculator will have an almanac programmed into it, plus can identify stars for you, so you can shoot shiny objects first and ask questions later. I recently replaced my faithful and much loved Celesticomp V calculator (the ephemeris, or internal almanac, has expired and the company is now, alas, out of business) with a brand new T89 StarPilot calculator. I'll be sure to give you a run-down on it as soon as I figure out how the hell it works.
BoaterMouth link: here