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    Tuesday, 25 May 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 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.

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    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.

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    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 Slocumfor 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.

    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-Shockand a current copy of the Nautical Almanacyou 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 locationyou 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 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: 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. 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. 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. One answer will make perfect sense; the other will be nonsense. Finding Longitude 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 GHAwhich 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 quicklyand 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.

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    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 calledrather 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. 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 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 milebut 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.

    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. Get a friend who knows celestial to teach you or take a class.

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    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. 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. They are a great value and definitely give you the most bang for your buck.

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    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.
    Altitude corrections for sextant sights Jan 27, David Berson The corrections made to the Hs sextant altitude are necessary because the mathematical premise of celestial navigation has the observer taking a sight to the center of the celestial object from the center of the earth.

    Since we cannot physically replicate that assumption we have to factor in some additional corrections. Suffice it to say that the dip correction is always subtracted and is dependent upon the height of eye of the observer over the visible horizon.

    During a passage that height usually remains constant provided that the navigator takes sights from the same place on deck. The index error also usually remains constant unless of course the sextant is dropped. On a good sextant the error remains relatively constant and is not usually more than 2 or 3 feet.

    The next set of corrections referred to as altitude corrections, or 3rd corrections, are found on page A2 in the Nautical Almanac. These corrections combine refraction, parallax and semi diameter. This is what we are seeking. Light is bent as it enters the denser atmosphere of the earth.

    We all have observed how a pencil looks bent when placed in a glass of water — it is the same phenomenon with the light arriving from a celestial body. The effect is that the celestial object appears to be higher above the horizon than it actually is. The correction for refraction is therefore always negative. On page A2, refraction corrections are listed for stars and planets in different sections than for the sun. This correction applies to the sun and moon.

    The moon tables are at the rear of the Nautical Almanac and are a subject of another newsletter. It varies roughly between An examination of the daily sun pages at the bottom of the page shows the daily semi diameter labeled SD.

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    There are two columns in the altitude correction tables noting the months of the years when the sight is taken. A mistake in entering these tables would only yield an error of 0. Semi diameter must be factored because navigators are not observing the center of the sun, but instead sight either the upper or lower limb of the sun.

    Semi diameter is always added if the lower limb is observed and subtracted for the upper limb.

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    These differences are made obvious by the apparent altitude correction tables, which list both upper and lower limb sights. This is the third correction, which is basically the change in position of a celestial object as seen from two different locations. These locations can be said to be the center of the earth and the place on the surface on the earth where the navigator took his sight.

    The moon has the largest parallax. There is a table on page A2 for Venus and Mars, the two closest planets. The day of a lower limb sight of the sun is Dec. Index error is 2 feet on the arc. The height of eye dip is 10 feet.

    It is the 3rd correction, which includes refraction, semi diameter and parallax. Always choose the higher number.

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    If a mistake is made here it is not that damaging. The wrong choice will only throw the accuracy of the sight out by 0.
    Navigational sextants[ edit ] Using a sextant This section discusses navigators' sextants. Most of what is said about these specific sextants applies equally to other types of sextants.

    Navigators' sextants were primarily used for ocean navigation. Advantages[ edit ] Like the Davis quadrantthe sextant allows celestial objects to be measured relative to the horizon, rather than relative to the instrument. This allows excellent precision. However, unlike the backstaffthe sextant allows direct observations of stars.

    This permits the use of the sextant at night when a backstaff is difficult to use. For solar observations, filters allow direct observation of the sun. Since the measurement is relative to the horizon, the measuring pointer is a beam of light that reaches to the horizon.

    The measurement is thus limited by the angular accuracy of the instrument and not the sine error of the length of an alidadeas it is in a mariner's astrolabe or similar older instrument. A sextant does not require a completely steady aim, because it measures a relative angle. For example, when a sextant is used on a moving ship, the image of both horizon and celestial object will move around in the field of view.

    However, the relative position of the two images will remain steady, and as long as the user can determine when the celestial object touches the horizon, the accuracy of the measurement will remain high compared to the magnitude of the movement.

    The sextant is not dependent upon electricity unlike many forms of modern navigation or anything human-controlled like GPS satellites. For these reasons, it is considered an eminently practical back-up navigation tool for ships. Both smaller and larger instruments are or were in use: All of these instruments may be termed "sextants".

    Marine Sextant Using the sextant to measure the altitude of the Sun above the horizon Attached to the frame are the "horizon mirror", an index arm which moves the index mirror, a sighting telescope, sun shades, a graduated scale and a micrometer drum gauge for accurate measurements. The scale must be graduated so that the marked degree divisions register twice the angle through which the index arm turns.

    The necessity for the doubled scale reading follows by consideration of the relations of the fixed ray between the mirrorsthe object ray from the sighted object and the direction of the normal perpendicular to the index mirror.

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    This is the case shown in the graphic alongside. There are two types of horizon mirrors on the market today. Both types give good results. Traditional sextants have a half-horizon mirror, which divides the field of view in two. On one side, there is a view of the horizon; on the other side, a view of the celestial object. The advantage of this type is that both the horizon and celestial object are bright and as clear as possible.

    This is superior at night and in haze, when the horizon can be difficult to see. However, one has to sweep the celestial object to ensure that the lowest limb of the celestial object touches the horizon.

    Whole-horizon sextants use a half-silvered horizon mirror to provide a full view of the horizon. This makes it easy to see when the bottom limb of a celestial object touches the horizon. Since most sights are of the sun or moon, and haze is rare without overcast, the low-light advantages of the half-horizon mirror are rarely important in practice. In both types, larger mirrors give a larger field of view, and thus make it easier to find a celestial object.

    In large part, this is because precision flat mirrors have grown less expensive to manufacture and to silver. An artificial horizon is useful when the horizon is invisible, as occurs in fog, on moonless nights, in a calm, when sighting through a window or on land surrounded by trees or buildings. Professional sextants can mount an artificial horizon in place of the horizon-mirror assembly. An artificial horizon is usually a mirror that views a fluid-filled tube with a bubble.

    Most sextants also have filters for use when viewing the sun and reducing the effects of haze. The filters usually consist of a series of progressively darker glasses that can be used singly or in combination to reduce haze and the sun's brightness. However, sextants with adjustable polarizing filters have also been manufactured, where the degree of darkness is adjusted by twisting the frame of the filter. Most sextants mount a 1 or 3-power monocular for viewing.

    Many users prefer a simple sighting tube, which has a wider, brighter field of view and is easier to use at night. Some navigators mount a light-amplifying monocular to help see the horizon on moonless nights. Others prefer to use a lit artificial horizon. Most sextants also include a vernier on the worm dial that reads to 0. Since 1 minute of error is about a nautical milethe best possible accuracy of celestial navigation is about 0. At sea, results within several nautical miles, well within visual range, are acceptable.

    A highly skilled and experienced navigator can determine position to an accuracy of about 0. Many navigators purchase weatherproof cases so that their sextant can be placed outside the cabin to come to equilibrium with outside temperatures. The standard frame designs see illustration are supposed to equalise differential angular error from temperature changes.

    The handle is separated from the arc and frame so that body heat does not warp the frame. Sextants for tropical use are often painted white to reflect sunlight and remain relatively cool. High-precision sextants have an invar a special low-expansion steel frame and arc.

    Some scientific sextants have been constructed of quartz or ceramics with even lower expansions. Many commercial sextants use low-expansion brass or aluminium.

    Brass is lower-expansion than aluminium, but aluminium sextants are lighter and less tiring to use. Some say they are more accurate because one's hand trembles less. Solid brass frame sextants are less susceptible to wobbling in high winds or when the vessel is working in heavy seas, but as noted are substantially heavier. Sextants with aluminum frames and brass arcs have also been manufactured.

    Essentially, a sextant is intensely personal to each navigator, and he or she will choose whichever model has the features which suit them best. Aircraft sextants are now out of production, but had special features. Most had artificial horizons to permit taking a sight through a flush overhead window. Some also had mechanical averagers to make hundreds of measurements per sight for compensation of random accelerations in the artificial horizon's fluid.

    Older aircraft sextants had two visual paths, one standard and the other designed for use in open-cockpit aircraft that let one view from directly over the sextant in one's lap.

    More modern aircraft sextants were periscopic with only a small projection above the fuselage. With these, the navigator pre-computed his sight and then noted the difference in observed versus predicted height of the body to determine his position. Taking a sight[ edit ] A sight or measure of the angle between the suna staror a planetand the horizon is done with the 'star telescope ' fitted to the sextant using a visible horizon.

    On a vessel at sea even on misty days a sight may be done from a low height above the water to give a more definite, better horizon. Navigators hold the sextant by its handle in the right hand, avoiding touching the arc with the fingers. By setting the index bar to zero, the sun can be viewed through the telescope.

    Releasing the index bar either by releasing a clamping screw, or on modern instruments, using the quick-release buttonthe image of the sun can be brought down to about the level of the horizon. It is necessary to flip back the horizon mirror shade to be able to see the horizon, and then the fine adjustment screw on the end of the index bar is turned until the bottom curve the lower limb of the sun just touches the horizon.

    The angle of the sight is then read from the scale on the arc, making use of the micrometer or vernier scale provided. The exact time of the sight must also be noted simultaneously, and the height of the eye above sea-level recorded. Fine adjustments are then made as above. This method is less likely to be successful for sighting stars and planets.

    There is no need to use shades or to distinguish the lower limb as the body appears as a mere point in the telescope. The moon can be sighted, but it appears to move very fast, appears to have different sizes at different times, and sometimes only the lower or upper limb can be distinguished due to its phase.

    The simplest sight reduction is to draw the equal-altitude circle of the sighted celestial object on a globe. The intersection of that circle with a dead-reckoning track, or another sighting, gives a more precise location. Sextants can be used very accurately to measure other visible angles, for example between one heavenly body and another and between landmarks ashore. Used horizontally, a sextant can measure the apparent angle between two landmarks such as a lighthouse and a church spire, which can then be used to find the distance off or out to sea provided the distance between the two landmarks is known.

    Used vertically, a measurement of the angle between the lantern of a lighthouse of known height and the sea level at its base can also be used for distance off. For this reason a sextant should be checked frequently for errors and adjusted accordingly. There are four errors that can be adjusted by the navigator and they should be removed in the following order. Perpendicularity error This is when the index mirror is not perpendicular to the frame of the sextant. The arc of the sextant should appear to continue unbroken into the mirror.

    If there is an error, then the two views will appear to be broken. Adjust the mirror until the reflection and direct view of the arc appear to be continuous. To test for this, first zero the index arm then observe a star through the sextant. Then rotate the tangent screw back and forth so that the reflected image passes alternately above and below the direct view.

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    If in changing from one position to another, the reflected image passes directly over the unreflected image, no side error exists. If it passes to one side, side error exists. The user can hold the sextant on its side and observe the horizon to check the sextant during the day. Side error is generally inconsequential for observations and can be ignored or reduced to a level that is merely inconvenient. Collimation error This is when the telescope or monocular is not parallel to the plane of the sextant.

    Bring the two stars into coincidence either to the left or the right of the field of view. Move the sextant slightly so that the stars move to the other side of the field of view. If they separate there is collimation error. As modern sextants rarely use adjustable telescopes, they do not need to be corrected for collimation error.

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