sextant

 

instrument for measuring the altitude of the sun or another celestial body; such measurements can then be used to determine the observer's geographical position or for other navigational, surveying, or astronomical applications. The term sextant is used generally to include related devices such as the quadrant, quintant, and octant. The sextant was invented independently in England and America in 1731. Its construction is based on the principle that a reflected ray of light leaves a plane surface at the same angle at which the direct ray strikes the surface. The sextant consists basically of a triangular frame, the bottom of which is a graduated arc of 60°; a telescope is attached horizontally to the plane of the frame. A small index mirror is mounted perpendicular to the frame at the top of a movable index arm or bar, which swings along the arc. In front of the telescope is the horizon glass, half transparent and half mirror. The image of the sun or other body is reflected from the index mirror to the mirror half of the horizon glass and then into the telescope. If the index (or image) arm is then adjusted so that the horizon is seen through the transparent half of the horizon glass, with the reflected image of the sun lined up with it, the sun's altitude can be read from the position of the index arm on the arc. By reference to navigational tables, the geographical position can then be determined. A sextant may be used on land with an “artificial horizon”—a small, shallow receptacle containing mercury, which gives a truly horizontal surface. In aerial navigation a bubble octant—sometimes called a bubble sextant—is used, in which a spirit level is reflected into the field of view in such a way that the center of the bubble indicates the true horizon.

This article is about the Sextant as used for navigation. For the astronomer's sextant, see Sextant (astronomical).

For the history and development of the sextant see Reflecting instruments

A sextant is a measuring instrument generally used to measure the angle of elevation of a celestial object above the horizon. Making this measurement is known as sighting the object, shooting the object, or taking a sight. The angle, and the time when it was measured, can be used to calculate a position line on a nautical or aeronautical chart. A common use of the sextant is to sight the sun at noon to find one's latitude. See celestial navigation for more discussion. Held horizontally, the sextant can be used to measure the angle between any two objects, such as between two lighthouses, which will, similarly, allow for calculation of a line of position on a chart.

The scale of a sextant has a length of ¹⁄₆ of a full circle (60°); hence the sextant's name (sextāns, -antis is the Latin word for "one sixth"). An octant is a similar device with a shorter scale (¹⁄₈ of a circle, or 45°), whereas a quintant (¹⁄₅, or 72°) and a quadrant (¹⁄₄, or 90°) have longer scales.

Sir Isaac Newton (1643-1727) invented the principle of the doubly reflecting navigation instrument (a reflecting quadrant - see Octant (instrument)), but never published it. Two men independently developed the octant around 1730: John Hadley (1682-1744), an English mathematician, and Thomas Godfrey (1704-1749), a glazier in Philadelphia. The octant and later the sextant, replaced the Davis quadrant as the main instrument for navigation.

Navigational Sextants

This section discusses navigator's sextants. Most of what is said about these specific sextants applies equally to other types of sextants. Navigator's sextants were primarily used for celestial navigation.

Advantages

Like the Davis quadrant (also called backstaff), the sextant allows celestial objects to be measured relative to the horizon, rather than relative to the instrument. This allows excellent precision. However, unlike the backstaff, the 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 alidade, as it is in a mariner's astrolabe or similar older instrument.

The horizon and celestial object remain steady when viewed through a sextant, even when the user is on a moving ship. This occurs because the sextant views the (unmoving) horizon directly, and views the celestial object through two opposed mirrors that subtract the motion of the sextant from the reflection.

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.

Anatomy of a sextant

The index arm moves the index mirror. The indicator points at the arc to show the measurement. The body ties everything together.

There are two types of sextants. Both types can give good results, and the choice between them is personal.

Traditional sextants have a half-horizon mirror. It 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, where the horizon can be difficult to see. However, one has to sweep the celestial object to assure 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. Modern sextants often have 5 cm or larger mirrors, while 19th century sextants rarely had a mirror larger than 2.5 cm (one inch). 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. This 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.

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 lighted artificial horizon.

Professional sextants use a click-stop degree measure, and a worm adjustment that reads to a minute, 1/60 of a degree. Most sextants also include a vernier on the worm dial that reads to 0.2 minute. Since 1 minute of error is about a nautical mile, the best possible accuracy of celestial navigation is about  nautical miles ( m). 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  nautical mile ( m).^[1]

A change in temperature can warp the arc, creating inaccuracies. Many navigators purchase weatherproof cases so their sextant can be placed outside the cabin to come to equilibrium with outside temperatures. The standard frame designs (see illustration) are supposed to equalize differential angular error from temperature changes. The handle is separated from the arc and frame so 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 aluminum. Brass is lower-expansion than aluminum, but aluminum sextants are lighter and less tiring to use. Some say they are more accurate because one's hand trembles less.

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, to compensate for random accelerations in the artificial horizon's fluid. Older aircraft sextants had two visual paths, one standard, another 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.

After a sight is taken, it is reduced to a position by following any of several mathematical procedures. The simplest sight reduction is to draw the equal-elevation 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.

Care

A sextant is a delicate instrument. If dropped, the arc might bend. After one has been dropped, its accuracy is suspect. Recertification is possible with surveying instruments and a large field, or with precision optical instruments. Repair is not possible.

To avoid worries about bent arcs, serious navigators traditionally buy their sextants new. Common wisdom is that a used sextant is probably bent. Many navigators refuse to share their sextant, to assure that its integrity is traceable. A used sextant lacking a case is very likely to have a bent arc.

Most sextants come with a neck-lanyard, and all but the cheapest come with a case. Traditional care is to put on the neck lanyard before removing the sextant from its case, and to always case the sextant between sights.

Adjustment

Due to the sensitivity of the instrument it is easy to knock the mirrors out of adjustment. 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. To test for this, place the index arm at about 60° on the arc and hold the sextant horizontally with the arc away from you at arms length and look into the index mirror. 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.

Side error

This occurs when the horizon glass/mirror is not perpendicular to the plane of the instrument. 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. 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. If there are two horizons there is side error; adjust the horizon glass/mirror until the stars merge into one image or the horizons are merged into one.

Collimation error

This is when the telescope or monocular is not parallel to the plane of the sextant. To check for this you need to observe two stars 90° or more apart. 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.

Index error

This occurs when the index and horizon mirrors are not parallel to each other when the index arm is set to zero. To test for index error, zero the index arm and observe the horizon. If the reflected and direct image of the horizon are in line there is no index error. If one is above the other adjust the index mirror until the two horizons merge. This can be done at night with a star or with the moon.

Further information on sextants

The "Bris" sextant

Sven Yrvind (Lundin) developed his "Bris" sextant as part of his quest for low-cost, low-technology equipment for ocean crossings. The "Bris" is a low-technology high-precision fixed-interval sextant. It's made of three narrow flat pieces of glass (microscope slides) permanently and rigidly mounted in a V-shape. When the sun or moon is viewed through the V, it is split into eight images. The sextant is small and rugged-enough that it can be kept in a film can (about 2 cm radius, 3 cm tall) on a lanyard around one's neck.

The "Bris" sextant is calibrated at a known geographic position with a good clock and a nautical almanac. As the day passes, one works the sight reductions backwards to develop exact angles for each of the images' tops and bottoms. The Sun and Moon have the same angular width from the surface of the Earth, and can use the same calibrations.

In use, one waits until an image's edge touches the horizon, and then records the time and reduces the sight using the recorded angle for that edge of the image.

See also

Notes

References

• Bowditch, Nathaniel (2002). The American Practical Navigator. Bethesda, MD: National Imagery and Mapping Agency. ISBN 0939837544. 
• Cutler, Thomas J. (December 2003). Dutton's Nautical Navigation, 15th, Annapolis, MD: Naval Institute Press. ISBN 978-1557502483. 
• Department of the Air Force (March 2001). Air Navigation (PDF), Department of the Air Force. Retrieved on 2007-04-17. 
• Great Britain Ministry of Defence (Navy) (1995). Admiralty Manual of Seamanship. The Stationery Office. ISBN 0117726966. 
• Encyclopædia Britannica (1911). "Navigation". Encyclopædia Britannica (11th edition) 19. Ed. Chisholm, Hugh. Retrieved on 2007-04-17. 
• Encyclopædia Britannica (1911). "Sextant". Encyclopædia Britannica (11th edition) 24. Ed. Chisholm, Hugh. 749-751. Retrieved on 2007-04-17. 
• Maloney, Elbert S. (December 2003). Chapman Piloting and Seamanship, 64th, New York, NY: Hearst Communications Inc.. ISBN 1-58816-098-0. 

External links

• Her Majesty's Nautical Almanac Office: http://www.nao.rl.ac.uk/
• The History of HM Nautical Almanac Office: http://www.nao.rl.ac.uk/nao/history/
• The home page of Mr Sven Yrvind: http://www.yrvind.com/ and his self-biography in Swedish, "Konstruktören" ("The Constructor"), ISBN 91-518-4154-1.
• A three page article on the Bris sextant appeared in Yachting Monthly magazine, June 1997.
• A two page article on the Bris sextant appeared in Die Yacht magazine, 22/1997: Mini-Sextant: Mit einem genial einfachen Gerät verblufft Weltumsegler Sven Lundin jetzt die gesamte Fachwelt.
• Instruments for Celestial NavigationPDF (361 KiB) Chapter from the online edition of Nathaniel Bowditch's American Practical Navigator
• CD-Sextant - Build your own sextant Simple do-it-yourself project.
• Lunars web site. online calculation
• Complete celnav theory book, including Lunars

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