Chapt-16.pdf

CHAPTER 16

INSTRUMENTS FOR CELESTIAL NAVIGATION

THE MARINE SEXTANT

1600. Description and Use

In Figure 1601 , AB is a ray of light from a celestial body.

The index mirror of the sextant is at B, the horizon glass at C,

and the eye of the observer at D. Construction lines EF and

CF are perpendicular to the index mirror and horizon glass,

respectively. Lines BG and CG are parallel to these mirrors.

Therefore, angles BFC and BGC are equal because their

sides are mutually perpendicular. Angle BGC is the

inclination of the two reflecting surfaces. The ray of light AB

is reflected at mirror B, proceeds to mirror C, where it is

again reflected, and then continues on to the eye of the

observer at D. Since the angle of reflection is equal to the

angle of incidence,

The marine sextant measures the angle between two

points by bringing the direct image from one point and a

double-reflected image from the other into coincidence. Its

principal use is to measure the altitudes of celestial bodies

above the visible sea horizon. It may also be used to measure

vertical angles to find the range from an object of known

height. Sometimes it is turned on its side and used for

measuring the angular distance between two terrestrial

objects.

A marine sextant can measure angles up to approxi-

mately 120

. Originally, the term “sextant” was applied to

the navigator’s double-reflecting, altitude-measuring

instrument only if its arc was 60

ABE = EBC, and ABC = 2EBC.

BCF = FCD, and BCD = 2BCF.

in length, or 1/6 of a

circle, permitting measurement of angles from 0

Since an exterior angle of a triangle equals the sum of

the two non adjacent interior angles,

ABC = BDC+BCD, and EBC = BFC+BCF.

Transposing,

BDC = ABC-BCD, and BFC = EBC-BCF.

In modern usage the term is applied to all modern naviga-

tional altitude-measuring instruments regardless of angular

range or principles of operation.

to 120

1601. Optical Principles of a Sextant

Substituting 2EBC for ABC, and 2BCF for BCD in the

first of these equations,

BDC = 2EBC-2BCF, or BDC=2 (EBC-BCF).

When a plane surface reflects a light ray, the angle of re-

flection equals the angle of incidence. The angle between the

first and final directions of a ray of light that has undergone

double reflection in the same plane is twice the angle the two

reflecting surfaces make with each other (Fi gure 1601).

Since BFC=EBC - BCF, and BFC = BGC, therefore

BDC = 2BFC = 2BGC.

That is, BDC, the angle between the first and last

directions of the ray of light, is equal to 2BGC, twice the

angle of inclination of the reflecting surfaces. Angle BDC

is the altitude of the celestial body.

If the two mirrors are parallel, the incident ray from any

observed body must be parallel to the observer’s line of sight

through the horizon glass. In that case, the body’s altitude

would be zero. The angle that these two reflecting surfaces

make with each other is one-half the observed angle. The

graduations on the arc reflect this half angle relationship

between the angle observed and the mirrors’ angle.

1602. Micrometer Drum Sextant

Figure 1601. Optical principle of the marine sextant.

Figure 1602 shows a modern marine sextant, called a

micrometer drum sextant . In most marine sextants, brass

or aluminum comprise the frame , A. Frames come in

261

262

INSTRUMENTS FOR CELESTIAL NAVIGATION

various designs; most are similar to this. Teeth mark the

outer edge of the limb , B; each tooth marks one degree of

altitude. The altitude graduations, C, along the limb, mark

the arc . Some sextants have an arc marked in a strip of

brass, silver, or platinum inlaid in the limb.

The index arm , D, is a movable bar of the same material

as the frame. It pivots about the center of curvature of the

limb. The tangent screw , E, is mounted perpendicularly on

the end of the index arm, where it engages the teeth of the

limb. Because the observer can move the index arm through

the length of the arc by rotating the tangent screw, this is

sometimes called an “endless tangent screw.” The release ,F,

is a spring-actuated clamp that keeps the tangent screw

engaged with the limb’s teeth. The observer can disengage

the tangent screw and move the index arm along the limb for

rough adjustment. The end of the tangent screw mounts a

micrometer drum , G, graduated in minutes of altitude. One

complete turn of the drum moves the index arm one degree

along the arc. Next to the micrometer drum and fixed on the

index arm is a vernier , H, that reads in fractions of a minute.

The vernier shown is graduated into ten parts, permitting

readings to 1 / 10 of a minute of arc (0.1'). Some sextants have

verniers graduated into only five parts, permitting readings to

0.2'.

, if the instrument is in perfect adjustment. Shade

glasses , K, of varying darkness are mounted on the

sextant’s frame in front of the index mirror and horizon

glass. They can be moved into the line of sight as needed to

reduce the intensity of light reaching the eye.

The telescope , L, screws into an adjustable collar in

line with the horizon glass and parallel to the plane of the

instrument. Most modern sextants are provided with only

one telescope. When only one telescope is provided, it is of

the “erect image type,” either as shown or with a wider

“object glass” (far end of telescope), which generally is

shorter in length and gives a greater field of view. The

second telescope, if provided, may be the “inverting type.”

The inverting telescope, having one lens less than the erect

type, absorbs less light, but at the expense of producing an

inverted image. A small colored glass cap is sometimes

provided, to be placed over the “eyepiece” (near end of

telescope) to reduce glare. With this in place, shade glasses

are generally not needed. A “peep sight,” or clear tube

which serves to direct the line of sight of the observer when

no telescope is used, may be fitted.

Sextants are designed to be held in the right hand.

Some have a small light on the index arm to assist in

reading altitudes. The batteries for this light are fitted inside

a recess in the handle , M. Not clearly shown in Figure 1602

are the tangent screw , E, and the three legs.

The index mirror , I, is a piece of silvered plate glass

mounted on the index arm, perpendicular to the plane of the

instrument, with the center of the reflecting surface directly

over the pivot of the index arm. The horizon glass ,J,isa

piece of optical glass silvered on its half nearer the frame.

Figure 1602. U.S. Navy Mark 2 micrometer drum sextant.

It is mounted on the frame, perpendicular to the plane of the

sextant. The index mirror and horizon glass are mounted so

that their surfaces are parallel when the micrometer drum is

set at 0

INSTRUMENTS FOR CELESTIAL NAVIGATION

263

There are two basic designs commonly used for mounting

and adjusting mirrors on marine sextants. On the U.S. Navy

Mark 3 and certain other sextants, the mirror is mounted so that

it can be moved against retaining or mounting springs within

its frame. Only one perpendicular adjustment screw is

required. On the U.S. Navy Mark 2 and other sextants the

mirror is fixed within its frame. Two perpendicular adjustment

screws are required. One screw must be loosened before the

other screw bearing on the same surface is tightened.

index arm with the drum or vernier slowly until the Sun

appears to be resting exactly on the horizon, tangent to the

lower limb. The novice observer needs practice to

determine the exact point of tangency. Beginners often err

by bringing the image down too far.

Some navigators get their most accurate observations

by letting the body contact the horizon by its own motion,

bringing it slightly below the horizon if rising, and above if

setting. At the instant the horizon is tangent to the disk, the

navigator notes the time. The sextant altitude is the

uncorrected reading of the sextant.

1603. Vernier Sextant

Most recent marine sextants are of the micrometer

drum type, but at least two older-type sextants are still in

use. These differ from the micrometer drum sextant

principally in the manner in which the final reading is

made. They are called vernier sextants .

The clamp screw vernier sextant is the older of the

two. In place of the modern release clamp, a clamp screw is

fitted on the underside of the index arm. To move the index

arm, the clamp screw is loosened, releasing the arm. When

the arm is placed at the approximate altitude of the body

being observed, the clamp screw is tightened. Fixed to the

clamp screw and engaged with the index arm is a long

tangent screw. When this screw is turned, the index arm

moves slowly, permitting accurate setting. Movement of the

index arm by the tangent screw is limited to the length of the

screw (several degrees of arc). Before an altitude is

measured, this screw should be set to the approximate mid-

point of its range. The final reading is made on a vernier set

in the index arm below the arc. A small microscope or

magnifying glass fitted to the index arm is used in making

the final reading.

The endless tangent screw vernier sextant is identical to

the micrometer drum sextant, except that it has no drum, and

the fine reading is made by a vernier along the arc, as with the

clamp screw vernier sextant. The release is the same as on the

micrometer drum sextant, and teeth are cut into the underside

of the limb which engage with the endless tangent screw.

1605. Sextant Moon Sights

When observing the Moon, follow the same procedure

as for the Sun. Because of the phases of the Moon, the upper

limb of the Moon is observed more often than that of the

Sun. When the terminator (the line between light and dark

areas) is nearly vertical, be careful in selecting the limb to

shoot. Sights of the Moon are best made during either

daylight hours or that part of twilight in which the Moon is

least luminous. At night, false horizons may appear below

the Moon because the Moon illuminates the water below it.

1606. Sextant Star and Planet Sights

While the relatively large Sun and Moon are easy to

find in the sextant, stars and planets can be more difficult to

locate because the field of view is so narrow. One of three

methods may help locate a star or planet:

Method 1 . Set the index arm and micrometer drum on

and direct the line of sight at the body to be observed.

Then, while keeping the reflected image of the body in the

mirrored half of the horizon glass, swing the index arm out

and rotate the frame of the sextant down. Keep the reflected

image of the body in the mirror until the horizon appears in

the clear part of the horizon glass. Then, make the

observation. When there is little contrast between

brightness of the sky and the body, this procedure is

difficult. If the body is “lost” while it is being brought

down, it may not be recovered without starting over again.

Method 2 . Direct the line of sight at the body while

holding the sextant upside down. Slowly move the index

arm out until the horizon appears in the horizon glass. Then

invert the sextant and take the sight in the usual manner.

Method 3 . Determine in advance the approximate

altitude and azimuth of the body by a star finder such as No.

2102D. Set the sextant at the indicated altitude and face in

the direction of the azimuth. The image of the body should

appear in the horizon glass with a little searching.

1604. Sextant Sun Sights

For a Sun sight, hold the sextant vertically and direct the

sight line at the horizon directly below the Sun. After moving

suitable shade glasses into the line of sight, move the index

arm outward along the arc until the reflected image appears in

the horizon glass near the direct view of the horizon. Rock the

sextant slightly to the right and left to ensure it is perpen-

dicular. As you rock the sextant, the image of the Sun appears

to move in an arc, and you may have to turn slightly to prevent

the image from moving off the horizon glass.

The sextant is vertical when the Sun appears at the

bottom of the arc. This is the correct position for making the

observation. The Sun’s reflected image appears at the

center of the horizon glass; one half appears on the silvered

part, and the other half appears on the clear part. Move the

When measuring the altitude of a star or planet, bring

its center down to the horizon. Stars and planets have no

discernible upper or lower limb; you must observe the

center of the point of light. Because stars and planets have

264

INSTRUMENTS FOR CELESTIAL NAVIGATION

no discernible limb and because their visibility may be

limited, the method of letting a star or planet intersect the

horizon by its own motion is not recommended. As with the

Sun and Moon, however, “rock the sextant” to establish

perpendicularity.

1608. Reading the Sextant

Reading a micrometer drum sextant is done in three

steps. The degrees are read by noting the position of the

arrow on the index arm in relation to the arc. The minutes

are read by noting the position of the zero on the vernier

with relation to the graduations on the micrometer drum.

The fraction of a minute is read by noting which mark on

the vernier most nearly coincides with one of the

graduations on the micrometer drum. This is similar to

reading the time with the hour, minute, and second hands of

a watch. In both, the relationship of one part of the reading

to the others should be kept in mind. Thus, if the hour hand

of a watch were about on “4,” one would know that the time

was about four o’clock. But if the minute hand were on

“58,” one would know that the time was 0358 (or 1558), not

0458 (or 1658). Similarly, if the arc indicated a reading of

about 40

1607. Taking a Sight

. Take

sights of the brightest stars first in the evening; take sights

of the brightest stars last in the morning.

Occasionally, fog, haze, or other ships in a formation

may obscure the horizon directly below a body which the

navigator wishes to observe. If the arc of the sextant is

sufficiently long, a back sight might be obtained, using the

opposite point of the horizon as the reference. For this the

observer faces away from the body and observes the

supplement of the altitude. If the Sun or Moon is observed

in this manner, what appears in the horizon glass to be the

lower limb is in fact the upper limb, and vice versa. In the

case of the Sun, it is usually preferable to observe what

appears to be the upper limb. The arc that appears when

rocking the sextant for a back sight is inverted; that is, the

highest point indicates the position of perpendicularity.

If more than one telescope is furnished with the

sextant, the erecting telescope is used to observe the Sun. A

wider field of view is present if the telescope is not used.

The collar into which the sextant telescope fits may be

adjusted in or out, in relation to the frame. When moved in,

more of the mirrored half of the horizon glass is visible to

the navigator, and a star or planet is more easily observed

when the sky is relatively bright. Near the darker limit of

twilight, the telescope can be moved out, giving a broader

view of the clear half of the glass, and making the less

distinct horizon more easily discernible. If both eyes are

kept open until the last moments of an observation, eye

strain will be lessened. Practice will permit observations to

be made quickly, reducing inaccuracy due to eye fatigue.

When measuring an altitude, have an assistant note and

record the time if possible, with a “stand-by” warning when

the measurement is almost ready, and a “mark” at the

moment a sight is made. If a flashlight is needed to see the

comparing watch, the assistant should be careful not to

interfere with the navigator’s night vision.

If an assistant is not available to time the observations, the

observer holds the watch in the palm of his left hand, leaving his

fingers free to manipulate the tangent screw of the sextant. After

making the observation, he notes the time as quickly as possible.

The delay between completing the altitude observation and

noting the time should not be more than one or two seconds.

and 70

, and 58' on the micrometer drum were opposite

zero on the vernier, one would know that the reading was

58'. Similarly, any doubt as to the correct

minute can be removed by noting the fraction of a minute

from the position of the vernier. In Figure 1608a the reading

is 29

58', not 40

42.5'. The arrow on the index mark is between 29

, the zero on the vernier is between 42' and 43', and

the 0.5' graduation on the vernier coincides with one of the

graduations on the micrometer drum.

The principle of reading a vernier sextant is the same, but

the reading is made in two steps. Figure 1608b shows a typical

altitude setting. Each degree on the arc of this sextant is

graduated into three parts, permitting an initial reading by the

reference mark on the index arm to the nearest 20' of arc. In

this illustration the reference mark lies between 29

40' and

00', indicating a reading between these values. The reading

for the fraction of 20' is made using the vernier, which is

engraved on the index arm and has the small reference mark as

its zero graduation. On this vernier, 40 graduations coincide

with 39 graduations on the arc. Each graduation on the vernier

is equivalent to 1/40 of one graduation of 20' on the arc, or 0.5',

or 30". In the illustration, the vernier graduation representing 2

1/2' (2'30") most nearly coincides with one of the graduations

on the arc. Therefore, the reading is 29

42.5', as

before. When a vernier of this type is used, any doubt as to

which mark on the vernier coincides with a graduation on the

arc can usually be resolved by noting the position of the vernier

mark on each side of the one that seems to be in coincidence.

Negative readings, such as a negative index correction,

are made in the same manner as positive readings; the

various figures are added algebraically. Thus, if the three

parts of a micrometer drum reading are(-)1

42'30", or 29

, 56' and 0.3',

the total reading is ( - )1

+ 56' + 0.3' = ( - )3.7'.

1609. Developing Observational Skill

A well-constructed marine sextant is capable of

measuring angles with an instrument error not exceeding 0.1'.

Lines of position from altitudes of this accuracy would not be

Unless you have a navigation calculator or computer

that will identify bodies automatically, predict expected

altitudes and azimuths for up to eight bodies when

preparing to take celestial sights. Choose the stars and

planets that give the best bearing spread. Try to select

bodies with a predicted altitude between 30

and 30

INSTRUMENTS FOR CELESTIAL NAVIGATION

265

Figure 1608a. Micrometer drum sextant set at 29

42.5'.

Figure 1608b. Vernier sextant set at 29

42'30".

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