TAB 4 Celestial Navigation - Chapter 16 - Instruments for Celestial Navigation.pdf - N. Bowditch - towotowo

CHAPTER 16

INSTRUMENTS FOR CELESTIAL NAVIGATION

THE MARINE SEXTANT

1600. Description And Use

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 inclina-

tion 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 ray from one point and a dou-

ble-reflected ray 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 mea-

suring 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 in-

strument 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

. In mod-

ern usage the term is applied to all modern navigational

altitude-measuring instruments regardless of angular range

or principles of operation.

to 120

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.

1601. Optical Principles Of A Sextant

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 (Figure 1601).

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

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

first of these equations,

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

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

BDC = 2BFC = 2BGC.

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

tions 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 be-

tween 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 vari-

ous designs; most are similar to this. Teeth mark the outer

273

274

INSTRUMENTS FOR CELESTIAL NAVIGATION

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

tude. 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.” Contrast this

with the limited-range device on older instruments. The re-

lease , F, is a spring-actuated clamp that keeps the tangent

screw engaged with the limb’s teeth. The observer can disen-

gage 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 al-

titude. 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 (generally of European manufacture) have verniers

graduated into only five parts, permitting readings to 0.2'.

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.

, if the instrument is in perfect adjustment. Shade

glasses , K, of varying darkness are mounted on the sex-

tant’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 “ob-

ject glass” (far end of telescope), which generally is shorter

in length and gives a greater field of view. The second tele-

scope, 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 invert-

ed 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 di-

rect 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 read-

ing 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.

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

275

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 re-

quired. 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.

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 im-

age 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 uncor-

rected reading of the sextant.

1603. Vernier Sextant

1605. Sextant Moon Sights

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 princi-

pally 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 be-

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

clamp screw and engaged with the index arm is a long tan-

gent 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 th-

eclamp 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.

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 day-

light 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

Use one of these three methods when making the initial

altitude approximation on 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 observa-

tion. 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 recov-

ered 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 alti-

tude 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.

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; observe the center of the

point of light. Because stars and planets have 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.

1604. Sextant Sun Sights

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 perpendicular. As the

observer rocks the sextant, the image of the sun appears to

move in an arc, and the observer 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 bot-

tom 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 index

arm with the drum or vernier slowly until the sun appears to

276

INSTRUMENTS FOR CELESTIAL NAVIGATION

1607. Taking A Sight

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 dis-

tinct 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 mo-

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

comparing watch, the assistant should be careful not to in-

terfere 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 not-

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

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 suf-

ficiently 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 sup-

plement 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 ap-

pears 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 sex-

tant, 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 ad-

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

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

and 70

1608. Reading The Sextant

Reading a micrometer drum sextant is done in three

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

row on the index arm in relation to the arc. The minutes are

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

Figure 1608a. Micrometer drum sextant set at 29

42.5'.

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 se-

lect bodies with a predicted altitude between 30

INSTRUMENTS FOR CELESTIAL NAVIGATION

277

Figure 1608b. Vernier sextant set at 29

42'30".

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

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 var-

ious figures are added algebraically. Thus, if the three parts

of a micrometer drum reading are ( - )1

42'30", or 29

and 58' on the micrometer drum were opposite zero on the

vernier, one would know that the reading was 39

58', not

58'. Similarly, any doubt as to the correct minute can be

removed by noting the fraction of a minute from the posi-

tion of the vernier. In Figure 1608a the reading is 29

, 56' and 0.3', the

42.5'.

total reading is ( - )1

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

, the

zero on the vernier is between 42' and 43', and the 0.5' grad-

uation 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 grad-

uated 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

and 30

1609. Developing Observational Skill

40' and

A well-constructed marine sextant is capable of measur-

ing angles with an instrument error not exceeding 0.1'. Lines

of position from altitudes of this accuracy would not be in er-

ror by more than about 200 yards. However, there are various

sources of error, other than instrumental, in altitudes mea-

sured by sextant. One of the principal sources is the observer.

The first fix a student celestial navigator plots is likely

to be disappointing. Most navigators require a great amount

of practice to develop the skill necessary for good observa-

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

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

graved 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

The arrow on the index mark is between 29

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