TAB 4 Celestial Navigation - Chapter 20 - Sight Reduction.pdf - N. Bowditch - was72

CHAPTER 20

SIGHT REDUCTION

BASIC PRINCIPLES

2000. Introduction

a chart required to plot this large distance would be imprac-

tical. To eliminate this problem, the navigator does not plot

this line of position directly. Indeed, he does not plot the GP

at all. Rather, he chooses an assumed position (AP) near,

but usually not coincident with, his DR position. The navi-

gator chooses the AP’s latitude and longitude to correspond

to the entering arguments of LHA and latitude used in the

Sight Reduction Tables . From the Sight Reduction Tables ,

the navigator computes what the body’s altitude would

have been had it been measured from the AP. This yields

the computed altitude (h c ). He then compares this com-

puted value with the observed altitude (h o ) obtained at his

actual position. The difference between the computed and

observed altitudes is directly proportional to the distance

between the circles of equal altitude for the assumed posi-

tion and the actual position. The Sight Reduction Tables

also give the direction from the GP to the AP. Having se-

lected the assumed position, calculated the distance

between the circles of equal altitude for that AP and his ac-

tual position, and determined the direction from the

assumed position to the body’s GP, the navigator has

enough information to plot a line of position (LOP).

To plot an LOP, plot the assumed position on either a

chart or a plotting sheet. From the Sight Reduction Tables ,

determine: 1) the altitude of the body for a sight taken at the

AP and 2) the direction from the AP to the GP. Then, deter-

mine the difference between the body’s calculated altitude

at this AP and the body’s measured altitude. This difference

represents the difference in radii between the equal altitude

circle passing through the AP and the equal altitude circle

passing through the actual position. Plot this difference

from the AP either towards or away from the GP along the

axis between the AP and the GP. Finally, draw the circle of

equal altitude representing the circle with the body’s GP at

the center and with a radius equal to the distance between

the GP and the navigator’s actual position.

One final consideration simplifies the plotting of the

equal altitude circle. Recall that the GP is usually thousands

of miles away from the navigator’s position. The equal alti-

tude circle’s radius, therefore, can be extremely large. Since

this radius is so large, the navigator can approximate the sec-

tion close to his position with a straight line drawn

perpendicular to the line connecting the AP and the GP. This

straight line approximation is good only for sights of rela-

tively low altitudes. The higher the altitude, the shorter the

distance between the GP and the actual position, and the

Reducing a celestial sight to obtain a line of position

consists of six steps:

1. Correcting sextant altitude (hs) to obtain observed

altitude (ho).

2. Determining the body’s GHA and declination.

3. Selecting an assumed position and finding that po-

sition’s local hour angle.

4. Computing altitude and azimuth for the assumed

position.

5. Comparing computed and observed altitudes.

6. Plotting the line of position.

This chapter concentrates on using the Nautical Alma-

nac and Pub. No. 229, Sight Reduction Tables for Marine

Navigation.

The introduction to each volume of the Sight Reduction

Tables contains information: (1) discussing use of the publi-

cation in a variety of special celestial navigation techniques;

(2) discussing interpolation, explaining the double second

difference interpolation required in some sight reductions,

and providing tables to facilitate the interpolation process;

and (3) discussing the publication’s use in solving problems

of great circle sailings. Prior to using the Sight Reduction

Tables , carefully read this introductory material.

Celestial navigation involves determining a circular

line of position based on an observer’s distance from a ce-

lestial body’s geographic position (GP). Should the

observer determine both a body’s GP and his distance from

the GP, he would have enough information to plot a line of

position; he would be somewhere on a circle whose center

was the GP and whose radius equaled his distance from that

GP. That circle, from all points on which a body’s measured

altitude would be equal, is a circle of equal altitude . There

is a direct proportionality between a body’s altitude as mea-

sured by an observer and the distance of its GP from that

observer; the lower the altitude, the farther away the GP.

Therefore, when an observer measures a body’s altitude he

obtains an indirect measure of the distance between himself

and the body’s GP. Sight reduction is the process of con-

verting that indirect measurement into a line of position.

Sight reduction reduces the problem scale to manage-

able size. Depending on a body’s altitude, its GP could be

thousands of miles from the observer’s position. The size of

307

308

SIGHT REDUCTION

smaller the circle of equal altitude. The shorter this distance,

the greater the inaccuracy introduced by this approximation.

the radii of the circles of equal altitude passing through the

AP and the observers actual position. The position having

the greater altitude is on the circle of smaller radius and is

closer to the observed body’s GP. In Figure 2003, the AP is

shown on the inner circle. Therefore, h c is greater than h o .

Express the altitude intercept in nautical miles and la-

bel it T or A to indicate whether the line of position is

toward or away from the GP, as measured from the AP.

A useful aid in remembering the relation between h o ,

h c , and the altitude intercept is: H o M o T o for H o More To-

ward. Another is C-G-A: Computed Greater Away,

remembered as Coast Guard Academy. In other words, if h o

is greater than h c , the line of position intersects a point mea-

sured from the AP towards the GP a distance equal to the

altitude intercept. Draw the LOP through this intersection

point perpendicular to the axis between the AP and GP.

2001. Selection Of The Assumed Position (AP)

Use the following arguments when entering the Sight

Reduction Tables to compute altitude (h c ) and azimuth:

1. Latitude (L).

2. Declination (d or Dec.).

3. Local hour angle (LHA).

Latitude and LHA are functions of the assumed posi-

tion. Select an AP longitude resulting in a whole degree of

LHA and an AP latitude equal to that whole degree of lati-

tude closest to the DR position. Selecting the AP in this

manner eliminates interpolation for LHA and latitude in the

Sight Reduction Tables .

Reducing the sight using a computer or calculator sim-

plifies this AP selection process. Simply choose any

convenient position such as the vessel’s DR position as the

assumed position. Enter the information required by the spe-

cific celestial program in use. Using a calculator reduces the

math and interpolation errors inherent in using the Sight Re-

duction tables. Enter the required calculator data carefully.

2003. Plotting The Line Of Position

Plot the line of position as shown in Figure 2003. Plot

the AP first; then plot the azimuth line from the AP toward

or away from the GP. Then, measure the altitude intercept

along this line. At the point on the azimuth line equal to the

intercept distance, draw a line perpendicular to the azimuth

line. This perpendicular represents that section of the circle

of equal altitude passing through the navigator’s actual po-

sition. This is the line of position.

A navigator often takes sights of more than one celes-

tial body when determining a celestial fix. After plotting the

lines of position from these several sights, advance the re-

sulting LOP’s along the track to the time of the last sight

and label the resulting fix with the time of this last sight.

2002. Comparison Of Computed And Observed

Altitudes

The difference between the computed altitude (h c ) and

the observed altitude (h o ) is the altitude intercept (a).

The altitude intercept is the difference in the length of

Figure 2003. The basis for the line of position from a celestial observation.

SIGHT REDUCTION

309

2004. Recommended Sight Reduction Procedure

lists these corrections.

Additional Correction: Enter this additional correction

from Table A 4 located at the front of the Almanac when ob-

taining a sight under non-standard atmospheric temperature

and pressure conditions. This correction is a function of at-

mospheric pressure, temperature, and apparent altitude.

Horizontal Parallax Correction: This correction is

unique to reducing moon sights. Obtain the H.P. correction val-

ue from the daily pages of the Almanac . Enter the H.P correction

table at the back of the Almanac with this value. The H.P correc-

tion is a function of the limb of the moon used (upper or lower),

the apparent altitude, and the H.P. correction factor. The H.P.

correction is always added to the apparent altitude.

Moon Upper Limb Correction: Enter -30' for this

correction if the sight was of the upper limb of the moon.

Correction to Apparent Altitude: Sum the altitude cor-

rection, the Mars or Venus additional correction, the additional

correction, the horizontal parallax correction, and the moon’s

upper limb correction. Be careful to determine and carry the al-

gebraic sign of the corrections and their sum correctly. Enter

this sum as the correction to the apparent altitude.

Observed Altitude: Apply the Correction to Apparent

Altitude algebraically to the apparent altitude. The result is

the observed altitude.

Just as it is important to understand the theory of sight

reduction, it is also important to develop a working proce-

dure to reduce celestial sights accurately. Sight reduction

involves several consecutive steps, the accuracy of each

completely dependent on the accuracy of the steps that went

before. Sight reduction tables have, for the most part, re-

duced the mathematics involved to simple addition and

subtraction. However, careless errors will render even the

most skillfully measured sights inaccurate. The navigator

must work methodically to reduce these careless errors.

Naval navigators will most likely use OPNAV 3530, U.S.

Navy Navigation Workbook, which contains pre-formatted

pages with “strip forms” to guide the navigator through sight

reduction. A variety of commercially-produced forms are also

available. Pick a form and learn its method thoroughly . With

familiarity will come increasing understanding.

Figure 2004 represents a functional and complete

worksheet designed to ensure a methodical approach to any

sight reduction problem. The recommended procedure dis-

cussed below is not the only one available; however, the

navigator who uses it can be assured that he has considered

every correction required to obtain an accurate fix.

SECTION ONE consists of two parts: (1) Correcting

sextant altitude to obtain apparent altitude; and (2) Correct-

ing the apparent altitude to obtain the observed altitude.

Body: Enter the name of the body whose altitude you

have measured. If using the sun or the moon, indicate which

limb was measured.

Index Correction: This is determined by the charac-

teristics of the individual sextant used. Chapter 16 discusses

determining its magnitude and algebraic sign.

Dip: The dip correction is a function of the height of

eye of the observer. It is always negative; its magnitude is

determined from the Dip Table on the inside front covert of

the Nautical Almanac .

Sum: Enter the algebraic sum of the dip correction and

the index correction.

Sextant Altitude: Enter the altitude of the body mea-

sured by the sextant.

Apparent Altitude: Apply the sum correction deter-

mined above to the measured altitude and enter the result as

the apparent altitude.

Altitude Correction: Every observation requires an

altitude correction. This correction is a function of the ap-

parent altitude of the body. The Almanac contains tables for

determining these corrections. For the sun, planets, and

stars, these tables are located on the inside front cover and

facing page. For the moon, these tables are located on the

back inside cover and preceding page.

Mars or Venus Additional Correction: As the name im-

plies, this correction is applied to sights of Mars and Venus. The

correction is a function of the planet measured, the time of year,

and the apparent altitude. The inside front cover of the Almanac

SECTION TWO determines the Greenwich Mean

Time (GMT) and GMT date of the sight.

Date: Enter the local time zone date of the sight.

DR Latitude: Enter the dead reckoning latitude of the

vessel.

DR Longitude: Enter the dead reckoning longitude of

the vessel.

Observation Time: Enter the local time of the sight as

recorded on the ship’s chronometer or other timepiece.

Watch Error: Enter a correction for any known watch

error.

Zone Time: Correct the observation time with watch

error to determine zone time.

Zone Description: Enter the zone description of the

time zone indicated by the DR longitude. If the longitude is

west of the Greenwich Meridian, the zone description is

positive. Conversely, if the longitude is east of the Green-

wich Meridian, the zone description is negative. The zone

description represents the correction necessary to convert

local time to Greenwich Mean Time.

Greenwich Mean Time: Add to the zone description

the zone time to determine Greenwich Mean Time.

Date: Carefully evaluate the time correction applied

above and determine if the correction has changed the date.

Enter the GMT date.

SECTION THREE determines two of the three argu-

ments required to enter the Sight Reduction Tables : Local

Hour Angle (LHA) and Declination. This section employs

the principle that a celestial body’s LHA is the algebraic sum

of its Greenwich Hour Angle (GHA) and the observer’s lon-

310

SIGHT REDUCTION

Figure 2004. Complete sight reduction form.

SIGHT REDUCTION

311

gitude. Therefore, the basic method employed in this section

is: (1) Determine the body’s GHA; (2) Determine an as-

sumed longitude; (3) Algebraically combine the two

quantities, remembering to subtract a western assumed lon-

gitude from GHA and to add an eastern longitude to GHA;

and (4) Extract the declination of the body from the appropri-

ate Almanac table, correcting the tabular value if required.

addition or subtraction.

Assumed Longitude: If the vessel is west of the prime

meridian, the assumed longitude will be subtracted from the

GHA to determine LHA. If the vessel is east of the prime

meridian, the assumed longitude will be added to the GHA

to determine the LHA. Select the assumed longitude to

meet the following two criteria: (1) When added or sub-

tracted (as applicable) to the GHA determined above, a

whole degree of LHA will result; and (2) It is the longitude

closest to that DR longitude that meets criterion (1) above.

Local Hour Angle (LHA): Combine the body’s GHA

with the assumed longitude as discussed above to deter-

mine the body’s LHA.

(1) Tabulated Declination and d Correction factor:

(1) Obtain the tabulated declination for the sun, the moon,

the stars, or the planets from the daily pages of the Almanac .

The declination values for the stars are given for the entire

three day period covered by the daily page of the Almanac .

The values for the sun, moon, and planets are listed in hourly

increments. For these bodies, enter the declination value for

the whole hour of the sight. For example, if the sight is at 12-

58-40, enter the tabulated declination for 1200. (2) There is

no d correction factor for a star sight. There are d correction

factors for sun, moon, and planet sights. Similar to the v cor-

rection factor discussed above, the d correction factor does

not equal the magnitude of the d correction; it provides the

argument to enter the Increments and Corrections tables in

the Almanac . The sign of the d correction factor, which de-

termines the sign of the d correction, is determined by the

trend of declination values, not the trend of d values. The d

correction factor is simply an interpolation factor; therefore,

to determine its sign, look at the declination values for the

hours that frame the time of the sight. For example, suppose

the sight was taken on a certain date at 12-30-00. Compare

the declination value for 1200 and 1300 and determine if the

declination has increased or decreased. If it has increased,

the d correction factor is positive. If it has decreased, the d

correction factor is negative.

d correction: Enter the Increments and Corrections ta-

ble with the d correction factor discussed above. Extract the

proper correction, being careful to retain the proper sign.

True Declination: Combine the tabulated declination

and the d correction to obtain the true declination.

Assumed Latitude: Choose as the assumed latitude

that whole value of latitude closest to the vessel’s DR lati-

tude. If the assumed latitude and declination are both north

or both south, label the assumed latitude same . If one is

north and the other is south, label the assumed latitude

contrary .

(1) Tabulated GHA and (2) v Correction Factor:

(1) For the sun, the moon, or a planet, extract the value for

the whole hour of GHA corresponding to the sight. For exam-

ple, if the sight was obtained at 13-50-45 GMT, extract the

GHA value for 1300. For a star sight reduction, extract the val-

ue of the GHA of Aries (GHA ), again using the value

corresponding to the whole hour of the time of the sight.

(2) For a planet or moon sight reduction, enter the v

correction value. This quantity is not applicable to a sun or

star sight. The v correction for a planet sight is found at the

bottom of the column for each particular planet. The v cor-

rection factor for the moon is located directly beside the

tabulated hourly GHA values. The v correction factor for

the moon is always positive. If a planet’s v correction factor

is listed without sign, it is positive. If listed with a negative

sign, the planet’s v correction factor is negative. This v cor-

rection factor is not the magnitude of the v correction; it is

used later to enter the Increments and Correction table to

determine the magnitude of the correction.

GHA Increment: The GHA increment serves as an in-

terpolation factor, correcting for the time that the sight

differed from the whole hour. For example, in the sight at

13-50-45 discussed above, this increment correction ac-

counts for the 50 minutes and 45 seconds after the whole

hour at which the sight was taken. Obtain this correction

value from the Increments and Corrections tables in the Al-

manac . The entering arguments for these tables are the

minutes and seconds after the hour at which the sight was

taken and the body sighted. Extract the proper correction

from the applicable table and enter the correction here.

Sidereal Hour Angle or v Correction: If reducing a

star sight, enter the star’s Sidereal Hour Angle (SHA). The

SHA is found in the star column of the daily pages of the

Almanac . The SHA combined with the GHA of Aries re-

sults in the star’s GHA. The SHA entry is applicable only

to a star. If reducing a planet or moon sight, obtain the v cor-

rection from the Increments and Corrections Table. The

correction is a function of only the v correction factor; its

magnitude is the same for both the moon and the planets.

GHA: A star’s GHA equals the sum of the Tabulated

GHA of Aries, the GHA Increment, and the star’s SHA.

The sun’s GHA equals the sum of the Tabulated GHA and

the GHA Increment. The GHA of the moon or a planet

equals the sum of the Tabulated GHA, the GHA Increment,

and the v correction.

+ or – 360

(if needed): Since the LHA will be deter-

mined from subtracting or adding the assumed longitude to

the GHA, adjust the GHA by 360

SECTION FOUR uses the arguments of assumed lati-

tude, LHA, and declination determined in Section Three to enter

the Sight Reduction Tables to determine azimuth and computed

altitude. Then, Section Four compares computed and observed

altitudes to calculate the altitude intercept. The navigator then

has enough information to plot the line of position.

if needed to facilitate the

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