Chapt-20.pdf

CHAPTER 20

SIGHT REDUCTION

BASIC PROCEDURES

2000. Computer Sight Reduction

or on the Navigator of the Navy Web site at

The purely mathematical process of sight reduction is

an ideal candidate for computerization, and a number of

different hand-held calculators and computer programs

have been developed to relieve the tedium of working out

sights by tabular or mathematical methods. The civilian

navigator can choose from a wide variety of hand-held

calculators and computer programs which require only the

entry of the DR position, altitude and azimuth of the body,

and GMT. It is not even necessary to know the name of the

body because the computer can figure out what it must be

based on the entered data. Calculators and computers

provide more accurate solutions than tabular and

mathematical methods because they can be based on actual

values rather than theoretical assumptions and do not have

inherent rounding errors.

U.S. Naval navigators have access to a program called

STELLA (System To Estimate Latitude and Longitude As-

tronomically; do not confuse with a commercial astronomy

program with the same name). STELLA was developed by

the Astronomical Applications Department of the U.S. Na-

val Observatory based on a Navy requirement. The

algorithms used in STELLA provide an accuracy of one

arc-second on the Earth’s surface, a distance of about 30

meters. While this accuracy is far better than can be ob-

tained using a sextant, it does support possible naval needs

for automated navigation systems based on celestial ob-

jects. These algorithms take into account the oblateness of

the Earth, movement of the vessel during sight-taking, and

other factors not fully addressed by traditional methods.

STELLA can perform almanac functions, position up-

dating/DR estimations, celestial body rise/set/transit

calculations, compass error calculations, sight planning,

and sight reduction. On-line help and user’s guide are in-

cluded, and it is a component of the Block III NAVSSI.

Because STELLA logs all entered data for future reference,

it is authorized to replace the Navy Navigation Workbook.

STELLA is now an allowance list requirement for Naval

ships, and is available from:

http://www.navigator.navy.mil/navigator/surface.html.

2001. Tabular Sight Reduction

The remainder of this chapter concentrates on sight re-

duction using the Nautical Almanac and Pub. No. 229,

Sight Reduction Tables for Marine Navigation . The method

explained here is only one of many methods of reducing a

sight. The Nautical Almanac contains directions for solving

sights using its own concise sight reduction tables or calcu-

lators, along with examples for the current year

Reducing a celestial sight to obtain a line of position

using the tables consists of six steps:

1. Correct the sextant altitude (hs) to obtain observed

altitude (ho).

2. Determine the body’s GHA and declination (dec.).

3. Select an assumed position (AP) and find its local

hour angle (LHA).

4. Compute altitude and azimuth for the AP.

5. Compare the computed and observed altitudes.

6. Plot the line of position.

The introduction to each volume of Pub. 229 contains

information: (1) discussing use of the publication for a va-

riety of special celestial navigation techniques; (2)

discussing interpolation, explaining the double second dif-

ference 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 Pub. 229 , 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.

Superintendent

U.S. Naval Observatory

Code: AA/STELLA

3450 Massachusetts Ave. NW

Washington, DC, 20392-5420

295

296

SIGHT REDUCTION

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 of scale to man-

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

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

size of a chart required to plot this large distance would be

impractical. 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 navigator chooses the AP’s latitude and longitude to

correspond to the entering arguments of LHA and latitude

used in Pub. 229 . From Pub. 229 , the navigator computes

what the body’s altitude would have been had it been mea-

sured from the AP. This yields the computed altitude (h c ).

He then compares this computed 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 al-

titude for the assumed position and the actual position. Pub.

229 also gives the direction from the GP to the AP. Having

selected the assumed position, calculated the distance be-

tween the circles of equal altitude for that AP and his actual

position, and determined the direction from the assumed

position to the body’s GP, the navigator has enough infor-

mation 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 altitude circle’s

radius, therefore, can be extremely large. Since this radius is so

large, the navigator can approximate the section close to his po-

sition with a straight line drawn perpendicular to the line

connecting the AP and the GP. This straight line approximation

is good only for sights at relatively low altitudes. The higher the

altitude, the shorter the distance between the GP and the actual

position, and the smaller the circle of equal altitude. The shorter

this distance, the greater the inaccuracy introduced by this

approximation.

2002. Selection of the Assumed Position (AP)

Use the following arguments when entering Pub. 229

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

position. Select an AP longitude resulting in a whole degree

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

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

manner eliminates interpolation for LHA and latitude in

Pub. 229 .

2003. 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

the radii of the circles of equal altitude passing through the

AP and the observer’s 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 2004 , the AP is

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

Express the altitude intercept in nautical miles and

label 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

Toward. 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

measured 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.

2004. Plotting the Line of Position

Plot the line of position as shown in Figure 2004 . 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

position. This is the line of position.

A navigator often takes sights of more than one

celestial body when determining a celestial fix. After

plotting the lines of position from these several sights,

advance the resulting LOP’s along the track to the time of

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

last sight.

SIGHT REDUCTION

297

Figure 2004. The basis for the line of position from a celestial observation.

2005. Sight Reduction Procedures

an accurate fix.

Just as it is important to understand the theory of sight

reduction, it is also important to develop a practical

procedure to reduce celestial sights consistently and

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, reduced the mathematics

involved to simple addition and subtraction. However,

careless errors will render even the most skillfully

measured sights inaccurate. The navigator using tabular or

mathematical techniques must work methodically to reduce

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, speed and

accuracy.

Figure 2005 represents a functional and complete worksheet

designed to ensure a methodical approach to any sight reduction

problem. The recommended procedure discussed 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

SECTION ONE consists of two parts: (1) Correcting

sextant altitude to obtain apparent altitude; and (2)

Correcting 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 cover 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

measured by the sextant.

Apparent Altitude: Apply the correction determined

above to the measured altitude and enter the result as the

apparent altitude.

Altitude Correction: Every observation requires an alti-

tude correction. This correction is a function of the apparent

altitude of the body. The Almanac contains tables for determin-

298

SIGHT REDUCTION

SECTION ONE: OBSERVED ALTITUDE

Body

_________________

Index Correction

_________________

Dip (height of eye)

_________________

Sum

_________________

Sextant Altitude (h s )

_________________

Apparent Altitude (h a )

_________________

Altitude Correction

_________________

Mars or Venus Additional Correction

_________________

Additional Correction

_________________

Horizontal Parallax Correction

_________________

Moon Upper Limb Correction

_________________

Correction to Apparent Altitude (h a )

_________________

Observed Altitude (h o )

_________________

SECTION TWO: GMT TIME AND DATE

Date

_________________

DR Latitude

_________________

DR Longitude

_________________

Observation Time

_________________

Watch Error

_________________

Zone Time

_________________

Zone Description

_________________

Greenwich Mean Time

_________________

Date GMT

_________________

SECTION THREE: LOCAL HOUR ANGLE AND DECLINATION

Tabulated GHA and v Correction Factor

_________________

GHA Increment

_________________

Sidereal Hour Angle (SHA) or v Correction

_________________

GHA

_________________

+ or - 360

if needed

_________________

Assumed Longitude (-W, +E)

_________________

Local Hour Angle (LHA)

_________________

Tabulated Declination and d Correction Factor

_________________

d Correction

_________________

True Declination

_________________

Assumed Latitude

_________________

SECTION FOUR: ALTITUDE INTERCEPT AND AZIMUTH

Declination Increment and d Interpolation Factor

_________________

Computed Altitude (Tabulated)

_________________

Double Second Difference Correction

_________________

Total Correction

_________________

Computed Altitude (h c )

_________________

Observed Altitude (h o )

_________________

Altitude Intercept

_________________

Azimuth Angle

_________________

True Azimuth

_________________

Figure 2005. Complete sight reduction form.

SIGHT REDUCTION

299

ing 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 pre-

ceding page.

Mars or Venus Additional Correction: As the name

implies, this correction is applied to sights of Mars and Ve-

nus. The correction is a function of the planet measured, the

time of year, and the apparent altitude. The inside front cov-

er of the Almanac lists these corrections.

Additional Correction: Enter this additional correction

from Table A-4 located at the front of the Nautical Almanac

when obtaining a sight under non-standard atmospheric tem-

perature and pressure conditions. This correction is a

function of atmospheric pressure, temperature, and apparent

altitude.

Horizontal Parallax Correction: This correction is unique

to reducing Moon sights. Obtain the H.P. correction value 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 correction is a

function of the limb of the Moon used (upper or lower), the ap-

parent 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

correction, 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 algebraic 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.

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 Pub. 229 : Local Hour Angle (LHA)

and Declination. This section employs the principle that a ce-

lestial body’s LHA is the algebraic sum of its Greenwich

Hour Angle (GHA) and the observer’s longitude. Therefore,

the basic method employed in this section is: (1) Determine

the body’s GHA; (2) Determine an assumed longitude; (3)

Algebraically combine the two quantities, remembering to

subtract a western assumed longitude from GHA and to add

an eastern longitude to GHA; and (4) Extract the declination

of the body from the appropriate Almanac table, correcting

the tabular value if required.

Tabulated GHA and (2) v Correction Factor:

For the Sun, the Moon, or a planet, extract the value for

the whole hour of GHA corresponding to the sight. For

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

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

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

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

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

correction 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

correction 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

interpolation 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

accounts 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

Almanac . 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.

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

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

to a star. If reducing a planet or Moon sight, obtain the v

correction from the Increments and Corrections Table. The

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

SECTION TWO determines the Greenwich Mean Time

(GMT; referred to in the Almanac s as Universal time or UT) 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 Greenwich 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

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