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Introduction    Corrections to Sextant   Time   Finding GHA and Declination   Assumed Position and Local Hour Angle   Computed Altitude and Azimuth    Interpolation    Altitude Intercept    Using Position Plotting Sheets    Plotting Lines of Position

                                                Corrections To The Sextant Reading

When you use your sextant to "shoot" a star or planet, you obtain the angle between the horizon and the celestial body. This is called the sextant altitude, which is abbreviated as hs. The angle will be expressed in degrees, minutes, and tenths of a minute, as shown here. View image4

   In order to use this information, it must be corrected for a number of factors. After the corrections are made, the resulting angle will be observed altitude (Ho), which is needed to find distance from the ship to the G.P. the first error to be aware of is instrument error, which may be found in some less expensive sextants. It is a "built in" error resulting from the manufacturing process and cannot be removed. A simple mathematical calculation can compensate for it. Good sextants usually have no instrument error. Because the coast guard exam assumes you are using a "perfect" sextant, all their problems and those in this course will ignore it.

   Even a perfect sextant can develop index error (I.E.), which may change every day. The index and horizon mirrors getting slightly out of adjustment cause this error. You check for this each time you use the sextant by lining up the actual horizon with the reflected image of the horizon. When the view through the sextant looks like this, the reading should be 0°-00'. 0. View image5  

  Chances are, however, that the sextant may be reading 0°-02.5' meaning that it has an index error (I.E.) of plus 2.5'. This is sometimes stated as an i.e. of 2.5' "on the arc.

   Another sextant might show a reading of 1.2’ less than zero, or “off the arc.” This could also be expressed as an i.e. of -1.2’. 

   Rather than continually adjusting the mirrors of your sextant, it is easier to apply an index correction (I.C.) to compensate for index error. Suppose your sextant was reading 2.5' too high (on the arc) when it should have read zero. In order to bring it back to zero must subtract that amount. You’re' index correction (I.C.) would therefore be -2.5'.

   If you’re sextant was 1.2' "off the arc". Too low, your (I.C.) would be plus 1.2’.  

   Coast guard problems will give you either the "index error" or the “index correction,” so make sure you keep them straight. Here are some practice problems:  

   1. Your sextant reading is 22°-28.6’ index error is 2.5’ on the arc. What is the corrected reading?  Answer   ______________________ 

Answer: because an index error  “on the arc" is too high, the number must be subtracted:

 

Hs       22°- 28.6

I.C.              -2.5

           22°- 26.1

 

2. Your sextant is reading 42°- 13.8'. Index correction is -1.2' what is the corrected reading? Answer____________________  

Answer:  An index correction is applied directly by following the  + or  - sign.

 

Hs          42°- 13.8'

I.C.                  -1.2

               42°- 12.6’

 

3. Your sextant reading is 35°-29.6’. I.E. is 1.8' off the arc. Corrected reading: _________________  

Answer:  if the index error is "off," you add it.

 

Hs        35° -29.6’

I.C.               +1.8

             35° -31.4’

   

4. Your sextant reading is 42°- 05.4'.     I.C. IS +2.1, corrected reading________________

Answer: Follow the plus or minus sign when working with I.C. (Index correction).

 

HS         42°- 05.4

                     + 2.1

              42°- 07.5

  Now break out that scratch pad and work these for practice.  Correct answers are listed after.    

1.  Sextant reading:    32° -49.8'       “i.e.”       1.8 off the arc                  corrected: _______________  

2.  Sextant reading:    49° -18.4’      “i.c”.     +2.7                                   corrected: _______________  

3.  Sextant reading:   18° -52 .7’      “i.e”       1.9  off the arc                   corrected: _______________  

4.  Sextant reading:    58° -22.0’      “i.e”        2.7 on the arc                   corrected: _______________  

5.  Sextant reading:    24° -16.5’      “i.c”      -0.8                                   corrected: _______________

  Answers:  1.  32° -51.6’    2.  49° -21.1’   3.  18° -54.6’  4.  58° -19.3’   5.  24° -15.7’

 

Dip Correction

   The "dip correction" must be made to Hs (sextant altitude) to compensate for your height of eye above sea level. This correction, which is always subtracted from Hs, can be found in the "altitude correction tables" on the inside front cover of the nautical almanac. For now, however, simply refer to the reproduction of the table provided here. View table  the table gives the height of eye in either meters or feet. Be especially careful when using this table because the coast guard problems may use either meters or feet

EXAMPLES: click to view.

THE DIP CORRECTION FOR HEIGHTS OF EYE GREATER THAN 8.0 FEET THROUGH 8.6 FEET IS 2.8’.

THE DIP CORRECTIONS FOR HEIGHTS GREATER THAN 20.1 FEET THROUGH 21.0 FEET IS -4.4.

THE DIP CORRECTIONS FOR 20.1 FEET IS 4.3' .

IF YOUR HEIGHT OF EYE IS 9.7 METERS, WHAT IS THE DIP CORRECTION? 9.7 METERS WOULD FALL BETWEEN 9.5, METERS AND 9.9 METERS IN THE TABLES, SO THE DIP CORRECTION WOULD BE -5.5.  

THE DIP CORRECTION FOR A HEIGHT OF EYE OF 48'4 FEET IS -6.7'.

  TRY THESE FOR PRACTICE AND CHECK THE ANSWERS BELOW:

1. HEIGHT OF EYE: 22.8', DIP CORRECTION: _______________________

2. HEIGHT OF EYE: 3.4 METERS, DIP CORRECTION: ___________________

3. HEIGHT OF EYE: 42.5', DIP CORRECTION: _____________________

4. SEXTANT READING: 19°-56.4', INDEX ERROR 1.3 ON THE ARC, HEIGHT OF EYE: 30.4', CORRECTED READING: ______________________

5. SEXTANT READING: 24°-16.5', I.C.: -0.8, CORRECTED READING: ___________________

ANSWERS:

1. -4.6         2. -3.2       3. -6.3      4.   HS         19°-56.4'             5.   HS      24°-16.5'

                                                           I.C.                -1.3                    I.C.            -0.8'

                                                                         19° -55.1                               24° 15.7'

                                                           DIP                -5.3

                                                                         19° -49.8'

 

   After you correct “hs” for index error and dip, you have apparent altitude (ha) .it is used to find the last (thankfully!) Correction you will need. This correction compensates for the refraction of the light coming through the earth's atmosphere, among other things. There is no standard abbreviation for this correction, so we will abbreviate it alt. In the case of a sun shot, it also corrects for the fact that you are measuring the angle to either its upper or lower edge (called a "limb"), rather than to its exact center. To find the alt corrections we'll use the altitude correction table from the nautical almanac, a portion of which appears here: "view table"  notice how the table is divided into two halves of the year. Make sure you enter the table for the month of your sighting. Also notice that the corrections differ greatly depending upon whether you are using the upper or lower limb of the sun. You enter the table with your apparent altitude (ha). Suppose that when you corrected hs for i.e. and dip, the resulting ha is 12°-27.31. You sighted the sun's upper limb. The date of the sight is March 10. What is the "alt" correction? The answer is -20.3. That correction, when applied to ha, will give you the observed altitude (ho):

                (Ha)         12°-27.3’

                ALT              -20.3

                (Ho)        12°-07.0’

Suppose you observed the lower limb "view table" of the sun on December 18. Ha is 14°-42.0’. What is the "alt" correction?      Answer: plus 12.6’.

If you are shooting a star, the "alt" correction is found in a different part of the altitude correction table.

Because a star is just a "dot" of light, there is no upper or lower limb. Nor do we need to worry about the month. Just enter the table with ha and find the correction.

Suppose you sight the star “spica” on April 19. Ha is 10° 32.8'. "View table" what is the "alt" correction?  Answer:  5.1.

Suppose you sight the star "spica" on January 23. Ha is 12° 15.1'. "View table" what is ho?

Ha         12° 15.1 '

ALT             - 4.4

Ho          12° 10.7 '

 For practice, find the correction for the following: "View table"

     BODY                                        MONTH                    Ha                                 CORRECTION

1. SUN UPPER LIMB                   APRIL                     27° 54.8'                  ____________________           

2. STAR                                         JULY                        18° 27.3'                   _____________________

3. SUN LOWER LIMB                 MARCH.                 38° 29.2’                   _____________________

4. STAR                                        JUNE                        33° 07.6’                     _____________________

5. SUN LOWER LIMB                  DEC                        12° 18.1’                     _____________________

 ANSWERS:   1.       –17.6    2.       –2.9      3.       +15.0      4.       –1.5      5.       +11.9  

 

Practice Problems

Here, "view table" , you will see the complete "altitude correction tables" as it appears in the nautical almanac. Use it to work the following problems.

Problem:     

You observe the lower limb of the sun on November 15.

The sextant reading was 19° 22.6. 

Index error was 2.4 off the arc.

Your height of eye was 32 feet.

What was the observed altitude? Ho

Solution:  

Hs

19° 22.6'

I.C.

     + 2.4

 

19° 25.0

DIP

     - 5 .5

Ha

19° 19.5

ALT

   +13 .5

Ho

19° 33.0

    Here are some more for practice. Work them out on a separate sheet of paper using the format you have learned. The answers are below. 

Find ho for these sun shots "view table" 

 

MO.

HS

I.E.

I.C.

HT. OF EYE

LIMB OBSERVED

1

OCT

47° 56.0'

1.9’ ON THE ARC

 

26 FEET

UPPER

2

APR

25° 12.6'

 

(+) 2.0’

  8 METERS

LOWER

3

MAR

36° 49.9'

2.1’ OFF THE ARC

 

45 FEET

LOWER

4

SEP

58° 38.8'

 

(-) 1 .6’

22 FEET

UPPER

5

DEC

64° 17.5'

1.3' ON THE ARC

 

12 METERS

LOWER

6

MAY

43° 56.4'

3 .6' OFF THE ARC

 

60 FEET

LOWER

 

Find ho for these star sights "view table" 

7

JULY

32° 08.0'

 

(+) 1. 8'

18 FEET

8

AUG

22° 56 .4'

2.7’ ON THE ARC

 

9 METERS

9

SEP

47°19.1'

 

(+) 2.1

37 FEET

10

OCT

61° 22 .3'

1.6’ OFF THE ARC

 

5 METERS

 

Answers  1.  47° 32.3’   2. 25° 23.6’   3. 37° 00.5’   4. 58° 16.3’   5. 64° 25.8’   6. 44° 07.5’   7. 32° 04.2’    8. 22° 46.1’   9. 47° 14.4’   10.  61° 19.5’

 

Time