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2 | Celestial Navigation Solving and Plotting a 3 Star Running Fix | ||||||||

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4 | The explaination below will show the differences between running fixes and "simultaneous" fixes in celestial navigation. | ||||||||

5 | The procedures are for solving and plotting a celestial fix from observations of bodies in addition to the sun. | ||||||||

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7 | Celestial Fixes | ||||||||

8 | A running fix is generally accepted, from piloting, as a fix where earlier LOP's are advanced to cross a later LOP. | ||||||||

9 | In celestial navigation this is also true up to a point. When several observations of different bodies are taken in a relatively short period of time (5) in 30 minutes), the resulting fix is regarded as a simultaneous "fix," rather than a "running fix," even though the earlier LOP's are advanced to the final LOP time. Star fixes taken at morning or evening twilight are examples of these fixes. | ||||||||

10 | Obviously, a single observer at sea cannot observe three or more bodies at the same instant. But, if weather permits, the bodies can be observed in a short time. | ||||||||

11 | In the problem below you will find twilight "fixes" and daytime "running fixes" of the sun and other bodies where the interval between observations is longer than 30 minutes. The Coast Guard calls all of these problems "running fixes" even though most fall into the category of "star fix". In any case, the solution steps are all the same. | ||||||||

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13 | Procedures for solving and plotting a 3 Star Fix | ||||||||

14 | Problems of this type found on Coast Guard exams are straightforward and the format is identical with the multiple sun line running fix. | ||||||||

15 | The typical problem gives the following information: | ||||||||

16 | 1. A DR position at a zone time prior to the observations. | ||||||||

17 | 2. The vessel's course and speed. | ||||||||

18 | 3. Information about each body observed including: name of each body, ZT each body was observed, and GHA, declination, and observed altitude (Ho) of each body at the instant of observation. | ||||||||

19 | Note: Read each problem carefully. Not all problems ask for the position at the time of the last LOP. | ||||||||

20 | As you can be seen from the information above, your work involves determining computed altitude (Hc) and azimuth (Zn) either with publication 229, or the calculator formulas, and plotting. Use of the Nautical Almanac is not required at all. The values normally obtained with use of the Almanac, GHA, declination, and corrected altitude (Ho), are all given in these types of problems. | ||||||||

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22 | Example Problem 1: | ||||||||

23 | On 19 September 1981, your 0300 ZT DR position is LAT 24°35.0' N, LONG 88°00.0' W. You are on course 288° T at a speed of 14.0 knots. The following bodies are observed and information determined: | ||||||||

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25 | Body | Zone Time | Observed GHA | Altitude (Ho) | Declination | | |||

26 | Regulus | 0530 | 18°56.5' | 22°45.0' | 12°03.6' N | | |||

27 | Sirius | 0532 | 70°12.2' | 44°30.6' | 16°41.3' S | | |||

28 | Hamal | 0536 | 140°44.1' | 43°16.5' | 23°22.5' N | | |||

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30 | What is the latitude of your 0600 zone time running fIx? | ||||||||

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32 | Step 1: Set up your universal plotting sheet with the middle parallel of latitude labeled 24° N and the central meridian labeled 89° W. Plot the 0300 zone time DR position which was given in the problem. Next, determine and plot the vessels 0530, 0532, and 0536 zone time DR positions. The positions you get should be close to: | ||||||||

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34 | 0530: LAT 24°45.8' N, LONG 88°36.6' W | ||||||||

35 | 0532: LAT 24°45.9' N, LONG 88°37.1' W | ||||||||

36 | 0536: LAT 24°46.2' N, LONG 88°38.1' W | ||||||||

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38 | Step 2: Using the GHA's, which were given, and the DR longitudes found in step 1, determine the assumed longitude and the LHA for each body. Next, determine assumed latitude and place its value as well as the given declination in your form. | ||||||||

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40 | Step 3: Using the following values enter publication 229: | ||||||||

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42 | Body | Assumed LAT | LHA | Declination | |||||

43 | Regulus | 25° N | 290° | N 12°03.6' | |||||

44 | Sirius | 25° N | 342° | S 16°41.3' | |||||

45 | Hamel | 25° N | 052° | N 23°22.5' | |||||

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47 | Extract the Hc, altitude difference (d), azimuth angle (Z), and azimuth angle difference (difference between the azimuth angle (Z) for the entry value of declination and Z, for the next greater declination) for each star observed. | ||||||||

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49 | Step 4: Compare the computed altitudes (Hc), just obtained with observed altitudes (Ho), which were given, to find altitude intercept (a). Convert azimuth angles (Z) to true azimuths (Zn) by following the guidelines printed on the bottom of the main table pages of Pub 229 "north latitude: LHA greater than 180°, Zn = Z" and "north latitude: LHA less than 180°, Zn = 360°- Z" | ||||||||

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51 | Step 5: Plot the assumed positions (assumed LAT and assumed LONG) for each body observed. Next advance the 0530 and 0532 AP's, on course 288° T at 14 knots, to the time of the last sight at 0536. The initial AP's of the three sights are: | ||||||||

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53 | 0530: ALAT 25° N, ALONG 88°56.5' W | ||||||||

54 | 0532: ALAT 25° N, ALONG 88°12.2' W | ||||||||

55 | 0536: ALAT 25° N, ALONG 88°44.1' W | ||||||||

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57 | Step 6: Plot each LOP from its respective AP (advanced AP in the case of the 0530 and 0532 sights). First, measure the appropriate azimuth line through the AP, then measure the intercept, and last construct the LOP. | ||||||||

58 | Note: Your plot will be much cleaner looking and less cluttered if the azimuth Iine is Iightly plotted and then erased after each Iine of position is plotted. | ||||||||

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60 | A new DR track should be constructed from the 0536 star fix and a 0600 DR position plotted. The coordinates of the 0600 position should be close to LAT 24°52.5' N, LONG 89°22.4' W. | ||||||||

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62 | Note: The complete format and solution are on sheet 2 |

1 | BODY | SUN | BODY | SUN | BODY | SUN | |||
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2 | DATE | 23 Sept. 1981 | DATE | 23 Sept. 1981 | DATE | 23 Sept. 1981 | |||

3 | DR LAT | 20° 20. 0 N | DR LAT | 20° 33. 0 N | DR LAT | 20° 38. 0 N | |||

4 | DR LONG | 81° 48. 0 W | DR LONG | 82° 11. 5 W | DR LONG | 82° 21. 0 W | |||

5 | Ho | 19° 00. 0 | Ho | 51° 42. 0 | Ho | 62° 11. 5 | |||

6 | ZT | 0700 | ZT | 1030 | ZT | 1100 | |||

7 | GHA | 12° 50. 0 | GHA | 50° 20. 4 | GHA | 65° 20. 5 | |||

8 | A LONG | 81° 50. 0 | A LONG | 82° 20. 4 | A LONG | 82° 20. 5 | |||

9 | LHA | 291° | LHA | 328° | LHA | 343° | |||

10 | DEC | S 1° 38. 8 | DEC | S 1° 36. 5 | DEC | S 1° 35. 5 | |||

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13 | SAME | CONTRARY | SAME | CONTRARY | SAME | CONTRARY | |||

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15 | DEC | S 1° 38. 8 | DEC | S 1° 36. 5 | DEC | S 1° 35. 5 | |||

16 | A LAT | N 20° | A LAT | N 21° | A LAT | N 21° | |||

17 | LHA | 291° | LHA | 328° | LHA | 342° | |||

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20 | Z 98.5° | Z 121.1° | Z 140.8° | ||||||

21 | TAB Hc | 19° 18. 8 | Z 99.4° | TAB Hc | 51° 45. 2 | Z 122.4° | TAB Hc | 62° 25. 4 | Z 142.1° |

22 | DIFF | - 22.3 | + .9 | DIFF | - 36. 5 | + 1.3 | DIFF | - 48 .8 | + 1.3 |

23 | DEC INC | x 38.8 | x 38.8 | DEC INC | x 36. 5 | x 36. 5 | DEC INC | x 35. 5 | x 35.5 |

24 | INT | ÷ 60 | ÷ 60 | INT | ÷ 60 | ÷ 60 | INT | ÷ 60 | ÷ 60 |

25 | CORR | - 14.4 | + .6 | CORR | - 22. 2 | + .8 | CORR | - 28. 9 | + .8 |

26 | TAB Hc | 19° 18. 8 | Z 98.5 | TAB Hc | 51° 45. 2 | Z 121. 1 | TAB Hc | 62° 25. 4 | Z 140.8° |

27 | Hc | 19° 04. 4 | Z 99.1 | Hc | 51° 23. 0 | Z 121. 9 | Hc | 61° 56. 5 | Z 141.6° |

28 | Ho | 19° 00. 0 | Rule Zn = Z | Ho | 51° 42. 0 | Rule Zn = Z | Ho | 62° 11. 5 | Rule Zn = Z |

29 | a | 4.4 mi Away | Zn 99. 1° | a | 19.0 mi Towards | Zn 121. 9 | a | 15.0 Towards | Zn 141.6° |

30 | A LAT | 20° N | A LAT | 21° N | A LAT | 21° N | |||

31 | A LONG | 81° 50. 0 W | A LONG | 82° 20. 4 W | A LONG | 82° 20. 5 W | |||

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