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Sunrise … Sunset

Sunrise … Sunset. Navigation Chapter 2. Learning Objectives. Understand difference between local mean time (LMT) & zone time (ZT) & how to convert Determine ZT of: sunrise, sunset moonrise, moonset civil & nautical twilight from the Nautical Almanac. Solar Phenomena.

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Sunrise … Sunset

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  1. Sunrise … Sunset Navigation Chapter 2

  2. Learning Objectives • Understand difference between local mean time (LMT) & zone time (ZT) • & how to convert • Determine ZT of: • sunrise, sunset • moonrise, moonset • civil & nautical twilight from the Nautical Almanac

  3. Solar Phenomena • Sunrise (SR) - UL of apparent sun first appears on visible horizon. • Sunset (SS) - UL of apparent sun last seen on visible horizon. • Twilight - periods of incomplete darkness following sunset or preceding sunrise.

  4. Visible Horizon

  5. Solar Phenomena • Civil Twilight (CT) - period of incomplete darkness • UL of sun is below visible horizon • & center of sun not more than 6° below celestial horizon. • Nautical Twilight (NT) - period of incomplete darkness • UL of sun is below visible horizon • & center of sun not more than 12° below celestial horizon.

  6. Visible Horizon

  7. Morning Twilight & Sunrise • Morning NT – begins when center of sun is 12° below the celestial horizon • continues until SR. • Morning CT – begins when center of sun is 6° below the celestial horizon • continues until SR. • Sunrise - upper limb of apparent sun first appears on visible horizon. • Start of morning CT - midpoint of best time for sights on stars & planets.

  8. Evening Sunset & Twilight • Sunset (SS) - upper limb of apparent sun last seen on visible horizon. • Evening CT – begins at SS, continues ‘til center of sun is 6° below celestial horizon. • Evening NT – begins at SS, continues ‘til center of sun is 12° below celestial horizon. • End of evening CT - midpoint of best time for sights on stars & planets.

  9. Local Mean Time • Local mean time (LMT) - measured from lower branch of observer’s meridian (local meridian) • Times of solar phenomena in Almanac - UT at Greenwich meridian • Consider LMT listed in Almanac equivalent to ZT on central meridian of any zone.

  10. LMT to ZT • Must apply correction to LMT to find ZT • difference between your Lo & your ZM • Difference of longitude: DLo • DLo = Lo – ZM • Convert DLo to time units; • Apply to LMT of phenomenonto get ZT at your Lo.

  11. ZT & LMT Relationships

  12. Time – Arc Conversion TimeArc • 24 hr = 360° • 1 hr = 15° • 60 min = 15° • 4 min = 1° TimeArc 1 min = 15' 60 sec = 15' 4 sec = 1' 1 sec = 0. 25'

  13. Example 1: Convert LMT to ZT If LMT is 1200, what is ZT at 51°W? 1. Find ZM: 51°  15° = 3.4 ZD = +3 , ZM is 45°W 2. Find DLo: DLo = Lo – ZM = 51°W - 45°W = 6°W 3. DLo to time: 6° x 4 min per ° = 24 min 4. Find ZT: LMT 1200 DLo (W) + 24 min ZT 1224

  14. Example 1:Time Diagram

  15. Skill 1 – Find ZT of Sunset The sun sets at 1858 LMT for a particular date. What is ZT of sunset for an observer at Lo 109° 39'E on this same date? 1. Find ZM: Lo 109°39'E  15° = 7.3 hr ZD = –7, ZM = 105°E. Skip

  16. Skill 1 – Find ZT of Sunset 2. Find DLo: DLo = DR Lo – ZM = 109°39'E – 105°E = 4°39'E = 4.7°E 3. DLo to time: 4.7° x 4 min/degree = 18.8 min, rounded to 19 min

  17. Skill 1 – Find ZT of Sunset 4. Find ZT: LMT 1858 DLo (E) – 19 min ZT 1839

  18. Predicting Solar Phenomena • Almanac – LMT for twilight, SR, & SS as a function of latitude. • Times - nearest minute for middle day • High Latitudes - Sun sometimes continuously above or below horizon, or twilight lasts all night. • clear rectangle - above horizon; • black rectangle - below horizon; • group of hash lines - twilight lasts all night.

  19. Example 2: Find ZT- end of evening CT Position is L 26°16'N, Lo 62°26'W, 30 Jun. Find ZT of the end of evening CT.

  20. Example 2: Find ZT- end of evening CT 1.

  21. Example 2: Find ZT- end of evening CT 1 . Tab L LMT CT 30°N 1933 20°N1908 10° interval 25 min interval 2. L 26° 16’ -20° 00’ 6° 16’ = 6.27° 3. (6.27°/ 10° interval) x 25 min interval = 15.68 min, rounded to 16 min

  22. Example 2: Find ZT- end of evening CT 4.LMT of CT for L 20°N 1908 Corr’n for L 26°16'N + 16 min LMT of CT for L 26°16'N 1924

  23. Example 2: Find ZT- end of evening CT 5. DLo = DR Lo – ZM DR Lo 62° 26'W ZM - 60° 00'W 2° 26'W = 2.43° W 2.43° x 4 min per degree = 9.72 min, rounded to 10 min LMT = 1924 DLo (W) + 10 min ZT for CT 1934

  24. Skill 2 - Find ZT of Morning NT • Find ZT of the beginning of morning nautical twilight on December 25 at Christmas Island, L 10°25'S, Lo 105°43'E. 1. Extract values from NA & find intervals. Tab L LMT NT 10°S 0448 20°S0426 10° interval 22 min interval Skip

  25. Skill 2 - Find ZT of Morning NT 2. 10° 25'S -10° 00'S 0° 25' = 0.42° 3. (0.42°/10° interval) x 22 min = 0.92 min, rounded to 1 min. 4. LMT of NT at L 10°00'S 0448 Corr’n for L 10°25'S – 1 min LMT of NT for L 10°25'S 0447

  26. Skill 2 - Find ZT of Morning NT 5. DLo = DR Lo - ZM DR Lo = 105° 43'E ZM - 105° 00'E DLo 43' E 43'  15'/min of arc = 2.87 min, rounded to 3 min. LMT 0447 DLo (E) - 3 min ZT 0444

  27. Moonrise and Moonset • To find precise time for MR or MS: • must account for observer’s Lo. • Tables, pg xxxii Almanac - precise times • For Sight Planning, approx times OK. • Almanac – LMT for MR & MS as a function of Latitude • At higher Lat - periods when moon continuously above or below horizon: • above horizon - clear rectangle • below horizon - black rectangle

  28. Example 3: Find ZT of Moonrise • Determine approx. time of MR on 20 March at projected DR position: L 37°25'S, Lo 86°36'W. 1. Extract values from NA & find intervals. Tab LLMT MR 35°S 0522 40°S0518 5° interval 4 min interval

  29. Example 3: Find ZT of Moonrise 2. 37° 25'S -35° 00'S 2° 25' = 2.4° 3.(2.4° / 5° interval) x 4 min interval = 1.92 min, rounded to 2 min 4. LMT of MR for L 35° S 0522 Corr’n for L 37°25'S -2 min LMT of MR for L 37°25'S 0520

  30. Example 3: Find ZT of Moonrise 5.DLo = Lo – ZM 86°36'W – 90° W 3° 24'E = 3.4° E 3.4° x 4 min per degree = 13.6 min, rounded to 14 min. LMT 0520 DLo (E) - 14 min ZT 0506

  31. Skill 3 - Find ZT of Moonset • Find approx. ZT of moonset on 10 May at L 27°15'N, Lo 81°12'W. 1. Extract values from NA & find intervals Tab L LMT Moonset 30°N 1029 20°N1052 10° interval 23 min interval Skip

  32. Skill 3 - Find ZT of Moonset 2. 27° 15’ - 20° 00’ 7° 15’ = 7.25° 3. (7.25°/10° interval) x 23 min = 16.7 min, rounded to 17 min 4. LMT at L 20°N 1052 Corr’n for L 27° 15'N - 17 min LMT at L 27° 15'N 1035

  33. Skill 3 - Find ZT of Moonset 5. DLo = 81°12'W – 75° W = 6° 12’ W = 6.2°W 6.2° x 4 min/degree = 24.8 min, rounded to 25 min. LMT 1035 + 25 min ZT 1100

  34. Aboard a Moving Vessel 1. From Almanac, extract LMT of event for Tab L closest to current position. 2. Extend intended track & measure coordinates of projected DR. 3. Find ZT of phenomenon for Lat & Lo of projected DR. • Called “First Estimate” • can get 2nd Estimate, but no practical need.

  35. Example 4:Find ZT of NT - moving vessel • 2 March. GPS position at ZT 0000:L 25°26'S, Lo 11°39'W; C 115°T, 9.0 kn. • What is ZT of beginning of morning NT? 1. Extract data from NA – Tab L. Calculate distance to be traveled: 0459–0000 = 4hr 59min = 299 min 60 D = ST D = (9.0 kn x 299 min) / 60 D = 44.9 nm

  36. Example 4:Find ZT of NT - moving vessel Step 2: Plot 0459 projected DR position

  37. Example 4:Find ZT of NT - moving vessel 3. Extract data from NA. 4. Tab LLMT NT 20°S 0510 30°S0459 10° interval 11 min interval

  38. Example 4:Find ZT of NT - moving vessel 5. 25° 44.9'S – 20° S 5° 44.9' = 5.75° (5.75°/ 10° interval) x 11 min interval = 6.33 min, rounded to 6 min 6. LMT of NT at L 20° S 0510 Corr’n for L 25°44.9'S – 6 min LMT of NT at L 25°44.9'S 0504

  39. Example 4:Find ZT of NT - moving vessel 7. DLo = Lo – ZM 10° 53.9'W – 15° W 4° 06.1'E = 4.1° E 4.1° x 4min/degree = 16.4 min, rounded to 16 min LMT 0504 DLo(E) – 16 min ZT 0448

  40. Skill 4 – Find ZT, evening CT on moving vessel • At 1500, 10 May, GPS position: L 37°15'N, Lo 123°00'W; C 225°T, 8 kn. • Find approx. ZT of the end of evening CT. 1. Extract data from NA – Tab L. Calculate distance to be traveled: 1921 – 1500 = 4hr 21min = 261 min 60D = ST D = (8.0 kn x 261min) / 60 D = 34.8 nm Skip

  41. Skill 4 – Find ZT, evening CT on moving vessel • Step 2: Plot 1921 projected position

  42. Skill 4 – Find ZT, evening CT on moving vessel 3. Extract data from NA. 4. Tab LCT 40°N 1934 35°N1921 5° interval 13 min interval

  43. Skill 4 – Find ZT, evening CT on moving vessel 5. 36° 50.3'N -35° N 1° 50.3' = 1.84° (1.84° / 5° interval) x 13 min = 4.78 min, rounded to 5 min 6. LMT of CT at L 35°N 1921 Corr’n for L 36°50.3'N +05 min LMT of CT at L 36°50.3'N 1926

  44. Skill 4 – Find ZT, evening CT on moving vessel 7. DLo = Lo – ZM 123° 30.9'W – 120° W 3° 30.9'W = 3.52°W 3.52° * 4 min/degree = 14.08 min rounded to 14 min. LMT 1926 DLo(W) + 14 min ZT 1940

  45. Summary • Understand difference between LMT & ZT, & how to convert. • Determine ZT of: • sunrise, sunset • moonrise, moonset • civil & nautical twilight from the Nautical Almanac

  46. Sunrise … Sunset End of Navigation Chapter 2

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