1. Navigation NAU 102 Lesson 23

2. Special Case Bearings We can determine a running fix mathematically as well as graphically. Using: Rules of Thumb Bowditch Table 18

3. Special Case Bearings Rules of Thumb Double the Angle on the Bow Bow and Beam 7/10 Rule (2 points/4 points Rule) 7/8 Rule (30-60-90 Rule)

4. Special Case Bearings Double the Angle on the Bow When the angular distance of an object on the bow is doubled, the distance run between the bearings equals the distance from the object at the second bearing.

5. Special Case Bearings

6. Example You are on course 193° T at 20 knots. At 0800 you sight a light bearing 157° T. At 0836, the same light bears 121° T. What is the distance off the light at the second bearing?

7. Special Case Bearings 1 st angle on bow = 193° - 157° = 36° You are on course 193° T at 20 knots. At 0800 you sight a light bearing 157° T. At 0836, the same light bears 121° T. What is the distance off the light at the second bearing? 2 nd angle on bow = 193° - 121° = 72° Distance Run = = 12 nm 36 min 60 min/hr X 20 nm/hr At 0836, the light bears 121° T at 12 nm.

8. Special Case Bearings Bow and Beam When the 1 st bearing is 45° on the bow and the 2 nd is 90°, the distance run between the bearings equals the distance from the object when abeam.

9. Special Case Bearings

10. Example You are on course 193° T at 20 knots. At 0840 you sight a light bearing 238° T. At 0855, the same light bears 283° T. What is the distance off the light when abeam?

11. Special Case Bearings 1 st angle on bow = 238° - 193° = 45° 2 nd angle on bow = 283° - 193° = 90° Distance Run = = 5 nm 15 min 60 min/hr X 20 nm/hr At 0855, the light is abeam at 5 nm. You are on course 193° T at 20 knots. At 0840 you sight a light bearing 238° T. At 0855, the same light bears 283° T. What is the distance off the light when abeam?

12. Special Case Bearings 7/10 Rule When the 1 st bearing is 22.5° (2 points) on the bow and the 2 nd is 45° (4 points) 0.7 X distance run = the distance off when abeam. 0.7 X time run + time of 2 nd bearing = ETA abeam.

13. Special Case Bearings Example You are on course 090° T at 10 knots. At 1020 you sight a light 2 points to port. At 1100, the same light bears 045° T. At what distance and time will you be abeam the light?

14. Special Case Bearings 1 st angle on bow = 2 points = 22.5° 2 nd angle on bow = 090° - 045° = 45° Distance Run = = 6.7 nm 40 min 60 min/hr X 10 nm/hr Distance off abeam = 6.7 nm X 0.7 = 4.7 nm You are on course 090° T at 10 knots. At 1020 you sight a light 2 points to port. At 1100, the same light bears 045° T. At what distance and time will you be abeam the light? Time abeam = 40 min X 0.7 + 1100 = 1128

15. Special Case Bearings 7/8 Rule When the 1 st bearing is 30°on the bow and the 2 nd is 60° 0.875 X distance run = the distance off when abeam. 0.5 X time run + time of 2 nd bearing = ETA abeam.

16. Special Case Bearings Example You are on course 295° T at 15 knots. At 1215 you sight a light bearing 325° T. At 1300, the same light bears 355° T. At what distance and time will you be abeam the light?

17. Special Case Bearings 1 st angle on bow = 325° - 295° = 30° 2 nd angle on bow = 355° - 295° = 60° Distance Run = = 11.25 nm 45 min 60 min/hr X 15 nm/hr Distance off abeam = 11.25 nm X 0.875 = 9.8 nm Time abeam = 45 min X 0.5 + 1300 = 1322 You are on course 295° T at 15 knots. At 1215 you sight a light bearing 325° T. At 1300, the same light bears 355° T. At what distance and time will you be abeam the light?

18. Special Case Bearings The problems can also be solved using Bowditch Table 18.

19. Running Fix

20. Special Case Bearings

21. Running Fix

22. Special Case Bearings Example You are on course 180° T at 22 knots. At 1400 you sight a light bearing 200° T. At 1430, the same light bears 218° T. What is your distance off at 1430? At what distance will you be abeam the light?

23. Special Case Bearings 1 st angle on bow 200° - 180° = 20° 2 nd angle on bow 218° - 180° = 38° You are on course 180° T at 22 knots. At 1400 you sight a light bearing 200° T. At 1430, the same light bears 218° T. What is your distance off at 1430? At what distance will you be abeam the light?

24. Special Case Bearings

25. Distance Run = = 11 nm 30 min 60 min/hr X 22 nm/hr Distance at 2 nd bearing = 11 nm X 1.11 = 12.21 nm You are on course 180° T at 22 knots. At 1400 you sight a light bearing 200° T. At 1430, the same light bears 218° T. What is your distance off at 1430? At what distance will you be abeam the light? Distance off abeam = 11 nm X 0.68 = 7.5 nm

26. Introduction to Navigation Questions?