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NAU 102
Lesson 23
Special Case Bearings
We can determine a running fix mathematically as well as graphically.
Using:
•Rules of Thumb
•Bowditch Table 18
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)
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.
Special Case Bearings
Special Case Bearings
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?
Special Case Bearings
1st 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?
2nd angle on bow = 193° - 121° = 72°
Distance Run = = 12 nm 36 min
60 min/hrX 20 nm/hr
At 0836, the light bears 121° T at 12 nm.
Special Case Bearings
Bow and Beam
When the 1st bearing is 45° on the bow and the 2nd is 90°, the distance run between the bearings equals the
distance from the object when abeam.
Special Case Bearings
Special Case Bearings
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?
Special Case Bearings
1st angle on bow =
238° - 193° = 45° 2nd angle on bow = 283° - 193° = 90°
Distance Run = = 5 nm 15 min
60 min/hrX 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?
Special Case Bearings
7/10 Rule
When the 1st bearing is 22.5° (2 points) on the bow and the 2nd is 45° (4 points)
0.7 X distance run = the distance off when abeam.
0.7 X time run + time of 2nd bearing = ETA abeam.
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?
Special Case Bearings
1st angle on bow =
2 points = 22.5° 2nd angle on bow = 090° - 045° = 45°
Distance Run = = 6.7 nm 40 min
60 min/hrX 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
Special Case Bearings
7/8 Rule
When the 1st bearing is 30°on the bow and the 2nd is 60°
0.875 X distance run = the distance off when abeam.
0.5 X time run + time of 2nd bearing = ETA abeam.
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?
Special Case Bearings
1st angle on bow =
325° - 295° = 30° 2nd angle on bow = 355° - 295° = 60°
Distance Run = = 11.25 nm 45 min
60 min/hrX 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?
Special Case Bearings
The problems can also be solved using Bowditch Table 18.
Running Fix
Special Case Bearings
Running Fix
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?
Special Case Bearings
1st angle on bow
200° - 180° = 20° 2nd 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?
Special Case Bearings
Special Case Bearings
Distance Run = = 11 nm 30 min60 min/hr
X 22 nm/hr
Distance at 2nd 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
Introduction to Navigation
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