A quick easy solution can be provided by using the extract of TABLE 7 from Pub. No. 9, American Practical Navigator (Vol. II) "Green Bowditch". To determine the distance of an object as a vessel steams past, observe two bearings of the object, note the time interval between the bearings, and determine the distance run. Determine the angular difference between the course and the first bearing and the angular difference between the course and the second bearing. Using the extract of TABLE 7, find the difference in degrees between the course and the first bearing going across the top of the table to that degree. Then go down that column until you come to the degrees of difference between the course and the second bearing. Multiply the distance run between bearings by the number in the first column to find the distance of the object at the time of the second bearing and then by the number in the second column to find the distance when you come abeam.
Note: The solution from TABLE 7, as with any of the "special cases," is accurate only if a steady course has been steered, the vessel has been unaffected by the current, and the speed used is the speed over the ground.
Example Problem : The course is 050°, the speed is 15 knots, the first bearing of the lighthouse at 1130 was 024° , and the second bearing of the lighthouse at 1140 was 359° .
Required: The distance the ship was off at 1140 at the second bearing and the distance off when abeam.
Solution: The distance run between the first and second bearing:
Required: The distance the ship was off at 1140 at the second bearing and the distance off when abeam.
Solution: The distance run between the first and second bearing:
D = 15 x 10 ÷ 60 = 150 ÷ 60 = 2.5 miles
Use Table above: Bowditch Table 7 (Green)
The difference between the course and the first bearing is 26° (050° – 024° ). The difference between the course and the second bearing is 51° (050° + 360° – 359° ). From TABLE 7 the two numbers (factors) are 1.04 and 0.81. This is found by interpolation between 50° and 52° for the second bearing.
Distance from lighthouse at second bearing:
1.04 X 2.5 = 2.6 miles.
Distance off lighthouse when abeam:
0.81 X 2.5 = 2.0 miles.
1.04 X 2.5 = 2.6 miles.
Distance off lighthouse when abeam:
0.81 X 2.5 = 2.0 miles.
