Great strides have been made in the simplification of navigation. Ships, however, run into their greatest dangers while in pilot waters or maneuvering.
The diagrams accompanying this article were made in an attempt to expedite parts of this phase of a navigator’s work. The need of these diagrams arose during my various tours of duty as a navigator.
Figure 1 is a diagram for finding (1) the distance an object will be passed abeam, and (2) the distance from an object at the second bearing. The speed-time-distance part of the diagram alone will save considerable computation and does away with the approximations of tables. The scales on all diagrams are counted from left to right.
The need for such a diagram arose when entering a harbor, such as Subig Bay, P.I., on a dark night where only one navigational light was visible until the ship was well within the harbor.
Scale I is of especial interest in that it shows clearly the degree of accuracy required in taking a bearing. An error of 1° when taking a bearing broad on the bow will not have as much effect on the result as an error of ¼° when the bearing taken is 15° on the bow. This conclusion follows from the length of the corresponding graduations. Like conclusions should be drawn from any nomographic solutions.
Scale III has not been extended abaft the beam because the diagram was intended primarily for finding the chance of danger before it was encountered and not after it had been passed.
In correcting the course the following approximate rule is of help:
angle on the bow=distance to pass object abeam X60°/distance of object
The following table is a little more exact and complete than the one given in paragraph 147, Bowditch. The distance run between bearings gives the distance the light (or object) should be passed abeam. No computation or chart is needed but it has the disadvantage that one must wait for the second bearing.
[FIGURE 1]
[FIGURE 2]
[FIGURE 3]
TABLE I
Bearings Bearings
1st | 2d | 1st | 2d |
10 | 12.1 | 28 | 48.6 |
11 | 13.6 | 29 | 51.2 |
12 | 15.1 | 30 | 53.8 |
13 | 16.8 | 31 | 56.4 |
14 | 18.4 | 32 | 59.0 |
15 | 20.1 | 33 | 61.6 |
16 | 21.9 | 34 | 64.2 |
17 | 23.8 | 35 | 66.8 |
18 | 25.7 | 36 | 69.4 |
19 | 27.7 | 37 | 71.9 |
20 | 29.8 | 38 | 74.4 |
21 | 31.9 | 39 | 76.8 |
22 | 34.1 | 40 | 79.1 |
23 | 36.4 | 41 | 81.4 |
24 | 38.7 | 42 | 83.7 |
25 | 41.1 | 43 | 85.9 |
26 | 43.6 | 44 | 88.0 |
27 | 46.1 | 45 | 90.0 |
Table II is given for pairs of bow angles by which the distance at which an object will be passed abeam is double the run between bearings. The value of this table is in the shorter times permitted between bearings.
Figure 2 is a diagram for finding the distance from a mountain peak for various heights of eye. It may be used when the base of the mountain is beyond or on the
TABLE II
Bearings Bearings
1st | 2d | 1st | 2d |
20 | 24.0 | 42 | 58.6 |
21 | 25.4 | 43 | 60.2 |
22 | 26.9 | 44 | 61.8 |
23 | 28.3 | 45 | 63.4 |
24 | 29.8 | 46 | 65.0 |
25 | 31.3 | 47 | 66.6 |
26 | 32.8 | 48 | 68.2 |
27 | 34.4 | 49 | 69.7 |
28 | 35.9 | 50 | 71.3 |
29 | 37.5 | 51 | 72.8 |
30 | 39.1 | 52 | 74.3 |
31 | 40.7 | 53 | 75.8 |
32 | 42.3 | 54 | 77.2 |
33 | 43.9 | 55 | 78.7 |
34 | 45.5 | 56 | 80.1 |
35 | 47.1 | 57 | 81.5 |
36 | 48.8 | 58 | 82.9 |
37 | 50.4 | 59 | 84.2 |
38 | 52.0 | 60 | 85.6 |
39 | 53.7 | 61 | 86.9 |
40 | 55.3 | 62 | 88.2 |
41 | 57.0 | 63 | 89.4 |
|
| 63. | 4 90.0 |
near side of the horizon. The determinant was derived from the formula given in the article “offshore Position” by Mr. Sanford L. Cluett, in the November, 1935, issue of the Naval Institute PROCEEDINGS.
Figure 3 is of use in finding the distance to vessels whose dimensions are not known, low islands and breakers, floating wreckage, submarine periscopes, etc. The formulas used are those given for tables 14, 15, and 34, of Bowditch.
Before his campaign in Italy Bonaparte had held no command. He had no practical experience of handling troops. What he knew he had picked up from study. To the last, even as Emperor, he remained inferior to many of his lieutenants in the actual practical formations and evolutions necessary for executing his designs. Where he surpassed all was in his vast and profound conceptions. Imagination, well restrained, predominated in him. He supplied his want of knowledge of the mechanical side of warfare {in which a Sergeant may surpass a Colonel) by stubborn will and inflexible resolution, by reflection, by the extent of his wide-spread knowledge, by the fertility of his imagination and his practical common sense, by the clearness of his thoughts, undeviating attention and by the implacable energy of his will.—Bouvier, “Bonaparte en Italie."