The methods outlined in this article were designed as an aid in the solution of the large number of piloting problems that the professional navigator or yachtsman meets in his work.
The value of the charts described in this article were designed as an aid in lessening the labor of computation and should be of practical appeal to any navigator not equipped with a stadimeter or range-finding equipment. It will be noted that each chart contains complete direction for its use, and is, therefore, capable of application without other text.
The charts used in connection with this method were constructed on the nomographic or alignment principle and consist of a series of logarithmic scales, to an individual base, so placed in relation to one another that one value of a variable may be multiplied or divided by a value of the second variable and the result read directly from the third scale. The trigonometric formulas applicable to each chart will be found thereon. It may be preferable for the reader to omit the following paragraph, which is offered for those interested as to the details of the theory upon which the charts were constructed, until after a thorough understanding of the application of the charts to practical problems has been obtained.
1930J
Graphical Piloting Methods
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The charts have been assembled for three separate types of problems:
Chart A.—To obtain the distance to an object when the sextant angle and the height or length of the object is known.
Chart B.—To obtain the distance when the object bears 90° or abeam, knowing the run and a previous bearing.
Chart C.—To obtain the distance at any time knowing one previous bearing and the run between that bearing and the bearing of the point or position desired.
The scales of any of the charts designating distance are of arbitrary value and may be read as 0.1, 1.0, or 10.0 provided the resultant is similarly applied. Scales may also be expressed in any system of units.
The application of the charts is as follows :
Chart A.
Enter Column A with the height or length of object observed.
Enter Column C with the corrected sextant angle.
A straight line intersecting the two points found in Column A and Column C will indicate the distance in Column B in terms of Column A.
Chart B.
Enter Column C with the difference between the course and the first bearing.
Enter Column A with the run from the first bearing until object bears abeam or 90°.
A straight line intersecting the two points found in Column A and Column C
Chart C.
Enter Column D with the difference between the course and the first bearing.
Enter Column B with the run.
A straight line intersecting the two points found in Column D and Column B will indicate a point in Column C.
Enter Column E with the difference between the first and second bearings.
A straight line intersecting the points found in Column C and in Column E will indicate the distance off in Column A in terms of Column B.
Examples of the application of these charts are as follows:
Chart A.—Height of object 150 feet; corrected sextant angle 9°26'; distance 900 feet.
Chart Difference between the course and first bearing 40°; run 3 miles; distance 2.5 miles.
Chart C.—Difference between the course and the first bearing 10° ; run 3 miles, giving point on scale Column C; difference between the first and second bearing 20° ; distance 1.5 miles.
As will be seen, the application of this group of charts makes it possible for the navigator to lay aside the time-honored methods of waiting for two- and four-point bearings, or pairs of bearings, whose natural cotangents differ by unity, and to simply obtain a fix with whatever bearings and distance run may be available.