Problem of Intercepting.
The increased facilities enjoyed at present for collecting and issuing information regarding the movements, speed, coal capacity, etc., of steamers of all kinds, give additional interest and importance to the problem of intercepting a vessel or squadron while on its passage.
In dealing practically with questions of this kind we are often obliged to use estimates instead of the exact data desired, and the uncertain elements of wind, weather and sea will in general operate to render the result an approximation only. These facts make it the more necessary that the principles which underlie the subject, as it is presented under normal conditions of wind and sea, should be well understood, and that they may require modification to meet special circumstances argues nothing against their truth or importance.
It has been found convenient to distinguish between Intercepting and Chasing. In the former we consider the principles involved when neither vessel is trying to avoid the other ; while by Chasing is understood the manoeuvring and management adopted when a vessel is endeavoring to overtake or bring within range another which is trying to escape.
Two vessels are said to intercept each other when they reach simultaneously the point where their courses intersect.
The problem of intercepting may be stated as follows:
Given the bearing of the steamer B from the steamer A, the course and speed of B, and the speed of A; required the course of A so as to intercept B.
The problem may be solved by geometrical construction, and unless the distances are very great, is sufficiently accurate when plotted upon an ordinary chart.
Let the line AC (Plate I., Fig. 1) represent the bearing of the two ships ; and assume their positions respectively at A and B.
Let m be the rate of B in miles per hour,
and let n be the rate of A in miles per hour,
BP making an angle c with BC represents the course of B. It is required to find the angle which determines the course AP. Since the distances to be run by the two vessels are in the ratio of their speeds, we first find all the points (a curve) whose distances from A and B are in the ratio of w to m.
The points r and s are two such points found by dividing the distance AB internally and externally in the ratio of n to m; and by geometry it is shown that the circumference described upon rs as a diameter contains all such points. Since the point of interception must lie on this circumference we have simply to mark the point P where it is met by the course BP; then joining AP, we have the required angle or course AP.
The figure is drawn to illustrate the case u greater than m, i. e. the speed of A greater than that of B ; and it is clearly seen that whatever course B may steer, A can intercept him.
If the course of S is known and B wishes to intercept A, the same construction gives the angle (f> (two solutions (c and c')' In this case we see that B can intercept A whenever the course of the latter falls between the tangents AR and AL, (that is, crosses the circle), and that it is impossible for B to intercept A when the course of A does not cross the circle. Moreover, when it is possible for B to intercept A, it may be done by steering either of the two courses BP' or BP. These are the limiting directions for B to steer. If he should steer any course between them as Bt, he would reach the point of intersection before A and could there await his arrival. BP' makes the interception in the shortest possible time and BP in the longest possible time.
Thus B having a choice of courses would select that one which would best suit the particular circumstances of the occasion; for example, if he should wish to transfer stores or armament to A he would have more time to make the necessary preparations by taking the course BP, and might thereby not detain A so long as by taking the course BP'.