





Case XV 



TO REMAIN OUTSIDE A SPECIFIED RANGE FOR MAXIMUM TIME 



GIVEN: COURSE AND SPEED OF GUIDE, INITIAL RELATIVE POSITION AND SPEED OF MANEUVER- 

 ING UNIT, AND RANGE OUTSIDE OF WHICH IT IS DESIRED TO REMAIN FOR THE MAXIMUM TIME. 



TO DETERMINE: COURSE OF MANEUVERING UNIT AND RESULTANT TIME MANEUVERING UNIT 

 REMAINS OUTSIDE OF THE SPECIFIED RANGE 



Example. — A cruiser on course 210° at a speed of 18.0 knots orders a tanker, now located 10° on the port bow and distant 

 14.0 miles, to remain outside of a range of 10.0 miles from the cruiser as long as possible. The tanker can make 10.0 knots. 



Required. — (a) Course for the tanker, (b) Length of time tanker remains outside the specified range, (c) Relative 

 bearing of the cruiser when the 10.0-mile range is reached. (See fig. 19.) 



Procedure. — Plot the position of the cruiser at any convenient point, G, and the initial position of the tanker, the Maneu- 

 vering Unit, at M. Draw the 10.0-mile-range circle about G. 



Speed of G 



From G, lay off the line G .... X, in the same direction as the course of G and in length equal to ~ j — f 



M 



X 



Specified range. Join X and M, extending the line until it cuts the 10.0-mile-range circle. It will be noted that this line inter - 

 sects the circle at two points, Y and Y' . The first intersection, Y, is the one to be used as it is nearest to X. M . . . . Y 

 is the line of Relative Movement. 



Lay out the Guide's vector e . . . . g, and then transfer the slope M . . . . Fto g, cutting the 10.0-knot-speed circle at 

 m and m' . The course for the Maneuvering Unit is indicated by e . . . . m. 



By means of the Relative Distance M . . . . Y and the Relative Speed g . . . . m, the time that the Maneuvering Unit 

 will remain outside of the 10.0-mile range is readily found from the Logarithmic Scale. 



The true bearing of G from Mat the time that the 10.0-mile range is reached is given by the line Y . . . . G, which is the 

 reverse of the course of the Maneuvering Unit. 



Answer. — (a) Course 175°. (b) 35 minutes, (c) Dead astern. 



NOTE. — Unless the initial position of M lies within the area bounded by the tangents from X to the given range circle, and the arc of this 

 circle between the points of tangency, the Maneuvering Unit need not worry about coming within the prescribed range. If the initial position is 

 outside of this area, the Maneuvering Unit can remain outside of the range indefinitely. 



A glance at the Vector Diagram will show why the vector e . . . . m and not the vector e . . . . m' was used for the Maneuvering Unit. 

 While the Relative Distance remains the same before the range is reached, the Relative Speed would be increased from g . . . . m to g .... zn 

 and the time remaining before reaching the range thereby reduced. This is contrary to the results desired. 



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