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Case XIV 



TO REMAIN WITHIN SPECIFIED RANGE FOR MAXIMUM TIME 



—ati—s. 



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

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



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

 REMAINS WITHIN THE REQUIRED RANGE. 



Example.- — A cruiser is proceeding on course 190° at 21.0 knots. A merchant vessel, now bearing 280° and distant 5.0 

 miles from the cruiser desires to remain within 10.0 miles of the cruiser as long as possible; maintaining its best speed of 12.0 

 knots. 



Required.— (a) Course for the merchant vessel, (b) Length of time remaining within specified range, (c) Relative 

 bearing of the cruiser when the limiting range is reached, (d) Minimum range reached. (See fig. 18.) 



Procedure. — With the cruiser as Guide, plot its position at any convenient point G. Plot the merchant vessel's initial 

 position at M and about G draw a circle of radius 10.0 miles. 



Lay off G 



Speed of G . 



X in direction the reverse of the cruiser's course and in length equal to g— j— j-^X Specified range. 



M 



Y is the line of Relative Movement for M while within the required 

 . . . . Xto g, cutting the 12.0 knot speed circle at 



Join M and X, cutting the 10.0 mile' circle at Y. 

 range. 



Lay out G's vector, e . . . . g, and transfer the slope M . . . 

 m. Vector e .... in represents the course and speed for M. 



By means of the Logarithmic Scale, the Relative Distance M . . . . Y, and the Relative Speed g . . . . m, the length 

 of time that the merchant ship remains within the required range is readily found. 



A perpendicular from the line of Relative Movement through the position of the Guide indicates the closest approach to 

 the Guide. 



Answer. — (a) Course 177°. (b) 63 minutes, (c) Dead ahead, (d) 4.8 miles. 



NOTE. — If the speed of M is equal to the speed of G, the point X will fall on the given range circle, locating Y at this point. The course of 

 M will then be parallel to the course of G, and since both are making the same speed, the initial relative positions will be maintained. 



If the speed of M is greater than the speed of G, the line G .... X should be plotted in the same direction as the Guide's course and the 

 point Y located by extending the line G .... X until it cuts the required range circle. When the required range is reached, in this event, the 

 Guide will bear dead astern of the Maneuvering Unit. 









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