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Case XIX-C 



FINDING BEARING WHERE REQUIRED RCR TO TARGET OBTAINS WITHOUT ALTERING PRESENT COURSES 



OR SPEEDS 



GIVEN: COURSES AND SPEEDS OF TARGET AND MANEUVERING UNIT, AND REQUIRED RCR. 



TO DETERMINE: BEARING OF TARGET WHEN REQUIRED RCR WILL OBTAIN. 



Example. — Maneuvering Unit, M, on course 035° at a speed of 21.0 knots, has Target Vessel, T, bearing dead ahead. 

 T is known to be on course 080°, speed 12.0 knots. 



Required. — (a) Bearing of T when RCR is ( — ) 300 yards per minute. (See fig. 27.) 



Procedure. — Draw vectors e . . . . m and e . . . . f and connect m and t. With m as center and radius equal to 9.0 

 knots (300 yards per minute) describe a circle. This circle is the locus of all relative vectors which will produce the required 

 rate. 



From r draw tangents t . . . . r 3 and t . . . . r 4 to this circle and connect m with r z and r 4 . 



From M, draw bearing lines M . . . . b 3 and M . . . . b t parallel to the slopes m . . . . r 3 and tn 

 Draw M ... .hi, the initial bearing of T, and M . . . . b 2 , the bearing of T when RCR is zero. M . 

 approach side of the zero RCR bearing line is the required bearing, since a closing RCR is required. 



Answer.— (a) 054°. 



NOTE. — Since the bearing line required is one which will produce a RCR of ( — ) 300 yards per minute, perpendiculars dropped from tn and r 

 to this bearing line should be separated by an amount equal to this required RCR. By drawing the tangent r .... i: to the locus circle from r and 

 drawing the radius xn .... 73 to this point, we find the radius which is normal to t . . . . r 3 , and since it passes through m, it is of the proper length. 



From a glance at the diagram, it is seen that as the required RCR increases, the radius of the circle about m increases until the circle passes 

 through t. This is the limiting RCR which can be attained with the vectors presented, and in the illustrated example becomes m .... t or 502 

 yards per minute. Since r itself is then located on the circumference of the circle, m . . . . T3 and m . . . . it will coincide with m . . . . t, and the, 

 slope m . . . . t transferred to M indicates a collision bearing with a constant RCR. The two units would therefore either be heading for each other 

 at the maximum and constant RCR or would have started from a common point and be separating at a constant RCR. 



. r 4 respectively.; 

 b 3 , being on the 







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