

Case VI 



(1) TO PASS AT SPECIFIED RANGE FROM GUIDE (SHOWN IN FIG. 8) 



(2) TO PASS OUTSIDE SPECIFIED RANGE OF GUIDE (SHOWN IN FIG. 9) 



(3) TO PASS WITHIN SPECIFIED RANGE OF GUIDE 



GIVEN: COURSE AND SPEED OF GUIDE, INITIAL RELATIVE POSITION OF MANEUVERING UNIT, 

 COURSE OR SPEED REQUIREMENTS (IF ANY), AND RANGE (1) AT WHICH IT IS DESIRED TO PASS, (2) 

 OUTSIDE OF WHICH TO PASS, OR (3) TO PASS WITHIN. 



TO DETERMINE: LIMITING COURSE, LIMITING SPEED, OR BOTH, FOR MANEUVERING UNIT AND 

 TIME OF REACHING MINIMUM RANGE. 



Example A. — Guide on course 335° speed 18.0 knots. Ship M, now 18.0 miles bearing 340° from the Guide, wishes to 

 pass the latter at a range of 8.0 miles. 



Required. — (a) Course or courses of M at 12.0 knots if crossing ahead of G. 



(b) Course(s) of Mat 12.0 knots if passing to eastward of G. 



(c) Speed of M if course used is 295°. 



(d) Course(s) of M using minimum speed. (See fig. 8.) 



Procedure. — Plot Guide at any point G, and initial position of M at M x . About G draw a circle with radius equal to 

 the given range. 



From Mi draw tangents to circle about G, establishing points K and K' . M may either travel down the Relative Move- 

 ment Lines M x .... X or M x . . . . K' , based upon either crossing ahead of and passing to westward of G or else passing 

 to eastward of G. 



Transfer slopes M x . . . . K and M t . . . . K' to g, cutting M's 12.0-knot speed circle at m x and m 2 for the former slope 

 and at m 3 and 1214 for the latter. Slope M x . . . . K also cuts the projected 295° course line at m 5 . Vectors e . . . . zzii, 

 e . . . . m 2 , e . . . . m 3 , or e . . . . m 4 can be used by M at the given speed. Vector e . . . . m s indicates M's speed on 

 the given course. 



To obtain minimum speeds and the courses corresponding, drop perpendiculars e . . . . m 6 and e . . . . m 7 from e on 

 the transferred slopes. 



Answer.— (a) 315° or 238°. (b) 347° or 100K°. (c) 10.0 knots, (d) Course 276K° speed 9.5 knots or course 043K° 

 speed 6.5 knots. 



NOTE. — The vectors found above will cause M to pass G at exactly the given range. If it were desired to pass within the given range, the slopes 

 Mi . . . . K and M\ .... K' would be drawn so as to pass within the limiting range circle about G, and the same procedure followed. If it 

 is desired to pass outside of the given range, the slopes Mi . . . . K. and Mi .... K! and inclined so as to neither cut nor touch the limiting 

 range circle, followed by the procedure mentioned above. A special application of this latter problem is given in example B on the following pages. 



It will be noted that where the speed of Mis less than that of the Guide, two solutions will be found for each transferred slope, unless the trans- 

 ferred slopes are tangent to the speed circles, when only one solution is possible for each slope. In case the transferred slopes neither cut nor touch 

 the speed circles, no solution is possible. The conditions imposed by the statement of the problem should indicate which of the resultant vectors 

 to use. 



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