Case VII 



WITH SPEED LESS THAN GUIDE, TO PASS CLEAR AT. MAXIMUM DISTANCE 



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

 UNIT. 



TO DETERMINE: COURSE OF MANEUVERING UNIT AND MINIMUM RANGE ATTAINED. 



Example. — A submarine with maximum submerged speed of 8.0 knots wishes to keep clear as far as possible from a cruiser 

 now bearing 135° distant 12.0 miles, whose course and speed have been determined as 345° and 24.0 knots. 



Required. — (a) Best course for submarine, (b) Minimum range and time to reach this range, (c) Relative bearing of 

 cruiser from submarine at minimum range. (See fig. 10.) 



Procedure. — Plot the cruiser as Guide at G. Locate the present position of the submarine at S. 



Lay out e . . . . g, representing course and speed of Guide. 



About e draw an 8.0-knot circle representing the maximum submerged speed of S. From g draw tangents to this speed 

 circle, points of tangency being S! and s 2 . Vectors e .... Si and e .... s 2 represent the two courses open to Sat 8.0 knots. 



Transfer the slopes g . . . . s t and g . . . . s 2 to S. Although the Relative Speed is the same for either course it is readily 

 apparent that the Relative Movement Line S .... X passes farther away from G than the line S . . . . Y. e . . . . s,, 

 is the best course for the submarine. 



Draw perpendiculars G ..... K and G .... K' to slopes S .... X and S . . . . Y respectively. G .... K is 

 the minimum distance reached when on the course and speed represented by the vector e . . . . s x . The relative bearing is 

 the difference between the bearing of G from K and the course indicated by vector e . . . . s t . 



Answer. — (a) 274^°. (b) 9.15 miles; 20.8 minutes, (c) 180° relative or dead astern. 



NOTE. — If the slopes S .... X and S . . . . Y are on the same side of G, the preferable course under the required conditions is always 

 away from the Guide. If vector e . . . . sj is used, then the minimum range would be G . . . . K ' or 2.2 miles, with the cruiser bearing dead 

 ahead of the submarine. 



G must be located between the slopes S .... X and S . . . . Y, for the submarine to make contact with the cruiser. 



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