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Case XVIII-B 



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TO CIRCLE GUIDE AT CONSTANT RATE OF CHANGE OF BEARING IN A GIVEN TIME, REMAINING WITHIN 

 A LIMITING RANGE, AND RUNNING FOR SAME TIME INTERVAL ON EACH COURSE 



GIVEN: COURSE AND SPEED OF GUIDE, BEARINGS TO BE REACHED AT LIMITING RANGE FROM 

 GUIDE, AND TOTAL TIME ALLOWED. 



TO DETERMINE: COURSES AND SPEEDS OF CIRCLING UNIT AND TIME ON EACH LEG. 

 Example. — Guide on course 020°, speed 10.0 knots, requests Destroyer D, now stationed 8,000 yards dead ahead of the 

 Guide, to circle in a clockwise direction at as nearly a constant rate of change of bearing as possible, remaining within 8,000 

 yards range and completing the maneuver within 3.0 hours. The Commanding Officer of the Destroyer decides to change 

 course every 30° relative bearing and to run the same length of time on each leg. 



Required. — (a) Courses and speeds for D. (b) Time spent on each leg. (See fig. 24.) 



Procedure. — Plot the Guide at G and the initial position of the Destroyer at D. About G draw the 8,000-yard range 

 circle. 



Lay out the relative bearing lines from G 30° apart, cutting the 8,000-yard circle at D, D lt D 2 , etc. Connect D .... D u 

 A . . . . D 2 , etc. Determine length of D . . . . A> multiply by 12 to obtain the total Relative Distance run, and divide 

 by 3.0 to obtain the Relative Speed of D. 



Lay out Guide's vector, e . . . . g, and about g draw a circle of radius equal to the Relative Speed found above. 

 Transfer slopes D .... A> A .... A> etc., to g, cutting the Relative Speed circle at d u d 2 , etc. Vectors e . . . . d u 

 e . . . . d 2 , etc., represent the courses and speeds for D. 



Time on each leg is total time allowed divided by number of courses run. This may be checked by dividing one side of the 

 polygon by the constant rate g . . . . di. 



Answer. — (a) First course 066°. Speed 11.2 knots. 

 Second course 075°. Speed 7.2 knots. 

 Third course 067°. Speed 3.0 knots. 

 Fourth course 333°. Speed 3.0 knots. 

 Fifth course 325°. Speed 7.2 knots. 

 Sixth course 334°. Speed 11.2 knots. 

 Seventh course 346$°. Speed 14.5 knots. 

 Eighth course 359^°. Speed 16.8 knots. 

 Ninth course 013°. Speed 18.2 knots. 

 Tenth course 027°. Speed 18.2 knots. 

 Eleventh course 040K- Speed 16.8 knots. 

 Twelfth course 053^°. Speed 14.5 knots, 

 (b) 15 minutes. 



NOTE. — In the conditions imposed in this type of problem, it is possible to construct a regular polygon symmetrical about the course 

 line of the Guide. In such cases it is necessary to obtain courses and speeds for one-half of the vector diagram only, the courses and 

 speeds in the other half being symmetrical with respect to e .... g. 



If it is desired that the circling vessel maintain any of the relative positions reached for a specified length of time, it will be necessary 

 to subtract the total time so spent from the time allotted to the maneuver in obtaining the constant rate to be used by D. 



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