



Case XVIH-A 



TO CIRCLE GUIDE AT A CONSTANT SPEED, REMAINING BETWEEN GIVEN RANGE LIMITS 



GIVEN: COURSE AND SPEED OF GUIDE, LIMITING RANGES, AND SPEED TO BE USED BY CIRCLING 

 UNIT. 



TO DETERMINE: COURSES OF CIRCLING UNIT, TIME ON EACH LEG, BEARINGS ON WHICH TO 

 CHANGE COURSE, AND TOTAL TIME FOR OPERATION. 



Example. — Ship G, on course 020° at speed 10.0 knots, requests the ship A to circle clockwise around G, using a speed of 

 20.0 knots and remaining between 7,000 and 8,000 yards range. A is now located 8,000 yards dead ahead of G and decides to 

 return to its initial position on the final leg of the circling. 



Required. — (a) Courses for A. (b) Bearing of G at each change of course, (c) Time on each leg. (d) Total time 

 required for the maneuver. (See fig. 23.) 



Procedure. — Plot the Guide at any point G, and locate the initial position of the circling vessel at A. About G, draw 

 the range circles of 7,000 and 8,000 yards, respectively, the latter passing through A. Since the only restrictions on A are 

 those of speed, range, and return to initial position, draw chords of the 8,000-yard range circle which are tangent to the 7,000- 

 yard range circle, except for the last leg, giving Relative Movement Lines A . . . . A u A x . . . . A 2 , A 2 . . . . A 3 , etc. 

 Lay out the Guide's vector, e . . . . g, and draw A's 20.0-knot speed circle about e. 



Transfer the slopes A . . . . A u A t . . . . A 2 , A 2 . . . . A 3 , etc., to g, cutting the 20.0-knot speed circle at a u a 2 , a 3 , etc. 

 The successive vectors for A are e .... a u e .... a 2 , e .... a 3 , etc. 



Time on first leg is A .... Ai divided by g . . . . a x ; time on second leg is A x . . . . A 2 divided by g . . . . a 2 , etc 



and the total time for the maneuver is the sum of the times spent on each leg. 



True bearing of the Guide at each turn is A .... G, At .... G, etc. 



Answer. — (a) First course 113°. (b) Bearing 200°. (c) 10.3 minutes. 



Second course 195°. Bearing 258°. 7.8 minutes. 



Third course 279K°- Bearing 316°. 9.8 minutes. 



Fourth course 340K°. Bearing 014°. 16.8 minutes. 



Fifth course 015K°- Bearing 072°. 22.8 minutes. 



Sixth course 047°. Bearing 130°. 19.4 minutes. 



Seventh course 074K°- Bearing 188°. 3.1 minutes. 



(d) 90.7 minutes. 



NOTE. — In case the initial position of A is not within the limiting ranges, his first move must be to attain a position on either of the range circles. 

 The solution is then accomplished as shown above. 



The normal procedure for A in the example shown is to change course every time the listed bearings are reached, at which time the range should 

 be exactly the outside limits. 



This case is most common when the two ships involved are checking bearings for direction finder calibration. If it becomes necessary for A to 



remain on one particular bearing for checking purposes, A turns to the Guide's course and takes up the Guide's speed. 











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