Case XXVm 



TO SCOUT IN A GIVEN RELATIVE DIRECTION FOR MAXIMUM DISTANCE AT GIVEN SPEED, RETURNING TO 

 ORIGINAL RELATIVE POSITION IN GIVEN TIME, USING GIVEN SPEED (OR SPEEDS) 



GIVEN: COURSE AND SPEED OF GUIDE, COINCIDENT INITIAL AND FINAL RELATIVE POSITIONS OF 

 SCOUT, DIRECTION OF RELATIVE LINE TO BE SCOUTED, SPEED OF SCOUT, AND TOTAL TIME INTERVAL. 



TO DETERMINE: COURSES OF SCOUT, TIME TO TURN TO SECOND COURSE, AND LENGTH OF RELA- 

 TIVE LINE SCOUTED. 



Example.- — A Carrier is on course 090°, speed 17.5 knots, and at 0600 launches a plane to scout a relative line in direction 

 150° from the Carrier, as far as possible at an air speed of 85.0 knots, returning to the Carrier at 0820. Wind is from 110°, 

 velocity 18.0 knots. 



Required.- — (a) Air courses for the plane, (b) Time to turn to incoming course, (c) Length of relative line covered. 

 (See fig. 40.) 



Procedure. — Plot Carrier at any point, C, and lay out the Relative Line C .... X in direction 150° from C and of 

 indefinite length. 



Lay out e . . . . c, the vector of the Carrier, and e . . . . w, the vector of the wind. With w as center and the airspeed 

 of the plane as radius, inscribe a circle. 



Transfer the slope of C . . . . X to c, cutting the plane's airspeed circle at pi and p 2 . The plane's outgoing air course is 

 w .... pi and the incoming air course is w . . . . p 2 . 



The time on the first course is either found by means of the Time Line p x .... c .... p 2 or else by the graphical 

 method explained in case XXI. This time is added to 0600 to find the time to turn. 



The length of Relative Line scouted is found by multiplying the Relative Speed, c .... pi, by the time on the first leg 

 or the Relative Speed, c . . . . p 2 , by the time on the second leg, and drawn as C .... P. 



Answer. — (a) First air course 131'/ 2 °; second air course 348°. (b) 0730. (c) 87.0 miles. 



NOTE. — With both the direction of relative movement and the plane's airspeed given, it is a simple matter to find the desired air courses. 

 The utilization of the Time Line provides a ready solution for the time on first and second legs. 



As in case XXVII, the Fictitious Ship's vector coincides with the Guide's vector since the initial and final relative positions of the scout are 

 the same. The line pi .... c .... pi is therefore a Time Line. 



The Relative Plot is not required if the scout leaves and returns to the Guide, but it is necessary otherwise if it is desired to know the scout's 

 position relative to the Guide at the turning point. 



In case the scout is a surface vessel, the speed circles are drawn from e instead of w. 



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