Case m 



TO PROCEED FROM ONE RELATIVE POSITION TO ANOTHER AT A SPECIFIED SPEED 



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

 BE USED BY MANEUVERING UNIT. 



TO DETERMINE: COURSE OF MANEUVERING UNIT AND TIME TO ARRIVE IN FINAL POSITION. 



Example. — Guide on course 037°, speed 16.0 knots. Ship "M", now bearing 060° (true) and distant 11.5 miles from the 

 Guide, is ordered to take position 16.0 miles 30° abaft the starboard beam of the Guide, using a speed of 12.0 knots enroute. 



Required. — (a) Course or courses for "M". (b) Time required to reach final position. (See fig. 5.). 



Procedure. — Plot Guide at "G", and locate initial and final positions of "M" at M : and M 2 respectively. M 2 bears 120° 

 relative from "G" or 157° (true) from "G". Join M t . . . . Af 2 . 



Draw vector "e .... g", representing course and speed of "G". 



With "e" as center and with radius equal to the specified speed for "M" (12.0 knots), describe a circle. This circle, of 

 course, will contain all the courses available to "M" at the specified speed, no matter what the other requirements. 



Transfer the slope M x .... M 2 to "g", cutting the speed circle of "M" at points "m" and "zn 2 ". 



"e . . . . m/' and "e .... m 2 " are vectors that "M" could use. An inspection of the diagram quickly reveals the fact 

 that the latter vector yields the greatest Relative Speed; therefore "M" would naturally choose the course indicated by this 

 vector unless there were other vessels or obstacles present which would dictate the use of the vector "e .... m/', 



The time required to arrive at the final position is found by dividing the Relative Distance by the Relative Speed as usual. 

 For vector "e . . . . m 2 " and using the Logarithmic Scale this is shown graphically. 



Answer. — (a) 153}i° or alternate course 047°. (b) 52 minutes by most expeditious course or 4.43 hours by steering course 

 047°. 



NOTE. — Only one solution can be obtained if the speed of the Maneuvering Unit is greater than the speed of the Guide. Two solutions are other- 

 wise possible unless the specified speed for the Maneuvering Unit is the minimum speed that would allow him to reach the final position. 



In case the Maneuvering Unit is a plane, draw the wind vector "e" .... w", and about "w" draw the speed circle with radius equal to the 

 given air speed of the plane. This speed circle is treated in precisely the same manner as the ground speed circle, drawn about "e" in figure 5. 

 Since the air course would be desired in this case, it is obtained by reference to "w" instead of "e". 



