Case I 



TO PROCEED FROM ONE RELATIVE POSITION TO ANOTHER IN A SPECIFIED TIME 



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

 ALLOWED. 



TO DETERMINE: COURSE AND SPEED OF MANEUVERING UNIT. 



Example. — Guide "G" is on course 205° true, speed 10.0 knots. The Maneuvering Unit "M", now 12.0 miles due west 

 of "G", is ordered to take station 20.0 miles dead ahead of "G", arriving on station in 1.5 hours. 



Required.— (a) Course for "M". (b) Speed of "M". (See fig. 3). 



Procedure. — PlotGuideat "G" and locate initial and final positions of "M" at Mi and irrespectively. JoinMi. . . . M 2 . 



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



Since the Maneuvering Unit moves along the Relative Movement Line Mi .... M 2 , transfer the slope of this line to 

 "g". From "g", in the same direction that M 2 lies from M it measure a vector equal to the rate of Relative Travel, which is 

 equal to the Relative Distance Mi . . . . M 2 divided by the time available, 1.5 hours. This is found most readily by using 

 the Logarithmic Scale at the bottom of the Maneuvering Board, placing a straight edge along the Relative Distance (18.5 

 miles) and the time allotted (1.5 hours or 90 minutes). This Relative Speed is found to be 12.4 knots, which is the length 

 of "g . . . . m". Vector "e . . . . m" represents the required course and speed of the Maneuvering Unit. 



Answer.— (a) 185°. (b) 21.4 knots. 



NOTE. — Had the Maneuvering Unit in this problem been a plane, there would have been no change in the Relative Plot. In the Vector 

 Diagram, however, the Wind Vector, "e . . . . w" would be laid off from "e" if it measured the true wind; if it were apparent wind on " G" 

 it would be laid off as "£ . . . . w"{Tom"g". The Air Course and Air Speed would be found by joining " m" and "w" instead of " m" and "e" 

 as shown. The true course to be steered would be found by transferring the Slope "w .... m" to the compass rose on the diagram. This is 

 illustrated more fully in some of the following examples. 



Successive positions of the Maneuvering Unit are shown in the Relative Plot of figure 3 in order to stress the important fact that although the 

 maneuvering Unit is travelling down the Relative Movement Line, its heading does not necessarily coincide with the slope of this line. It is, how- 

 ever,. inclined in the direction shown by the vector "e . . . . m". 



