Case IV 



TO PROCEED FROM ONE RELATIVE POSITION TO ANOTHER AT MINIMUM SPEED 



GIVEN: COURSE AND SPEED OF GUIDE AND THE INITIAL AND FINAL RELATIVE POSITIONS FOR 



THE MANEUVERING UNIT. 



TO DETERMINE: COURSE AT MINIMUM SPEED AND TIME REQUIRED FOR MANEUVERING UNIT 

 TO REACH FINAL POSITION. 



Example. — Guide on course 148° at speed 15.0 knots. A vessel, M, now located 600 yards dead astern of the Guide, 

 receives orders to open out to a distance of 19,000 yards and a bearing of 280° from the Guide, using minimum speed enroute 

 to conserve fuel. 



Required.- — (a) Course and speed for M. (b) Time required to reach final position. (See fig. 6.) 



Procedure. — Plot Guide at G and the initial and final positions of M at Mi and M 2 . In this example, realizing that the 

 Maneuvering Board is 20 divisions wide, a more accurate result is obtained by plotting G and M 2 on the final line of bearing 

 and separated by 19 units. Mi is located 600 yards bearing 328° from G. Join M x .... M 2 . 



From point e, lay out vector e .... g in direction 148°, length 15.0 knots. 



Transfer the slope M t .... M 2 to g, extending it in the same direction from g that M 2 lies from M x . 



From e drop a perpendicular on this transferred slope, intersecting at m. This is most readily done by observing the 

 direction of the slope on the compass rose and subtracting or adding 90° to this, e .... m is the vector of the course and 

 minimum speed for M. 



The time required to complete this evolution may be found by dividing the Relative Distance Mi .... M 2 by the 

 Relative Speed g . . . . m. By using the Logarithmic Scale, this time may be obtained in minutes. 



Answer.- — (a) Course 189° at minimum speed 11.4 knots, (b) 57 minutes. 



NOTE. — The foot of the perpendicular, m, must fall on the same side of g that M2 lies in respect to Mi. Should it fall on the other side of 

 g, it indicates that M must use a speed greater than that of the Guide and the solution becomes indeterminate. 



For a plane, draw the wind vector, e . . . . w, and drop the perpendicular from w instead of from e. The corresponding air course is obtained 

 by reference to w instead of e. Note that the course is always normal to the line of Relative Movement and can therefore be obtained without 

 plotting if the direction of the latter is known. 



8 



