SECTION II 

 TWO COURSES FOR GUIDE, SINGLE COURSE FOR MANEUVERING UNIT 



The cases thus far discussed have comprised either those in which both Guide and Maneuvering Unit maintain constant 

 courses and speeds throughout the problem, or else they have involved successive applications of cases of this type. In this 

 lection we deal with situations which require a change of course or speed or both on the part of the Guide while the Maneu- 

 vering Unit is proceeding from one Relative Position to another. When the total time for the maneuver is given, as well as 

 the exact time the Guide changes course or speed or both, the obvious and most rapid solution is a simple Navigational Plot. 



When the Navigational Plot may not be thus employed, the problem may be solved by so manipulating or distorting the 

 Relative Movement Diagram that the cases resolve themselves into the Single Vector Cases discussed in section I. This 

 distortion is required because the Guide does not maintain its course and speed throughout the problem, and consists in em- 

 ploying an imaginary or Fictitious Guide which does maintain its course and speed throughout the problem. The use of a 

 Fictitious Guide should be readdy understood by any practical navigator who has had to compute the net run of a vessel in 

 Traverse Sailing, for finding the Course and Distance made good between Fixes of Position. 



This Fictitious Guide may be considered as accompanying the real or actual Guide on either its first or its second leg, 

 depending upon the conditions of the problem. The course and speed of the Fictitious Guide will therefore be represented 

 by one of the vectors of the real Guide. Since the Fictitious Guide uses this vector throughout the problem, it may be em- 

 ployed in exactly the same manner as previously described in section I. 



In the Relative Plot, positions are located with reference to the real Guide by the statement of the problem. If, however, 

 the problem requires the employment of a Fictitious Guide for purposes of solution, it is essential that all positions in the 

 Relative Plot be referred to the Fictitious Guide (reorienting as necessary) and not to the actual Guide. As long as the real Guide 

 and the Fictitious Guide are together, any position plotted relative to the one is plotted relative to the other; but this relation- 

 ship does not hold when the real Guide and the Fictitious Guide are not together. In order that we may keep our Fictitious 

 Guide stationary in the Relative Plot, it is necessary to offset one of the positions of the Maneuvering Unit by the amount 

 this position would be shifted with respect to the Fictitious Guide during the time that the Fictitious Guide and the real 

 Guide are not in company. 



In general, the initial set up of the Vector Diagram comprises the vectors representing the two courses and speeds of the 

 actual Guide, one of which vectors will therefore also be the vector of the Fictitious Guide. The Relative Plot initial set up 

 consists of the real Guide and the Fictitious Guide located together at any convenient point, and the initial and the final 

 relative positions of the Maneuvering Unit plotted with reference to the real Guide. One of these Relative Positions is next 

 offset the proper amount to relocate it in respect to the Fictitious Guide. The other relative position remains untouched 

 since it is plotted for the time when the real Guide and the Fictitious Guide are together. 



The following rules govern cases involving employment of the Fictitious Guide: 



(1) When the time of departure of the Maneuvering Unit is known, the vector of the Fictitious Guide coincides with the 

 second vector of the real Guide. The initial relative position of the Maneuvering Unit is therefore offset by the relative run 

 of the real Guide with respect to the Fictitious Guide, while the real Guide is on its first course. 



(2) When the time of arrival of the Maneuvering Unit at its final relative position is known, the vector of the Fictitious 

 Guide coincides with the first vector of the real Guide. The final relative position of the Maneuvering Unit is therefore offset 

 by the relative run of the real Guide with respect to the Fictitious Guide, while the real Guide is on its second course. 



(3) The direction of offset is always toward the second vector of the real Guide. 



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