Case X 



TO DETERMINE SPEED OF GUIDE FROM THREE OR MORE BEARINGS, KNOWING GUIDE'S COURSE 



GIVEN: OWN COURSE AND SPEED, COURSE OF GUIDE AND THREE OR MORE BEARINGS OF GUIDE 

 WITH TIME INTERVALS BETWEEN BEARINGS. 



TO DETERMINE: SPEED OF GUIDE AND RELATIVE POSITION AT ANY SUBSEQUENT TIME. 



Example. — Ship A, on course 140° at speed 12.0 knots, is taking bearings of ship M, which is known to be on course 180°. 

 Bearings taken at 1130, 1230, and 1310 are 090°, 117°, and 149V2° respectively. 



Required. — (a) Speed of M. (b) Estimated relative position of M at 1350. (See Fig. 14.) 



Procedure. — Plot the ranging vessel at any convenient point A and lay out bearings of M at 1130, 1230, and 1310 as 

 A .... pi, A .... Pi, and A . . . . p 3 , respectively. 



By any of the methods described for case IX, draw slope Pi .... P 2 .... P 3 across the bearing lines at such an 

 angle that the intercepts are proportional to the time intervals between bearings. 



From any convenient point e, lay out A's vector e .... a, and M's known course line e . . . . m'. 



Transfer the slope P : . . . . P 2 . . . . P 3 to a, cutting e . . . . m' at m. e .... m is the vector representing 

 the course and speed of M. 



Using the Relative Speed indicated by vector a .... m, the Relative Distance run by M during the time the bearings 

 were taken is found by means of the Logarithmic Scale. By trial and error or the method indicated in case IX, this is plotted, 

 locating M u M 2 , and M 3 . These positions are those occupied by M relative to A at 1130, 1230, and 1310, respectively. The 

 relative position of M at 1350 is also found through the Logarithmic Scale as a 2 h 20 m run from 1130 or a 40-minute run 

 from 1310, and is designated as Mi. 



Answer— (a) Speed 14.5 knots, (b) Bearing 167°, distant 10.7 miles. 



NOTE. — This case becomes indeterminate if the slope Pi .... P 2 .... P 3 is parallel to the vector of the ranging ship. This 

 can occur only if M is on the same course as A or the reverse of this course. In this event, since the course of M is known, A should steer another 

 course for taking bearings. 



If the bearing does not change, it will not be possible to determine the relative position of M by this method. 



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