Case XXVI 



TO PROCEED FROM ONE RELATIVE POSITION TO ANOTHER IN GIVEN TIME AT MINIMUM SPEED, PASSING 



THROUGH A GIVEN CHART POINT EN ROUTE 



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

 TION OF CHART POINT, AND TOTAL TIME OF OPERATION. 



TO DETERMINE: COURSES AND SPEEDS OF MANEUVERING UNIT, TIME OF REACHING CHART 

 POINT, AND RELATIVE POSITION OF TURNING POINT. 



Example.-Fleet is on course 140°, speed 12.0 knots. At 0630 a plane is launched from the Saratoga with orders to 

 investigate a chart point bearing 200° and distant 105.0 miles from Saratoga and to land on the Ranger, which is located 

 45.0 miles ahead of Saratoga, and is on fleet course at fleet speed. The plane is to complete the maneuver at 0930, usmg mini- 

 mum speed en route. Wind is from 010°, velocity 21.0 knots. _. - •• 



Required.-**) Minimum air speed for plane, (b) Air courses for plane, (c) Time chart point is reached, (d) Bearing 

 and distance of plane from Saratoga when chart point is reached. (See fig. 37.) 



Procedure-Lay out the wind's and the Saratoga's vectors as e. . . . w and e . . -. : ^respectively. The latter 

 is also the vector of the Ranger, which is also using Fleet Course and speed. / 



At anv convenient point lay out the position of the Saratoga at S, and the relative position of the chart point at 0630 

 at P f Lcl^SpoitiTn of the Ranger at R. Advance the position of R to R>, representing 0930 position of tins 



ship, 36.0 miles ahead of the 0630 position. _ 



Connect S and P and transfer this slope to e. In a similar manner, connect P and R' and transfer this slope to e. The 



^"DTviS^sfance T § ' '• * by'theVo hours allowed, giving the rate travelled by the Fictitious Ship in its direct 

 ron^Iot^^rZgL^ Rangel From s, draw s . . . . /, parallel to S . . . R and equal to the rate obtained 



° V pivot a straight-edge at /and orient it until it cuts the slopes drawn from e and parallel to S . ... PandP. . . . R', 

 respectively, at points equidistant from w , these points being Pl and p 2 , respective^ T^ie air speed for the plane is gv.en by 

 either w . ... Pi or w . . . . P*. The first course for the plane is indicated by the direction of w .... Pi and the 



"tislw a Relative Movement Line parallel to the slope of s . . . . Pl and from R draw a Relative Movement 

 Line parTlldtotTe slope of p, . . . . .. These two lines intersect at P", the turning point. The time required to reach this 



the Time Line Pl .../.... P 2 , as previously explained. The bearing and distance of P from S is the bearing 

 It will be noted that the Navigational plot is shown by S . . . . P ■ ■ • - * . wmle 



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