Page 645 radio acoustic ranging 683 



at the desired point P. The manipulation of the device is facilitated if vertical pins are set at the 

 positions of the R.A.R, stations A, B, and C, for the arras to be held against. 



D. ANALYTICAL METHOD 



In this method the R.A.R. position is found by computing the total distance between station A 

 and the desired point P, and plotting by conventional methods. The following formulas express the 

 necessary relations between the given data for the solution of the problem, in which a = distance between 

 B and C; fc = distance between A and C; and c= distance between A and B. 



r2 — pi _ ^2_(p-^g,)2 



2{p + ccose) 2[p + q+b COS {A-e] 



where A is the angle PAB, and d is the angle measured from AB toward AC in such a direction that 

 the direction of AP is reached before AC is reached. 



q + p{l — m) — (mc—b cos A) cos d~b sin A sin d (2) 



J,2_(p_|_o)2 



where m is^ 2^~2 Note that m is always positive. (3) 



Now let mc—b cos A — d cos 5 (4) 



and b sin ^ = d sin 5 

 Solve for d and S. Let d be always positive, then 5 is uniquely determined. 

 Then, 



cos ((9+3)= ^ . (5) 



Mathematically, there are two solutions for (0 + 5) and hence for 6. However, in practice, the ap- 

 proximate angle d will usually be known and hence the proper 9 can be determined immediately. 



The order of the solution should be as follows: Solve for m in equation (3), for d and 5 from equa- 

 tion (4), for (0 + 5) and 9 itself from (5). All values are now known so that x can be computed from 

 equation (1). 



Forms for logarithmic and machine computation can be furnished by the Washington Office. 



683. R.A.R. Sounding Lines 



In hydrography it is desirable to sound along a regular system of lines to cover an 

 area thoroughly in an efficient and economic manner. In R.A.R. surveys, especially 

 where strong currents prevail, it is frequently difficult to follow proposed lines, prin- 

 cipally because of the time that elapses after each position before it is plotted. Depend- 

 ing on the reliability of the data and the expertness and diligence of the chronograph 

 attendant and the plotter, the ship's position is not known until 4 to 6 minutes after 

 the time of the position. The officer-in-charge must always bear this in mind and, 

 where a position plots off the line, the course must be changed more than is apparent 

 from the boat sheet to bring the ship back on fine, because of the distance that the ship 

 has traveled since the position. 



The change in course needed to bring the ship back on line may be determined from 

 its dead-reckoning position at the instant of change. The new course must be measured 

 relative to the last course made good so as to take account of the leeway. To follow the 

 proposed line, the course should be changed again when the ship is judged to have 

 regained the line, making due allowance for the known leeway. 



Carefully calculated courses should rarely need to be changed more than 1° or 2° 

 after each position, although larger changes are sometimes necessary where there are 

 erratic currents. Excessive changes in course, causing the positions to plot alternately 

 on opposite sides of the proposed line, should be avoided. 



