The form can be simplified by putting: 



F = W+W^ 



sin - W/F (i4.) 



cos = D/F . 



Then 



dT ^ D sin(Q-0) ^ (5a) 



dx cos 



d© ^ D cos(9--0) . (5b) 



dx T cos 



This is a pair of non- linear simultaneous differential equations 

 for the two variables T and Q with the fixed parameters D and 0. 

 The boundary conditions to be met are that T(o) is to have a value 

 Tq = F^ and Q(0) is to have a value ©^ = tan-^i^Dij/Bjj). The offset 

 Y can then be determined f rem 



= I tan dx = I © dx (6) 



Y 



'o •'o 



where we have introduced the small angle approximation for tan Q. 



The above equations can be solved by numerical computation if 

 desired^ but some rather goo<3. simplifying approximations can be made 

 which enable analytical expressions to be obtained. Before doing 

 this we introduce the numerical values of the constants typical of 

 our experimental test conditions. Assuming a viniform current vel- 

 ocity of 0.2 knot we can calculate the pressure drag for the buoy 

 and line. Surface drag is neglected. 



B^ = 1300 lb. 



D^, = 0.53 lb. 



X = 1300 ft. 



D = 11 Ib./1300 ft. = .0085 lb. /ft. 

 W = 0.35 lb/ft. X (1.1^4-1.03) = .039 Ib./ft. 

 Hence F^ = I300 lb. 



©o = .00041 radians 



= 77.7' = 1.35 radians. 



289 



