F (R^, .j,) = -R (R^) • f^ (.j,) (1) 



G (R^, (|)) = -R (R^) • ft (<i>) (2) 



where R is the towline drag per unit length when the towline is normal to the 

 direction of tow (R = 1/2 C^ tV^), 



R^ is the Reynolds number (R^ = V c/ v ), 



is the fluid density, 



Ct, is the towline normal drag coefficient expressed as a function of 

 Reynolds number, 



t is the towline maximum thickness, 



c is the fairing chord, 



V is the free-stream flow velocity, 



V is the fluid kinematic viscosity, and 



fj^, f^ are the normal and tangential loading functions, respectively. 



The negative (-) signs in the equations for F(Rjj, <}) ) and G(R^, cf) ) above 

 appear since the towline drag is in the negative (-) X-direction as defined in 

 Figure 5. 



For purposes of evaluation, the side force component per unit length is 

 assumed to be composed of a product of a maximum side force that is dependent only 

 upon Reynolds number R^ and a loading function that is dependent only upon cable 

 angle ^ as follows: 



H(R„, .j.) = Fg (R^) • fg (<!.) (3) 



where Fg is the towline side force per unit length at the cable angle that 



2 

 produces the maximum value (Fg = 1/2 p Cg t V ); which for the 



integrated towline occurs when the towline is normal ((j) = 90 degrees) 



to the direction of tow. 



Cg is the towline side force coefficient expressed as a function of Reynolds 

 number, and 



fg is the hydrodynamic side loading function. 



24 



