(8 knots), the hydrodynamic force becomes dominant and the system (towline and 

 depressor) steady-state force variations become essentially proportional to the 

 square of tow speed. 



As shown in Figure 9 configuration A-1 demonstrated approximately 3 degrees 

 of kite at speeds above 4.12 m/s (8 knots). The truncated 0020 towline (shown in 

 this figure for comparative purposes) demonstrated 7 degrees of kite from 4.12 m/s 

 (8 knots) to 6.19 m/s (12 knots) and at speeds above 7.22 m/s (14 knots) demon- 

 strated approximately 4-1/2 degrees of kite. The reduction in the kite angle 

 between 6.19 and 7.22 m/s (12 and 14 knots) is believed to be attributable to the 

 hydrodynamic forces and moments above 6.19 m/s (12 knots) overcoming those 

 produced by the fairing structural instability. 



The kite angles for configurations B-1 and C-1 are compared to A-1 in Figure 

 10. B-1 demonstrated approximately 5-1/2 degrees of kite at speeds above 4.12 m/s 

 (8 knots), which is approximately 1 degree more kite than configuration A-1, while 

 C-1 demonstrated approximately 4 degrees of kite, which essentially is the same 

 degree of kite demonstrated by A-1. The slightly larger kite angle measured with 

 the B-1 configuration is believed to be caused by asymmetries introduced during 

 the truncation process. 



Figure 11 presents the kite angle for configurations C-2 and C-3 compared to 

 C-1. The C-2 and C-3 configurations demonstrated a trend of reduced kiting with 

 increasing frequency of chordwise cuts. Above 4.12 m/s (8 knots) the C-2 configu- 

 ration demonstrated 3 degrees of kite and approximately 1-1/2 degrees of kite for 

 C-3 while C-1 demonstrated 4 degrees of kite. 



DETERMINATION OF TOWLINE HYDRODYNAMIC COEFFICIENTS 

 The three-dimensional equilibrium configuration and forces of a towline-body 

 system were solved using a computer program which required the following hydro- 

 dynamic input parameters: the tension vector at some point on the towline, the 

 towline drag and side force coefficients and the towline drag and side force 

 loading functions. The towline drag components, normal and tangential, are 

 assumed to be the product of a drag per unit length, which is a function of 

 Reynolds number R and a loading function which is a function of cable angle cj). 

 Using this convention, the normal force per unit length F and the tangential force 

 per unit length G are of the following form: 



23 



