The tow assembly design of Figure 2A was analyzed for structural 

 adequacy and for performance using the force loading diagram of Figure 

 B-4. Figure B-4A is a diagram of forces on the entire assembly, and 

 Figure B-4B is a free body diagram of the vertical member to which 

 the boom is attached. This is the member most likely to fail under 

 the loads encountered during field use. 



Referring to Figure B-4A, expressions can be written for the 

 vertical and horizontal force components and solved for the unknown 

 paravane area, A, (an inclined flat plate) by eliminating the towline 

 force, F . The resulting expression is 



2(Fg + F^) 



2 ^ / . 2 cos9 . 3 

 p v C„ sm acosa — : — - - sin 

 D \ sin9 



(B-6) 



where F = tension force exerted by boom (lb) 

 B 



F = drag force of tow assembly alone (lb) 



p = mass density of water (slug/ft-^) 



V = tow speed (ft /sec) 

 C = drag coefficient for flat plate 



= towline angle 



a = paravane angle 



The highest straight line tensile tow force occurs when Type II 

 boom is towed at 10 knots. In this case, the tensile tow load, Fg, 

 is estimated from Appendix A to be 2,800 pounds. The estimated drag 

 force of the assembly itself was calculated to be 254 pounds. Using 

 these values and a towline angle of 5 degrees, a paravane angle of 

 55 degrees, and a flat-plate drag coefficient of 1.28 [5], the para- 

 vane area. A, necessary to counteract the vertical component of the 

 towline force is 



A = 2.2 ft^ 



The required areas for Type I, Class 1 and Type I, Class 2 would, of 

 course, be smaller. The paravane angle of 55 degrees was chosen to 

 maximize the terms involving a in Equation B-6. Changing the towline 

 angle 5 to 10 degrees increases the vertical towline force component 

 and Increases the required paravane area to 5.1 ft^. Thus, for the 

 paravane to be effective, a small towline angle (long scope on towline) 

 is essential. 



42 



