stable, although low, platform for these location aids. Approximately one 

 meter of line was used between units, with the current meter being located 

 3.5 meters off the bottom. 



Instrument Descent Speed and Overshoot 



To estimate the speed of descent of the instrument package, the 

 following formula for form drag was employed (Rouse, p. 244). 



^d "r^d/^ Av^ eqn I 



where pj = drag force 



CLi= dimensionless, shape-dependent drag coefficient 



^ = density of fluid through which float travels 



f\ = cross sectional area normal to direction of motion 



V= velocity of moving body 



The drag coefficient was estimated as 1.0 (Rouse, Table HI, p. 249). 

 The cross sectional area of the float was 1.68 square meters. On descent 

 the drag force was made equivalent to the difference between the net buoy- 

 ant force and the ballast weights; on ascent the drag force was taken as 

 equal to the net buoyant force. The drag forces were designed to be equal 

 at approximately 178 newtons (40 pounds) apiece, yielding a speed of 45 

 cm/sec. 



Instrument overshoot on hitting the bottom did not prove to be a problem 

 The following linearized equation was taken as an approximate description of 

 the motion of the instrument package immediately after the ballast weights 

 hit bottom: 



"^ di^ ■^•^dt" ^ ^ eqn 2 



where jj = vertical displacement of instrument 



pTl = total mass of instrument package 



k = % cd p A Vp 



w = descent velocity (terminal velocity) 



P" = restoring force (equal to force exerted by ballast) 



Using the values of vt and Cj as obtained from our instrument records, the 

 overshoot was considered negligible; and no attempt was made to solve for 

 the overshoot based on the proper expression for drag force involving the 

 square of the velocity. 



239 



