304 KNAUSS [chap. 14 



in the case of a drogue designed to measure subsurface currents as the following 

 calculation indicates (Fig. 1). The drag force equation is 



F = \C P Av*, (2) 



where C is a non-dimensional drag coefficient whose approximate value is unity, 

 p is the density of the water, A the cross-sectional area, and v the velocity. 

 Since there must be a balance of horizontal forces, the drag on the drogue must 

 be balanced by the drag on the surface float and other appendages : 



\C s pA s {v s -v) 2 = \C<tpA d {v-v d ) 2 , 



where the subscripts s and d refer to the surface float and drogue respectively, 

 and v is the velocity of the drogue system. Thus 



The criterion for a well designed drogue is that v — v d is made as small as 

 possible, and this can only be done by making (CdAd)l(C s A s ) as large as possible ; 

 and, since this is a square-law relationship, a factor of a hundred in the ratio 

 of cross-sectional areas results only in a factor of ten in the ratio of velocity 

 differences. At best, drogues can give only approximate values of subsurface 

 currents, although, with careful design and care in applying corrections, it is 

 believed that subsurface currents can be measured to an accuracy of 5-10% of 

 the surface current. 



Drogues were used to measure subsurface currents in the Gulf Stream 

 nearly a hundred years ago (Mitchell, 1867, 1868). Mitchell was also apparently 

 the first man to anchor a buoy in deep water for the purpose of measuring 

 currents. "In this last cruise we were able to anchor buoys and thus measure 

 the current with accuracy. This can be done anywhere, and our charts ought to 

 contain this kind of data. Our way of working was this : we first anchored a 

 buoy, then having reeled the log-line within a free float, fastened the end of 

 this line to the buoy, and as it reeled out, counted seconds. By this maneuver 

 we avoided securing the boat to the buoy, which might have caused the anchor 

 to drag" (Mitchell, 1868). 



Drogues were used in 1871 to measure the subsurface outflow across the 

 Straits of Gibraltar by W. B. Carpenter and Capt. G. S. Nares, the latter of 

 whom served as captain on the first half of the Challenger Expedition (Carpenter, 

 1872). Eighty years later drogues were used to discover the Pacific Equatorial 

 Undercurrent (the Cromwell Current) (Cromwell, Montgomery and Stroup, 

 1954). More recently drogues made from aviators' parachutes have been used 

 successfully (Jennings and Schwartzlose, 1960). 



The ideal drogue is one in which there are no surface appendages, and, 

 therefore, there will be nothing to keep the drogue from moving at exactly the 

 speed of the water in which it rests. This ideal was achieved in 1955 with the 

 first successful use of neutral-buoyant subsurface floats by Swallow (1955) 

 (see Chapter 13). 



