the output is sampled, low- frequency aliasing must be kept in mind. Optical 

 tracking consists of sampling positions, usually at equal time intervals. 



The drogue, which must respond to the horizontal components of all 

 velocities present, should either follow the dc and ac velocities perfectly or act 

 like a low-pass filter— have a reduced response to the ac flow, but follow the dc 

 flow perfectly. However, the drogue would not normally follow the ac flow 

 perfectly. A difference in velocity between the drogue and the ac flow will exist 

 and vary with time. The drogue is a passive device that requires an external force 

 obtained from this velocity difference in order to operate. The resulting force, 

 however, on the drogue is not linear with velocity and can generate a false dc 

 level except when the true dc level is zero. With the fixed drag-force meters 

 equipped with electrical readout, the nonlinear force vs velocity effect could in 

 principle be taken out in the process of data reduction, but this is impossible with 

 drogues. 



Assume a velocity difference in the horizontal plane, U, between the drogue 

 and the water given by V = Uq + U„ sin 9, where L'q and U„, are constant. Assume 

 that equation 24 can be used to describe the resulting force on the drogue. Assume 

 Kj and K'2 ^^ constant throughout the wave cycle (this might not be a valid as- 

 sumption in actual practice). Also assume that U^> Vq. The net force per cycle, 

 F, can be found. 



2tt 



2 



TT 



/('^^-■= 



F=— / (K'l^ +K2U\U\] dQ (34) 







K2_ 



2tt 



2tt 



f (L/q + V^ sin 9) 1 L/g + (J„ sin 9 | dQ 



(35) 



\j III ' w "( 







The mean value, F, was evaluated numerically for one set of values. For a ratio 

 of U^/Uq = 5, the net force per cycle, F, was about 6.4 times larger than the ideal 

 force which was found by using only Uq. False dc levels can thus be generated 

 by filtered nonlinear ac terms and was in this case a function of U^/Uq. This 

 was only a crude example to show that the effect can occur. A more complete 

 description would be quite complicated. Model studies would probably be 

 necessary to show how serious the effect would be with real drogue configurations. 



Another disadvantage appears with drogues constrained to stay at one 

 preset depth. At any given time and at a constant depth, some horizontal velocity 

 distribution exists. Assume that this is a sine wave. This sinusoidal spatial 

 distribution travels through space as a function of time at the phase velocity, c, 

 of the surface wave. Since the drogue is free to move only in the horizontal plane, 

 the condition for the net horizontal force on the drogue to be minimum would exist 

 only when the drogue is traveling at the velocity, c, also. This condition would be 

 independent of the initial depth of the drogue as long as it stays at this depth. 

 The use of drogues in shallow water is not recommended. 



39 



