A Survey of Ship Motion Stabilization 



^ (1) 



S 



where 



oj^ = tank frequency, by U-tube analogy, and 

 S = effective length of the U-tube. 



(-L A 



where 



A^ is the area (constant) of free surface in one "wing tank" of the U-tube, 



A is the cross section area of the U-tube normal to the U-tube centerline, 



S is the girth-like coordinate along the centerline, and 



L is the total "girth length" of the centerline. 



In the case of a free surface tank, the U-tube analogy is applied by assuming 

 that the U-tube centerline is as shown in Fig. la. 



Reference 34 presents an approximate solution for the natural frequency of 

 a tank of the configuration shown in Fig. lb, 



V S' S' 



_ _ (3) 



-L y s' ''°"" s' 



ivhere 



co^ = tank frequency, by "exact" theory, 

 S' = "effective beam of tank," and 

 h = fluid depth. 

 The effective beam of the given tank configuration is shown by Lamb to be 



,2 



Relating the two methods of calculating frequency; 



S' = B + 2ZL^ . (4) 



2(1 + 8) coth (3^) (5) 



221-249 0-66 



753 



