Semisubmerged Ships 551 
FOR ALL SPEEDS 
ee “ga 
See ir 
i ea 
Vi Fal A 
i fares 
STABLE FOR ALL AREAS 
° 200 400 600 800 1000 
TAIL AREA IN FT° 
Fig. 12. Coefficient b versus tail fin area 
Froude numbers but is not troublesome in regard to this type of instability at high Froude 
numbers. However, for Froude numbers where M, is maximum, the attending increase in d 
can contribute to oscillatory instability. Figure 14 is a graph of das a function of tail area. 
The coefficient 
(15) 
is negative for zero tail area. Figure 15 shows that the minimum tail area to prevent ex- 
ponential divergence at 60 knots is 255 ft. Thus, the free-surface effects at high speed 
require a bit more tail area than the condition imposed by c for deep operation. 
Oscillatory-Exponential Instability 
If a pair of the roots of the quartic characteristic equation are complex, either damped 
or undamped sinusoidal oscillations will occur subsequent to an initial disturbance, depending 
