Kaplan, Sargent and Goodman 
me ss Zap eZiz + 2g + 20 = AApae 20) 
Z Z 6 6 waves 
log = M0 +-MO 4+ Miz-4+.Miz + M (41) 
ng 6 6 Z Zz waves 
where Zwaves and Mwaves are the wave-induced vertical force 
and pitch moment, respectively, which are random forcing functions. 
The quantities m, Iy and A (plenum area) are known constants, 
and the unknown coefficients are Z>, Zz, Z*; Zp 5 Mo . Mg P 
M; and M,. For these equations there is also appended a relation 
involving the pressure, leakage rate, fan characteristics, etc. which 
is derived on the basis of consideration of mass in the air cushion, 
In the representation given by Equations (40) and (41) 
it is assumed that the center of pressure of the bubble volume is at 
the CG, and the mathematical model only represents the vehicle 
motion, with no consideration of any seal motion or even of a direct 
presence of any seals. Similarly there is no direct dynamic force 
influence of the seals embodied in the mathematical relations above, 
except for the possible influence of the seal forces in determining 
the total hydrodynamic stability derivatives in the equations. 
Mathematical experiments were carried out with these 
equations, using computer generated data. In these experiments on 
the application of the system identification method, it is assumed 
that the pressure is a precisely known function, which is still a ran- 
dom function in general, and that this pressure variation is obtained 
from measurements, Thus the problem is reduced to treating only 
the two degrees of freedom of heave and pitch, and 8 coefficients 
have to be determined. The basic procedures were applied to this 
problem, which contained 4 state variables and 8 unknown coeffi- 
cients, leading toa requirement for 156 equations for this case, 
Various difficulties in regard to long computation time and small 
movement of the coefficients were found, and other approaches were 
considered. 
Instead of using a noisy input function to excite the system, 
which was attempted with the use of a random number generator in 
the digital computer, it was decided to make use of trajectory data 
that was generated using the large digital computer simulation pro- 
gram for rigid sidewall SES craft. This particular simulation also 
included a complete representation of seal dynamics, which allowed 
for seal motions nnd the generation of water contact forces that 
would be transmitted to the craft. The type of wave system exciting 
1654 
