Kaplan, Sargent and Goodman 
milar to our own results, although the particular cases considered 
for illustration are different in each paper. There is a problem which 
has not been mentioned and emphasized in any evaluation of coef- 
ficients using system identification. This is concerned with the time 
required for obtaining convergent values of the coefficients, which in 
the case of the hydrofoil craft required computation time 22 times as 
long as real time (of the trajectory time history) in order to deter- 
mine these values. We had 14 state variables, including the coef- 
ficients, and since computation time increases as the cube of the 
number of state variables in your system, too many coefficients in a 
representation will involve a tremendous computational effort. Thus 
the simplest possible representation of a dynamic system is neces- 
sary when carrying out system identification, as well as any simulat 
ion work, as long as the major features of the craft dynamics are 
adequately represented. 
With regard to the aspect of fitting the curve that Mr Norrbin 
presented, I am fully aware of the paper wherein he presented these 
results, since I have seen it and also looked into the same question. 
The real issue of importance is notthe value of the linear coefficient 
that is obtained by using different representations (for the nonlinear 
portion of the force) in the mathematical form used to express the 
force. The major point is how well the overall representation fits the 
total measurement of the force, and most important of all how well 
whatever mathematical formulation you use for the hydrodynamic 
forces and moments results in matching the trajectory of the vehicle 
under varied motions and maneuvers. Thus it is easy to see that there 
is more than one mathematical form that can represent any set of 
data, with different coefficients associated with different powers of 
the variables, and the particular choice may be dictated by consider- 
ations of formulation,ease of manipulation and subsequent evaluation, 
etc. I hope that this answers your question. 
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