Kaplan, Sargent and Goodman 
the controls. The product K,F, , which varies slightly throughout 
the depth range covered in the full scale tests and the simulation 
data, is found to compare very well using the respective parameter 
values obtained in each case. This indicates the same lift effec- 
tiveness being manifested by the forward foil elevator control. 
The values of the product KF, » representing the rear 
foil flap effectiveness were quite different, ranging up to about 3-4 
times as large in the case of the full scale data value when compared 
to the mathematical simulation model value. This result indicates a 
possible difference in the flap areas (or other dimensional changes) 
between the values assumed for the mathematical model exercise 
and the actual craft flap characteristics, or it may also imply a 
defect in the form of mathematical representation used, as given in 
Equation (44). Still another possibility is that since there were 
separate port and starboard flap deflections, the use of an average 
value may not be proper for the present application test of system 
identification ; there may be some rolling motion developed by the 
different flap deflections that causes different relative immersions 
on each side of the craft ; etc. 
With regard to the question concerning the basic mathem- 
atical model given in Equation (44), as well as the representation 
in Equation (42), the quantity F, (or F, ) represents the foil lift 
coefficient rate Cr for the particular foil. The depth dependence 
inherent in this type of representation appears to be appropriate, as 
exhibited in Figure 14, which was the basis for its selection in the 
mathematical model. However that functional form of F,; and Fy, 
implies that the same depth dependence is present for the control 
elements of the foil as is the case for a total foil angle of attack 
change. This does not appear to be a reasonable assumption, in 
view of the small sizes of the control element chords relative to the 
craft foil submergences. It would appear to be more appropriate to 
assume a realistic depth dependence, with known values similar to 
the variation exhibited in Figure 14, for the terms associated with 
the angle of attack variables in Equations (42) - (44). The unknown 
functional form of F, and F, , which would just be associated 
with the unknown elevator and flap parameters K, and Ky, would 
then be sought by means of the present system identification tech- 
nique to determine the appropriate parameter values and check the 
resulting trajectory tracking. Thus the results of system identifi- 
cation provide a means of judging the general validity of particular 
mathematical model representations that are assumed to represent 
vehicle dynamics, 
1666 
