Free Surface Effects tn Hull Propeller Interaction 
From here on the further analysis is of a semi-empirical 
nature and must be conducted in an essentially predetermined sequen- 
ce because at each new step certain information from previous stepsis 
required . It is helpful to list separately the pure hull analysis , the 
pure propeller analysis , and the interaction analysis . 
The purpose of the hull analysis is to verify the mathematical 
representation of the hull as a source distribution and to establish the 
degree and range of validity of the linearized wave theory . 
H 1 ) The total resistance measured in step El can be subjected 
to a simple form-factor analysis (based on a suitable plane friction 
formula) so as to yield the viscous and wavemaking components . 
H 2 ) An alternative estimate of wavemaking resistance can be 
obtained from a Fourier analysis of the wave profiles measured in step 
B54) 
H 3 ) The experimental estimates of wavemaking resistance 
derived in the two preceding steps may now be compared with the theo- 
retical calculations of step Tl . 
H 4 ) For a more exacting test of the theory the experimental 
and theoretical free-wave spectra can be compared at each speed . 
H 5 ) An additional test of the theory lies in comparing the sum 
of the calculated wave wake and potential wake from steps T 2 and T 3 
to the measured wake in reverse motion from step E4 since the latter 
is essentially free of viscous effects . 
H 6 ) If the mathematical model of the hull flow can be verified 
in the preceding steps then the calculated wave wake and potential wake 
may be subtracted from the measured total wake in forward motion to 
yield the important viscous wake component . 
The purpose of the propeller analysis is to determine a vortex 
model of the propeller and to verify the validity of its alternative 
representation as a source distribution which is to serve as the basis 
for calculating thrust deduction and wave effects . 
P 1) A computer program based on lifting line theory in con- 
junction with the Lerbs ( 1952 ) induction factor method may be used 
to calculate for any given propeller geometry and assumed foil cha - 
racteristics the equivalent distribution of bound circulation over the 
radius and hence by Kutta-Joukowsky's theorem the thrust and torque 
coefficients as functions of the advance ratio . 
1849 
