Nowackt and Sharma 
A certain ambiguity arises in interpreting the speed V in 
the above relations when the propeller is operating in a wake behind 
the hull . We believe that the physical sink strength of the propeller 
should be determined by the local speed of advance VA while its wa- 
ve pattern must be characterized by the speed V_ relative to the 
fluid at infinity . Hence the corresponding relations in the presence 
of an effective axial wake Ww, become 
git (Bon by = -(¥l+Cry - 1)(1l- wp )/4n 
= 2 2 
Cr, = 2 D/ » Va* (Ry - Ry) (B15) 
in the Dickmann approximation , and 
@ (Bon @). =n, Zia (RY, ME JS eR) 
in the Hough and Ordway approximation . In either case , the left hand 
side is the appropriate dimensionless source density ¢9 to be used in 
the subsequent calculations of wavemaking and thrust deduction 
It may be noted that source disk representations of the propel- 
ler are only useful for calculating the induced flow field (outside the 
slipstream) . For calculating propeller performance (thrust and 
torque) resort must be taken to the correct vortex model . In princi- 
ple , it is possible to calculate also flow field and wavemaking directly 
from the vortex model , cf. e.g. Nakatake (1968) . However , the 
increased computational effort is hardly justified in view of the other 
approximations in the analysis. 
B,.3.. Free-Wave Spectrum 
A useful description of the wavemaking characteristics ofa 
ship is provided by its free-wave spectrum as defined for example 
in Eggers , Sharma and Ward (1967) . Given an arbitrary source 
distribution o (x, y, z) over adomain D , its complex-valued 
free-wave spectrum (as a function of transverse wave number u ) 
becomes 
G (u)i+ iF (u) = Pb ue aw ies y, Zz) exp {8° z+i(sxtuy) } ie 
D 
v = y l+4u2, ss and~—s 8 = yt /2 (B18) 
The significance of the free-wave spectrum lies in its ability to yield 
a simple description of the asymptotic wave pattern behind the ship . 
where 
1890 
