Free Surface Effects tr. Hull Propeller Interactton 
are propeller induced velocities in the ultimate wake. 
If the rotation of the slipstream is ignored (up <F*) and 
G is assumed to be independent of the radius x 
u 
Aso -Z G 
gla tial aga t ADe u 
ifs 1 Aco 
2 Va 
Inserting 
Aus 
= Z 
Coy J & 
“Aco 
see [1], and eliminating Taare Dickmann formula 
A 
q! +ICede 
Th 
é(R70 8 je (2) 
4a 
is obtained. 
If on the other hand G is assumed to vary along the radius, 
u u 
but both oe and ae are ignored, the formula proposed by 
A A 
Hough and Ordway is obtained : 
ZG 
a(R; Oie == TATE (3) 
This formula is strictly valid only for very lightly loaded propellers, 
Fig. 1 illustrates the different values of o obtained with the 
exact formula, Eq. (1) and the approximate ones, Eq. (2) and (3), for 
a propeller loading typical for the investigation in question, As seen 
the Dickman approximation agrees much better with the exact solu- 
tion than the light load approximation of Hough and Ordway. Thus the 
reason for the higher o values obtained with Eq. (3) is not the more 
realistic distribution of circulation but the erroneous ignoration of 
the propeller induced velocities. This means that the calculated 
- self induced free surface wake of free-running propeller 
an, Big... LA, 
- wave resistance of free-running propeller in Fig. 14, 
- free-wave spectrum of propeller and hull with propeller 
in Figs 18, 19, 21 and 22 and 
- thrust deduction fractions in Fig. 30. 
1951 
