CALCULATIONS ILLUSTRATING THE EFFECT OF BOUNDARY LAYER ON WAVE RESISTANCE 
Hence from (7) and (8) 
22 prl2 
Ra APP (e+ Peos edd. (13) 
0 
1 
with 1+iJ=—2|éereae. 5 8 CO) 
-1 
where y = yo sec 8; Yo = Kol = gl? 
Using P functions, which are defined for integral values 
of n by 
r/2. 
Pn) = (& 1p [ cos 6 sin (p sec 6) d 0 
‘0. 
x/2 (15) 
P41 (Pp) =(— 1)"*! [costes Acos (psec 6) d0 
0 
we obtain 
RES? p28 1 
Fe galatisgt ew 
D, 1 
— 5 PQy) + GPs v)| Bac) 
This has been graphed on a base fin curve A of Fig. 1, 
corresponding to the form section A in the same diagram. 
Suppose this form has, say, a length of 16ft. and a 
beam of 1:5 ft., and consider the virtual modifications 
which might be ascribed to boundary layer effect. Let 
BMS be one side of the contour of the model. The 
wave resistance formulae are, in fact, derived by follow- 
ing the streamline which starts from the bow B, follows 
the contour BMS to the stern S, and then goes off 
along the central line. Suppose we know the displace- 
ment thickness of the boundary layer at each point and 
set it off to form a new curve B M’S’; we propose to 
take this as the virtual streamline form and to apply 
wave resistance theory to this line instead of the original 
curve BMS. This new line starts from the bow B, 
deviates slightly from the model except possibly near the 
stern, and we shall suppose that it becomes parallel to 
the central line at a point S’ somewhat to the rear of 
the stern S and possibly at some small distance from the 
central line. In default of sufficient information about 
the boundary layer in such cases, we shall make some 
arbitrary assumptions and see what effect is produced on 
the wave resistance. 
We shall neglect the displacement thickness calculated 
as if for a plank, as we have seen already that this has 
no appreciable effect; this simplifies the work consider- 
ably, as it enables us to follow the actual form from the 
bow to some point near the stern. We suppose that the 
* 
: i 
7 a 
L END 
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a eae t/a ee 
O 
Le 
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uJ 
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x 
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Ww 
-lOO 
0-21 
ie 
ais ic 
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ran, | 
AY Vans G2 
na 
SCALE Of f =v /G.t 
Figure 1 
