CALCULATIONS ILLUSTRATING THE EFFECT OF BOUNDARY LAYER ON WAVE RESISTANCE 
and this leads to 
ett +2 | 7 sin Gr) 
7) + pla +teo+(57) 
(2) Mma 
— > 008 
(31) 
Values computed from this are shown in curve E of 
Fig. 2. 
In the next place we take the new curve to extend 
similarly from 2 ft. before the stern to 2 ft. behind the 
stern. The conditions are thus 
3 
I= 16 Tae oe 
(32) 
dy Os tires a= 
dic SLOT: = A 
From these we get 
Ties 3 
D> att a6 ara (33) 
the curve shown starting from the point F on the section. 
It passes the stern at a transverse distance 5 5/32, and 
finishes leaving a narrow wake of half-width 5/16. 
In this case 
1 as 
I+iJ= ~2 | ereaes (Bi se)enae 
4 fis (34) 
and for the resistance we obtain 
alo p 
—8y2) 4 4 t 3 si 2 
m7), e | 1 sin | 47 
wife 1 9 9 
era) Assent 
scos (77) 7 05(57) | }eos oa 
2 
(35) 
This resistance is graphed as Curve F in Fig. 2 
It is submitted that inspection of the curves in Fig. | 
and Fig. 2 supports the general conclusion that these 
small modifications give the required kind of change in 
the resistance curve for the original model, namely 
elimination of the humps and hollows at low speeds 
with a much smaller relative effect at high speeds; 
= 
‘ 
534 
further, it is considered that the modifications of form 
are such as might be caused by displacement of the 
streamlines by boundary layer effects near the stern. 
No doubt the results could be improved by further 
detail: for instance, by change of boundary layer with 
velocity which might possibly correspond to a change 
in the point of departure of the new line, or by assuming 
a greater virtual extension of the form to the rear with 
a permanent wake. However, the.simple cases given 
now are sufficient to illustrate the point of view. 
Unsymmetrical Model 
We consider finally a model which is unsymmetrical 
fore and aft. The difference in resistance according to 
the direction of motion may have various contributing 
factors; for example, wave reflection might be important 
if there were considerable difference between bow and 
stern angles. However, the main effect may be taken as 
due to boundary layer modifications. We choose, as 
the simplest case, a model with vertical sides and with 
draught equal to one-twentieth of the length, and with 
the lines given by 
N= USAC 38) (36) 
This gives a bow angle twice the stern angle. When 
going bow first, we take the new streamline near the 
stern to be given by (27) with the conditions 
i ee 
dyn : 9 
GS OF fore = — 8 
from which we obtain the curve 
Be ee 
With the fine end leading, the model is given by 
T= (Wes) (es) (39) 
To lighten the numerical work, we assume the two 
ends of the new streamline to be in the same relative 
positions as when going bow first. The conditions are 
now 
155 dy 419. 
I= FOP ie op 2es= 
4 9 (40) 
n : Man ca 
Fs 0; for é = 3 
and hence the curve 
341038 sil 419 5 
1= Gia + gaa $+ 96 & Gw) 
The form of the model with the modifications (38) and 
(41) is shown in the section in Fig. 3. 
