Hydrofoils Running Near a Free Surface wel 
THEORETICAL CONSIDERATIONS 
The velocity field of a hydrofoil of great span running at the depth h=h/c = h*/2 be- 
neath the undisturbed water surface in deep water can be represented by the well-known re- 
lations (for instance, Ref. 8) 
u(x,z) _ u,(x,z) 
+1 
1 z + h* 
= cat 7 ee ip aan A 
ee o aya hal Zt) 2 
+1 
1 z — ht 
os ey ye SE 
"On J, es ee 
+1 
+ © exp i (ht | {| «oa, ber rest) dé (1a) 
Uo %6 a4 Uo 
wOX,Z) _ wy(x,Z) 
Uy 4G 
: +1 Z 
aie Fe aaa ae ee 
of E Ge ees 
1 +1 é 
a oe f ee ea ses Li, RR MOR 
7 [ ‘a Ga) ee) 
0 0 0 
+1 
age Po (- ee = j f(2)G, ao ae ab) 
u u I u 
where u, denotes the running speed and f(£) the pressure distribution over the profile length. 
At the free surface the velocity field fulfils the boundary condition resulting from the line- 
arized Bernoulli law 
u,? du,(x,0) 
0 1 2 = 
The shape of the surface results as well from the Bernoulli law by linearization to 
