Hydrofoils Running Near a Free Surface 183 
on one 
ae =" fu beC, K,Kp cos 6 K, = (26a) 
dh Aybyh ho A oh hy, ho 
Thus 
OK; hy 
= = soe == : = | 1 Ges dh 7 b ; (Ki rs cs Ks; 
Rata: hh. = base iy 
oh ee oh 1 ire sin 2 1 
This gives 
Ke “7 
i+ ee 
ee = C. Kk. K; cos 0 K Edie DS al a (26b) 
205 at it Lo a P A b sin ‘iY 
A,b,h,,h, $ 
An improvement for the submerged dihedral foil will be possible by arranging horizontal 
auxiliary foils at the upper ends as near as possible to the surface such that they are within 
the range of substantial OK_/ dh (Fig. 30). 
ROLLING STABILITY 
A surface-piercing nonrolling dihedral foil with the dihedral angle #, constant profile 
length, and wetted aspect ratio A may be examined now. For an inclination df a differen- 
tial stabilizing moment relative to the lowest point is produced according to 
om 
gl sp = 
a M 
db + —* dh. 
A ob h 
(27) 
The differentials dA, db, and dh can be obtained from the geometry of the foil: 
: 1 
+d -= dA 
ee 
a 
o 
T 
Q 
=a 
iT} 
+ 
+ dBb7 cos ¢ 
with the dimensionless distance from the lowest point 7 = 7/6. For evaluating 0M,/0A, 
OM ,/0b, and 0M ~/0h the spanwise lift distribution will be given by the term f(y, h) = f@) fh), 
where with sufficient accuracy an elliptical law may be chosen for the function f (7): 
za as 4 = 
(mq). = 6 (7)i 6,0 Ky, vl - 4 - 
