Hydrofoils Running Near a Free Surface 181 
bi. 
ie aK KOK, Kee (20) 
By means of this relation the results of wind-tunnel tests or of theoretical calculations can 
be compared with the results of hydrofoil measurements. 
VERTICAL STABILITY OF HYDROFOILS 
For the sake of good driving properties a suitable vertical stability of hydrofoils is very 
important. However, it should again not be too great since the foils then will respond to 
minor disturbances, for instance to small waves on a surface otherwise calm; that means 
such foils will run stiff. Therefore not too steep a dL/dh curve is desirable. 
For a nonrolling surface-piercing foil, the lowest point of which is at depth ho with 
wetted aspect ratio A, the total change of lift 
ab. db + 2h 
dA + — = 
= oh 
(21) 
0,h, 
is dependent on the variations of aspect ratio, span, and depth of submergence. From the 
geometry of the foil it follows that 
ee eee 
sin } 
so that 
dL oL 1 oL 1 oL 
z ~ @A sin ® 35 Si es 
LN sete. A g ad a 
From 
L = putbeC, KK, cos @ K, Ky (22) 
it follows that for each panel of the foil 
CS ais | ey OK , 
Se pwitakhos cLakakr £O5;% com eA. Ry (23a) 
OL} Pare y raat : 1 
5B _ = gy PY bcC, K Kp cos z K, Ky (23b) 
b A ho 
e 1 pu2beC, °K_K ee 
Se oO c cos ¢ = 
Silo. 2 °° ee he ORG) ie oe 
