Hydrofoils Running Near a Free Surface 163 
The results of this first test series were complemented in 1958 by six component meas- 
urements in the circulating water tunnel of the VWS[7]. The dihedral hydrofoil model al- 
ready described for the measurements of the pressure distribution with a fixed dihedral angle 
® = 33 degrees was used. The flow speed was about 2 m/sec. The influence of rolling and 
sideslipping in particular were examined. 
First of all Fig. 18 shows the geometrical variation of the effective angle of attack of 
the pressure-side chord along with the roll angle and with the sideslip angle. For instance 
if such a hydrofoil is running straight-on with 0 = 1 degree, then for the profiles, 0.8 degree 
is the effective angle. If there does exist a sideslip angle of y = 10 degrees toward star- 
board — for instance when turning to port — the effective angle of attack will increase on the 
starboard side to +6 degrees while on the port side it will decrease to —4 degrees. If there 
is an additional roll angle of about 8 = +20 degrees toward the center of the turning circle, 
then this angle of attack difference will be increased to +8 degrees and —7 degrees respec- 
tively. For a rolling angle of 8 = —20 degrees to the outside, a diminution of the effective 
angles of attack to +2.5 degrees and —1.5 degrees respectively will result. An augmentation 
of the sideslip angle causes a nearly linear augmentation of these angles of attack. 
Since therefore for hydrofoil boats under service conditions the angle of attack can 
spread over a very wide range, the course of the coefficients for lift, drag, and pitching 
moment has been measured for a 45-degree variation of the angle of attack (Fig. 19). Here 
the flow separated at about +8 degrees on the upper side and at about —10 degrees on the 
lower side. The lift coefficient will increase, of course, after such a sudden breakdown but 
the drag-lift ratio € = Cp/C, then will be three times as high as it was before (Fig. 20). 
The fact thatrelatively high negative lift values can be obtained is of no importance for prac- 
tice. In turning circles for the inner side, i.e., on the port side when turning to port, a de- 
crease of lift may, of course, be desired, even down to zero. But it should not reach nega- 
tive values, since an adequate raising of lift on the outer side beyond twice the value as 
before seems to be unlikely considering the augmentation of drag, the diminution of speed, 
and the smaller submerged area of the outer foil, which is reduced by rolling. For running 
with a following sea — a situation when negative angles of attack will occur easily — such 
a negative lift also will be dangerous even if it occurs only for a short period. 
Figures 21 and 22 demonstrate the variation of forces and moments versus the sideslip 
angle and the roll angle. The coefficients for lift, drag, and roll moment are practically con- 
stant; the coefficient for the yawing moment is insignificant. The coefficients for lateral 
force and roll moment increase linearly from zero upward with increasing sideslip angle and 
roll angle. For instance a sideslip of +8 degrees toward starboard causes a lateral force 
toward port of eight times the value brought about by -8 degrees rolling toward starboard; 
the roll moment due to a sideslip is 70 percent higher. Both roll moments relative to the 
keel point are stabilizing, i.e., any rolling will reduce itself and a sideslip will produce a 
rolling toward the inside of the curve. 
Simultaneous systematic variations of the angles of attack, of rolling, and of sideslip 
produced only unessential differences relative to drag and lateral forces compared with the 
separate variations. But the situation deteriorated relative to the lift. For a sideslip angle 
around 10 degrees the flow separated throughout. Lift then broke down much more com- 
pletely as the additional rolling increased (Fig. 23). 
Summing up, it can be stated: 
1. The range of the angle of attack of the profiles of a dihedral foil with a circle seg- 
ment characteristic which can be utilized is about 4 degrees < @ <+6 degrees. 
