Hydrofoil Size and Seaworthiness 195 
of hydrofoil craft will not affect its static stability. Constructional properties, proper means 
of navigation, and lifesaving equipment are (although very important) not to be discussed. 
Hence the following will be limited to the dynamic stability and its influence on the 
comfort of hydrofoil craft. The main factors which define the movements are: static ampli- 
tude, (already discussed), excitation frequency, (already discussed), natural frequency, and 
damping ratio. 
The motions of hydrofoil craft are defined by a number of basic equations. There is 
equilibrium when the weight of the craft equals the combined lift forces of the foils: 
moa= 2b. 
The lift force of a foil is proportional to dynamic pressure, lift coefficient, and submerged 
foil area: 
L = 5pV2q F. 6) 
A deviation in pitch from the equilibrium position creates an extra lift AL which tries to 
restore the craft to its original position. The restoring moment is called R. It will be 
clear that: AL :: mg since L :: mg (Eq. (5)), so R:: mgl. Further, for the moment of 
inertia, / :: ml? if the mass distribution can be supposed to be similar. Thus the natural 
frequency of the craft can be calculated: 
Auf nn aha 
ae ee 
where the index p is used for pitch, or 
Way = ken ve : (7) 
In an analogous way the natural frequency for heaving motions can be found to be 
Wap ken, VE (8) 
The dimensionless damping ratio in case of pitch, d,, is the damping N divided by the 
critical damping: 
Neus is 1 
d,= 9/tTR Where V: as : (9) 
In this equation D, is the damping force: 
1 
D, = zpV2AC) Fa (10) 
in which Ay = W/P and Wc. 00" soN = VOR, - 
