Page 145 - Practical Design Ships and Floating Structures

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creating difficulties for the early steeped hull hybrids and that this is why they are not now common,
despite their obvious potential. We also believe that we have solved them, and present our suggestions.

2 PITCH INSTABILITY
Pitch instability is the chief issue in a hybrid hydrofoil. Planing hybrid hydrofoils can exhibit a
dynamic pitch instability similar to porpoising. This phenomenon can be best understood for a
nominal configuration with a single hydrofoil beneath the center of gravity of a planing hull. If such a
configuration is slightly disturbed bow up from an equilibrium position, the lift on both the foil and the
hull will increase. The hull accelerates upwards and the intersection of the water surface and the keel
moves aft. This develops a bow down moment, but at a relatively slow rate. By the time the bow
drops enough to reduce the excess lift, the vessel is well above the equilibrium position, and the
keeVwaterline intersection is well aft. It falls back down toward the equilibrium position bow down,
as if it had tripped on its stem. Then, it carries through equilibrium, takes a deep dive and springs up
again. This cycle repeats, each time growing more severe. The only way that this motion can damped
is if the hull provides enough damping to prevent the increasing overshoot. Note that this is a smooth
water instability and occurs with only a nominal initial disturbance.

3 STEPPEDHULL

The stepped hull concept is obvious from this discussion. The foil is at the extreme stern of the vehicle
and a step is provided forward of the CG. The step confines the planing lift to the forward part of the
hull so that the relative position of the center of gravity, the step and the foil control the proportioning
of lift between hull and foil. Bow up pitch of the vehicle produces a strong bow down moment,
directly proportional to pitch, that reduces the pitch much more rapidly than the movement of the
center of planing lift. The step also means that the running attitude of the planing hull can be set at a
trim producing optimum lift. (This is the whole point of a stepped planing hull.)

The authors developed a simple program, discussed in more detail in Barry and Duffty (1999), using a
standard BIount and Fox (1976) approach to calculating planing forces combined with standard
methods form DuCane (1974) and Hoerner (1958) for calculating foil forces. The input and output
parameters are per figure 1. The coordinate system is fixed to the vehicle with the origin at the
stepkeel intersection.
The terms used in the figure are:
BX Planing beam, the effective beam of the each hull, generally the beam at transom.
P The deadrise at the station chosen for effective beam.
Stagger Location of the foil fore and aft, negative if aft of the step or transom.
Gap Location of the foil below the transom, negative if below.
Dekalage The angle of the nominal foil midline to the coordinate system.
LCG The longitudinal ccnter of gravity, positive if forward of the step.
Le The length of the wetted chine, including wave rise.
Lk The length of the wetted keel.
Drag The angle of the keel with respect to the coordinate system.
z Trim of the coordinate system from the dynamic waterline, positive bow up.
Draft Draft of the origin below the dynamic waterline.