Page 93 - Theory and Design of Air Cushion Craft

Calculation of cushion stability derivatives 77

a vibration system with one degree of freedom (only the heaving motion is considered
here) and the frequency response can be shown in Fig. 2.25, in which co e/co n denotes
the tuning factor, co e represents the encounter frequency, namely the exciting frequency
of ground relative to craft, co n is the natural vibration frequency, i.e. the heaving nat-
ural frequency of craft, and M represents magnification factor, i.e. the ratio of heave
displacement to ground amplitude.
In Fig. 2.25, it can be seen that the higher the damping coefficient, the lower the
magnification factor in the case where the tuning factor is close to 1. In the case of
lower tuning factor, then higher damping coefficients give higher magnification factor.
This means that the vertical motion of craft with a large damping coefficient will be
violent in the case where the craft run in short waves or on a rough ground surface.
Therefore the damping coefficient is very important for decreasing the vertical vibra-
tion of craft.
Before discussing these problems, we prefer to introduce three typical flow modes
for craft in heaving motion as shown in Fig. 2.26: (a) shows equilibrium flow, i.e. sta-
tic hovering mode of craft; (b) shows the flow underfed, i.e. the instantaneous skirt
clearance will be smaller than the equilibrium skirt clearance as the craft drops down,
consequently the jet flow cannot seal the cushion air causing some air leakage from
the cushion; (c) shows the flow overfed, i.e. the instantaneous skirt clearance will be
larger than the equilibrium skirt clearance as the craft lifts up, consequently more air
flow will get into the cushion to fill up the air cavity. These three modes appear alter-
nately as the craft heaves.

Calculation method for heaving stability derivatives and damping
coefficients

First of all, the profile of the skirt is assumed unchangeable in the case of deriving
the air cushion stability derivatives and damping coefficient. This assumption is

(=0.2

co e/co,,

Fig. 2.25 Frequency response for heave motion with one degree of freedom.