A high-speed craft moving in waves may transit through several regimes that have 
different hydrodynamic flow characteristics. For example, as the craft moves away from the 
crest of wave, the flow may be characterized by unsteady-state planing until the craft collides 
with the oncoming wave crest and enters another regime in which impact forces are important. 
After the impact, the craft may enter still another regime in which it is planing but in which 
buoyancy forces are rather significant. 
The most promising approach to a method that would incorporate all three types of flow 
conditions into a general formulation would seem to be a modified strip theory. The 
mathematical justification for this approach is not rigorous; however, there is sufficient 
precedent to expect promising results. For example, impact loads on landing seaplanes can 
be estimated reasonably well using a strip theory incorporating the Wagner two-dimensional 
(2-D), expanding-wedge theory,! and Chuang? has provided a strip method for determining loads 
on an impacting prismatic form that agrees extremely well with experimental results. 
More recently, Martin? has developed a linear strip theory for estimating motions of a 
planing craft at high speed, which shows good agreement with experimental results. A 
nonlinear model of the equations of motion would be expected to provide, in addition to the 
motions, reasonable estimates of the vertical accelerations which are an important consideration 
in designing a planing craft. 
TWO-DIMENSIONAL HYDRODYNAMIC FORCE 
Implicit with any strip method is the need to define the 2-D hydrodynamic force acting 
on an arbitrary cross section of the body. The 2-D flow problem is not simple; however, it 
lends itself to an empirical approach, using a combination of techniques used in hydrodynamic 
impact and low-aspect-ratio theories. 
The typical cross section of a hard-chine, V-shaped prismatic body such as that being 
considered here is shown in Figure 2. Figure 2 actually illustrates two different idealized- 
flow conditions, assumed to represent the crossflow during unsteady planing, depending upon 
whether the flow separates from the chine (Figure 2a) or not (Figure 2b). Nonwetted-chine 
flow conditions are typical of the sections near the leading edge of the wetted length of the 
craft. Wetted-chine flow conditions are more typical of sections near the stern, except 
possibly in the most extreme motion and wave conditions. Some sections between leading 
edge and stern may alternate between flow conditions as the wetted length changes with the 
motions. 
*A complete listing of references is given on page 33. 
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