Page 18 - WestlawnMasthead23_Sept12.pub

The Masthead
Planing Craft Analysis: Static vs. Dynamic Trim
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Continued
Sept. 2012 Page 18
tal “Offset” between their corresponding directions.
The craft’s weight is usually assumed to be acting along the
Vertical direction, or “-z” in Rhino World coordinates,
whereas the Buoyancy force is considered to be acting along
the “+z” direction.
Figure 2 shows the boat’s final attitude (i.e., hull orientation)
after performing a Free-Float hydrostatic analysis of the
case shown in Figure 1.
As can be seen in Figure 2, a new “Waterplane” was found
(“
wl-1”) that represents the craft’s actual attitude for the
given weight value and CG position. This is the “Design” wa-
terline (“wl-1”).
Thus, it can be said that, with reference to the previous
situation (Figure 1), the hull is now trimming by the stern by
the calculated “Trim” angle; and, since the hull is considered
to be “at rest,” this is also called a “Static Trim” angle.
Remember that, as the boat is rotated and moved to find an
equilibrium, the CG also rotates and moves with the craft,
since it always remains fixed to the hull geometry. For this
kind of hydrostatic analysis, it is always assumed that the
CG remains fixed to the hull geometry. On the other hand,
we cannot assume the same behavior with the CB, since the
CB corresponds to the centroid of the wetted volume; be-
cause the shape of this volume changes at each iteration in
the analysis, the CB position will change.
So, in this condition (Figure 2), we can see that the net force
acting on the craft is zero (i.e., Weight = Displacement) and
the net moment is also zero (the horizontal offset between
these forces is zero). The boat is in “Static” equilibrium.
Note that for this simplified analysis, it is assumed that the
CG lies in the Vertical center plane of the craft (usually the “x
-
z” plane in Rhino World coordinates), and that the hull
shape is port-starboard symmetrical. To find the final vessel
attitude the hull was rotated about its transverse axis
(
trimmed) and moved vertically, until a new wetted volume
was found, such that the Buoyancy force it generates equals
the boat’s Weight, and its CB is aligned vertically with the
CG. Orca3D will compute the resultant static heel angle as
well if the hull is not symmetric or if the transverse location
of the CG is not in the centerplane.
Another simplification for the sake of this discussion is
whether the final equilibrium condition of the vessel is
Stable” or not. The requirements for the “Static” equilibrium
of the craft discussed so far are necessary, but not suffi-
cient, to guarantee a “Stable” equilibrium. Once a valid
Static” equilibrium condition is achieved, the next question
to ask is what would happen if we apply a small perturba-
tion (e.g., a very small angular displacement) to the craft in
the “Static” equilibrium configuration found. Will it return to
the “pre-perturbation” condition, or it will adopt a new equi-
librium attitude? If it will return, it is a stable equilibrium. An
example of an
unstable
equilibrium is a cone, balanced
point-down on a table. When perfectly balanced, it is in equi-
librium, but if disturbed, it will not return to that equilibrium.
Reference 3 provides further explanation of this subject, in
the context of hydrostatics.
Dynamic Trim
When performing a Resistance calculation on a planing hull
with the aid of the Planing Analysis module available in Or-
ca3D, the “Trim” angle that is reported, also called
Dynamic or Running Trim Angle,” comes from a similar
static equilibrium analysis, but for a different kind of prob-
lem.
We say “similar,” because one of the tasks that the algo-
rithms within the Planing Analysis module has to perform is,
again, to find a balance of forces and moments; but the dif-
ference here comes from the very nature and origin of the
forces to be considered acting over the craft.
On a planing craft, considering that is running on calm wa-
ters at a steady speed, apart from its Weight, three (3) new
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3
The default coordinate system is positive X aft, positive Y to star-
board, and positive Z up. However, Orca3D can accommodate any
right-hand rule coordinate system that the user chooses.
4
Remember that Orca3D’s Weight & Cost module provides an excel-
lent tool for weight and CG estimation on your 3D model.
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