Masthead28_Dec2013 H.pub - page 22

The Masthead
By Bruce Hays, Principal Naval Architect, DRS Technologies, Inc.
Finding the Height and Trim
Angle of the Pour Line for
the Ballast in a Keel
Dec. 2013 Page 22
T
his article is intended to help you solve the problem of how
to specify a pour line of the ballast in a keel. It assumes
that you have the keel surface(s) modeled in Rhino and you
know the target ballast weight, target longitudinal center of
gravity (LCG), and the density of the ballast material. The chal-
lenge is to find the planar intersection (height and trim angle)
with the keel surface(s) that represents the top of the ballast.
The process assumes that the keel is symmetric port and star-
board.
To solve this problem, we approach it as a standard “free float”
hydrostatics calculation, but with the keel “floating” in the bal-
last material (we’ll assume lead for this example). At first
glance, it would seem very easy; simply set the fluid density
appropriately, and then enter the desired weight and LCG.
However, we don’t know the VCG, which will affect the final
equilibrium and flotation plane. If you run the calculation with
the same weight and LCG, but varying VCG’s, you will get
different solutions. What is different about this analysis
than a standard hydrostatics calculation is that we need
the solution where not only the LCB and LCG are aligned,
but also where the VCG and VCB are coincident. Another
way to state this is that the volumetric centroid of the bal-
last is also the center of gravity (which is not the case when
analyzing a boat hull).
Fig. 1
Fig. 2
Fig. 3
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