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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