Basics of Fluid Mechanics, 2014a

4.6. BUOYANCY AND STABILITY 135
A new point can be defined as G c . This point is the intersection of the center line with
the vertical line from G ′ .
GG c = GG′
sin β
(4.169)
The distance that was used before GM is replaced by the criterion for stability by G c M
and is expressed as
G c M = gρ A I xxA
ρ s V body
− BG − 1
m total
I xxb
V b
(4.170)
If there are more than one tank partially filled with liquid, the general formula is
G c M = gρ A I xxA
ρ s V body
− BG − 1
m total
n ∑
i=1
I xxbi
V bi
(4.171)
One way to reduce the effect of
the moving mass center due to liquid
is done by substituting a single
tank with several tanks. The moment
of inertial of the combine two
h
T d
tanks is smaller than the moment of
G
inertial of a single tank. Increasing
the number of tanks reduces the moment
of inertia. The engineer could
design the tanks in such a way that Fig. -4.45. Measurement of GM of floating body.
the moment of inertia is operationally
changed. This control of the stability, GM, can be achieved by having some tanks
spanning across the entire body with tanks spanning on parts of the body. Movement
of the liquid (mostly the fuel and water) provides way to control the stability, GM, of
the ship.
4.6.1.2 Metacentric Height, GM, Measurement
The metacentric height can be measured by finding the change in the angle when a
weight is moved on the floating body.
Moving the weight, T a distance, d then the moment created is
This moment is balanced by
M weight = Td (4.172)
M righting = W total GM new θ (4.173)
Where, W total , is the total weight of the floating body including measuring weight.
The angle, θ, is measured as the difference in the orientation of the floating body. The