Examination of the intact stability and the seakeeping behaviour

3.6 Free surface correction
3.6 Free surface correction
When tanks are partly lled in a loading condition, the free surface of the containing uid
inuences the stability of the ship. The liquid's center of gravity moves when the ship heels.
This leads to an apparent reduction of the GM. The corrected GM is usually determined by
the formula 3.1 shown below
GM corrected = GM solid − ∑ i
ρ liquid i · I tank i
△
(3.1)
for each partly lled tank i with the particular density of the liquid in tank ρ liquid , the particular
moment of inertia of the free surface I tank and the displacement △ belonging to the particular
loading condition .
For the quasi-static intact stability analysis, this procedure is permissible. But for the highly
nonlinear motions of a ship in seaways the correction is inaccurate, because the damping eect
of the sloshing uid in the tank is not considered. For example this eect is used intentionally
in roll damping tanks.
For the seakeeping calculations it has been gured out, that both eects (roll damping due to
sloshing and stability reduction due to the free surface) approximately compensate each other.
Therefore the seakeeping calculations in E4 are always performed with an uncorrected GM solid .
3.7 Intact stability
The intact stability is calculated according to the intact stability code of the IMO [4]. It is
performed to determine the limiting intact stability criterion in the examined ballast arrival
loading condition. The following six criteria are considered:
1. The initial metacentric height GM 0 (including free surfaces) shall not be less than 0.15 m.
(named in the following: Initial GM is 0.15 m)
2. The righting lever GZ shall be at least 0.2 m at an angle of heel equal to or greater than
30 ◦ . (named in the following: GZ is 0.2 at 30 ◦ )
3. The maximum righting lever shall occur at an angle of heel not less than 25 ◦ . (named in
the following: Max. GZ at 25 ◦ )
4. The area under the GZ curve shall not be less than 0.055 metre − radians up to 30 ◦ angle
of heel. (named in the following: Area (0, 30) = 0.055 m · rad)
5. The area under the GZ curve shall not be less than0.09 metre − radians up to 40 ◦ angle
of heel. (named in the following: Area (0, 40) = 0.090 m · rad)
6. The area under the GZ curve between the angles of heel of 30 ◦ and 40 ◦ shall not be less
than 0.03 metre − radians. (named in the following: Area (30, 40) = 0.030 m · rad)
3.8 Cross-curves of stability
Furthermore the cross-curves of stability of the hull for xed and free trim are calculated. The
resulting curves in E4 are compared to the curves derived from the stability booklet. The better
the curves match, the better the E4 calculation model matches the calculating model of the
shipyard. Thereby its assured, that the result of the calculations are applicable to the realized
vessel.
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