3.3.1 For all loading conditions, the initial
metacentric height and the righting lever curve should be corrected
for the effect of free surfaces of liquids in tanks.
3.3.2 Free surface effects should be considered
whenever the filling level in a tank is less than 98% of full condition.
Free surface effects need not be considered where a tank is nominally
full, i.e. filling level is 98% or above. Free surface effects for
small tanks may be ignored under condition specified in 3.3.9.
3.3.3 Tanks which are taken into consideration
when determining the free surface correction may be in one of two
categories:
-
.1 Tanks with filling levels fixed (e.g. liquid
cargo, water ballast). The free surface correction should be defined
for the actual filling level to be used in each tank.
-
.2 Tanks with filling levels variable (e.g. consumable
liquids such as fuel oil, diesel oil and fresh water, and also liquid
cargo and water ballast during liquid transfer operations). Except
as permitted in 3.3.5 and 3.3.6, the free surface correction should
be the maximum value attainable between the filling limits envisaged
for each tank, consistent with any operating instructions.
3.3.4 In calculating the free surface effects
in tanks containing consumable liquids, it should be assumed that
for each type of liquid at least one transverse pair or a single centreline
tank has a free surface and the tank or combination of tanks taken
into account should be those where the effect of free surfaces is
the greatest.
3.3.5 Where water ballast tanks, including anti-rolling
tanks and anti-heeling tanks, are to be filled or discharged during
the course of a voyage, the free surface effects should be calculated
to take account of the most onerous transitory stage relating to such
operations.
3.3.6 For ships engaged in liquid transfer operations,
the free surface corrections at any stage of the liquid transfer operations
may be determined in accordance with the filling level in each tank
at that stage of the transfer operation.
3.3.7 The corrections to the initial metacentric
height and to the righting lever curve should be addressed separately
as follows.
-
3.3.7.1 In determining the correction to initial
metacentric height, the transverse moments of inertia of the tanks
should be calculated at 0° angle of heel according to the categories
indicated in 3.3.3.
-
3.3.7.2 The righting lever curve may be corrected
by any of the following methods subject to the agreement of the Administration:
-
.1 Correction based on the actual moment of fluid
transfer for each angle of heel calculated.
-
.2 Correction based on the moment of inertia,
calculated at 0° angle of heel, modified at each angle of heel
calculated.
-
.3 Correction based on the summation of Mfsvalues
for all tanks taken into consideration (see 3.3.8).
With the exception of .3 above, corrections may be calculated
according to the categories indicated in 3.3.3.
Whichever
method is selected for correcting the righting lever curve, only that
method should be presented in the ship's stability booklet. However,
where an alternative method is described for use in manually calculated
loading conditions, an explanation of the differences which may be
found in the results, as well as an example correction for each alternative,
should be included.
3.3.8 The values of M
fs for
each tank may be derived from the formula:
where:
|
M
fs
|
= |
is the
free surface moment at any inclination, in m.tonnes |
|
v
|
= |
is the tank total capacity,
in m3
|
|
b
|
= |
is the tank maximum
breadth, in m |
|
ρ |
= |
is the mass density of liquid
in the tank, in tonnes/m3
|
|
δ |
= |
is equal to v/blh (the tank
block coefficient) |
|
h
|
= |
is the tank maximum
height, in m |
|
l
|
= |
is the tank
maximum length, in m |
|
k
|
= |
is the dimensionless coefficient to be determined from table 3.3.8 according to the ratio b/h. The
intermediate values are determined by interpolation. |
3.3.9 Small tanks which satisfy the following
condition using the values of "k" corresponding to an angle of inclination
of 30°, need not be included in the correction:
where:
|
Δmin
|
= |
is the minimum
ship displacement calculated at dmin, in tonnes
|
|
dmin
|
= |
is the minimum mean
service draught of the ship without cargo, with 10% stores and minimum
water ballast, if required, in m. |
3.3.10 The usual remainder of liquids in empty
tanks need not be taken into account in calculating the corrections,
provided that the total of such residual liquids does not constitute
a significant free surface effect.
Table 3.3.8 Values for coefficient
"k" for calculating free surface corrections
|
|
|
| where
|
where
|
|
|
5
|
10
|
15
|
20
|
30
|
40
|
45
|
50
|
60
|
70
|
75
|
80
|
85
|
|
| b/h
|
b/h
|
| 20
|
.11
|
.12
|
.12
|
.12
|
.11
|
.10
|
.09
|
.09
|
.09
|
.05
|
.04
|
.03
|
.02
|
20
|
| 10
|
.07
|
.11
|
.12
|
.12
|
.11
|
.10
|
.10
|
.09
|
.07
|
.05
|
.04
|
.03
|
.02
|
10
|
| 5
|
.04
|
.07
|
.10
|
.11
|
.11
|
.11
|
.10
|
.10
|
.08
|
.07
|
.06
|
.05
|
.04
|
5
|
| 3
|
.02
|
.04
|
.07
|
.09
|
.11
|
.11
|
.11
|
.10
|
.09
|
.08
|
.07
|
.06
|
.05
|
3
|
| 2
|
.01
|
.03
|
.04
|
.06
|
.09
|
.11
|
.11
|
.11
|
.10
|
.09
|
.09
|
.08
|
.07
|
2
|
| 1.5
|
.01
|
.02
|
.03
|
.05
|
.07
|
.10
|
.11
|
.11
|
.11
|
.11
|
.10
|
.10
|
.09
|
1.5
|
| 1
|
.01
|
.01
|
.02
|
.03
|
.05
|
.07
|
.09
|
.10
|
.12
|
.13
|
.13
|
.13
|
.13
|
1
|
| .75
|
.01
|
.01
|
.01
|
.02
|
.02
|
.04
|
.04
|
.05
|
.09
|
.16
|
.18
|
.21
|
.16
|
.75
|
| 0.5
|
.00
|
.01
|
.01
|
.02
|
.02
|
.04
|
.04
|
.05
|
.09
|
.16
|
.18
|
.21
|
.23
|
0.5
|
| 0.3
|
.00
|
.00
|
.01
|
.01
|
.01
|
.02
|
.03
|
.03
|
.05
|
.11
|
.19
|
.27
|
.34
|
0.3
|
| 0.2
|
.00
|
.00
|
.00
|
.01
|
.01
|
.01
|
.02
|
.02
|
.04
|
.07
|
.13
|
.27
|
.45
|
0.2
|
| 0.1
|
.00
|
.00
|
.00
|
.00
|
.00
|
.01
|
.01
|
.01
|
.02
|
.04
|
.06
|
.14
|
.53
|
0.1
|