3.2.2.1 The ability of a ship to withstand the
combined effects of beam wind and rolling should be demonstrated for
each standard condition of loading, with reference to the figure as follows:
-
.1 the ship is subjected to a steady wind pressure
acting perpendicular to the ship's centreline which results in a steady
wind heeling level (1w1).
-
.2 from the resultant angle of equilibrium (θo), the ship is assumed to roll owing to wave action to an angle
of roll (θ 1) to windward. Attention should be paid
to the effect of steady wind so that excessive resultant angles of
heel are avoided;footnote
-
.3 the ship is then subjected to a gust wind pressure
which results in a gust wind heeling lever (1w2);
-
.4 under these circumstances, area “b”
should be equal to or greater than area “a”;
-
.5 free surface effects (section
3.3) should be accounted for in the standard conditions of
loading as set out in section 3.5;
The angles in the above figure are
defined as follows:
|
θ1
|
= |
angle
of roll to windward due to wave action |
|
θ2
|
= |
angle
of downflooding (θf) or 50° or θc,
whichever is less,
|
- where:
|
θf
|
= |
angle
of heel at which openings in the hull, superstructures or deckhouses
which cannot be closed weathertight immerse. In applying this criterion,
small openings through which progressive flooding cannot take place
need not be considered as open. |
|
θc
|
= |
angle
of second intercept between wind heeling lever lw2 and
GZ curves.
|
Figure 1 Severe wind and rolling
3.2.2.2 The wind heeling levers lw1and
lw2 referred to in 3.2.2.1.1 and 3.2.2.1.3 are constant values at all angles of inclination and should
be calculated as follows:
where:
|
P |
= |
wind pressure
of 504 Pa. The value of P used for ships in restricted service may
be reduced subject to the approval of the Administration; |
|
A |
= |
projected lateral
area of the portion of the ship and deck cargo above the waterline
(m2);
|
|
Z |
= |
vertical distance
from the centre of A to the centre of the underwater lateral area
or approximately to a point at one half the mean draught (m); |
|
Δ |
= |
displacement
(t) |
|
g |
= |
gravitational
acceleration of 9.81 m/s2
|
3.2.2.3 The angle of roll (θ 1)footnote referred to in 3.2.2.1.2 should
be calculated as follows:
where:
|
X1
|
= |
factor
as shown in table 1
|
|
X2
|
= |
factor
as shown in table 2
|
|
k |
= |
factor as follows: |
|
k |
= |
1.0 for round-bilged
ship having no bilge or bar keels |
|
k |
= |
0.7 for a ship
having sharp bilges |
|
k |
= |
as shown in table 3 for a ship having bilge keels,
a bar keel or both
|
with:
|
OG |
= |
distance between
the centre of gravity and the waterline (m) (+ if centre of gravity
is above the waterline, - if it is below) |
|
d |
= |
mean moulded draught
of the ship (m) |
Table 1 Values of factor
X1
| B/d
|
X1
|
| ≤ 2.4
|
1.0
|
| 2.5
|
0.98
|
| 2.6
|
0.96
|
| 2.7
|
0.95
|
| 2.8
|
0.93
|
| 2.9
|
0.91
|
| 3.0
|
0.90
|
| 3.1
|
0.88
|
| 3.2
|
0.86
|
| 3.3
|
0.84
|
| 3.4
|
0.82
|
| ≥ 3.5
|
0.80
|
Table 2 Values of factor
X2
| CB
|
X2
|
| ≤ 0.45
|
0.75
|
| 0.50
|
0.82
|
| 0.55
|
0.89
|
| 0.60
|
0.95
|
| 0.65
|
0.97
|
| ≥ 0.70
|
1.0
|
Table 3 Values of factor
k
|
k
|
| 0
|
1.0
|
| 1.0
|
0.98
|
| 1.5
|
0.95
|
| 2.0
|
0.88
|
| 2.5
|
0.79
|
| 3.0
|
0.74
|
| 3.5
|
0.72
|
| ≥ 4.0
|
0.70
|
Table 4 Values of factor
s
| T
|
s
|
| ≤ 6
|
0.100
|
| 7
|
0.098
|
| 8
|
0.093
|
| 12
|
0.065
|
| 14
|
0.053
|
| 16
|
0.044
|
| 18
|
0.038
|
| ≥ 20
|
0.035
|
(Intermediate values in tables 1-4 should be obtained by
linear interpolation.)
where:
|
C |
= |
|
The symbols in the above tables and formula for the rolling
period are defined as follows:
|
L |
= |
length of the
ship at waterline (m) |
|
B |
= |
moulded breadth
of the ship (m) |
|
d |
= |
mean moulded draught
of the ship (m) |
|
Ak
|
= |
total
overall area of bilge keels, or area of the lateral projection of
the bar keel, or sum of these areas (m2)
|
|
GM |
= |
metacentric height
corrected for free surface effect (m). |