1 TECHNISCHE UNIVERSITET Laboratorium voor Scheepshydromechanica Archlef Mekehveg 2, 2828 CD Delft 1aIO16.786873- Fax 018-781838.
A SIMPLE MODEL OF DYNAMIC HEELING OF A SHIP
WITH WATER ON DECK
Jerzy Matusiak, Associate Professor Helsinki University of Technology
Otakaari 4, 02150 Espoo, Finland
Dynamic behaviour of a damaged vessel is a very complex subject. Time simulation
of ship dynamics, which takes into account coupled motions, flooding and
environmental conditions, is certainly a proper theoretical approach to evaluate the risk of capsizing. However at present, the time simulation technique may be too laborious and difficult to conduct in the standard process of stability evaluation. Amore pragmatic approach, which is known in the intact stability evaluation as weather criterion, can parhaps be used instead_ This criterion (Code on Intact
Stability, 1993) is based on the concept of dynamic stability (Rahola, 1939). In
this criterion the areas bounded by a static stability curve and a wind heeling
moment lever are investigated. The general idea is that the work done by external loading (heeling moment) can not be higher than the work done by a heeling ship
exposed to this load (Fig. 1). The allowance for ship rolling is included. The
concept of dynamic stability makes it possible to investigate ship heeling and the
risk of ship loss in a realistic sea environment.
The same deterministic approach can be applied in the case of a damaged
ship. However the effect of flooding should be properly included in this analysis.
In the following a simple dynamic heel model of a ship with water on deck is
proposed. This model can easily be incorporated into the standard stability
analyses. The proposed method is illustrated by an analysis of maximum heel of a ro-ro type vessel with water on deck.57,3
Pig. :The' effect:of gusty wind cindroll the..40417:40.
:A' heeled vessel; Avitli:Vv Volume of water on the car-deck thatiS':l30 brciad and Lb '1 F;
iofig; preented: in .Fig: 2 (Matusiak, 1995). We .assurtie that flooded water
In other words, the free surface -offloOded,water AS'
MOrealierlhertia forces and sloshing:'.ofithe flooded:4a:ter aft:.
_
iSr,Pg4T4.ecl. These aSSilititions may be justified bY0i-e effeCt: of CaraiO
loCited OddeCk.-fliairing made these assumption's, WeTcan .eyaluate,the cptitero
triyity of.tfie flOOded4ater.
, =V
(13D
V 2
V2 Sy/tan (I)) cos 4) .
3
Pv = p g
Fig.2 Water on the car deck
In particular we are interested in lever rv of the heeling moment Mv. This level is
related to heel, deck breadth and flooded water volume as follows:
rv =3112
1-, Sy/tan 4)
2 3
where the area of a triangular cross section of the flooded water volume is Sv = = tan (1).
Flooded water causes the heeling moment
Mv = p g Vv (132D 2 Sv/tan4))cos 4) .
Dividing expression (8) by the bouyancy force we obtain the static lever of this
heeling moment
This in turn affects the stability curve as follows
h'(4)) = h(4)) iv (4)), (11)
Where h(4)) is the static righting lever with flooded water regarded as rigid cargo on the car deck and h'(4)) is the stability curve that includes the effect of water motion.
Dynamic stability analysis will be illustrated using as an example ro-ro trpe vessel having ,displacement volume V = 11000 m3. The open car deck is 25 m
broad and 120 m long. We assume that the volume of flooded water is 725 m3, ..:which is only 58% of the maximum static balance value. Static equilibrium is given
by the heel angle (Os= 199 (Fig. 3).
h[m]
-
[in],Fig. 3 Static lever of the righting moment (h- original, h after water flooding On. the car deck). Flooded water volume is _72.5 m3.
Next we assume that the ship with .water
on the car deck is rolling with an
amplitude of OA.= 50. At the instant Oh 7 (1)s-- = 140, the ship is hit by a gust.The heeling moment due to the gust is Msw = 24 MNrn. This value is
representative for a car and passenger ferry subjected to side wind of a speed Vw =25 rn/s. In order to include the effect of the .flooded car deck we take the , dynamic lever values that include the effect of flooding., That is, we calculate the
dynamic lever function for the damaged conditionas
4) TO
e'(4) =I
h'() d4= = h(4)) cid? lv(0) d4),0
iyhere Iv() His given by formula (9). The dynamic lever curve for the damaged
-25 0,06 0,04 0,02 of
ID
-0,1 e' [m rad]--
[m rad] fl)h (ris0 0
! 5 25 53,7IC
50 [deg]Fig. 4 Ship with flooded car deck capsizes by the combined action of rolling
motion and gust. The volume °Blooded water V, = 725 m3.
The work done by the gust when heeling the vessel (dashed line on the Fig. 4)
exceeds the work done by ship righting moment (solid line). This means that the
ship is unable to withstand the gust loading and capsizes. If the ship was not
rolling, it would withstand the gust loading. Steady wind would not cause capsize
either.
This simple analysis of the dynamic heel of the ship with flooded deck
indicates that stability of the vessel is strongly dependent on the volume of flooded water and on the environmental conditions. Static analysis will underestimate the
risk of ship capsizing. The concept of a dynamic lever is very useful when
evaluating dynamic heel of the ship with water on deck. This method can easily be applied to evaluate the stability of the vessel in the damaged conditions without the need of a time simulation. The method can be used also to evaluate the optimum division of the car decks. The drawback of the method is that the wave action isrepresented by the roll motion amplitude that has to be given. References
Code on intact stability for all types of ships covered by IMO instruments,
Assembly Resolution A.749, 1993.
Matusiak, J. Ship bouyancy and stability, Helsinki 1995, Otatieto Oy 557. Textbook in Finnish.
pla, J. The jUdgini,of the,stability of Ships and the determination of the minimum amount ofstability, Heltinki 1939, Yhteitkirjapaino
