Survivability of Damaged Ro-Ro Passenger Vessels
B o r - C h a u Chang, T U Hamburg-Harbuig^Peter Blume, Hamburg Ship Model Basin^
1. Introduction
Concerns for the safety and vulnerability of ro-ro ships have been expressed constantly i n the past. After several disasters with ro-ro passenger vessels, there has been strong pressure for increasing the safety level of this ship type, resulting in a new SOLAS-Resolution SOLAS and requirements accepted at the Stockholm Conference (known as the S T O C K H O L M R E G I O N A L A G R E E M E N T ) , IMO (1996). The latter demands that a vessel satisfies SOLAS'90 criteria i n the presence of a given height of water on the vehicle deck. A n alternative has been allowed also: to perform model tests to detect whether the damaged ship will capsize i n certain seaways. The experiments have to be performed i n accordance with the Model Test Method required by IMO. Existing ro-ro passenger ships shall comply with the provisions of the new agreement from a date between April 1, 1997 and October 1, 2002, depending on the present standards of safety of the ship.
Ships which fail to satisfy the Stockholm Regional Agreement have to be modified for further operating. To this end, above all the vehicle deck arrangement will be considered; however, the effect of various deck arrangements is still uncertain. Therefore the present research is intended to show such influences i n model experiments and to validate a motion simulation method for testing the survival conditions of damaged ships in waves. After validations by comparisons with model tests the numerical simulation model shall be used for parametric investigations.
2. Method of Simulation
The simulation of ship motions i n irregular seaways is based on combining the method developed by Kröger (1986a,h) for intact ships with the method of Petey (1986), which deals with the simulation of liquid flow in ship compartments and on deck. The ship is considered as a six-degree-of-freedom system travelling at a given mean angle relative to the dominant direction of a stationary seaway. The seaway is simulated as a superposition of a large number of component waves having random frequency, amplitude, direction and phase angle. The random quantities are computed from a given sea spectrum. For the heave, pitch, sway, and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonhnear motion equations coupled with the other four degrees of freedom. Thus the four first mentioned motions have been treated linearly, including hydrostatic and hydrodynamic forces. Both the wave exciting moment and the roll moment induced by the sway and yaw motions of the ship are determined by response amplitude operators. The following nonlinear motion equation is used for the determination of rolling:
<P = {-Ma-m{g~'()hs-I^^[(é + 6<p^)&m<p~{'^ + ^tp^)cosip] (1) +Myjind + -h Msy + M^aves]/{Ixx - Lxz{lp sinyj + 9 COS ( f ) }
where a dot designates time derivatives, (fyOyiJj = roll, pitch and yaw angle
m = mass of ship including the water on the vehicle deck and compartments gX = gravitational acceleration and heaving acceleration at the c.o.g.
hs = righting arm in an "effective" longitudinal wave
^Lammersieth 90, D-22305 Hamburg, Germany; email: changOschifFbau.uni-hamburg d400 de ^Bramfelder Str. 164, D-22305 Hamburg, Germany
Md = nonlinear damping moment following Blume (1979). The effect of bilge keels is taken into account following Gadd (1964) and Martin (1958)
Mwind = moment of wind, according to Blendermann (1986)
Med = moment due to water motion on the vehicle deck and in compartments
Msy = moment due to sway and yaw motions, using response amplitude operators determined by means of the strip method
Mr^aves = moment due to waves, using response amplitude operators determined by means of strip method
7^^ = moment of inertia about longitudinal axis through the centre of gravity of the ship, including added inertia due to water on the vehicle deck and compartments and outside water
Ja;2 = product of inertia relating to the centre of gravity of the ship
For computing righting arms hs in seaways, Grim's effective wave concept, Grim (1961), in the form modified by Söding (1982) is used. The height Z of the actual water contour along the ship's centre line plane is approximated i n the form
Z{x, t) = a{t) + b{t)x + c{t) COS{2TTX/XE) (2) in the region of ship length using the method of the least squares of errors. The length
between perpendiculars Lpp is used as length of the effective wave A^;. Grim showed that the response amplitude operators between regular waves and the quantities a{t),b{t),c{t) in (2) can be computed easily Using these transfer functions together with the heave and pitch transfer functions, the mean ship immersion, its t r i m and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle.
I n the simulations, time is advanced in small increments. The rate of inflow and outflow of water through the openings is estimated from the motion of the internal and the external water surface relative to the openings at each time step, Söding (1982). The variations of the mass and moment of inertia of the ship due to the inflow and outflow are considered. The forces and moments due to the interior fluid motion in partly flooded rooms and on the vehicle deck also are determined and added to the external forces and moments due to wave excitation, wind etc. Two different methods of computing the internal water flow are used, depending on the height of flood water: for low flll depth compared to the tank width, the velocity vector of fluid particles is almost parallel to the tank bottom. The velocity component perpendicular to the tank bottom is neglected, and the depth-averaged water velocity is computed from the so-called shallow-water equations in two dimensions for an accelerated reference system, Petey
(1986). Glimm's method (a random choice method), Petey (1986), Dillingham (1981), is used to obtain the solution, because this method is capable of dealing with the frequently occurring cases of hydraulic jumps and of a partially dry bottom. However, this method gives correct results only for small heel (ca.< 25°). Therefore, if the average water fill depths are larger than ca. 15% of the tank width, or'if the heel angle exceeds 25°, another method is used: The free surface of the liquid is assumed oblique but plane, since the greatest natural period of the fluid oscillation is much smaller than the dominant period of the ship motions in this case. A simple equation of motion of the liquid free surface is thus derived from Lagrange's equation, Söding
(1982), which can be solved in the time domain using the familiar Runge-Kutta integration scheme.
3. Model Tests
A series of model tests regarding the survivability of damaged ro-ro ships was carried out in accordance with the "Model Test Method" required by IMO at the Hamburg Ship Model Basin
(HSVA). For three ships, each with different subdivisions on the ro-ro deck, damage positions and drafts, the limit between safe and unsafe is determined by testing the models with different KG values. At present the results for one ship are available.
A model suitable for such tests must have a thin shell and thin interior walls in order to attain the correct permeability. Therefore the models are built from GRP. The undamaged part of the model must be fully watertight, avoiding leakage in case of capsize. Thus the models are much more complicated than those for standard propulsion or seakeeping tests.
The first ship (Ship A ) investigated in the project is a ro-ro ferry with the following main dimensions:
Length over all 161.00 m Length between perpendiculars 144.00 m Breadth 29.00 ni Design draught 6.05 m lieight to vehicle deck at midship 8.10 m
The ship was designed to satisfy the SOLAS 74 requirements. Two damage cases called D l H - 1 2 and D9-I-10 (Figures 1 and 2) have been investigated. Case Dll-f-12 represents the worst damage case defined for compliance with paragraph 2.3.2 of SOLAS regulation II-1/8 (SOLAS 90). According to the "Model Test Method", the midship damage case D9-f 10 is also required for testing, because the damage in case D l l + 1 2 is outside of the range ± 1 0 % Lpp fi-om the midship section. Figures 1 and 2 show that compartments below the main deck were fiooded through an opening on port side. The statical fiooding resulted in a small heel ( < 4°) to port side. The damage opening had a length of 7.32 m (3m + 0.03 • LWL) and ranged vertically from the bottom up to 16 m above the base. The depth of penetration was 5.8 m {BWL/^)- Three drafts of the intact ship (5.9 m, 6.2 m, and 6.4 m) and three vehicle deck subdivisions were investigated:
Version A The only obstruction to the water flow on the vehicle deck is a longitudinal trunk extending from frame 36 to frame 163 with a gap between frame 122 and 124 (1.5 m) as shown in Figure 3a (orginal construction).
Version E Centre trunk as in Version A and two full transverse bulkheads respectively at frames 40 and 137 (Figure 3b).
Version F Two transverse bulkheads as i n Version E and a longitudinal bulkhead with 7.82 m distance from the centre line (Figure 3c).
The model was built in a scale 1:30. I t was fltted with two propefiers, rudders and bilge keels. During the tests the model was exposed to long-crested irregular seas in the "dead ship" condition. This means the model was drifting freely without speed ahead more or less parallel to the wave crests, with the opening on the side facing the wave. The measurements were started when the sea state was fully developed at the location of the model, and were generally continued for a time corresponding to 30 minutes in f u l l scale.
The sea states were defined by (a) a JONSWAP spectrum with 7 = 3.3 having a modal period Tp = 8 s, and (b) a Pierson-Moskowitz spectrum with modal period 12 s. The signif-icant wave height Hy^ was 4 m. For each case different KG-values were tested in order to determine the limit between safe and unsafe conditions with respect to capsizing. For each sea state repeated runs with different seaway realizations were performed.
4. Results
Motion simulations were performed for the same conditions as used i n the model tests; however, the duration of each simulation was 50 minutes. The time step of the simulation was 0.2 s for ship motion and 0.02 s for the deck water motion. The statical equilibrium floating
^ ^ ^ 1 f
«83 «114
Figure 1: Damage case D l l + 1 2 Figure 2:Damage case D9+10
Version A 1 1 1 1 '' • • I 1 1 . Version E Version F Figure 3: Variations of vehicle deck subdivision for ship A
1
3000 [s]
Figure 4a; Rolling motions for a capsizing case; draft of intact ship 5.9m, GML = 2.577i, Damage case D l l + 1 2 , sea state 4m/8s
ST 4500 J 4000 e 3500 ^ 3000 E 2500 = 2000 § 1500 S 1000 -2000 2500 500 1000 1500
Figure 4b: water volume on vehicle deck; conditions as i n Figure 4a
3000 limets]
position of the damaged ship was used as initial condition in all simulations.
Figures 4a and 4b show typical time histories of rolling motions and water volume on vehicle deck for a capsizing case. From beginning up to ca. 2200 s the water volume on the vehicle deck and the mean heel angle increase only slowly. When about 12° heeling angle is attained, the heel rises rapidly, and the ship capsizes within a short time. The same was observed during the model tests.
Tables 1 and 2 summarize the results of both model tests and motion simulations, for damage cases D9+10 and D l l + 1 2 , by giving the number A'' of accomplished model tests runs or simulations and the number Nc of runs in which the ship capsized. Comparing the results, a good correlation is found between model tests and simulations. Both methods give very similar metacentric heights in damaged equilibrium condition GMD for the limit between safe and unsafe. These limiting GMD values by observing capsize/survival i n the model tests are shown also i n Table 3. The conclusions obtained from the results are as follows:
1. Smaller initial draft and, thus, larger damage freeboard reduces the necessary stability of a damaged ship to avoid capsizing drastically.
2. Unreasonably large metacentric height is required for the ship built according to SOLAS 74 in its origial state to avoid capsizing.
3. Additional vehicle deck subdivisions increase the capsize resistance considerably. Trans-verse bulkheads were found to be a better alternative than longitudinal subdivisions with respect to the survivability.
4. Our numerical simulation model is capable of predicting, with good engineering accurary, the necessary metacentric height to avoid capsizing. I t shall be used for systematic param-eter variations to identify the paramparam-eters which are more significant for the survivability of damaged vessels.
5. Applications for parametric studies 5.1. Conditions of Simulations
The Ro-Ro ship "Prinsesse Ragnhild" is used for the following parametric investigations by our numerical simulation model. The principal dimensions of the ship are:
Length over all 170.47 m Length between perpendiculars Lpp 148.00 m Breadth 24.00 m Draught 5.82 m Height to car deck at midship 8.00 m Height to car deck at bow flap 8.47 m Height to wheel house top 27.15 m Breadth of bow flap 5.90 m A detailed description of the ship is given i n HANS A (1981).
The compartments below the car deck remain intact. Only the bow flap and forward ramp are assumed to be damaged, allowing water to spill onto the car deck. The lower edge of the opening is 2.65 m above the design load water line. The breadth of the bow flap opening is 5.9 m in ah simulations. The computation of righting arms includes superstructures to wheel house top. Three car deck arrangements were investigated:
(a) The only obstruction to the water flow is a longitudinal trunk extending over 68% of the ship length as shown i n Fig. 5a.
(b) Centre trunk as in (a) and a transverse bulkhead at midship section (Fig. 5b).
^ ^ ^ ^
(a) (b) (C) Figure 5: Variations of veiiicle declc subdivision for ship "Prinsesse Ragnhild"
Table 1: Number N of model tests or simulations and number of them ending with a capsize Ship A, Damage case D9+10
Draft of Damaged Sea state 4m/8s Sea state 4m/12s intact ship ship Test Simulation Test Simulation
T [ m ] GMD [m] N Na N N , iV Nc N
without subdivision on vehicle deck (Version A)
5.9 3.83 2 - 2 - - 2 -3.45 2 - 2 - - 2 -3.26 2 - 2 - - 4 -3.07 1 1 4 - - 4 1 2.87 - - 6 2 - 6 2 2.77 - - 6 2 - 6 5 6.2 4.44 2 - 2 - - 2 -4.09 2 1 4 - - 4 -3.95 1 1 4 1 - 4 1 3.73 1 1 6 4 - 6 2 6.4 4.60 - - 4 - - 4 -4.45 - - 6 5 - 6 3 4.22 2 - 4 4 - 4 4 4.01 1 1 2 2 - 2 2 3.54 1 1 2 2 - 2 2 3.02 1 1 2 2 - 2 2
with a longitudinal bulkhead (Version F)
5.9 2.52 2 - 4 - - 4 -2.14 2 - 4 - - 4 -1.74 2 1 4 - - 4 -1.44 - - 4 2 - 4 3 6.2 2.65 2 - 4 - - 4 -2.30 2 1 4 - - 4 -2.00 - - 6 - - 6 -6.4 2.75 2 - 4 - - 4 -2.58 2 - 4 - - 4 -2.40 2 - 4 - - 4 -2.20 - - 4 - - 4
-with two full transverse bulkheads on vehicle deck (Version E)
5.9 2.06 2 - 4 - - 4 -1.7^ 2 - 4 - - 4 -1.60 1 1 4 1 - 4 4 1.45 - - 4 4 - - -6.2 2.70 2 - 4 - - 4 -2.34 2 - 4 - - 4 -1.98 2 - 4 4 - 4 4 1.88 1 1 4 4 - 4 4 6.4 2.79 2 - 4 - - 4 -2.51 2 - 4 - - 4 -2.34 2 - 4 4 - 4 4 2.17 1 1 4 4 - 4 4
(c) The centre trunk is extended by centre bulkheads until both ends of the deck (watertight connection at the aft end) (Fig. 5c).
The following conditions were investigated:
- Height of the bow flap opening: 0.5 m; 1.0 m; 5.23 m. - Wave conditions (Jonswap spectrum with 7 = 3.3) :
1. Significant wave height i ï i / 3 : 5.5 m; 4.2 m 2. Significant wave period Tg : 9.7 s ; 8.0 s
3. Angle of encounter Jl : 180° (head sea); 135°; 90° (starboard sea); 15°; 0° - Wind: zero wind or 25 m/s from starboard.
- Metacentric height GM: 1.9 m ; 1.3 m - Speed: 15, 9 and 4.5 knots
5.2. Results
Numerous motion simulations for diverse combinations of the parameters were carried out. The simulation duration was 1 hour. The time step of the simulation was 0.5 s.
Tables 4-9 give the following results: minimum roll angle {(p^iin), maximum roll angle
ifmax), average water volume on the car deck {VOLa) and maximum water volume on the car deck (VOLmax) during the simulation (1 hour). The conclusions obtained from comparing the results are as follows:
1. As was expected, the most severe rolling motions occur i n head seas. I n following and quartering seas the rolling angles and the amount of flooding water on the car deck are also considerable, whereas in beam seas the ship takes over only very little water and has maximum roll angles < 5°.
2. Table 5 demonstrates that transverse wind of 25 m/s (Beaufort 9-10) appears hardly important here.
3. Opening heights 1.0 m and 5.23 m have nearly the same effect. For opening height 0.5 m the water volume on the car deck increases somewhat slower i n time.
4. Waves of Ts = 9.7 s cause lighter roll motions, though the wave length closely matches the ship length.
5. Tables 4, 6 and 7 show clearly the effects of ship speed: lower speed is favourable. 6. Comparing Tables 8, 9 with Table 4 shows that the subdivisions of the car deck reduce
the rolling motions extremely.
7. Effects of metacentric height are small.
8. The smaller wave height (4.2 m instead of 5.5 m) reduces the flooding of the deck very considerably.
The simulations show that a Ro-Ro ship with damaged or open bow flap can survive for many hours even i n severe seaways i f i t sails with small speed transverse to the seaway. The ship may survive in this condition even for arbitrary time i f bilge pumps are used.
References
BLENDERMANN, W. (1986), Windkrafte am Scfiiff, report no. 467 Institut für Schiffbau, Hamburg BLUME, R (1979), Experimentelle Bestimmung von Koeffizienten der wirksamen Rollddmpfung und ihre Anwendung zur Abscliatzung extremer Rollwinkel, Schiffstechnik 29, pp. 3-23
DILLINGHAM, J. (1981), Motion Studies of a Vessel with Water on Deck, Marine Technology Vol. 18 No. 1
GADD, G. E. (1964), Bilge Keels and bilge vanes, National Physical Lab., Ship Division, report 64
GRIM, O. (1961), Beitrag zu dem Problem der Sicherfieit des Sctiiffes im Seegang, Schiff und Hafen, No. 6 '
HANS A (1981), Sciiiffbau, Zur Nor-Shipping '81, HANS A, Nr. 8, pp.557-563
IMO (1996), Regional agreement concerning specific stability requirements for ro-ro passenger ships, IMO Giro. Letter No. 1891 dated 29*'' April 1996
KRÖGER, P. (1986a), Rollsimulation von Schijjen im Seegang, Schiffstechnilt 33, pp.187
KRÖGER, P. (1986b), Ship Motion Calculation in a Seaway by means of a Combination of Strip Theory
with Simulation, 3rd International Conference on Stability of Ships and Ocean Vehicles (STAB), Gdansk
MARTIN, M. (1958), Roll damping due to bilge keels, Iowa Inst, of Hydraulic Res. report, Contr. No. 1611 (01)
PETEY, F. (1986), Numerical Calculation of Forces and Moments due to Fluid Motion in Tanks and
Damaged Compartments, STAB 86 Proceedings
SÖDING, H. (1982), Leckstabilitiit im Seegang, report no. 429, Institut für Schiffbau Hamburg SOLAS (1974), International Convention for the Safety of Life at Sea (SOLAS) 1974, including
amend-ments
Table 2: Number N of model tests or simulations and number of them ending with a capsize Nc\ Ship A, Damage case D l l + 1 2
Draft of intact ship T H Damaged ship GMD H Sea st Test N Nc ate 4m/8s Simulation Nc Sea Test Nc state 4m/12s Simulation N N, 5.9 wit 4.45 3.24 2.85 2.50 lout subdi 2 2 5 5 1 vision on veh 4 4 8 8 4 icle deck ( 2 2 5 5 Version A) 4 4 8 8 6.2 3.76 3.35 2.48 2 2 1 1 1 4 4 3 4 4 -4 4 4 4 5.9 1.95 1.62 1.48 with a Ion 2 2 2 1 ptudinal bulk 4 4 3 4 3
head (Ver. iion F) 4 4 4 2 6.2 2.42 2.12 1.82 1.40 2 2 4 4 4 4 4 4 4 -4 4 2 4 4 4 4 5.9 with two fu 2.32 1.94 1.55 1.44 11 transvei 2 2 2 2 se bulkheads 4 4 4 4
on vehicle deck (Version E) 4 4 4 4 6.2 1.67 1.37 1.10 2 2 1 1 4 4 3 4 4 -4 4 4 4 4
Table 3; Limiting GMD values for ship A by observing capsize/survival in the model tests Draft of
intact ship
Original case (Version A) D l l / 1 2 D9/10
with transverse bulkheads (Version E)
D l l / 1 2 D9/10
with a longitudinal bulkhead (Version F) D l l / 1 2 D9/10 GMD = GMD = GMD = GMD = GMD = GMD = 6.4 m 4.2 m - 2.3 m - 2.4 m 6.2 m 3.5 m 4.2 m 1.3 m 2.0 m 1.8 m 2.4 m 5.9 m 2.6 m 3.2 m 1.4 m 1.7 m 1.6m 1.9 m
Table 4: Results of simulations. Speed 15 knots; without wind; subdivision (a) GM Hl/3 Opening + * * Jl = 1 8 0 ° 1 3 5 ° 9 0 ° 1 5 ° 0 ° Vmin [°] - 7 3 . 0 - 4 7 . 8 - 4 . 9 - 2 2 . 7 - 4 5 . 8 5 . 2 3 'pmax [ I roi 7 2 . 1 4 . 5 4 . 4 5.9 2 4 . 7 m VOLa [m^i 2 7 3 8 . 0 1 2 5 2 . 0 4 0 . 7 1 7 7 . 8 9 3 7 . 6 VOLmax [m^] 4 4 0 6 . 0 2 4 5 6 . 0 7 2 . 3 6 3 9 . 3 1 6 2 8 . 0 roi fmin [ J - 6 8 . 0 - 2 9 . 2 - 4 . 9 - 2 1 . 2 - 4 3 . 0 5 . 5 1. fmax [°] 7 0 . 9 2 2 . 2 4 . 4 5.9 2 1 . 5 m m VOLa [m^i 2 1 3 0 . 2 9 9 2 . 7 4 0 . 6 1 6 1 . 7 8 0 5 . 2 VOLmax [m^] 3 5 1 6 . 4 2 0 3 1 . 6 7 2 . 1 5 7 8 . 6 1 4 3 0 . 7 'Pmin. [°] - 5 2 . 7 - 2 0 . 0 - 4 . 9 - 1 5 . 9 - 3 4 . 7 0 . 5 ^max [ \ roi 3 . 7 4 . 5 4 . 4 5.9 2 0 . 6 m VOLa [m^] 1 4 3 9 . 0 4 1 1 . 3 3 8 . 5 1 1 3 . 0 5 3 3 . 9 9 . 7 VOLmax [m^] 2 8 4 1 . 5 1 0 6 6 . 0 6 6 . 5 3 9 5 . 0 9 9 7 . 7 s roi ^min [ J - 4 8 . 8 - 9 . 8 - 4 . 9 - 5 . 2 - 8 . 8 5 . 2 3 roi y^maa: [ J 3 . 7 4 . 3 4 . 2 4 . 8 3 . 6 m VOLa [m^i 1 1 5 2 . 6 1 7 4 . 7 2 . 2 1 7 . 3 1 2 8 . 0 VOLmax [m^] 2 5 4 2 . 9 4 5 1 . 0 4 . 9 5 9 . 0 1 9 9 . 0 roi Vmin L J - 3 4 . 7 - 5 . 8 - 4 . 9 - 5 . 2 - 8 . 8 4 . 2 1. ^max [ ] 3 . 7 4 . 3 4 . 2 4 . 8 3 . 6 m m VOLa [m^i 8 5 6 . 9 8 3 . 7 2 . 2 1 7 . 3 1 2 7 . 4 VOLmax [m^] 2 0 0 1 . 0 2 5 0 . 6 4 . 9 5 9 . 0 1 9 8 . 6 1.9 roi <pmiTi [ J - 2 1 . 3 - 4 . 9 - 4 . 9 - 5 . 2 - 4 . 9 m 0.5 roi ^max [ J 3 . 7 4 . 3 4 . 2 4 . 8 3 . 6 m VOLa [ m ' l 4 4 5 . 3 5 1 . 5 2 . 2 1 7 . 2 5 0 . 9 VOLmax [ m ' l 1 1 7 8 . 6 8 5 . 3 4 . 9 5 9 . 0 8 4 . 4 fmin [°] - 7 6 . 6 - 6 9 . 7 - 2 0 . 4 - 4 7 . 3 - 5 6 . 0 5 . 2 3 roi ^Tnax [ J 7 4 . 4 6 8 . 9 5 . 4 5.1 3 . 8 m VOLa [m^] 3 0 1 3 . 8 2 4 2 3 . 9 3 2 4 . 5 5 5 9 . 3 1 6 7 0 . 7 5 . 5 VOLmax [m^] 4 6 2 4 . 3 3 6 4 0 . 6 7 3 3 . 6 1 7 2 8 . 1 2 4 0 6 . 5 m roi <Pmin [ J - 6 4 . 9 - 2 8 . 9 - 5 . 9 - 2 9 . 3 - 3 8 . 6 0 . 5 ^max [ ] 6 4 . 1 5 0 . 3 6 . 8 2 4 . 0 2 1 . 7 m VOLa [m^i 1 6 3 9 . 4 1 3 7 4 . 2 5 6 . 4 3 4 9 . 2 7 6 7 . 3 8 . 0 VOLmax [m^] 3 1 2 5 . 3 2 7 5 8 . 5 1 2 3 . 9 9 9 0 . 6 1 2 3 6 . 1 s Ifimin [°, - 6 4 . 6 - 2 8 . 8 - 4 . 9 - 1 4 . 3 - 2 7 . 1 5 . 2 3 ^max [ ro 6 3 . 4 4 4 . 7 4 . 9 5.1 3 . 4 m VOLa [m^[ 1 5 5 2 . 5 8 5 5 . 5 3 9 . 2 9 2 . 6 5 0 5 . 6 4 . 2 VOLmax [m^ 3 1 0 6 . 5 1 9 0 0 . 4 7 0 . 4 3 4 1 . 5 7 5 5 . 6 m 'pmin [° - 2 7 . 6 - 1 9 . 7 - 4 . 9 - 8 . 2 - 1 9 . 0 0 . 5 'Pmax \ ro 4 . 2 4 . 9 4 . 9 5.1 3.1 m VOLa [rn^ 6 1 4 . 2 4 4 2 . 8 3 6 . 6 5 5 . 3 2 9 8 . 5 VOLmax [m^ 1 5 8 1 . 9 1 0 2 8 . 0 6 6 . 4 1 9 3 . 9 4 5 8 . 5 ro ^min [ - 5 6 . 6 - 1 3 . 4 - 4 . 9 - 7 . 5 - 1 3 . 6 5 . 2 3 ro 4 . 2 4 . 8 5.1 8 . 9 6 . 1 m VOLa [nv' 1 0 7 4 . 2 1 7 3 . 8 2 . 2 1 7 . 3 1 2 7 . 8 9 . 7 4 . 2 VOLmax W 2 1 5 2 . 5 4 4 7 . 0 4 . 8 5 9 . 1 1 9 8 . 2 s m ro ^min [ . - 2 8 . 0 - 4 . 9 - 4 . 9 - 7 . 5 - 5 . 6 0 . 5 ^max [ ro 4 . 3 4 . 8 5.1 8 . 9 6.1 m VOLa [m^ 4 4 1 . 2 5 1 . 4 2 . 2 1 7 . 1 5 0 . 9 1.3 VOLmax [m^ 1 1 6 1 . 3 8 5 . 2 4 . 8 5 9 . 1 8 4 . 5 m to - 8 2 . 6 - 7 8 . 3 - 2 6 . 0 - 3 8 . 1 - 6 1 . 5 5 . 2 3 ^max [ 8 1 . 8 7 5 . 4 6 . 0 5 6 . 8 4 . 8 m VOLa [m^ 2 8 1 1 . 0 2 2 0 9 . 6 3 2 2 . 5 5 1 7 . 1 1 4 9 7 . 3 8 . 0 5.5 VOLmax [m^ 4 3 3 3 . 2 3 4 2 1 . 6 7 2 8 . 6 1 4 4 3 . 0 1 9 9 8 . 9 s m TO - 6 9 . 8 - 2 8 . 1 - 5 . 2 - 4 2 . 0 - 4 9 . 9 0 . 5 TO 7 1 . 5 6 6 . 6 6 . 0 3 0 . 4 8 . 5 m VOLa [m^ 1 5 2 0 . 0 1 3 0 0 . 8 5 6 . 4 3 4 0 . 4 7 3 6 . 0 VOLmax [m^ 2 7 5 3 . 6 2 3 7 2 , 2 1 2 3 . 5 9 4 7 . 2 1 1 3 0 . 0
Minimum roll angle in simulation duration; " - " means a deeper immersion of the port side Maximum roll angle in simulation duration; " + " means a deeper immersion of the starboard side Average water volume on the car deck in simulation duration
Maximum water volume on the car deck in simulation duration
* * *
fmin ifmax VOLa VOLrr
Table 5: Results of simulations. Speed 15 knots; with wind; subdivision (a) GM Hl/3 Opening + * + Ji = 180° 135° 90° 15° 0° 'Pmin [°] - -5.3 — _ 5.23 iPmax [ ] — 1.4 — _ m VOLa [m^j — 40.0 _ 5.5 VOLmax [m^j - 71.8 — — m fmin [°] -53.0 — -5.3 -19.6 — 0.5 iPmax [ ] 8.1 — 1.4 3.9 _ m VOLa [m^j 1420.6 — 37.9 113.0 — 1.9 9.7 VOLmax [m^] 2789.7
-
66.3 393.8 — m s fmin [°] -12.0 -4.9 -8.1 -13.9 5.23 iPmax [ J 0.9 0.6 2.8 4.0 m VOLa [m^] 172.4 2.0 17.3 127.7 4.2 VOLmax [m^]-
444.5 4.5 59.2 198.7 m <Pmin ["] - -5.0 -4.9 -8.1 -9.6 0.5 fmax [ ]-
0.9 0.6 2.8 4.0 m VOLa [m^j-
51.4 2.0 17.2 50.9 1 VOLmax [m^] - 85.0 4.5 59.2 84.4Table 6: Results of simulations. Speed 9 knots; without wind; subdivision (a)
GM % Opening * * * // = 180° 135° 90° 15° 0° fmin [°] -69.3 -33.2 -4.9 -15.6 -36.8 5.23 fmax [°] 65.8 4.4 4.7 5.4 28.9 m VOLa [m^j 2218.6 887.0 28.7 158.7 642.7 5.5 VOLmax [m^] 3221.3 1738.5 55.1 433.8 1240.6 m fmin [°] -40.2 -16.7 -4.9 -11.4 -24.1 0.5 fmax [°] 3.8 4.4 4.7 5.4 5.9 m VOLa [m^] 1146.6 291.7 26.1 116.9 332.9 9.7 VOLmax [m^] 2129.9 698.6 50.4 299.0 726.3 s fmin [°] -23.2 -7.3 -4.9 -4.9 -10.3 5.23 fmax [°] 3.8 4.3 4.4 4.3 3.5 m VOLa [m^] 627.5 136.0 1.2 17.6 154.1 4.2 VOLmax [m'] 1203.3 298.9 2.2 4G.4 290.3 m fmin [°] -12.8 -4.9 -4.9 -4.9 -5.6 0.5 fmax [°] 3.8 4.3 4.4 4.3 3.6 m VOLa [m^] 239.0 47.5 1.2 17.2 74.9 1.9 VOLmax [m^] 561.5 84.1 2.2 39.5 149.9 m fmin [°] -71.7 -69.4 -4.9 -45.2 -49.0 5.23 fmax [ ] 71.5 65.2 4.7 6.1 22.8 m VOLa [m^] 2692.3 2022.5 52.6 756.9 1264.7 5.5 VOLmax [m^] 3783.7 2951.5 85.9 1812.7 2047.6 m fmin [°] -48.5 -36.3 -4.9 -27.2 -35.3 0.5 fmax [°] 6.8 6.7 4.7 31.5 5.4 m VOLa [m^j 1427.3 967.5 49.5 416.6 670.7 8.0 VOLmax [m^] 2608.4 1799.5 73.7 1083.2 1225.7 s fmin [°] -32.8 -19.3 -4.9 -10.7 -16.4 5.23 fmax [°] 5.4 5.8 4.5 5.0 4.5 m VOLa [m^j 1022.2 594.4 5.1 140.6 312.6 4.2 VOLmax K ] 1910.2 984.4 18.0 363.1 487.5 m fmin [°] -20.8 -12.6 -4.9 -7.8 -11.1 0.5 fmax [ ] 5.4 5.8 4.5 5.0 4.7 m VOLa [ m ' i 567.6 320.9 5.1 94.6 188.5 VOLmax [m^] 1084.1 564.4 17.7 248.1 321.3
Table 7: Results of simulations. Speed 4.5 knots; without wind; subdivision (a) GM T , Hi IS, Opening + + + ^ = 1 8 0 " 135° 90° 15° 0° roi fmin [ J -73.7 -39.2 -4.9 -33.7 -34.1 5.23 fmax [ ] 70.4 5.1 4.0 6.4 6.8 m VOLa [m^j 2222.3 1105.1 34.4 849.9 902.7 5.5 VOLmax [m^] 3294.7 2150.5 81.4 1357.1 1442.9 m fmin [°] -41.3 -23.0 -4.9 -21.1 -23.1 0.5 roi fmax [ J 4.5 5.1 4.0 6.4 6.8 m VOLa [m^] 1126.8 518.7 33.6 429.9 497.1 1.9 8.0 VOLmax [m^] 2208.5 1134.5 70.8 721.1 874.4 m s fmin [°] -25.5 -10.5 -4.9 -4.9 -4.9 5.23 ro] fmax [ J 4.1 4.9 4.1 5.7 6.0 m VOLa [m^\ 659.0 173.8 9.3 72.6 51.3 4.2 VOLmax [m^] 1336.6 377.5 16.5 113.3 75.0 m fmin [°] -16.0 -4.9 -4.9 -4.9 -4.9 0.5 fmax y J 4.1 4.9 4.1 5.7 6.0 m VOLa [m^j 296.2 51.4 7.8 48.8 51.0 V OLmax [m^] 678.4 84.7 14.0 86.0 70.2
Table 8: Results of simulations. Speed 15 knots; without wind; subdivision (b)
GM Hl/3 Opening * * * Ji = 180° 135° 90" 15° 0° fmin [°] -48.1 -34.0 — -22.2 -38.4 5.23 fmax [° 3.7 4.5 - 5.9 7.3 m VOLa [m^' 2428.3 1178.3 - 199.7 894.5 5,5 VOLmax [m': 3544.5 2037,2 - 688.6 1374.4 m fmin [°. -39.0 -21.8 — -16.5 -32.7 0.5 fmax [ 3.7 4.5 - 5.9 4.2 m VOLa [m^ 1381.8 672.7 - 135.3 538.0 9.7 VOLmax [m^] 2560.5 1358.8 - 450.3 997.3 s fmin [ ro -37.4 -10.1 - -5.2 -11.1 5.23 ro fmax i 3.7 4.3
-
4.8 3.4 m VOLa [m^ 1739.0 264.7-
21.8 185.2 4,2 VOLmax [m^ 2494.8 562.2 - 77.8 262.0 m fmin [° -21.8 -7.0-
-5.2 -9.0 0.5 fmax [ 3.7 4.3 - 4,8 3.4 m VOLa [m^ 642.1 170.1 — 19.8 143.0 1.9 VOLmax [m^ 1402.7 365.4 - 71.8 208.4 m -48.8 -40.8 — -39.1 -41.7 5.23 ^max [ 11.0 39.3 - 5.1 7.9 m VOLa [m^ 2437.7 1782.4-
541.7 1223.1 5.5 VOLmax [m^ 3581.1 2517.0 - 1500.6 1563.7 m ro fpmin [ -37.9 -36.1 - -30.2 -33.3 0.5 'pmax I ro 22.3 5.2-
5.1 4.4 m VOLa [m^ 1458.3 1252.5 - 357.1 778.6 8.0 VOLmax K 2256.3 1970.0 - 998.1 1193.4 s fmin [° -45.2 -31.4 — -14.8 -25.1 5.23 fmax [ 4.2 4.9-
4.9 3.0 m VOLa [m^ 1573.5 874.2-
101.4 517.2 4.2 VOLmax K 3163.0 1864.3-
367.7 766.0 m fmin [° 1 -27.9 -18.0-
-10.2 -17.9 0.5 fmax [ 1 4.2 4.9 - 5.0 3.3 m VOLa [ m ' 1 832.3 512.1-
66.8 302.6 VOLmax [m^ 1 1814.8 1103.3 — 1 230.7 463.0Table 9: Results of simulations. Speed 15 knots; without wind; subdivision (c) GM Opening *• = 1 8 0 ° 1 3 5 ° 1 5 ° 0 ° fmin [°] - 5 7 . 6 - 3 4 . 1 - 1 1 . 4 - 2 8 , 3 5 . 2 3 fmax [°] 3 . 7 4 . 4 5.9 5,2 m Vap Vas 2 1 4 3 . 5 2 9 2 . 4 8 5 0 . 0 1 4 7 . 6 9 7 . 0 5 8 . 1 5 0 8 . 5 1 2 2 . 3 5 . 5 Vmp Vms 3 4 6 6 . 5 5 7 8 . 0 2 0 3 8 . 0 3 1 0 . 9 3 5 0 . 6 1 7 3 . 5 9 1 7 . 2 2 0 2 . 7 m 0.5 fmin [ ] fmax [ ] - 3 7 . 9 3 . 7 - 1 2 . 0 4 . 4 - 7 . 5 5.9 - 2 0 . 0 4 . 7 m Vap Va, 9 2 9 . 9 1 2 1 . 0 3 3 8 . 5 4 3 . 8 6 0 . 5 5 1 . 8 2 8 0 . 2 1 1 4 . 2 9 . 7 Vmp Vms 2 1 4 8 . 0 2 4 1 . 7 7 6 4 . 1 1 1 7 . 1 2 1 6 . 0 1 6 0 . 5 5 3 1 . 6 1 7 3 . 6 s 5 . 2 3 fmin I ] fmax [ ] - 3 5 . 9 3 . 7 - 7 . 1 4.3 - 5 . 2 4 . 8 - 5 . 2 3.4 m Vap Vas 7 6 2 . 3 1 0 0 . 1 1 3 5 . 2 4 2 . 8 8 . 7 8 . 7 8 7 . 7 5 9 . 4 4 . 2 Vmp Vms 2 0 7 0 . 4 2 0 1 . 4 3 1 1 . 0 1 2 1 . 2 2 9 . 1 3 0 . 0 1 2 7 . 3 9 2 . 1 m 0.5 fmin [°] fmax [ ] - 1 1 . 1 3 . 7 - 4 . 9 4 . 3 - 5 . 2 4 . 8 - 4 . 9 3 . 6 1.9 m Vap Vas 3 3 2 . 1 4 5 . 5 3 6 . 0 2 5 . 7 8.6 8.6 5 7 . 5 2 6 . 4 1.9 Vmp Vms 7 9 8 . 0 1 1 5 . 7 9 9 . 3 4 2 . 5 2 9 . 0 3 0 . 0 8 9 . 0 4 2 . 8 m f n tin [ J - 5 7 . 2 - 5 6 . 6 - 2 7 . 3 - 4 0 . 3 5 . 2 3 'Pmax [ ] 4 . 3 5.0 4 . 9 5 . 5 5 . 5 m Vap Vas 2 2 7 5 . 0 3 5 4 . 3 1 8 9 2 . 0 2 5 7 . 8 2 9 9 . 6 1 2 6 . 5 9 5 2 . 3 1 7 1 . 3 5 . 5 Vmp Vms 3 5 2 7 . 0 6 4 2 . 9 3 3 4 2 . 0 4 8 7 . 2 9 3 8 . 7 3 4 6 . 9 1 5 6 0 . 0 3 4 4 . 3 m 0 . 5 fmin [ ] fmax [ ] - 4 7 . 7 4 . 3 - 3 2 . 6 5.1 - 1 7 . 7 4 . 9 - 2 1 . 5 5.5 8 . 0 m Vap Vas 1 1 3 7 . 0 1 5 0 . 8 8 4 0 . 9 1 4 8 . 0 1 8 3 . 2 6 3 . 0 4 1 6 . 7 1 3 2 . 5 8 . 0 Vmp Vms 2 6 6 1 . 0 3 8 2 . 1 1 8 9 3 . 0 3 6 5 . 0 5 2 7 . 7 1 9 9 . 0 6 7 5 . 4 2 1 7 . 7 s 5 . 2 3 fmin [°] fmax [ ] - 5 2 . 9 4 . 2 - 1 6 . 5 4 . 8 - 7 . 0 4 . 3 - 1 4 . 5 3 . 3 4 . 2 m Vap Vas 1 1 9 4 . 0 1 2 3 . 4 5 3 7 . 6 1 2 5 . 0 5 2 . 0 3 6 . 6 2 6 3 . 9 1 4 8 . 1 4 . 2 Vmp Vms 3 0 4 2 . 0 2 5 8 . 0 1 3 2 3 . 0 2 5 7 . 0 1 8 8 . 2 1 3 5 . 3 3 9 8 . 5 2 5 8 . 6 m 0 . 5 fmin [ ] fmax [ ] - 1 4 . 4 4 . 2 - 9 . 4 4 . 9 - 5 . 1 4.6 - 9 . 3 2 . 8 m Vap Vas 4 6 7 . 7 8 2 . 8 2 4 5 . 1 2 8 . 5 2 7 . 9 1 5 . 4 1 5 3 . 9 1 2 1 . 0 L Vmp
1
Vms 1 1 1 1 . 0 1 7 0 . 8 5 9 5 . 6 4 5 . 6 9 6 . 9 4 6 . 8 2 4 0 . 2 1 7 5 . 0Vap Average water volume on the car deck of the port side in simulation duration Vas Average water volume on the car deck of the starboard side in simulation duration Vmp Maximum water volume on the car deck of the port side in simulation duration Vms Maximum water volume on the car deck of the starboard side in simulation duration
