**Published at : ** 25 Jan 2021

**Volume :** **IJtech**
Vol 12, No 1 (2021)

**DOI :** https://doi.org/10.14716/ijtech.v12i1.4246

Paroka, D., Muhammad, A.H., Rahman, S., 2021. Hydrodynamics Factors Correspond to the Weather Criterion Applied to an Indonesian Ro-Ro Ferry with Different Weight Distributions.

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Daeng Paroka | Department of Ocean Engineering, Faculty of Engineering, Hasanuddin University, Gowa Campus, Jl. Poros Malino Km. 6 Bontomarannu, Gowa, South Sulawesi, 92171, Indonesia |

Andi Haris Muhammad | Department of Marine System Engineering, Faculty of Engineering, Hasanuddin University, Gowa Campus, Jl. Poros Malino Km. 6 Bontomarannu, Gowa, South Sulawesi, 92171, Indonesia |

Sabaruddin Rahman | Department of Ocean Engineering, Faculty of Engineering, Hasanuddin University, Gowa Campus, Jl. Poros Malino Km. 6 Bontomarannu, Gowa, South Sulawesi, 92171, Indonesia |

Abstract

The
effect of weight distribution on hydrodynamics factors in the weather criterion
was investigated. Two types of weight distribution were examined. With the
first type of distribution, the weight was concentrated near the centerline of
the model. With the second, the weight was positioned farther from the
centerline in order to obtain a natural roll period corresponding to that
provided by the standard formula in the weather criterion of the International
Maritime Organization (IMO). The three-step procedure recommended by the IMO
was applied. A roll decay test and a roll test in a regular beam wave were
conducted to obtain the natural roll period, the damping factors corresponding
to the breadth-to-draught ratio and the bilge keels, and the effective wave
slope coefficient. The damping factor corresponding to the breadth-to-draught
ratio for the ship with a larger radius of gyration was larger than that for
the ship with a smaller radius of gyration. The ship with a smaller radius of
gyration had a larger damping factor due to bilge keels compared to the ship
with a larger radius of gyration. The effective wave slope coefficient of the
ship with the larger radius of gyration was larger than that for the ship with
the smaller radius of gyration. The effect of bilge keels on the effective wave
slope coefficient for the ship with a radius of gyration equal to that obtained
by the weather criterion formula was not significant. The effect of weight
distribution on the weather criterion was significant for the ship without
bilge keels. A significant effect of bilge keels on the weather criterion
occurred for the ship with a weight
distribution corresponding to a radius of gyration
coefficient closer to that obtained by the formula in the weather criterion.

Ro-ro ferry; Roll radius of gyration; Stability; Weather criterion; Weight distribution

Introduction

Indonesian ro-ro ferries are used for the inter-island transport of
passenger and vehicles, particularly on short-sea and inland river routes. The vehicles are
located on the main deck, while the passengers are accommodated in a
superstructure above the main deck. The ships are designed with small draughts
because the ports in the service areas are generally characterized by shallow
water. To satisfy the capacity requirement, the ships are designed with a large
breadth. This requirement results in designs with breadth-to-draught ratios of approximately 2.3
to 8.3 (Paroka et al., 2020a). Most of the
ships have breadth-to-draught ratios larger than 3.5. The data collected about
ro-ro passenger shipsworldwide also show a breadth-to-draught ratio of approximately 2
to 7.5 (Kristensen, 2016). Indonesian ro-ro
ferries have small freeboards to facilitate vehicle loading and unloading at
ports. Therefore, the freeboard-to-breadth ratios of most Indonesian ro-ro
passenger ferries are smaller than 0.1 (Paroka et
al., 2020a). Thus, the heel angle associated with the maximum righting
arm is typically smaller than

The stability of Indonesian ro-ro ferries is assessed by using the
International Code on Intact Stability of the International Maritime
Organization (IMO) (IMO, 2008). The weather
criterion is one of the criteria applied to ro-ro ships. This criterion was
developed based on ships with breadth-to-draught ratios smaller than 3.5,
ratios between ship draught and vertical center of gravity ranging from 0.7 to 1.5, and natural roll
periods of up to 30 seconds. The values of the variables for calculating the
roll angle to windward due to waves may be inappropriate when applied to a
ship with geometric characteristics different from those used to develop the
criteria (Vassalos et al., 2003; Francescutto,
2007; Sato et al., 2008). For ships with large breadth-to-draught
ratios, the associated damping factor was found to be smaller than that
obtained with the recommended value of the IMO (Deakin,
2008; Paroka et al., 2020b), and the effective wave slope coefficient
obtained with the weather criterion formulae resulted in a larger value than
that obtained by model experiments (Fujino et al.,
1993; Ishida et al., 2011; Paroka et al., 2020b). Therefore, the IMO has
recommended the use of model experiments when the weather criterion is applied
to ships with geometric characteristics different from those used to develop
the criteria (IMO, 2006). Adjustment values
for the effective wave slope coefficient, wave steepness for roll periods of up
to 30 seconds, and a damping factor correspond to breadth-to-draught ratio for ships with
breadth-to-draught ratios up to 6.5 had been proposed (IMO,
2003; Francescutto, 2015). Recently, an extension of the roll period has
been adopted in the International Code on Intact Stability (IMO, 2015), but the damping factors corresponding
to the breadth-to-draught ratio and bilge keels as well as the effective wave
slope coefficient have not been changed.

The damping factor corresponding to bilge keels in the weather criterion
was assumed to depend only on the ratio between the bilge keels area and the
product between the length of the waterline and the ship’s breadth. However,
the damping moment induced by the bilge keels depends on the distance between
the bilge keels and the ship’s center of gravity in addition to the depth of
the bilge keels from the water surface (Ikeda et
al., 1978a; Ikeda et al., 1978b).The effect of distance between the
bilge keels and the roll axis for a shallow draught ship with a large
breadth-to-draught ratio has been verified by Katayama
et al. (2018). The increase of the equivalent damping moment was not
commensurate with the increasing height of the bilge keels (Jiang et al., 2020). Fesman
et al. (2007) found that the use of bilge keels could reduce the roll
angle of a ship by about 30%. Therefore, the damping factor due to bilge keels
given in the weather criterion results in an overestimated roll angle due to
waves when it is applied to a ship with a large breadth-to-draught ratio, as
found by Paroka et al. (2020b). The effect
of bilge keels on roll motion has been widely investigated, including the
effect of dimension and position (Irkal et al.,
2014), but the effect on the damping factor in the weather criterion has
never been investigated.

Another factor that should be considered when the weather criterion is applied to an Indonesian ro-ro ferry is weight distribution. The loading conditions do not always follow the designed loading plan, in which the heaviest vehicles are meant to be located near the center line. Under certain conditions, depending on the vehicles to be transported, a heavy vehicle can be located near the portside or the starboard. This different payload weight distribution could have significant effects on the natural roll period, as well as on roll damping and the effective wave slope coefficient. However, the adjustment values of these parameters in the weather criterion are independent of weight distribution. The radius of gyration can be calculated by a formula given in the weather criterion. A significant error can be obtained when the formula is applied to a ship with a larger breadth-to-draught ratio and a large metacentric height (GM) (Borisov et al., 2015). The effective wave slope coefficient depends on the wave frequency (IMO, 2013). The damping moment of a roll can decrease due to slower roll motion, which is associated with a larger natural roll period (Grimm et al., 2017). The roll period increases with increasing total inertia of mass, which is calculated based on the weight distribution. The added inertia of a roll increases when the wave frequency increases (Kianejad et al., 2017). This means that the hydrodynamics factors corresponding to the weather criterion can be different due to alterations of the weight distribution. The effect of weight distribution described by variations of the radius of gyration on the roll motion of a ship’s midsection with bilge keels has been investigated by Irkal et al. (2017), but the effect on the values of the parameters in the weather criterion has not yet been examined.

This paper discusses the effects of weight distribution on the values of the parameters in the weather criterion applied to an Indonesian ro-ro ferry. This is important because the weight distribution could vary on the basis of the vehicles transported during the operation of the vessels. The effects of weight distribution on the hydrodynamics factors corresponding to the calculation of the roll angle toward windward due to waves can be determined. The effect of bilge keels on the effective wave slope coefficient was also investigated with different weight distributions. The results can be used to develop stability criteria for ro-ro ferries, which have been categorized as non-conventional ships by the IMO, and to extend the tabulated values of damping factors due to breadth-to-draught ratios and bilge keels in the weather criterion. The results can also provide operational guidance for the distribution of vehicles on the main deck of ro-ro ferries.

Conclusion

The
damping factors corresponding to the weather criterion and the effective wave
slope coefficients of an Indonesian ro-ro ferry with and without bilge keels and
with different weight distributions were determined in model experiments. The
value for the damping factor related to the breadth-to-draught ratio for the
ship with a radius of gyration that was approximately
the same as that calculated by the weather criterion formula (0.48B) was larger
than that for the ship with a radius of gyration of approximately 0.36B. The
damping factor corresponding to the bilge keels for the ship with a radius of
gyration of 0.49B was smaller compared to that for the ship with a radius of
gyration of 0.38B. The effective wave slope coefficient of the ship with a radius of gyration of 0.48B
was larger than that of the ship with a radius of gyration of 0.36B. The
formula used to calculate the effective wave slope coefficient can be applied
to an Indonesian ro-ro ferry if the radius of gyration is equal to that calculated
by the formula of the weather criterion. The
effective wave slope coefficient for the ship with a radius of gyration
approximately equal to that calculated with the weather criterion formula was
not significantly affected by the bilge keels. The effect
of weight distribution on the

Acknowledgement

This paper is part of the research supported by the
Directorate General of Higher Education of Indonesia and Hasanuddin University:
Grant No.1516/UN4.22/PT.01.03/ 2020. The authors express their sincere
gratitude to these institutions for their support. The authors
express appreciation to Ardedi Yusuf for his assistance during
the experiments.

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