STUDY ON THE LIGHTSHIP CHARACTERISTICS OF MERCHANT SHIPS

Lightship weight and its distribution have significant influence on the intact/ damage stability and longitudinal strength of the ship. In this study, the range of limiting lightship longitudinal and vertical centre of gravity for different types of merchant ships have been determined. The merchant ships considered are bulk carriers, crude oil tankers, liquefied gas carriers, container ships and pure car carriers. Detailed hull form and general arrangement layout of the merchant ships were developed. Applicable rules and regulations and design considerations for each type of merchant ships were considered for this purpose. The principal dimensions, form coefficients, powering, stability and statutory rules and regulations are matched to the ships in service. At this stage, different rules and regulations concerning ship’s stability and trim were considered. Finally, after deducting the vertical and longitudinal center of gravity of the deadweight components (cargo, fuel and fresh water), the limiting lightship vertical and longitudinal center of gravity are determined.


Introduction
Ship design is considered more art than science. The design is continually improved based on the experience gained from similarly built ship types. The knowledge obtained from existing ships is converted as semi-empirical formula and statistical data. Ship designers while optimizing ship design consider various aspects like, carrying capacity, propulsion efficiency, construction cost and freight rate. Besides above safety of crew, cargo and structural integrity must be satisfied. Last but not the least, the design should have minimum environmental impact. Some of the design requirements are contradictory. Therefore, rational choice should be made for owner's requirements. Merchant ships can be divided into two categories, i.e. deadweight carriers and volume carrier. Deadweight carriers carry relatively dense cargoes having stowage factor about 1.3 3 mt [1]. Typical examples of this ship category are bulk carriers and tankers. Volumetric carriers carry relatively less dense cargo having stowage factor more than 2.0 3 mt [1]. Typical examples of this ship category are the Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai, Vishwanath Nagarajan, Om Prakash Sha 39 operation is quite economical and further development and improvement of their design was recommended. Kalajdžic and Momcilovic [9] developed a procedure for determining the characteristics of an optimum multi purpose cargo vessel in the preliminary design stage. Statistical analysis of successful multi purpose cargo ships built over the past 30 years was carried out. Using the proposed set of diagrams and formulas, the ship's principal dimensions were determined based upon required deadweight as a main prerequisite, as well as optimum energy efficiency design index, tank capacities, lightweight, etc. It was also concluded that preliminary design stage is very important, as once the main ship parameters are estimated the design cannot be repaired later. All the above studies show that improvement in estimation of ship particulars in preliminary design stage for different ship types still needs improvement. For some specialized ship types the design charts for preliminary ship design may not be available in public domain. This paper is a contribution to the preliminary design process for some popular merchant ship types. In the present study, the approach is as follows. Hull form and general arrangement design for different types of merchant ships are developed using commercial design software (Maxsurf Ⓡ ). For this purpose, the rules and regulations for the applicable ship types are complied with. The lightship weight and its distribution are determined using existing regression formula and the ship design characteristics. Thereafter we apply statutory rules and regulations regarding intact and damage stability for the different ship types. It is well known that maximum permissible KG for ship can be obtained based on these requirements. Similarly, the forward and aft limit of the ship's CG L is determined.
The centroid of deadweight components are thereafter determined based on the actual tank layout and load distribution. Finally, the deadweight component moments are deducted and the limiting lightship vertical centre of gravity ( LS KG ) and limiting longitudinal centre of gravity ( LS LCG ) is determined. Based on the analysis, we show the variation of lightship weight and its centroid for different merchant ship types.

Design of ships
The accompanying analysis is based on 58 different hull forms. The hull forms consist of crude oil tanker, chemical tanker, bulk carrier, container ship, LNG, LPG carrier and pure car carrier. The numbers of ship and main dimensions are described in Table 1. The principal dimensions were selected from statistical data of previously built ships. That provides a good starting point for developing the particulars of hull form and primary dimensions of ships. In initial design stage, the mission requirements are translated into technical characteristics of shipbuilding nature. The present work deals with the first two phases (Fig. 1) of ship design, i.e. preliminary design and concept design. Preliminary design is an elaboration of the various ship-design steps, partly addressed in the first phase. It involves an accurate determination of ship's principal characteristics namely, length, beam, depth, draft, block coefficient and effective powering. It is understood that calculating the above parameters of the ship is subject to Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai, Vishwanath Nagarajan, Om Prakash Sha 41 compliance with national and international maritime rules. The primary ship dimensions (length, beam, draft, depth), and hull form characteristics (hull form coefficients, powering, weight components, stability and trim, freeboard, load line), are required in the first phase of ship design. After selecting the above basic ship design elements followed by the estimation of the lightship weight, the displacement of ship is calculated. The selection of primary dimensions and form coefficients are based on statistical data, empirical design formulas, coefficient tables and graphs. The above characteristics are guide to design individual ship type. For all ship types, we should refer the limitations of principal dimensions (length, beam, draft and depth) based on limitations of ports of call. Besides above, there are restrictions because of transiting canals, for e.g. Panama Canal, St. Lawrence Seaway and Suez Canal. The estimation of main dimensions is based on data available from the similarly built ship, commercial and internal databases. The equivalent data and semiempirical formulas are sufficient for the successful application of the empirical method. The ship's principal dimensions, weight components and powering requirement are dependent on each other. For displacement ships, for small variation of ship's length, the variation in ship's resistance and powering may be proportionate [1]. The data of principal dimensions and coefficients of similar ships help to reduce the design work. It also serves as validation for computer generated design data. Typical data required for designing different ship types are shown in  In this paper, the sequence of determining the primary dimensions and form coefficients are briefly described. We first present the principles for the selection of the primary dimensions and secondly, the different semi-empirical formulas. The procedure for selecting the main dimensions and form coefficients are based on an iterative approach shown in Fig. 1. The displacement and speed are primarily dependent on the ship's length. It has a significant influence on the hull weight, machinery and outfitting. It also reflects on the construction cost and, it has a strong influence on the ship's resistance and sea keeping performance. Froude number is representative of the ship's speed. The tanker and bulk carriers have high B C and P C coefficients with low Froude number up to 0.20. The above form corresponds to full hull. They have high frictional resistance as a percentage of total resistance [2]. For reduction of frictional resistance, ships must have minimum wetted surface for a given displacement. On the other hand, container and passenger ships have low P C and B C coefficients with high Froude number above 0.25. They have a significant proportion of wave/ residuary resistance as a percentage total resistance. To reduce the wave resistance, relatively slender hulls are designed. For other types of ships the percentage share of the residuary and frictional resistance components may differ with total resistance [10]. The position of longitudinal centre of buoyancy varies depending on the longitudinal distribution of displacement. The basic influencing factors of main dimensions on the steel and outfitting, and the effect of speed on the lightship weight were investigated by Strohbusch [1]. Strohbusch also investigated the effect of slenderness ratio and prismatic coefficient on ship hull performance [1]. Ship's beam has significant influence on stability. An increase of beam by 10 % leads approximately to a rise in T GM by 30% [11]. Propeller diameter depends on the draft of the ship. High draft vessels, like tankers and bulk carriers are fitted with a large diameter propeller for achieving higher efficiency with the low propeller revolution. This is because higher diameter propeller will have lower revolution. Also, the size of the rudder is large for better manoeuvrability. Limitation of draft involuntarily increases the primary dimensions especially the beam of ship. While selecting the draft of the ship, the depth of the navigation route, water depth of the calling ports, channels, canals, estuaries, bays, and narrow sea straits must be checked. The selection of the depth is inherently linked to the permissible draft. Indirectly, it is related to the ship's length (in consideration of the longitudinal strength) and beam (in consideration of the transverse stability). For example,  [2]. One prefers an increase of the ship's depth rather than changes of other main dimensions in case the ship's hold volume is inadequate. The depth is the "cheapest" and least problematic primary dimension of a ship. Classification societies define a limit of the / LD ratio, which varies between 10 to 14 [12]. If / > 14 LD , then a special investigation of longitudinal strength is required. Increase of the depth means reduction of the ratio / LD . Due to the increase in section modulus, ship's longitudinal bending stress will reduce. The increase in depth results in the increase of the hull weight and rise in vertical center of gravity of the hull [1]. Also, the weight of superstructures and outfitting increases accordingly. This leads to an increase of the ships KG in all the load conditions. The loadline rules consider / LD ratio of a standard ship as 15. If the actual / LD ratio is lower, then the freeboard has to be increased. Here the idea is to have sufficient reserve buoyancy for ship motions in waves and also during damage stability. The / BT ratio has a strong influence on the residuary resistance of the ship. It decides the contribution of wave making resistance to the total resistance of the ship. It is preferred to have the / BT around 2.5 [1]. The / LB ratio has an influence on the wave resistance of ship. The lower / LB ratio has an increased effect on wave resistance. The increased beam (reduced / LB ratio) improves the maneuverability of the ship [1]. As discussed before, container ships and car carriers have comparatively slim hull. This means P C and B C values are low and Fr is higher as shown in Fig. 2. In container ships, due to low P C , there is concentration of loaded containers in the midship region below deck. To compensate for this, container ships are provided with large flare at the forward and aft section for accommodating the containers on deck. Similarly, in PCCs, huge space is provided above the freeboard deck throughout the Sree Krishna Prabu Chelladurai, Study on the lightship characteristic of merchant ships Vishwanath Nagarajan, Om Prakash Sha 44 length of the ship to accommodate the cars/ trucks. Both the ship types have reduced lower deck spaces and sharp entrance in the bow region which helps to achieve the relatively high speed. Figure 2 describes the position of CB L for dead weight and volumetric carriers. The CB L of the container ships and car carriers are located aft of mid ship, while for the bulk carrier and tanker vessel it is located forward of mid ship. Load Line Regulations need to be complied with to achieve the minimum freeboard and bow height for all designs [13]. The minimum freeboard requirements are classified in two categories. Oil tankers/ gas carriers come under 'type A' and dry cargo ships come under 'type B' category. The required freeboard is calculated based on the length of the ship. Thereafter corrections based on the B C (0.68), depth, sheer of the ship is applied on the tabular freeboard [13]. Figure 3 describes the minimum freeboard requirement for different length of ship. From Fig. 3 it is understood, that the volumetric carriers have high freeboard/ depth ratio as compared with the deadweight carriers. High freeboard ensures that there is sufficient reserve buoyancy and better survivability in case of hull damage.   The bow height, is measured at forward perpendicular between summer load line and the ship's weather deck or the forecastle deck. Minimum bow height is calculated based on the regression formula proposed in loadline regulation [13]. All bulk carrier ships are provided with forecastle as per the loadline regulations [13]. Some of the container ships and small LPG ships are also provided with forecastle complying with loadline regulations. Some LPG ships and oil tankers are provided with poop deck meeting the loadline regulations. Figure 3 shows the freeboard and bow height provided for various ships. The minimum value required by regulation is also plotted. It is observed that the volumetric carriers have relatively large freeboard than the dead weight carriers. The freeboard and the bow height for all types of ships is more than the regulatory requirement. The large bow height helps to reduce the risk of green-water thereby giving protection against damage of deck cargo or containers due to large pitching and heaving motions. The next stage of ship design is general arrangement. The general arrangement provides the location/ dimension and extent of engine room, cargo compartment. It also shows the type and number of bulkheads to be provided on the ship. Using this information along with the volume and density of cargo in individual compartments, the CG L and KG position for different loading conditions can be estimated. This information is used to calculate the stability of ship at a later stage. First, the common regulations applicable for all the ship types will be described. Forepeak bulkhead is fitted as per classification society's regulations. Classification society's rules also specify the minimum number of transverse bulkheads for various ship types. This mainly depends on the type and length of the ship. Transverse bulkheads need to be located along the length of the ship both from the aspect of strength and distribution of volume in different cargo holds. This is because for the same length, we get lower volume in the forward and aft part of the ship due to the narrow ship sections. All ships are provided with a forward and an aft peak bulkhead. The distance between the forward collision bulkhead from the forward perpendicular must be within the limits of 5 % or 10 m and 8 % of bp L as specified by class rules. From Fig. 4, it is observed that most of the ships have forepeak tank length nearing the upper limit. This is because the ships need to achieve minimum draft at forward in the ballast condition for protection against bottom slamming. The after peak bulkhead is located such that the length of the propeller shaft is less than the intermediate shaft. This is for the ease of maintenance of propeller shaft. Steering gear deck is provided as per the parent ship configuration. The aft peak bulkhead location is also decided based on the required capacity of the aft peak tank. The length of the engine room compartment depends on ship's lines plan, the propulsive machinery power and displacement of ship. In this study, it is based on the similar ship types. When the engine room is at aft, the aft peak bulkhead coincides with the aft bulkhead of the engine room. The aft peak bulkhead location is also based on the requirement of minimum volume of ballast required in aft peak tank for trimming purpose. It is evident from Fig. 4, that the tankers and liquid gas carrier have larger engine room length. The reason is tankers and liquid gas carriers have a pump room in the forward part of the engine room. The pump room contains cargo/ ballast pumps for loading/ unloading the cargo and ballast. The machinery for driving the cargo/ ballast pumps is located in the forward part of the engine room in these ships. Also in these ships, engine room is located in aft. Due to narrow section at aft, the engine have to be located in forward part of the engine room such that sufficient space is available on the side for maintenance. In case of container ships, the engine room is located near to midship. As the ship section is wider, smaller length of engine room is sufficient to accommodate the propulsion machinery with the auxiliaries. In oil tankers and gas carriers, the fuel tanks are also located within the engine room. While in container ships, the fuel oil tanks are located away from the engine room.  The weight estimation at primary stage is an early milestone of ship design. Also, the accuracy and centroid of different components are vital to calculate the limiting KG . On the other hand, inaccuracy has a substantial influence on the capacity, speed, and stability of the ship. Therefore, in the general arrangement design, we must give importance to calculation of hull, machinery and outfit weight. The ship's displacement can be estimated more accurately by estimating various weight components that constitute the displacement. This requires information from similar ships for different designs. There are different methods available for the estimation of steel weight of ships. The modern ships are usually lighter than older ones for the same capacity. However, for tankers stringent safety regulations MARPOL and OPA90 [14] has resulted in double hull construction resulting in increased steel weight. We assumed that mild steel is used as shipbuilding materials. In recent years, ships are built with some percentage (30 % to 59 % ) of high tensile steel, to lower lightship weight and increase the cargo carrying capacity. Different lightship weight components are calculated by using the semi-empirical formulas proposed by D'Almeida [15]. The lightship weight is considered to be the sum of three main components: The hull weight, superstructure, machinery weight, and outfit weight are estimated in the initial stage of design process. Besides above, the lightship weight ( LS W ) also includes lubrication oil, cooling water, feed water (boilers). Steel weight includes the weight of main hull, bed plates of machinery, etc. Accommodation weight includes the weight of superstructure and deckhouses. This also includes the weight for the improved quality of accommodation spaces, sanitary facilities, and air-conditioning besides regulatory requirements. To comply with regulatory requirements for temperature and noise, larger Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai, Vishwanath Nagarajan, Om Prakash Sha 47 quantity of insulation materials is used in the engine room and accommodation. Generally, an increase of ship's length leads to a simultaneous increase of cargo carrying capacity, and steel weight. From Fig. 5, it is evident that an increase of length leads to linear increment in the steel weight. Outfit weight includes the weight of all fittings to the "naked" ship and detachable fitting on hull [16]. Recently, there is an increase in outfit weight due to higher quality of weather tight hatch covers, cranes and windlass/ mooring winches, deck machinery, firefighting equipment, etc. From Fig. 5, it appears that an increase of outfit weight is primarily governed by the ship's length. From Fig. 5, it is noticed that container ship has the maximum outfit weight. The reason is container ships have large longitudinal profile area above the waterline. It is common to accommodate containers on top of the main deck. Moreover, the containers have to be mandatorily secured by lashing equipment. Typical weight of lashing equipment is 0.024 t/TEU and 0.031 t/FEU container [1]. The fundamental component of machinery weight is the main engine, which depends on the speed and power requirement of different ships [17]. An increase of Froude number indicates an increased machinery weight and increased values of weight coefficients LS (W /Δ) and LS /) (W LBD [1]. Besides above, machinery weight is also influenced by the type of ship and the position of the propulsion machinery (shaft length) and power demand for auxiliary machineries (pumps, separators, refrigeration etc.) [18]. The propulsion machinery can be categorized into three different types like, two stroke diesel engine, four stroke diesel engine and steam turbine. The four stroke main engine and Sree Krishna Prabu Chelladurai, Study on the lightship characteristic of merchant ships Vishwanath Nagarajan, Om Prakash Sha 48 steam turbine must be coupled with reduction gear or with the accessories of controllable pitch propeller. If the propulsion machinery is steam turbine, the ship needs the main boiler to produce steam at high pressure. Some types of ships, container ship (refrigerated container), LNG and LPG carriers require a high demand for electrical energy for operating the refrigeration units. Finally, position of the engine room. In container ship it is located just aft of midship. This implies ship must have a lengthy propeller shaft to connect the propulsion machinery and the propeller. After identifying all elements which contribute to the machinery weight, it is evident from Fig. 5 that machinery weights of container ship are higher when compared with tanker and bulk carrier. Tanker vessels and bulk carriers have low Froude number that therefore required lower power of the main engine. On the other hand, container ships have high Froude number ( Fr ,  0.25), low P C , B C and high slenderness coefficient. This is because wave resistance is significant proportion to the total resistance. The container ships require high-speed as it carries perishable cargo in large volume which must reach the port at scheduled time. Therefore, containerships have relatively high engine power. It is evident from Fig. 6 that container ship has higher main engine power, even though their dead weights are low. This leads to an increase of the main machinery, and auxiliary machinery weight. The auxiliary machineries are supporting the operation of main machinery (pumps, separators, boiler etc.).   The ballast water capacity is an important element to operate ship safely at sea. The ballast water capacity is an important feature for both volumetric and dead weight carriers. In the ballast voyage, ships must satisfy safety requirements like minimum mean draft and forward draft, maximum permissible trim, and sufficient propeller immersion. Also the ship shall not trim by bow in loaded departure condition. Therefore, all the ships require a sufficient amount of ballast to satisfy the above mentioned safety requirements. The capacity of the ballast tanks shall be determined as described in Table 3 (MARPOL Regulation 18 [14]). The ballast tanks are placed along the ship's sides or wing, double bottom, fore and aft depending on the type of vessel. In tanker vessel, the whole cargo tank should be protected by double bottom and side ballast tanks. The side and bottom tank width and height have to comply with the requirements of MARPOL to avoid the pollution at the time of collision or grounding [14].   Figure 7 illustrates that volumetric carriers require relatively low ballast water capacity to achieve the safety requirement as the design draft is less as compared with deadweight carrier. On the other hand, tankers and bulk carriers have relatively high P C , B C and M C coefficients as shown in Fig. 2 and also, the design draft are relatively high for dead weight carriers. As a result from Fig. 7, it is obvious that dead weight carriers require higher volume of ballast water to ensure safety of vessel (MARPOL Regulation 18 [14]). It is evident from the previous discussions that crude oil tankers and bulk carriers have comparatively smaller / LB , high / LD ratio with high P C and B C resulting in high cargo carrying capacity as seen in Fig. 7.  As discussed before, deadweight includes the machinery supplies like heavy fuel oil (HFO), diesel oil and fresh water. The cooling water for machinery and feed water of boilers constitute part of lightship weight. HFO is used as fuel in main engine, boilers and auxiliary engine. A significant quantity of HFO is consumed by the main engine. The consumption of HFO depends on the main engine power (Fig. 6) and specific fuel consumption. Figure 8 shows that tanker and container ships require large volume of HFO. Also, the HFO carrying capacity is relatively larger for container ships as compared to other ships, because in every voyage bunkering cannot be afforded to decrease the turn-around time of the ship. Similarly, liquefied gas carriers require refrigeration facilities to maintain the temperature (-55 °C ~ -163 ℃) in cargo tanks. Therefore, LNG carriers have higher HFO consumption as shown in Fig.  8. In the case of consumption of diesel, the crude oil tanker required relatively large volume diesel for the inert gas generation unit. Inert gases are pumped into cargo tanks to prevent the fire hazard. From Fig. 8, one can conclude that tankers require large volume of diesel oil. MARPOL regulation [19] is followed for double hull protection of fuel oil tanks on all type of ships. Individual oil fuel tanks capacity is kept less 2,500 m 3 for compliance with the MARPOL regulations [19]. As discussed before, steam is used for different application like preheating of crude and fuel, and cleaning. From Fig. 8, it is evident that the tankers require relatively high volume of fresh water as boiler feed water. On the other hand, for LNG carriers, steam turbines are used as the main propulsion machinery. In LNG carriers, steam is used in main turbine and auxiliary preheating services. They use the boil off-gases from the cargo to reduce the fuel consumption of the main boiler. However, they require a significant quantity of fresh water, to produce steam for running turbines. For all ships, fresh water tanks capacity and location were based on parent ship arrangements.
Design considerations for oil tanker will be discussed. The present analysis consists of 17 different tanker ship designs. The design for the oil tanker is very elaborate and based on (iii) Regulation 23, Accidental oil outflow performance: It is based on probabilistic concept. It specifies a limit on the amount of oil outflow from the tank in case of damage. The deepest load line draft is taken as the design draft and the minimum tide is considered as -2.5 m (low tide). It is assumed that after collision, all cargo in the damaged cargo tanks are spilled out. Some reduction in oil spillage is given in case of double hull tanks. (iv) Regulation 28, Subdivision and damage stability: It is based on deterministic concept. It specifies the damage stability requirements to be complied by the vessel in case of damage. It is assumed that all the liquid cargo in the damaged cargo tanks are spilled out.
(v) Regulation 29, It specifies the minimum capacity of the slop tanks.
All the ship designs investigated in this paper are assessed to sustain the damage extent requirement [20] and to fulfill the damage stability requirements as shown in Table 4. The accidental oil outflow in different damage scenario is shown in Fig. 9. The mean oil outflow is calculated independently for side and bottom damage and then combined into non-dimensional oil outflow parameter M O as shown in Fig. 9. Figure 9 shows that the spilled volume varies depending on the side or bottom damage. The estimated oil outflow from the side damage is higher as compared to bottom damage. The tank's bottom plate experience higher hydrostatic pressure as compared to the side tank plates. Therefore, the bottom oil outflow is lower as compared with the side oil outflow. It is observed from Fig. 9 that the mean outflow gradually reduces with increasing cargo capacity. Design considerations for gas carriers will be discussed. For gas carriers general arrangement design is based on the requirements of International Gas Carrier (IGC) code [21]. The design requirements depend on the type of cargo. The gas carrier ships investigated in this paper are designed for carrying cargo suitable for "Type 2G/ 2PG" ships. The ships are mainly intended for carrying LPG, LNG, ammonia and ethane. Even for Type 2G/ 2PG ships, the design requirements depend on the cargo carrying temperature. If the cargo temperature is less than -55 ℃, a continuous side longitudinal bulkhead in way of cargo tanks is provided. If the cargo temperature is between -10 °C and -55 °C, only double bottom is provided. For all cases, there shall be minimum 0.76 m clearance between the tank and the ship's shell plate. The refrigerated cargo tanks must be insulated to maintain the temperature of the cargo tank and prevent boil-off. The insulated independent tanks are located in hold space. In case of independent tanks, minimum spacing must be provided between the insulation and the ship structure to permit passage of personnel for inspection. In case of membrane tanks, when insulation is applied on one side of the main hull structure, the other side shall be always accessible for inspection. Therefore, for membrane type LNG ships, between two cargo tanks, void space/ cofferdam shall be provided. Similarly sufficient size of opening must be provided on horizontal and vertical structural members for taking out injured personnel strapped on stretcher from the cargo/ ballast tank spaces. Therefore, the gap between the cargo tank and the main hull and depth and width of the double bottom and double side spaces shall be carefully designed [21]. In this paper all LPG carriers have independent self supporting tanks. For LNG carriers, both independent self supporting tank and membrane type tank designs are considered. In LNG carriers, there are some differences between the layout of independent type tank and membrane type tank design. In case of independent type tank design, a number of large diameter spherical tanks are placed along the ship's length. The spherical tank diameter depends on ship's beam. Each one of the spherical tank, is insulated from outside. The hold space supporting the spherical tank is covered by weathertight steel plate. In membrane type design, void space is provided between transverse bulkheads on which the membrane type insulation is applied. On the deck, void space is Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai, Vishwanath Nagarajan, Om Prakash Sha 53 provided above the cargo tank for compliance with regulation. Therefore, length and beam are an important factor to attain the cargo capacity of LPG/ LNG carrier. For both the LPG and LNG ships, water ballast tanks, configuration is provided as per parent ship design configuration. There are some differences in the deterministic damage stability calculations for oil tankers and gas carriers as described in Table 5. This will influence the limiting LS KG and LS LCG characteristics of these ship types. Tankers of more than 225 m in length should be assumed to sustain damage anywhere in its length.
A type 2G ship of more than 150 m in length should be assumed to sustain damage anywhere in its length.

2
Oil tankers 20,000 tonnes deadweight and above, shall be able to sustain bottom raking damage. Not applicable. 3 The angle of heel due to unsymmetrical flooding shall not exceed 25°. This angle may be increased up to 30° if no deck edge immersion occurs.
The angle of heel due to unsymmetrical flooding should not exceed 30°.
Design considerations for bulk carrier will be described. The top side tanks were designed based on angle of repose. The bottom hopper tanks were designed based on parent ship configuration. Most of the bulk carriers are single hull construction. The common design feature of the ship is to achieve maximum volume in cargo holds to accommodate maximum cargo quantity, up to the maximum allowable draft. Bulk ore carriers are designed for "alternate hold loading" condition for stability and motion considerations. This means the cargo can be loaded in "alternate holds" i.e. odd number (1, 3, and 5) of holds. This loading pattern significantly increases the shear force and bending moment on the ship. It also requires extra strengthening of the tank top plating in order to endure higher cargo loading. Their longitudinal strength need to be investigated in detail for this purpose.
For PCC ships ballast capacity is checked for minimum sailing draft requirements. The freeboard deck is fixed based on the cargo loading / unloading ramp location. The numbers of transverse bulkheads are kept to a minimum for ease of loading / unloading cargo. Above the freeboard deck, several decks are provided for storing the cargo. However these deck are non watertight and do not contribute to either reserve buoyancy or structural strength. For some container ships, the accommodation is located in the forward side. The cargo holds are also provided at aft. The cargo hold lengths were based on standard container sizes. Transverse non watertight bulkheads were provided based on parent ship design. The side tanks boundaries were made vertical and sizes were compatible with the standard container dimensions. Container ships during some voyages may carry less number of loaded containers onboard and significant amount of empty containers may be carried on top two tiers of deck. This can cause a rise in KG of ship. To make sure that the ship has adequate T GM , ballast water may be carried in the partially loaded condition. In practice, each ship type may experience different loading condition. Due to this the vessel may trim based on the CG L position. In all the loading condition, it is preferred to have trim by aft.

Method of analysis
In this section, the analysis methodology will be described as shown in Fig. 10  KG of various ships First, intact stability analysis will be described. Different intact stability loading conditions namely, "loaded departure condition", "loaded arrival condition", "ballast departure condition" and "ballast arrival condition" specified in the regulations are developed for each ship type [13] and the intact stability criteria requirement shown in Table 6. For oil tankers and gas carriers in "loaded departure condition", the cargo holds are filled up to 98 % and fuel oil, diesel oil, fresh water are filled up to 95 % of full capacity. In "loaded arrival condition" the fuel oil, diesel oil and fresh water are assumed to be consumed 85 % of full capacity in transit and the cargo quantity remains as 98 % . For LNG carrier 0.2 % boil off is assumed. In case of bulk carriers, for the "loaded departure condition", the cargo holds are loaded for "uniform" and "alternate hold" loading condition respectively.  In case of container ships, the average weight of containers (14 tonnes) in the cargo hold and deck is considered to achieve the desired draft for the "loaded departure condition". In case of PCC ship, the loading of cars is carried out in the hold to achieve the desired draft for the "loaded departure condition". For all the ships, ballast tanks are suitably filled up to comply with the regulations for "ballast departure condition". For bulk carriers, container ships and PCC ships, loading of fuel oil, fresh water is carried out in the same manner as for the oil tankers and gas carriers. All the ships were loaded to respective ballast and loaded draft. For oil tankers and gas carriers, the additional "in port" operating condition was checked. During this condition, the cargo tanks are unloaded and the ballast tanks are loaded simultaneously. There will be a situation where all the cargo and ballast tanks are slack simultaneously. This will increase the free surface effect. In this condition, it must be ensured that T GM ≥ 0.15 m.
(1) In "ballast departure condition", the cargo tanks/ holds are empty. The ballast tanks, fuel oil, diesel oil and fresh water tanks are filled up to 95 % of full capacity. The tank capacities and arrangement are so designed that the ballast draft satisfies full propeller immersion, minimum trim by aft, minimum mean draft and minimum draft at forward to prevent slamming. The conditions are described in Table 3. In ballast arrival condition at the port the fuel oil, diesel oil, fresh water tank quantity was consumed to 50 % or 15 % of full capacity. For some ships leftover of 15% of fuel is unlikely due to large HFO capacity.
(2) The limiting LS KG at any desired draft is determined for complying with the intact stability condition as shown in Eq. 1 and other rules are described in Table 6

LCG
corresponding to maximum permissible trim by aft is given as the input. The LS KG calculated as per Schneekluth's method [2] is given as input.  Table 6  KG , this assumption needs to be made. First the computations for deterministic damage stability will be described. This is applicable for oil tankers, gas carriers and ships complying with damage stability rules of load line regulations. During asymmetric damage, the inferior part of the Damaged

GZ
curve is considered for compliance with rules. The following damage cases are checked: (1) The longitudinal, transverse and vertical extent of damage is applied as specified in MARPOL [14], IGC [21] and Loadline rules [13]. Single/ multiple compartment damage for cargo area and engine room is applied as per rules.
(2) When a loaded tank is damaged, the liquid inside the tank (cargo or fuel or freshwater) is assumed to be lost from the damaged tank. In this case the displacement and centre of gravity of the ship before and after the damage will be different.
(3) When a loaded cargo hold is damaged, its permeability is considered for damage stability as per rules. For example, in case of bulk carrier, PCCs and container ships, the entire hold cannot be flooded with water due to the presence of cargo. The permeability values used for damage stability calculation are described in Table 7 [3].
(4) For double bottom/ double side ships, in the loaded condition, the damage to only outer hull is also checked. In this case, usually there is no change in the displacement or the centre of gravity of the ship. This is because double hull spaces are empty during loaded condition. This includes the "bottom raking damage" for oil tankers. Here, the outer hull is damaged to a length, as specified in the rules due to grounding. This damage condition imposes strict requirement on the water ballast tank design configuration. The "bottom raking damage" is applied only for the oil tankers (MARPOL rule requirement) and not the gas carriers. Also, the permeability of a tank containing liquids is assumed that the contents are completely lost from that tank and replaced by water. Consumable liquids 0.95 The damage stability requirements are different for oil tankers, gas carriers and general cargo ships. In case of oil tankers and gas carriers, the damage stability check is only done for loaded condition [14], [21]. The damage stability survival requirements are not applied to the ship in the ballast condition. All the tanker designs are assessed to sustain the damage requirement [20] to fulfil the damage stability requirements as shown in Table 4. The damage Sree Krishna Prabu Chelladurai, Study on the lightship characteristic of merchant ships Vishwanath Nagarajan, Om Prakash Sha 58 stability requirements for gas carriers were checked as per IGC code as described in Table 8 [21]. The procedure followed is same as that for oil tankers. The intact and damage criteria requirements are shown in Tables 6 and 8.  KG can be calculated for each loading condition as shown in Eq. 6. The weight and KG of individual components like cargo, ballast and fuel were determined as per the exact geometry of the compartment. In case of oil tankers and gas carriers, the contents of the damaged tanks are assumed to be completely lost. In case of bulk carrier and container ships, permeability of the damaged cargo tank is considered.
A ship is assumed to survive a damage condition if the final waterline, taking into account sinkage, heel and trim, is below the lower edge of any opening through which down flooding may take place. It is difficult to get a mathematical expression for CG L using the ship geometric particulars from Eq. 7 as is done for KG from Eqs. 4 and 5. Therefore, an iterative method is followed in this paper for this purpose. The LS LCG lower and upper limit determined from the intact stability conditions are used during the damage stability conditions. The number of damaged combinations for each loaded conditions is very high. The damage stability calculations are first carried out using the LS LCG lower and upper limit. If all the damage stability rule requirements are satisfied, then the intact stability LS LCG lower/ upper limits are retained. If not, the upper/ lower limit, as the case may be, is decremented by 0.01 bp L % in steps and the damage stability calculations are repeated. The process is continued till the assumed LS LCG upper/ lower limit meets all the damage stability requirements. It is ensured that the vessel remains in floating condition (with heel and trim) as per the requirements of MARPOL/ IGC for all the permissible damage cases. Therefore, the final limiting values specified would comply with both the intact and damage stability requirements as described in Fig. 10. The KG calculated as per Schneekluth's method [2] is given as input while computing LS LCG . The damage stability calculation for general cargo ships will be described. The ships under this category are bulk carrier, container ship and pure car carrier. For general cargo ships, damage stability is checked as described in Table 8. The probabilistic methodology is used for this purpose. The probability of damage is estimated with factors that affect the Sree Krishna Prabu Chelladurai, Study on the lightship characteristic of merchant ships Vishwanath Nagarajan, Om Prakash Sha 60 three-dimensional damage extent of the ship with the given watertight subdivision (transverse, horizontal and longitudinal). The damage parameters, such as longitudinal, vertical and transverse extent are determined based on the geometric layout of the subject ships. Single/ multiple compartment damage are considered as per the rule requirement. Unlike the deterministic damage stability computation which is primarily based on ship's length, there is no restriction on single, two compartment damage in probabilistic damage stability calculations. Similarly, there is no restriction on machinery compartment being part of one or two compartment damage. Also, permeability values of each compartment, tank and cargo space are explicitly given as input for the damage stability [3]. The key points or air vent for all the tanks are mentioned as per requirement, minimum 760 mm height from the main deck.
This key point is taken as input to calculate the immersion angle [13]. The required subdivision index depends on ship's length as shown in Eq. 8 [3]. The method of calculating attained subdivision index for a ship is expressed as shown in Eq. 9.
Where the subscripts S , P and L represent the three loading conditions and '0.4' and '0.2' are the weighting factors. In our case ' S ' corresponds to the deepest subdivision draft, ' P ' corresponds to the ballast departure draft and ' L ' corresponds to the ballast arrival draft. It is understood that light draft ' L ' should correspond to sailing condition only. The general formula for computing the attained index is shown in Eq. 10.
The subscript ' C ' represents one of the three loading conditions shown in Eq. 9. The subscripts ' i ' represent each investigated damage or group of damages and ' t ' is the number of damages to be investigated to calculate C A for the particular loading condition. The probability factor ' i p ' is dependent on the geometry of the watertight arrangement of the ship. In case of double hull ships, a reduction factor ' r ' is computed based on the double hull geometry. The probability that only double hull space is flooded is shown in Eq. 11a. The probability that both the double hull space and adjacent inboard compartment is flooded is shown in Eq. 11b.
The factor ' i v ' is dependent on the geometry of the watertight arrangement (decks) of the ship and the draught of the initial loading condition. It represents the probability that the spaces above the horizontal subdivision will not be flooded. The factor ' i s ' is the survivability of Study on the lightship characteristic of merchant ships Sree Krishna Prabu Chelladurai, Vishwanath Nagarajan, Om Prakash Sha 61 the ship after the considered damage for a specific initial condition. It is computed as shown in Eq. 12. LCG which will satisfy all the rule requirements will be taken as the new limit. Each ship design is checked for survivability in case of damage.
After summarizing all possible damage cases from the three load cases, the survivability are estimated for single/ multiple compartment flooding. For all the methods, safety of ships against sinking/ capsizing in case of loss of their watertight integrity is the main concern of regulatory bodies. The analysis is concluded by computing limits of LS LCG and LS KG for different loading condition. Finally, to evaluate survivability criteria, the attained subdivision index must be more than the required subdivision index.

Results and discussion
The upper and lower limit of LS

LCG
for different ship types determined from intact stability regulations is shown in Fig. 11. The lies between midship to forward of midship. The trend of PCC and LPG carrier is also similar. Container and PCC ships have significant quantity of cargo loaded above the main deck of the vessel. As a result, LS LCG also move towards forward compared with other ship types. Also, it is evident from Fig. 11 Fig. 13. The results demonstrate the superior damage survivability characteristics of the vessel as compared to the minimum rule requirement. This shows that the internal subdivisions applied for the vessels are satisfactory. The probabilistic damage stability criteria requirement applicable for different ship types are shown in Table 4. The required subdivision index for each vessel was computed as per rule requirement. The attained subdivision index was computed for 3 different loading conditions for each ship type. These were then added after multiplying with the respective weighting factors as specified in the rules. The variation of subdivision index for different ship types is shown in Fig. 14. Figure 14 demonstrates that all the ship types have achieved probabilistic damage stability requirements. For the same length, the attained subdivision index for different ship types is different. There is contribution of geometric layout of the transverse and longitudinal subdivision bulkheads and the Damage

KG
value as shown in Fig. 16. On the other hand, when damage occurs in crude oil tanker, LNG and LPG tanker, the cargo escapes into sea or atmosphere decreasing the displacement of vessels. The decrease of displacement reduces the limiting LS KG value as shown in Fig. 16. From Fig. 16 it is observed that for some ship types limiting LS KG / D is > 1.0. For merchant ships this is an unlikely scenario. This is because most of the hull weight is located at a height less than D . Only the accommodation weight is located at a height above D . But accommodation weight is much less as compared to other lightship weight components. In merchant ships the lightship weight is usually much less than the deadweight component. Most of the deadweight components are located at height less than D except in case of some volumetric carriers. Therefore, we have the benefit of keeping the LS KG higher, although it will never be utilized during actual ship design.
The present work is validated for each one of the ship designs, namely tanker, bulk carrier LNG/ LPG carrier, container and car carrier. One unique vessel (9 th design) is selected for validation for oil tanker and bulk carrier. While for the other ship types the validation vessel is chosen from the existing ship designs. The selected vessels are designed as per the general arrangement and criteria requirement as we discussed earlier. For validation, LS LCG is assumed as 0.3 bp L (forward of midship) for all the investigated ship types. This LS LCG is outside the limit shown in Fig. 15. With this value of LS LCG stability criteria requirements are checked. During this time the KG is kept as actual value. The results are presented in Fig. 13. Figure 13 shows that crude oil tanker, and LNG/ LPG carriers do not meet the stability requirements when LS LCG = 0.3 bp L . Similarly, it can be noticed from Fig. 14 that bulk carrier, container and PCC ships also do not meet the stability requirements. When LS LCG is kept outside the limit shown in Fig. 15, vessels experience unusual trim. The excessive trim causes the vessel to fail to meet the stability requirements shown in Fig. 13. Similarly, validation is carried out by assuming KG exceed beyond certain limits then the vessels will fail to meet the stability requirements. Therefore it is important to keep this in consideration when designing new ship type. For merchant ships, lightship weight is less than the deadweight. Amongst merchant ships, for deadweight carrier lightship weight is much less than the deadweight as compared to volumetric carriers. Therefore for deadweight carriers LS KG limit may come higher than the ship's depth. This scenario is unlikely because LS

KG
should be within ship's body dimensions. Besides the lightship weight, and limiting LS KG and LS LCG , its distribution along the ship's length is also important. This will have a significant influence on the variation of shear force and bending moment in waves. This will be investigated in our future work.