drill ship dissertation_sachin kumar

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5/19/2018 DrillShipDissertation_SachinKumar-slidepdf.com http://slidepdf.com/reader/full/drill-ship-dissertationsachin-kumar 1/267  PROJECT REPORT “ “ “ANVESHAK ANVESHAK ANVESHAK ANVESHAK” ” DESIGN OF A 4500 FEET RWD DRILL SHIP Thesis submitted in partial fulfillment of the Requirements for the Award of The Degree of Bachelor of Technology In Naval Architecture & Ship Building BY SACHIN KUMAR DEPARTMENT OF SHIP TECHNOLOGY COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY COCHIN-682022 2011

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This is Final year academic project copy of Sachin Kumar. Please note it doesn't include Drawings as drawings were drawn by hand on paper sheets.

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  • PROJECT REPORT

    ANVESHAKANVESHAKANVESHAKANVESHAK

    DESIGN OF A 4500 FEET RWD DRILL SHIP

    Thesis submitted in partial fulfillment of the Requirements for the Award of

    The Degree of

    Bachelor of Technology

    In

    Naval Architecture & Ship Building

    BY

    SACHIN KUMAR

    DEPARTMENT OF SHIP TECHNOLOGY

    COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY

    COCHIN-682022

    2011

  • Certified that this is a bonafide record of the thesis submitted in partial fulfillment of the requirements for the award of the Degree of

    Bachelor of Technology

    In

    Naval Architecture and Ship Building

    By

    SACHIN KUMAR

    Department of Ship Technology Cochin University of Science and Technology

    Cochin-682022

    Thesis approved by Thesis accepted by

    Dr. K. Roby Reader Department of Ship Technology, Cochin University of Science and Technology. Kochi-682022

    Dr. Ing K.P. Naraynan Head of the Department, Department of Ship Technology, Cochin University of Science and Technology. Kochi-682022

  • AcknowledgementAcknowledgementAcknowledgementAcknowledgement I take this opportunity to express my sincere gratitude to one and all who have helped me through this thesis. Firstly, I would like to thank my guide and mentor, Dr. K. Roby, for the immeasurable help he lent me during the course of my project. I am also thankful to Dr Dileep k Krishnan, Dr. K Siva Prasad and all other faculty members of the Department for their timely help and advice. The technical support lent by the Department Library and the Computer Lab was also outstanding. I am thankful to IHC Holland , Gusto Engineering and Mr. J.P. Singh for providing me with technical support and advice.

    Patience, understanding and enthusiasm of challenging task played a major factor in the completion of this thesis. The wholehearted cooperation, affection and timely help of my classmate Chandan Kumar and juniors specially Amit kumar, and Abdusalam are remembered with great appreciation and gratitude.

    Above all I would like to thank God Almighty for harboring me safely this far.

    Sachin Kumar Batch XXXII Department of Ship Technology CUSAT Cochin 22

  • DEDICATED TO SINCERITYDEDICATED TO SINCERITYDEDICATED TO SINCERITYDEDICATED TO SINCERITY

  • ASSIGNMENT SHEET

    COCHIN UNIVERSITY OF SCIENCE & TECHNOLOGY (CUSAT) DEPARTMENT OF SHIP TECHNOLOGY

    KOCHI 682022 INDIA

    Ship Design Project Work Assignment Sheet

    (VIII Semester)

    Student Name : Mr Sachin Kumar

    It is to design a Drill Ship

    The ship should have the following parameters:

    Rated Water Depth : 4500 Feet

    Transit, Service : 12Kn

    Endurance : 75 Days

    Classification Rules : Det Norske Veritas

    Signature of Project Guide

  • OWNER REQUIREMENT /THE DESIGN PROBLEM

  • AIM OF THE PROJECT

    Aim of the project is to prepare a preliminary design to meet the given requirements.

    Rated Water Depth : 4500 Feet

    Transit Speed : 12 knots

    Endurance : 75 Days

    Classification Society : Det Norske Veritas

    Ship Classification : DNV MODU +1A1, POSMOORATA,

    DRILL, HELDK, CRANE

    Type : Drill Ship

    All approximations, assumptions and formulae are based on references quoted. Symbolic notations are based on the above Classification Rules.

  • Department of Ship Technology, CUSAT, B.Tech (NA&SB), Batch XXXII

    LIST OF DRAWINGS

    Sheet No: Title Dwg No.

    1 LINES PLAN XXXII/01

    2 HYDROSTATIC CURVES XXXII/02

    3 GENERAL ARRANGEMENT XXXII/03

    4 MIDSHIP SECTION XXXII/04

  • Department of Ship Technology, CUSAT, B.Tech (NA&SB), Batch XXXII

    NOMENCLATURE

    Awp - Area water plane

    A - Area of Midship

    B - Overall Breadth of the ship b - Breadth of Demihull BM - Distance from Center of Buoyancy to Metacenter CB - Block Coefficient

    CB8 - Block Coefficient at 80% Depth CF - Coefficient of Frictional Resistance

    CG - Center of Gravity CM - Midship Area Coefficient CP - Prismatic Coefficient CR - Coefficient of Residual Resistance CT - Coefficient of Total Resistance CW - Water plane Area Coefficient

    D - Depth

    Dwt - Dead Weight E - Lloyds Equipment Number Fn - Froude Number g - Acceleration due to Gravity GM - Distance from Center of Gravity to Metacenter

    GMo - Initial Metacentric Height GZ - Righting Arm

    ILLC - International Load Line Convention IL - Longitudinal Moment of Inertia IMO - International Maritime Organization IT - Transverse Moment of Inertia

    J - Advance Coefficeint KB, VCB - Vertical Height of Center of Buoyancy

    KG, VCG - Vertical Height of Center of Gravity Kn - Knots

  • Department of Ship Technology, CUSAT, B.Tech (NA&SB), Batch XXXII

    KN - Normal Distance from Keel to GM Line KQ - Torque Coefficient

    KT - Thrust Coefficient LBP, L - Length between Perpendiculars LCB - Longitudinal Center of Buoyancy LCF - Longitudinal Center of Floatation LCG - Longitudinal Center of Gravity LOA - Length overall

    LWL - Load Water Line MARPOL - Marine Pollution (A convention of IMO) MCT1cm - Moment to Change Trim by 1cm n - Number of revolutions per second nm - Nautical Miles

    PB - Break Power

    PD - Delivered Power PE - Effective Power

    RA - Model-ship correlation resistance RB - Additional Pressure resistance of bulbous bow Rapp - Appendage Resistance RT - Total Resistance of the Ship Rf - Total frictional Resistance

    RW - Wave making & Wave breaking Resistance S - Wetted Surface Area of the Ship s - Frame Spacing Sc - Separation distance between hulls SFC - Specific Fuel Consumption SOLAS - Safety of Life at Sea (A convention of IMO) T - Draft

    t - Thrust deduction fraction TPC - Tonnes Required per Centimeter of Immersion Vs - Service Speed Va - Velocity of Advance.

  • Department of Ship Technology, CUSAT, B.Tech (NA&SB), Batch XXXII

    Vj - Jet Inlet Velocity

    w - Wake fraction

    Z - Section Modulus

    - Mass Displacement

    BG - Mass of Baggage

    CR - Mass of Crew

    EP - Engine Plant Mass

    FO - Mass of Fuel Oil.

    FW - Mass of Fresh water.

    LS - Light Ship Mass

    OU - Outfit Mass

    PS - Mass of Passengers

    SE - Steel Mass

    ST - Mass of Stores.

    - Volume Displacement H - Hull efficiency

    t - Shaft Efficiency

    oa - Overall Propulsive Coefficient - Density

    fo - Fuel Oil bo - Base Oil dw - Draw Works wb - Water Ballast fw - Fresh Water

  • CONTENTS 1. Introduction.... 1

    2. Fixing of Main Dimensions......14

    3. Hull Geometry ... ..49

    4. Resistance and Powering.. ..66

    5. Station keeping.97

    6. Floating Drilling method....104

    7. Final General Arrangement....114

    8. Drill floor..140

    9. Helideck...147

    10. Capacity...158

    11. Trim stability...167

    12. Midship Section Design..191

    13. Outline Specifications.219

    14. Discussion on the design and conclusion..229

    15. Special Assignment. ...233

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 1

    CHAPTER-1.

    INTRODUCTION

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 2

    1.1 Drill rigs :

    There are two main categories of drilling rig structures used offshore: A. Mobile bottom- supported and floating rigs

    B. Stationary production structures used exclusively for development wells

    The first category of mobile structures includes the following rigs: a. Jack-up rigs

    b. Submersible rigs (swamp barges)

    c. Anchor-stationed or dynamically positioned semisubmersible rigs

    d. Anchor-stationed or dynamically positioned Drillships

    There is a guideline to choose roughly the type of offshore drilling rigs according to water depth and conditions of sea state and winds: - Water depth less than 25 m: submersible rigs (swamp barges) - Water depth less than 50 m and calm sea: tender or jack-up assisted platforms - Water depth less than 400 m and mild sea: self-contained platforms - Water depth from 15 m to 150 m: jack-up rigs - Water depth from 20 m to 2000 m: anchored drillships or semisubmersible rigs - Water depth from 500 m to 3000 m: drillships or semisubmersible rigs with dynamic positioning system

    - Isolated area with icebergs: drillships with dynamic positioning system - Severe sea conditions: semisubmersible rigs or new generation drillships

    1.2 Drillship: A drillship is a maritime vessel that has been fitted with drilling apparatus. It is

    most often used for exploratory drilling of new oil or gas wells in deep water but can also be used for scientific drilling. Unlike the semi submersible and the Jackup, it does not require tugboats to tow it to location. It can also drill in very deep waters. The drillship can also be used as a platform to carry out well maintenance or completion work such as casing and tubing installation or subsea tree installations. It is often built to the design specification of the oil production company and/or investors, but can also be a modified tanker hull outfitted with a dynamic positioning system to maintain its position over the well. In order to drill, a marine riser is lowered from the drillship to the seabed with a blowout preventer (BOP) at the bottom that connects to the wellhead.

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 3

    Drill ship is an adaptation of a standard seagoing ship of mono-hull form with the addition of a substructure with a moon pool and/or cantilevers from which the drilling operations may be carried out. It is well known that ship type drilling units are very susceptible to wave action and will tend to move in a direct relationship with the sea state encountered. Since the vessel is connected to the seabed by a riser and the drill string is in contact with the bottom of the bore hole, motions of the vessel with respect to the seabed are extremely important to be able to maintain the drilling posture.

    Drillships are exactly as they sound: ships designed to carry out drilling operations. These boats are specially designed to carry drilling platforms out to deep-sea locations. A typical drillship will have, in addition to all of the equipment normally found on a large ocean ship, a drilling platform and derrick located on the middle of its deck. In addition, drillships contain a hole (or 'moonpool'), extending right through the ship down through the hull, which allow for the drill string to extend through the boat, down into the water. Drillships are often used to drill in very deep water, which can often be quite turbulent. Drillships use what is known as 'dynamic positioning' systems. Drillships are equipped with electric motors on the underside of the ships hull, capable of propelling the ship in any direction. These motors are integrated into the ships computer system, which uses satellite positioning technology, in conjunction with sensors located on the drilling template, to ensure that the ship is directly above the drillsite at all times

    1.3 History of Drill Ships : The first offshore well was drilled in 1947 in the Gulf of Mexico by a drilling

    ship, at a water depth of 6 m. The first drilling ships were usually old colliers, whalers or cruisers, with their hulls suitably adapted to make an opening, still known as the moon pool, vertically above the centre of gravity. The derrick was installed above this, together with the relevant equipment. The deck was organized to accommodate the tubular materials, while the pumps and the mud treatment plant were housed in the hold. Modern drilling ships are designed and built specifically to act as drilling sites and they are equipped with particularly complex technological systems. Drilling ships are used for operating in deep waters, often under extreme environmental conditions, such as drilling in arctic areas. To this day it is the best means of drilling exploratory wells in remote areas, far removed from supply points, as it can carry all the material necessary

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 4

    for drilling even a particularly difficult well. Just as for semi-submersible rigs, drilling ships are kept in a vertical position over the well by means of mooring or dynamic positioning systems. These ships when moored can be used for drilling in depths of up to about 1,000 m, while for greater depths dynamic positioning systems must be used, and with these the ship is capable of operating in 3,000 m of water. In this case, the depth limit depends only on the weight and the mechanical strength of the connecting system with the subsea wellhead.

    1.4 Features of Drill Ship : 1.4.1 The mooring system

    The traditional positioning system for a vessel foresees the use of mooring lines with cables or chains which run from the hull and become fixed to the seabed by anchors, arranged according to schemes depending on the geometry of the vessel and on the expected sea and weather conditions. In general, drilling ships have three or four pairs of mooring lines at least two lines in the stern, two in the bows and one on each side while semisubmersible rigs have at least one pair on each column at the apexes of the platform. The mooring lines are usually made of various parts, an upper part consisting of a steel cable connected to the vessel, and a lower part, consisting of a chain fastened to the anchor. Should just a single anchor not be sufficient to grip the seabed, two or more anchors in series are used, connected by another chain. The anchors are lowered vertically by a tug using a special cable. The tug tows the anchor to the anchorage, stretching the mooring line, and when the right position has been reached, it lowers the anchor to the seabed so that the flukes become embedded in the bottom. Vertically above each anchor there is a buoy marking its position and facilitating its retrieval when operations are over. In the case of very deep waters (more than 1,000 m), the traditional mooring system requires long, heavy lines, more powerful tugs and lengthy, difficult positioning and retrieval operations, which involve considerably higher costs. The mooring of vessels is programmed according to the force exercised by the wind and the stresses induced by the sea. For example, drilling ships are normally moored with their bows towards the waves and the prevalent winds, if possible, or at least towards the strongest expected force. If the direction of the wind and of the waves changes, the vessels stability can suffer, causing the rolling and the pitching to increase, as also the tension in the mooring lines and the pull on the anchors.

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 5

    If these movements exceed a given limit, drilling has to be suspended and it may be necessary to detach the connection with the subsea wellhead, allowing the vessel to move away safely. Regarding the wind direction, it is as well to remember that it must be possible to safely ignite the flare of the drilling rig at any moment, and that the helicopter landing pad must be accessible during the majority of weather and marine events (the helicopter has to take off into the wind, and the derrick must not hinder this operation). As mentioned, these problems are less serious in floating rigs with dynamic positioning systems, which are able to rotate more easily than anchored rigs.

    1.4.2 The dynamic positioning system An offshore rig can be kept in a relatively fixed position vertically above the

    well also by means of the dynamic positioning system. This technology is necessary when the water depth is such that it is no longer possible to use traditional mooring systems due to the weight of the mooring lines and the excessive elasticity of the system. For this purpose, the vessel must have pairs of screw propellers in the stern, in

    the bows and on both sides, which are always kept working The wellhead, which is always positioned on the seabed when drilling fro floating rigs, is fitted with a device that sends an acoustic signal to the vessel, and under the keel there is a series of hydrophones which pick up the signal arriving from the seabed. This signal is then relayed to an electronic control device, which identifies in real time the position of the vessel in relation to the wellhead and, depending on its movement, it restores its vertical position by varying the speed of one or two pairs of propellers. Compared with a mooring system, dynamic positioning has the advantage of permitting a certain possibility of rotation on the part of the vessel, and therefore permits the best orientation vis--vis the direction of the wind, the currents and the waves. In some cases various systems of measuring the vertical position are used, as the presence of gas bubbles in the water or the interference of the sound of the screws can falsify the hydrophone recordings. It is possible, by means of special devices, to measure the angle of inclination of a cable, connected to a fixed point on the seabed and kept at a constant tension. More refined methods use modern satellite positioning systems, called GPS (Global Positioning System).

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 6

    Fig:1- A typical Drilling vessel with dynamic positioning systems. Pelican Class Drill Ships GustoMSC is the designer of the 'Pelican' class dynamically positioned

    drillships. The 'Pelican' class design has been the market leading design for more than 20 years, performing in various harsh environments all over the world to the satisfaction of the drilling contractors as well as the oil companies. This revolutionary vessel was designed and elaborated in close co-operation between Total, Foramer and GustoMSC. In comparison with earlier drilling units, the 'Pelican' is able to operate in deeper water under worse conditions (arctic and tropical) and is self supporting for a longer time (2 average 3,000 m wells). Moreover, the mobilization time of the vessel is improved due to its minimum sailing speed of 12 knots.

    The vessel is propelled by two controllable pitch main propellers running at a constant speed. The dynamic positioning is effectuated by the

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 7

    two main propellers (in longitudinal direction) generating 60 tons thrust , five transverse propellers (in lateral direction). And Two Azimuth Thrusters (1 Stbd Forward and 1 Port aft) .Three transverse propellers generate 45 tons of thrust at the bow; two transverse propellers generate 30 tons of thrust at the stern. The installed power allows the vessel to maintain its heading within 2 degrees even while subjected to 100 knot winds, 4.9 m waves and surface currents running at 2 knots. The recorded fuel consumption in DP mode is between 15 and 27 tons per day. The accuracy of the positioning management system is largely independent of the percentage of water depth. The position reference measurement system is a short baseline, passive acoustic system. Two tautwire inclinometer systems are used as a back-up system, later complemented with additional dual riser angle sensors. Heave is the main limiting factor for the progress of work aboard. Overall percentage of idle time due to weather was recorded at 6.5 percent. This is a very low figure for a ship-shaped floater. The maximum allowable rig offset before disconnecting is 6 percent of the water depth. The recorded maximum offset did not exceed 3 percent during 93 percent of the time. The only disconnections were prescheduled due to excessive weather or icebergs. The assigned heading variation was kept within 4 degrees for 94 percent of the time.

    Most of the drilling equipment and systems were supplied by renowned manufacturers. GustoMSC designed and built the riser tensioning and heave compensating device. The riser tension is controlled by a hydro-pneumatic system. The vessel's heave is compensated by vertical adjustment of the derrick crown block. This hydraulic system is controlled by a patented GustoMSC Unicode device.

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 8

    1.5 Basis design: The design of the 'Pelican' series drill ships has evolved over the years with

    progressing client requirements. The first units, 'Pelican', 'Havdrill' and 'Petrel' laid the foundation for the enhanced design of the next series of 'Pelerin', 'Polly Bristol', 'Ben Ocean Lancer' and 'Pacnorse I'.'Pelican' design was further enhanced to construct the ice-class drill ships 'Valentin Shashin', 'Mihail Mirchink' and 'Viktor Muravlenko'.

    This demonstrates the versatility of the original 'Pelican' design, not only for new build but also for subsequent upgrades of each of the units in later years.

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 9

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 10

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 11

    1.6 Feasibility Study:

    1.6.1 Exploration Projects The total exploration project is expected to cost $10 billion. The KG-DWN-98

    / l (KG-D6) block lies in the Krishna-Godavari basin 50km off the coast of Kakinada of the Bay of Bengal on India's east coast. The seabed slopes sharply causing water depths to vary between 700m (2,297ft) and 1,400m.

    In March 2003 the deepwater rig Discover 534located Dhirubhai-4, which has in-place gas volumes of 1,700 billion standard cubic feet.

    This fast-track development involved one of the biggest and most complex underwater installation campaigns ever

    1.6.2 Drilling contractors and their day rate TRANSOCEAN:-$ 630,000 a day in west africa

    SEADRILL:- $ 600,000 a day and 4.1 billion for 3 deepwater drill well

    NOBLE:- $646,000 a day

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 12

    In reference to the cost model proposed by Rough Engineering Design report of Drill Ship Nersus $148500000 is found to be reasonable as cost is surely proportion to the RWD so is the Length. Based on This approximation the Break even estimated is in 4 years.

    1.6.3 Few facts regarding oil Industry in India India is the fifth largest energy consumer in the world

    India is the ninth largest crude importer in the world

    Oil and gas industry size is estimated at about 110 billion

    Constitutes about 32 % of Indias imports Huge import bill for the govt.

    India has the worlds sixth largest refining capacity 2,56 million bbls/day representing approx 3 % of world capacity

  • Project Report Introduction

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 13

    From the above scatters it is clear that the oil exploration is an evergreen investment so the project is proved to be economically feasible .

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 14

    CHAPTER 2.

    FIXING OF MAIN DIMENSIONS

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 15

    2.Fixing Of Main Dimension:

    2.1 Preliminary Investigation This is a very important chapter, which deals with the fixing of the main dimensions. For this we make use of the Regression analysis to find out an approximate Variable Deck Load (VDL) corresponding to Rated Water Depth (RWD). In short we plot a graph between VDL and RWD, and then calculate the length for the required VDL by regression. Corresponding to this value of length main particular is calculated and these values are iterated till satisfying all the preliminary condition, which is illustrated below. 2.1.1 Mission Analysis Aim of the project is to perform exploratory drilling .

    Type of ship : Drill Ship

    Rated Water Depth : 4500 Feet

    Drilling Site : KG Basin

    Classification : DNV

    Speed : 12 Kn

    Endurance : 75 Days

    Shape of stern : Transom stern

    2.1.2 Selection of Site :

    To perform the exploratory Drilling , we have these potential areas in sight :

    1)Bombay high,Maharashtra 2)Saurashtra coast,Gujrat 3)Konkan Basin,Goa,Karnataka and Maharashtra 4)Mahanadi Basin,Orrisa 5)Andaman Island 6)Krishna-Godavari Basin,Andhra Pradesh We need to find the site which is most appropriate and reliable, subjected to offshore growth, owners demand and conditions.

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 16

    Bombay High and Saurashtra coast: It has achieved stagnation phase due to monopoly of ONGC in research and exploration in this region. New discoveries are least expected

    Konkan Basin and Mahanadi Basin: It is still in developmental stage.Quality and Quantity is yet to be known precisely. The economics of Drilling is difficult to be estimated in these areas.

    Krishna-Godavari Basin: It is in youth stage.Over the last ten years a lot of construction projects have been started. A huge reserve and potentially profitable business have invited some of top players from the field of oil and gas exploration.

    So after studying various sites KG basin is found to be more suitable site for which the vessel will be designed

    Krishna-Godavari basin is a peri-cratonic passive margin basin in India. It is spread across more than 50,000 square kilometers in the Krishna River and Godavari River basins in Andhra Pradesh. The site is known for the D-6 block where Reliance Industries discovered the biggest natural gas reserves in India in 2002. It was also the world's largest gas discovery of 2002.

    2.1.3 Discoveries

    14 trillion cubic feet of gas by Reliance Industries in KG-DWN-98/l (KG-D6) in 2002. 4200 feet below the sea floor.

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 17

    20 trillion cubic feet (5.71011 m3) cubic feet of gas by Gujarat State Petroleum Corporation in June 2005.

    20 trillion cubic feet (5.71011 m3) of gas at D-3 and D-9 blocks by Reliance Industries in May 2009.

    10 trillion cubic feet (2.81011 m3) of gas by ONGC in June 2009

    The D-6 block includes an area of 1,850km on the KG basin. GSPC is the main operator, with an 80% participating interest. GSPC has already spent more than $0.4bn on drilling ten wells in a 120km offshore area and plans to dig five further wells. The company initially found 20.3 million cubic metres of gas. The KG-21 well is estimated to produce more than 100 million cubic feet of gas a day. This is subject to approval by the director general of hydrocarbons (DGH), Ministry of Petroleum & Natural Gas, Government of India, According to GSPC, a total investment of $1.5bn is to be made in exploration of gas at Krishna-Godavari basin.

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 18

    2.1.4 Geographical Features 1)Location:-Bay of Bengal(between 15 to 17 north latitude) 2)Extended over:- Onland-28000 sq km Shallow water(depth

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 19

    Current Fleet :-Existing 49,Under Construction 37

    Cost of modern drillships has reached over $900 million

    Average Day Rates (as of April 2009)

    4,000 ft WD $355K

    Current Newbuilds - Summary Samsung (SHI)

    20 units based on Saipem 10000 enhanced design or 12000 version,1 unit of Drillmax Ice for Stena Total of 34

    Daewoo (DSME) 5 units based on DSMEs 42 m beam design,4 units based on Gustos Enhanced

    Enterprise design

    Hyundai (HHI) 3 units based on Gustos Enhanced P10000 design

    STX

    1 unit based on Huismans HuisDrill 10000 design

    China / KFELS 1 unit based on MPF 1000 design,2 units based on Gusto PRD 12000 design

    (Bully I & II)

    2.1.7 Shipyard Design Activity Most shipyards that are involved in building drillships are working on

    developing designs for a new generation of compact drillships to support the expected demand in deepwater exploration and production

    Many shipyards that traditionally built ships are looking towards offshore as the next opportunity, especially with Brazils requirements to develop its deepwater fields and a down-turn in the shipping sectors

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 20

    China looking to expand its drillship building capabilities

    2.1.8 Design objective Develop a versatile design on a smaller platform that can do the work of a

    traditional drillship in deepwater and harsh environments by:

    Increasing efficiencies

    Improving safety

    Minimizing single point failures

    Reducing OPEX

    Accommodating emerging technologies

    Reducing Environmental Impact

    2.1.9 Speed, engine plant and propulsion system

    Speed: The vessel is to be designed to function at a service speed of 12 knots.

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 21

    Engine plant: For smooth cargo handling and reduced shaft length, the engine

    room is situated aft. From an analysis of parent ships, 5 4800 kW is required.

    Propulsion system: Twin screw propulsion system is decided for the initial design.

    2.1.10 Superstructures and deckhouses From parent ships, and a general study of Drill Ships, a total of five decks

    including the wheel house is decided upon. A forecastle is present, if in case sufficient bow height is not attained, poop deck and Helideck is also to be provided 2.1.11 Endurance The number of wells a floater will drill in one year varies depending upon transit time drilling equipment, crew , the weather and the problem encountered at different well sites. An average of 5 wells per year is found to be reasonable. This gives an endurance period of 75 days

    2.1.12 Special requirements Since during drilling operation handling of pipes and equipments has to be done with the cargo handling gears onboard so the ship is intended to have its own cargo handling equipment.

    Relevant rules and regulations:

    2.1.13 Rules And Regulations For Drill Ships

    Rules for classification of offshore drilling and support units DNV-OSS-101

    Hull structural design ships with length 100 metres and above DNV

    Guide for the Building and Classing Floating Production Installations (FPI Guide)

    Guide for Building and Classing Facilities on Offshore Installations (Facilities Guide)

    Flag Administration Requirements

    IMO Resolution A.649(16) Code for the Construction and Equipment of Mobile Offshore Drilling Units-Consolidated Edition 2001 (IMO MODU Code)

    MARPOL IMO International Convention for Prevention of Pollution from Ships

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 22

    Compliance to Annex I/Reg. 21 Annex I Regulation 21 Special requirements for drilling rigs and other platforms

    ICLL 1966 IMO International Convention of Load Lines Type-B Freeboard

    ITC 1969 - IMO International Convention on Tonnage Measurements of Ships

    COLREGS 1972 - IMO International Convention for the Prevention of Collisions at Sea

    INMARSAT Convention on the International Maritime Satellite Organization

    ILO Conventions 92, 133, and 147

    MARPOL Annex IV, Sewage Pollution Prevention

    MARPOL Annex V, Garbage Management

    MARPOL Annex VI, International Air Pollution Prevention 69

    2.2 Parent ship data: The Drill Ship is designed as a special service craft. Rated Water Depth is the

    main Design parameter. For the fixing of main dimensions empirical relations and ratios are used. These ratios are checked with the given parent ship ratios.

    Source for the data: 1. www.maritimedata.com

    2. www.Rigzone.com

    3. DNV exchange

    4. Various journals like Naval Architect, S&B International etc.

    Various ships in the Rated Water Depth of 4000 and 5000 are selected as Parent Basis Ships. Ships with ice breaking capabilities were discarded, as they dont comply with the requirements for this vessel. The parent ship data are as given on Table 2.1.3

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 23

    SL NO Name RWD(Feet) LBP(m)

    B(with sponsons (m) D(m) T(m) V(kn) CLASS

    1 PEREGRINE 1 4140 136.8 27.81 12.65 7.4 13 DNV

    2 D/S DEEP VENTURE 4200 136.8 28 12.65 7.4 13 DNV

    3 NOBLE MURAVALE 4600 137 29.8 12.7 7.4 14 BV

    4 SC LANCER 4921 138 28.2 12.7 7.4 12 BV

    5 NOBLE PHOENIX 5000 137 27.4 12.5 7.5 12 DNV

    5 NOBLE DISCOVERER 5000 138 29.75 12 7.4 12 DNV

    Table 2.1

    SL NO Name L/B B/T T/D L/D B/D Fn

    1 PEREGRINE 1 4.92 3.76 0.58 10.81 2.20 0.18

    2 D/S DEEP VENTURE 4.89 3.78 0.58 10.81 2.21 0.18

    3 NOBLE MURAVALE 4.60 4.03 0.58 10.79 2.35 0.20

    4 SC LANCER 4.89 3.81 0.58 10.87 2.22 0.17

    5 NOBLE PHOENIX 5.00 3.65 0.60 10.96 2.19 0.17

    5 NOBLE DISCOVERER 4.64 4.02 0.62 11.50 2.48 0.17

    TABLE 2.2

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 24

    2.3 Classification and Analysis of Data: 2. 3.1 Determination of length and ratios from parent ship From the selected parent ship the most appropriate length and ratios can be determined by curve fitting method for a given Rated Water Depth (4500 feet). [Ref : Computer methods for ship surface design by Chengikuo]

    a) Determination of length : Using the least square method in curve fitting The equation of straight line (trend line) is assumed as

    Y = Ao + A1 X

    Y - Ao1 - A1X = 0 (1) XY - AoX - A1X2 = 0 (2)

    Where Ao and A1 can be determine by the equations From the parent ship data ,table 2.2 below can be derived

    DEPTH vs LBP

    Rated water Depth (Feet) LBP(m) RWD *LBP RWD2

    4140 136.8 566352 17139600 4200 136.8 574560 17640000 4600 137 630200 21160000 4921 138 679098 24216241 5000 137 685000 25000000 5000 138 690000 25000000 sum total 27861 823.6 3825210 130155841

    Y, 1=n=13, X, XY and X2

    Y=44000, 1=n=5, X=22861, XY=201686900 and X2=105155841

    Putting the above values in ( 1) and ( 2 ) we get

    A0 =5102.53 and A1 =0 .8086

    Final equation is Y = 0.0084x + 41.242 (3)

    To get length for DEPTH 4500 Feet put X = 4500

    Y= 137

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 25

    Similarly different ratios like L/B, B/D, B/T, L/D and Froude number (Fn) can be estimated as given below. Put the value of X as 4500 to get the appropriate ratios. The ratios thus estimated are as follows.

    b) Determination of L/B

    L/B = 4.6 c) Determination of L/D

    L/D vs RWD

    Rated water Depth (Feet) L/D

    RWD *L/D RWD2

    4140.00 10.81 44770.91 17139600.00 4200.00 10.81 45419.76 17640000.00 4600.00 10.79 49622.05 21160000.00 4921.00 10.87 53472.28 24216241.00 5000.00 10.96 54800.00 25000000.00 5000.00 11.50 57500.00 25000000.00 sum total 27861.00 65.74 305585.00 130155841.00

    L/D = 10.96

    L/B vs RWD

    Rated water Depth (Feet) L/B

    RWD *L/B RWD2

    4140.00 4.92 20365.05 17139600.00 4200.00 4.89 20520.00 17640000.00 4600.00 4.60 21147.65 21160000.00 4921.00 4.89 24081.49 24216241.00 5000.00 5.00 25000.00 25000000.00 5000.00 4.64 23193.28 25000000.00 sum total 27861.00 28.93 134307.47 130155841.00

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 26

    d) Determination of B/D

    B/D vs RWD

    Rated water Depth (Feet) B/D

    RWD *B/D RWD2

    4140.00 2.20 9101.45 17139600.00 4200.00 2.21 9296.44 17640000.00 4600.00 2.35 10793.70 21160000.00 4921.00 2.22 10926.94 24216241.00 5000.00 2.19 10960.00 25000000.00 5000.00 2.48 12395.83 25000000.00 sum total 27861.00 13.65 63474.38 130155841.00

    B/D = 2.38

    e) Determination of B/T B/T vs RWD

    Rated water Depth (Feet) B/T

    RWD *B/T RWD2

    4140.00 3.76 15558.57 17139600.00 4200.00 3.78 15891.89 17640000.00 4600.00 4.03 18524.32 21160000.00 4921.00 3.81 18753.00 24216241.00 5000.00 3.65 18266.67 25000000.00 5000.00 4.02 20101.35 25000000.00 sum total 27861.00 23.05 107095.80 130155841.00

    B/T = 3.95

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 27

    2.3.3 Sketches (Not to scale) The approx general arrangement, cargo tank distribution etc. are analyzed from

    Noble Discoverer(Name of vessel). Some typical features of Drill Ships can be noted: [Ref : www.rigzone.com]

    1. The engine room is amidships. 2. Cylindrical tanks are used for carrying cement. 3. Cargo handling equipment are on the deck. 4. Adequate tank capacities for drilling cargo to be carried.

    2.4 First estimates of displacement/volume: Preliminary calculation of displacement is based on the coefficient of deadweight, CD CD = Deadweight/Displacement For Drill Ships the value of CD falls in between 0.4 and 0.55. So CD is taken as 0.42, Variable deck load is the function of Rated water Depth. Which is determined form the basis ship and thus is treated as owners requirement, Then the preliminary displacement can be estimated as,

    Displacement, = 8800/0..42 = 20952 t.

    2.4.1 First estimates of main dimensions and coefficients The process of arriving at the design requirement i.e., finally at the main dimensions of the vessel is based on the optimization of the hull form using non- dimensional ratios and coefficients. The concept is to find the average of parent ship main particulars of

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 28

    each ship such as L/B, L/D, B/D etc: and then using empirical relation, the range of length is fixed. From the graph plotted RWD and VDL, we get the length of the vessel corresponding to the VDL to be used . In the design procedure, the coefficients also play an important role.

    Factors to be considered during selection of Ratios: - 1). L/D: - Deflection and structural strength is influenced by L/D ratio 2). L/B - Low L/B means, Higher Stbility, and hence lower power is required to operate the ship

    - Building cost is high - Restriction on Breadth and Depth and Depth during voyage plays an important role in the selection of L/B 3). B/T - B/T governs the stability as BM = f (B). 4). T/D - This ratio must be reduced as much as possible so as to increase the freeboard.

    2.4.2 Length between perpendiculars (LBP) Parent ship analysis gives

    LBP = 137 m Breadth = 29.75 m Depth = 12.5 m Draft = 7.5 m

    2.5 Mass estimation:

    Here only an approximate judgment of light ship mass can be done as the thickness of plates are unknown. In the preliminary design stage, the lightweight of the ship can be estimated either by the method suggested by Lamb or by Watson and Gilfilan. According to Lamb, the lightweight is subdivided into 4 groups, viz. steel mass, wood and outfit mass, hull engineering mass and machinery mass. But this method cannot be used because it wont take into account ships having wide openings such as moon pool. Therefore the method given by Watson and Gilfilan is used.

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 29

    According to Watson and Gilfilan, the lightweight is subdivided into three groups namely- steel mass (MSE), outfit mass (MOU) and engine plant mass (MEP). The respective masses and their centres of gravity are calculated in the following sections.Details of each weight category is approximated by the relative Rated Water Depth parameter of Ship.It was further matched as maximum as possible with the specifications of standard equipments/practice

    2.5.1 Lightweight Estimation Table 2.3

    Drilling Equipments Item weight(tonnes) LCG from AP(m) VCG from base Group DP System 426 78.27 2.83 Group equip on celler deck 426 68.35 9.02 Group equip on main deck 639 68.35 12.50 Group equip on drill floor 639 68.35 25.40 Group equip under derrick 64 68.35 65.22

    Total drilling equip mass 2195 70.28 15.25

    Electrical Equipments Item Equipments in control room 264 35.24 9.73 Eqipments on main Deck 264 68.50 12.50

    Total Electrical Equipment Mass 527 51.87 11.11

    Steel mass Item Hull 5060 74.87 5.97 Forcastle Deck 197 120.32 15.60 Poop Deck 130 7.15 15.60 accomodation space 382 111.19 20.23 Heliport 129 69.81 21.52 Substructure 234 68.35 16.30 Group Derrick 160 68.35 42.39 Mooring system 65 71.30 15.60

    Total Steel Mass 6357 76.54 9.03

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 30

    Outfit mass Item outfit on Helideck 35 0.00 26.75 Outfit on main deck 750 68.50 12.50 accomodation Space 960 94.11 10.38

    Total outfit Mass 1745 81.22 11.62

    CG OF ENGINE PLANT MASS

    Item weight(tonnes) LCG from AP(m)

    VCG from base

    C.P Propellers & Thrustes 9.8 3 2.6 Shaft 11.4 10.7 3 Generator Set 240 23.85 8.31 Hull Engineering D.B. Level 133.7 69 3.2 Celler Deck Level 133.7 69 8.3 Auxiliary m/c room 136 8.75 8.95 Propulsion Room 600 26.55 3.85 Engine Plant Mass 1264.6 32.77398 5.629314

    CG of Lightship weight

    Item weight(tonnes) LCG from AP(m)

    VCG from base

    Steel Mass 6357 76.54 9.03 Outfit Mass 1745.00 81.22 11.62 Drilling Equipment Mass 2195 70.28 15.25 Electrical Equipment Mass 527 52.25 10.23 Engine Plant Mass 1264.6 32.77398 5.629314 Light Ship Mass 12089.2122 70.43952 10.23201

    TABLE 2.4

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 31

    Deadweight distribution

    Item weight(tonnes) Drill Pipe Casing Tools Etc 1350 Riser Pipes 350 Bop Stack 170

    Barytes 6 silos

    800

    Bentonite 1 silos

    Cement 7 silos

    Sack Storage 500 Liquid Mud 270 Chemicals 75 Drill Water 1700 Total Mass Of Cargo 5195 Mass Of Stores 3581 Total Deadweight 8795

    2.5.1 Displacement

    Displacement () = LBTCB1.025 (1+0.006) [Ref: 11] Where 0.006 is a side shell correction factor, and 1.025 is the density of seawater in t/m3

    2.5.2 Water plane area coefficient CW = 0.76CB + 0.273 for normal sections [Ref :2] = 0.76 0.8095 + 0.273

    = 0.78

    2.5.3 Midship Section Coefficient [Ref:2] CM = 0.9 + 0.1CB

    = 0.9 + 0.10.8095

    = 0.97 2.5.4 Prismatic Coefficient CP = CB/CM

    = 0.882/0.981 = 0.68

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 32

    2.6 Preliminary Check on Stability: 2.6.1 Prohaskas stability computation method A preliminary check on stability is done by Prohaskas method . Prohaskas method in short can be stated as to find GZ, calculate D/B and T/B of the vessel and see the values h1 in the plot of Prohaskas curves, to determine the stability at various angles of heel. The formula used [5] (i) CW = 0.743CB + 0.297 = 0.7926 (ii) KB = [CW / (CW + CB)] * T = 4.072 m (approx) or KB = 0.52 T = 3.9 m

    (iii) BM = C1t * B2/ (12 CB T) Murray formula [8

    where , C1t = 0.13 CW + 0.87 CW2 + 0.005 = 0.654 BM = 0.654 29.752 / (12 * 0.667 * 7.5) = 9.64 m (iv) KG = 0.56D TO 0.58D

    = 7.1 m

    (v) GM = KB + BM KG = 3.987 + 9.64 7.1 = 6.527 m

    (vi) D/B = 12.5/29.75 = 0.42

    (vii) T/B = 5.4/15= 0.252

    GZ = GM Sin + BM * h1

    where the notations carry their usual meaning. The computed table of GZ can be summed up as : GM/B should be between 0.08 and 0.12 for sea going vessels GM / B = 6.527/ 29.75 = 0.219 This is in excess of what is required for a normal seagoing vessel.which is prove to be advantageous in order to serve for station keeping requirement ie lesser motion.Note this is achieved due to added breadth by sponsons tank.

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 33

    Conclusion The stability criteria are satisfied by Prohaskas method. However, Drill ships

    have typical hull form lesser L/B ratio which is the cause of highly increased stability . Detailed calculations will be followed in the later stage.

    L = 137m

    B = 29.75m D = 12.5m T = 7.5 m CB = 0.667

    = 20890 t

    E = 6167.9

    SE7 = 6566.66

    PB = 4860 kW CB8 = 0.7

    SE = 6579.79 t

    OU = 1134.083 t

    EP = 989.165 t

    LS = 8667.024 t

    Dwt = 8800 t

    2.7 Preliminary General Arrangement: [Ref: 6]

    The General Arrangement is done in order to calculate, initially, the volume of holds, and do a capacity check. The G.A. gives a detail picture of how the vessel looks, position of holds and various allocation of rooms. The various spaces allocated are: 1) Cargo space 2) Machinery space 3) Storage for fuel and stores 4) Ballast Tanks The requirements on the spaces which have to be met are:

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 34

    1) Watertight subdivision and integrity 2) Structural integrity 3) Adequate stability 4) Adequate access to spaces

    Preliminary G.A. is based on this, and subsequently during the design of the final G.A., the allocation for the spaces of the crew is done.

    2.7.1 Location of machinery spaces Every mechanically propelled ship must have sufficient machinery space. Most ships now-a-days have machinery space located aft., thereby reducing shaft length and increasing cargo handling facilities. For now, the engine room is assumed located aft. 2.7. 2 Minimum number of bulkheads (DNV Pt.3 Ch.2 Sec.3 A) Form the DNV Classification Rules, the ship is required to have 6 bulkheads, inclusive of fore, aft and engine room bulkhead.

    2.7.3 Position of frames (DNV Pt.3 Ch.1 Sec.3 A) a) Frame spacing a) Forward of 0.05L from fore perpendicular s = (470 + L/0.6) mm or 600mm whichever is lesser = (470 + 142.6/0.6) = 707.7mm s = 600mm b) Between 0.05L and 0.2L from fore perpendicular s = (470 + L/0.6) mm or 700mm whichever is lesser = (470 + 142.6/0.6) = 707.7mm s = 700mm c) Between 0.2L from fore perpendicular to 0.15L from aft perpendicular s = (510 + L/0.6) mm or 850 mm whichever is lesser = (510 + 142.6/0.6) = 807.7mm s = 800 d) Between 0.15L from aft perpendicular to 0.05L from aft perpendicular s = (510 + L/0.6) mm or 700 mm whichever is lesser = (510 + 142.6/0.6) = 807.7mm s = 700mm

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 35

    e) Aft of 0.05L from aft perpendicular s = (470 + L/0.6)mm or 600mm whichever is lesser = (470 + 142.6/0.6) = 773.33mm s = 600mm

    Location of frames from aft

    Frames Number of frames Frame spacing

    (mm) Length (m) Aft 6 20 600 12 6 to 31 25 700 17.5

    31 to 141 110 800 88

    141 to 171 31 700 21

    171 to 190 20 600 11.59

    Table 2 .5 Location of frames

    2.7.4 Length of aft peak tank, engine room and fore peak tank Aft peak tank The aft peak bulkhead is situated approximately at 5% LBP from aft perpendicular.

    0.05 182 = 6.85 m [Ref: 4] Fore peak tank: 2.7.5 Location of collision bulkhead [ DNV Pt.3 Ch.1 Sec.3 A] Cargo ships the distance xc from the perpendicular to the collision bulkhead is to be taken between the following limits. For ships with ordinary bow: xc (min) = 0.05 LF xc (max) = 0.08 LF LF = length of the ship as defined in the International Convention of Load Lines 1966 = 142.6 m Collision bulkhead lies between 7.13 m and 11.41 m abaft the reference point. Thus the collision bulkhead was fixed at a distance of 7.8 m from FP. Engine Room: [Ref: 4] The length of the engine room is taken as 15% of LBP = 0.15137 = 20.55 m

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 36

    Selected length of engine room is = 814X34 = 27.676 m 2.7.6 Height of superstructure

    It depends on the required dead visual range Max dead visual range = 1.25L =171.25 m With the help of similar triangle between height of super structure and forecastle deck from the summer load line, minimum height of super structure is 11.1 m. From the parent ship the number of deck in super structure is 4, hence the height of super structure for crew can be taken as 12 m.

    2.8 Initial estimates of consumables, stores and cargo: [Ref: 11] Endurance - 75 days Speed - 12 knots Hours of use - 1800 hrs Compliment - 140 (approx).

    MASS OF STORE

    a. Mass of heavy fuel oil(t) HFO =sfc x PB x hours of travel x10-6

    2300.000 Density of HFO(t/m3) 0.95 Volume of HFO(m3) = 2421.05 HFO HFO ALLOW= 2530.00

    b. Mass of Diesel Oil, DO(t) = HFO/3

    766.67 DO(t) ALLOW = 843.33 Volume of DO. 992.16 c Mass of lube oil(t) 0.04(DO+HFO) 134.93 Volume of LO(m3) = 149.93

    d Mass of fresh water(t) =

    Volume x complement x days of voyagex10^-3

    1060

    Volume of fresh water = 1060.00

    e mass of provision(t) = 64.35

    f) mass of crew and Effect(t) = 21.45

    g Mass of stores(t) = 4347.40

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 37

    Therefore we see that the total weight of the consumable stores is 4347.4 t.. It is adequate volume for drill cargo to be carried, thus the volume check has been successful..

    2.9 Check On Displacement : From the design equation,

    Available Displacement () = L B T CB 1.025(1+s) Where s is the shell correction factor it varies between 1.005 and 1.006. 1.006 is chosen. 1.025 is the density of seawater in t/m3

    Available Displacement () = 18227.510.50.8111.0251.006 = 21024.05 t

    Also,

    Required displacement () = Deadweight +light ship Light ship = steel mass + engine plant mass +

    outfit mass

    = 12089 Dead weight = 8800 t

    = 12089 + 8800 t

    = 20889 t Displacement check is satisfactory

    2.10 Checks on hold and tank capacity

    Preliminary general arrangement of basis ship is referred. For the check of capacity minimum number of bulkheads according to classification rules is 5 provided engine room is located at the aft. Due to the variation in the type of consumables, calculation of stowage factor is extremely difficult. Empirical formulae are used to calculate the volume of holds below the main deck by subtracting other volumes from the enclosed volume of the ship. Volume of holds = (Vdd + Vsh + Vca + Vht + Vhs) - (Vfp + Vap + Vpr + Ver+ Vdb + Vta + Vst)

    Where Vdd - Volume of under deck space

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 38

    Vsh - Volume of sheer

    Vca -Volume of camber Vht - Volume of hatchway trunk

    Vhs - Volume of super structure holds Vfp - Volume of fore peak tanks

    Vap - Volume of aft peak tanks

    Vpr - Volume of pump room

    Vdb - Volume of double bottom Vta - Volume of tanks in hold Vss -Volume of shaft tunnel

    Ver - Volume of engine room

    1) Volume of under deck space

    Vdd = L.B.T.CB.(D/T)CW/CB = 137 * 29.75 * 7.5 * 0.67* (12.5 /7.5)0.792/0.667 = 37412.68 m3

    2) Volume of camber

    = LBP* B*CW* B / 75 = 137* 29.75*0.79*29.75/75 = 1277.2 m3

    3) Volume of aft peak tank

    Vap = Kap * [Lap/LBP]2 *LBP * D *CBD * B Where Kap = 2.16 * (2-k) = 2.2003 where k = (3.33 AB/LBP) - 0.667 = 0.9812 where AB = distance of LCB from AP taken from Townsends chart = 67.81m Lap = 0.06 LBP = 8.22 m CBD = CB + (0.25/T)(D -T)(1-CB) = 0.70 Vap = 282.5 m3 (4) Volume of forepeak tank Vfp = Kfp [Lfp / LBP]2*LBP*B*D*CBD Kfp = 1.7 Kb , b = 1 with ships having V stem

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 39

    = 1.7*0.965*1 = 1.668

    Lfp = 0.07L = 9.59 m Therefore Vfp = 1.668 [9.59 /137]2 * 137 *29.75* 12.5* 0.67 = 278.98 m3 (5) Volume of engine room Volume of machinery space between double bottom and plane (deck at Depth D),it can be considered as a rectangular volume if engine room is at amidships. Ler = 0.15*LBP = 20.55 m Ver = Ler * B * (D-Ddb) * CM = 20.55* 29.75*(12.5-1.2)*0.99 = 6839.31 m3 (6) Volume of pump room Vpr = 3.5 * B* D = 1301.56 m3 (7) Volume of Double bottom Vdb = * [Ddb / To]CW/CB (

    =total under water volume=L*B*T*CB) = 137*29.75*7.5*0.667 * [1.2 /7.5]0.79/ 0.67

    = 2349.46 m3 Note : Vhs = Vht = 0 (as no sheer or hatch) Therefore volume of hold = (Vdd + Vca) - (Vfp + Vap + Ver + Vpr + Vdb = 27637.48 m3 which is large enough to accommodate consumables and other material needed for drilling operation.

    2.11 Preliminary check on Resistance and Propulsion performance: 2.11.1 Resistance calculation by Harvald method [Ref: 7]

    Total resistance, RT = CT (1/2)SV2

    CT = CF + CR + CA CF = coefficient of frictional resistance

    CR = coefficient of residuary resistance

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 40

    CA = allowance for surface roughness = 0.0004 S = wetted surface area

    = 2.5( X L)^0.5 = 2.5 (20890 X 137) = 4229.3 m2

    CF = 0.075/(log10 Rn - 2)2 (ITTC formula) Rn = VL/ = 12X0.5144 137/(1.18810-6) = 7.1 X108 Where,

    = 1.18810-6

    CF = 0.075/(log10 1.182109 - 2)2 = 1.59810-3

    CR is found out from the LWL/1/3 graph A set of 103 CR Vs Froude number are given for different Cp values, for a given

    LWL / 1/3 value For the case in question, LWL / 1/3 = 4.975 But we have curves only for LWL / 1/3 = 5 and 4.5. So we have to interpolate to get intermediate values. For LWL / 1/3 = 5 103 CR = 1.24 For LWL / 1/3 = 4.5 103 CR = 1.15 For LWL / 1/3 =4.975 , by linear interpolation we get, CR = 1.23710-3

    Now go for correction

    1) B/T correction

    B/T = 3.97 Therefore Add correction = 0.16(B/Tdesign-2.5) = 0.16(3.97-2.5) = 0.2352 103 CR = 0.2352

    2) LCB correction

    103CR corrected = 103CR + 103 CR/LCB LCB

    LCB =LCB -LCBSTD

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 41

    LCBSTD is taken from a graph of LBP Vs Fn and it is taken as 2.2386m ford of mid ship. LCB is calculated by using approximate formula as (52% of LBP) = 3.64m ford of Midship.

    LCB = 1.4014

    Corrected value of 103 CR = 0.385 3) Roughness correction (Incremental resistance)

    For L = 130 m , 10 3 CA = 0.2 For L = 200 m 10 3 CA = 0.0

    Hence, for L = 137 m 10 3 CA = 0.2

    4) Air resistance,

    103 CAA = 0.07

    5) Correction for Steering resistance

    10 3 CAS = 0.04

    6) Correction for section shape

    For normal sections there is no correction

    Therefore correction to 103 CR = 0

    7) Correction for bow

    For Abt / Ax < 0.10 no correction Here Abt / Ax = 0 Now 103 CR = (1.236+0.2352+0.385+0.2+0.07+0+0+0.04) = 2.1662 2.11.2 Powering calculation and selection of Main engine

    Propulsion is diesel electric and powering is based on requirements of all the loads for drilling, station keeping and propulsion. So merely on the basis of propulsive co-effecients engine cant be selected. So primary engine selection is done based on basis ship

  • Project Report Fixing of Main Dimensions

    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 42

    Main Engine selection Name : Wartsila VASA 12V32

    RPM : 720 Power at MCR : 4860 kW Bore : 320 mm Stroke : 350 mm Mean effective pressure : 24 bar

    2.12 Initial trim ,Stability and Freeboard calculations

    2.12.1 Stability Calculation (Prohaskas method) Source: Guidelines for the design and construction of ship shaped drilling unit

    - Intact Stability Rules DNV Pt.3 Ch.3 Sec.9 D101 The following stability criteria are recommended (for all ships)

    1) The area under the righting-lever curve (GZ curve) should not be less than 0.055 meter - radians up to = 30 angle of heel and not less than 0.09

    meter radians up to = 40 or the angle of flooding f* , if this angle is less

    than 40 . Additionally the area under the righting lever curve (GZ curve between the angles of heal of 30 and 40 or between 30 and f1 , if this

    angle is less than 40, should not be less than 0.03 meter-radians. 2) The righting lever GZ should be at least 0.20 m at an angle of heel equal to or greater than 30. 3) The maximum righting arm should occur at an angle of heel preferably exceeding 30 but not less than 25 4) The initial metacentric height GMO should not be less than 0.15 m

    The following equivalent criteria are recommended for Offshore Vessels. 1) The area under the curve of righting levers (GZ curve) should not be less than 0.070 meter-radians up to an angle of 15 when the maximum righting lever (GZ) occurs at 15 and 0.055 meter-radians up to an angle of 30 when the maximum righting lever (GZ) occurs at 30 or above. Where the maximum righting lever (GZ) occurs at angles of between 15 and 30, the corresponding area under the righting lever curve should be :

    0.055 + 0.001 (30 - max) meter-radians [11]

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    2) The area under the righting lever curve (GZ curve) between the angles of heel of 30 and 40 or between 30 and f if this angle is less than 40, should

    be not less than 0.03 meter-radians. 3) The righting lever (GZ) should be at least 0.20 m at an angle of heel equal to or greater than 30. 4) The maximum righting lever (GZ) should occur at an angle of heel not less than 15. 5) The initial transverse metacentric height (GMO ) should not be less than 0.15 m.

    Note:

    f is the angle of heel in degrees at which openings in the hull, superstructure or

    deckhouses which cannot be closed watertight immerse. In applying this criterion, small openings through which progressive flooding cannot take place need not be considered as open

    max is the angle of heel in degrees at which the righting lever curve reaches its

    maximum.

    2.12.2 Prohaskas stability computation method A preliminary check on stability is done by Prohaskas method . Prohaskas method in short can be stated as to find GZ, calculate D/B and T/B of the vessel and see the values h1 in the plot of Prohaskas curves, to determine the stability at various angles of heel. The formula used [5] (i) CW = 0.743CB + 0.297 = 0.7926 (ii) KB = [CW / (CW + CB)] * T = 4.072 m (approx) or, KB = 0.52 T = 3.9 m (iii) BM = C1t * B2/ (12 CB T) Murray formula [8

    where , C1t = 0.13 CW + 0.87 CW2 + 0.005 = 0.654 BM = 0.654 29.752 / (12 * 0.667 * 7.5) = 9.64 m (iv) KG = 0.56D TO 0.58D

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    = 7.1 m

    (v) GM = KB + BM KG = 3.987 + 9.64 7.1 = 6.527 m

    (vi) D/B = 12.5/29.75 = 0.42 (vii) T/B = 5.4/15= 0.252 GZ = GM Sin + BM * h1

    where the notations carry their usual meaning. The computed table of GZ can be summed up as : GM/B should be between 0.08 and 0.12 for sea going vessels

    GM / B = 6.527/ 29.75 = 0.219 The requirement is satisfied.

    Constant h* is read from Prohaskas curve, knowing GM, BM and h* corresponding to

    each angle of loll, GZ is calculated (table2.10) and GZ - curve is plotted (figure 2.6). sin GM BM h* GZ angle in rad 0 0 6.527 9.64 0 0 0

    15 0.26 6.527 9.64 0.009 1.77595 0.26 30 0.49 6.527 9.64 0.016 3.41774 0.52 45 0.71 6.527 9.64 -0.08 3.84408 0.79 60 0.87 6.527 9.64 -0.24 3.33895 1.05 75 0.97 6.527 9.64 -0.45 1.9666 1.31 90 1 6.527 9.64 -0.67 0.0682 1.57

    Table 2.6 Table 2.11.1 Prohaskas chart readings

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    GZ values are plotted against to obtain the GZ curve

    Figure 2.4 Initial stability curve From GZ curve, the IMO stability criteria are checked. It is seen from the GZ curve that the range of stability is greater than 90o.

    2.12.3 Check for IMO Regulations

    Specification Recommendations Available

    Area under the graph up to 300 0.055 m rad 0..533 m rad

    Area under the graph up to 400 0.09 m rad 0.898 m rad

    Area under graph between 300 and 400 0.03 m rad 0.365 m rad

    Righting lever at an angle 300 0.2 m 3.84

    Angle of maximum GZ 300 45o

    Initial GM 0.15 3.17 m Table Initial stability check All the stability requirements are satisfied and hence the ship possesses adequate

    2.12.4 Freeboard check The freeboard is measured downwards from the freeboard deck to the

    waterline corresponding to the load line mark. In this case, the main deck is considered as the freeboard. The basic freeboard of a ship depends on the type of ship and its freeboard length. . The freeboard calculation is based on the International Load Line rules(1966 IMCO).

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    Freeboard influences the following: - 1. Reserve buoyancy 2. The angle of deck immersion 3. The stability at large angle of heel Drill Ships are classified as type B ships. The steps involved in freeboard check

    are:-

    1. Note tabular freeboard from the table 2. Calculate the correction for CB

    3. Calculate the correction for depth 4. Calculate the correction for sheer

    5. Calculate correction for superstructure 6. Calculate final freeboard from above results.

    Tabular freeboard Length of ship = 137 m

    Tabular freeboard = 2086 mm [Linear Interpolation from Freeboard table] (i) Correction for CB CB at 0.85 D = Cb+[{1-Cb}*{0.85D-T}/3T] = 0.7133 tf = tabular freeboard Corrected freeboard = tf* (CB0.85+0.68)/1.36 = 2086(0.7133 + 0.68)/1.36 = 2137 mm Correction = 2137 2086 = 51 mm (ii) Correction for depth

    If L/15 120 m Correction = (12.5-9.13) 250= 842.5 mm

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    (iii) Correction for sheer

    The ship has no sheer. Hence correction is applied for sheer deficiency. This means that freeboard is to be increased. Sheer deficiency = (standard sheer aft + standard sheer fore)/16 Sheer aft = 22.23L+667 = 3712.51 Sheer fore = 44.47L+1334 = 7426.39

    Sheer deficiency = 696.18

    Sheer correction =Sheer deficiency * (0.75 S/2L) Where S = 0.2 x L = 0.2 * 137 = 27.4

    Therefore Sheer correction = 696 * (0.75- 27.4/(274)) = 452.4 mm (iv) Correction for superstructure Super structure length is assumed as 0.2L If length of superstructure is same as the length of the ship a deduction of

    freeboard of 1070 mm is permitted for ships with L > 122m.

    But LSS = 0.2 L

    If superstructure is partial the deduction of freeboard is given in the table 2.11.4.

    E 0.1L 0.2L 0.1L 0.2LDeduction 7% 14% 6.30% 12.70%

    Type A Type B

    Table 2.11.4 For E = 0.2L, Linear interpolation gives a deduction of 12.7% for type B ships

    Freeboard correction = -10700.127 = -136 mm

    Summary Tabular freeboard = 2086 mm Correction for CB = 51 mm Correction for Depth = 842.5 mm Correction for superstructure = 136 mm Correction for sheer = 452.4 mm

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    Therefore required freeboard = 3295.9 mm Available excess freeboard = Actual-Required = 1704.1 mm

    So excess freeboard of 1640.5 mm is available hence check has been satisfied. Final Main Dimensions

    LBP 137m

    B 29.75m

    D 12.5mm

    T 7.5m

    CB 0.667 Table 2.7

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    CHAPTER 3

    HULL GEOMETRY

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 50

    Hull Form: The lines trend of a Drill Ship vessel is not so standardized. Most of the times it

    has got Hull Form similar to tanker few examples are there for similarity with OSV too. So during the lines design of a new ship, this has to be taken into account. A reference lines plan of tanker was taken into account and suitably the new lines was designed using Townsends method. Hull form is kept as simple as possible for ease in construction.

    3.1 Final Lines Plan

    In the previous chapter, the main dimensions of the ship are determined as LBP = 137m

    BREADTH = 29.75m DEPTH = 12.5m DRAFT (LWL) = 7.5m CB = 0.67 CM = 1 CP = 0.667 DWT = 8800 t

    With the following details, Townsend s method is used to develop lines. The parent ship selected for the trend of lines is of TANKER and modified it in to DRILL SHIP. There is characteristic feature of Enhanced Pelican Class Drill ship as they have sponson tanks attached to considerable length of hull. The purpose of sponson tank is to provide for greater stability in case of extreme weather conditions.This is found suitable so as to reduce the hull cost and provide extra Deck Space for positioning of heavy cargo handling and other machineries. This also serves as segregated ballast tank. Sponson tanks are fitted depending on the Drilling Site and Future prospects of Ship. As in our condition the environmental condition provided by met ocean data is very rough. So optimum Length and breadth of sponsons are provided.

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    So in order to design the hull form we need to consider the main hull parameters.after subtracting sponson beam the following inputs for hull design are obtained.

    LBP = 137m

    BREADTH = 21.35 m DEPTH = 12.5m DRAFT (LWL) = 7.5m CB = 0.745

    The details from the Townsends chart are, From the chart of AB/LPP Vs CB ____

    AB/ LPP = 0.512 From the AB/ LPP Vs CP chart,

    CPF = 0.785 CPA = 0.732

    The values of ASP/Amax for each station are taken from the charts CPF Vs ASP , CPA Vs ASP

    parabolic camber is provided and again a standard was set by the loadline rules as breadth/50. [ref Watson]

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    TABLE 3.1: Sectional areas obtained from Townsends chart

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    wl/stn -0.83 -0.41 0 0.5 1 1.5 2 3 4 5 6 7 8 to 12 13 14 15 16 17 18 18.5 19 19.5 200 0.376 0.5 0.611 0.72 0.98 1.79 4.29 6.85 8.56 9.37 8.48 6.97 5.91 3.92 2.04 1.06 0.51 0.09

    0.5 0.758 1.15 1.365 1.58 2.65 4.72 6.82 8.63 9.78 10.254 10 8.98 7.57 5.86 4.05 2.5 1.79 1.09 0.391 0.846 1.31 1.615 1.97 3.54 5.86 7.8 9.28 10.2 10.56 10.4 9.62 8.33 6.65 4.72 2.98 2.15 1.33 0.52 0.891 1.47 1.988 2.66 4.9 7.22 8.92 9.94 10.5 10.675 10.7 10.3 9.3 7.66 5.56 3.55 2.52 1.54 0.623 0.929 1.64 2.443 3.44 6.01 8.12 9.52 10.3 10.7 10.675 10.7 10.6 9.89 8.31 6.14 3.94 2.78 1.7 0.784 1.045 1.95 3.062 4.36 7.04 8.85 9.92 10.5 10.7 10.675 10.7 10.7 10.3 8.79 6.6 4.31 3.05 1.88 0.915 1.47 2.73 4.076 5.43 7.87 9.42 10.2 10.6 10.7 10.675 10.7 10.7 10.5 9.13 6.99 4.69 3.4 2.14 1.086 1.5 2.894 4.15 5.364 6.54 8.61 9.85 10.4 10.7 10.7 10.675 10.7 10.7 10.6 9.4 7.37 5.06 3.76 2.46 1.287 0.886 1.8 2.89 4.238 5.43 6.534 7.55 9.23 10.2 10.6 10.7 10.7 10.675 10.7 10.7 10.7 9.64 7.78 45.5 4.21 2.83 1.55

    7.5 1.226 2.35 3.509 4.835 6.016 7.067 9.499 10.31 10.63 10.68 10.7 10.7 10.675 10.7 10.7 10.7 9.755 7.994 5.72 4.43 3.04 1.72 0.338 1.577 2.875 4.1 5.412 6.56 7.563 8.43 9.75 10.4 10.7 10.7 10.7 10.675 10.7 10.7 10.7 9.86 8.21 5.97 4.65 3.25 1.9 0.59 2.318 3.821 5.16 6.47 7.53 8.44 9.2 10.2 10.6 10.7 10.7 10.7 10.675 10.7 10.7 10.7 10.1 8.67 6.5 5.16 3.72 2.28 0.8710 3.066 4.711 6.13 7.43 8.41 9.187 9.8 10.5 10.7 10.7 10.7 10.7 10.675 10.7 10.7 10.7 10.2 9.1 7.09 5.73 4.24 2.74 1.2211 3.852 5.619 7.08 8.333 9.2 9.836 10.3 10.6 10.7 10.7 10.7 10.7 10.675 10.7 10.7 10.7 10.4 9.58 7.71 6.35 4.84 3.32 1.73912 4.631 6.453 7.93 9.149 9.91 10.36 10.6 10.7 10.7 10.7 10.7 10.7 10.675 10.7 10.7 10.7 10.6 10.1 8.38 7.06 5.55 4.01 2.466

    12.5 5.031 6.861 8.34 9.536 10.2 10.57 10.7 10.7 10.7 10.7 10.7 10.7 10.675 10.7 10.7 10.7 10.7 10.3 8.73 7.44 5.93 4.32 2.8

    Table 3.2 Faired Offset without sponsons[All dimensions in meter]

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    Figure 3.1 Body Plan (faired)

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    wl/stn -0.83 -0.41 0 0.5 1 1.5 2 3 4 5 6 7 8 to 12 13 14 15 16 17 18 18.5 19 19.5 200 0.376 0.5 0.611 0.72 0.98 1.79 4.29 6.85 8.56 9.37 8.48 6.97 5.91 3.92 2.04 1.06 0.51 0.09

    0.5 0.758 1.15 1.365 1.58 2.65 4.72 6.82 8.63 9.78 10.254 10 8.98 7.57 5.86 4.05 2.5 1.79 1.09 0.391 0.846 1.31 1.615 1.97 3.54 5.86 7.8 9.28 10.2 10.56 10.4 9.62 8.33 6.65 4.72 2.98 2.15 1.33 0.52 0.891 1.47 1.988 2.66 4.9 7.22 8.92 9.94 10.5 14.875 10.7 10.3 9.3 7.66 5.56 3.55 2.52 1.54 0.623 0.929 1.64 2.443 3.44 6.01 8.12 9.52 10.3 14.9 14.875 14.9 10.6 9.89 8.31 6.14 3.94 2.78 1.7 0.784 1.045 1.95 3.062 4.36 7.04 8.85 9.92 10.5 14.9 14.875 14.9 10.7 10.3 8.79 6.6 4.31 3.05 1.88 0.915 1.47 2.73 4.076 5.43 7.87 9.42 10.2 10.6 14.9 14.875 14.9 14.9 10.5 9.13 6.99 4.69 3.4 2.14 1.086 1.5 2.894 4.15 5.364 6.54 8.61 9.85 10.4 14.9 14.9 14.875 14.9 14.9 10.6 9.4 7.37 5.06 3.76 2.46 1.287 0.886 1.8 2.89 4.238 5.43 6.534 7.55 9.23 10.2 10.6 14.9 14.9 14.875 14.9 14.9 14.9 9.64 7.78 45.5 4.21 2.83 1.55

    7.5 1.226 2.35 3.509 4.835 6.016 7.067 9.499 10.31 10.63 14.88 14.9 14.9 14.875 14.9 14.9 14.9 9.755 7.994 5.72 4.43 3.04 1.72 0.338 1.577 2.875 4.1 5.412 6.56 7.563 8.43 9.75 10.4 14.9 14.9 14.9 14.875 14.9 14.9 14.9 9.86 8.21 5.97 4.65 3.25 1.9 0.59 2.318 3.821 5.16 6.47 7.53 8.44 9.2 10.2 10.6 14.9 14.9 14.9 14.875 14.9 14.9 14.9 10.1 8.67 6.5 5.16 3.72 2.28 0.87

    10 3.066 4.711 6.13 7.43 8.41 9.187 9.8 10.5 10.7 14.9 14.9 14.9 14.875 14.9 14.9 14.9 10.2 9.1 7.09 5.73 4.24 2.74 1.2211 3.852 5.619 7.08 8.333 9.2 9.836 10.3 10.6 14.9 14.9 14.9 14.9 14.875 14.9 14.9 14.9 10.4 9.58 7.71 6.35 4.84 3.32 1.73912 4.631 6.453 7.93 9.149 9.91 10.36 10.6 14.9 14.9 14.9 14.9 14.9 14.875 14.9 14.9 14.9 10.6 10.1 8.38 7.06 5.55 4.01 2.466

    12.5 5.031 6.861 8.34 9.536 10.2 10.57 14.9 14.9 14.9 14.9 14.9 14.9 14.875 14.9 14.9 14.9 10.7 10.3 8.73 7.44 5.93 4.32 2.8Table 3.3 Faired Offset with sponsons[All dimensions in meter]

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    STEM PROFILE

    WATER LINE OFFSET FORM STN 19.5 (m)

    0 -0.1986 0.5 0.8632 1 1.1231

    1.5 1.4206 2 1.7902 3 2.717

    3.75 3.5991 4 3.8258 5 4.7777 6 5.703

    6.25 5.9298

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    Department of Ship Technology, CUSAT, B.Tech. (NA & SB), Batch XXXII 58

    STERN PROFILE

    WATER LINE OFFSET FORM STN 0 (m)

    0 -0.6593 0.5 0 1 0

    1.5 0 2 0 3 -2.5426

    3.75 -5.3075 4 -5.4472 5 4.7777 6 -6.5648

    6.25 -6.705

    3.2 Bonjeans And Hydrostatics Curves:

    Bonjean curves Three sets of curves are to be drawn. First for bonjean curves sets,

    representing the sectional area up to the given water line and second represents the moment this area about the base line. The third is the sectional area curve upto LWL and is drawn by plotting the sectional