hydrostatic and intact stability analysis for a surface ship

7/27/2019 Hydrostatic and Intact Stability Analysis for a Surface Ship

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Hydrostatic and Intact Stability Analysis for a Surface Shipby

Joshua James JahnkeB.S., Mathematics, University of West Florida, 2003

Submitted to the Department of Mechanical EngineeringIn Partial Fulfillment of the Requirements for the Degree of

Master of Science in Naval Architecture and Marine Engineeringat the

Massachusetts Institute of TechnologyFebruary 2010

2010,Joshua James JahnkeAll Rights Reserved

ARCHIVESMASSACHUSETTS INSTITUTEOF TECHNOLOGY

MAY 0 5 2010LIBRARI ES

The author hereby grants to MIT permission to reproduce and to distribute publicly paper andelectronic copies of this thesis document in whole or in part.

Signature of the Author............................................... James JahnkeCenter for Ocean Engineering, Departmept of Me nical Engineering/ O}p/anuary 2010

Certified by ..................................................... .......................Mark S. WelshProfessor of the Practice of Naval Construction and EngineeringThesis Supervisor

A ccepted by ................................... ....... - - -- ---.-----------------David E. HardtRalph E. and Eloise F. Cross Professor of Mechanical EngineeringChairman, Department Committee on Graduate Students


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Hydrostatic and Intact Stability Analysis for a Surface Shipby

Joshua James Jahnke

Submitted to the Department of Mechanical Engineeringon 30 January 2010 in Partial Fulfillment of theRequirements for the Degree ofMaster of Science in Naval Architecture and Marine Engineering

ABSTRACT

Ship's lines are designed such that they are fair. To the naval architect, fairness means that thelines exhibit a continuous second derivative. This is the definition of a spline. Before the adventof digital computers, naval architects checked every line on a lines plan for fairness by bending athin stick of wood, called a batten, on the line. If the line followed the natural bend of the batten,the line was fair. This phenomenon follows from the beam equation, which shows that theminimum energy in the beam occurs when the beam has a continuous second derivative ofposition.Hydrostatics lies at the heart of naval architecture. The hydrostatic properties of a hull aredetermined by the lines and their interpretation using rules of integration. The resulting analysisis presented in the form of graphs, termed the "curves of form" or "displacement and othercurves." An intact stability analysis follows naturally from the hydrostatic analysis. Hydrostatics(determination of KM) coupled with a KG value can be used to predict initial stability. Thisintact stability analysis evaluates the range of stability at both small and large angles ofinclination.The responses of the hull to static and dynamic loading situations can be inferred from the curvesof form. Their most basic use is to determine the static waterline in various loading scenarios. Amore subtle use is to determine the correct placement of the vertical center of gravity to ensure asea kindly roll period, stability in beam winds, and stability in high speed turns.Various computational tools can be used to compute the hydrostatic and stability properties of aship. This thesis explores the results from two computer aided design tools used by the U.S.Navy and commercial industry; Advanced Surface Ship and Submarine Evaluation Tool(ASSET) and Program for Operational Ship Salvage Engineering (POSSE).

Thesis Supervisor: Mark S. WelshTitle: Professor of the Practice of Naval Construction and Engineering


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AUTHOR BIOGRAPHYLieutenant Joshua Jahnke is from Pensacola, Florida. He holds a Bachelor of Science degree inMathematics with a minor in Law from the University of West Florida (2003). He received adirect commission from Naval Reactors and completed Officer Indoctrination School inNewport, Rhode Island. LT Jahnke then reported to Naval Nuclear Power Training Command inApril 2004, and served in the Nuclear Power School (NPS) as an Enlisted Mathematicsinstructor, followed by instructor duty in the Enlisted Reactor Plant Technology division. InMarch 2006 he was assigned to Nuclear Field "A" School (NFAS), serving as the NFASMathematics division director and Assistant Director of Academics. After serving as the NFASCommand Training Evaluator, LT Jahnke was selected for lateral transfer into the EngineeringDuty Corps and reported to the Massachusetts Institute of Technology in Cambridge,Massachusetts, as a graduate student in the Naval Construction and Engineering Program in theDepartment of Mechanical Engineering in May 2008. Lieutenant Jahnke has been awarded theNavy Commendation Medal, Navy Achievement Medal, and the Humanitarian Service Medal.He has been married to Mrs. Tricia Jahnke since November 2004. They have two daughters,Gracie and Juliana.


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ACKNOWLEDGEMENTS

First of all to God, who has so graciously kept me alive long enough to see the end of thisendeavor.To my wife Tricia, who has constantly encouraged me and looked after my every need,especially when I felt I could not continue; and my two little girls Gracie and Juliana for bringingso much happiness and joy.To CAPT Welsh, CDR Gooding, and Pete Beaulieu, who have constantly providedencouragement, ensured that my needs were being met, and fought so hard to keep me on activeduty.To Leslie Regan, Joan Kravit, Mary Mullowney, and the rest of my MIT family who haveworked so hard behind the scenes to make my degree a reality.To all my Course 2N buddies, especially CD R Greg Fennell , LCDR Wes Gray, LT DarrinBarber, LT Eric Brege, LT Ethan Fiedel, LT Brian Heberley, LT Rich Hill, and LT Jon Page,who have been incredibly supportive all along and literally carried me over the finish line.Iam humbled and amazed to have such incredible friends!


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TABLE OF CONTENTSAB ST RA CT.................................................................................................................................... 3AUTHOR BIOGRAPHY.......................................................................................................... 4ACKNOWLEDGEMENTS........................................................................................................ 5TABLE OF CONTENTS .......................................................................................................... 6L ST OF TA BL ES .......................................................................................................................... 8LIST O F FIG URES ........................................................................................................................ 9LIST OF ABBREVIATIONS................................................................................................... 10CHAPTER 1. INTRODUCTION ............................................................................................ 12CHAPTER 2: SHIP HULLFORM DEVELOPMENT ................................................................ 14

2.1 FORM COEFFICIENTS................................................................................................. 152.2 H ULL OFFSET S................................................................................................................. 182.3 HULLFORM ISOMETRIC AND SECTION VIEWS........................................................ 19

CHAPTER 3. SHIP HYDROSTATIC CHARACHTERISTICS AND PROPERTIES.......... 243.1 BONJEAN CURVES..................................................................................................... 243.2 CURVES OF FORM........................................................................................................ 28

3.2.1 ASSET DERIVED CURVES OF FO RM ...................................................................... 303.2.2 POSSE DERIVED CUR VES OF FORM................................................................. 31

3.3 DESIGN WATERLINE CHARACTERISTICS............................................................. 353.3.1 ASSET DERIVED DESIGN WATERLINE CHARA CTERISTICS............... 363.3.2 POSSE DERIVED DESIGN WATERLINE CHARACTERISTICS............... 393.3.3 MANUAL DERIVED DESIGN WATERLINE CHARACTERISTICS............. 393.3.4 COMPARISON OFRESUL TS..................................................................................... 40

CHAPTER 4. STATIC STABILITY C HARACTERISTICS ................................................. 424.1 CROSS-CURVES OF STABILITY................................................................................. 424.2 GENERAL STABILITY CURVE .................................................................................. 44

4.2.1 ASSET DERIVED GENERAL STABILITY CURVE.................................................. 45


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4.2.2. POSSE DERIVED GENERAL STABILITY CURVE ................................................... 454.2.3 COMPARISON OFDERIVED GENERAL STABILITY CUR VES .............. 46

4.3 LIM ITING CON DITION S .............................................................................................. 474.3.1 BEA M WINDS.............................................................................................................. 484.3.2 HIGH SPEED TURNING ............................................................................................ 484.3.3 ROLL PERIOD ............................................................................................................ 494.3.4 META CENTRIC HEIGH ....................................................................................... 49

CHAPTER 5. SUMMARY AND CONCLUSIONS................................................................ 51BIB LIO G R APH Y ......................................................................................................................... 53APPENDIX A. ASSET PRINTED AND GRAPHIC REPORTS........................................... 54APPENDIX B. POSSE DATA/OUTPUT ............................................................ 95


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LIST OF TABLESTable 2-1. Hullform Characteristics ......................................................................................... 16Table 2-2. Hull Offsets ............................................................................................................ 19Table 3-1. ASSET sectional area output................................................................................... 28Table 3-2. Hand calculated hull characteristic spreadsheet ...................................................... 40Table 3-3. M odeling method comparison table ......................................................................... 41

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LIST OF FIGURESFigure 2-1. Body Plan .................................................................................................................. 20Figure 2-2. Hull Isometric View............................................................................................... 21Figure 2-3. Hull Profile And Weather Deck View .................................................................. 22Figure 2-4. Ship's Waterline Plan View ................................................................................... 22Figure 2-5. Sectional Area Curve ............................................................................................ 23Figure 3-1. Body plan section (a) and Bonjean Curve (b) [7]................................................. 25Figure 3-2. Bonjean curves [7] ................................................................................................ 26Figure 3-3. POSSE generated Bonjean Curves.......................................................................... 27Figure 3-4. Calculation of waterplane characteristics [7]......................................................... 30Figure 3-5. ASSET generated curves of form ........................................................................... 31Figure 3-6. POSSE generated displacement curve .................................................................... 32Figure 3-7. POSSE generated MT1 "curve.............................................................................. 32Figure 3-8. POSSE generated TPI curve .................................................................................. 33Figure 3-9. POSSE generated BMT curve ................................................................................ 33Figure 3-10. POSSE generated BML curve ............................................................................ 34Figure 3-11. POSSE generated KB curve................................................................................. 34Figure 3-12. POSSE generated LC B curve.............................................................................. 35Figure 3-13. POSSE generated LCF curve ................................................................................ 35Figure 3-14. ASSET hull geometry summary output ................................................................ 37Figure 3-15. ASSET hull boundary conditions output ............................................................. 37Figure 3-16. ASSET hydrostatic variables of form output...................................................... 38Figure 3-17. POSSE hydrostatic table output ............................................................................ 39

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LIST OF ABBREVIATIONSAbbreviationASSETAMAw pBB/TBM LBM (BMT)CBCILCITCMCpCWPCxDioDisp (A)DW LFTft-BLft-CLGM (GMT)GM LGZHECSALVKB (VCB)KG (VCG)KM (KMT)KM LKTSL/BL/TLBPLCBLCFLTLW LMTl"

MeaningAdvanced Surface Ship and Submarine Evaluation ToolArea, Midships SectionArea of WaterplaneBeamBeam to Draft RatioLongitudinal Metacentric RadiusTransverse Metacentric RadiusBlock CoefficientLongitudinal-Waterplane Inertia CoefficientTransverse-Waterplane Inertia CoefficientMidships Section CoefficientPrismatic CoefficientWaterplane CoefficientMaximum Transverse Section CoefficientDepth at Station 10DisplacementDesign Load WaterlineFeetFeet from BaselineFeet from CenterlineTransverse Metacentric HeightLongitudinal Metacentric heightRighting armCommercial Version of POSSEDistance from keel (baseline) to Vertical Center of BuoyancyDistance from keel (baseline) to Vertical Center of GravityDistance from keel (baseline) to the Transverse MetacenterDistance from keel (baseline) to the Longitudinal MetacenterKnotsLength to Beam RatioLength to Draft RatioLength Between PerpendicularsLongitudinal Center of BuoyancyLongitudinal Center of FloatationLong-TonsLength of Ship on the WaterlineMoment to Trim 1 inch


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POSSE Program for Operational Ship Salvage EngineeringT DraftTCG Transverse Center of GravityTPI Tons-Per-Inch ImmersionTroi Roll PeriodWL Any Waterline Parallel to Baseline


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CHAPTER 1. INTRODUCTIONNaval architecture since the earliest attempts by man has begun ship design by focusing

on the hydrostatics of a ship. Even the first efforts by a child at designing a paper sailboat focuson the forms that stabilize the ship while reducing drag to allow the greatest speed. Navalarchitects today focus on those same basic principles of stability and equilibrium and read thesehydrostatic properties using graphs often called "curves of form". While many methods exist todetermine the "curves of form", most today are created by a computer program which reducesthe lengthy hand calculations required.

The first portion of this thesis will focus on generating and comparing a set of "curves ofform" for two widely accepted computer programs, Advanced Surface Ship and SubmarineEvaluation Tool (ASSET) and the Program for Operational Ship Salvage Engineering (POSSE),for which the commercial version is called HECSALV developed by Herbert Software Solutions,Inc. Additionally a hand calculation will be performed to verify these two models.

Completing the curves of form are the Bonjean curves, Displacement (SW), KB, LCB,Awp, LCF, TPI, BMT, KMT, BML, KML, MT1". By hand these graphs would have takenweeks while the computer analysis will provide the results within minutes. While this completesthe analysis of a non-moving ship in still seas the analysis must continue to prove seaworthiness.

Once the static loading condition is determined from the curves of form, analysis beginsin dynamic situations such as rolling induced by the sea. Correct placement of a vertical centerof gravity determines the roll period which ensures stability without excessive roll or snap.Coupling KG with hydrostatics produces intact stability which illustrates the behavior of the shipat both small and large angles of inclination.


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Both POSSE and ASSET are used again to independently create the righting arm (GZ)cross-curves and static stability curves for an expected displacement range a given hull. Amaximum KG was determined for the 4 different conditions of beam winds (100 kts), high speedturning (35 kts), roll period > 15 seconds, and GM > 2.0 ft. These were based on the cross-curves of stability and the static stability curve produced by each of the two computer programs.


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CHAPTER 2: SHIP HULLFORM DEVELOPMENTThe development of a ship's hullform can be a complex and involved exercise. The

general size and characteristics of a ship are usually decided upon based on the ship's intendedmission. Usually there is set of operational requirements for a ship such as a required payload(commercial cargo or military), speed, and range. There may also vessel size restrictions basedon canal size, dry-docks, or channel depth. When these requirements and restrictions are puttogether, the ship's design characteristics can be developed. Although the hullforms of differentships are usually unique, they are typically based on proven past designs. The starting part ofmost design work is looking at what has been done in the past and using what works andimproving upon what doesn't. The design of a ship's hull is no different.

Historically, once the size of a ship has been determined, a naval architect would developa set of ship's lines that describe the shape of the hull. This was traditionally done by use ofwood battens and lead ducks that were manipulated by hand to create 'fair lines'. These fairlines were necessary to ensure that the ship was hydrodynamically smooth. These lines werethen used for several things. The naval architect would generate a table of offsets from the linesplan for numerical analysis of the hullform to ensure the exact hydrostatic properties wereknown. A shipyard would also use the lines plan and table of offsets to construct the vessel intothe desired shape.

The use of computers now allows for the laborious process of developing lines plans byhand to be done by sophisticated naval architecture programs. Although this relieves the modemnaval architect of the tedious task of fairing lines in on paper, these programs by themselves willnot develop a satisfactory hullform unless the proper data and inputs are used. The AdvancedSurface Ship and Submarine Evaluation Tool (ASSET) is a U.S. Navy computer program that


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allows for the creation of a ship's hullform using complex regression algorithms based on pastdesigns and user inputs. This thesis utilized the ASSET program to assist in the development ofa hullform based on desired characteristics.

2.1 FORM COEFFICIENTSA ship's length, beam and molded depth are typically known when the ship's hullform is

designed. As mentioned earlier, the size of a vessel is usually determined based on the mission.The ship's shape is also derived on the mission. For example, the hullform of a Very LargeCrude Carrier (VLCC) which carries time-insensitive cargo at relatively slow speeds will notlook like the hullform of a large containership carrying time-sensitive cargo at relatively highspeeds. This is because the ability to either carry significant amounts cargo or travel at high ratesof speed are related to how 'fine' the hullform is. A very fine hullform, such as those on navydestroyers allows for a ship to slice through water at high speeds. A 'fat' hullform, such as thoseon VLCCs provides a lot of volume to carry cargo but is not conducive to moving at fast speeds.

In naval architecture there are coefficients used to generalize how fine a hullform is.These are described below:

(1) Block Coefficient (CB) is the ratio of the volume of displacement of a ship to thevolume of a rectangular block having the same length, beam and draft of the ship atthe maximum transverse section area. C1 can range from 0.53 for a fast navaldestroyer to 0.87 for a slow moving bulk carrier.

(2) Prismatic Coefficient (Cp) is the ratio of the volume of displacement of a ship to thevolume of a prism having a cross-sectional area equal to the maximum transversesection area and length of vessel. Cp will typically range from 0.55 for very finehullforms to 0.88 for fat hullforms.


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(3) Maximum Transverse Section Coefficient (Cx) is the ratio of the maximumtransverse section area to area of a rectangle whose sides are equal to the beam anddraft at that section. Cx can range from values ~ 0.75 for faster vessels to -1.0 forbulk carriers.

Generally, the smaller the coefficient, the finer the hullform. Significant work has beendone to assist naval architects in establishing the proper coefficients for a design throughregression analysis. Several references provide a good summary of the parametric design workthat has been done to date for naval architecture. [2] [3] [4] [7]

The hullform created was based on a naval surface combatant. The ASSET program wasutilized to assist in the creation of a hullform. The specific characteristics used to develop thehull are listed in Table 2-1.

Characteristic ValueLBP 380ft

Cr 0.58Cx 0.836B 40.6 ft

Dio 26 ftDraft at Design Waterline 14 ft

Table 2-1. Hullform Characteristics

Several data inputs were entered into ASSET to further assist in the program developinga hullform. These are described below:


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(1) Ship Type Ind = Surface Combatant. This ensures the ASSET developed hullformis based on past surface combatant designs such as U.S. Navy destroyers andcruisers.

(2) Hull BC Ind = Cony DD. This ensures that the ASSET developed hullform isspecifically based on 'conventional' destroyer-type hullforms developed before1982.

(3) Design Mode Ind = Ship WT. This directs ASSET to use the full load weight of theship as input and calculate the usable fuel weight and endurance based on that.

(4) Bilge Keel Ind = None. This directs ASSET to develop a hullform without a bilgekeel.

(5) Skeg Ind = None. This directs ASSET to develop a hullform without a skeg. Thisdirectly affects the ship offsets.

(6) Appendage Ind = Without. This directs ASSET to perform hydrostatic calculationswith just a bare hull.

(7) Aviation Facilities Ind = None. This directs ASSET to develop the hullformwithout factoring in and allocating for a indigenous aviation facility.

(8) Embarked Commander Ind = None. This directs ASSET to not account for theadded weight and volume required for an embarked commander and staff.

(9) Hull Sta Ind = Optimum. This allows ASSET to automatically select a series ofstations to develop the offsets that provides an optimal numerical model of thehullform.


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(10) Hull Offsets Ind = Generate. This directs ASSET to internally generate the hulloffsets based on the hull boundary conditions and the principal characteristics listedabove.

2.2 HULL OFFSETSWith the principal characteristics and data inputs determined for the desired vessel,

ASSET was used to develop the hull offsets. Hull offsets are typically provided at variousstations along the length of the hull and at various waterlines to allow for an accurate numerical

representation of the hull. Th e specific numerical value of each offset is for the half-breadth ofthe vessel - meaning the distance from the ship's centerline to the outside of the hull. For thisproject these offsets were done for the 0, 2, 4, 8, 12, 14, 16, 20, 24 foot waterlines and fromstation 0 (forward perpendicular) to station 20 (aft perpendicular). An additional half-station wasadded aft at station 19.5 and forward at stations 0.5, negative 0.43 and negative 0.86 to helpdefine the hullform where there is significant curvature.

Th e resulting hull offsets are shown in Table 2-2.Station 0 2 4 8 12 14 16 20 24

-0.86-0.43 0.01

0 0.10 0.32 1.26 2.810.5 0.26 1.00 1.30 1.64 2.79 4.491 0.07 0.28 1.17 2.15 2.55 2.99 4.34 6.152 0.25 1.24 1.96 3.38 4.64 5.19 5.78 7.34 9.333 0.87 2.95 4.19 5.98 7.33 7.92 8.55 10.20 12.23

4 1.00 4.66 6.60 8.77 10.05 10.60 11.22 12.83 14.735 1.00 6.32 8.94 11.46 12.63 13.11 13.66 15.09 16.796 1.00 7.94 11.08 13.87 14.93 15.31 15.76 16.95 18.327 1.00 9.49 12.95 15.88 16.85 17.13 17.47 18.36 19.378 1.00 10.85 14.47 17.47 18.35 18.54 18.75 19.35 19.999 1.00 11.77 15.57 18.63 19.41 19.53 19.64 19.96 20.2810 1.00 12.11 16.10 19.29 20.05 20.13 20.17 20.29 20.3911 1.00 11.91 15.90 19.31 20.28 20.39 20.41 20.42 20.4312 10.60 15.09 19.04 20.21 20.36 20.41 20.42 20.44


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13 7.94 13.58 18.47 19.89 20.10 20.22 20.35 20.4014 3.11 10.88 17.44 19.32 19.63 19.84 20.17 20.3815 6.02 15.76 18.51 18.97 19.27 19.83 20.1816 13.05 17.43 18.09 18.50 19.26 19.7517 7.74 15.94 16.99 17.52 18.47 19.1018 13.78 15.64 16.28 17.46 18.2419 9.23 14.09 14.85 16.23 17.18

19.5 2.31 13.27 14.08 15.56 16.5920 12.45 13.33 14.85 15.95

Table 2-2. Hull Offsets

2.3 HULLFORM ISOMETRIC AND SECTION VIEWSAlong with the hull offsets, an ASSET developed body plan was created. The body plan

is a presentation of what the transverse sections look like at each station. Figure 2-1 shows thebody plan for this projects vessel. Stations -0.86 to 10, corresponding to the forward half of thevessel, are shown on the right side. Stations 10 to 20, corresponding to the after half of thevessel are shown on the left side. It is clear to see that the vessel generated, based onconventional destroyers, has a transom stem, no parallel midbody and a very fine bow to slicethrough seas. These features are typical of naval surface combatants and provide a goodindication that the hullform shape is satisfactory.


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BLSCALE0 5 10 15 FT

Figure2-1. Body Plan

Figure 2-2 shows an isometric view of the hull. This view shows how fine the hull is inthe bow and provides a good overall sense of the volume available to the designer in the hull formission essential equipment.


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//1

~- K

Figure 2-2. HullIsometric View

Figure 2-3 shows the ship's hull profile and weather deck plan view. It should be notedthat the actual vessel would have a deckhouse on top of the weather deck. This deckhouse is notshown in this view but the weight, size and shape of the deckhouse is taken into account in thestability analysis outlined in Chapter 4. Notable features on this hull are the upsweep of the keelas one moves aft of midships. This provides the space for the strut/shaft configuration typical ofdestroyers. Without this upsweep, the vessel would require an excessive propulsion shaft angleas well as increase the operating draft of the vessel. Figure 2-4 provides a view of the designwaterplane of the vessel.


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FP0 .8 0.7 0.6 0.5 0.4 0.3 0 .2 0.1 0.0

0

Figure2-3. Hull Profile And50 100

Weather Deck View

j~ SCALE15 0 FT

II 10.9 0.8 0.7 0.6 0.5 0.4FP

0.3 0.2 0.1 0.0

___ SCALE150 FT

The sectional area curve of the ship is shown in Figure 2-5. This curve can be extremelyuseful in hydrostatic analysis of the vessel. It is also a good indicator of the hullform fairness.

22

AP1.0 0.9

AP1.0

0 50 100Figure 2-4. Ship's Waterline Plan View


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There should not be any sharp corners, edges, or knuckles in a sectional area curve. Anexamination of the sectional area curve reveals no sharp edges or discontinuities, indicating a fair

hullform.

/

/1.0 0.9 0.8AP

///

/

/

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0FRACTION OF SHIP LBP FROM FP FP

Figure2-5. Sectional Area Curve

500

400

300

200

100

0


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CHAPTER 3. SHIP HYDROSTATIC CHARACHTERISTICS AND PROPERTIESTo put it in layman's terms, a ship's hydrostatic characteristics and properties are the

means by which a ship is described; whereas humans are described by height, weight, hair color,etc., ships are defined by displacement, waterplane area, and a series of coefficients. Thesecharacteristics go beyond "just descriptions;" the characteristics represent definitions. Fromthese characteristics selected by a naval architect, the architect can manipulate their design to befast or slow, bulky for carrying cargo or graceful for pleasure. The "trial and error" process tochoose these characteristics to meet the customer's requirements requires iterations of the designspiral; doing this procedure manually can be "very time consuming."[7] Each iteration of thedesign spiral generally results in refinements to one or more characteristics; manually redrawingthe design each time the characteristics change is where a significant amount of time can beconsumed.

To expedite the design process, computer programs have been developed to assist thenaval architect with his selection; "with the aid of computers, it is possible to make a study of alarge number of varying design parameters and to arrive at a ship design which is not onlytechnically feasible but, more importantly, is the most economically efficient."[3] Rather thanhand-drawing and recalculating the characteristics after each refinement, programs like ASSETand POSSE become invaluable as they have been specifically designed to do these calculationsrapidly.

This chapter details the ship's characteristics and demonstrates how the aforementionedtools can be used to aid in the design process.

3.1 BONJEAN CURVESBonjean Curves are the curves of cross sectional area for all body plan stations. [7]

Translating this, the Bonjean Curves display the submerged area at a given location (or station)along the length of the ship, for a given draft. To further illustrate this concept, an example isshown in Figure 3-1.


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Figure 3-1. Body plan section (a) and Bonjean Curve (b) [71

In Figure 3-1, the curve on the left is a sample station curve of the body plan of a ship;generally, as most vessels are symmetrical about the vertical axis, only half of the ship is shownin most body plans. The curve on the right is the Bonjean Curve. Assume that the draft of theship is at the level "W1" as seen in the left picture. To derive the area under the curve (which isequal to half the submerged area at that station) the curve would be integrated from point "K" topoint "L1." This value, when doubled, would equal the value "Q" in the curve on the right.

Bonjean Curves can provide a great deal of useful data to a naval architect. One of theprinciple characteristics defining any ship is its displacement (how heavy the ship is). Byintegrating the values of obtained at a given draft from the Bonjean Curves, the submergedvolume of the ship can be determined. By accounting for the density of the fluid which the shipis floating, the displacement of the ship can subsequently be calculated. Knowing thedisplacement is a vital factor which further affects almost all stages of the design process.

While the plotting of, and withdrawing data from the Bonjean Curves is a complicatedmethod for determining displacement, determination via any other method for a ship not at evenkeel, would be significantly more complicated. Figure 3-2 displays the ease at which submergeddata can be easily obtained for a ship trimmed by the stern.


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Figure 3-2. Bonjean curves [7]The ship in the image above is shown to have a draft at the bow of 30 feet and a draft of

35 feet at the stem. The lines plotted on the Bonjean Curves highlight the sectional areas at eachstation down the length of the ship. Integrating the data obtained from this curve will give thedisplacement for the ship at the 5 foot, trimmed by the stem, condition.

To plot these curves by hand would take some time. Each sectional area at each draft, foreach station would have to be measured so it could be plotted. In working through the iterativedesign process, if the ship is found to not have enough internal volume (for cargo or passengerspace) and has to lengthened or widened, the sectional areas would change, and subsequently sowould the curves. The ASSET and POSSE programs can perform the re-calculations and re-plotting significantly faster than a human can, thereby expediting the design process.

For the ship, POSSE was the tool utilized to plot the Bonjean Curves. With each revisionmade to the design (changing dimensional coefficients or dimensions), the curves wereautomatically updated. Figure 3-3demonstrates why POSSE is such a valuable tool as it clearlydisplayed the curves in moments vice what would have taken hours to produce by hand.


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Bonieansull

Arfea(2)38000ARFP DrK"ee(Ft) 37050A t-FP DrdKeet(Ft) 361 QAWP DraKo4Ftl 34200A -FP DrAKeW(Ft)32300A -FP DraKee(Ft) - 304OOA-FP DraftKeel(Ft) 286OOA-FP DfaftKaCFt) 266OOAt-FP DaKee(Ft)- 24700A tfP DrafKeel(Ft) 22800A ftFP rafKeel(Ft) 209ODAt-FP DraltKee(Ft) 190 0A t-FPDraftKe(F)171O0AR-FPDrKeel(Ft) - 152 0A -FP DrtKee4(Ft) 133.00AFP DrKe(Ft) 114 0AR-FP DraftKe(Ft)95 00A t.FP DratKee(Ft) 7600A t-FPDrafKe(Ft) 67.0AA-FP DraftKee(F) 38OOAt-FPDraeI(Ft)19 0A ftFP DraftKee(Ft) - 9 50At-FP DraftKeel(Ft) 000 A4-PDraftKe(Ft) 81TF -FP DraftKeM(Ft)2 P164F t-FP Dr0A Pr((Ft)

Figure3-3. POSSE generated Bonjean Curves

ASSET, on the other hand, cannot directly output the Bonjean curves but it can providedata which can be used to verify the curves; to compare the outputs of both ASSET and POSSE,the sectional area for a given draft can be checked. Table 3-idisplays the ASSET sectional areadata for the designed vessel at a draft of 14 feet. The ASSET and POSSE data correlate.


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Table 3-1. ASSET sectional area output

3.2 CURVES OF FORMThe curves of form, like the Bonjean curves, are another method of graphically

displaying the characteristics and properties of a ship; "these curves represent the standardpresentation of hull characteristics that are functions of form."[2] The following paragraphsbriefly explain what each of the curves are and how they are obtained. The main take-away isthat the hand calculation and plotting of these curves is highly time intensive. Like with theBonjean curves, each modification made to the design will affect each curve and require theirrecalculation and re-plotting. The use of a computer aided tool to plot these curves againexpedites the design process.

Displacement - Measurement of weight of water displaced.Am tng

MTlI - Moment to Trim 1 Inch. The moment necessary to change trim by a fixed quantity.

Location Areaft aft of FP ft 2

1 -16.28 02 -8.14 03 0 04 9.5 10.225 19 29.066 38 83.17 57 147.868 76 214.819 95 278.9910 11 4 337.3511 133 387.7512 152 428.2913 17114 190 472.4215 20 9 2.316 22 8 456.2617 24 7 423.918 26 6 376.4819 28 5 317.0420 30 4 250.121 32 3 181.3422 34 2 116.923 36 1 62.124 370.5 39.3325 38 0 19.67


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MTI" = (A * GML) / (12 * L)

TPI - Tons Per Inch Immersion. Amount of weight (in long tons) that would need to be added tothe ship to increase its draft by one inch, with no change in overall trim.

TPI= Awp / 420

BM T - Transverse Metacentric Radius. Th e vertical distance from the center of buoyancy to thetransverse metacenter.

BMT= IT/V

BML - Longitudinal Metacentric Radius. The vertical distance from the center of buoyancy tothe longitudinal metacenter.BML = IL / V

KB - Vertical Center of Buoyancy. Height of the center of buoyancy above the vessel'sbaseline.LC B - Longitudinal Center of Buoyancy. The geometric centroid of the submerged volume of abody or ship through which the total buoyancy may be assumed to act. It's position is measuredas the distance from midships.

LCF - Longitudinal Center of Flotation. The geometric centroid of the area of the waterplane ofany waterline. Its position is measured as the distance from midships.

A sample demonstrating one potential method of performing the hand calculations isshown in Figure 3-4.


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Half-breadth (Haff-Station (M) %SM Prod. Lever Prod. Lever' Prod. breadthY Prod.0 0 0.25 0 5.0 0 25.0 0 0 0% 1.245 1.0 1245 4.5 5,603 20.25 25.211 1.93 1.931 3.140 0.50 1.570 4.0 6.280 16.0 25.120 30.96 15.481% 5.859 1.0 5.359 3.5 18.757 12.25 65.648 158.90 158.902 7.597 0.75 5.698 3.0 17.094 9.0 51.282 48846 328.843 10.956 2.0 21.912 2.0 43.824 4.0 87.648 1315.09 2680.184 12.007 1.0 12.007 1.0 12.007 1.0 12.007 1731.03 1781.035 12.039 2.0 24.078 0 0 0 0 1744.90 3489.806 12.039 1.0 12.039 -1.0 -12.039 1.0 12.089 1744.90 1744.907 11.899 2.0 283.798 -2.0 -47.596 4.0 95.192 1664.73 369468 10.271 0.75 7.703 -8.0 -23.109 9.0 69.327 1088.52 812.648% 8.417 1.0 8.417 -3.5 -29.460 12.25 103.108 596.31 596.319 5.962 0.5 2.981 -4.0 -11.924 16.0 47.696 211.92 105.969 3.057 1.0 3.057 -4.5 -13.756 20.25 61.904 28.57 28.5710 0 0.25 0 -5.0 0 0 0 0 0Y, - 129.864 Y, -34.319 Y. 656.182 L - 15009.00

Station sp., a = L 15.499 mT 10Waterplane area, A w, = 1 x x a = (129.864 x 20.666) = 2,683.77 m'Waterplane coeff., Cw , - A,,/(L x B) - 2683.77 /(154.99 x 24.078) = 0.719Tonnes per cm immersion = 2,683.77 x 1.025/100 = 27.51 t (S.W.)Long'l Center of Flotation LCF = (1,/2,) x a = (-34.319/129.864) x 15.499 4.10 m abaft Sta. 5Long'l moment of inertia about Sta. 5 - 1, x x a' - 656.182 x x (15.499P = 8,257,400 m'Long'l moment of inertia about LCF, I, = 3,257,400 - 2,63.77 x (4.10Y - 3.212.300 m'Trans. moment of inertia, 1,= 1, x 4s = 15,009 x 6.8884 = 103,890 m'Vol. of displacement, V (from displacement curve) = 17,845 m'Long' BM - IL/V - 8,212,800/17,845 = 180.0 mTransverse BM = Ir/V = 103,90/17,845 = 5.79 m.

Figure3-4. Calculationofwaterplanecharacteristics 71

While the use of a spreadsheet program like EXCELC would help to expedite the handcalculations and minimize errors, it would take a great many spreadsheets to obtain all of thedata for all of the drafts to plot the curves of form. Just as with the data for the Bonjean Curves,ASSET and POSSE can be used to generate the data and plots and facilitate design modificationsby minimizing the time to produce these curves for each variant. When viewed side-by-side, theplots from both programs are similar; this indicates that either program can be used tosuccessfully generate the curves of form.

3.2.1 ASSET DERIVED CURVES OF FORMFor the design studied, Figure 3-5 shows the curves of form.


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ASSET/MONOSC V5.3.0 - HYDROSTATIC ANALYSIS - 1/ 8/2010 13:21.50DATABANK-JOSH PROJ 1 AND 2 2.701 FALL SHIP-JOSH 1GRAPHIC DISPLAY NO. 2 - HYDROSTATIC VARIABLES OF FORM30

25 41

20___

S15

10

5

0 0 1 2 3 4 5 6DISPL, MT1, TP1, BMT, BML, KB, CIAFT-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2LCB, LC F

1000 LTON)/UNIT100 FT-LTON/IN)/UNIT5 LTON/IN)/UNIT5 FT)/UNIT500 FT)/UNITBY STERN), FT 0.00

F KBG CID1TS(H WSURFI LCBJ LC FAPPENDAGE

7 8D1TS, WSURF.0 3.0 4.0

9 105.0 FWD

2 FT)/UNIT5 LTON/FT)/UNIT5000 FT2)/UNIT10 FT)/UNIT10 FT)/UNITIND-WITHOUT

Figure 3-5. ASSET generated curves ofform

There are several different ways to illustrate the curves of form. The plot shown above is oneof the more standard methods where all of the curves are drafted on a single sheet. The scalingfactor for each curve is printed in the legend.

3.2.2 POSSE DERIVED CURVES OF FORMWhile the image shown above is one of the standard display methods, it can be seen how

this viewing can be complicated. POSSE gives the opportunity to display each curve separately.A similar analysis of the design was run using POSSE; the results are displayed in Figures 3-6through 3-13.

A DISPLB MT1C TP1D BMTE BMLTRIM (+VE


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Displacement:Hydrostatics Table Hull

10

0 000 2000 3000 4000 6000 6000BuoyancyDisp(LT)

DraftKeel(Ft)

Figure3-6. POSSE generateddisplacementcurve

MT1 ":Hydrostatics TableHull

20

0A0 100 200 300 400 600 600 700WaterplaneMT(f-LT/inj

DraftKeel(Ft)

Figure3-7. POSSE generatedMT1" curve


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TPI:Hydro1icst TableMull

20

S16

10

0 10 20 30WaterplaneTP1(LT/inl- DraftKeel(Ft)

Figure3-8. POSSE generated TPI curve

BMT:Hydrostatics Table Hull

20

Sr10 -.....----5..-.-.-.-- -.-

00 1 2 3 4 6 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22 23 24 25 26MetacenterBMt(Ft)

-+--- DraftKeel(Ft)

Figure3-9. POSSE generated BMT curve


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BML:Hydrostatics Table Hull

20

~1610

0,0 1000 2000 3000 4000MetaceterBM(Ft)

-,-- DraftKeel(Ft)

Figure3-10. POSSE generatedBML curve

KB:Hydrostatics TableHull

20

0 1 2 3 4 6 6 7 8 9 10 11 12 13 14Buoyancy B(Ft)

--- DraftKeel(Ft)

Figure 3-11. POSSE generatedKB curve


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LCB:Hydrostatics Table Mull

20

0200 190 180 170 160BuoyancyLC(ft-FP

-,--- DraftKeel(Ft)

Figure 3-12. POSSE generated LCB curve

LCF:Hydrostatics Table Hull

20

0210 200 190 180 170

WaterplaneLCF(t-FP)

-,---- DraftKee(Ftj

Figure 3-13. POSSE generated LCF curve

3.3 DESIGN WATERLINE CHARACTERISTICS

For this and for other assessments, a design waterline (DWL) draft of 14 feet wasselected based on design criteria. Introduction o NavalArchitectureby Gilmer and Johnson [2]gives the most comprehensive explanation of "waterline:"

The intersection line of the free-water surface with the molded surface of a ship,either in still water or when she is surrounded by waves of her own making. The


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intersection line of any selected plane, parallel to the baseplane, with the moldedsurface of a ship. The angle of the waterline at the bow in the horizontal planeneglecting local shape at the stem is the angle of entrance. The angle of thewaterline at the stem in the horizontal plane neglecting local shape of stem frameis the angle of run.

To verify that ASSET and POSSE could produce reliable results for a given condition,several design waterline characteristics were hand calculated, as well as outputted from ASSETand POSSE to be compared. The chosen characteristics used for the comparison were the DWLAWP, LCF, Transverse Waterplane Inertia Coefficient (CIT), and the Longitudinal WaterplaneInertia Coefficient (CIL). Any of the characteristics could have been chosen to compare against,but these thought to be complex and well rounded comparison data points.

3.3.1 ASSET DERIVED DESIGN WATERLINE CHARACTERISTICSASSET's analysis tools can provide the naval architect with virtually all required design

characteristics and properties, though not necessarily explicitly (to be further illustrated below).Figures 3-14 through 3-16 show samples of these outputs and how the aforementionedcomparison characteristics can be obtained.


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ASSETf/EM3C T.3.0 - KILL WO N MDULE - 1/ 8/20LO 13:10.35DATAANK-10IK PRO I AMD 2.701.FALL. UIP-IOK IPRITEED FOPT NO . 1 - HULL OEOMTRY UERAR3ULL WFSETS ZED-ENERA7EHULL DE I IND- NOWE MIN AM, TUL L STA ED- 0215 IAX aEm, FTHULL DC D- CUNV DD HULL FLAE MLKE, KGFORU BULAW, FT

uLL PRINCIPAL D3IRM ON (03 DEL)3lL. LGA, T 396.30Hn, rr 0.60Ans I KATWR DECK, rr 40.02DRAf, r 14.00DEPmTA 0, r 33.60DE M 9TA , rr 30.42

EIN TA Lo, IT 26.00DEPT ETA 30, rr 26.767a0Am I TA , F 3.42rADLWam , rr 29.33

DAR KILL DATA 05 LULILE 01 91, rrDNM, FTDRAr, rrRE10AD 8ETA 3, rrPRIATEC CaFlux UCTEIO COarWATRPLAE cUFWn -, n 2arD suRrACE, mTa

DAE HULL DEFL, 11N0APPENDAE DnPL, L1NIPULL LOAD UT, LTOK

40.6013.9720.450.00.0340. 74L1431.11

1eSa0.S293.0261.293044.31

30.00103.60.004.00

PRIKIATIC CarF 0.50Ax ECTION Car 0.036WATERPLAN COEr 0.737I.CD/LUa 0.UssHnLr1D135imE, FT L.00DO T Uan, rr 0.00RAI=D DICK HT, F 0.00aAIn DECK ED LZI, ErAUAM DICK Arr LIE, STADARE NULL Dzlii, 11m 3992.55A=A DEA, rr 38.00UTADILZTY DATA ON LU T

0, rrNET, FrIw rrri s* r COR, FSOV LzrE n AE , rrrr rrONF

GT/u AVAILnr/a Ao

6.44LL.OLLI. s00.000.003.05ee0.LL0.0950.060

Figure3-14. ASSET hull geometry summary output

Figure3-15. ASSET hull boundary conditionsoutput

ASVET/MOSC T.3.0 - KULL OROK MODULE - 1/ S/3010 13.119.31DATABA-aOSE PROS I ND 2 2.O.FAL. SKZP-FUONS LPRINTED REPORT NO. 3 - W1LL BOUNDARY CONDITZONSILL OFFSETS ZND-OERRATEEA.L NC ZED-0Mw DO MULL ETA EM-ZEVERz, T am.u LCS/LeP 0.mEAK, 73 40.40 AL/lW *DRAFT, 1T 14.00 HALF XZDGES 5EDT1 FTDEFE ErA 0, FT 32.10 Ba r mAmE, FrDEPT XT A 3, r 30.42 FlA RAZED DECK LEMZTDEpm ETA 10, FT 26.00 AFT RAZIED DECK LIKET

DMT1 ETA 30, FT 26.76 PAZm DEC w, T 0PRzEKATiC CEF 0.580 UATERPLAKE COEFMAX ECTIO CORF 0.936N0 P0Es13 BELOW DO L 1. 7E D |EL/ LEMIT &.

w 10E113 ABOVE DIU. 13. AFT EEL/XL LZUTPOINT DIST FA C A B O V E DE L 1.000 DOW ANLE, DECPOUNT DIET FA C BELOW DU L 1.000 Do w AFE AC 00OW OVESMRG 0.043 TA SETIzON CoEF

vzm OYERNAW 0.007 KILL FLARK ANLE, DES

0. SLS8.869L. 000.000.000.737

0.0870.3030.000.0000.T00


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ASIT/RONOSC V5.3.0 - ETDS10TATIC ANALTZI - 1/ 8/2010 13:22.43DATABANK-502H PR03 I AD 2 2.701_FALL_ MKIP-402I 1PRIMED EPORT N0 . 2 - KTDROsTATiC vARIABLES OF FORnTOTAL APPDG TOTALDRAFT TOLUH VOLUE DIPL LCD B LCF

IT TS 13 YON FT IT IT2.00 4716. 0. 134.8 27.72 1.21 22.064.00 L4492. 0. 414.3 20.36 2.46 12.126.00 27760. 0. 793.7 14.46 3.70 4.066.00 43774. 0. 1231.5 9.15 4.92 -3.8010.00 62075. 0. 1774.7 4.15 6.13 -11.5812.00 8407. 0. 3356.1 -0.78 7.33 -19.9014.88 164633. S. 2991.1 -a.72 8.54 -26.2716.00 127788. 0. 3613.1 -9.40 9.71 -21.6616.00 111557. 0. 4333.1 -11.87 10.65 -24.3420.00 175993. 0. 5031.7 -13.52 11.99 -22.9222.00 201120. 0. 5750.1 -14.57 13.11 -20.8624.00 336935. 0. 6495.2 -15.15 14.24 -16.4226.00 250524. 0. 7162.6 -14.63 15.24 37.10-------------BULL ONLY-------------DRAFT CZDLTT317 LONG DR TRNY BN LON R TRET MS RTLIT LTON/IT FT IT IT IT FT-LITON/N2.00 -6.36 2496.23 26.82 2497.4 25.07 73.64.00 -5.50 1546.11 23.79 1548.59 26.27 140.56.00 -2.25 1226.94 20.52 1230.64 24.23 213.58.00 2.46 1070.15 17.52 1075.07 22.43 293.710.00 6.43 966.73 14.97 992.66 21.09 364.012.00 15.95 952.30 12.91 15964 20.24 492.014.9 22.6 961.55 11.31 912.69 19.75 592.516.00 22.15 780.26 9.64 769.97 19.35 625.116.00 22.24 697.57 8.57 708.42 19.42 662.920.00 21.36 638.42 7.78 650.40 19.76 704.822.00 19.99 593.66 7.16 606.60 20.27 748.624.00 18.12 557.99 6.66 572.23 20.59 793.926.00 -20.06 313.11 2.97 326.35 15.21 491.5

Figure3-16. ASSET hydrostatic variablesofform output

As stated above, not all output data from ASSET is explicit. To obtain the LCF valuefrom ASSET, the LCF/LBP ratio must be multiplied by the LBP provided. To obtain the CIL andCIT values, the equations have to be used:

CIT = (12 * BM T * V) / (B3 * L)CIL = (12 * BML * V) / (B * L3)

Each of the values required for these equations are provided in the figures above.


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3.3.2 POSSE DERIVED DESIGN WATERLINE CHARACTERISTICSPOSSE, on the other hand, provides significantly less of a detailed output, however, it

does print the output in a much more tabular and user-friendly format. Figure 3-17 is the POSSEoutput for the selected design.

I HYDROSTATIC TABLE - HULLOptions

Denety LT~t3 0.02Long DraftRef LCFTrim ft 0.00Heel den

Hydrostatic PropertiesDraft Buoyancy Waterplane MetacenterKt Disp KB LCB Area LCF TPI BMt KMt OM KFt LT Ft ft-FP ft2 ft-FP LTnn Ft Ft Ft0.00 0 190,00A - 190.OA - -1.00 46 0-61 157.24A 2,492.4 161.42A 59 26.57 2718 4,169.07 4.

2.00 137 1,23 162.62A 3,811.6 167.39A 91 26.16 2739 2,426.82 2,3.00 262 186 166.34A 4,896.3 172.67A 117 25.14 26.99 1.83209 1.4.00 416 2,47 169.71A 6,817.2 177-14A 13.8 23.66 2613 1.523.79 1.5.00 596 308 172.86A 6.625.9 181.47A 16.8 22,01 2509 1.337.09 1.6.00 794 3.69 176.46A 7.366.9 186.96A 17.6 20.47 24.16 1.22711 1.,7.00 1.014 4,30 178.24A 8.010.3 189.84A 19.1 18.94 23.26 1.131.60 1,8.00 1.252 491 180.90A 8,6848 193.61A 20.4 17.48 22.39 1.059.71 1.19.00 1,607 62 183.62A 9,121.2 197.26A 217 16.11 21 3 1,009.04 1,10.00 1,774 612 185.80A 9,6781 201.80A 23.0 14.94 21.06 9916011.00 2,058 6.73 188.32A 10,166.305.51A 24.2 13.87 20.60 969.9012.00 2,356 733 190.79A 10,641.9 209.73A 26.3 1289 2022 947.9913.00 2.667 7.93 193,28A 11.148.8 214.49A 26.6 12.06 19,99 960.3614A0 2,990 8.54 195.70A 1134.7 216.27A 272 11.21 19.74 903.1715.00 3,319 9.13 197.3A 11.677.2 216.02A 27.6 10.35 19.47 836.4016.00 3,652 971 199 8A 11.727.5 21566A 27.9 9.64 19.35 7803617.00 3,989 1028 20073A 11.884U8216.16A 283 9.06 19.34 736.0510.00 4.331 1085 2018SA 12.049.6 21452A 28-7 8566 1941 69758 7

M11Ft159.6842706833.94526,26340. 7230.6013680064.62014.56997629666396632168.289111.70844.62790.07746.33AR AA

Waterplane Coefficients WettedMT1 Cit Cil CM MaxBeamt-LT/In Ft41 0.020 0.046 0.279 17.3773 0.069 0.073 0.399 2427106 0.109 0.098 0486 2893139 0.162 0.125 0553 32.25174 0.216 0163 0.608 3466214 0.268 0,184 0.662 3642252 0.317 0.216 0.690 3769291 0.362 0.251 0,721 38.64333 0.401 0.289 0.747 39.40386 0.438 0.339 0.770 39.94433 0.472 0386 0.789 4032490 0.602 0.443 0.806 40.66656 0.531 0.614 0,820 40.71592 0.654 0.662 0.832 40.78608 0.667 0.665 0.843 40,81626 0.682 0,579 0853 40.84643 0.697 0.693 0862 40.87

O=' A lA0 (I9 7 A 8

Figure3-17. POSSE hydrostatictable output

The DWL draft of 14 feet has been highlight above. Obtaining data from this figure ismuch less complicated than trying to extract it from the numerous ASSET reports; therefore,based on the level of design detail the naval architect is looking for, one tool might be preferredover the other.

3.3.3 MANUAL DERIVED DESIGN WATERLINE CHARACTERISTICSTo demonstrate the hand calculations, several tools were used. The first tool was

EXCEL. As a cross-platform accepted standard, EXCEL was the chosen spreadsheet. Thesecond tool applied was a numerical rule called Simpson's Rule. Simpson's Rule is anintegration tool that "rigorously integrates the area under a curve of the type y = a + bx + cx 2which is a second order parabola, or polynomial of degree 2, by applying multipliers to groups ofthree equally spaced ordinates." [7]


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Using these two rules and the table of offsets for the hullform, Table 3-2 was created.Note the Simpson's Rule multipliers inserted as the "1st (SM)" column.

AREA My Mx ly lxx y 1st (SM) y*SM x*y*SM (y^2*SM)12 xA2*y*SM (yA3*SM)/30.00 0.102 0.5 0.05 0.00 0.00 0.00 0.009.50 1.298 2 2.60 24.65 1.68 234.22 1.4619.00 2.547 1.5 3.82 72.60 4.87 1379.43 8.2738.00 5.185 4 20.74 788.15 53.77 29949.61 185.8857.00 7.917 2 15.83 902.49 62.67 51442.18 330.7776.00 10.603 4 42.41 3223.46 224.87 244982.99 1589.5995.00 13.106 2 26.21 2490.21 171.78 236569.76 1500.91114.00 15.309 4 61.24 6981.02 468.75 795835.74 4784.10133.00 17.133 2 34.27 4557.30 293.53 606120.73 3352.64152.00 18.539 4 74.15 11271.53 687.37 1713273.24 8495.27171.00 19.527 2 39.05 6678.22 381.30 1141975.91 4963.78190.00 20.127 4 80.51 15296.83 810.23 2906398.58 10871.83209.00 20.388 2 40.78 8522.35 415.69 1781170.35 5650.12228.00 20.364 4 81.46 18571.88 829.38 4234388.33 11259.57247.00 20.102 2 40.20 9930.20 404.07 2452758.98 5415.04266.00 19.632 4 78.53 20888.89 770.86 5556445.47 10089.28285.00 18.966 2 37.93 10810.53 359.70 3081002.33 4548.05304.00 18.091 4 72.37 21999.06 654.59 6687713.41 7894.97323.00 16.988 2 33.98 10974.21 288.59 3544670.42 3268.37342.00 15.644 4 62.58 21401.45 489.49 7319295.53 5105.17361.00 14.091 1.5 21.14 7630.49 148.93 2754608.01 1399.05370.50 13.269 2 26.54 9832.27 176.06 3642856.48 1557.46380.00 12.449 0.5 6.22 2365.35 38.75 898832.24 321.57

902.60 195213.15 7736.93 49681903.95 92593.1219.00 19.00 19.00 19.00 19.000.33 0.33 0.33 0.33 0.33SUM*s*mult 5716.49 1236349.96 49000.54 314652058.32 586423.10Th e Other Side 5716.49 1236349.96 49000.54 314652058.32 586423.10Totals 11432.98 2472699.93 98001.09 629304116.65 1172846.19

Awp 11432.98 ft2LCF 216.28 ft2Ixbar 1172846.19 ft4CIT 0.55I bar 94514099.56 ft4CIL 0.51 1 _ 1

Table 3-2. Handcalculatedhull characteristic preadsheet

3.3.4 COMPARISON OF RESULTSTable 3-3 shows how the hand calculated values compare with those derived using the

computer based software.


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Hand ASSET % Error POSSE % ErrorAw, (ft2) 11433.0 11432.8 0.00% 11434.7 0.02%LCF (ft) 216.28 216.22 0.03% 216.27 0.00%

CIT 0.553 0.554 0.10% 0.554 0.10%CL 0.509 0.509 0.02% 0.552 8.43%

Table 3-3. Modeling method comparison table

The "%Error" columns measure the difference between the hand calculations and each ofthe computer programs. The primary source of error expected stems from the Simpson's ruleintegration simplifications. With the average error being less than 1.1%, ASSET and POSSE canbe deemed as useful and adequate tools for the naval architect. The significant error in CIL alsoillustrates the point that no single tool should be relied upon for the data.


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CHAPTER 4. STATIC STABILITY CHARACTERISTICSThe basic tenets of ship design evaluation are that the ship float and float upright. From

the earlier analysis, the metacentric height has been shown to be positive, and the draft of theship is less than the available free-board. While these two conditions indicate that the ship hasinitial stability, that is it will float and float upright, more analysis is needed to determine thesuitability of the ship's stability. Stability cannot be confined to a still water case with no otherinfluences on the ship. The following analysis determines the stability characteristics for theship.

The art of ship design has led to many thumb-rules that can be used to evaluate a ship'spotential performance based on the ship's parameters, mentioned above. However, an in-depthanalysis of the ship's stability must be completed to insure the ship remains stable through aseries of likely and expected conditions. Additionally, the stability of the ship should bequantified to help operators plan their actions in a truly safe manner. Furthermore, ship stabilityis not a set of go-no go requirements. Each type of ship has different operational requirementswhich will compete with each in a design compromise to achieve the most appropriatecharacteristics for each ship type.

The ship is evaluated using ASSET and POSSE to validate the data and results.Additionally, calculations are performed where required to provide a comprehensive analysis.The Naval Architect performs all of these analyses prior to ensuring a hull is adequate for furtherconsideration.

4.1 CROSS-CURVES OF STABILITYWhile an adequate design does vary somewhat based on the ship's purpose as mentioned

above, the stability also changes with the displacement of the ship as well as at large angles of


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inclination. For a given hullform, one can imagine that the draft will influence the effects of thefreeboard on producing a righting force.

The Cross-Curves of Stability are shown below in Figure 4-1. Evaluating the hullrequires knowledge of the center of gravity. An initial estimate of KG is 0.6 of the depth atstation 10. This yields 15.6 feet for this hullform. The Cross-Curves show that the hullformproduces a positive righting arm for all heel angles from 0 to 89 degrees.

At this stage of evaluating the hullform, it is difficult to determine whether the rightingarm developed is adequate. Most ship designs will have a target displacement range that will bemuch smaller than that shown below. The data from the Cross-Curves will likely be taken for agiven displacement for the desired ship design evaluating a range for loading and designchanges.


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Cross Curves of Stability(lines of constant heel angle)

4

32.5

2-- 1.5

10.5

01,500 2,000 2,500 3,000 3,500 4,000 4,500

Displacement (tons)+0 -+-5 10 x*15 -x-20 +.30 +40 -50 -60 70 80 89

Figure 4-1. POSSE Data plotted in Excel

4.2 GENERAL STABILITY CURVEWhile the above data provides a broad evaluation of the hullform, draft is another parameter

that is often specified. The hullform is only valuable in as much as it will be used in an eventualship design which comes with a function and often areas where it must operate which dictatelimits on draft. Based on the desired draft of 14ft and the hull volume below the water, thedisplacement of the ship to analyze is approximately 2990 long tons. General stability curves areformed by taking the data from the Cross-Curves of Form for a certain displacement and plottingrighting arm versus heel angle. These graphs are perhaps more useful because they remove theunneeded displacement data from consideration.


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4.2.1 ASSET DERIVED GENERAL STABILITY CURVEASSET produces General Stability curves for various displacements as shown in Appendix

A. These curves are produced from the hull offsets which ASSET generated for the hull typeand characteristics as defined in chapter 2.

4.2.2. POSSE DERIVED GENERAL STABILITY CURVEPOSSE takes the offsets from ASSET and the center of gravity as estimated above and

determines its own curves of form for the ship. The program can then calculate the righting armdata and produce its own general stability curves. The output from POSSE is shown in Table 4-1below. The curves shown in Figure 4-2 represent the righting arm for the entire range ofdisplacements.POSSE

Hee Angle (deg)Disp 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 89

1, 0 0.52 1.01 1.43 1.76 2.01 2.2 2.35 2.49 2.68 2.94 3.13 3.21 3.16 3.05 2.82 2.48 2.06 1.462, 0 0.44 0.86 1.25 1.6 1.9 2.17 2.42 2.69 2.98 3.16 3.21 3.14 3.02 2.81 2.53 2.18 1.75 1.342,5 0 0.39 0.78 1.15 1.51 1.86 2.2 2.55 2.89 3.11 3.19 3.15 3.03 2.81 2.53 2.22 1.86 1.45 1.093, 0 0.36 0.72 1.09 1.47 1.86 2.27 2.67 2.94 3.08 3.08 2.98 2.8 2.54 2.24 1.91 1.55 1.17 0.843,5 0 0.33 0.68 1.06 1.46 1.89 2.33 2.66 2.85 2.91 2.85 2.72 2.51 2.24 1.95 1.62 1.27 0.92 0.634, 0 0.33 0.67 1.05 1.47 1.92 2.29 2.53 2.64 2.64 2.56 2.4 2.19 1.94 1.66 1.35 1.03 0.7 0.454,5 0 0.34 0.7 1.08 1.51 1.9 2.16 2.3 2.35 2.31 2.21 2.06 1.86 1.63 1.38 1.11 0.82 0.53 0.34,5 0 0.34 0.7 1.08 1.51 1.9 2.16 2.3 2.35 2.31 2.21 2.06 1.86 1.63 1.38 1.11 0.82 0.53 0.31

Table 4-1: POSSE Static Stability Data


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Static Stability Curves(lines of constant displacement)

0o LC 5

-10 10 30 50 70 90Heel Angle (degrees)

-0-1500 -0-2000 -*-2500 -4+-3000

Figure 4-2: POSSE Curves

4.2.3 COMPARISON OF DERIVED GENERAL STABILITY CURVESWith an expected nominal displacement of 2990 LT for the final ship design, the ASSET

and POSSE data for this particular configuration are compared. With the complexities inherentin ship design and the immense number of calculations being performed by the different analysistools, it is a good idea to verify that the data is consistent. Figure 4-3 shows the comparison ofthe ASSET data for 2992 LT to the POSSE data for 3000 LT. It is evident that both programsprovide nearly identical predictions of static stability.


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Static Stability Curves(lines of constant displacement)3.5

3

2.5

2

1.51

0.5

00 10 20 30 40 50 60 70 80 90

Heel Angle (degrees)-- POSSE000T * ASSET991.5TFigure 4-3 ASSET data overlay

4.3 LIMITING CONDITIONSThe Cross Curves of Stability and the General Stability Curves provide the righting arm

values for consideration, but if this was the only factor, any value greater than zero would beadequate. Of course, the ship will be operating in conditions with wind and seas that will tend toroll the ship as well as maneuvering and other operations and conditions. The momentsproduced from these plausible circumstances will be compared to the righting arm to determineif the ship remains upright. However, a hullform's characteristics also include the speed atwhich the ship corrects itself from a roll. If the ship responds too quickly, the sailors couldbecome sick, equipment could damaged, or even personnel injured. Several key parameters areevaluated below to provide a first pass of the suitability of the hullform.


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The close correlation shown in Figure 4-3 helps to verify the analysis completed inASSET. Now ASSET is also used to determine the suitability of the hullform in a variety of

conditions that are meant to simulate worst reasonable cases of real-world conditions. Theresults of these analyses will give the ship designers an idea of the superstructure that can beplaced on the ship as well as the loading necessary to provide adequate stability.

The analysis was based on the range of likely ship displacements of 2991.5 LT plus orminus 500 tons to allow for variations in the eventual design as well as loading changes. Theheight of the transverse metacenter, KM, was determined from the curves of form for thedifferent displacements.

4.3.1 BEAM WINDSAll ships except a submerged submarine experience wind loading. A common approach

is to evaluate beam winds which produce the highest roll moment on the ship. As should beexpected, the more surface area and the higher from the waterline that surface area is, the largerthe moment that will be produced. A 100 knot beam wind is a common specification used forNaval Vessels and is used for this analysis. A notional sail area factor of 1.25 was used. ASSETalso predicts a notional superstructure to determine the center of the wind loading. Appendix Ashows the results in graphical forms for different displacement ships.

4.3.2 HIGH SPEED TURNING

Another large moment that ships experience occurs during high speed maneuvers. Asurface ship rolls outward during the steady state turn. To prevent the ship from rolling over, amoment must be produced by the righting arm.


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4.3.3 ROLL PERIODThe roll period is important for several reasons. If the roll period of the ship corresponds

to the period of the waves, the ship will exhibit a much larger response without additionalmitigations. Also, if the ship rolls too quickly, the crew tends to suffer higher rates ofseasickness, and equipment and cargo can be forcibly moved about the ship. The roll period wascalculated and analyzed. [2] The equation below provides a good first estimate of the roll period.The typical range for the constant C is 0.38 to 0.55 for this size vessel. [2] A value of 0.44 wasselected. The roll period was required to be greater than 15 seconds to allow operation in aprobable sea-state 7 in the Northern Hemisphere. [2] The metacentric height, GM, wasdetermined from the relationship between KM and KG. From these two equations, a maximumKG was then determined to maintain the desired roll period.

GM=KM-KGTroll = C*B/GM1/2

4.3.4 METACENTRIC HEIGHTThe metacentric height is typically required to be greater than 1 foot for operations.

However, as a ship design evolves and a ship is modified throughout its life, the metacentricheight typically decreases. As a result a margin of 1 foot minimum is typically added. Thisresults in a minimum GM of 2 feet.

The table below shows the results of the above analyses. Over the range ofdisplacements, the most limiting case for KG is the high speed turns. Based on the desired draftof approximately 14ft, the ship would displace 2991.5 LT. Loading and modifications to a shipdesign typically increase the weight which would make 2991.5 to 3491.5 LT the most likely


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range for this vessel's final displacement. Even so, the estimated 15.6 ft KG is a little bit high.If the ship is designed with a lower KG , this would increase the stability marginally.

Maximum KG for given condition and displacemtDisplacement 2491.5 2991.5 3491.5KM 20.10 19.74 19.2C100ktbeamwind 19.19 19.32 19.3835 kt turn 15.06 15.24 15.52roll period>15seconds 21.52 21.16 20.62GM >2 ft. 22.10 21.74 21.2C

Table 4-2 Maximum KG limits


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CHAPTER 5. SUMMARY AND CONCLUSIONSWhile ships have historically been designed and analyzed using well-proven manual

methods and hand calculations, computer systems have enabled the naval architect to design,analyze under various conditions, and modify a hullform in a fraction of the time that waspreviously possible, even with a team of experienced naval architects. The two programscurrently used by the US Navy for conducting initial design and analysis, ASSET and POSSE,are used to develop a hullform, quickly calculate the numerous hull coefficients and curves ofform used in naval architecture, and analyze the hullform under stable and certain dynamicconditions.

The hullform is found to be within safe limits at all cases with the exception of high-speed turning, where KG is limiting. This provides invaluable information to the naval architectwhen further design work commences; special attention can be paid during detailed design tolower KG prior to conducting a second round of stability analysis on POSSE.

A comparison of the two programs with standard hand-calculations, derived from navalarchitecture references, is performed to validate the accuracy of both programs. Both programsmatched well with each other and with the hand-calculations, within 1.1% on average, with theexception of Longitudinal Waterplane Inertia Coefficient (CIL), where POSSE's value differedfrom ASSET and hand-calculations by over 8%. This provides a reminder for any navalarchitect to never rely solely on any one design tool or method but to consider all tools.


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ASSET and POSSE are both well-established tools in the US Navy. Each has its strengthsand weaknesses and should be used together to provide an efficient composite analysis tool.

'Composite' here refers to the concurrent use of both tools in designing and evaluating a new orexisting hullform. ASSET is most useful in creating the hullform and deriving the initial hullcoefficients. POSSE is found to present the information in a clearer format and provides the bulkof analysis tools for various loading conditions. Finally, hand calculations provide the final back-up check to verify the tools have been used correctly and the results can be trusted for a safe,efficient design.


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BIBLIOGRAPHY1. Advanced Surface Ship Evaluation Tool (ASSET) Introduction TrainingCourse. CarderockDivision Naval Surface Warfare center. Print2. Gillmer, Thomas Charles. Introduction o Naval Architecture.Annapolis, Md: NavalInstitute, 1982. Print.3. Lamb, Thomas. Ship Design and Construction Vol. I. Grand Rapids: 1s' Impression, 2003.4. Lamb, Thomas. Ship Design and Construction Vol. II. 1l"mpression, 2003.5. Taggart, Robert. Ship Designand Construction.New York, NY: The Society of NavalArchitects and Marine Engineers, 1980.6. User'sHandbook or Programof Ship Salvage Engineering POSSE Version 1.0). Naval SeaSystems command, 1992. Print7. Lewis, Edward V. PrinciplesofNavalArchitecture, Volume I StabilityandStrength.

Washington D.C.: The Society of Naval Architects and Marine Engineers, 1989.8. Rawson, K. J., and E. C. Tupper. Basic Ship TheoryHydrostaticsand Strength/Chapters1 to9 (BasicShip Theory). New York: Longman Pub Group, 1994.


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APPENDIX A. ASSET PRINTED AND GRAPHIC REPORTS

ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:17. 3DATABANK-JOSH PROJ 1 AND 2 2.701 FALL SHIP-JOSH 1GRAPHIC DISPLAY NO. 1 - B~ODY PLAN

DWL

BLi i i i SCALE0 5 10 15 FT

'


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ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:17. 3DATABANK-JOSH PROJ 1 AND 2 2.701 FALL SHIP-JOSH 1GRAPHIC DISPLAY NO. 2 - HULL ISOMETRIC VIEW


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ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:17. 3DATABANK-JOSH PROJ 1 AND 2 2.701 FALL SHIP-JOSH 1GRAPHIC DISPLAY NO. 5 - HULL SECTIONAL AREA CURVE500

400

300

200

100

0 ' 1 1 1 1 1 1 1 1 -- 11.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0AP FRACTION OF SHIP LBP FROM FP FP

ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:19.35DATABANK-JOSH PROJ 1 AND 2 2.701_FALL_ SHIP-JOSH 1

PRINTED REPORT NO. 1 - HULL GEOMETRY SUMMARYHULL OFFSETS IND- GENERATEHULL DIM IND- NONEHULL STA IND- GIVENHULL BC IND- CONV DD

MIN BEAM, FTMAX BEAM, FTHULL FLARE ANGLE, DEGFORWARD BULWARK, FT

HULL PRINCIPAL DIMENSIONS (ON DWL)LBP, FTHULL LOA, FTBEAM, FTBEAM @ WEATHER DECK, FTDRAFT, FTDEPTH STA 0, FTDEPTH STA 3, FTDEPTH STA 10, FTDEPTH STA 20, FTFREEBOARD @ STA 3, FTSTABILITY BEAM, FT

380.00396.2840.6040.8214.0033.6030.4226.0026.7620.42

39.33

PRISMATIC COEFMAX SECTION COEFWATERPLANE COEFLCB/LBPHALF SIDING WIDTH, FT

BOT RAKE, FTRAISED DECK HT, FTRAISED DECK FWD LIM, STARAISED DECK AFT LIM, STABARE HULL DISPL, LTONAREA BEAM, FT

30.00105.60

.004.00

0.5800.8360.7370.5151.00

0.000.00

2992.5538.00


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STABILITY DATA ON LWL

LGTH ON WL, FTBEAM, FTDRAFT, FTFREEBOARD @ STA 3, FTPRISMATIC COEFMAX SECTION COEFWATERPLANE COEFWATERPLANE AREA, FT2WETTED SURFACE, FT2BARE HULL DISPL, LTONAPPENDAGE DISPL, LTONFULL LOAD WT, LTON

379.9840.6013.9720.450.5800.8340.741

11431.1116220.88

2983.0261.29

3044.31

KB, FTBMT, FTKG, FTFREE SURF COR, FTSERV LIFE KG ALW, FT

GMT, FTGML, FTGMT/B AVAILGMT/B REQ

8.4411.0115.60

0.000.003.85

880.110.0950.080

ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:19.35DATABANK-JOSH PROJ 1 AND 2 2.701 FALL_ SHIP-JOSH 1

PRINTED REPORT NO. 2 - HULL OFFSETSNO. 1, AT X =

HALF BEAM,FT0.0000.1210.1720.2480.3440.4530.5690.6860.7970.8960.9771.0351.061

NO. 2, AT X=HALF BEAM,FT

0.0000.2190.4680.8291.2831.8122.3943.0113.6434.2714.8765.4375.935


0.1020.2560.5400.9401.4452.042

-16.282 FTWATERLINE,FT

34.39334.41034.42834.44534.46234.47934.49634.51434.53134.54834.56534.58234.600

-8.141 FTWATERLINE,FT

23.93724.78225.62626.47127.31628.16129.00629.85030.69531.54032.38533.23034.074

0.000 FTWATERLINE, FT

14.00015.63017.26118.89120.52122.152

STATIONPOINT

123456789

10111213

STATIONPOINT

123456789

10111213

STATIONPOINT

123456

BARE HULL DATA ON LWL


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789

10111213STATION

POINT123456789

101112131415161718192021222324252627

STATIONPOINT

123456789

10111213141516171819202122

2.7183.4614.2595.0995.9686.8557.746NO. 4, AT X=

HALF BEAM,FT0.0000.0310.0830.1600.2550.3620.4750.5920.7090.8230.9321.0361.1321.2201.2991.5511.9132.3772.9313.5674.2755.0465.8696.7367.6368.5609.499


0.0000.0970.1810.3140.4850.6830.8981.1221.3491.5741.7922.0022.1992.3832.5502.8753.2963.8054.3945.0575.7846.569

23.78225.41227.04328.67330.30431.93433.5649.500 FT

WATERLINE, FT5.5426.1476.7517.3557.9598.5639.1679.771

10.37510.97911.58412.18812.79213.39614.00015.58217.16518.74720.32921.91223.49425.07726.65928.24129.82431.40632.988

19.000 FTWATERLINE, T

1.5582.4473.3364.2245.1136.0026.8907.7798.6689.55710.44511.33412.22313.11114.00015.53617.07218.60820.14421.68123.21724.753


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2324252627

STATIONPOINT

123456789

101112131415161718192021222324252627

STATIONPOINT1

23456789

101112131415161718192021222324

7.4048.2819.192

10.13011.088


0.2480.8691.2441.6041.9642.3242.6823.0353.3813.7164.0404.3514.6474.9265.1895.5986.0826.6357.2547.9308.6599.434

10.25011.10111.98112.88513.806

NO. 7, AT X=HALF BEAM,FT0.865

2.1472.9583.6254.2014.7125.1735.5955.9856.3506.6947.0207.3327.6327.9218.3458.8329.3789.976

10.62011.30612.02612.77713.551

26.28927.82529.36130.89732.433

38.000 FTWATERLINE,FT

0.0001.0002.0003.0004.0005.0006.0007.0008.0009.00010.00011.00012.00013.00014.00015.44916.89818.34619.79521.24422.69324.14225.59027.03928.48829.93731.385

57.000 FTWATERLINE, FT0.000

1.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.36816.73718.10519.47420.84222.21023.57924.94726.316


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252627

STATIONPOINT

123456789

101112131415161718192021222324252627

STATIONPOINT

123456789

1011121314151617181920212223242526

14.34315.14815.959


1.0003.2504.6735.7606.6207.3137.8858.3648.7759.1379.4639.765

10.05110.33010.60810.99911.44511.94012.47813.05413.66014.29214.94215.60516.27516.94517.609


1.0004.3236.3437.8328.9599.827

10.50211.03511.46411.81712.11712.38312.63012.86913.11013.43813.81314.23014.68315.16415.66816.18916.71917.25317.78518.308

27.68429.05330.421


0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.29516.59017.88519.18020.47521.77023.06524.36025.65526.95028.24529.540


0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.22816.45717.68518.91420.14221.37122.59923.82825.05626.28527.513


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27STATION

POINT123456789

101112131415161718192021222324252627

STATIONPOINT

123456789

101112131415161718192021222324252627

STATION

18.816NO. 10, AT X =

HALF BEAM,FT1.0005.4617.9699.76811.10112.10012.85513.43013.87214.21614.49314.72414.92915.12015.31215.56315.85416.17916.53216.90717.29817.69918.10318.50618.89919.27919.638

NO. 11, AT X =HALF BEAM,FT

1.0006.6679.524

11.51812.97114.04614.84715.44515.89216.22816.48516.68616.85116.99617.13517.30817.51317.74417.99718.26518.54418.82819.11219.39019.65719.90820.136

NO. 12, AT X =

28.742114.000 FT

WATERLINE, T0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.16916.33817.50718.67619.84421.01322.18223.35124.52025.68926.85828.027


0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.11616.23317.34918.46519.58120.69821.81422.93024.04625.16326.27927.395

152.000 FT


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POINT123456789

101112131415161718192021222324252627

STATIONPOINT

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101112131415161718192021222324252627

STATIONPOINT

1

HALF BEAM,FT1.0007.791

10.88412.98614.49815.60716.42617.03117.47617.80318.04118.21618.34818.45118.54018.64418.77118.91719.07719.24719.42419.60219.77819.94720.10520.24820.371


1.0008.510

11.80614.01815.59516.74217.58118.19218.63318.94619.16419.31319.41319.48019.52819.57919.64319.71719.79919.88619.97520.06420.15020.23120.30320.36320.411


1.000

WATERLINE, FT0.0001.0002.0003.0004.0005.0006.0007.0008.0009.00010.00011.00012.00013.00014.00015.07116.14117.21218.28219.35320.42321.49422.56523.63524.70625.77626.847


0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.03216.06417.09518.12719.15920.19121.22322.25523.28624.31825.35026.382


0.000


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23456789

101112131415161718192021222324252627

STATIONPOINT

123456789

101112131415161718192021222324252627

STATIONPOINT

123

8.70212.14714.47116.12917.33418.21218.84719.30019.61719.83119.96920.05420.10220.12820.14920.17520.20320.23320.26320.29420.32220.34920.37220.39120.40420.411


1.0008.57511.94914.25215.92617.17118.10518.80319.32219.70219.97320.15920.28120.35320.38920.40620.41920.42620.43020.43120.43020.42720.42220.41820.41420.41120.411


1.0007.639

11.056

1.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00015.00016.00017.00018.00019.00020.00021.00022.00023.00024.00025.00026.000


0.0001.0002.0003.0004.0005.0006.0007.0008.0009.000

10.00011.00012.00013.00014.00014.97515.95016.92517.90018.87619.85120.82621.80122.77623.75124.72625.701


0.1651.1532.141


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4 13.4905 15.3016 16.6707 17.7088 18.4959 19.085

10 19.52211 19.84012 20.06413 20.21514 20.31115 20.36516 20.39617 20.41818 20.43219 20.43920 20.44121 20.43922 20.43423 20.42724 20.42025 20.41426 20.41127 20.411

STATION NO. 17, AT X =POINT HALF BEAM,FT

1 1.0002 6.5413 10.0294 12.6165 14.5726 16.0597 17.1888 18.0419 18.679

10 19.15111 19.49412 19.73913 19.90914 20.02515 20.10316 20.16217 20.21218 20.25519 20.29020 20.32021 20.34422 20.36223 20.37724 20.38925 20.39826 20.40527 20.411

STATION NO. 18, AT X =POINT HALF BEAM,FT

1 1.0002 5.7823 9.1644 11.7395 13.716

3.1294.1185.1066.0947.0828.0719.05910.047

11.03512.02413.01214.00014.95715.91416.87217.82918.78619.74320.70021.65722.61523.57224.52925.486


0.7041.6542.6043.5534.5035.4536.4027.3528.3029.252

10.20111.15112.10113.05014.00014.94615.89216.83817.78518.73119.67720.62321.56922.51523.46224.40825.354


1.6612.5423.4244.3055.186


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6789

101112131415161718192021222324252627

STATIONPOINT

123456789

101112131415161718192021222324252627

STATIONPOINT

1234567

15.23916.40917.30517.98718.50118.88519.16819.37519.52519.63419.73319.82719.91720.00220.08120.15320.21720.27420.32120.35920.38620.402


1.0005.1948.37110.83812.76514.27215.45116.37217.08917.64418.07118.39618.64318.82918.96819.11419.25819.40019.53719.66719.78919.89919.99720.08120.14720.19620.224


1.0004.6727.5859.892

11.72513.18714.353

6.0686.9497.8308.7129.593

10.47511.35612.23713.11914.00014.94215.88416.82617.76818.71019.65320.59521.53722.47923.42124.36325.305


3.0303.8144.5975.3816.1646.9487.7328.5159.29910.08210.86611.64912.43313.21614.00014.94515.89016.83517.78018.72519.67020.61521.56022.50523.45024.39525.339

304.000 FTWATERLINE, T

4.7565.4166.0766.7377.3978.0578.717


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89

101112131415161718192021222324252627

STATIONPOINT

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101112131415161718192021222324252627

STATIONPOINT

123456789

15.28316.02416.61217.07617.43817.71917.93318.09418.29318.49118.68518.87319.05119.21819.37119.50619.62219.71519.78319.823


1.0004.1686.7758.88310.59311.98613.12114.04714.80015.41015.90116.29016.59316.82316.99117.25017.50617.75617.99718.22618.43918.63418.80718.95519.07519.16419.218

NO. 22, AT X =HALF BEAM, FT

1.0003.6645.9307.8099.372

10.67511.76212.66913.421

9.37810.03810.69811.35912.01912.67913.34014.00014.95515.91016.86417.81918.77419.72920.68321.63822.59323.54824.50225.457


6.7327.2517.7718.2908.8099.3289.847

10.36610.88511.40411.92412.44312.96213.48114.00014.97115.94316.91417.88618.85719.82920.80021.77222.74323.71524.68625.658


8.8259.1959.5659.934

10.30410.67311.04311.41311.782


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101112131415161718192021222324252627

STATIONPOINT

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101112131415161718192021222324252627

STATIONPOINT

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1011

14.04114.54614.94815.26015.49015.64715.97216.29316.60516.90517.18917.45317.69417.90818.09218.24218.35418.425


1.0003.1625.0656.6948.0909.28710.31111.18411.92212.53913.04313.44513.75013.96514.09314.49214.88215.26015.62215.96416.28216.57116.82917.05017.23217.37017.460


1.0002.9184.6376.1387.4478.5879.57710.42911.15611.76712.267

12.15212.52212.89113.26113.63014.00014.99515.99016.98617.98118.97619.97120.96621.96122.95723.95224.94725.942


10.89911.12111.34211.56411.78512.00712.22812.45012.67112.89313.11413.33613.55713.77914.00015.02616.05217.07718.10319.12920.15521.18022.20623.23224.25825.28426.309


11.89912.04912.19912.34912.49912.64912.79912.94913.09913.24913.400


68/96

12131415161718192021222324252627

STATIONPOINT

123456789

101112131415161718192021222324252627

12.66312.96013.16213.27113.70714.13314.54314.93415.30315.64515.95716.23316.47216.66816.81916.919


1.0002.6904.2275.6006.8227.9058.8599.691

10.40611.00911.50411.89312.17912.36512.45012.92513.38413.82414.24014.63114.99215.32015.61115.86216.07016.23116.341

ASSET/MONOSC V5.3.0 - HULL GEOM MODULE - 1/ 8/2010 13:19.35DATABANK-JOSH PROJ 1 AND 2 2.701_FALL_ SHIP-JOSH 1

PRINTED REPORT NO. 3 - HULL BOUNDARY CONDITIONSHULL OFFSETS IND-GENERATEHULL BC IND-CONV DDLBP, FTBEAM, FTDRAFT, FTDEPTH STA 0, FTDEPTH STA 3, FTDEPTH STA 10, FT

380.0040.6014.0033.6030.4226.00

HULL STA IND-GIVENLCB/LBPLCF/LBPHALF SIDING WIDTH, FTBOT RAKE, FTFWD RAISED DECK LIMITAFT RAISED DECK LIMIT

13.55013.70013.85014.00015.04416.08717.13118.17519.21820.26221.30622.35023.39324.43725.48126.524

380.000 FTWATERLINE

12.87212.95213.03313.11313.19413.27513.35513.43613.51613.59713.67813.75813.83913.91914.00015.06316.12717.19018.25319.31720.38021.44322.50723.57024.63325.69726.760

0.5150.569

1.000.00


69/96

DEPTH STA 20, FTPRISMATIC COEFMAX SECTION COEFNO POINTS BELOW DWLNO POINTS ABOVE DWLPOINT DIST FAC ABOVE DWLPOINT DIST FAC BELOW DWLBOW OVERHANGSTERN OVERHANG

26.760.5800.83615 .12.

1.0001.0000.0430.007

RAISED DECK HT, FTWATERPLANE COEF

FWD KEEL/BL LIMITAFT KEEL/BL LIMITBOW ANGLE, DEGBOW SHAPE FACSTA 20 SECTION COEFHULL FLARE ANGLE, DEG

SECTIONAL AREA AND DWL CURVESAREA DWL

STA 0 ORDINATESTA 0 SLOPESTA 20 ORDINATESTA 20 SLOPEPARALLEL MID LGTHSTA MAX ORDINATESTA MAX AREA SLOPETENSOR NO 1TENSOR NO 2TENSOR NO 3TENSOR NO 4TENSOR/POLY SWITCH

DECK AT EDGE CURVESTATION 0 OFFSETSTA 0 SLOPESTA 10 OFFSETSTA 10 SLOPESTATION 20 OFFSETSTA 20 SLOPEPARALLEL MID LGTHSTA OF PARALLEL MID

0.000-0.2060.0410.7670.000

10.5000.0000.0000.0000.0000.000

-1.000

0.380-1.800

1.0000.0000.8010.5840.254

11.205

0.005-1.146

0.6100.7900.000

11.4000.0000.0000.0000.0000.000

-1.000FLAT OF BOTTOM CURVEST A OF TRANS STARTSLOPE-STA OF TRANS STARTSTA OF START OF MIDSTA OF END OF MIDST A OF TRANS ENDSLOPE-STA OF TRANS ENDFLAT OF BOT ANGLE, DEGELLIPSE RATIO

SLOPES AT SECTION CURVES

STA 0 ORDINATE, DEGSTA 0 SLOPESTA 10 ORDINATE, DEGSTA 10 SLOPESTA 20 ORDINATE, DEGSTA 20 SLOPEPARALLEL MID LGTHSTA OF PARALLEL MID

0.000.737

0.0870.55050.000.0000.700

10.0000.000

10.00010.00010.000

0.0000.0501.000

BO T36.750

104.1611.570

-0.5003.000

60.0000.060

10.500

DW L

87.00088.09789.000

0.00065.64128.462

0.00010.335

DAE61.38952.18590.000

0.00085.497

9.3590.000

10.

hydrostatic and intact stability analysis for a surface ship

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