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LNB 20303 Naval Architecture 1

CHAPTER 2: HULL GEOMETRY

Prepared by: Muhammad Nasuha Mansor

Hull Form

The way to represent hull form?The Lines Plan

What is lines plan???What is lines plan???

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•A ship's hull is a very complicated 3 dimensional shape.

•The ship's hull form is represented graphically by a lines drawing.

•The lines drawing consist of projections of the intersection of the hull with a series of planes.

•Planes in one dimension will be perpendicular to planes in the other two dimensions.

•these series of planes are projected to represent views p p j pfrom the front, top, or side of the ship.

•This three separate projections, or views, called the Body Plan, the Half-Breadth Plan, and the Sheer plan,

The Projection of Lines onto 3 Orthogonal Planes

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The Half-Breadth Plan

The Profile Plan

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The Body Plan

Example 1: Lines Plan of the USNA Yard Patrol Craft

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Example 2: Lines plan

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Example 3: Lines plan

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Table of Offsets

To calculate geometric characteristics of the hull using numerical techniques, the information on the lines plan drawing is converted to a numerical representation in adrawing is converted to a numerical representation in a table called the table of offsets. It is a digital description of the entire hull (hull form representation in coordination form)The table of offsets lists the distance from the center plane to the outline of the hull at each station and waterline. This di t i ll d th “ ff t” “h lf b dth di t ” Bdistance is called the “offset” or “half-breadth distance”. By convention this is the “y” direction. It is needed during the calculation of geometric properties of the hull such as sectional area, waterplane area, submerged volume and the longitudinal center of flotation.

Example 1: Table of Offsets of the USNA Yard Patrol Craft

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Example 2: Table of Offsets

TABLE OF OFFSETS (HALF BREADTH) in metresWaterline Name and Distance from Baseline in metres

BASELINE WL 0.5m WL 1.0m WL 2.0m WL 3.0m WL 4.0m WL 5.0m

Dis

tanc

e fro

m S

tatio

n 0

in m

etre

s

TRSM -3.50 3.09 3.09 3.09AP 0.00 4.50 4.50 4.500.5 .14 0.29 4.50 4.50 4.501.0 2.28 0.25 0.27 0.27 0.29 4.50 4.50 4.481.5 3.41 0.25 0.27 0.27 2.54 4.50 4.50 4.462.0 4.55 0.25 0.27 0.27 4.24 4.50 4.50 4.452.5 5.69 0.25 0.27 0.27 4.43 4.50 4.50 4.433.0 6.83 0.25 0.27 3.20 4.49 4.50 4.50 4.423.5 7.96 0.25 0.93 3.83 4.50 4.50 4.50 4.414.0 9.10 2.09 4.06 4.50 4.50 4.50 4.415.0 11.38 2.90 4.04 4.50 4.50 4.50 4.406.0 13.65 2.43 3.51 4.16 4.37 4.47 4.46

Stat

ion

Nam

e an

d D

6.5 14.79 2.04 3.09 3.85 4.20 4.42 4.507.0 15.93 1.59 2.57 3.44 3.92 4.29 4.487.5 17.06 1.14 1.99 2.92 3.52 4.03 4.458.0 18.20 0.74 1.42 2.31 2.98 3.64 4.378.5 19.34 0.37 0.86 1.65 2.33 3.09 4.119.0 20.48 0.38 0.96 1.58 2.37 3.579.5 21.61 0.31 0.77 1.51 2.70FP 22.75 0.00 0.33 1.39

Example 3: Table of Offsets

T A B L E O F O F F S E T S (H A L F B R E A D T H) i n m e t r e s

Waterline Name and Distance from Baseline in metres

BASELINE WL 0.25m WL 0.50m WL 0.75m WL 1.00m WL 1.25m WL 1.50m WL 2.00m WL 2.50m WL 3.00m WL 3.50m WL 4.00m

Dis

tanc

e fro

m S

tatio

n 0

in m

etre

s

TRSM -1.20 0.08 2.08 3.42 3.47 3.52 3.62 3.72AP 0.00 0.31 2.17 3.42 3.47 3.52 3.62 3.722.0 2.40 0.78 2.34 3.42 3.47 3.52 3.61 3.714.0 4.80 1.12 2.47 3.42 3.47 3.51 3.61 3.70 3.796.0 7.20 0.20 1.38 2.57 3.42 3.46 3.51 3.60 3.69 3.788.0 9.60 0.53 1.59 2.65 3.42 3.46 3.51 3.60 3.68 3.7710.0 12.00 0.79 1.75 2.70 3.42 3.46 3.50 3.59 3.68 3.7612.0 14.40 0.88 1.76 2.65 3.41 3.46 3.50 3.58 3.67 3.75BP 15.40 0.00 0.86 1.72 2.59 3.41 3.45 3.49 3.58 3.66 3.75

14.0 16.80 0.00 0.83 1.66 2.49 3.40 3.44 3.49 3.57 3.66 3.7415.0 18.00 0.00 0.79 1.59 2.38 3.18 3.44 3.48 3.57 3.65 3.7416.0 19.20 0.00 0.76 1.51 2.27 3.02 3.43 3.47 3.56 3.64 3.7317.0 20.40 0.00 0.71 1.43 2.14 2.85 3.41 3.45 3.54 3.63 3.72 3.80 3.8018.0 21.60 0.00 0.67 1.33 2.00 2.67 3.37 3.42 3.51 3.61 3.71 3.80 3.8019.0 22.80 0.00 0.62 1.24 1.86 2.48 3.10 3.36 3.47 3.58 3.69 3.80 3.8020 0 24 00 0 00 0 55 1 10 1 66 2 21 2 76 3 25 3 38 3 52 3 66 3 80 3 80

Stat

ion

Nam

e an

d D 20.0 24.00 0.00 0.55 1.10 1.66 2.21 2.76 3.25 3.38 3.52 3.66 3.80 3.80

21.0 25.20 0.00 0.48 0.95 1.43 1.90 2.38 2.85 3.21 3.40 3.59 3.78 3.8022.0 26.40 0.00 0.39 0.79 1.18 1.57 1.97 2.36 2.93 3.20 3.47 3.74 3.7823.0 27.60 0.00 0.31 0.62 0.94 1.25 1.56 1.88 2.52 2.88 3.24 3.59 3.6924.0 28.80 0.00 0.21 0.43 0.66 0.89 1.13 1.36 1.97 2.40 2.83 3.26 3.4324.5 29.40 0.07 0.27 0.47 0.67 0.87 1.08 1.49 2.07 2.55 3.03 3.2525.0 30.00 0.03 0.20 0.37 0.55 0.73 1.09 1.67 2.20 2.74 3.02FP 30.80 0.00 0.15 0.48 1.02 1.64 2.26 2.66

26.0 31.20 0.13 0.63 1.29 1.96 2.4126.5 31.80 0.69 1.42 2.0027.0 32.40 0.38 1.36

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Hull Geometry

Forward Perpendicular (FP): A perpendicular the point where the foreside of the stem meets the summer load line.After Perpendicular (AP): A perpendicular drawn at the point where the aft side of the rudder post meets the summer load line. Where no rudder post is fitted it is taken as the centre line of the rudder stock.Length Between Perpendiculars (LBP): The length between the forward and aft perpendiculars measured along the summer gload line.Amidships: A point midway between the after and forward perpendiculars.Length Overall (LOA): Length of vessel taken over all extremities.

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Moulded dimensions are often referred to; these are taken to the inside of plating on a steel ship.

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Base Line: A horizontal line drawn at the top of the keel plate All vertical moulded dimensions are measuredplate. All vertical moulded dimensions are measured relative to this line.Moulded Beam: Measured at the midship section is the maximum moulded breadth of the ship.Moulded Draft: Measured from the base line to the summer load line at the midship section.Moulded Depth: Measured from the base line to the heel of the upper deck beam at the ship’s side amidships.

Extreme Beam: The maximum beam taken over all extremitiesextremities.Extreme Draft: Taken from the lowest point of keel to the summer load line. Draft marks represent extreme drafts.Extreme Depth: Depth of vessel at ship’s side from upper deck to lowest point of keel.Half Breadth: Since a ship’s hull is symmetrical about the longitudinal centre line, often only the half beam or half breadth at any section is given.

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Freeboard: The difference between the depth at side and the draught It is vertical distance from the waterlineand the draught. It is vertical distance from the waterline to the upperside of the deck plating at sideSheer: Tendency of a deck to rise above the horizontal in profile.Camber (or Round of Beam): Curvature of decks in the transverse direction. Measured as the height of deck at

t b th h i ht f d k t idcentre above the height of deck at side.Rise of Floor (or Deadrise): The rise of the bottom shell plating line above the base line. This rise is measured at the line of moulded beam.

Tumblehome: The inward curvature towards the middle line (centerline) of the side shell above the waterlineFl Th t d t t d th idl liFlare: The outward curvature towards the midle line (centerline)of the side shell above the waterline. It promotes dryness and is therefore associated with the fore end of ship.Stem Rake: Inclination of the stem line from the vertical.

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Last but not least, in the hull geometry definition, there are certain coefficients, called as form coefficientsa e ce a coe c e s, ca ed as o coe c e sNon- dimensionalThey will later used as the values as guide to describe the fatness of slimness of the hull, especially below the waterline.4 basic form coefficients are:

Bl k ffi i t Cb1.Block coefficient, Cb.2.Midship coefficient, Cm.3.Waterplane area coefficient, Cwp4.Prismatic coefficient, Cp

1. Block coefficient, CbGives the ratio of the volume of the underwater body (∇) and the rectangular block bounded by length (Lpp)and the rectangular block bounded by length (Lpp), breadth (B), and draught (T). A vessel with a small Cb is referred to as ‘fine’ (fast ships). Customary values for the Cb of several types of vessel:

Type Cb FormVery fast ship 0.50 - 0.65 Fine

Ordinary cargo ship 0.65 – 0.75 Moderate

Slow bulk carrier 0.75 – 0.90 Full

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1. Midship coefficient, CmRatio of the immersed midship section area (Am) to the

f th t l h i th b dth darea of the rectangular having the same breadth and draught of the ship. 0.85 fast ship, 0.99 slow ship

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1. Waterplane coefficient, CwpThe ratio of the area of the waterplane area to the area of the rectangular having a length (L) and a breadth (B)of the rectangular having a length (L) and a breadth (B) equal to the ship moulded breadth.

1. Prismatic coefficient, CpThe ratio of the volume of displacement to the volume of

i ( l t th l th b t di l Lprism (equal to the length between perpendiculars , Lppmultiply with a cross- sectional area of the midship, AmApproximate range of values: 0.55 fine ship, 0.85 full ship.

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SUMMARYAs groundwork, knowledge of Naval Architecture can be started with

the familiarization of types of floating objects and ships and how they are categorized. Insightful of this part could bring better perspective in going deeper about Naval Architecture study. At the same time terminologies and geometries

f th t i l hi i l b di t dof the typical ship, progressively can be digested.

Types of floating objects and ships basically are categorized in several ways. It can be possibly classed base on the functions, and some references clustered the types of ship according to their means of physical support while in operation. Three broad classifications that are frequently used by naval architects are aerostatic support, hydrodynamic support and hydrostatic support.

Definitely with the well briefed of basic terminologies and geometriesDefinitely with the well briefed of basic terminologies and geometries of the ship will be helpful for learner to further explore about the naval architecture. The earliest drawing in this study that should be discussed is called a lines plan drawing. A ship's hull basically is a very complicated 3 dimensional shape. The lines plan graphically represents this hull form in scaled 2D view. The drawing usually displays information in three reference planes. These series of planes are projected to represent views from the front, top, or side of the ship.

In marine terminology, it is called the Body Plan, the Half-Breadth Plan, and the Sheer plan (sometimes known as Profile plan). The basic lines plan consists of three (3) reference lines drawn in each of those views. They are station lines, buttock lines and waterlines. Besides, lines plan drawing should also include principle dimensions of that particular ship. Thisdrawing should also include principle dimensions of that particular ship. This basically describes a size of the ship in term of length, breadth, height and many more.

This lines plan drawing can also be interpreted into numerical presentation. It is called a table of offsets. Table of offsets is a digital description of the entire hull form, represents in coordinates form. It is needed in order to calculate geometrics of the hull using numerical techniques, which mainly a part of the naval architecture works.

The completed lines plan drawing and table of offsets basically will be the main input to proceed with the next stage. Hydrostatics calculation is one of the earliest parts in naval architecture study, and can be determined right after the lines plan and table of offsets are generated.