Lecture Notes of Naval Architecture I

7/15/2019 Lecture Notes of Naval Architecture I

http://slidepdf.com/reader/full/lecture-notes-of-naval-architecture-i 1/151

Course Contents

• Ship Types and Hull forms

• Transverse stability at small and large angles

• Longitudinal stability and trim• Stability when grounded

• Horsepower and hull resistance

• IMO regulations

2



3

1 Ship Types



Classification of Ship by UsageClassification of Ship by Usage

•Merchant Ship

• Naval & Coast Guard Vessel

• Recreational Vessel

• Utility Tugs

• Research & Environmental Ship

• Ferries

3



Classification of Ship by Support Type

• Aerostatic Support

- ACV (Air Cushion Vehicles)- SES (Captured Air Bubble)

• Hydrodynamic Support

- Hydrofoil

- HYSWAS (HYdrodynamic Small Waterplane Area Ship)

- Planning Hull

• Hydrostatic Support

- Conventional Ship

- Catamaran

- SWATH (Small Waterplane Area Twin Hull)

- Deep Displacement

• Submarine

- Submarine

- AUV/ROV4



- Supported by cushion of air generated by a fan.

- ACV (Air Cushion Vehicle)

hull material : rubber

propeller : placed on the deck

amphibious operation

- SES (Surface Effect Ship)side hull : rigid wall(steel or FRP)

bow : skirt

propulsion system : placed under the water

water jet propulsionsupercavitating propeller

not amphibious operation

Aerostatic Support

5



Air Cushion VehicleAir Cushion Vehicle6



SES Ferry

NYC SES

Fireboat

7



250’ SES Ferry

8



• Planning HullPlanning Hull

-- supported by the hydrodynamic pressure developed supported by the hydrodynamic pressure developed under the hull at high speed under the hull at high speed

-- V or flat type shapeV or flat type shape-- commonly used in pleasure boat, patrol boat,commonly used in pleasure boat, patrol boat,missile boat, racing boatmissile boat, racing boat

Hydrodynamic SupportHydrodynamic Support

9



10



• Hydrofoil ShipHydrofoil Ship

-- supported by a hydrofoil, like wing on an aircraftsupported by a hydrofoil, like wing on an aircraft

-- fully submerged hydrofoil shipfully submerged hydrofoil ship

-- surface piercing hydrofoil shipsurface piercing hydrofoil ship

Hydrodynamic Support

Hydrofoil Ferry

11



Hydrostatic Support

• Displacement ship

- conventional type of ship

- carries high payload

- low speed

• SWATH

- small water plane area twin hull (SWATH)- low wave-making resistance

- excellent roll stability

- large open deck

- disadvantage : deep draft and cost

• Catamaran/Trimaran- twin hull

- other characteristics are similar to the SWATH

• Submarine12



SWATH vessel13



14



15



16



Archimedes Principle

Law: a body floating or submerged in a fluid

is buoyed up by a force equal to the weight of

the water it displaces

Depth to which ship sinks depends on density

of water (r = 1 ton/35ft3

seawater)

17



Ship sinks until weight of water displaced by

the underwater volume is equal to the weight

of the ship

Forces of gravity: G = mshipg =Wship

Forces of buoyancy: B =rwaterVdisplaced

Wship = rwater Vdisplaced

18



• A FLOATING BODY DISPLACES A VOLUME

OF WATER EQUAL IN WEIGHT TO THE

WEIGHT OF THE BODY.

DISPLACEMENT

00

G

19



DISPLACEMENT

00

G



DISPLACEMENT

04

G

B



DISPLACEMENT

09

G

B



DISPLACEMENT

16

G

B



DISPLACEMENT

20

G

B



20

Center of Gravity (G):Center of Gravity (G): all gravity forces as

one force acting downward through ship’sgeometric center

Center of Buoyancy (B):Center of Buoyancy (B): all buoyancy forcesas one force acting upward through

underwater geometric center



21



22

Definition

11-- PerpendicularsPerpendiculars Imaginary lines perpendicular to the base line or plane (and the

water line)

On the ship there is a :

-- Forward PerpendicularForward Perpendicular (F(Fpppp or For Fpp))

This is the line crosses the intersection of the water line and the

front of the stem

--Aft PerpendicularAft Perpendicular (A(Apppp or Aor App))

This line usually aligns the centre line of the rudder stock. This

is the imaginary line around which the rudder rotates.



23



24



25

2. Waterlines2. Waterlines

The waterline of a ship lying in the water . There are different

waterlines (i.e load-lines) for different loading conditions, suchas:

-- Light waterlineLight waterline

The waterline of a ship carrying only her regular inventory.

-- Fully loaded waterlineFully loaded waterline

The waterline of maximum load draft in sea water.

-- Construction (Scantling) waterlineConstruction (Scantling) waterline (C(CWLWL))

The waterline used as the limit to which the various structuralcomponents are designed .



26

33-- Plimsoll Mark (freeboard mark)Plimsoll Mark (freeboard mark)

The freeboard mark is a symbol indicating the maximal

immersion of the ship in the water, leaving a minimal freeboard for safety.

The mark consists of a circle

with a diameter of 300 mm,

through which a horizontallines is drawn with its upper

edge going through the centre

of the circle.



27

This level indicates the minimal freeboard in salt water summer

conditions. Beside this circle the loadline mark consists of a number of

horizontal lines indicating the minimal freeboard required for other than

summer conditions.All freeboard lines are 25 mm wide and are connected by a vertical line.



28

The freeboard mark is placed

midships on each side of the ship.

The minimal operating freeboard

depends on:

-Ship’s position at sea

-The time of year (summer, winter,etc,.._



29

44-- Deck LineDeck Line

In general this is the extended line from the upper side of the

freeboard deck at the ship’s side.

The deck line is placed above the Plimsoll mark so that the

freeboard can be easily monitored by the ship’s crew or other

interested parties

55-- Permanent marks on the shipPermanent marks on the ship’’s hulls hullIt is very important the draft marks can be accurately read

as easily as possible.



30

1. Draft to portside fore :

53.8 dm



31

2. Draft to portside fore:

5.17 meters



32

3. Draft on the stern is given in

meters and feet: 9.36 m = 30’ 7”



33

4. Draft to starboard aft: 9.35

meters



34

5- Draft midships: 7.00 meters

6- Deck line

7. Plimsoll mark



35

Dimensions

FP Forward Perpendicular

AP After Perpendicular

WL Waterline



36 WL WaterlineWL Waterline

CL CentrelineCL Centreline



37

11- Length over all LOA

It is the overall length of the vessel, i.e the horizontal distance over the

extremities from stem to stern

22- Length between perpendicular LPP

It is the horizontal distance between the FP and AP

33-- Length waterline LLWLWL

Horizontal distance between the fore and aft when the ship is loaded atthe summer mark, less the shell.

44-- Breadth over allBreadth over all BBOAOA

The maximum breadth of the ship as measured from the

outer hull on the starboard to the outer hull on port side,including rubbing bars, permanent fenders.



38

44-- Breadth or beamBreadth or beam BMLD

The greatest moulded breadth, measured from side to side at the

outside of the frames, but inside the shell

55- DepthDepth D

The vertical distance between the base line and the upper continuous

deck and is measured at the half L pp at the side of the ship

66- Draft ForwardDraft Forward (TFWD)

Vertical distance between the waterline and the underside of the

keel, as measured at the forward perpendicular

66- Draft at the sternDraft at the stern (TAF)

Vertical distance between the waterline and the underside of the

keel, as measured at the after perpendicular



39

77- FreeboardFreeboard

The distance between the waterline and the top of the deck at the side ( at

the deck line). The term summer freeboard means the distance from the

top of the summer loadline and the upper edge of the deck line

88- Air draftAir draft

The vertical distance between the waterline and the highest point of the

ship. The air draft is measured from the summer mark.

SheerSheer

This is the upward rise of the ship’s deck from mid length towards the

bow and stern. The sheer gives the vessel extra buoyancy at the stem

and stern

CamberCamber

The transverse curvature of the weather deck. The curvature

helps to ensure sufficient drainage of any water on deck



40

Base lineBase line

Top of the flat keelplace

Keel (K)Keel (K)Inter section of the base line and the center line plane

Beam: B Camber

Depth: D

Draft: T

Freeboard WL

K

CL



41

FlareFlare

•• FlareFlare : outward curvature of ship’s hull surface above the waterline

• Tumble HomeTumble Home : opposite of flare

Tumble HomeTumble Home



42

Positions of the shipPositions of the ship

ListList

Heeling to one side about the fore and aft axis

Heel to port side



43

Trim (t)Trim (t)

The difference between the draft at the stern and the draft at the stem i.e

the trim fore (tF) + the trim aft (tA)

On an even keelOn an even keel, in proper trim

The draft of the stern equals the draft of the stem

Trim by head TF

more than TA



44

Trim by stern TA more than TF



45

Volumes and weightsVolumes and weights

Register ton (RT)To determine the size of a ship the RT is used. It is based on

volume where one register ton equals 100 cubic feet or 2.83

m3



43

Gross Register TonnageGross Register Tonnage

The Gross Register Tonnage (GRT or GT) usually called Gross Tonnage,

is calculated using a formula that takes into account the ship’s volume in

cubic meters below the main deck and the enclosed spaces above themain deck

Net Register TonnageNet Register Tonnage

The Net Register Tonnage is also a non-dimensional number that

describes the volume of the cargo space. The NT is derived from the

GT by subtracting the volume of space occupied by:

- crew

- Navigation equipment

-The propulsion equipment- work stations

- Ballast



44

Volume of DisplacementVolume of Displacement V mV m33

The displacement is the volume of the part of the ship below the

waterline including the shell plating, propeller and rudder

DisplacementDisplacement ΔΔ tonton

The displacement is the weight of the volume of water displaced by the

ship

Lightship weight (ton)Lightship weight (ton)

This is the weight of the ship including the regular inventory

but without any cargo, fuel or crew. The regular inventory

includes: anchors. Life-saving equipment, lubricating oil,

paint



45

Deadweight (ton)Deadweight (ton)

This is the weight of the a ship can take on until the maximal allowable

immersion is reached. This is a fixed value, unique to each ship.

Cargo Capacity (t)Cargo Capacity (t)

This is the total weight of cargo a ship is designed to carry at a

given time.



46

Hull Form CoefficientsHull Form Coefficients

Line coefficients define the characteristics of the vessel’s shape at and

below the waterline. This makes it possible to get an impression of the

shape of the underwater body of a ship without extensive use of anydata.

11-- Block Coefficient, Coefficient of finenessBlock Coefficient, Coefficient of fineness CCBB

The block coefficient gives the ratio of the volume of the underwater

body (V) and the rectangular block bounded by LPP

, BMLD

and draft (T).

The vessel with a small block coefficient is reoffered to as fine.



47



48

2- Waterline coefficient CW

The waterline coefficient gives the ratio of the area of the waterline (Aw)

and the rectangular plane bounded by LPP, BMLD.



49

Midship Section CoefficientMidship Section Coefficient CCMM

The midship (main frame) coefficient gives the ratio of the area of the

midship section (AM

) and the area bounded by BMLD

and T.



50

Prismatic CoefficientPrismatic Coefficient CCPP

The prismatic Coefficient gives the ratio of the volume of the underwater

body and the block formed by the area of the Midship Section AM and LPP.



51

When the principal dimensions, displacement and hull form coefficients

are known, one has an impressive amount of design information, but not

yet a clear image of the exact geometrical shape of the shape. The shape

is given by the lines plane.

The shape of a ship can vary in height, length and breadth. In order to

represent this complex shape on paper, transverse sections of the hull

are combined with two longitudinal sets of parallel planes, each one

perpendicular to the others

Since the ship is a 3-dimensional shape, data in x, y

and z directions is necessary to represent the ship hull.

(Table of Offsets)Table of Offsets)

Lines

- body plan (front View)- shear plan (side view)

- half breadth plan (top view)



52



53

Half Half --Breadth PlanBreadth Plan

- Intersection of planes (waterlines) parallel to the baseline (keel).



54

Shear PlanShear Plan

-Intersection of planes (buttock lines) parallel to the centerline

plane



55

Body PlanBody Plan

- Intersection of planes to define section line

- Sectional lines show the true shape of the hull form

- Forward sections from amidships : R.H.S.- aft sections from amid ship : L.H.S.



56

WaterlinesWaterlines

Horizontal sections of the hull are called waterlines. When

the waterlines are projected and drawn into one view fromabove, the result is called a waterline model.



57

StationsStations

Evenly spaced vertical cross-section in transverse direction are

called sections (ordinates). Usually the ship is divided into 20ordinates, from the centre of the rudder stock (ordinate 0) to

the intersection of the waterline and the mould side of the stem

(ordinate 20)



58

Verticals / Bow and ButtocksVerticals / Bow and Buttocks

Lengthwise section are called verticals or bow and buttocks

lines. These longitudinal sections are parallel to the plane of symmetry of the ship.



59



60



61

General ArrangementGeneral Arrangement

There are a number of

stationary components

and spaces. These have

an indirect relationship to

Ship stability.



62



63

There are a number of variables important to stability. The

location of these variables is dependent upon:

-The distribution of weight on the ship

-The distribution of upward force (buoyancy) on the

submerged part of the hull.

These variables are:

Geometrical centre of the water plane area or tipping centerCentre of flotationCOF or C.F

KeelKeelK

MetacenterMetacenterM

Volumetric centre of the submerged part of the hullCentre of buoyancyB or COB

Mean mass of spacesCentre of gravityg or COg

Mass or centre of gravity of ship, cargo and added cargoCentre of gravityG or COG

ExplanationExplanationTermTermAbbreviationAbbreviation



64



65



66

E l 1E l 1



1

Example 1Example 1

A ship has a length and breadth at the waterline of 40.1 m and 8.6

m respectively. If the water-plane area is 280 m2 calculate the

coefficient of fineness of the water-plane area (CW

).

SolutionSolution

Example 2Example 2

A ship floats at a draught of 3.20 m and has a waterline length and

breadth of 46.3 m and 15.5 m respectively. Calculate the block

coefficient (C B) if its volume of displacement is 1800 m3.

SolutionSolution

E l 3E l 3



2

Example 3Example 3

A ship has length 200 m and breadth 18 m at the waterline. If the

ship floats at an even keel draught of 7.56 m in water RD 1.012 and

the block coefficient is 0.824 calculate the displacement.

SolutionSolution

Example 4Example 4

A ship floats at a draught of 4.40 m and has a waterline

breadth of 12.70 m. Calculate the underwater transverse area

of the midships section if C M is 0.922.



3

Example 5Example 5

A ship has the following details: Draught 3.63 m; Waterline length

48.38 m; Waterline breadth 9.42 m;

Cm 0.946; Cp 0.778.

Calculate the volume of displacement.

SolutionSolution



4

Tonnes per Centimetre immersion TPCTonnes per Centimetre immersion TPC

The TPC for any given draught is the weight that must be

loaded or discharged to change the ship’s mean draught by

one centimetre (1cm)



5

Where:

TPC : tonnes per cm

WPA : water plane area m2

ρ : water density 1.025 t/m3

E l 6E ample 6



6

Example 6Example 6

Calculate the TPC for a ship with a water-plane area of 1500 m2

when it is floating in:

(a) fresh water;

(b) dock water of RD 1.005;

(c) salt water

Solution:Solution:

LOAD/DISCHARGELOAD/DISCHARGE



7

LOAD/DISCHARGELOAD/DISCHARGE

Example 7Example 7

M.V. Almar has a displacement of 13200 ton at an initial mean draught of 4.40 m in salt water and is required to complete loading with a

draught of 6.70 m (displacement will reach 20610 ton). Calculate the

amount of cargo that must be loaded.



8

Load line dimensionLoad line dimension

Fresh Water Allowance (FWA)Fresh Water Allowance (FWA)



9

Fresh Water Allowance (FWA) is the number of millimetres by which

the mean draught changes when a ship passes from salt water to

fresh water, or vice-versa, when the ship is loaded to the Summer

displacement.The FWA is found by the formula:

TPCSW is the salt-water TPC value for the summer load draught.

Example 8Example 8

A ship floats in SW at the Summer displacement of 1680

tonnes. If the TPC SW is 5.18, how much will the draught

change by if the ship is towed to a berth where the density

of the water is 1.000 t/m3?



10

Example 9Example 9



11

Example 9Example 9

A section of steel plate to be used in the construction of a ship’s deck has

dimensions as shown.

Calculate the area of the plate.

Example 10Example 10



12

A ship’s water-plane area has half-ordinates from aft to forward as

follows:

0.6 m, 1.5 m, 1.6 m, 1.4 m and 0.0 m. If the half-ordinates are equally

spaced at 4.2 m apart, calculate:(a) the total water-plane area;

(b) the TPC if the ship is floating in salt water (RD 1.025).



13


A plate section has dimensions as shown. Calculate the area.




14

A small boat has a half water-plane area with equally spaced half-

ordinates as follows:

0.20 m, 1.20 m, 1.70 m, 1.82 m, 1.75 m, 1.65 m and 1.21 m.

The half-ordinates are equally spaced at 1.40 m apart.Calculate the water-plane area.



Ship CentroidsShip Centroids



Centre of buoyancy C.Bentre of buoyancy C.B

B (centre of buoyancy C.B) indicates the location of the

result ing buoyancy of the displaced seawater. The location of

B is dependent upon the hull’s form. B is the volumetric

centre of the hull. Buoyancy is equal to the weight

(displacement) of the ship.

Location of Metacenter M



Location of Metacenter MWith a heeling angle up to about(5-10)º.It is assumed the point MM

lies at the intersection of the vectorof buoyancy and the centerline

With larger lists, point M isdefined as follows: The

intersection of 2 successive linesof buoyancy with a very smallincrease of angle of inclination. MM

is then found outside the verticaloutside the vertical

plane of symmetryplane of symmetry

F l l ti t k ith MM t id th



For calculation purposes, we can not work with MM outside thevertical plane of symmetry. Thus, a false metacenter, NN is usedfor the calculation the intersection

Point NN is on the centreline at theintersection of the buoyancy loadline and the centreline.

The importance of M’s location totransverse (initial) stability is great.

The location of M depends on thelocation of B.

The location of G in relation to M ismainly for the stability as follows:

- Positive (G under M)- Neutral (G at M)

- Unstable (G above M)



Centre of GravityCentre of Gravity



Centre of GravityCentre of Gravity

The total weight of the ship is concentrated at point G(centre of gravity)

g = centre of gravity of component

G = centre of gravity of the entire ship



Movement of centre of gravityMovement of centre of gravity



g yg y

The movement of G can be quickly made clear if only one (large )weight is relocated on board or loaded, G then moves:

-In the movement direction of the weighty

- across a distance of GG1 = (w x h)/ Δ (for transferring load)

GG1 = (w x h) / ( Δ+w) (for adding weight)

Inclining Test ( Experiment)Inclining Test ( Experiment)

In order to calculate the correct GM of the empty ship, theship must undergo an inclining experiment ( stability test) todetermine KG

The weight of the empty ship mustbe as accurate as possible



The weight of the empty ship must be as accurate as possible

During the test:

-The ship must be free to roll ( mooring wires slack, etc..)- it must be calm with no wind

- no disturbance waves

-The test must be conducted multiple times both starboard

and portside with consistent outcome to ensure an accurateresult.

A known weight (1) is moved transversely across distance (2)



A known weight (1) is moved transversely across distance (2)as a result of which the

ship lists.

(1)The weight must be so large that:- The ship remains within an initial range of stability max list 9-10º

- Equal to about 2 % displacement(2) Approximately ½the breadth

The ship’s list due to relocating the weight is accuratelymeasured. This can be done by means of a plumb line. If theplumb line is used, it is usually suspended in a hold where theweight hangs in a tank of water to stabilize the plumb line.

The result is determined by measuring the distance the pendulummoves on a tape line (QR)



STABILITY REFERENCE POINTS



CL

M

G

B

K

etacenter

ravity

uoyancy

eel

STABILITY REFERENCE POINTS



other

oose

eats

ids

CL

M

G

B

K



B

WATERLINERESERVE BUOYANCY

B1

B

THE CENTER OFBUOYANCY

RESERVE BUOYANCY FREEBOARD DRAFT



B

WATERLINERESERVE BUOYANCY

RESERVE BUOYANCY, FREEBOARD, DRAFTAND DEPTH OF HULL

CENTER OF BUOYANCY



B

WLWL

B

WL

B

WL

B

WL

B

CENTER OF BUOYANCY



BBBBBBBB

B



G

G1

KGo

KG1

GG1

KGo

KG1

THE CENTER OFGRAVITY

CENTER OF GRAVITY



CENTER OF GRAVITY

• POINT AT WHICH ALL WEIGHTS COULDBE CONCENTRATED.

• CENTER OF GRAVITY OF A SYSTEM OFWEIGHTS IS FOUND BY TAKINGMOMENTS ABOUT AN ASSUMED CENTEROF GRAVITY, MOMENTS ARE SUMMEDAND DIVIDED BY THE TOTAL WEIGHT OF THE SYSTEM.

MOVEMENTS IN THE



MOVEMENTS IN THE

CENTER OF GRAVITY

• G MOVES TOWARDS A WEIGHT ADDITION



G

KGo

G1

KG1

MOVEMENTS IN THE



MOVEMENTS IN THE

CENTER OF GRAVITY


• G MOVES AWAY FROM A WEIGHT REMOVAL



GGGGGG

G1

KG1

KGo

G

MOVEMENTS IN THE



MOVEMENTS IN THE

CENTER OF GRAVITY


• G MOVES AWAY FROM A WEIGHT REMOVAL

• G MOVES IN THE DIRECTION OF A WEIGHT SHIFT



G G2

METACENTER



THE

METACENTER

C L

B

B20

B45

M

M20

M45

M70

B70

METACENTER

M

BB1 B2

METACENTER



BBBBBBBBB

METACENTER



B SHIFTS

M

0o-7/10o



CL

B

M

0 7/10



C L

BB20

M

M20



C L

M

M20

M45

B

B20 B45



C L

B

B20

B45

M

M20

M45

M70

B70



C

L

M20M45

M70

M90

B

B20

B45B70

B90

M



MOVEMENTS OF THE



MOVEMENTS OF THE

METACENTER

THE METACENTER WILL CHANGEPOSITIONS IN THE VERTICAL PLANE WHENTHE SHIP'S DISPLACEMENT CHANGES

THE METACENTER MOVES IAW THESE

TWO RULES:

1. WHEN B MOVES UP M MOVES DOWN.2. WHEN B MOVES DOWN M MOVES UP.



M

G

B

M

G

B

G

M

B

M1

B1

G

M

B

M1

B1

G

M

B

M1

B1

G

M

B

M1

B1

LINEAR MEASUREMENTS INSTABILITY



CL

M

G

B

K

GM

KG

BM

KM

STABILITY

M



G

B1

Z

G

B1

M

B

G

B1

M

B

THE THREE CONDITIONS

OF STABILITYPOSITIVE

NEUTRAL

NEGATIVE

Vertical Weight Shifts



G

B

M

G1G1G1G1

G1

G1G1

KGo

KG1

GG1= KG1 - KGo

GG1

KG1 = (Wo KGo) (w x kg)



Wf

WHERE;w = Weight Shifted

kg = Distance ShiftedWo = Original Displacement

KGo = Original Height of G

Wf = Final Displacement±= + if shift up/- if shift down

KG1 = (Wo x KGo) ±(w x kg)

W



G

B

M

G1G1G1G1

G1

G1G1

12 FT

Wo = 2000 T

30 FT

25 T

KG1?

Wf

45T



M

B

G

17T

8 FT

33 FT

Wo = 3400 T

15.5 FT

KG1 = (Wo x KGo)±(w1xkg1)±(w2xkg2)



Wf

WHERE;w1&2 = Weights Shifted

kg1&2 = Distances Shifted

Wo = Original Displacement

KGo = Original Height of G

Wf = Final Displacement±= + if shift up/- if shift down

Vertical Weight Additions



g

G1

M

B

G

Vertical Weight Additions



g

M

B

G

G1

M

B

G

M1

B1

G1

M

B

GG1

M

B

G

M1

B1

G1

M

B

GG1

M

B

G

M1

B1

G1

M

B

G

G1

M

B

G

M1

B1

G1

KGoKG1

GG1

KG1 = (Wo x KGo) ±(w x kg)



Wf

WHERE;KGo = Original Height of G

Wo = Original Displacement±= + if addition/- if removalw = Weight Added/Removed

kg = Distance Keel to "g" of wtWf = Final Displacement

16 TONS ADD



42 FT

Wo = 2000 TONS

KGo = 12 FT



Examples

A ship displaces 5000 t and has an initial KG of 4.5 m. Calculate thefi l KG if i ht f 20 t i d ti ll d f th l

Example 1Example 1



final KG if a weight of 20 t is moved vertically upwards from the lowerhold (Kg 2.0 m) to the upper deck (Kg 6.5 m).

Example 2Example 2A ship displaces 12500 t and has an initial KG of 6.5 m. Calculate thefinal KG if 1000 t of cargo is loaded into the lower hold at Kg 3.0 m.

Example 3Example 3A ship has a displacement of 13400 t and an initial KG of 4.22 m. 320 tof deck cargo is discharged froma position Kg 7 14 m Calculate the



of deck cargo is discharged from a position Kg 7.14 m. Calculate thefinal KG of the ship.

Example 4Example 4

A ship displaces 10000 t and has a KG of 4.5 m. The following cargo is worked:Load: 120 t at Kg 6.0 m;

730 t at Kg 3.2 m.Discharge: 68 t from Kg 2.0 m;

100 t from Kg 6.2 m.Shift: 86 t from Kg 2.2 m to Kg 6.0 m.Calculate the final KG.



Example 5Example 5

Prove that the KM of a box-shaped vessel changes with draught asshown below for the range of draughts 1.00 m to 15.00 m given that



s o beo o e a ge o d aug s 00 o 5 00 g e alength is 100 m and breadth is 20 m.



From the values calculated it is seen that as draught increases, KM reduces to aminimum value and then starts to increase again.

Example 6A box-shaped vessel has length 20 m and breadth 6 m.Calculate:



(a) the moment of inertia for all the axis’ of rotation shown;(b) the moment of inertia about the two axis’ passing through the centre

of flotation using the parallel axis’ theorem.



Example 7Example 7

A ship of 6000 tonnes displacement has KM 7.3 m and KG 6.7 m, andis floating upright. A weight of 60 tonnes already on board is shifted 12m transversely. Find the resultant list.

Example 8Example 8

A ship of 8000 tonnes displacement has a GM 0.5 m. A quantity of grain in the hold, estimated at 80 tonnes, shifts and, as a result, the



gcentre of gravity of this grain moves 6.1 m horizontally and 1.5 mvertically. Find the resultant list.

Example 9Example 9

A ship of 13 750 tonnes displacement, GM 0.75 m, is listed degrees tostarboard and has yet to load 250 tonnes of cargo. There is space



available in each side of No. 3 between deck (centre of gravity, 6.1 mout from the centreline). Find how much cargo to load on each side if

the ship is to be upright on completion of loading.




A ship of 9900 tonnes displacement has KM 7.3 m and KG 6.4 m. Shehas yet to load two 50 tonne lifts with her own gear and the first lift is to

be placed on deck on the inshore side (KG 9 m and centre of gravity 6m out from the centreline). When the derrick plumbs the quay its head is15 m above the keel and 12 m out from the centreline. Calculate themaximum list during the operation

Lecture Notes of Naval Architecture I

Documents

Transcript of Lecture Notes of Naval Architecture I