m 159 section 4

Small Engines

Naval Architecture (2)

Section 4

Prepare a Stability Statement

Lesson Plan 9Weight Estimation

Lesson Plan 10The Weight Estimation Process

Lesson Plan 11Stability (a)

Lesson Plan 12Stability (b)

Objectives of this section are:

To develop knowledge and skills to prepare a stability statement.

Lesson PlanLesson Plan No 9Weight Estimation

Duration

120 Minutes

Performance Criteria4.1The principles of weight estimation are analysed

VenueClassroom

Plan

Discuss and explain weight estimation as an essential feature in ship design.

HO M159-4-01Refer notes for weight estimation.

Additional information refer Ship Design and Construction textbook.Page 37 subsection 4.7 Weights and measures of gravity estimate.

Discuss and explain weight definition.

HO M159-4-01Refer notes for weight definition.

Discuss and explain moments of mass.

HO M159-4-01Refer notes for moments of mass.

Discuss and explain centroids and the centre of gravity.

HO M159-4-01Refer notes for centroids and the centre of gravity.

Overhead Transparencies

OHTs are to be site specific and the content identified as MIMET facilities and equipment become available. Trainers/tutors should create, review and update OHTs as needed to enhance delivery of the module material

Handouts

HO M159-4-01.Section 4 notes

Resources

Ship Construction HandbookVictoria University publication, this handbook should be available to all students. Students should have been issued with it at the beginning the course.

Ship Design and Construction

The Society of Naval Architects and Marine Engineers, (1980), One World Trade Centre, Suite 1369, New York 10048

Ship Construction Sketches & NotesKemp and Young, revised by David J. Eyres (1997), Second Edition, Butterworth Heinemann.

Basic Ship Theory Combined VolumeKJ Rawson and E.C.Tupper (2001), , Fifth Edition, Butterworth Heinemann.

Ships & Naval Architecture (S.I Units)R.Munro-Smith (1997), The Institute of Marine Engineer.

Basic Ship Theory Volume 1KJ Rawson and E.C.Tupper (1997), Fourth Edition, Longman

Teach Yourself Naval ArchitectureBrian Baxter (1976), Second Edition, Warsash Publishing, Southhampton.

Lesson PlanLesson Plan No 10The Weight Estimation Process

Duration

120 Minutes

Performance Criteria4.1 The principles of weight estimation are analysed

4.2 A tabular criterion is prepared using a computer-based spreadsheet

VenueClassroom

Plan

Discuss and explain the weight estimation process.

HO M159-4-01Refer notes for the weight estimation process.

Discuss and explain the weight engineering process.

HO M159-4-01Refer notes for the weight engineering process.

Discuss and explain the work breakdown structure.

HO M159-4-01Refer notes for the work breakdown structure.

Discuss and explain the database structure in weight estimation.

HO M159-4-01Refer notes for the database structure in weight estimation.


OHTs are to be site specific and the content identified as MIMET facilities and equipment become available. Trainers/tutors should create, review and update OHTs as needed to enhance delivery of the module material

Handouts

HO M159-4-01Section 4 notes

Resources









Lesson PlanLesson Plan No 11Stability (a)

Duration

120 Minutes

Performance Criteria4.3 An intact stability statement is prepared from a set of hydrostatic data and weight estimate which meets the requirements of the set of stability criteria provided

VenueClassroom

Plan

Discuss and explain capacities, trim and intact stability.

HO M159-4-01Refer notes for the capacities, trim and intact stability.

HO M159-4-02Stability and loading of the ship.

Trainees to complete revisions questions. HO M159-4-03.Revision questions on trim.

Discuss and explain taking moments about the centre of gravity and the internal righting moment produced by a heeling ship.

HO M159-4-01Refer notes or taking moments about the centre of gravity.

HO M159-4-04Curve of intact statical stability.

OHT M159/4/01Curve of intact statical stability.

Stability criteria, international requirements.Refer HO M159-4-02 for additional notes

Stability criteria, the uniform shipping laws code (USLC) or Malaysian requirementsRefer USLC Stability Section


OHT M159/4/01Curve of intact statical stability.

Handouts

HO M159-4-01Section 4 notes.

HO M159-4-02Stability and loading of the ship.

HO M159-4-03Revision questions on trim.

HO M159-4-04Curve of intact statical stability.

Resources









Lesson PlanLesson Plan No 12Stability(b)

Duration

180 Minutes

Performance Criteria4.3 An intact stability statement is prepared from a set of hydrostatic data and weight estimate which meets the requirements of the set of stability criteria provided

VenueClassroom

Plan

Discuss and explain cross curves of stability.

HO M159-4-01Refer notes for cross curves of stability.

HO M159-4-05Cross curves of stability.

OHT M159/4/02Cross curves of stability.

Discuss and explain the sine correction derivation.

HO M159-4-01Refer notes the sine correction derivation.

HO M159-4-06The sine correction derivation.

Trainees to complete exercise Refer HO M159-4-06

Discuss and explain the cosine correction derivation.

HO M159-4-01Refer notes the cosine correction derivation.

HO M159-4-07The cosine correction derivation.

Trainees to complete exercise Refer HO M159-4-07

Discuss and explain permeability.

HO M159-4-01Refer notes for permeability.

Trainees to prepare an intact stability statement.


OHT M159/4/02Cross curves of stability.

Handouts

HO M159-4-01Section 4 notes

HO M159-4-05Cross curves of stability.

HO M159-4-06The sine correction derivation.

HO M159-4-07The cosine correction derivation.

Resources









Section4

Prepare a Stability Statement

Weight Estimation

A weight estimate is a prediction of the weight and location of the center of gravity of the ship. The weight estimation process begins at the preliminary design stage. By using the information from the owners specification, equipments, and general arrangement plan, a calculation for the total weight and the location of the center gravity can be obtained.

Throughout the entire design and construction process, it is essential to be aware of the weight of the vessel. It is important that individual weights of units for modular construction and components is known prior to placing into position.

The weight estimation is an essential feature of the overall ship design process. It is usually required in the general arrangement and stability study carried by naval architect or marine (weight) engineers for final weight control and preliminary costing.

Weight definition

Mass - In the S.I. system of units it is most important to distinguish between the mass of a body and its weight. Mass is the fundamental measurement of the quantity of matter in a body and is expressed in terms of the kilogram and the tonne, whilst the weight of a body is the force exerted on it by the Earths gravitational force and is measured in terms of the Newton (N) and kilo-Newton (kN).

Weight and mass are connected by the formula: -

Weight = Mass x Acceleration

Example; The weight of a body mass 100 kilograms at a place where the acceleration due to gravity is 9.81 meters per second per second.

Weight = mass x acceleration

= 100 kg x 9.81 ms2 = 981 kgms2 or 981 N

Moments of Mass If the force of gravity is considered constant then the weight of bodies is proportional to their mass and the resultant moment of two or more weights about a point can expressed in terms of their mass moments.

Example; A uniform plank is 3 meters long and is supported at a point under its mid-length. A load having a mass of 30 kilograms is placed at a distance of 0.5 meters from one end and a second load of mass 50 kilograms is placed at a distance of one meter from the other end. Find the resultant moment about the middle of the plank.

Moments are taken about Z, the middle of the plank.

Clockwise moment

= 50 kg x 0.5 m

= 25 kg m

Anti-clockwise moment = 30 kg x 1 m

= 30 kg m

Resultant moment

= 25 30

= - 5 kg m (Anti-clockwise)Centroids and the centre of gravity The centroid of an area is situated at its geometrical centre. The centre of gravity of a body is the point at which all the mass of the body may be assumed to be concentrated and is the point through which the force of gravity is considered to act vertically downwards, with a force equal to the weight of the body.

Formulas;

Effect of removing/discharging mass and effect of adding/loading mass to ships application.

GG1 =w x d

Units meters

Final displacement

G= Center of gravity

G1= Alter in Center of gravity

W= Mass (tonne)

D= distanceThe weight estimation process

The weight estimate is a process to predict the final weight of the ship design in a weight control process. The purpose of the weight control process is to insure that the ship will be delivered within the naval architecture limits of the hull design.

The overall weight estimation is important for two main reasons: -

It is essential for designers to know the final weight and its distribution throughout the vessel for launching and trim calculations.

Preliminary costing is done in terms of costs/tones for steel etc.

As the detailed design is developed, final detailed weight estimate is refined to include new information. The final weight of the ship is monitored through a weight control process during all the different stages of design and construction.

For example; during detail design, the weight of paint on the ship may be estimated using known factors because it may not be cost effective to do surface area weight calculations.

Figure M159.4.01- Weight engineering process

Weight engineering process

At the first step of the weight estimation process, weight is confirmed by weighting individual components, assemblies and eventually the whole ship. Estimating methods may be used as a check of the reasonableness of detailed weight calculations. During the ship weighting or inclining experiment, a surveyor may estimate the weight of stores in a storeroom based on the available volume and a stowage factor. All of these examples employ the same principals of weight estimating.

First weights and centre of gravity:

At the preliminary design stage, using information from the owners specification, list of equipment, and general arrangement plan, we should be able to estimate the LCB and LCG line up. If they do not line up, we must either shift weights or alter the lines until they do.

Weighting of material and equipment

The actual weight estimation of all components and equipment depend on accuracy. They depend on actual scale weights of equipment, material and components provided from the suppliers, vendors and weight database. A reliable weight and center of gravity is essential to maintain and ensure the ship parameters and operations such as: -

Deadweight

Trim & Stability

Speed

Cost evaluation

Sea keeping

Sea launching

Small deviations between real weight/center of gravity compared to estimated weight, always represents acost for designer, ship builder or ship owner.

More significant deviation between real weight/center of gravity compared to estimated weight can lead tolarge rebuilding of the vessel or dramatically changed performance, both representing great costs.

Continuous weight take off with control against budget at an early stage or preliminary design stage, will identify critical deviations. Actions can be taken to secure that owners requirements are met at completion.

The total mass of the ship in any condition of loading can be divided into: -

1. Hull

2. Propelling machinery

3. Deadweight

4. Additional weight i.e. cargo, fuel, water, stores, ballast etc.

Work Breakdown Structure

The ship weight concept is based upon the knowledge that in an early stage of the designprocess, weight and center of gravity must be estimated, based on past ship data.

Using breakdown structures, ship weights are divided into weight groups containing informationon weight, center of gravity and other relevant information.

Figure M159.4.02 Work breakdown structure.

Estimation of weight and center of gravity is done according to the breakdown structure. In every weight group, an estimation method of the form:

Weight = coefficient * parameters

To obtain the right coefficient for an estimation method the coefficients from relevant shipsare plotted in a graph. By setting parameter criteria, only relevant coefficients are plotted inthe graph. A regression line is inserted according to a plot parameter to help the user selectthe right coefficient. When a coefficient is selected, the weight is estimated

The database structure in weight estimation method

The ship weight system contains two modules, Asbuilt weight and Design weight. In the Asbuiltmodule, data from weight take off during construction is structured and stored together withrelevant parameters for the items.

When the vessel is complete and the Asbuilt weight is corrected according to the results fromthe incline test report, the ship is ready to be exported to the ship database.

Figure M159.4.03 the database structure.

When the Asbuilt project file is complete, the data should be exported to the ship database.The ship database should contain content data from all complete projects. When a new estimationproject is started, estimation can be done on the basis of the past ship data in the ship database.

Stability

Capacities, trim and intact stability, the GZ curve

Capacities

Capacity is the amount that can be contained in a vessel. The maximum and minimum capacities of a vessel are important, as it will affect the stability of the vessel. When we mentioned about capacities, the two main components, which will affect the stability, are the weight and the free surface effect of the amount contained in

HO M159-4-02 Stability and loading of the shipLearning activities

HO M159-4-02 Stability and loading of the ship

In HO M159-4-02, the data needed for the capacities column are the cubic metre for 100% full and 98% full of capacities. This information is important because 100% full of capacity provides the maximum weight of the vessel and 98% full of capacity gives the data on the free surface effect. In HO M159-4-02, the samples of tanks given are the cargo-oil tank, ballast water tank, oil fuel tank and engine room and lube oil tank. The first two tanks have a great affect on the stability of a vessel, as they take up a large area of a vessel. The last two tanks give less effect to the stability as they take up a very small space and the position is lower in the vessel.

Trim and intact stability

Trim: Inclination of a vessel in the forward or aft direction

Even keel

Trimmed by the stern

Trimmed by the bow

A vessel will trim at Longitudinal Centre of Floatation (LCF)

Why does trim occur?

1. Shifting mass from aft to forward or forward to aft

2. Adding and removing mass

3. Changes of density of water; from SW to FW or vice versa

4. Bilging

Taking moments about the centre of gravityIt is convenient to take moments about the centre of gravity when dealing with the horizontal movements and vertical movements of weight.

The bar AB represents a vessel of weight W tonnes acting through the centre of gravity G. Consider a weight of w tonnes loaded d metres from G. Take moments.

Weight x Distance = Moment

W 0 0

w d w x d

W + w w x d

The distance of the new centre of gravity (G1) from the point moment are taken (G) is known as the shift of G or

GG1 = Sum of the moments Sum of the weights

GG1 = w x d W + w

Similar expressions may be found for discharging and shifting weights, these are summarised below.

Shift of G (GG1)

When loading, where W is the vessels displacement before loading the weight

w is the weight loaded

d is the distance of the loaded weight from the old centre of gravity

G always moves towards the loaded weights.

When discharging

where W is the vessels displacement before discharging the weight

w is the weight discharged

d is the distance of the discharged weight from the old centre of

gravity

G always moves away from the discharged weights

When shifting

where W is the vessels displacement( this include the weight shifted)

w is the weight shifted

d is the distance that the weight is shifted

G always moves in the same direction as, and parallel to, the shifted weight.

Effect of adding small masses

The effect of an added mass on the draught may be divided into:

a) a bodily increase in draughtb) a change in trim due to the movement of the mass from the centre of flotation to its final positionThe bodily increase in draught may be found by dividing the mass by the TPC. The change in trim due to any longitudinal movement of mass may be found by considering its effect on the centre of gravity of the ship.Consider a ship displacement ( and length L, lying at waterline WL and having a mass m on the deck. The centre of gravity G and the centre of buoyancy B lie in the same vertical line.If the mass is moved a distance d aft,

a) the centre of gravity moves aft from G to G1, and GG1 = w x d

( b) the ship changes trim through the CLF until it lies at waterline W1L1c) the centre of buoyancy moves aft from B to B1, in the same vertical line as G1d) the vertical through B1 intersects the original vertical through B at MLIf the vessel trims through an angle (, thenGG1 = GML tan ( and

GML tan ( = m x d (tan ( = m x d ( x GMLDraw RL1 parallel to WLChange in trim = WW1 + LL1 = W1R = t (m) 100where t = change in trim in cm over length L mBut

tan ( = t 100LTherefore,

t = m x d100L ( x GMLt = m x d x 100L (cm) ( x GMLtrimming moment = m x dm x d = t x ( x GML (tonne m) 100LLet t = 1 cmThen moment to change trim one cmMCTI cm = ( x GML (tonne m) 100LChange in trim t = trimming moment (cm) MCTI cm = m x d (cm by the stern) MCTI cmBy similar triangles,t = LL1 = W1WL FL WF t, LL1 and W1W may be expressed in cm while L, FL and WF are expressed in m.Change in draught forward LL1 = -t x FL (cm) LChange in draught aft W1W = + t x WF (cm) LLearning activities

HO M159-4-03 Revision questions on trim

The GZ CurveThe Internal Righting Moment Produced by a Heeling Ship

Understanding overall stability comes down to understanding how the relative positions of the resultant weight of the ship and the resultant buoyant force change when a ship is heeled over by an external moment or couple. The External CoupleThe external couple can be caused by the action of wind pushing on one side of the ship, and the water pushing back on the hull in the opposite direction. The resultant forces from these two distributed forces would be acting parallel to the waters surface. The two resultant forces would not be aligned as the resultant wind force would be above the water and the resultant water force would be below the water. They would form an external couple or moment causing the ship to rotate.

A good analogy can be made by picturing a steering wheel -- the wind is pushing at the top of the steering wheel and the water is pushing in the opposite direction at the bottom. The steering wheel will rotate when acted upon by these unbalanced forces. Refer to Figure M 159.4.04. The Internal CoupleA ship will also tend to rotate when acted upon by wind and water. However, as the ship heels over due to an external moment it also develops an internal moment. The internal moment acts in response to the external moment and in the opposite rotational direction. If the internal and external moments balance the ship will stay heeled at that angle of inclination, otherwise it will keep heeling until the ship capsizes.

Figure M 159.4.04 shows the sectional view of a ship that is being heeled over due to an external moment. It shows the relative positions of the center of gravity and center of buoyancy for a ship that has been designed properly. Notice the perpendicular distance between the lines of action of the resultant weight and resultant buoyant force. This distance is the righting arm ( GZ ).

Figure M159.4.04 External and Internal CouplesTo find the internal righting moment multiply the righting arm by the magnitude of the resultant weight of the ship (or the magnitude of the resultant buoyant force since the magnitude of these forces are equal). The equation below shows this relationship.

where

RM is the internal righting moment of the ship (tonne-metre).

( is the displacement of the ship (tonne).

FB is the magnitude of the resultant buoyant force (tonne).

GZ is the righting arm (metre). It is the perpendicular distance between

the line of action of the resultant buoyant force and the resultant

weight of the ship.

This distance is a function of the heeling angle.The Curve of Intact Statical Stability

Figure M 159.4.04 External and Internal Couples, is only a snapshot of the total stability picture. We are really interested in how Figure M 159.4.04 External and Internal Couples, changes as the ship is heeled over from zero degrees to large enough angles of heel to make the ship capsize. To help us conceptualize this process, a graph of heeling angle (degrees) versus righting arm, GZ (metres) is constructed. This graph is called the curve of intact statical stability or the Righting Arm Curve.

HO M159-4-04 Curve of intact statical stability

OHT M159/4/01- Curve of intact statical stability

shows a typical intact statical stability curve. When the ship is in equilibrium with no outside forces acting on it, the resultant weight of the ship will be vertically aligned with the resultant buoyant force. As an external moment heels the ship to port or starboard, the resultant weight and the resultant buoyant force will become out of vertical alignment creating the righting arm. The righting arm will obtain a maximum value and then decrease until the resultant weight of the ship and the resultant buoyant force are again in vertical alignment. Heeling any further will cause the ship to capsize. See Figure 2.Typically only the starboard side of the intact statical stability curve is shown. The entire curve is shown in HO M159-4-04 Curve of intact statical stability to give the entire picture of the statical stability curve. Notice how the port side is drawn in quadrant 3 since angles to port are assigned a negative and righting arms to port are assigned a negative. This is only a convention used to distinguish between port and starboard heeling.

Each intact statical stability curve is for a given displacement and given vertical center of gravity. The process of obtaining the actual intact statical stability curve is done by reading values off the cross curves of stability for a given displacement of the ship, and then making a sine correction to account for the proper vertical location of the center of gravity of the operating ship.

Point A 0 degrees of heel

GZ = 0 ft

Point B 25 degrees of heel

GZ = 2.5 ft

Point C 50 degrees of heelGZ = 4.0 ft (max)

Point D 75 degrees of heel

GZ = 2.0 ft

Point E 85 degrees of heel

GZ = 0 ft

Vertical Alignment

Beyond Point E - > 85 degrees of heelGZ < 0 ft

Capsizing Arm

Figure M159.4.05 Vector Drawings

Cross Curves of Stability

The cross curves of stability are a series of curves on a single set of axes. The X-axis is the displacement of the ship in tonne. The Y-axis is the righting arm of the ship in metres. Each curve is for one angle of heel. Typically angles of heel are taken each 5 or 10 degrees. HO M159-4-05- Cross Curves of Stability and Student exercises has a set of cross curves for the FFG-7.

OHT M159/4/02- Cross Curves of Stability

HO M159-4-05 Cross Curves of Stability

The entire series of curves assumes an arbitrary location for the vertical center of gravity of the ship. Sometimes the assumed location of the center of gravity is at the keel. This may seem strange to you at first but it makes sense when you consider the following. The actual location of the center of gravity of the ship will always be above the keel. This means that the sine correction can always be subtracted from the value read off the cross curves. Otherwise, the sine correction would sometimes be subtracted and sometimes be added. The actual location of the assumed value of the center of gravity of the ship will always be marked on the cross curves.

In summary, the intact statical stability curve, for a single displacement, comes from reading values off the cross curves of stability and using a sine correction for the actual location of the vertical center of gravity.Obtainable Stability Characteristics from the Curve of Intact Statical Stability

There are several overall stability characteristics that can be obtained from the curve of intact statical stability (Refer HO M159-4-04 Cross Curves of Stability , this sub topic is actually a reiteration from NA1) Range of Stability

This is the range of angles for which there exists a righting moment. The range starts at the angle corresponding to the ships equilibrium position with no external moments applied to it and goes to the angle at which the ship will capsize. For a ship with no initial angle of list the starting angle would be zero degrees. If the ship has a permanent angle of list, then the range is given from that angle of list to the capsizing angle of the heeled side.

In HO M159-4-04 Cross Curves of Stability, the Range of Stability is 0 - 85 degrees for starboard heels

0 - 85 degrees for port heels

The greater the range of stability, the less likely the ship will capsize. If the ship is heeled to any angle in the range of stability, the ship will exhibit an internal righting moment that will right the ship if the external moment ceases.

Maximum Righting Arm (GZmax)

This is the largest internal moment arm created by the vertical mis-alignment of the buoyant force and the resultant weight vectors. It is simply measured as the peak of the curve of intact statical stability.

In HO M159-4-04 Cross Curves of Stability, the Maximum Righting Arm is 4.1 ft

Maximum Righting Moment

This is the largest static moment the ship can produce. It is simply calculated from the product of the ships displacement (() by the maximum righting arm (GZmax ). The units are LT-ft. (or tonnemetres in metrics)

The larger the value of the maximum righting moment the less likely the ship will capsize. The maximum righting moment cant be shown directly on the curve of intact statical stability. Only the maximum righting arm can be shown. However, there is only a scaling difference between the righting arm and righting moment.

Angle of Gzmax

This is the angle of heel at which the maximum righting moment occurs. Beyond this angle the righting moment decreases to zero.

In HO M159-4-04 Cross Curves of Stability, the Angle of GZmax is 50 degrees.

It is desirable to have this angle occur at large degrees of heel so that a rolling ship will experience a righting moment that increases in magnitude over a greater range of heeling angles.

Dynamic Stability

This is the work done by quasi statically (very slowly) rolling the ship through its range of stability to the capsizing angle. Mathematically, this work is,

(

This is the product of the ships displacement with the area under the curve of intact statical stability. The units are LT-ft. The dynamic stability can t be shown directly on the curve of intact statical stability but the area under the curve can be shown.

The work represented by dynamical stability is not necessary representative of the work required to capsize a ship in a real seaway. This is because the statical stability curve does not account for rotational momentum, or additional forces that may be present on a real ship in a seaway. It is useful for a comparative basis with other ships or ships of the same type under different operating conditions.

A Measure of the Tenderness or Stiffness

The initial slope of the intact statical stability curve indicates the rate at which a righting arm is developed as the ship is heeled over.

If the initial slope is large, the righting arm develops rapidly as the ship is heeled over and the ship is said to be stiff. A stiff ship will have a short period of roll and react very strongly to external heeling moments. The ship will try to upright itself very quickly and forcefully. If the ship is too stiff, violent accelerations can damage ship structures and be harmful to personnel.

If the initial slope is small, the righting arm develops slowly as the ship is heeled over and the ship is said to be tender. A tender ship will have a long period of roll and react sluggishly to external heeling moments. Too tender of a ship can compromise stability and leave too little margin for capsizing.

The Effects of a Vertical Shift in the Center of Gravity of the Ship on the Righting Arm ( GZ )

The Curve of Intact Statical Stability can be created from the Cross Curves of Stability. However, the Cross Curves assume a value for KG (regularly KG = 0 ft). To obtain the true Righting Arm Curve, the values from the cross curves must be corrected for the true vertical location of G. This is achieved using the sine correction.

The Sine Correction

There are 2 instances when the sine correction is necessary.

Correcting the Curve of Intact Statical Stability for the true vertical location of G.

Correcting the Curve of Intact Statical Stability for changes in KG.

The theory behind the sine correction can be seen by an analysis of Figure 3. It is obvious from the Figure that a rise in KG decreases the righting arm. If Gv is the final vertical location of the center of gravity, and G0 is its initial location, then the value of GvZv at each angle of heel may be found using the following relationship:

where:

GVZV is the righting arm created by the final center of gravity (ft).

GOZO is the righting arm created by the initial center of gravity (ft).

GOGV is the vertical distance between G0 and Gv (ft).

GOGV sin ( is the sine correction term (ft).

This equation should be evident from Figure M 159.4.06 The Sine Correction Derivation by examining the right angled triangle GOPGV and by observing that the distance GVZV is the same as the distance PZ0.

A similar analysis Figure M 159.4.06 The Sine Correction Derivation should reveal that the sine correction term must be added if KG is reduced.

Figure M159.4.06 The Sine Correction Derivation

In this Figure the following segments are defined:

W0L0 is the original waterline

W1L1 is the new waterline

G0Z0 is the righting arm prior to a shift in the center of gravity

GvZv is the righting arm after a shift in the center of gravity

B1 is the center of buoyancy after the ship lists

B0 is the center of buoyancy before the ship lists

HO M159-4-06 The sine correction derivation

HO M159-4-06 The sine correction derivation

The Effects of a Transverse Shift in the Center of Gravity of the Ship on the Righting Arm ( GZ )

The stability analysis so far has considered the center of gravity on the centerline, or TCG = 0 ft.

We have learnt that the center of gravity may be moved off the centerline by weight additions, removals, or shifts such as cargo loading, ordinance firing, and movement of personnel. When this occurs, there is an effect upon the stability of the ship. The effect upon stability of a transverse shift in G can be calculated using the cosine correction.

The Cosine Correction

There are 2 instances when the cosine correction is necessary.

Correcting the Curve of Intact Statical Stability for the true transverse location of G

Correcting the Curve of Intact Statical Stability for changes in TCG.

An analysis of Figure 4 showing a shift in the transverse location of G from the centerline enables the cosine correction to be quantified. The new righting arm may be computed at each angle using the following equation.

where:

GtZt is the corrected righting arm (ft). GVZV is the uncorrected righting arm (ft).

GVGt is the transverse distance from the centerline to the center of

gravity (ft).

GVGt cos ( is the cosine correction term (ft).

This equation should be evident from Figure 4 by examining the enlarged right-angled triangle at the top of the Figure.

Figure M159.4.07 - The Cosine Correction DerivationThe new righting arm (GtZt ) created due to the shift in the transverse center of gravity is smaller than the righting arm created if the transverse center of gravity had not been moved (G0Z0).

However, if heeling to port was considered the righting arm would increase. A similar diagram to Figure M159.4.07 can show that for the opposite side to the weight shift, the cosine correction is added to give the corrected righting arm.

HO M159-4-07 The cosine correction derivation

Permeability

Permeability is the volume of a compartment into which water may flow if the compartment is open to the sea. It is expressed as a ratio or percentage of the total volume of the compartment. For example, a compartment in a bulk carrier which is completely empty would have a permeability of 100% while an engine compartment would have a permeability of about 85% because volume is taken up by machinery.

From this it can be seen that the effect on stability of damage to the hull will depend largely upon which compartments are holed. The higher the permeability of the compartment holed, the more water will enter the vessel. The flooded compartments are no longer contributing to the ships buoyancy. This reduces the total buoyancy of the vessel and the C of B rises. The value of BM (Buoyancy to Metacentre) decreases. If B rises above G the vessel will become unstable and will capsize if flooding is not controlled.

Puncturing of the shell will allows flooding in both longitudinal and transverse directions. The degree of flooding in each direction will be dependent upon the framing system in the vessel, how far between watertight bulkheads etc. The ship will list both port/starboard and fwd/aft and both possibilities must be considered when calculating damage control procedures and stability.

A vessel such as the Navy's ANZAC vessels has vertical sides in its upper strakes. This means that as the vessel is listing to one side the change in hull shape immersed at the waterline will mean a larger volume is needed to be immersed as the leaning continues. The rate of listing (sinking) will slow down as a larger hull volume reaches the water line, hence the vessel is more stable than one of similar size with sloping sides.

Loose waterLoose Water is the shifting of liquid from side to side as a ship rolls. Water that partially fills a compartment, as a result of underwater damage, drainage, or fire fighting, is Loose Water. Free Surface Effect

Liquid that only partially fills a compartment is said to have a free surface that tends to remain horizontal (parallel to the waterline). When the ship is inclined, the liquid flows to the lower side (in the direction of inclination), increasing the inclining moment.Background:

If the tank contains a solid weight, and the ship is inclined, the center of buoyancy shifts in the direction of the inclination and righting arms (GZ) are formed.Replacing the solid with a liquid of the same weight, when the ship is inclined, the surface of the liquid remains horizontal. This results in a transfer of "a wedge of water," which is equivalent to a horizontal shift of weight, causing gravity to shift from G0 to G2.

The wedge of water transferred increases as the angle of inclination increases; therefore, the center of gravity shifts a different amount for each inclination.

Due to the horizontal shift of the center of gravity, the righting arm is now G2Z2. To determine the effect on stability, a vertical line is projected upward through G2 (see below). Where this line crosses the ships centreline is labelled G3. The righting arm G3Z3 is the same length as the righting arm G2Z2. Therefore, moving the ships center of gravity to position G2 or G3 yields the same effect on stability. Movement from G0 to G3 is referred to as a Virtual Rise of the center gravity.

Factors Effecting Free Surface Effect

POCKETING

Free Surface Effect can be reduced, to some extent, by creating pocketing. Pocketing occurs when the surface of the liquid contacts the top or bottom of the tank, reducing the breadth (B) of the free surface area.

Pocketing with top of tank.

Pocketing with bottom of tank.

Since the effects of pocketing cannot be calculated, it is an indeterminate safety factor. The Free Surface correction will therefore indicate less overall stability than actually exists.

SURFACE PERMEABILITY

Impermeable objects (engines, pumps, piping systems, etc) inside a flooded space project through and above the liquid surface. These objects inhibit the moving water and the "shifting of the wedge" may or may not be complete, thus reducing Free Surface Effect. The impermeable objects also occupy volume, reducing the amount of flooding water (movable weight) that can fill the space.

SWASH BULKHEADS (BAFFLE PLATES)

In addition to some structural support, these bulkheads are designed to reduce Free Surface Effect. They are longitudinal bulkheads that hinder, but do not prevent, the flow of liquid from side to side as the ship rolls or heels. They are found in tanks, voids, double bottoms, bilges, etc.

SLUICE VALVES

Sluice valves allow opposing tanks to be cross-connected. When large, partially filled tanks are connected, Free Surface Effect increases, and the vessel become less stable. Ships like oilers and tenders use these valves to create long, slow roll periods during ammunition handling and refuelling.

SluiceValve Closed

Sluice Valve Open

To summarise, remember that:

1. FSE increases with increased length and width of compartment.

2. FSE increases when displacement decreases (de-ballasting).

3. Depth or quantity of the liquid in the tank does not affect free surface to any great degree. Free surface area is the main factor.

4. Free surface reduces stability by causing a virtual rise of G, thereby reducing GM and GZ.

5. Longitudinal divisions of tanks will reduce FSE.

6. Only a completely empty or completely full tank will have a zero free surface. Free Communication Effect

Free Communication Effect occurs when the ships hull is ruptured, allowing seawater to flow in and out as the ship rolls. This continuous weight addition and removal causes a horizontal shift in the center of gravity, which then equates to another virtual rise in the center gravity.

Three conditions must exist for Free Communication Effect:

1. The compartment must be open to the sea.

2. The compartment must be partially flooded.

3. The compartment must be off centreline or asymmetrical about centreline.

When the vessel below is inclined, it experiences a horizontal weight shift due to the Free Surface Effect. The center of gravity shifts from G0 to G2. The center of gravity is shifted further from centreline due to the flooding weight addition/removal as the ship rolls. This reduces the righting arm from G2Z2 to G4Z4. By extending the line of gravitational force up to the centreline, position G5 is found. This increase from G3 to G5 is the virtual rise of gravity due to the Free Communication Effect.

The factors which minimize Free Surface Effect (pocketing, surface permeability, swash bulkheads, etc) will also minimize Free Communication Effect. There is one additional factor associated with Free Communication: the size of the hole in the ship.

How the size of the hole affects Free Communication is not something that can be calculated. The FCE equation does not account for the hole. Basically, if the hole is small, less water will be added/removed to/from the ship. The larger the hole, the closer Free Communication Effect is to its calculated value

Review questions for

Section4Prepare a Stability Statement

HO M159-4-02 Review Questions on Trim

Exercise 1

A ship of 5000 tonne displacement, 96 m long, floats at draughts of 5.6 m forward and 6.3 m aft. The TPC is 11.5, GML 105 m and centre of floatation 2.4 m aft of midships.Calculate:

a) the MCTI cmb) the new end draughts when 88 tonne are added 31 m forward of midshipsAnswers to Review Questions.

a) MCTI cm = ( x GML tonne m 100L = 5000 x 105 100 x 96 = 54.69 tonne mb) Bodily sinkage = 88 11.5 = 7.65 cmd = 31 + 2.4 = 33.4 m from FTrimming moment = 88 x 33.4 tonne mChange in trim = 88 x 33.4 54.69 = 53.74 cm by the headDistance from F to fore end = 96 + 2.4 2 = 50.4 mDistance from F to after end = 96 - 2.4 2 = 45.6 mChange in trim forward = + 53.74 x 50.4 96 = + 28.22 cmChange in trim aft = - 53.74 x 45.6 96 = - 25.52 cmNew draught forward = 5.60 + 0.076 +0.282 = 5.958 mNew draught aft = 6.30 + 0.076 - 0.255 = 6.121 mExercise 2

A ship 150 m long has draughts of 7.70 m forward and 8.25 m aft, MCTI cm 250 tonne m, TPC 26 and LCF 1.8 m forward of midships. Calculate the new draughts after the following masses has been added:50 tonnes, 70 m aft of midships170 tonnes, 36 m aft of midships100 tonnes, 5 m aft of midships 130 tonnes, 4 m forward of midships40 tonnes, 63 m forward of midshipsMass(tonne)

Distance from

F (m)Moment forward(tonne m)Moment aft(tonne m)

5071.8A-3590

17037.8A-6426

1006.8A-680

1302.2F286

4061.2F2448

490273410696

Answers to Review Question

Excess moment aft = 10696 - 2734 = 7962 tonne mChange in trim = 7962 250 = 31.85 cm by the sternChange in trim forward = -31.85 (150 - 1.8( 150 ( 2 ( =-15.54 cmChange in trim aft = +31.85 (150 + 1.8( 150 ( 2 ( =+16.31 cmBodily sinkage = 490 26 = 18.85 cmNew draught forward = 7.70 + 0.189 - 0.155 = 7.734 mNew draught aft = 8.25 + 0.189 - 0.163 = 8.602 m

Assessment tools for

Section4Prepare a Stability Statement

Assessment task

Completion of an intact stability statement.

Criteria: Students to work individually or in pairs to produce an intact stability statement..

Vessel type to be nominated by teacher, as many different types as possible within the group.

Students are to develop and draw the righting arm curve and identify the following:

deck edge immersion angle

down flooding angle

maximum righting moment.

Using past ship data when estimating for new projects

Calculation

Weighting

NC cutting data

Components information

Weight Control

Estimating

Weight

Assessment task

Learning

activity

Learning

activity

Learning

activity

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W W + w

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GG1 = w x d

W - w

GG1 = w x d

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L

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W

R

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L1

F

B1 B

G1 G

ML

m

m

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m 159 section 4

Documents

weight estimation lesson

weight estimation duration

weight definition

weight engineering process

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basic ship theory volume