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.
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 M159-4-01Section 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 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
Overhead Transparencies
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
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 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.
Overhead Transparencies
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
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.
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
A G G1 B
d
W W + w
w
GG1 = w x d
W - w
GG1 = w x d
W
L
d
W1
W
R
L
L1
F
B1 B
G1 G
ML
m
m
(
(
(