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MARINE
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METRIC Instructional MANUAL
CONTENTS Chapter Page
1 Introduction 1
2 Ship Draft, Trim and Stability Notes 14
3 Draft Survey 30
4 Cargo Deadweight 50
5 Trim and Stability 58
6 Grain Loading 73
7 Rolling Period Test for GM 88
Appendix 94
Draft and Stability Problems and Answers 94
- 1 -
CHAPTER 1
INTRODUCTION PURPOSE
1.1 This Handbook is intended to assist Deck Officers with their loading calculations.
Practical solutions are emphasised, and the most common questions about ship
loading are answered.
1.2 More detailed knowledge may be obtained from published tomes on the subject
which will provide fuller coverage of stability.
DESCRIPTION
1.3 Chapter One, Introduction - describes the purpose of the Handbook. There is a
summary of the contents of each chapter. An alphabetical listing of abbreviations
used, a listing by chapter of formulas, and some recommended materials and
equipment for performing ship-loading computations are also included.
1.4 Chapter Two, Ship Draft, Trim and Stability Notes -defines and discusses points
and practices which have a practical effect on safe and economic ship loading.
1.5 Chapter Three, Draft Survey - describes in detail, complete with worked
examples, the procedure for performing an International Standard Draft Survey.
1.6 Chapter Four, Cargo Deadweight - summarises the main considerations when
performing cargo deadweight calculations. Each step in the procedure is then
described in detail, complete with worked examples.
1.7 Chapter Five, Trim and stability - summarises the main considerations when
performing trim and stability calculations. Each step in the procedures is then
described in detail, complete with worked examples.
- 2 -
1.8 Chapter Six, Grain Loading - summarises the IMCO and SOLAS requirements for
loading grain. Each step in the procedure is then described in detail, complete with
worked examples.
1.9 Chapter Seven, Rolling Period Test for Timber Carriers -describes the procedure
for measuring the rolling period of a ship. This is most frequently required when
there is timber deck cargo, but is applicable for any vessel or cargo. The
calculations to convert rolling period into GM are then described in detail, complete
with worked examples.
1.10 Appendix I, Problems - consists of twenty-seven (27) questions relating to the
material covered in this Handbook. All questions are worked out in detail.
1.11 The following abbreviations are commonly used through- out the text:
AP After Perpendiculars
DISP Displacement
DWT Deadweight
FP Forward Perpendiculars
GM Metacentric height
KB Transverse Centre of Buoyancy
KG Transverse Centre of Gravity
LBP Length Between Perpendiculars
LCB Longitudinal Centre of Buoyancy (Pg.26)
LCF Longitudinal Centre of Flotation
LCG Longitudinal Centre of Gravity (Pg 22)
LKM Longitudinal Metacentric Distance
MG Centre of Gravity from Midship or LCG
MTC Moment to Change Trim by One Centimetre
P Port
- 3 -
QM Quarter Mean
S Starboard
SF Stowage Factor [M3/T ]
Sg Specific gravity [ T/M3 ]
TKM Transverse Metacentric Height
TPC Tonnes per Centimetre (Immersion)
VHM Volumetric Heeling Moment
VVM Volumetric Vertical Moment
FORMULAS
1.12 The following formulas are used in ship loading computations:
DRAFT SURVEY (Chapter 3)
Forward Draft = Fwd(P) + Fwd(S) 2 Aft Draft = Aft(P) + Aft(S) 2 Mid Mean = Mid(P) + Mid(S) 2
Trim = Aft - Fwd
Fwd/Aft Mean = Fwd + Aft
2 Mean of Mean = Fwd & Aft Mean + Mid Mean 2 QM = Mean of Mean + Mid Mean 2
DISPLACEMENT correction = TPC x Draft remainder in cm. Displacement = DISP + DISP
correction
- 4 -
First correction = TRIM xTPC x LCF x 100 = Corr for trim LBP Vessel trimmed by the STERN:
LCF is Fwd - you SUBTRACT
LCF is Aft - you ADD Vessel trimmed by the HEAD:
LCF is Fwd - you ADD
LCF is Aft - you SUBTRACT
Second Correction = T² x 50 x MTC diff = Final Trim Correction LBP Displacement = TPI x Draft remaining in inertia
First Correction = Trim x TPI x LCF x 12”
LBP Second Trim Correction = T² x 6” x MTI diff LBP MTC difference ( Metric ) :
(a) QM + 50cm = MTC (Found from Ship’s Data)
(b) QM - 50 cm = MTC (Found from Ship’s Data) MTC diff = a – b (a) MTC - (b) MTC = MTC difference MTI difference (Imperial): (a) QM + 6” = MTI ( Found from Tables )
(b) Qm – 6” = MTI ( Found from Tables )
WEIGHT DEDUCTIONS ( Metric ) : FUEL OIL_________________ MT DIESEL OIL ____________ MT LUBE OIL ____________MT FRESH WATER ____________MT DRINK WATER ____________MT BOILER WATER ___________MT BALLAST WATER _________MT
- 5 - SLUDGE __________________MT STORES,etc _______________MT CONSTANT _______________MT TOTAL weight deductions WEIGHT DEDUCTIONS ( Imperial ) : Calculations are done in LT - Long Tons.
CARGO DEADWEIGHT (Chapter 4) ; Pg 70
Cargo DWT = DISP. corrected for density (2nd condition)
- TOTAL weight deductions (2nd condition)
= NETT displacement (2nd condition) - NETT displacement (lightship = 1st condition)
= CARGO LOADED
PERCENTAGE (%) = Hold Capacity x 100
Total Capacity
DEFLECTION = MID MEAN Hogging = MID MEAN - FWD & AFT MEAN [ Peregib ] , See Pg.23
Sagging = MID MEAN - FWD & AFT MEAN [ Progib ] , See Pg.23 Even Keel = MID MEAN - FWD & AFT MEAN TRIM FORMULAS (Chapter 5) ; Page 58 LCG(FP) = LBP + MG 2
MG is Aft - you ADD
MG is Fwd - you SUBTRACT
Longitudinal Moment = Weight x LCG(FP) New LCG(FP) = Total Longitudinal Moments Displacement
- 6 - Trim Lever = LCG(FP) - LCB(FP) TRIM = Trim Lever x Displacement x 100(m) MTC
Final Longitudinal Moments = DISP x LCG(FP)
Longitudinal Moments of Constant = Final - all other Longitudinal Moments
LCFG(FP) of the Constant = Longitudinal Moment
Weight (CD) Change of Draft = Trim 2
Mean Sinkage = + Weight TPC
Distance = 2 x MTC TPC
Weight = TPC x Trim(cm) 2
Vertical Moment = Weight x KG KG = Total Moments (P) _ Total Moments (S) Total Weights (P) Total Weights (S) New KG = Old KG = Total Change in Moments Total Change in Weights GM = TKM - New KG *GG = Total Inertia / Total Weights G1M = GM - GG1 Rolling Period : ( Imperial ) ( Metric )
0.44B Ft___ 0.7978B Metres sq.rt of G M sq. rt of GM
Rise of G due to Free Surface = _L x B³ x Sg___ 12 x DISP x n²
- 7 - Where:
L = Length of tank
B = Breadth of tank Sg = Specific Gravity of liquid in tank n = # of Longitudinal compartments into which the tank
ROLLING PERIOD TEST (Chapter 7) ( IMPERIAL ) ( METRIC ) GM = 0,1936 x B² GM = 0,6532 x B²
T² T²
Where :
T = Rolling Period in Seconds of time
B = Breadth of Ship
GG1 = w x dKG
DISP Where:
GG1 = Shift in Centre of Gravity
DISP = W +/ - w
W = Original Displacement
w = Weight to be loaded or discharged
dKG = Distance from KG to G of weight
GM = W x D x cot.0°
DISP
Where:
W = Weight
D = Distance from water line cot.0° = Angle of List
- 8 -
GRAIN LOADING (Chapter 6)
HHM = ___VHM___ SF( cargo)
G0 G1 = VHM DISP x SF
CUBIC METRES ( M ³) = Cubic Feet ( Ft³ )
35.315 NECESSARY MATERIALS
1.13 Work Forms are recommended to ease the work of calculations. Several forms are
included as part of the examples in this Handbook. These may be used as is, or
altered to suit personal or operational requirements.
1.14 Stability Booklet and Loading Manual, complete with:
- hydrostatic and deadweight tables;
- grain loading plan;
- general arrangement plan;
- capacity plan, and
- tank capacity plan or manual.
These items are all supplied by the shipbuilder to the ship and should be studied with care.
1.15 Certified hydrometer and water sampler (water thief). These are used to measure
the specific gravity (Sg) of the water in which the ship is floating. A special
hydrometer for measuring the Sg of fuel and lubricating oils should also be
available.
- 9 -
1.16 A sounding tape for measuring tank contents, and a standard tape for measuring
holds, lockers, and other spaces.
1.17 A good calculator will speed up calculations. Any of the better scientific calculators
will have a program for integration by Simpson’s Rule.
- 10 -
- 11 -
- 12 -
Figure 2
- 14 -
CHAPTER TWO
SHIP DRAFT, TRIM AND STABILITY NOTES CONSTANT
2.1 The constant, in draft survey calculations, includes all
weights aboard ship, which are not included in the manuals.
These would include crew, crew's effects, provisions and
stores, lifesaving equipment, water in pipelines, mud in
the chain locker, and fouling of the hull.
2.2 A vessel’s constant will alter appreciably over a period
of time. It must be checked, and probably recalculated,
for every loading survey. Stores, paint especially,
together with lubricating oils, spare cylinder liners,
and additional equipment will often change the constant
by more than 100 tonnes in 6 months.
2.3 The constant also increases with age. Corrosion and the
accumulation of “it might be useful” stores are the main
causes for this increase. The old rule of thumb was:
"For a vessel of 10,000 tons, add one inch of draft
for each five years of vessel life".
Most vessels are now much larger, so the estimate will have to
depend on the surveyor’s experience. Check for unlisted stores
especially used lumbers and rope.
2.4 The weight of bottom growth is the most difficult to
allow for. It is frequently significant, and value of 50
- 15 -
Kg/M² has been suggested. A check of the fouling exposed
when the vessel is light can be helpful.
A bottom survey by a qualified diver provides the most
accurate data.
2.5 One apparent change in constant must be guarded against.
A draft survey at anchor, or alongside with one anchor
down, will be minus the weight of the anchor and chain.
If, at the discharge port, both anchors are put on the
bottom whilst alongside, the difference between the
initial and final surveys will produce an apparent
increase in the weight of the cargo out-turn.
2.6 Ensure the weights of anchors and chains are properly
added or subtracted from the loading and unloading
constant calculations. SPECIFIC GRAVITY ( Sg ) [ T/M3 ]
2.7 Specific gravity (Sg) is ratio of the weight of a given
volume of a substance compared to the weight of the same
volume of distilled water. The theoretical Sg
of distilled water is 1.000 T/M3 , the Sg of sea water is 1.025 T/M3
times as much as one cubic meter of distilled (fresh)
water. Therefore, a ship will displace 1.025 T/M3 less
seawater than fresh water.
2.8 The actual Sg is always changing, particularly in the
harbour. The effect of tide water and rivers is such that
constant measuring of the Sg is required throughout
loading. In some harbours where the effects of sea and
fresh water mixing are extreme, it is necessary to
- 16 -
measure Fwd. Aft, and Amidships Sg’s, and use the average
for Draft and Deadweight calculations. It may be
necessary to get measurements for both port and starboard
sides of the ship if maximum accuracy is required.
Measuring the Sg at different depths may also be
required.
2.9 Use a partly stopped, weighted container and a line equal
in length to the distance from the deck to the keel, to
sample the water for Sg measurement. Drop the container
into the water and withdraw it at an even rate. With
practice, the container will be just filled as it breaks
the surface. Water samples collected in this way will
represent a good average of the water in which the ship
is floating.
2.10 Sg measurements for Draft and Deadweight surveys must be
made with a certified hydrometer.
DENSITY AND TEMPERATURE
2.11 A great deal has been written regarding the effect of
temperature on density. This is important when
viscosity is a consideration, or when specific gravity is
required for scientific calculations.
2.12 However, in draft surveys, it is unnecessary to measure
the temperature of the river, lake, or ocean water in
which the vessel is riding. The hydrometer reading. if
taken as soon as the sample is drawn, will include the
- 17 -
temperature, as well as the salinity effect on specific
gravity.
A GOLDEN RULE IS. THEREFORE, MEASURE THE WATER TEMPERATURE IF
YOU MUST,BUT DO NOT USE IT IN DRAFT SURVEY CALCULATIONS.
The Sinkage and Trim caused by Currents and Tidal Streams*
Most seafarers are well aware of the effect known as “squat” which causes ships to increase their draft when travelling at speed in shallow water. What they may not be aware of is that a ship moored or anchored in shallow water experiences the same effect when there is a tidal stream or current running. The cause of both effects is similar.
Consider a ship moored in a river (Figure 4). When a current is running the shin constricts the flow. The water must then increase its speed In order that the same quantity passes through the restricted space as does through the unrestricted space. In any given period of time. The water flowing at a higher speed under the bottom of the vessel causes a reduction In pressure on the bottom (this occurs by virtue of the Bernoulli effect) arid the ship sinks deeper in the water.
- 18 -
* E. Stokoe, Weight/Volume Relationship Required for Draft Survey Calculations, Seawaves, Vol.Feb.1984, pp.15, 17.
The Bernoulli effect can be demonstrated by trying to blow a piece of card off the end of a cotton reel (Figure 5). It is impossible to blow the card off. The high air velocity on the inner face of the card causes a local drop in pressure relative to the outer face of the card; thus keeping it firmly pressed on the end of the reel. Bernoulli’s equation, which governs this effect, is P + p V²/2 + pgh = constant, where P + p V²/2 + pgh = constant, where P - is pressure,
p - the water density, v - Is the velocity, and h - the depth of water.
Clearly as v increases, at a given water depth, P must decrease for the equation to remain constant.
The amount of sinkage caused by this effect will depend, therefore, on the water velocity. It will also depend on the depth of water beneath the keel and the ship’s length. The sinkage in some cases will be considerable. For example, a 1,600 tonne coaster moored In a river where the current Is running at 4 knots will experience a sinkage of at least 5 cm where there is about 0.35 in of water under the keel. It is therefore desirable to wait until the depth of water under the keel is as large, as possible before measuring draughts if there is any current.
Clearly In a tidal stream It would be better to measure the draughts at slack Hater thus avoiding this sinkage effect If’ at all possible. With data currently available it would not be
- 19 - possible for the sinkage likely to be experienced to be estimated in all cases. An approximate theoretical estimate can be made but the procedure involved is relatively complicated (see Dand & Ferguson. The Squat of Full Form Ships In Shallow Water, TRINA Vol.115. 1973.
DISPLACEMEHT AND DEADWEIGHT
2.13 Displacement is the weight of water displaced by the
ship, which, for a floating vessel, equals the weight of
the ship. Light Ship’s weight plus Deadweight equals
Displacement (DISP).
2.14 Deadweight is the total weight carried by the ship.
Included in deadweight are: cargo, constant and stores,
fresh water, fuel and ballast.
SHIP STRUCTURE
2.15 All vessels must be able to remain afloat after certain
heavy seas. Watertight bulkheads are one of the major
structural items built into the ship for this purpose.
The length of the ship regulates the number of these
bulkheads.
2.16 Four is the usual minimum number of bulkheads required:
2.16.1 A collision bulkhead placed at one-twentieth
(1/20) of the ship’s length, measured from the
stem.
2.16.2 A bulkhead forward and the engine (and boiler, if
steam powered) space.
2.16.3 An afterpeak bulkhead positioned to enclose the
shaft tubes in a watertight compartment.
- 20 - SHIP STRUCTURAL STRESSES
2.17 A ship is considered a variably loaded, variably sup-
ported beam, for strength analysis. That is:
2.17.1 The weight of the ship, its equipment and
cargo, will vary meter by meter along its
length.
2.17.2 The water in which it floats supports the ship.
In still water, there is more support per meter
at the stern than at the bow because the ship is
fuller aft.
2.17.3 In a sea there is more displacement, and there-
fore more support or upward force, at the crest
of a wave. There is less displacement and
therefore less support in the troughs.
2.18 The major stresses are: longitudinal tension (or
stretching), compression in the deck and keel, and
shearing forces, as shown in Figure 7.
2.18.1 When the ratio of weight-to-support is greater at
the ends than amidships, the ship “hogs”. The
keel is in compression, the deck is in tension,
and the ship bends upward in the middle.
2.18.2 when the ratio of weight to support is greater
amidships than at the ends, the ship “sags”. The
keel is in tension, the deck is in compression,
and the ship bends downward in the middle.
2.19 Since the keel is constructed with a heavier weight
of metal, the deck is where almost all failures occur.
- 21 -
The deck of a cargo vessel is further weakened by
hatchways and other necessary openings. These openings
must be reinforced. Sharp corners tend to concentrate
stresses, so hatch corners require special attention.
2.20 The deck is subject to other stresses such as deck cargo
and the weight of water when heavy seas are shipped.
Since deck beams must be cut out at hatch comings, the
load bearing strength is reduced. The weight and
placement of deck cargo and the effects of heavy seas
must be carefully considered. The deck plates should be
strengthened, if required. Hatch comings should be
checked for strength and rigidity.
LONGITUDINAL CENTRE OF GRAVITY
2.21 The longitudinal centre of gravity (LCG) of a ship is
that point along its length where one-half of all weights
are forward, and one-half aft. That is, it is the balance
point for the ship and its contents.
( Page 22 is skipped.)
- 23 -
Figure 7
- 24 -
LONDITUDIONAL CENTRE OF GRAVITY
METRIC MEASURE
- 25 -
LONGITUDIONAL CENTER OF GRAVITY ( IMPERIAL MEASURE )
- 26 -
LONGITUDINAL CENTRE OF BUOYANCY
2.22 The longitudinal centre of buoyancy (LCB) is that point
where one-half of the ship buoyancy is forward, and one-
half aft. Because a ship is finer at the bow than at the
stern, the LCE is usually aft of the longitudinal centre
of gravity. The LCB will also tend to move aft as
displacement increases. For cargo vessels, the distance
is so small, however, in ratio to the length between
perpendiculars (LBP), that one-half of LBP is used for
practical calculations.
TRIM
2.23 When calculating the projected trim of a ship:
2.23.1 When LCG is Aft of LCB, the ship is “trimmed by
the stern”.
2.23.2 When LCG is Fwd of LCB, the ship is “trimmed by
the head”
2.23.3 When LCG and LCE are the same, the ship is on an
“even keel”.
2.24 A ship trimmed by the head will be difficult to steer. It
will also be subject to excessive shipping of seas in a
seaway.
2.25 A trim of one meter by the stern is generally considered
ideal. Cargo stowage, fresh water, fuel oil, usage and
ballasting should be calculated to achieve this.
- 27 -
- 28 -
2.26 Cargo segregation and port rotation sometimes make ideal
trimming difficult and costly. The consumption of fresh
water and fuel on a long voyage must be considered. The
removal of weight can make a poor trim worse or it can
improve it, depending on where the weight is located.
2.27 There are times when a ship is put on even keel because
of port requirements. The only good reason for having a
ship down by the head is for making emergency repairs to
the rudder or propeller.
BALLAST TANKS
2.28 All ships, except tankers, are built with double bottoms
to form tanks for fuel oil or ballast. These tanks are
divided Fwd and Aft and Athwartship.
2.29 When filling or checking ballast tanks, care must be
taken to avoid water damage to cargo. It is best done
when the hold above the tank is empty.
2.30 It is dangerous to assume these tanks are watertight,
even in a new ship. To check the ballast water tanks,
fill them until the water escapes through the overflow
pipes. Check the sounding to ensure the head is stable.
Also check the tank top seams and the manhole covers.
2.31 When a double bottom tank is filled there is considerable
upward force on the manhole covers. For a
- 29 -
manhole of 1,300 cm² (approximately 41 cm or 16 inches
across) with a head of fresh water six meters above the
tank top, the upward force is: 0.6 kg/cm² x 1.300 cm² = 780 kg.
- 30 -
CHAPTER THREE
DRAFT SURVEY SURVEY PROCEDURE
3.1 This Survey Procedure is International Standard for any
type of ship. The ship is first surveyed light, to
calculate the constant. It is then re-surveyed after
loading to determine the weight of cargo.
APPARENT TRIM ( Vidimy Different )
3.2 The Forward (Fwd), Aft (Aft), and Midships (Mid) drafts
are read at both Port (P) and Starboard (S) marks. The P
and S readings are added, and the result divided by two.
3.3 The Aft draft is subtracted from the Fwd draft, and the
result is Apparent Trim. If Trim is positive, the ship is
trimmed By the Head; if Trim is negative, the ship is
trimmed By the Stern.
Fwd Draft = Fwd(P) + Fwd(S) 2
Aft Draft = Aft(P) + Aft(s)
2
Mean Mid = Mid(P) + Mid(s) 2
Trim = Aft - Fwd
DRAFT CORRECTIONS TO THE PERPENDICULARS
3.4 The After Perpendicular is a right angle line to the keel
passing through the rudderpost; it is also the first frame
marked “0” on the vessels drawings.
- 31 -
The Forward Perpendicular is a right angle line to the keel
cutting the vessel’s Summer waterline at the stern. The
vessels stability information is calculated on the drafts
measured at the perpendiculars; as the draft marks rarely
coincide with these lines, a draft as read must be corrected.
3.5 If the marks are not on the perpendiculars, the vessel usually
has a tabulated plan in her hydrostatic books. However, some
of the older vessels do not have their tabulation and it is
therefore necessary to work out the correction to be applied
by referring to the vessels capacity plan and measuring the
horizontal distance between the draft marks and the
perpendiculars of the waterline. 3.6 The correction is calculated as follows: Aft Perpendicular Corr = 7.10 x 1.75(trim)= 0.0971 cm (+) 128.0
Fwd Perpendicular Corr = - 1.21 x 1.75(trim)= - 0.0165 cm(-)
128.0 How to determine Signs of FWD and AFT Corrections: (see pg 36) The Sign of A.P. / F.P. Corrections depending on Signs of two factors: Trim and Location of Distance between FWD / AFT perpendiclar to FWD / AFT Draft mark. Actually it appear atomatically when you insert in fomula all parametrs with their own algebraical sign . Trim by STEN ( + ) ; Tim by HEAD ( - ). Location of FWD /AFT perpendiculars FORWARD of FWD / AFT Draft mark ( - ) ; Location of FWD / AFT Perpendiculas AFT of FWD / AFT Draft mark ( + ) . Strictly say nesessary check all Signs in Ship’s Stability Manual to avoid any mistakes. (7.10) - represents the distance from the AFT Draft mark to the AFT Perpendicular. (-1.21) - represents the distance from the FWD Draft mark to the FWD Perpendicular. (128.0) - represents the length of the vessel between the Draft
marks (trim) - the difference between the Forward and After drafts
- 32 -
— 33 —
3.7 The above corrections are applied to the forward and after
drafts read.
Fwd Draft 2.64 m Aft Draft 4.30 m + Fwd Corr. -0.0165 + Aft Corr +0.0971 Corrected Fwd Draft 2.6235 Corrected Aft Draft 4.3971 3.8 CORRECTED DRAFT Corrected Draft Aft 5.019 = Aft - Fwd = Corr. Trim Fwd 2.361 Corrected Trim 2.658
NOTE: This value is used in Trim Correction Formulas to
adjust the displacement MEAN DRAFT CORRECTION ( M / M / M ) 3.9 The Quarter Mean ( QM ) or Mean Draft Corrected for Deformation must be solved next. Use the corrected draft values
3.10 First calculate the Fwd/Aft Mean Draft. Add Fwd to Aft,
and divide the result by two: Fwd /Aft Mean = Fwd + Aft 2
3.11 Next, calculate the Mean of Mean Add the Fwd/Aft Mean
(calculated in 3.10.) to the Mid Mean, and divide the result by two:
Mean of Mean = Fwd/Aft Mean + Mid Mean 2
3.12 Now calculate the QM Add the Mean of Mean (calculated
in 3.11) to the Mid Mean, and divide the result by two
NOTE: The Mid Mean is applied twice, first in calculating
the Mean of Mean, and second in calculating the QM.
- 34 - QM = Mean of Mean + Mid Mean 2 EXAMPLE (USED IN REPORT ON PAGE 49): FWD P 2.377 AFT P 5.017 MIDSHIP p 3.59 S 2.377 S 5.017 S 3.72 4.754 10.034 7.31
4.754 10.034 7.31 2 2 2
FWD = 2.377 AFT = 5.017 MEAN-MID = 3.655 TRIM = AFT – FWD ( APPARENT ) = 5.017 - 2.377 = 2.64 [Trim by the Stern (Apparent) because positive] DRAFT CORRECTION
Corrections for the Fwd and Aft Drafts (Fwd corr. and Aft
corr.) and Corrected Trim must be calculated. The corrections
values are different for each ship, and are found in the
Stability Manuals. If required, they can be calculated from the
formula given in Figure 12.
EXAMPLE:
Fwd Correction Value = +/-(distance from Fwd Draft to Fwd Perp)
(distance between Fwd and Aft Marks)
Fwd Correction = Fwd Correction Value x Trim ( Apparent )=
= -0.006037 x 2.64 = - 0.016 ( - )
Aft Correction Value = +/-(distance from Aft Draft to Aft Perp)
(distance between Fwd and Aft Marks)
Aft Correction = +0.034716 x 2.64 = +0.91 ( + )
Note: See Page 31 for explanation Sign +/- in abovementions Formulas.
-35-
Corrected Draft: Fwd Draft = 2.377 Aft Draft = 5.017 Fwd Corr = -0.016 Aft Corr = + 0.091 Fwd Draft Corrected = 2.361 Aft Draft Corrected = 5.108 Corrected Trim: Aft Draft Cor-ed - Fwd Draft Cor-ed = = Corrected Trim (CT) Aft Draft Corrected = 5.108
Fwd Draft Corrected = - 2.361 Corrected Trim (CT) 2.747
Note: This value used in the Trim correction Formulas to adjust the
displacement.
EXAMPLE:
Mid Mean = 3.655 M Fwd + Aft = 2.361 M + 5.019 M = 7.38 M
Fwd and Aft Mean = 7.38 = 3.69 M
2 Fwd and Aft + Mid Mean = 3.69
+3.655 7.345
Mean Mean of Means = 7.345 = 3.672 M 2
Mean Mean of Means + Mid Mean = 3.672 + 3.655 = 7.327 M Quarter Mean = 7.327 = 3.663 M 2 QM = 3.663 M The value for QM is used throughout the remaining Draft Survey Calculations. NOTE : QM is the same as M/M/M
M/M/M = ( Fwd + 6 x Mid + Aft ) = 3.663 M 8
Not
e: T
he S
ign
of A
.P./F
.P. C
orre
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epen
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on
Sign
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rim
and
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e be
twee
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/A p
erpe
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to F
/A D
raft
mar
k.
Act
ually
it a
ppea
r at
omat
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ly w
hen
you
inse
rt in
fom
la a
ll pa
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etrs
wit
h th
eir
own
alge
brai
cal s
igns
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T
rim
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Tim
by
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AD
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Loc
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F/A
per
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FO
RW
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of
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Stri
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- 37 -
3.13 Refer to the vessel's Stability & Hydrostatic Manuals
and Tables for the following values:
TPC: tonnes per Centimetre Immersion
MTC: Moment to change Trim One Centimetre
LCB: Longitudinal Centre of Buoyancy
LCF: Longitudinal centre of Flotation
KB: Transverse centre of Buoyancy
TKM: Transverce Metacentric Height 3.14 Interpolation
Calculate the Displacement Correction ( DISP. Corr.)
a) Subtract the nearest smaller Draft from the calculated
QM. b)Multiply the result by 100 to convert Meters to Centi- metres.
c) Multiply this by the TPC for the displacement.
d) This correction is added to the displacement given for
the nearest smaller draft.
NOTE: Refer to Figures 13 and 14 for sample Hydrostatic
Tables.
Draft Remainder (cm) = Draft remainder x 100 DISP. Corr. = TPC x Draft remainder (cm)
Displacement = DISP. + Disp. Corr. = Actual Displacement EXAMPLE: a) Draft remaining = 3.6635 - 3.66 = 0.0035 M
b) Draft remaining = Draft Remainder(M) x 100 = 0.0035 M =0.35cm
- 38 -
- 40 - c) Displacement Correction = TPC x Remaining draft (cm) = 17.66 x 0.35 cm = 6.181 MT d) DISPL.CORRECTED = DISPL.(at SMALLER DRAFT ) + correction
= 7587.00 + 6.181 = 7593.181 MT (corrected)
TRIM CORRECTION
3.15 Trim Correction values for a given Displacement is
tabulated in the Ship Stability Manual. Even if these are
readily available, the following formulas should be
studied in order that the principles governing a Draft
Survey are fully understood.
3.16 Before calculating the First Trim Correction, Corrected
Trim (CT) (Ref. 3.3) must be converted from meters to
centimetres. Multiply CT (in) by 100 to get centimetres.
Converted Corrected trim = CT x 100
3.17 To calculate the First Trim Correction, multiply TRIM by
TPC, then multiply the product by the longitudinal Centre
of Flotation (LCF) x 100. Then, divide the final product
by the Length Between Perpendiculars (LBP).
First Correction = TRIM x TPC x LCF x 100
LBP
Second Correction = T² x +/-50 cm x MTC diff. LBP
3.18 The first correction can be either positive (add), or
-41-
negative (subtract), depending on the location of the LCF
and the trim condition. (It's mean sign of LCF and TRIM )
3.18.1 VESSEL TRIMMED BY THE STEM
LCF is Forward (Fwd) (+) ADD Trim Correction LCF is Aft (Aft) (-) SUBTRACT Trim Correction
3.18.2 VESSEL TRIMMED BY THE STERN LCF is Fwd (—) SUBTRACT Trim Correction LCF is Aft (+) ADD Trim Correction
3.19 The second Trim Correction is required when the
Trim is greater than the LBP divided by 100. It may be
applied without adverse effect at smaller trims. Second Correction = T² x +/-50 cm x MTC diff. LBP
3.20 The second correction is always (+) (additive)
regardless of the trim or other factors.
3.21 Before calculating the Second Trim Correction, MTC
difference, sometimes referred to as dM/dZ, must be
found.
3.21.1 ADD 50 cm to the Quarter Mean Draft ( QM ) to
find the corresponding MTC from the vessel’s
Hydrostatic book.
3.21.2 SUBTRACT 50 cm from the Quarter Mean Draft
(QM) to find the corresponding MTC from the
Vessels Hydrostatic book.
3.21.3 The difference between 3.21.1 and 3.21.2 is
the MTC difference, or dM/dZ.
- 43 - EXAMPLE:
(1)First correction: Trim = 2.74 M ( By STERN "+" )
TRIM x LCF x TPC x 100 LBP (+)2.74 x (—)4.53 x 17.65 x 100 = 159.909 (-) MT 137.00 = 159.91(-) 2) Second Correction: T² x +/-50 x MTC diff
LBP MTC diff.: a) Q M + 50cm = MTC ( Found in Ship’s book)
b) Q M - 50cm = MTC ( Found in Ship’s book)
MTC diff= ( a) — ( b)
a) QM = 3.675 + 0.50 4.175 MTC = 169.4
b) QM = 3.675
— 0.50 3.175 MTC =160.7 (a) = 169.4 (b) = - 160.7 MTC diff = 8.7
7.5 x 50 x 8.7 = 23.81 + MT 137
(3) DISP Corrected for TRIM:
1st correction: a) 7587.00
b)- 159.91 =c) 7427.09 (-)
- 44 -
2nd Correction: c) 7427.09 d) + 23.81 = e) 7450.90 (+) = Displ. Corr.for Trim
NOTES for TRIM FORMULAS FOR IMPERIAL CALCULATIONS: TPI = Tons Per Inch (12 converts all to inches) 6” = +/-6” of the QM draft to obtain the two MTI differences. 1st Correction = TRIM x LCF x TPI x 12 LBP 2nd Correction = T² x +/-6” x MTI diff LBP SPECIFIC GRAVITY CORRECTION
3.22 A Specific Gravity (Sg) of 1.025 is generally assumed
for SeaWater in calculating Displacement (DISP).
Because the Sg. is almost never exactly 1.025, Sg. correction
must be calculated.
3.22.1 Sg. is always minus if the measured Sg. is
1.025 or less.
3.22.2 Sg. is plus if the measured S9. is 1.026 or
more.
3.23 Calculate the Sg. correction by subtracting the
measured density from 1.025, divide this by 1.025 and
then multiply that answer by the DISP.
Sg. corr. = 1.025 - Measured Density x DISP.
1.025 EXAMPLE:
Measured Density = l.020.4 1.025 — 1.0204 x 7450.9 = 32.71 1.025
- 45 -
DISP. corr. for Trim 7450.90
Density Corr. (Sg.) — 32.71
DISP. Corr. for Density 7418.19
VESSEL’S CONSTANT
3.24 Subtracting the Lightship, weights, ballast and
consumables from the Displacement solves the Constant
of an unladen vessel.
3.25 Tank tables or graphs should be available so the tank
soundings can be converted from measure to volumes and
corrected for trim.
3.26 Figure 16 is a typical tank graph. In addition to
volume against sounding information, it provides KG
and Inertia data for trim and stability calculations.
Figure 17 is a tank trim correction table and Figure
18 is a typical tank table.
3.27 Volume multiplied by Sg. equals weight. A Sg. of 1.000
is used for Fresh Water, and for Salt Water Ballast a
Sg. of 1.025 is used. Therefore, one cubic meter of
Fresh Water equals one Metric Tonne and one cubic
Meter of SeaWater equals 1.025 Metric Tonnes.
3.28 The Chief Engineer is obliged to supply the Sg. of the
various fuel oils on board. It is good practice, if
possible, to measure the Sg. at the same time the tanks
is being sounded.
- 46 -
3.29 WEIGHTS FUEL OIL 545.86 MT DIESEL OIL 100.70 MT LUBE OIL 21.00 MT FRESH WATER 401.00 MT DRINK WATER NIL BOILER WATER NIL BALLAST WATER 1870.84 MT SLUDGE (BILGE) 5.50 MT STORES, etc. NIL CONSTANT 200.42 MT = TOTAL WEIGHT 3145.32 MT NETT DISP. 7418.19 MT - TOTAL WEIGHT 31475.32 MT NETT DISP LIGHTSHIP 4272.87 MT
FINAL SURVEY
3.29 The Final Survey follows the same procedure as the
Initial Survey. Total cargo equals DISP. minus
Lightship Weight.
NOTE: See completed form – Figure 19 (Page 49 – Picture )
- 47 -
-50-
CHAPTER FOUR
CARGO DEADWEIGHT
GENERAL
4.1 The weight a ship can carry varies considerably with
location and season. More can be loaded in Tropical
countries, but less in a Summer Season Zone. Seasonal
Winter Zone loading, when applicable, is smaller still.
4.2 Study the Loadline Certificate carefully to avoid conflict
between the ship and the Port Authorities, or with the ship
owners. A Freeboard Table (Figure 1) is provided in the
Ship Stability Manual.
4.3 Consumables, such as fresh water, fuel oil, lubeoil,
ballast, etc., necessary for the intended voyage,must
be considered when calculating Cargo Deadweight.
4.3.1 Make adjustments for re-supply if a call at a
bunkering port is required.
4.3.2 If supply is much larger than projected
consumption, less Cargo Deadweight may be
CARGO DEADWEIGHT CALCULATION
4.4 Calculating the Cargo Deadweight Available is relatively
simple. Consult the Freeboard Table for Draft and Dis-
placement allowed, Subtract Lightship Weight. Constant,
Ballast and Consumables. The remainder is Cargo Deadweight
Available.
-51- EXAMPLE:
For a simple voyage with a Timber Cargo, in winter, through
a Seasonal Winter Zone. Timber Winter Displacement = 8.819 MT Draft Displacement = - 21654.000 MT Lightship Weight = - 4341.000 MT 17313.000 MT Constant = — 196.000 MT 17117.000 MT Ballast = — 2651.000 MT 14466.000 MT Fresh Water = - 308.000 MT 14158.000 MT Fuel Oils = - 696.000 MT CARGO DEADWEIGHT AVAILABLE = 13462.000 MT CONSUMABLE CONSUMPTION
4.5 If oil and fresh water are to be replenished at an
intermediate port, the Cargo Deadweight may have to be
reduced. If the planned intake, plus the fresh water and
fuel remaining after passage to the bunkering port, is
greater than the consumables on board at Final Survey, the
difference must be deducted from Cargo Deadweight
Available.
-52-
EXAMPLE:
Length of voyage to bunkering port = 16.5 days.
Fresh Water = 150 MT
Fuel Water = + 660 MT Total Consumables = 810 MT a) Fresh Water Consumption 8.0/day x 16.5 = 132 MT Fuel Oil Consumption 24.0/day x 16.5 = + 396 MT Total Consumption = 528 MT b)
Balance of Fuel and Water Left (810-528) = 282 MT (a-b) Planned Intake - Fresh Water = 200 MT - Fuel Oil = +400 MT - Total = 600 MT
Balance of Fuel and Water = +282 MT
Total after Replenishment = 882 MT
Consumables at Port of Lading = -810 MT
Difference of = 72 MT
The 72 MT must be deducted from Port of Lading Cargo Deadweight
Available.
SEASONAL ZONES
4.6 Less cargo may be carried if a ship loads in a Summer Zone
and will enter a Seasonal Winter Zone.
EXAMPLE:
Summer Timber Loadline = 9.07 M = 22336.00 MT
Winter Timber Loadline = 8.819 M = 21654.00 MT
Difference = 682.00 MT
-53-
4.7 The weight of Consumables used in the voyage from port of
lading to the Winter Zone may be added to the Winter Zone
allowable displacement when calculating allowable Cargo
Deadweight.
4.8 If the ship is to take on consumables at an intermediate
bunkering port in the Winter Zone, the total planned weight
of consumables on board at that port will govern the
allowable Cargo Deadweight.
LOW DENSITY CARGO
4.9 Total Cubic Capacity of the ship is available in the
Capacity Plan. Bale Capacity is used if the booked cargo is
not grain or other bulk commodities.
EXAMPLE:
Load a full, homogeneous cargo with Stowage Factor of 65
CF/LT.
Conversion - 1 Ft³ / LT = 0.0278715 M³ / MT 1 M³ / MT = 35.3145 Ft³ /LT
Therefore SF 65 Ft³/LT x 0.0278715 = 1.81 M³/MT
Bale Capacity = 19183.82 M³ Weight of Cargo = Bale Capacity SF
= 19183.82 1.81
= 1598.795 MT
NOTE: A number of good books on cargoes and their Stowage Factors
are available. “ STOWAGE - THE PROPERTIES AND STOWAGE OF
CARGOES ” by Captain R. E. Thomas, is a particularly
complete reference.
-54-
CARGO DISTRIBUTION
4.10 The first consideration is to distribute cargo so that
weight is evenly spread throughout the ship.
4.10.1 If Weight-to-Flotation is greater at the ends of
the ship than in the middle, the deck will deflect
up. This is called “ Hogging ”.
4.10.2 If Weight-to-Flotation is greater in the middle
than at the ends of the ship, the deck will deflect down. This is called “ Sagging ”.
4.11 In a Hogging condition, the deck is placed in tension, and
the keel in compression. In a sagging condition, the deck
is placed in compression, and the keel in tension.
4.12 The keel is stronger than the deck because of the greater
weight of metal used in construction. The deck is further
weakened by necessary openings, such as cargo hatches.
These openings are reinforced, but, since they are the
weakest points in the ship’s structure, careful inspection
is required.
4.13 To determine the amount that the ship is hogging or sagging
Measure deflection.
Deflection = Mid Mean – Fwd and Aft Mean
Fwd and Aft Mean = Fwd Mean + Aft Mean
2
4.13.2 If Mid Mean is greater than Fwd and Aft Mean, the
ship is Sagging.
4.13.3 If the Mid Mean equals Fwd Mean equals Aft Mean,
the ship is on an even keel.
NOTE: Ship’s decks are stronger in tension than in com-
therefore, a small amount of Hogging is preferred to
Sagging.
-55-
4.14 Most modern ships have their machinery and superstructure
Aft. This produces a large trim By the Stern. And a
Hogging moment, in the light condition.
4.14.1 First load the midships holds to eliminate the
Hogging.
4.14.2 Next load the Forward hold to decrease the trim.
4.15 Part loading, or other conditions may produce Sagging.
4.15.1 First load the forward hold to eliminate Sagging.
4.15.2 Distribute the remaining load for desired trim.
4.16 Distributing weight is easier with a homogeneous bulk
cargo, such as grain or concentrates. General cargoes
are often more difficult because of factors such as
port rotation and cargo segregation.
EXAMPLE:
(1) Check the Capacity of each hold (M³) Hold Number 1 = 3680.35 (M3) Hold Number 2 = 5293.91 (M³) Hold Number 3 = 5291.50 (M³) Hold Number 4 = 4918.06 (M³) TOTAL CAPACITY = 19183.81 (M³)
(2) Solve for Percentage of each hold
Percentage = Hold Capacity x 100 Total Capacity
Hold No. 1 = 3680.35 x 100 = 19.18%
19183.82 Hold No. 2 = 5293.91 x 100 = 27.60% 19183.82 Hold No. 3 = 5291.50 x 100 = 27.58%
19183.82 Hold No. 4= 4918.06 x 100 = 25.64%
19183.82
-56-
(3) Order is to carry 16,000 MT Cargo.
Hold No. 1 = 16000x .1918 = 3068.80 MT
Hold No. 2 = 16000x .2760 = 4416.00 MT
Hold No. 3 = 16000x .2758 = 4412.80 MT
Hold NO. 4 = 16000x .2564 = 4102.40 MT
TOTAL = 16000.00 MT
NOTE: If the ship has Twin Deck Holds, solve for each cargo
space as demonstrated.
4.17 The percentage of cargo per hold calculation will often
produce a concentration of weight in the middle. This
will cause Sagging. This can be minimised by shifting
some weight forward.
4.18 Inspection of the calculated results, and rounding to
100 Metric Tonnes, will give a good approximation.
EXAMPLE:
Hold No. 4 = 4102.40 — 2.40 = 4100.00 MT
Hold No. 3 = 4412.80 — 112.80 = 4300.00 MT
Hold No. 2 = 4416.00 - 116.00 = 4300.00 MT
Hold No. 1 = 3068.80 + 231.20 = 3300.00 MT
TOTAL = 16000.00 MT
4.19 The best practice is to part load each hold in rotation.
Deflection and Trim can be checked as loading
progresses.
4.20 Draft rust is watched constantly to avoid overloading.
Checking the Midships Drafts can do this.
If loading is critical for any reason, a Draft and
Deadweight Survey must be done.
-58-
CHAPTER FIVE
TRIM AND STABILITY GENERAL
5.1 Trim and Stability calculations are mainly a matter
of correctly interpreting plans, tables, and graphs.
Ship Stability and Tank manuals provide values for
Longitudinal Centre of Gravity (LCG). Transverse Centre
of Gravity (KG). Moment of Inertia, another data
necessary for ship loading calculations.
5.2 This data may be in graph form (Figure 14), or tabular
(Figure 16). Tables are more common, and are easier
to work from.
5.3 Longitudinal Centre of Gravity can be calculated from the
Forward Perpendicular (LCG EP), the After Perpendicular (LCG AP), or from Midships (MID).
5.4 Calculations of LCG from the PP are shorter, and avoid
dealing with two sets of longitudinal moments. This
greatly reduces the chance of error, so all our examples
will be based on LCG FP.
5.5 The LCG of a hold is assumed to be at the longitudinal
centre of that hold. The LCG of uniformly distributed,
homogeneous cargo, such as grain, is also at the centre of
the hold.
5.6 If the hold is to be loaded with mixed cargo, then an LCG
is assumed to be at the centre of each type of cargo.
5.7 For special cargoes such as heavy machinery, the shipper
should supply the centre of gravity information.
- 59 - TRIM CALCULATION
5.8 The LCG method is the most accurate for calculating the
trim of a ship, because all the major forces acting on the
ship, including buoyancy, are considered.
5.9 The Longitudinal Centre of Gravity from the Forward
Perpendicular LCG (FP) is equal to One-half of the Length
Between Perpendiculars (LEP) plus or minus The Centre of
Gravity From Midships (MG).
LCG (FP) = LBP + MG
2
5.9.1 If MG is Aft, it is added.
5.9.2 If NC is Forward, it is subtracted.
5.10 The Longitudinal Centre of Buoyancy From the
Forward Perpendicular LCB (FP) is equal to one half LBP
plus or minus the Longitudinal Centre of Buoyancy (LCB).
LCB (FP) = LBP + LCB
2
5.10.1 If LCB is Aft, it is added. 5.10.2 If LCB is Forward, it is subtracted.
5.11 The Longitudinal Moment of everything aboard
the ship, whether Cargo. Constant, Consumables.
or Ballast, is the Weight times the LCG (FP)
for that cargo.
Longitudinal Moment = Weight x LCG (FP)
5.12 The LCG (FP) changes whenever Cargo is loaded or
unloaded, supplies are taken or consumed, and ballast
tanks are filled or discharged. The new LCG (FP) is
equal to the total Longitudinal Moments divided by the
Displacement.
-60-
5.12.1 Cargo unloaded, ballast discharged, and supplies
consumed are subtracted.
5.12.2 Cargo, ballast, and supplies loaded are added.
New LCG (FP) = Total Longitudinal Moments
Displacement
5.13 The Trim Lever is equal to the LCG(FP) minus the LCB(FP). (BG) Trim Lever = LCG(FP) - LCB(FP) (Pg.27)
5.13.1 If the Trim Lever is Positive, that is, if
LCG(FP) is greater than LCB(FP), the ship is
trimmed By the Stern.
5.13.2 If the Trim Lever is Negative, that is, if
LCG(FP) is less than LCB(FP), the ship is Trimmed
by the Head.
5.13.3 if the Trim Lever is Zero, that is, if
LCG(FP) equals LCB(FP), the ship is on
an even keel. (See Pg. 27)
5.14 Trim is equal to the product of the Trim Lever and
Displacement, divided by the Moment to Change Trim by
One Centimetre (MTC).
Trim = Trim Lever x Displacement x 100 (M)
MTC
LCG(FP) OF THE CONSTANT
5.15 It is best practice to solve for the LCG(FP)
of the Constant after each Initial Survey of
the Ship’s Light Condition (Chapter Three).
An average may be used, unless an unusual amount
of stores has been delivered.
-61-
5.16 The LCG(FP) of the Constant moves fore and aft,
depending on the location and weight of crew effects,
stores, and all the additional weights that tend to
accumulate over the service life of a ship.
5.17 It is of interest to compare the work forms given in
Figure 11 and Figure 19 The procedure used in the
example is the reverse of the procedure used in Figure
11 The LCG(FP) of the constant in Figure 11 is 200.42 if
which was the average for that ship.
EXAMPLE: (see Figure 11 – Page 32)
From Initial Survey Chapter Three (Figures 11 and 19):
Constant = 196.10 MT DRAFT = 3.53265 M DISP. = 8035.5 MT LCB = 3.01 M MTC = 182.1 MT Trim = 1.773 M = 177.3 cm
(1) Trim Lever = Trim x MTC x 100 (M)
DISP = 177.3 x 182.1
8035.5
= 4.02 M (2) LCB(FP) = LBP +/- LCB = 136 - 3.01 M = 64.99 M 2 2
(3) New LCG(FP) = LCB(FP) + Trim Lever
New LCG(FP) = 64.99 + 4.02 = 69.01 M NOTE: Since the ship is trimmed By the Stern, the LCG(FP) is Aft of LCB(FP).
- 62 -
(4) Final Longitudinal Moments DISP x LCG(FP)
= 8035.5 x 69.01
= 554529.65
(5) Calculate the lightship weight longitudinal moments
of each tank. Subtract these from the Final
Longitudinal Moments. The difference is the
Longitudinal Moment of the Constant.
Longitudinal Moment of Constant
= Final - all other Longitudinal Moments
= 554529.85 — 536968.25
= 17561.60 Total Moment
(6) LCG(FP) of Constant = Longitudinal Moment
Weight
= 17561.60 196.10
= 89.55 M
CHANGE OF DRAFT
5.18 Change of draft at one end of the ship only is sometimes
required. Notice of draft requirements or limitations
are normally forwarded to a vessel in advance, because
weight added means greater mean draft. As little as
possible should be added to achieve the desired trim. If
possible, without adversely affecting the ship’s
stability, weight should be removed.
5.19 The change of draft is calculated, theoretically, as a
ratio of the trim to the proportion of the distance of
the actual Longitudinal Centre of Flotation (LCF) to the
FP and AP.
- 63 -
5.20 For practical purposes, because the distance from LCF to
Midships is so small in relation to the length of the
ship. LCF is assumed to be midships. Therefore, change
of draft is calculated with sufficient accuracy, as trim
divided by two.
Change of Draft = Trim
2
5.21 Mean Sinkage is equal to weight divided by TPC. If
weight is added, the mean sinkage is greater:
if the weight is removed, the mean sinkage is less.
Mean Sinkage = +/- Weight
TPC NOTE: TPC here is the final TPC. That is, the TPC for the
final loaded condition.
5.22 The weight is placed forward of the tipping centre to
increase the forward draft: it is placed aft of the
tipping centre to increase the after draft.
5.22.1 The weight required is equal to TPC times the
trim in centimetres divided by two.
Weight = TPC x TRIM
2
5.22.2 The distance to locate the weight is two times
the MTC divided by the TPC.
Distance = 2 x MTC
TPC
EXAMPLE: A vessel, trimmed by the stern, must be put on an
even keel. Fwd Draft = 8.36 M Aft Draft = 8.46 M TPC = 27 MTC = 233
- 64 - Weight = 27 x (8.46 - 8.36) x 100 = 135.0 M/T 2
Distance 2 x 233.0 — = 17.26 M
27
A weight of 135.0 M/T placed 17.26 M forward of the
tipping centre.
STABILITY CALCULATION FORMULAS
5.23 It is the responsibility of an office to always maintain
a stable ship, in order to protect lives, the ship and
its cargo.
5.24 Stability calculations are the most important aspect of
the loading calculations. Not only the crew’s comfort
but stress on a ship’s structure is affected by
stability, and a ship in stable equilibrium is not so
liable to capsize.
5.25 Transverse Stability is a subject all Deck Officers are
familiar with, so only the main, practical points are
summarised here.
5.26 The following formulas are used in calculating
Transverse Stability.
Vertical Moment = Weight x KG
New KG = Old KG * Total Change in Moments
Total Change in Weights GM = TKM – New KG
GG1 = Total Inertia + Total Weight GM = GM - GG1 Rolling Period (IMPERIAL) = 0.44B (feet) sq.rt GM Rolling Period (METRIC) = 0.797B (meters) sq.rt GM Where B = Breadth of Ship
- 65 - FREE SURFACE EFFECT
5.27 Full or empty tanks have no free surface, since there is
no liquid moving as the ship rolls in the seaway. Avoid
slack tanks to the greatest extent possible to minimise
the loss of GM caused by tree surface.
5.28 In a heavy seaway, the liquid in a slack tank will surge
with considerable speed and force, sometimes causing
damage to the tank itself.
5.29 Fuel oil tanks are normally only filled to 80 or 85
percent capacity so as to avoids overflow oil pollution.
Fresh water and fuel are both subject to daily
consumption, so it is impossible to keep these tanks
full for the entire voyage. Dividers, or swash plates,
can minimise the free surface to a large extent.
5.30 Seawater ballast tanks should be either filled to their
limit, or empty. When filling these tanks, it is good
practice to let them overflow sufficiently to ensure no
air pockets are trapped inside.
5.31 If Free Surface Correction data is not available, the
following formula can be used for metric measure
rectangular tanks only.
Rise of C due to Free Surface = L x B³ x Sg 12 x DISP x n³
Where: L = Length of Tank B = Breadth of Tank Sg = Specific Gravity of Contents
n = Number of Longitudinal Compartments
which into tank is divided
- 66 - EXAMPLE: (Figure )
DISP = 22129.6 MT
KG = 8.277 M
TKM = 9.240 M
L = 25 M
B = l0 M
Sg = 1.024 , GM = TKM - KG = 0.963
(1) If the tank is undivided:
Rise of G due to Free Surface = 25 x 10³ x 1.024 =
12 x 22129.6 x 1² = 0.096 M
KG = 8.277 M
New KG = 8.373 M
TKM = 9.240 M
New GM = 0.867 M
(2) If the tank is divided into two section:
Rise of G due to Free Surface = 25 x 10³ x 1.024
12 x 22129.6 x 2²
KG = 8.277 M New KC = 8.301 M
TKM = 9.240 M
New GM = 0.939 M
NOTE: The Rise of G due to Free Surface Effect can be
minimised by Longitudinal divisions in tanks. Properly
arranged dividing of tanks can make the problem neg-
ligible.
5.32 Stability and Trim Calculation Report was worked as
follows (Figure 22 ), (Pg.70)
- 67 - See Pg. 71
5.32.1 For Trim: Using LCG(FP) LCG(FP) = LBP + MG , (MG – Centre of Gravity
2 from midship ) (1) LCG(FP) of Constant = 136 + 53.40 M = 121.40 M
2 (2) LCG(FP) of No.1 FOT = 136 — 21.49 M = 46.51 M 2
(1) Longitudinal Moments of Constant = Weight x LCG(FP)
= 196 x 121.40 =
= 23794.40 Tx M (3) New LCG(FP) = Total Moments(Longitud)
Total Weights(Disp.) = 1483410.13(Total Moments) 22129.60 T = 67.03 M LCB(FP) = LBP +/- LCB = 136 – 1.42 = 2 2 = 66.58 M (4) Trim Lever = LCG(FP) - LCB(FP) = 67.03 — 66.58 = 0.45M (5) Trim = Trim Lever x DISP = MTC = 0.45 x 22129.6 = 41 cm 241.8
(6) Change of Draft = Trim = 41 = 2 2 = 20.5 cm or 0.205 M
LCG(FP) is Aft of LCB(FP), therefore Ship is trimmed “By the
Stern”
NOTE: Draft. NTC, LCB and DISP were calculated in Chapter Two,
Draft and Deadweight Surveys.
- 68 -
5.32.2 For Stability
NOTE: KG of Holds and Tanks are found in the Stability Manuals.
KG of a Cargo is assumed to be at its Geometrical Centre (Figure 20). (Pg.57)
(1) Vertical Moments of Constant = Weight x KG = 196 x 9.52 = 1865.92 TxM (2) New KG = Total Moments(Vert.) = Total Weights(Disp.) = 183154.84 = 8.277 M 22129.60 (4) GG1 = Total Inertia = Total Weight(Disp.)
= 7771.8 = 0.351 M
22129.6
NOTE: TKM was read from Hydrostatic Tables at DISP of 22129.6 MT (Figure 13). (Pg.38)
Inertia, KG and GM are found in the Hold and Tank Tables or Graphs (Figures 16 and 18).
GM = TKM – KG = 9.240 M — 8.277 = 0.963
G0M = GM - GG1 = 0.963 — 0.351 = 0.612 M
Rolling Period = 0.797 x 22.860 M = 18.22 = sq.rt. 0.612 M 0.78
= 23 seconds
- 72 -
LCG(FP) METHOD CHECK LIST
5.33 The following list summarises the steps to calculate
Trim and Fwd/Aft Drafts at the next loading or discharge
port.
5.33.1 Check Fwd and Aft Drafts upon arrival and solve
for corrected trim.
5.33.2 Deduct fuel oil and water consumed from DISP at
previous port. Add ballast water if taken in:
subtract if discharged.
5.33.3 Using DISP calculated in 5.33.2, refer to
Hydrostatic Tables and obtain Draft, MTC and
LCB. Check Sg to account for any difference from
Mean Draft found in 5.33.1.
5.33.4 Solve for Total Longitudinal Moments on arrival,
Work back from Trim to Trim Lever to LCG(FP).
5.33.5 Measure the LCG(FP) of all weights to be loaded
or discharged. Solve for their Longitudinal
Moments.
5.33.6 The New Total Longitudinal Moments equals 5.33.4 plus or minus 5.33.5.
5.33.7 Add all weights taken in and subtract all
weights discharged to find new DISP. Refer to
Hydrostatic Tables for new Draft, MTC and LCB.
- 73 -
CHAPTER SIX
GRAIN LOADING GENERAL
6.1 If a ship ts to carry grain. it must have a Grain
Loading Plan. This plan must meet with IMO and SOLAS
requirements, and must be approved by the appropriate
Government Agency.
IMO and SOLAS REQUIREMENTS
S.2 The IMO and SOLAS requirements for loading grain are:
6.2.1 The Angle of Heel due to shift of grain shall
not be greater than twelve (12°) degrees.
6.2.2 The residual stability area shall not be less
than 0.075 metre-radians.
6.2.3 The correct metacentric height shall not be
less than 0.30 metres.
GRAIN STABILITY CALCULATIONS
6.3 The trim and stability and Grain stability should be
made as soon as details of the grain cargo to be
loaded are received. Depending on the Stowage Factor
(SF) of tne grain to be loaded, slack holds may be
required. Check the approved Grain Loading Plan for
the designated slack holds in this situation.
6.4 The actual Horizontal Heeling Moment (HHM) is equal
to the Volumetric Heeling Moment (VEM) divided by the
Stowage Factor (SF) of the cargo.
Heeling Moment = Volumetric Horizontal Moment Stowage Factor ofCargo(M³/F³)
- 76 -
6.5 The increase in Vertical Centre of Gravity (GG0)
is equal to the Volumetric Vertical Moment (VVM)
divided by the product of the Displacement and
SF. GG0 = Volumetric Vertical Moment
Displacement x Stowage Factor
NOTE: If cargo data is given in Imperial Measure, then
convert your figures. Metric Tonnes = Long Tons x 1.01605
Cubic Metres(M³) = Cubic Feet(F³) x 35.31476
6.6 VHM, VVM and allowable HVM are found in the Grain
Loading Plan. The actual HVM is calculated and
compared with the allowable HVM. If the actual HVM is
greater than the allowable HVM a new stowage
distribution with less heeling moment must be
planned.
EXAMPLE: (See Pg.70)
A grain cargo is to be loaded at summer draft. The
designated slack hold is No. 3. Stowage Factor is
given as 42 F³/LT.
(1) Stowage Factor = 42 F³ /LT 42 = 42 = 1.1706 M³ = 35.314 x 1.016 35.879024
(2) Cargo Deadweight
16959.0 MT Summer Draft Deadweight —196.0 MT Constant 16763.0 16763.0 —1017.0 MT FO, LO, FW, Ballast, etc. 15745.0 MT Cargo Deadweight
- 77 - (3) Ships Capacity
HOLD #1 = 3976.51 M³ = 3396.9844 MT 1.1706
HOLD #2 = 5623.28 M³ = 4803.7587 MT
1.1706
HOLD #3 = 5654.54 M³ = 4830.463 MT 1.1706
HOLD #4 = 5158.16 MT³ = 4406.424 MT 1.1706
TOTAL = 17437.63 MT
This exceeds the cargo deadweight, therefore we must solve
f or allowable loading in No. 3 Hold, the designated slack
hold.
(4) Allowable Loading in the Slack Hold Cargo
Deadweight = 15746.00 MT HOLD #1 = 3396.9844 MT HOLD #2 = 4803.7585 MT HOLD #4 = 4406.424 MT TOTAL = - 12607.166 MT
Cargo space available in HOLD #3 = 3138.834 MT
Cargo space used in HOLD #3 x Stowage Factor =
= 3138.834 x 1.1706 = 3674.319 M³
(5) Stability and Trim calculations (Chapter Five)
revealed that the ship would be down by the Head by
1.6 cm. To correct the Trim, it was decided to shift
100.0 MT of fuel from No. 1 Fuel Oil Tank to No. 3
Fuel Oil Tank.
- 83 -
DISP = 21300.10 MT
Longitudinal Moments = 1414999.13 Total Moments
#3 F.O.T. = + 100 x 94.51 M = + 9451.00
#1 F.O.T. = — 100 x 46.51 M = — 4651.00 = + 4800.00 Total Moments New Grand Total = 1414999.13 + 4800.00 = 1419799.13 Total Moments At DIsplacement of 21300.10 MT = DRAFT = 8.69 M MTC = 237.45 T—M
LCB = 66.45 M
LCG = 66.657M
TL = 0.20 M
TRIM = 18.6 cm
CD = 9.3 cm, or
= 0.093 M Fwd Draft = 8.690 M Aft Draft = 8.690 M Mid = 8.69 M Correction = -0.093 M = +0.093 M New Draft = 8.597 M = 8.783 M = No change (6) Calculate the new KG :
To calculate the new KG, we must first calculate
the change in Vertical Moments caused by shifting
the Fuel Oil from No. 1 tank to No. 3 tank.
No. 1 tank = 355.4 - 100 = 255.4 MT x 0.44 M = 112.38 T—N
No. 3 tank = 186.6 + 100 = 286.8 MT x 0.82 M = 235.18 T—M TOTAL MOMENT = 347.56 T-M
Old Vertical Moment = 1419799.13 — 347.56
New Vertical Moment = 1419451.57
New KG = 1419451.51 = 6.64 M
21300.10
- 84 - (7) GRAIN STABILITY
Horizontal Vertical
Moments Moments Cargo Hold #1 669.857 154.946 Cargo Hold #2 949.838 233.758 Cargo Hold #3 8 350.000 1675.000 Cargo Hold #4 984.570 231. 828
TOTALS : 10954.265 2295.532
GGO = 2295.532 = 0.092 M 21300.10 x 1.1705 KG1 = 6.789 + 0.365 + 0.092 = 7.246 M
Allowable Heeling Moment (Figure ) = 99270.20
Actual Heeling Moment = 10954.265 = 9358.08 1.1705
JUDGEMENT GOOD !
- 85 -
Department of Transport Canadian Coast Guard Ship Safety Branch
CALCULATION OF STABILITY
FOR A VFSSEL LOADING BULK GRAIN
IN ACCORDANCE WITH
CANADIAN GRAIN REGULATIONS Captain:
You are required to complete a stability calculation prior to the commencement of loading. This is to indicate your vessel’s worst condition during the forthcoming voyage. The calculation should be made on this form and presented to the Port Warden before the vessel can be issued with a Certificate of Readiness to Load. If there are any subsequent changes to the original stowage plan, (tonnage’s, commodities or stowage factors, etc.) you should prepare a corrected plan for the Port Warden’ s approval.
The manner in which this calculation is made will depend upon:
(a) Your type of vessel:
(b) The geographical position of your loading port: and
(c) The type of grain stability information with which your
vessel has been provided.
TYPE 1 CALCULATION (5° ANGLE OF HEEL)
If your vessel is a bulkcarrier and an “existing ship under the provisions of IMO Resolution A264 (VIII) Part B, Sec. V(B), you are required to prove that your vessel’s angle of heel, if grain shifts, will not exceed 5° Your stability information will indicate if your vessel is of this type and if so you should complete only Tables I, II. III. IV and VII A.
If your vessel has to meet the provisions of Regulation 4 of
the above Resolution; i.e. Maximum Values of (a) Angles of Heel 12°, and Minimum Values of (b) Residual Stability 0.075 metre radians and (c) GM 0.30 M, you should complete the form by one of the following methods.
- 86 - TYPE 2 CALCULATION (ALLOWABLE *UPSETTING MOMENTS 12° ANGLE OF HEEL)
If your vessel’s grain stability information contains a table of Allowable Upsetting Moments, complete only Tables I II, III, IV, V,VI TYPE 3 CALCULATION (WITHOUT ALLOWABLE UPSETTING MOMENTS, 12° ANGLE
OF HEEL) ABBREVIATED
If you are not provide with a table of Allowable Upsetting Moments complete only Tables I II. III IV, V. VII B and VIII
If, however, the GZ curve depicted in your grain stability information booklet that is closest to your proposed loading condi-tion is not of a normal configuration, or if the maximum GZ value of such curve occurs before 400, then you should complete the Type 4 Calculation.
TYPE 4 CALCULATION (WITHOUT ALLOWABLE UPSETTING MOMENTS, 12° ANGLE OF
HEEL) FULL
In this case, COMPLETE Tables I, II III, IV. V. VII B and IX.
TYPE 5 CALCULATION (5° ANGLE OF HEEL) TANKERS
If your vessel is a tanker, all tanks except two (two wing tanks
or two centres) must be trimmed full or you will be required to meet the conditions described in TYPE I above (5° ANGLE OF HEEL)
Your Administration may have provided you with a statement stating that your vessel at all times meets the required conditions for draft and initial GM values and in this case, no calculation is necessary. Alternatively, you may have information enabling you to complete a TYPE I calculation. If not, you should complete only Tables I, II. III and VII C. TYPE 6 CALCULATION (REDUCED STABILITY CRITERIA SHELTERED WATERS)
If your vessel is loading at more than one port within sheltered waters, you may not be able to meet fully the requirements laid down in your stability documents whilst in transit between such ports. In this instance, you may take advantage of a relaxation of such requirements whilst in transit between ports. In this case, you should complete Tables I, II, III and X.
If you meet the requirements of Table X, your vessel will not in fact list more than 15° if grain in all slack holds shifts through an angle with the horizontal of 12°, nor will your available freeboard is immersed by more than 50%. Before taking advantage of this provision, you are advised to study Section II of the Canadian Grain Regulations.
— 87 —
If it is decided to take advantage of this relaxation, it should be borne in mind that your vessel will have to comply fully with the Regulations prior to departure from sheltered waters.
OTHER CONDITIONS
Vessels having onboard documents requiring other than the criteria described above, or no documents should consult with the Port Warden for further instructions. • It is possible that stability booklets. moment " and the two
the term "heeling moment is used in "some this term is an alternative for "upsetting are to be taken to mean the same.
- 88 -
CHAPTER SEVEN
ROLLING PERIOD TEST FOR GM GENERAL
7.1 When a large AMOUNT of deck cargo is carried, or when
port rotation produces unusual height concentration in
upper holds, stability must receive careful attention.
When a ship is nearing her stability limit, and there is
a significant amount of cargo deadweight allowances yet
available, it is good practice to conduct a rolling
period test in still waters.
7.2 The Rolling Period Test is most frequently used for
timber carriers, but should be applied whenever GM is an
important factor for loading. It should be noted that
ships having a minimum corrected GM of have made safe
ocean crossings not more than 0.03 M at any point in the
voyage.
7.3 The loss of GM through consumption of Fuel Oil and Fresh
Water must be taken into account. An average loss of GM
per day can be derived from the departure and arrival
Trim and Stability calculations.
7.4 The main advantage of conducting a rolling period test
is that the actual GM is observed, making the result
almost error free. There will be a large difference
between the computed GM based on the shipbuilder’s data
and the actual GM based on test. This is because the
shipbuilders base their computations on the Inclining
Experiment of an empty ship.
TIMBER DECK CARGO
7.5 When loading a deck cargo of TIMBER particularly dry,
sawn timber add fifteen (15) percent to the deck cargo
weight. Timber tends to absorb water at sea, and this
causes a considerable loss of GM.
- 89 -
7.6 A rule of thumb for calculating timber deck cargo weight
is:
Deck Cargo Weight = 50 percent of Hold Cargo Weight
that is, one third of the total cargo loaded is deck
cargo.
NOTE: This approximation is not reliable for purpose-built
timber carriers.
ROLLING PERIOD DIFFERENCE
7.7 The difference in rolling period obtained by testing in
still waters, and the average taken at sea, is not
significant enough to cause alarm.
ROLLING PERIOD STILL WATER TEST
7.8 For the rolling period test to give good results, the
following conditions must be met :
7.8.1 If the ship is alongside, she must be clear of her
berth, with her lines slack, so she can roll
freely.
7.8.2 Barges end lighters must be well clear so as to
not hinder the ship’s movement.
7.8.3 Enough weights must be available to list the ship
at least fifteen (15) degrees. Two or more
derricks may be required.
NOTE : The stevedores should be informed in advance if the
need for a test seems likely. Their co-operation in
lifting the weights is often required.
The best position for the observers is the forecastle
deck. There they can note the inclination of the
superstructure, especially the bridge wing, against a
reference point.
- 90 -
7.10 Lift the weights on one side of the ship. When the ship
has been steadied in the listed position drop the
weights onto the dock or into the water. Ensure the
cargo runners are slack, so they offer no resistance.
7.11 It is best to time the complete period of roll from
maximum angle of list through upright to opposite list,
and all the way back to original listed side That is:
STARBOARD - PORT - STARBOARD
or PORT - STARBOARD - PORT
7.12 Time the period of rolls at least three (3) times to
ensure good accuracy of the average. Use this average
in the Rolling Period Formula to calculate the GM
CALCULATING GM FROM ROLLING PERIOD ( IMPERIAL) ( METRIC)
T = 0.44 B T = 0.797 B Sq. Rt GM Sq. Rt GM
Therefore:
GM = 0.1936 x B² = 0.6352 x B² T² T²
Where : T = Rolling Period in Seconds
B = Breadth of Ship
GG1 = w x dKG
DISP +/- w
Where : GG1 = Shift of Centre of Gravity
w= Weight to be Loaded or Discharged W = Original Displacement
dKG = distance from KG to G of the Weight DISP = Displacement
- 91 –
NOTE : If w is added above KG, or removed from below KG, the
shift of G is upward, and GG1 is subtracted. If w is
removed above KG, or added below KG, the shift of G
is downward, and GG1 is added. EXAMPLE : DISP = 22129.6 MT KG = 8.277 M GM = 0.612 M
(1) Find the New Gm if 200 MT is loaded 9.5 M above the KG.
GG1 = W x dKG = 200 x 9.5 = 0.085 M New DISP (W +/- w) 22129.6 + 200
Since the shift of G is upward:
New GM = GM GG1 = 0.612 — 0.085 = 0.527 M
(2) Find the new GM it 200 MT is discharged from 8.0 M
above KG. GG1 = 200 x 8.0 = 0.073 M 22129.6 — 200
Since the shift of G is downward: New GM = GM + GG = 0.612 + 0.073 = 0.685
SIMPLIFIED GM MEASURMENTS
7.13 If a close estimate of GM is all that is required, it
can be calculated from a deliberate listing of the
ship. Weights are suspended from a derrick, or placed
on the deck if no derrick is available.
7.14 The weight (W), the distance of the weight from the
centre line of the ship (D), and the angle of list (0°)
are measured. The DISPL divides the product of the
weight (w) and the distance (D). The result is then
multiplied by the Cotangent of the Angle of List (cot
0°):
- 92 - GM = W x D x cot 0°
DISP
FXAMPLE:
A forty (40) ton weight is suspended from a derrick;
the derrick head is fifteen (15) metres from the
ship centreline; and the angle of list is read from
the clinometer as five (5°) degrees:
DISP = 8000 MT
GM = W x D x cot 0° DISP
GM = 40 x 15 x cot 5° =
8000
= 0.075 x 11.43 =0.875
- 95 -
BIBLIOGRAPHY • Pursey, H. J., MERCHANT SHIP STABILITY, Brown, Son & Ferguson, Ltd., 1954. • Kemp & Young, SHIP STABILITY NOTES & EXAMPLES,
Pitman Press, 1984. • LaDage, John & Van Gemert, Lee, STABILITY AND TRIM FOR THE SHIP’S OFFICER, D. Van Nostrand Co. Inc., 1956. • Klinkert, J., & White, G. W.NAUTICAL CALCULATIONS EXPLAINED, Routledge & Kegan Paul Ltd., 1969. • Wolfram, J., SEAWAYS, Nautical Institute Bulletin, 1978. • HYDROSTATIC TABLES, Ishikawajima Heavy Industries, 1979. • PLIMSOLL MARKS, M/V “Alpha Faith” 1987. • GRAIN STABILITY LOADING REGULATIONS AND. FORMS, Department of Transport (Canada) , 1960. • SURVEY OF LOAD LINE SHIPS, London, Her Majesty's Stationery Office, 1973.
Recommended