Draft Survey MANUAL (Canada)

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.

-21.8

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

-3QM

Quarter Mean

S

Starboard

SF

Stowage Factor [M3/T ]

Sg

Specific gravity

TKM

Transverse Metacentric Height

TPC

Tonnes per Centimetre (Immersion)

VHM

Volumetric Heeling Moment

VVM

Volumetric Vertical Moment

[ T/M3 ]

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

-4First 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 LBP

= Final Trim Correction

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

-5SLUDGE __________________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

-6Trim Lever TRIM

=

LCG(FP) - LCB(FP)

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 ) 0.44B Ft___ sq.rt of G M

Rise of G due to Free Surface = _L x B³ x Sg___ 12 x DISP x n²

( Metric ) 0.7978B Metres sq. rt of GM

-7Where: 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 = 0,6532 x B² T²

GM = 0,1936 x B² 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

=

D

=

Distance from water line

=

Angle of List

cot.0°

Weight

- 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

Page 13 is skipped

- 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

initial

and

alongside, final

surveys

the

difference

will

between

produce

an

the

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 ) 2.7

[ T/M3 ]

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

Measuring

the

Sg

if at

maximum

accuracy

is

different

depths

may

required. 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 Calculations, Seawaves, Vol.Feb.1984, pp.15, 17.

Survey

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 supported 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 therefore 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 of metal, the deck

constructed with a heavier weight is where almost all failures occur.

- 21 -

The deck

of a

cargo vessel is further weakened by

hatchways and other must be

reinforced. Sharp corners tend to concentrate

stresses, so hatch

2.20

necessary openings. These openings

corners require special attention.

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

METRIC

OF

MEASURE

GRAVITY

- 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 onehalf 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

calculate

ship. the

The

ship

constant.

is It

first is

surveyed

then

light,

re-surveyed

to

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 + Fwd Corr. -0.0165 Corrected Fwd Draft 2.6235

3.8

Aft Draft 4.30 m + Aft Corr +0.0971 Corrected Aft Draft 4.3971

CORRECTED DRAFT

Corrected Draft

Aft Fwd Corrected Trim

NOTE:

5.019 = 2.361 2.658

Aft - Fwd

=

Corr. Trim

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 Mean of Mean + Mid Mean 2

QM =

EXAMPLE (USED IN REPORT ON PAGE 49): FWD

P 2.377 S 2.377 4.754

AFT P 5.017 S 5.017 10.034

4.754 2 =

FWD TRIM

10.034 2 AFT = 5.017

2.377

= AFT – FWD

MIDSHIP p 3.59 S 3.72 7.31 7.31 2 MEAN-MID = 3.655

( 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 Note: See Page 31 Formulas.

= +0.034716 x 2.64 = +0.91 ( + ) for explanation Sign

+/-

in abovementions

-35Corrected Draft: Fwd Draft = 2.377 Fwd Corr = -0.016 Fwd Draft Corrected = 2.361 Corrected Trim:

Aft Draft = 5.017 Aft Corr = + 0.091 Aft Draft Corrected = 5.108

Aft Draft Cor-ed - Fwd Draft Cor-ed = = Corrected Trim (CT) Aft Draft Corrected = Fwd Draft Corrected = Corrected Trim (CT)

5.108 - 2.361 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 2 Fwd and Aft + Mid Mean

Mean Mean of Means

=

= 3.69 M =

3.69 +3.655 7.345

7.345 2

= 3.672 M

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 ) 8

= 3.663 M

-1.21m

FWD Perp.

Note: The Sign of A.P./F.P. Correstions depending on Signs of two factors: Trim and Distance between F/A perpendiclar to F/A Draft mark. Actually it appear atomatically when you insert in fomla all parametrs with their own algebraical signs. Trim by STEN ( + ) ; Tim by HEAD ( - ). Location of F/A perpendiculars FORWARD of F/A Draft mark ( - ) ; Location of F/A Perpendiculas AFT of F/A Draft mark ( + ) . Strictly say nesessary check all Signs in Ship’s Stability Manual to avoid any mistakes.

+

AFT Perp.

- 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: TKM: 3.14

Transverse centre of Buoyancy Transverce Metacentric Height

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 Centimetres. 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

-41negative (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

3.19

VESSEL TRIMMED BY THE STERN LCF is Fwd (—) SUBTRACT Trim Correction LCF is Aft (+) ADD Trim Correction

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 17.65 137.00

x

100 = 159.909 (-) MT = 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)

b)

QM =

QM =

3.675 + 0.50 4.175

MTC = 169.4

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 LBP

x 12

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 = TOTAL WEIGHT

200.42 MT 3145.32 MT

NETT DISP.

7418.19 MT

- TOTAL

31475.32 MT

WEIGHT

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

4.2

The weight a ship can

carry

varies

location and season.

More

countries, but less in

a

Winter Zone loading,

when applicable, is smaller still.

can

Summer

be

considerably loaded

Season

with

in

Tropical

Zone.

Seasonal

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, ballast,

such

etc.,

as

fresh

necessary

water,

for

the

fuel

oil,

intended

lubeoil,

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

placement

the

allowed,

Freeboard Subtract

Table

for

Lightship

Draft

Weight.

and

Dis-

Constant,

Ballast and Consumables. The remainder is Cargo Deadweight Available.

-51EXAMPLE: 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 — 196.000 MT 17117.000 MT

Constant = 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

intermediate

port,

the

are

Cargo

to

be

replenished

Deadweight

may

have

at

an

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 Available.

must

be

deducted

from

Cargo

Deadweight

-52EXAMPLE: Length of voyage to bunkering port = 16.5 days. Fresh Water Fuel Water Total Consumables

= 150 MT = + 660 MT = 810 MT

Fresh Water Consumption 8.0/day x 16.5

=

Fuel Oil Consumption

= + 396 MT

24.0/day x 16.5

a)

132 MT

Total Consumption

=

528 MT

Balance of Fuel and Water Left (810-528) Planned Intake - Fresh Water - Fuel Oil - Total Balance of Fuel and Water

= = = = =

Total after Replenishment Consumables at Port of Lading

= 882 MT = -810 MT

Difference of

=

282 MT 200 MT +400 MT 600 MT +282 MT

b) (a-b)

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

-534.7

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 Bale Capacity = 19183.82 M³ Weight of Cargo

M³/MT

= 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.

-54CARGO 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,

NOTE:

the ship is on an even keel. Ship’s decks are stronger in tension therefore, Sagging.

a

small

amount

of

Hogging

than is

in

com-

preferred

to

-554.14 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

4.14.2

Hogging. Next load the Forward hold to decrease the trim.

4.15 Part loading, or other conditions may produce Sagging. 4.15.1 4.15.2

First load the forward hold to eliminate Sagging. 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 Hold Number 1 Hold Number 2 Hold Number 3 Hold Number 4 TOTAL CAPACITY

of each hold (M³) = 3680.35 (M3) = 5293.91 (M³) = 5291.50 (M³) = 4918.06 (M³) = 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 19183.82

x 100 = 27.60%

Hold No. 3 =

5291.50 19183.82

x 100 = 27.58%

Hold No. 4=

4918.06 19183.82

x 100 = 25.64%

-56(3)

Order is to carry 16,000 MT Cargo. Hold No.

1 = 16000x .1918

=

3068.80 MT

Hold No. Hold No.

2 = 16000x .2760 3 = 16000x .2758

= =

4416.00 MT 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 progresses.

4.20

and

Trim

can

be

checked

as

loading

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 of

correctly

Ship

interpreting

Stability

and

Tank

plans, manuals

mainly a matter tables,

and

provide

graphs.

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 5.10.2

If LCB is Aft, it is added. 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

unloaded,

supplies

are

whenever

Cargo

taken

consumed,

or

tanks are filled or discharged. The

new

is

loaded and

LCG

or

ballast (FP)

is

equal to the total Longitudinal Moments divided by the Displacement.

-605.12.1

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) 5.13.1

(Pg.27)

If the Trim Lever is Positive, that is, LCG(FP) is greater than LCB(FP), the

if 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 of the An

is the

best

practice

Constant

Ship’s average

after

Light may

to

be

solve each

Condition used,

of stores has been delivered.

unless

for

the

Initial

Survey

(Chapter an

LCG(FP)

unusual

of

Three). amount

-615.16

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 DRAFT DISP. LCB MTC Trim

= = = = = =

(1) Trim Lever

=

196.10 3.53265 8035.5 3.01 182.1 1.773

MT M MT M MT M = 177.3 cm

Trim x MTC x 100 (M) DISP

=

177.3 x 182.1 8035.5

=

4.02 M

(2)

LCB(FP) =

LBP 2

+/- LCB =

136 - 3.01 M = 64.99 M 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 weight is added, the mean sinkage is greater:

TPC.

If

if the weight is removed, the mean sinkage is less. Mean Sinkage = +/- Weight TPC NOTE:

5.22

TPC here is the final TPC. That is, the TPC for the final loaded condition. 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 TPC = 27

Aft Draft = 8.46 M 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) =

Rolling Period (METRIC) Where B = Breadth of Ship

0.44B (feet) sq.rt GM

= 0.797B (meters) sq.rt GM

- 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 =

Where:

L

=

B = Sg = n

=

L x B³ x Sg 12 x DISP x n³

Length of Tank Breadth of Tank Specific Gravity of Contents Number of Longitudinal which into tank is divided

Compartments

- 66 -

EXAMPLE:

(1)

(Figure

)

DISP KG TKM L

= = = =

22129.6 MT 8.277 M 9.240 M 25 M

B Sg

= =

l0 M 1.024 ,

GM = TKM - KG = 0.963

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

(2)

KG

= 8.277 M

New KG

= 8.373 M

TKM

= 9.240 M

New GM

= 0.867 M

If the tank is divided into two section: Rise of G due to Free Surface =

KG

=

8.277 M

New KC

=

8.301 M

TKM

=

9.240 M

=

0.939 M

New GM

NOTE:

25 x 10³ x 1.024 12 x 22129.6 x 2²

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 negligible.

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 2

– Centre of Gravity from midship )

(1)

LCG(FP) of Constant = 136 + 53.40 M 2

= 121.40 M

(2)

LCG(FP) of No.1 FOT = 136 — 21.49 M 2

= 46.51 M

(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

LCB(FP)

(4) Trim Lever

(5) Trim

(6) Change of Draft

=

67.03 M

=

LBP +/- LCB = 136 – 1.42 = 2 2

=

66.58 M

=

LCG(FP) - LCB(FP)

=

67.03 — 66.58 = 0.45M

=

Trim Lever x DISP = MTC

=

0.45 x 22129.6 241.8

=

Trim 2

=

20.5 cm or 0.205 M

=

=

41 cm

41 = 2

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)

(4)

New KG

= Total Moments(Vert.) = Total Weights(Disp.)

GG1

=

183154.84 = 8.277 M 22129.60

=

= 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

G0M

=

GM - GG1

Rolling Period =

= 9.240 M — 8.277 = 0.963

= 0.963 — 0.351 = 0.612 M

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 Hydrostatic Tables and

in 5.33.2, refer to 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. Moments.

5.33.6

Solve

for

their

Longitudinal

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 less than 0.30 metres.

height

shall

not

be

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 is equal to the Volumetric Vertical Moment divided by the product of the Displacement SF. GG0 =

NOTE:

6.6

(GG0) (VVM) and

Volumetric Vertical Moment Displacement x Stowage Factor

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

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 35.314 x 1.016

(2)

=

=

42 F³ /LT

42 35.879024

= 1.1706 M³

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 1.1706

= 3396.9844 MT

HOLD #2 = 5623.28 M³ 1.1706

= 4803.7587 MT

HOLD #3 = 5654.54 M³ 1.1706

= 4830.463

MT

HOLD #4 = 5158.16 MT³ 1.1706

= 4406.424

MT

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 HOLD #2 HOLD #4 TOTAL

= = =

3396.9844 MT 4803.7585 MT 4406.424 MT

= - 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 =

Fwd Draft = 8.690 M Correction = -0.093 M New Draft = 8.597 M

(6)

DRAFT MTC LCB LCG TL TRIM CD

= = = = = = = =

8.69 M 237.45 T—M 66.45 M 66.657M 0.20 M 18.6 cm 9.3 cm, or 0.093 M

Aft Draft = 8.690 M = +0.093 M = 8.783 M

Mid = 8.69 M = No change

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 Moments

Vertical 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

10954.265

2295.532

TOTALS :

GGO

=

KG1

=

2295.532 21300.10 x 1.1705

= 0.092 M

6.789 + 0.365 + 0.092 = 7.246 M

Allowable Heeling Moment (Figure

Actual Heeling Moment

JUDGEMENT

GOOD !

= 10954.265 1.1705

) =

=

99270.20

9358.08

- 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 condition 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) T =

( METRIC)

0.44 B Sq. Rt GM

T =

0.797 B 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 w= W dKG DISP

= = = =

Shift of Centre of Gravity Weight to be Loaded or Discharged Original Displacement distance from KG to G of the Weight Displacement

NOTE :

91 –

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 New DISP (W +/- w) 22129.6 + 200

= 0.085 M

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 =

= 0.073 M 200 x 8.0 22129.6 — 200

Since the shift of G is downward: New GM = GM + GG =

SIMPLIFIED GM

0.612 + 0.073 = 0.685

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.