Ship Hydrostatics and Stability 2010 Part 8 pdf

The intact stability criteria ofthe code apply to 'ships and other marine vehicles of 24 m in length and above'.Countries that adopted these regulations enforce them by issuing correspon

7.5 Summary

Stability and trim calculations require the knowledge of the displacement and ofthe position of the centre of gravity To calculate these quantities it is necessary toorganize the ship masses into weight groups The sum of the weight groups that

do not change during operation is called lightship displacement; for merchantvessels it is the sum of hull, outfit and machinery masses The sum of the massesthat are carried in operation according to the different loading cases is calleddeadweight; it includes the crew and its equipment, the cargo and passengers,the fuel, the lubricating oil, the fresh water, and the stores

To find the displacement of a given loading case it is necessary to add themasses of the lightship and the deadweight items carried on board in that case

To find the coordinates of the centre of gravity, LOG, and VCG (KG), it

is necessary to sum up the moments of the above masses with respect to atransverse plane for the first, a horizontal plane for the second The calculationscan be conveniently carried out in an electronic spreadsheet or by software such

-For normal loading situations the trim is always small Then, the trimmed

water-line, W0Lg, intersects the waterlines of the ship on even keel, WQ£O> along a line passing through the centre of flotation, F, of W$LQ To obtain the forward

draught, Tp, and the aft draught, TA, it is necessary to add to, or subtract fromthe mean draught a part of the trim proportional to the distance of the respectiveperpendicular from the centre of flotation

grav-172 Ship Hydrostatics and Stability

distance, d, and the tangent of the resulting heel angle, tan 0, is measured The

statistical analysis of several inclining tests yields the product

pd

tan 6

The displacement, A, is found as a function of the draughts measured during theexperiment If a hull deflection is measured it must be taken into account Thevertical centre of gravity is calculated as

KG = KM - GM

If the trim is large the hydrostatic curves cannot be used The Bonjean curves arehelpful here, as is a computer programme Both Bonjean curves and computerprogrammes can be used to calculate the effect of hull deflection

7.6 Examples

Example 7.1 - Least-squares fit of the results of an inclining experiment

The results of the inclining experiment presented here are taken from an example

in Hansen (1985), but are converted into SI units The data are plotted as points inFigure 7.6 At a first glance it seems reasonable to fit a straight line whose slope

equals the mean of pd/tan 0 values In this example, some trials performed with

very small pd values produced zero heel-angle tangents Those cases must be discarded when averaging because they yield pd/t an 0 = oo After eliminating

the pairs corresponding to zero heel-angle tangents, we calculate the mean slopeand obtain 53 679.638 The reader can easily verify that the line having thisslope is far from being satisfactory Available programmes for linear least-squaresinterpolation cannot be used because, in general, they fit a line having an equation

of the form

y = cix + c 2

Obviously, in our case the line must pass through the origin, that is c^ — 0.

Therefore, let us derive by ourselves a suitable procedure

To simplify notations let Xi be the tangents of the measured heeling angles, and yi the corresponding inclining moments As said, we want to fit to the

measured data a straight line passing through the origin

y = Mx (7.11) The error of the fitted point to the ith measured point is

An example of a MATLAB script file that plots the data, calculates the slope,

M, and plots the fitted line is

%INCLINING Analysis of Inclining Experiment

% Format of data is [ moment tangent ] ,

% initial units [ ft-tons - ]

incldata = [

% separate data

174 Ship Hydrostatics and Stability

moment = incldata(:, 1); tangent = incldata(:, 2);plot(tangent, moment, 'k.'), grid

Mmin = M*tmin; Mmax = M*tmax;

plot( [ tmin tmax ], [ Mmin Mmax ], 'k-')

text(-0.015, 1100, ['Average slope = ' num2str(M)])hold off

Above, the user has to write the data of the inclining experiment in the matrixincldata The MATLAB programme shown here can be easily transformed

so that the user can input the name of a separate file that stores the incldatamatrix

7.7 Exercises

Exercise 7.1 - Small cargo ship homogeneous load, arrival

Using the data in Table 7.2 calculate the loading case homogeneous cargo,

arrival, of the small cargo ship earlier encountered in this book By arrival

we mean the situation of the ship entering the port of destination with the fuel,the lubricating oil and the provisions consumed in great part Using data inTables 6.2 and 7.3 calculate the trim, the mean draught and the draughts atperpendiculars

VCG (m) 5.93 9.60 7.00 2.17 0.62 1.61 0.55 4.35 6.08

LCG (m) 32.04 11.00 3.50 23.15 17.08 9.75 39.62 42.62 38.66

LCF from

midship (m) 0.518 0.460 0.398 0.330 0.260 0.190 0.119 0.041 -0.035 -0.017 -0.210 -0.314

Draught, T

(m)

4.32 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 5.96 6.00 6.20

MCT

(m)

3223 3260 3336 3413 3485 3567 3639 3716 3793 3863 3880 3951

LCB from

midship (m) 0.291 0.272 0.225 0.180 0.131 0.083 0.033 -0.018 -0.067 -0.108 -0.118 -0.167

LCF from

midship (m) -0.384 -0.430 -0.560 -0.698 -0.839 -0.960 -1.066 -1.158 -1.231 -1.281 -1.293 -1.348

Exercise 7.2

Check that substituting in Tp — TA the expressions given by Eqs (7.5) and (7.6)

we obtain, indeed, the trim

in simpler terms, how much stable a ship must be Analyzing the data of sels that behaved well, and especially the data of vessels that did not survivestorms or other adverse conditions, various researchers and regulatory bodiesprescribed criteria for deciding if the stability is satisfactory In this chapter, wepresent examples of such criteria To use picturesque language, we may say that

ves-in Chapters 2-7 we described laws of nature, while ves-in this chapter we present man-made laws Laws of nature act independently of man's will and they always

govern the phenomena to which they apply Man-made laws, in our case ity regulations, have another meaning Stability regulations prescribe criteria forapproving ship designs, accepting new buildings, or allowing ships to sail out

stabil-of harbour If a certain ship fulfils the requirements stabil-of given regulations, it doesnot mean that the ship can survive all challenges, but her chances of survivalare good because stability regulations are based on considerable experience andreasonable theoretic models Conversely, if a certain ship does not fulfill certainregulations, she must not necessarily capsize, only the risks are higher and theowner has the right to reject the design or the authority in charge has the right

to prevent the ship from sailing out of harbour Stability regulations are, in fact,

codes of practice that provide reasonable safety margins The codes are

com-pulsory not only for designers and builders, but also for ship masters who mustcheck if their vessels meet the requirements in a proposed loading condition.The codes of stability presented in this chapter take into consideration onlyphenomena discussed in the preceding chapters The stability regulations of theGerman Federal Navy are based on the analysis of a phenomenon discussed inChapter 9; therefore, we defer their presentation until Chapter 10 For obviousreasons, it is not possible to include in this book all existing stability regulations;

we only choose a few representative examples Neither is it possible to presentall the provisions of any single regulation We only want to draw the attention ofthe reader to the existence of such codes of practice, to show how the models

developed in the previous chapters are applied, and to help the reader in standing and using the regulations Technological developments, experienceaccumulation, and, especially major marine disasters can impose revisions ofexisting stability regulations For all the reasons mentioned above, before check-ing the stability of a vessel according to given regulations, the Naval Architectmust read in detail their newest, official version.

under-All stability regulations specify a number of loading conditions for whichcalculations must be carried out Some regulations add a sentence like 'and anyother condition that may be more dangerous' It is the duty of the Naval Architect

in charge of the project to identify such situations, if they exist, and check if thestability criteria are met for them

8.2 The IMO code on intact stability

The Inter-Governmental Maritime Consultative Organization was established in

1948 and was known as IMCO That name was changed in 1982 to IMO -

Inter-national Maritime Organization The purpose of IMO is the inter-governmental

cooperation in the development of regulations regarding shipping, maritime

safety, navigation, and the prevention of marine pollution from ships IMO is an

agency of the United Nations and has 161 members The regulations described

in this section were issued by IMO in 1995, and are valid 'for all types of shipscovered by IMO instruments' (see IMO, 1995) The intact stability criteria ofthe code apply to 'ships and other marine vehicles of 24 m in length and above'.Countries that adopted these regulations enforce them by issuing correspondingnational ordinances Also, the Council of the European Community publishedthe Council Directive 98/18/EC on 17 March 1998

8.2.1 Passenger and cargo ships

The code uses frequently the terms angle of flooding, angle of downflooding;

they refer to the smallest angle of heel at which an opening that cannot be closedweathertight submerges Passenger and cargo ships covered by the code shallmeet the following general criteria:

1 The area under the righting-arm curve should not be less than 0.055 m rad up

to 30°, and not less than 0.09 mrad up to 40° or up to the angle of flooding

if this angle is smaller than 40°

2 The area under the righting-arm curve between 30° and 40°, or between 30°and the angle of flooding, if this angle is less than 40°, should not be less than0.03 m rad

3 The maximum righting arm should occur at an angle of heel preferablyexceeding 30°, but not less than 25°

4 The initial metacentric height, <2M, should not be less than 0.15 m

Intact stability regulations I 179

These requirements are inspired by Rahola's work cited in Section 6.1 Example

8.1 illustrates their application Passenger ships should meet two further ments First, the angle of heel caused by the crowding of passengers to one sideshould not exceed 10° The mass of a passenger is assumed equal to 75 kg Thecentre of gravity of a standing passenger is assumed to lie 1 m above the deck,while that of a seated passenger is taken as 0.30m above the seat The secondadditional requirement for passenger ships refers to the angle of heel caused bythe centrifugal force developed in turning The heeling moment due to that force

require-is calculated with the formula

where VQ is the service speed in m s l Again, the resulting angle shall not exceed

10° The reason for limiting the angle of heel is that at larger values passengersmay panic The application of this criterion is exemplified in Figure 8.1 andExample 8.3

In addition to the general criteria described above, ships covered by the code

should meet a weather criterion that considers the effect of a beam wind applied

when the vessel is heeled windwards We explain this criterion with the help ofFigure 8.2

Small cargo ship, A = 26251, KG = 5 m, IMO weather criterion 0.35

-0.15

Heel angle (°)

Figure 8.2 The IMO weather criterion

The code assumes that the ship is subjected to a constant wind heeling armcalculated as

PAZ

(8.2)

where P = 504 Nm 2, A is the projected lateral area of the ship and deck

cargo above the waterline, in m2, Z is the vertical distance from the centroid

of A to the centre of the underwater lateral area, or approximately to draught, in m, A is the displacement mass, in t, and g = 9.81 m s~2 Unlike themodel developed in Section 6.3 (model used by the US Navy), IMO acceptsthe more severe assumption that the wind heeling arm does not decrease as

half-the heel angle increases The code uses half-the notation 0 for heel angles; we shall

follow our convention and write 0 The static angle caused by the wind arm/wi is 0o- Further, the code assumes that a wind gust appears while the ship is

heeled to an angle 0i windward from the static angle, fa The angle of roll is

given by

Intact stability regulations I 181

where 0i is measured in degrees, X\ is a factor given in Table 3.2.2.3-1 of the code, X<2 is a factor given in Table 3.2.2.3-2 of the code, and k is a factor defined

as follows:

• k — 1.0 for round-bilge ships;

• k = 0.7 for a ship with sharp bilges;

• k as given by Table 3.2.2.3-3 of the code for a ship having bilge keels, a bar

keel or both

As commented in Section 6.12, by using the factor k, the IMO code considers

indirectly the effect of damping on stability More specifically, it acknowledgesthat sharp bilges, bilge keels and bar keels reduce the roll amplitude By assumingthat the ship is subjected to the wind gust while heeled windward from the staticangle, the dynamical effect appears more severe, as explained in Section 6.6 andthe lower plot of Figure 6.5

The factor r is calculated from

r = 0.73 + 0.6 — (8.4)

-*m

where OG is the distance between the waterline and the centre of gravity, positive

upwards The factor s is given in Table 3.2.2.3-4 of the code, as a function of

the roll period, T The code prescribes the following formula for calculating the

roll period, in seconds,

Plotting the curve of the arm £w2 we distinguish the areas a and b The area b

is limited to the right at 50° or at the angle of flooding, whichever is smaller

The area b should be equal to or greater than the area a This provision refers

to dynamical stability, as explained in Section 6.6 When applying the criteriadescribed above, the Naval Architect must use values corrected for the free-

surface effect, that is GM e R and GZ e fi The free-surface effect is calculated for

the tanks that develop the greatest moment, at a heel of 30°, while half full Thecode prescribes the following equation for calculating the free-surface moment

where v is the tank capacity in m3, b is the maximum breadth of the tank in m,

7 is the density of the liquid in tm~3, 5 is equal to the block coefficient of the tank, v/bth, with h, the maximum height and £, the maximum length, and

k, a coefficient given in Table 3.3.3 of the code as function of b/h and heel

angle The contribution of small tanks can be ignored if Mp/Amin < 0.01 m at30° We would like to remind the reader that present computer programmes forhydrostatic calculations yield values of the free-surface lever arms for any tankform described in the input, and for any heel angle It is our opinon that, whenavailable, such values should be preferred to those obtained with Eq (8.8).The code specifies the loading cases for which stability calculations must beperformed For example, for cargo ships the criteria shall be checked for thefollowing four conditions:

1 Full-load departure, with cargo homogeneously distributed throughout allcargo spaces

2 Full-load arrival, with 10% stores and fuel

3 Ballast departure, without cargo

4 Ballast arrival, with 10% stores and fuel

8.2.2 Cargo ships carrying timber deck cargoes

Section 4.1 of the code applies to cargo ships that carry on their deck timbercargo extending longitudinally between superstructures and transversally on thefull deck breadth, excepting a reasonable gunwale Where there is no limitingsuperstructure at the aft, the cargo should extend at least to the after end of theaftermost hatch For such ships the area under the righting-arm curve shouldnot be less than 0.08 mrad up to 40° or up to the angle of flooding, whichever

is smaller The effective metacentric height should be positive in all stages ofloading, voyage and unloading The calculations should take into account theabsorption of water by the deck cargo, and the water trapped within the cargo

8.2.3 Fishing vessels

Section 4.2 of the code applies to decked seagoing vessels; they should fulfillthe first three general requirements described in Subsection 8.2.1, while themetacentric height should not be less than 0.35 m for single-deck ships If thevessel has a complete superstructure, or the ship length is equal to or largerthan 70 m, the metacentric height can be reduced with the agreement of thegovernment under whose flag the ship sails, but it should not be less than 0.15 m.The weather criterion applies in full to ships of 45 m length and longer For fishingvessels whose length ranges between 24 and 45 m the code prescribes a windgradient such that the pressure ranges between 316 and 504 Nm~2 for heights of1-6 m above sea level Decked vessels shorter than 30 m must have a minimum

Intact stability regulations I 183

metacentric height calculated with a formula given in paragraph 4.2.6.1 of thecode

8.2.4 Mobile offshore drilling units

Section 4.6 of the code applies to mobile drilling units whose keels were laid after

1 March 1991 The wind force is calculated by considering the shape factors ofstructural members exposed to the wind, and a height coefficient ranging between1.0 and 1.8 for heights above the waterline varying from 0 to 256m The areaunder the righting-arm curve up to the second static angle, or the downfloodingangle, whichever is smaller, should exceed by at least 40% the area under thewind arm The code also describes an alternative intact-stability criterion fortwo-pontoon, column-stabilized semi-submersible units

8.2.5 Dynamically supported craft

A vessel is a dynamically supported craft (DSC) in one of the following cases:

1 If, in one mode of operation, a significant part of the weight is supported byother than buoyancy forces

2 If the craft is able to operate at Froude numbers, F u — V/^/gL, equal or

greater than 0.9

The first category includes air-cushion vehicles and hydrofoil boats Hydrofoil

boats float, or sail, in the hull-borne or displacement mode if their weight is

supported only by the buoyancy force predicted by Archimedes' principle Athigher speeds hydrodynamic forces develop on the foils and they balance animportant part of the boat weight Then, we say that the craft operates in the

foil-borne mode.

Section 4.8 of the code applies to DSC operating between two ports situated

in different countries The requirements for hydrofoil boats are described inSubsection 4.8.7 of the code The heeling moment in turning, in the displacementmode, is calculated as

where V Q is the speed in turning, in m s"1, and MR results in kN m The formula

is valid if the radius of the turning circle lies between 2L and 4L The resulting

angles of inclination should not exceed 8°

The wind heeling moment, in the displacement mode, in kNm, should becalculated as

M =

and is considered constant within the whole heeling range The area subjected

to wind pressure, Ay, is called here windage area The wind pressure, Py,

corresponds to force 7 on the Beaufort scale For boats that sail 100 nauticalmiles from the land, Table 4.8.7.1.1.4 of the code gives Py values rangingbetween 46 and 64 Pa, for heights varying from 1 to 5 m above the water-

line The windage area lever, Z, is the distance between the waterline and the

centroid of the windage area A minimum capsizing moment, MC, is calculated asshown in paragraph 4.8.7.1.1.5.1 of the code and as illustrated inFigure 8.3 The curve of the righting arm is extended to the left to a roll angle

0Z averaged from model or sea tests In the absence of such data, the angle isassumed equal to 15° Then, a horizontal line is drawn so that the two greyareas shown in the figure are equal The ordinate of this line defines the value

MO According to the theory developed in Section 6.6 the ship capsizes ifthis moment is applied dynamically The stability is considered sufficient if