A new method fot the determination of the calculated rolling amplitude of carriers in stability standardization

ri"

DOCUMENTS OF EXPERTS OF THE USSR OF IMCO WORKING GROUP

V.V. LOUGOVSKOY

CENTRAL RESEARCH .INSTITUTE OF MERCHANT MARINE

1963

A NEW METHOD FOR THE DETERMINATION OF TH'E CALCULATED ROLLING AMPLITUDE OF CARRIERS IN STABILITY STANDARDIZATION

Lab.

v.

Tec!lithe?*

;

,

A NEW METHOD FOR THE DETERMINATI ON OF - THE CALCULATED ROLLING AMPLITUDE OF CARRIERS IN

-STANDARDIZATION

Leningrad.

1963

-5 CENTRAL -RESEARCH

INSTITUTE OF

:MERCHANT _MARINE .

U.S.S.R.

INTRODUCTION .

The fundamental criterion of "Standards of Stability Of sea and estuary ships"

₍₁₉₅₉

_{Edition) takes into account} the action of wind and waves causing ship roll. Therefore the method _{of roll calculation plays an essential part in} estimating the dynamic stability. In the existing Standards of Stability the rolling amplitude is calculated with the assumption that resonance regular waves of limited length act upon a ship. Hydrodynamic characteristics of rolling are determined by means of gendralizing tank model-test da-ta of ships of various types.

Systematic series model tests of modern carriers carri-ed out in the tank of The Leningrad Shipbuilding Institute

-on demand of the Central Research Institute of Merchant Ma-rine and Technical Board of M.M. Ministry as well as the theoretic studies of the disturbing moment carried out in the Section of Ship sea-going qualities of the CRIMM make

-it possible to give a more precise calculation of hydrody-namic roll parameters. The data we have now at our disposal,

on statistic characteristics of sea waves give possibility to pass from the conditional regular waves to the real wind waves in the calculation of rolling.

The proposed calculation scheme for the determination Of roll amplitudes is based on the statistic roll calcula-tion. in irregular ,sea waves with taking _{into account the} precise data of hydrodynamic roll parameters. _The

calcula-tion scheme is very simple and convenient for use. The

acceptability of the scheme is proved by the calculation of roll amplitudes and stability reserve coefficients of a great number of series carriers of the M.M. Ministry. _Therefore this scheme may be recommended for the insertion into the -Standarda of Stability of carriers at their republishing,

4

e AnakYsis of the methods of the roll amplitude calculation in the Standards of Stabili _of the USSR SHIPPING REGISTER (1959 edition) and

in for egn Standards of _tability

In estimating the

_dynamic

_{stability rolling is-taken} in-to account not only in the Standards of Stability of the USSR Shipping Register [1] but also in. the Japan Standards of Stability for passenger ships [2] and in the China Project of Stability Standards

[3]

_{The most unfavourable case of} the dynamic heel under the joint action of wind and waves was taken as a' basis for the roll calculation in these Standards. At the moment when a squall comes _{On a ship, the ship's} heel-ing angle is equal to the roll amplitude towards _{the wind. But} there-is a great difference between the method of the

determi-nation

of the roll amplitude and the calculation formulae _of the Standards.

The formula for the calculated roll _{amplitude in the} Standards of the USSR Shipping Register is obtained on the basis of the following assumptions [4] _{. It is believed,} that in the state of harmonic resonance a ship is subjected to a pure rolling. Regular waves of a constant amplitude and frequency run against the ship. The moment of water resis-tance forces to the ship's rolling varies according to thel p_gpare _{law. The period of ship's natural oscillationS is} de-termined by means of the linear roll theory formula:

T-

₂₉₇

(1)

where 27

-

ship's weight displacement;

770' -

the metacentric height, determined without taking into acdount the influence of free surfaces in tanks;

the ship mass inertia moment with reference to the for- and-, aft direction;

The use of the formula (1) for ships with.a small meta-centric height and S-shaped Reed's diagrams may lead to substantial errors and give higher period values. In order%

to minimize this error the value z-a is taken equal to 0,3 m in the Standards. Thus non-linearity of the S-shaped stability diagram is indirectly taken into consideration,

To excite resonance, the shipts rolling period in smooth 'water is 'to be equal to the waves period, the ship being beam on to the sea. The length of the running--on waves is determined by the formula:

(2)

The period increasing, the length of waves increases rapidly' too, and at Te >8sec exceeds100 m. In the

Stan-dards it is considered quite improbable that a master should put his ship parallel with such a long wave. It is believed' to be still more incredible that a ship would

sail for a long time parallel with such a wave till a squall coincides with the maximum ship's heeling angle, Such

case is quite possible only when a ship is disabled. There-fore in the Standards of the USSR Shipping Register the length of the calculated wave is limited by a certain maxi-mum value at which the probability of ship's

roll

when

legal on to the sea is great enough. The maximum length of the calculated.wave when an ocean-going ship of the 1-st

category may still sail beam on to the sea under resonance conditions is taken to be equal to 100m and for ships of the 2-nd-and 3-d,categories-sailing in enclosed seas and along the coast, where long waves of the surge are en-countered relatively seldom, it is taken as 60 m. Roll pe-riods having values corresponding to longer waves, a

ship

can get into resonance with waves of adopted length only-when heading an oblique course to the wave direction. The resonance course:angle is determined by the equality of the ship's natural oscillations period to the apparent wave pe-riod.

,

In accordance with the above-mentioned the calculat-ion of the amplitudes in the USSR Shipping _{Register Stan- '}

.dardsls bailed-On a well-known formula, used in the theory Of ship's rolling' in regUlar waves:

6

-here Zsqm:A; relative rolling amplitude in radians, 061,06 the maximum effective wave slope angle,

W-

proportionality coefficient at the sqUare law of resistance to the roll.

The value

oLts

is calculated by the formula:

ae,,9 =

406 se:pi/3

where

040_-

the maximum wave slope angle

/3

-

course angle formed by the direction of the ship's head and the direction of the wave travel,

- correcting coefficient taking into account the commensurability of the transverse dimensions and wave length,

09

correcting factor taking into account the influence of the course angle on the

amplitude of the main_paxt-of the disturb-ing moment;

Factors

ae;

and Z:# are obtained according to

S.N. Magovescensky's method

[51

based on the general roll-ing theory developed by N.A. Krylov and on the use of the parabolic approximation formula for the hull form.

- Resistance coefficient 1/7 is determined with taking

into account the following conditions.

1. Ship speed increases the resistance of water to ship rolling, so

W= Wo (i 4 a Ft)?

(3)

7

-where VS(

-

rolling resistance

factor

at sea,

Wo

-

rolling resistance factor at zero advanced speed,

ri = Proud number at the advanced speed and

at

the oblique course is determined by the

re=

sonance condition and when beam on to the sea is conditionally taken as 0,1,

a -

coefficient taking-into account the fact that resistance increases with the increasing of Proud number and is taken as

3,3

according

to some model test data [4]

2. Value

14

determined on

the

basis of the results 'of model tests of some types of ships

[61

depends on the frequency of ship oscillations and hull form characteristics - breadth and draught ratio B/T and it also depends on the -water-line block coefficient.

.3._ Bilge -Reels increase water reSistance to ship roll-ing and reduce rollroll-ing amplitudes; this reduction is

calcu-lated by an empiricat formula obtained in

the

paper

[63

.

_.4. Immersion of the

deck

edge int64ater also in-creases the'resistance:and reduces the

rolling

amplitude: this reduction is calculated according

to the model

test data

[1]

Even the 'simplified desCription

of the problem given

here involves the calculation, of correcting _factors, the. necessity of taking into account some- factors influencing the resistance, the necessity of determinating the eli-mets of resonance wave and the following calculation of

rolling amplitudes; it leads to a

bulky

calculation schemeu the usage ofwhich in the Standards is rather difficult.

Therefore the -calculation scheme .of the USSR. Shipping,

(6)

where and are .calculated according-to-the recommen-dations of

§.9

of the Standards41)--is simplified in.compa-riaon.with_the

(3)

by taking some preliminarily determined .

ea

values for ships hull form:characteristics.of which coup.

prise

the whole range of changes of these parameters in mer-chant Sea,-going-vessels.--.

The principal difference of the calculated rolling

Ampli-tuArge

Japan Standards of Stability from the USSR Shipping Register Standards consists in an attempt of taking into

ac-e'

coat the. effect of the irregularity of waves, i.e. to intro-duce into the calculation irregular

waves created by wind but

not the sinusoidal waves of

swell.

The rolling amplitude in the Japan Standards is determin-ed by the following formula

(7)

where

sip.?

resonance rolling amplitude,

2hf-

damping coefficient of rolling taken as 0,02 for ships with bilge keels,

aN

and

r

-

accordingly wave slope angle and its

effectivecoefficient_ealculated

according to the recommendations of the Standards 1.2]

-2 .

Thus, the calculation

of irregularity is to a great de-gree approximately made by multiplying the amplitude of syn-chronous rolling in regular

waves by the

factor 0,7 obtained from the comparison of statistic calculations of rolling with the full..scale.test data. Besides the wind character of waves affecting the ship is taken

into

account by introducing into the_calculation the relation between wave steelboss and wind velocity typical for the developed wind waves. It is clear why the authors of the Japan Standards limited themselves to such

irregularity of waves on the

an approximate calculation of the effect' of

theWaiiiii-am--plitude: a sufficiently

precise determination of statistic

Characteristics of rolling lead@ to a complicated calculat-ion scheme which is practically unacceptable for developing the Standeirds-of-Stability,

- The calculation formula (7) of the Japan Standards has

another important shortcoming:

Bertin's

extinction coeffi-dientlis taken as constant (0,02) for all ships

irrespee-, tive of their hull form and the period of natutal ship

os-_

-cillatiOns.

Nevertheless numerous model and full-scale

tests of ocean-going ships show [41,[61(7that the iesistance factor depends on such values as the relation of the breadth

B to the draught

T and the frequency

of ship rolling in smooth water. Since the formula for the synchronous rolling amplitude is taken as the initial formula for the determi-nation of the calculation amplitude in the Japan Standards,

than an error in the resistance

factor may lead to an

im-portant error in the calculation rolling amplitude.

Per the numerical comparison of calculation rolling

emplitudes'in the USSR,

Japan and Mina Standards

ampli-tude values for 17 passenger ships With different hull-form and load characteristics are calculated. The analyses shows that the amplitude values in the USSR and Japan Stan-dards are almost equal. The difference, on the whole, Aoes, not exceed 2-30 only in five load cases out of Y1

and

--it-readhesj6,6,70-:-. the- calculation amplitUdes-Ofthe

-Japan-Standards being, as a rule, higher than those of the USSR Standards.

It is worth noting that. the calculation accordinOthe

USSR Sipping Register Standards generally leads to. low iia].ues of rolling amplitudes especially for large passenger -- ships with moderate initial stability. For instance the

.rolling

amplitude

of m/v "Russia", -Vv. "Pobede, t/v -"Abkhatie'in moat case's of loading is lower than 100

-according to the calculation though a more intensive roll ing was observed during ship service. Consequently the mi-nimal capsize moment and the coefficient of stability re-serve is to a very small degree influenced by rolling and

_

the parametres of hull form witich cause it. As a result even the considerable' change

of

the ship's characteristics favourablejfor_rolling has no effect on the estimation of

stability according to the Standards and the improvement of sea-going qualities of ships is not stimulated. This fact is emphasied by a number of organizations in. the comments

on the Standards of ;Stability sent to-the USSR Shipping

-Register and it is proposed to change the

calculation

scheme of the Standards in such a way as to 'adopt the value of cal-culation amplitudes no less than 15-20° which corresponds to the case of a rather intensive rolling.

Low valuesiof calculation rolling amplitudes are typical for ships theAiatural oscillations period of which is rather great (practically more than 12-14 sec.). For such

ships-,

oscillatione resonance with the wave the length of which is limited to 60-100,m occurs either when the ship is moving at a very acute angle in relation to the waves or when

she is

moving at a greatt(sometimes even unreal) advanced speed. But in,the first case the etlactive wave slope

angle 06-7,A1111

not be

great

(taking

into account 'both the decreasing of .5L3 and the reduction of the correcting factor gf;)

and in the second case the roll damping coefficient motion appears to be great. In both cases the resonance rolling amplitude provesto be not great.

Consequently, it is

neces-sary to reject the assumption concerning the resonance cha-racter of rolling caused by swell wages the length of which is limited to 60:-:100 m so that the calculation scheme of

the

Standards

should not 'lead to low amplitude values. The re-lative character of this assumption is evident, therefore it is advisable to

choose

other, physically mpre valid, external conditions, especially sea waves conditions.

' Besides, for the trustworthy estimation of rolling

hydromechanie parametres of rolling the disturbing moment amplitude, the added mass coefficients and damping coeffi-cients. Formula (4) for the effective angle of wave slope and correspondingly the formula

(3) for

the resonance roll-ing amplitude _are based on the assumption that the correct-ing factor of the main (Krylav) part of the disturbing mo-ment is precisely equal to the correcting factors of the

inertial and damping components of the diffraction part of the disturbing moment. It is shown in the paper

LC

that this assumption is not always true for instance, with the reduction,,of metacentric height the difference in correct-ing factors for the main and diffraction parts of the dis-turbing moment instantly increases. Practical methods of hydrodynamic theory of rolling

₁₉₃

-[11

developed in recent years allowtto more

precisely

calculate the disturb-ing moment at rolldisturb-ing. It is advisable therefore to make use of this opportunity at tne

revision of

the calculation scheme for rolling ,amplitudes in the Standards of Stability.

It has already been noted that the added mass

and.ing

coefficients at the

calculation of

rolling amplitudes according to the USSR Shipping Register Standards are deter-mined, by the experimental data based on the systematization

of a great number of model tests data for varbus types of _

ships., Naturally, at such an approach individual

features

of ships of different types are to a great degree smoothed Out and the effect of hull form paranietres on the hydrody-namic-characteristics of rolling, especial4 on

a

damping

coefficient, is In some cases insufficiently reflected. It seems more advisable to adopt another method - to obtain 4ydrodynamic characteristics of rolling on the basis of sybtematic series model tests of a certain class of ships

the parametres of whiCh are logically changed in li-mited;ranges. It

has

some sense, for instance, to work out add-tO test-sUch seriei for carriers and fishing ships separately. .

In

the process of Calculating the amplitudes. Of roll-ing, that is carried out according to the USSR Shipping

-12-- Register Standaks'the metacentrical, height, as it-has-been

already stated, s determined without taking into account the _

influence of the open surfaces of lidid cargoes,

meanwhile

_

the minimum capsize moment is calculated with taking into _

account the influence which has been calculated according to the formulas ofishipstatics. The possibility of such an approach to the calculation of the minimum capsize moment is

confirmed by the results which were,recieved by N.Y. Maltzev who, on the bases of N.N. Moiseev's experiments, showed that if the ship is subjected to anemically attached heeling mo-Ment (in particular?if the ship is subjected to the, wind

profs-_ _

sure) the influence of the liquid cargoes open surface on the ship stability can; be calculated in the limits of ship

sta.-ties.

The

feat

that)the static correction of the effect of the open surface's essentially influences the period of natu-ral OsCillation,' 4e. under the given wave parametres it

in-, _

fluences the amplitude of the resonance rolling, gives the reason to feel aldoubt about the expediency of a flat refuse from taking intolaccount this influence on the calculated amplitude of rolling.

' Finally, the'calculation of lowering the amplitude of

rolling-at-the deck's immersion into the water is quite a disputable factor-in the calculated scheme of the USSR Ship.-ping Register Standards'. From the physical point ofview this calculation causes no doubts: when ,the edge of the deck is entering the Water the damping moment increases sharply but the disturbing Moment decreases. However, the Srandards do not include unfavourable consequences connected with the

ap-pearance of water,on deck (lowering of stability, the possi-bility of breaking hermitically closed places, and the pe--netrating of we:ter-into the hull and superstructures); those

unfavourable consequences often were the reasons of wrecking the ships of -e siell,height. It is hardly advisable to prefer iia-e-shiPd:of a siiil-height (expecially-transport'ships) from

the point-jif View of navigation when it is neccessary

to'va-,

lue their stability. It is not excluded that in certain cases it can lead tc6a wrong tendency - the decreasing of the height

--13

,height

of the abovewaterside in order to formally satisfy

the demands of

the

Standards of Stability. It is

neccessary

to mast: that acoording to the Japan Standards of Stability for the passenger ships and in the drafts of the Chinese

Standards the amplitude of rolling is calculated without tak7 ing into account the immersion of the deck's 'Ado into the water.

2. Physical-prerequisites of the suggested. calcu-lation schemie for the determinationof rolling

amplitudes of passenger ships

_ The suggested. scheme of.calculating_roll amplitudes is

based on physical prerequisites which differ essentially from

thoie on

which_the Standards of Stabiliti.are- based.

It is assumed that the ship is put in very hard

dyna-mic stability conditions:

she

has a zero speed and is

situated beam on to twodimensional irregular waves. The

mo-ment

the ship has weather lurch and the heeling angle is equal_to the maximum amplitude out of 50 oscillations she is

influenced by a squall, the speed of which corresponds to the wind pressure adopted in the Standards of Stability of the USSR Shipping Register* _

-- -$o, contrary to the Standards in force the-propOsed

Scheme. considers an emergency case of a ship being in a gale, when the ship has

no

possibility to escape the position beam

on to a large wave by means of reasonable manoeuvring. The =Analysis of casualties of cargo carriers, especially of little ones, shows, that some ships capsized when theit po-sition was beam on to large irregular waves. Such case-should be considered when evaluating dynamic stability. It should be noted that such a case is considered in the Japan Standards of Stability for passenger ships.

,- In view-of the fact that the proposed scheme provides for

the calculation of rolling amongst irregular waves, i.e. the ,oscillations of a ship are irregular, the question arises

which of the static characteristics of rolling is the most suitable for the evaluation of the

dynamic

stability of a.

-14-ship. The maximum.rolling amplitude may take

place during

the most dangerous

case

of the combined effect of waves and wind, though the probability of its appearince during wind

waves_action is very small. The probability of coincidence of weather' lurch with a squall of a large force, when the heel-ing angle is equal to this amplitude is eveft staIle±'. The /appearance of the maximum amplitude is more probable when

the number of oscillations is restricted. It is difficult to base this numberifrom the physical point of view. Therefore, it'ls advisable:to choose it taking into account a lot of cal-oulations.of rolling of abdern merchant ships and the analysis

Of their

rvice.

The results of such

calculations

are (Oren in 6 of this paper. They shite the,L;ceptability of the met-- hod to choose the maximum rolling-amplitude out of-..

oscil-lations. From the physical point of view this number also seems to be quite suitable: the probabilty of exceeding the. maximum amplitude out of 50 oscillations is very small, i.e. conditions of rolling chosen for the determination of the safety of navigation were hard enough.

.The propertied of sea wa.ves which-cause rolling and. .

which are

mentioned

in the Standards of Stability in force, do not depend on wind_strength taken into account during

-calculations.

That is why

it is advisable to eliminate this conditionality and to choose statistie characteristics of wa-ves typical for real wind speed, which in its turn should

correspond to calculated_ wind ppessura adopted In the

Stan-dards. The

calculated pressure, adopted. in the Standards for the ships of the.1st category, corresponds to wind strength

of 10 balls at squall, for the ships of the 2nd category -to the wind stregth of 8 balls and for the ships of the 3d category - to the wind strength of 6 balls, approximately.

In the zpropoaed. calculation

scheme

for the determina-tion of-rolling amplitudes statistic characteristics of waves

correspond to the mean speed. of 10 ball wind for untestrict-ed region of navigation (ships of the 2nd and 3d categories). From the physical-point of view this means that in the

re-gion. of shippi-navigation there act irregular waves, caused by the wind of the above-mentioned speed, which was blowing

during a

sufficiently large period of time. At-the moment

when-thelsqualLracts upon a.

ship, the latter is considered

to-hrte_nostatical heel,

i.e. it_is.supPosed that either

the average.windispeed.at this moment is equal to zero, or

the direction of the squall

does

not Coincide

with the di-.

INCtion_of,themindr.blowing withconstant speed._Biidently, ii.:case-of pulsations, of wind gusts at some average speed, considered in the Japan -Standards of Stability is often-met in practice. However, a more dangerous combination of wind and weve-actiont-when the statical

heel

of a.ship is

abv

den4 is_considared.in

the _chosen scheMe of the squall_which gUarantees

a

greater.degree of safety ..from

the point of view,

of-dynamic stability.

Besides,

while calculating:rolling-diplitudes_of a ship relative

to

some inclined position one-. meets with .a number of essential difficultiest in particular, thire_is no systematic information about the hydrodynaiical Characteristics.of,rolling_of.unsymmetric ships, the.calcu-lation of the distuibing moment.becomes_more.difficult,_the Method_of_the determination of statistic characteristics of. tolling.becomes more difficult

-too,

because the stability-mO-Ment.must be.calculated in this case with the consideration-Or'nou4inearity.l.That is why, it is advisable to remake.the

Scheme

,of-the,_calcUlation of rolling amplitudes

and

to-use _

the_same.methcid_of,the determinagqn of the minimum capsizing Moment as that given in the USSR

Viear

Standards of Sta-bility in force.

§ 3. Theoretical and experimental fundamentals of the

calculation ohydromechanic

characteristics

of rolling

. The .determination of roll characteristics is based on the

differential equation of the ship motion under the action of alsinusoidal wave, .which in accordance with the

linear

hydro-dynamic roll theory can be put darn in the following form:

and

-zaeTa) 40(0

.(9)

Az.)8

4-40÷ az

-a) 94-A49*

4,9

k---1\12),si7es-/-11coso'7e

₍₈₎

Where

_/)

Jr/

_{,. heeling angle in relation to the horizon,}

Iinearlaw_damping

coefficient of

_rolling,

small metacentric raa7As,

a

'616-elevation-of-the gravity

centre avobe the

centre of buoyancy,

-deflection of the gravity centre -of a ship_

ithéqiiilibriurn.posit.ion In the

transverse..

horizontal directiori,

&Med static moment,

daiping_Coefficient of transverse horizontal o6cillations,

'appgrenVreircular wave frequencY,,,

/1/4 --amPlitude .(:# the

mein_pert Of.dieturlAng

Moment,

dalaulgted on. the basis of A.N Krilov's

hypothe

-amplitudeATalues.g_tpe

diffraction.

part of .the

disturbing moment-41nertia and-damping

pro-r

perties of the disturbed

fluid, respectively,

The-most simple .method of finding the hydrodynamic pa--rameters.of

rolling9

which form equation

₍₈₎₉

is to combine theoretic calculation of

the

disturbing

moment with the

ex-perimental

determination of added masses and damping

coef-ficients.

The amplitude of the main part of the disturbing moment determined by means of the

static

calculation, based an gene-ral A.N. Krilov's theory can be represented as follows:

where

where

4 -

Correcting .factor, -taking-into -account the -influence of the course angle_and the

principal dimensions and wave length corn-Mensurability on the main part of the disturbing moment.

-To calculate the diffraction -part of -the -disturbing mo-ment. one .can use _the results of the. precise _solution_ of the

t1_ dimensions problem of -wave the ory_with subsequent

appli-datidn of -the hypothesis of striptheory. However, in case df -tolling at the oblique course such an approach to the .

tiroblem connected_with a number_of _difficulties. _Therefore,

it IA advisable ..to use the method of successive

approximat-Jona,

_based on_the application. of Green's formula for the. restricted

space*

_which_was developed .by M.D..Haskind

[lc&

_012

.

For low frequency _of oscillations typical for reso-nance zone of rolling _this method has a good agreement _with

the presice solution even in _the 1st approximation.- The_

am-plitude_values of the inertia and damping constituents of_the diffraction part of the disturbing moment can be represented in the following form02]

= 29,6

_d00-

!SI

/7

2.-

016

oje42

(lb))

/4r5/40(0C1/l'

(:1>(11)

- apparent circular wave frequency,

K

4. the wave form frequency

- Coefficient p.including the influence of the course angle,

- Correction factor, including the influence of the-principal-finite -in comparison .with the inEtiie_ length on the main part of the disturbing moment

0 , _

A94,

-

added , statia moment -relatively -to -the cross

line

of-the diametrical plane with the water-line plane,

18

-

--A13

-

infinite function, taking into-account the farms of the hull and the ratio.of the ship's

size

tä :the _wave length influencing .the.damp-ing component of the disturb.the.damp-ing-moment.

-For the ships, the hull forms of-which little-vary, the

ase.of-the

formulas of the parabolical approximation of the shipformsand the limitation of the_characteristics of the sea motions by means of the wave length zone

.4>

at-is-by

means of-the intensive-rolling zone, gave the op-portunity to get-the values,.-determining.

z,6,24,

which Sóañ be calculated-in quite a simple -and convinient way. : The added inertia moment, the added static moment 1/204/-and-the damping- coefficients _and_../Gq._ can be calcu-lated.on.the_basis-either of-the approximate formulasr.based on:syitekatizing various experimental_values.(for example,

on the .results of the.specially organized serial. mo-del_tests as_it_was done by V.A._Morenshildt. The_secondwAY kiwis More reliable-and, taking into consideration_the-absen-de Of such.data on transport ships,. the author worked out a seria of models .the hull forms parameters of which were sys-tematically-changed in the_limits typical-for modern.trans-port,bhibEi-and the hull forms-approached_seria N° 60. -'

_Thetests were carried out by order of the Central Re-Search-Institute-of_ Merchant -Marine in the tank of

the.red._Shipbuilding

Institute by Y.J.-Faddeev and.G.H. Tkat-_. chuck; theoretical drawings of the models were worked out. in the-Central-Design Bureau-N 1-of the Marine Ministry by V.M. Fedukov. The ratio,of_length.to width was kept constant

_ -L('AL,--7.3)L

however, there are_grounds_to believe -that

,

the_variation..2T_ _ in the limits 6,5 - 8,0 will.not

pra-atically influence the results of the experiments._The ratio Of_the.width. _,EL to the _draught 7-_ was chaged in the li-mits 2,5 -

3,5,

the block coefficient 0( was changed in the limits.0459?0.+74._and the waterplane area.coefficient_ was relatively changed .in the-limits_0,70.,0182. The results Morenshildt's.work gave the.opportunity far some extrapolat-ion of the recieved results° The tests_were carried out

1 9

-numbers was

C27ite.-.43O

these tests were carried out

in

ac-cordance with the methods adopted by the laboratory of ship re-search at the Leningrad Shipbuilding Institute L 133 The

mo-dels were chosen in such away as to exclude_the scale effect,

- The added inertia moment and the damping coefficient,

Open-;

ding on -7.2taa and as well as the formula for

the calculation of the snip's speed influence on the roll damp-ing were received as a result of the tests [7] It appeared that at the amplitudes of rolling

On.,,,O°

which are of the most practical interest the law of resistance_to the-rolling is not linear as it follows from the equation (8) but it is close

-to the square law,

so

the damping Moment should be written in the form of VA51/6/ where

I/V-

is a damping coefficient when the square law is in force.

As a result

of

reducing the theoretiC,formulas,for the dis-turbing moment components to the convenient form af using and for systematizing the experimental curves for the added masses

-and damping coefficients the following calculated formulas, cur-ves and nomograms were,obtained

For the calcUlition of the main part of the disturbing mo-ment the following formula was deduced:

z,K-T+

(-ze

27- °c-18----74R,

Lot

?5-=-1)K-77+

'')(1(724

Zi; (12)

where:

Zp -

the distance of the centre of gravity from the water-line plane, positive below the water-line,

4,

the !corresponding distance of the centre

of-buoyancy from the water-line,

z;

and i- the _coefficients; taking into account the

in-nuance of the course angle, and determined by thecUrves of Fig.. 1

[5]

as functions of the .water-line block coefficient and he argument

L

--(j=2-7- KT cos ;

2;

ah functions dependineon the ratio of the main measurements to the block coefficients and

AMINO

LW= .

U.

Irin1/41.44=

_MOM

moaxgralin

111NOSNIMIll10101101111 111111152:1% 0(.47 -41

-

20

-av;

..,

h.

_.-

_0011411

I

_.4 mow.moma maxowem . 111.111111110.1% wsealow . MIAMOOPONN Ili111111,11111011111M 1101111:101111M 1111101111111011 1111111111111111110111 INEW111111111E mi1.11111111111MMIION MIMEOS 11101110o

WIEN

_...

IIIIMMII

WI°

ENE to 2 -4>

The nomogram has seven scales for , for

0(

I two for

, for z, , for Zz and a blank scale. Dash - and - dot line

shows the key to the nomogram when 11- =2,8

;

o1Q78, x= qgo

are given. Connecting the point

-9=2,8( 1-1

scale) and the point

c4=0,78- ( scale) by the straight line we receive the inter-section point

F of this line with the blank scale;conneoting

the point

F

with the point

--(190of

the left

/

scale,

by the second straight line, we find (according to the inter-section point of this line with the Z, scale) the value.

2,- 605, connecting the point

F

and the point /,(1449of the right / scale by 'the third straight line, we find (accord-ing to the intersection point with

the ;

scale) the value of

_6;298

.

The correcting factor to the inertia component of the dif-fractional part of the disturbing -moment is calculated by the following formula:

=/---(1/1/81,p,s,i(1-0/3104apz5, (AJT) 2 (13)

where 4= 1,95a - 1,36 (14)

but the functions _('§),

_{(-78--): A (X) and}

(X)

6

fly 3

21

-are determined

by the diagrams

of Fig. 3 and 4. The

coeffi-cient Z,8

taking into conside-ration the influence of the

course angle at

/3

,° 5

can be found by the diagrams of Fog. 5.

The value determining the damping part of the

dis-turbing moment, can be calcu-lated by the following formula:

Nook, -Q 7610,,A-The,42;(15)

wherek5z= 2,5c7( -0,75

,

(16)

and the functions .13

(19, /3 ()

and A,Ware shown in the

dia-grams of Fig.3 and 4.

A

prilipall

1191111111:11911 MIOMMEMME Illri

lininalMAIMILIMIIII

moncr...,,,,,...

1...mmillraglis

rpdripni.

.L.

MMEMMMIM111 MMMEMICAMME

dilliIiiii

,

...

INElean

mum

SIM=

MEM=

..

__ IIME

L-1-- il,

MS IIMUMMIWAnmWI.

MIN

Rim

111111111

MIUMPORMIllira

rtaiMdgallingal

111100111111122:iirA51 WM MN

i

r,

s _ _

411-42m-0

11

AE3

A

l i

7 4 3 2

11111411

Wilig

11111EAMII 0

sounswass

arammus

ormassana

ININIZI

zo 1111111MION InSIBMIUMI AIIIIIIVW!!

AMOS

01110111111E,VIPP,..4111111111111111S

gig 11111101/_Ai _{11111111NIUMII} .1101101.1.... Wal.°0,14111111101116111111111 07.-":--=.--1;:rwaINUOMEN=111311101101140 04 470

-22-6

468 467 466 465 0,64 463 462 0,61 0,60 470 OW

The calculations show that in the zone of surficiently

long Waves

A> 107 the damping component, as a rul.e, he.si an

insignificant

influence on the summary- disturbing

moment and

therefore

it

_{15.7 be} neglected in

the

practical resonance ling calculations.

The added moment of inertia J1Liz and the damping coef-ficient at the square

law W can be calculated by

the no-' mograzis -(Fig. 6 and.?) plotted acOordingto the model tests .

results.

The nomogram

of Fig. 6 serves for the determination

of

value.-age

wb.ere

/qv&

- inertia

moment of the

sUbma-rine 'part of the ellipsoid

having the same principal

dimen-sions and -the block

coefficient

as the given ship. This va-, lue is changed in dependence on -,

6 and

0.< more

re-,

gularl.y than j1/44/ On Fig. 6 dash-and-dot line shows

the key to

the nomogram for Ti_3. = 8 ; oir ;

0(

0, 78

Connecting the point =2,8 ( scale) and the

point (-s-=(-)-,

70(

or

scale) by the straight line, we get the

intersection point

p

of this streight line with

the.

blank scale; connecting the point p with the point' = 0, 78?

o( scale) by the second straight line we find the value = 034'5according to the intersection point this line

with

the scale. Then the added inertia moment ifs Calculated

7

144, (/qi/ee,

;/14/4)Qc,26Zn

e7

(17)

For calculating the relative coefficient of

roll

damp-ing at ship's zero speed uro.--

W

.

Sem)onov-R+J244/

.Tianshansky

[71

suggested that the coefficient'

'

connected with

tilo

by the following formula, shuld be

in-troduced:

=

8

69 +Ai 9q)

z -

(18)

Unlike id;

the coefficient

ec :,/ practically does not

by--va-^

2vr

fig 7

12

lues of ratio T,

cr

and %." . For the calculation of cc:

the nomogram in Fig. 7

can be used, where by means of

dash-and - dot lines a key to using this nomogram with the same values of

3

or- .and CX as for -11-4,"

T

_/ivee

is given;

it results in c4'=g0.93 . The _{scheme S} of the calculation

.11/rv

of /J. and by nomograms 6 and.

7, respectevely,

/lye

fully coincide.

For the control of the increasing resistance to roll-ing at ship's advanced speed the

following formula

can

be

used: ,42.00 -452 4190 4148 0175 -060 opo 4110 4185

00/

4095 4090 4485 4080 4075 -482 - 481 4165 4160 4155 0150 405 ogo 4155 400 4115 4120 4115 --464 -462 -463 -5164 - 0,80 .479 478 - 0,77 4070 4065 -466 -467 468 -469 -470 -- 0,71 -472 473 -475. 475 473 -472' - 0,7/ -470

here

_25

6v= 6tro

/4- 2.7z_ + 10.7z 2),

(19)

where _{W.-- relative damping coefficient of rolling in} waves,

54.7i=iA

Froude's number.

vc9L.

For the ship with the',bilge keels, the determination of the relative damping coefficient

_6ti;

_{may be calculated} by the following formula, taken from [6] :

S,8

D3

ji<"(

zev

where .5)(

-

total bilge keels area .

- position of the geometrical centre of a 'bilge keel from the ship's centre of

gra-griV

(midship section).

Bilge keels influence: the added inertia moment with the normal bilge keels (

_5,<

_9O3

₎ the approximate increase of

ii,Z+4

may be taken at about 50%.

For the determination of added static moment there _may be used the following formula, derived from U.K. Usatchev's hypothesis of plane cross-sections and his experimental

da-ta:

/

Z17

=-023Z73

c7(

63

2 l

(2)

Dynamic qualities of the rolling ship with the different frequencies of waves in rough seas are determined by the dyna-mic coefficient,

.

For the irregular Waves the following formula can be used:'

(20)

(22)

26

-Where - roiling amplitude in abbolute coordinates,

.1'.-- Ti

()

ji." ii

-i

e

-( livvi )

"0 k (n±-,4,4 )

_

t7 - rolling frequency in smooth water

without

any resistance,

At the squar3 resistance law _{the coefficient JQ must}

.

be substituted by the _{relative damping coefficient Ur,} If the irregular rolling process is in accordance with the normal law, this substitution can be done by G.A. Firsov's

formula E14J

-/31)6) fi (24)

where -

dispersion of

_{angular speed, determined by}

the roll calculation ship motions in irregu7 lar waves in accordance with A.J. Voznesensky and G.A. Fillsovls method or

by L1530

In conclusion the 'question of the influence of liquid cargoes upon rolling is considered. 'The

presence

of the li-quid cargoes on board the ship can influence the frequencies of natural oscillations as well as the magnitude of the dis-turbing moment. It is quite possible to calculate the in-nuance of liquid cargoes' on the frequencies of natural os-cillations with quite sufficient precision for the ordinary size tanks which are used for fuel, storage and

so bus Such

calculations were done by G.V. Vilensky on the basis of

N.N.lioisceiv's experiments [16] in the limits of statics.

The

calculation of dynamic phenomena can be quite indispens-able

only

in cases when a liquid cargo floods very big com-partments' (cargo hold type), which rarely occurs in the sex'-viceS of an undamdged

The influence of the liquid cargoes on the disturbing mo-ment is more complicated. It is rather complicated to esti-mateithis influence by aTpure calculation because of bulky

-

the non-dimensional damping coefficient of rolling at the linear resistance law.

-27-calculation dependencies, affecting ship roll and liquid oscillations in tanks and in view of an evident condition-ality of assumptions, used in the calculation scheme of

amplitude characteristics, given in [16] e This scheme was

supllemented with the experimental data, which was made by N.N. Rahmanin. It gave an opportunity to come to a conclus-ion that the presence of the liquid cargoes with the open surface decreases the disturbing moment in case the centre of gravity of the liquid cargoes is situated below the gra-vity centre of the ship, The disturbing moment increases when the above mentioned centres are situated inversel. As the gravity centre of the majority of the transport

ships tanks is situated below the centre of gravity of a Ship the not taking into account the influence of the li-quid cargoes on the

value

of disturbing moment can

practi-cally give rise to the increasing of the rolling amplitude I .e. the demands to the Standards of Stability become more

rigid.'

- Thus, when the formulas given in the present paragraph

and those which are deduced from the previous ones determine the frequency of natural oscillations, it is neccessary to take into consideration the static correction on the in-fluence of the open liquid surfaces; when the amplitude va-lues of the disturbing moment are calculated it is quite pos-sible to neglect the influence of the liquid cargoes.

§ 4. Dependences, characterizing irregular sea waves

In accordance with the taken

physical

scheme it will be considered that the steady-state wind waves corresponding to the 10 balls wind for the unbounded basins and 8 balls for

bounded ones can influence the ship. For the calculation of

-ship's rolling in irregular waves it is necessary to knowthe spectrum of the latter, The

steady-state

wind wave spectrum

LS (0-) where CT

-

spectrum frequency, can be determined

in accordance with the existing theoretic and experimental dependences [17]

Neiman 's wave spectrum:

r

o =

e

u22

(25)

where C -empirical constant and

LL wind velocity

is inconvenient for the

calculation of

rolling_because_for-mula_(25) is applicable only for fully developed waves which

are seldom encountered at the wind of over 5-6 balls accord-. ing to Beauforils scale. Empirical spectrum given 'in [17] is more

sUitable:-Z

which doesn't provide a definite connection between wind ve-locity_and waves characteristics and is fitted for any wind force.

Here

17

and range of

maximum Sz(di,

- The inconvenience of

formula (26) for

roll calculations consists in rather overstating values of spectrum density at

-low frequencies, i.e. it brings to the unreasonable overstat-ing of amplitude characteristics of rolling.

The energetic spectrum of rolling obtained by G.A. Fir-sov theoretically seems most suitable:

cy.,gy

YiLiy 202_002w2

.6,),,'*-aVG61-GY(24,4---45q41:+34V-61;26Y

(27)

where constants Co. and &), are calculated by experimental

data,- obtained by NJ. RAWIlmian:

ao

0, 2/

(28)

here Te is the average wave period.

- --ForMulae (27), (28) are applicable for steady-state ir-regular waves at any.wind.forcein the range of speCtrum

fre-quencies, including the range- of heavy rolling of merchant

Ships.

0-2

÷

82

?a°

o--`/7 4.

20-1224,"

(26)

-

the dispersion of wave ordinates;._____

a2Fa02-(42

oz=a024-aftz

444 are empirical constants, characterizing the the wave irregularity'and the position of the curve

^

As the dispersion of wave ordinates is calculated by formula:

a/k3(

.(29)

and the wave height with 3 per cent probability of

exceed-ing

h"

is closely connected with the average wave height

;5

by the following formula:

:=2,/27

(30)

it is necessary to assign average wave parameters

h

and for the calculation of the spectrum curve (27). These values in accordance with the adopted 'physicalscheme of determining the calculated amplitude can be taken as the functions of average wind speed corresponding to the cal-culated pressure of the Standards a=257sec- for the

un-limited range of sailing9 and

a --/nector

the limited

ranges of sailing are taken as a typical average wind speed.

In I.N. Davidan's diagram that was plotted by the

re-sultb_of'treating a great number of experimental data

;7-and

Z76. are determined as the largest possible values of

the-average_height and period at-the chosen wind speeds:

A;=.01, Z-e=11,7sec

for the unlimited range of sailing;

);=275nt foP=9,4sec-

for limited ones. The values

of;77

,

12-8 are assigned in such a

way

that at evaluating

the

dy-/_

/namic stability the errors

allowed

were not-dangrous (due

to

the reserve they supply) and at the same time different ships in equal external conditions were compared. Then the constants included into formula (27) and characterizing ir-regular waves will be equal:

47, = a4/q0,5,-/,

ao 70 0925 sec

for the

imlimited ranges of sailing; and

:=-.221,174 for the limited ranges

Taking into account the

above-mentioned it

is not dif-ficult to get the final

calculated

formulae characterizing sea waves spectrum. The test way to get these formulae is to evaluate the dimensionless curve

'rg-4(5),

plotted by G.A. Firscv to the dimension form for the calculated

and Gt)2 Such curves of sea waves spectrum density are

1-1-

V22 ma

ter, =6;565

sec-',

of sailing.

4

-30-ishown in Fig. 8, a, b for the anlimited and, limited ranges of sailing accordingly. These curves were used for the cal-culation of statistic characteristics of rolling in irregu-lar waves. 2 0. '2 4'4 4:5 476" 97 fp If (2 - 45' 8)3, 01 6:2 04 06 Q7 06 4'.9 _et (2

Fig 8

(0)0 / 6

8

6?

§ 5.

Working out of a calculated roll amplitude scheme, applicable for the stability standartizatian

To calculate statistic amplitude characteristics of rol-ling in irregular waves, the maximum amplitude amongst 50

oscillations in -particular, it is quite enough to know the, dispersion of heeling angles Doconnected-with the speet -rum density of rolling , L.59(6) by fdrmula:

If the spectrum of rolling and the transmission funct-ion of rolling areknown then the spectral density of roll-ing can be determined by the followroll-ing formula:

2

SO( °:1=

(t) 4())

gm

(32)

where modul of the transmissive function a° is calculated. by (12) - (23); If the dispersion value is known then the

maxim= amplitude amongst

50

oscillations can be determined without any difficulty:

67250

= 2/2

V2 ,77;

(33)

However, usual calculations of _{4P7so_bY_(31)-(33)_for} the stability standardization are practically not suitable

(fitable) as it is' connectedwith the bulky calculations of hydrodinamic roll characteristics of every ship, with calcu-lating the ratio 77-(o) and the value of

.207/and

with making planimetric curve of the roll spectrum density. With taking into account that such calculations are necessary for

any case of loading, it will be clear, what volume of calcu-lations would be necessary to evaluate rolling by using for-mulae (31)-(33) in projecting.,

One of thOrays to simplify the roll calculation, which was apllied at working out the calculating schemes of the USSR Register Standards and the Japan Stability Standards,consists in: 1) preliminary roll calculation concerning ship

a

with

typi-cal ratios Of the principal dimentionsoblock coefficients and ( 31 )

- 32c

. 0

other parameters that influence transmissive function of rol-ling; 2) analysis of the influence of separate parameters, and at last; 3) making average results of the calculations. This method was'used in this paper as well.

It is known that amplitude characteristics of rolling in waves of given parameters are greatly influenced by the natural

oscillations period 724. and roll damping coefficient the latter

depends on the width to draught ratio rall frequencies and. block coefficients c) and d" (03c!

),

In.additd pa the= amplitude is rather influenced by

correct-ing factors to the principal and diffraction parts of the dis-turbing moment -Which also depend on the form parameters menti-oned and on the ratio of width and draught of,a ship to the wave length as well, thoggh as a rule for.the long beam seas position

this influence is of less importance.

In accordance with the above-mentioned the roll calculations were made for different variations of

0<

and

6/lilt

different displacements. The period varied in the range of

-6-15 sec typical for modern merchant ships, the limits of

chang-'

ing CX and o

-q)

were -determined by a chosen serie for model tests (

§3).

The analysis of the calculation results showed that the change, within limits mentioned, of coefficients -04 and drq) slightly influences roll amplitude characteristics in ir-regular waves; thus, maximum amplitude amongst 50 oscillations va-ries but not more than 5-1054

To illustrate this in Table 1 there were summerized the roll calculation results applied to the ships with (82) equal principal dimetions, characteristics of stability, and hull form parameters, with the exception of vertical block coefficients, A_ that

dif-fered rather greatly (

0,835

and 0,90 ). Fig. 9 shows the curves of the roll spectrUm density for both cases. It is evident that the difference between the dynamic coefficients and the

spectrum curves is rather slight; the difference btween maxim= -amplitudes amongst 50 oscillations does not exceed 1-20.

This result

can

be interpreted

physically

as well. In fact', the increase of the vertical' block coefficient (with constant

) results in a certain decrease of roll damping, which, is evident, for instance, from the nomogram in Fig,

7,

but the

am-0

0,6 Oh '0,3 42 41-a .1 categow - '

_

1,0

33-ng

11, 44 0,6 44 42 41

crawl

2 catefor,

1,0 10 6'. 45 44 45 t9

3L.

plitude of the disturbing moment as a rule, is decreasing as

--well, The latter is well illa3trated by GoE. Pavlenko's

appro-,

ximated curves for the correcting coefficient taking into

ac-count the finite draught of the ship .compared to the length of

-emitting waves.'

z

The influence of ratio

T

was found

to

be more essential.

'

The calculations show that the increase of ratio from

29*

to 395

results in changing the maximum amongst 5o oscillations

amplitude

2o-25% and it is not advisable to neglect this change.

However the natural oscillations period of a ship mostly in-fluences amplitude characteristics. From the simplified,cformula,

proposed by u,A, Firsav and A.V

voznesensky, it

fol.Lows in

PAP-ticular, that

for a certain regime (range) of rolling the mean

rolling amplitudes, under other equal conditions, are inversely

proportional to

tne square of the ratio of natural vibration

pe-riods. More exact

calculations

show that, in fact, this influence

is to Some extent slighter but

neVertilelesa it is undoubtedly of

great importance.

- accorda.lce with.thoe above7mentioneddynamid coefficients,

curVeS,"spectral density cues'of ro.J;

angles,

dispersions of . .

roll angles and maximum, amongst 5c oscillations, amplitudes were calCulated for the ships with average coefficients c< and dr at four

periodvalues.

of 79-= 6, 90712 . and 15 sec and at

3

vae-'lues of 4g m 2,46.390; 3,5n7 the sake of illustration the

'Spectral_Aensity curves

of rolling of the I categ--Ifships,

hay-ing

?H.15 sec at 4

3104t3, respectiVeI70ex4 shown

in Fige.10

The final resulit,of calculations of the maximum, amongst

- ,

r 50 oscillations,

_{amplitudes of rolling are summerized,in}

Table 2.

so 45 * 2 4.' To,7-153ec, T

icertepx,

42 Te s 15 sec COteR07 ts 405 78. 1.5.sec

fcategov

4,

0

35

Table

Table 2

/

=150 m--;

B

= 20

in;T

= 8,35 m,

,c)

= 0;78 m

mi, -

_{= 6:0-9 ni).2,= 3,04 la,. Z-r CY = 1,95.:m.:}

7= 3,93

"Block coefficient

,

cf =0,65

lo

= 0,70

Roll characterist

)[ =0,835

)(

= 0,9O

--(A7)/7767)(.

.

.10,6

10,2

category

0,67

0,60.1

. ,

(

j),-,,o,

II category

../-.0;62

0,56

1

.

I Category

.

33,4

_ _32..13_. 0

_{-±1---category}

_31,1

_30,4

-I category

II category

0 sec

2,4

3,0

.3---,5"---

2,4

3,0

-'

35_

,,... ._

6

₃₅

33

30

31

29

26

,9

32

30

26

28

26

22

12,

28

_

26

-

23

22

20

17.

--15

24

21

18

16

14

12

By the table data (Fig

11)

there have been plotted:,

-1) diagrams of ratio

ale (1/1,-ct).

where Om.

is

-an average maximum,_{_}

amongst 50

oscillations, amplitude of rolling of shipEi with

ratio9- --1,-.2,

;

(' r - a ) -

meta-centric height calculated

with regard to the

influence of

liquid cargoes free surgaces;

-,

18 Saes (Zcat

37

-013 3V'

2) ratios

Ai(")

where

k,t,

is the coefficient of

influence of ratio--

on the

amplitude of rolling. These ratios

are

tabled as well (Tables

3 and 4

The calculated roll amplitude of a Ship without bilge keels is rated by formula:

gm

=

m

₍₃₄₎

In connection with ratios

91"

and

Ko f)

it is

necessgry to note the following.

4

valued

&70.

is the funct-ion of the roll period; the latter, for the stability standar-tisation purposes, Can be determined exactly enough by

n7;

Q-58(/

(35)

go,m)

where

thrldis

a

static stability arm at the heeling angle, equal to the roll. amplitude. If the metacentric height is great enough and the static

stability

diagram

up

to the

angle

a

is linearc then the ratio

tn

can be replaced by the ratio 7.1:2-i-/ that helps in practical calculations. At small metacentric-heights and a distinct

S-

shaped stability dia-gram such a replacement would lead to a considerable oversta-tement of the roll period and., in accordance with the data in Table 3, to unreasonable reducing of the roll amplitude. Thus, making the replacement for the sake of symplifying it iS

Table 4 oop5

and

lower_ 01,06 __. 007 0,08 0,09 . 0,10 0,11 0,12

-003

and more

Yz-a

zi? gm'....,..-Iln / dfg

i

cats 24 26 28 30

32

33

34

34,5

35

IT' Ili cat

t

16 23

26 28

. 2 303 30,5 31 4 2,4 _i

3,5

41 and. 2,5i

g,fi

2,7 2,8 2,9

3,0

3,1

3,21

1,3

304 and

T lower

. - . _ more

K

- o 1,0 10,98 _

...

0,96 0,95 0493 0,91 0,90 0,88 0,86 0,84 0,82 0 80 Table'3

-38-39

able to limit the reduction of the roll amplitude by definite -limits, as it was made in the active Stability Standards. The

calculations showed-that the value 0,05 corresponding to the roll period of

1614

18 sec was the most advisable limit for the argument %--a7 In the calculated roll implitildes

gm> 12 4!

1543-the roll period of the finite amplitude of modern merchant ships can only exceed the mentioned value in

- some cases.

- A- similar limitation of

reducing the

amplitude was

carri-fed

Out

concerning coefficient

4

(19

as well.,The ratio

3

increasing,-this-coefficient decreases

discernibly,-owing to the increasing of the resistance to rolling; at

-2-739 5 4)

4,0 the amplitude of regular rolling, with the pe

7-nod great enough, can become a small value. However, sea

go-ing of

ships with similar ratio of width to draught in irre-gular-waves becomes (grows) worse, as rolling becomes rough and intensive at'the,expense of the added disturbing moment of the inertia nature growing with the increase of form stability at the invariable metacentric height

[18]

In order to

avoid the tendency to the artificial increasing of

f

for the formal satisfaction of the Standards and according to the calculation results of a number of series (typical) carriers it was advisable to_limit the decreasing of the coefficient

Ko

by the value 0,8 according to the argument

7-4=3,5

To receive the dependences giving the possibility to take, without any difficulties, into account the influence of the bilge keels on the rolling amplitude therChave been also calculated the curves of the dynamic.coefticient, the .curves-of-roll spectral

density, dispersions of

roll angles

and maximum, amongst 50 oscillations

amplitudes of

number of ships with the'specific

7; and # at the total

area of

bilge keels ratio S.

to L13 = 1, A4,3

and 4%, covering the possible variation range

A

The

calculation of the resistance increase to rolling with the installation of bilge

keels was made by the formula (20). In Fig. 12 the curves for spectral density of rolling for ships with bilge_keels are pre-sented. The mean results of calculations were presented in the

0 Se 42 Rf SOD

40

(0 05 6 d

form of a graph in Fig. 13 (Table 5 correspondingly) where

Ac _{- coefficient taking into account the effect of bilge}

keels in'the roll calculation amplitude.

Table_{_5}

It is supposed that the bilge keel may be determined withthe help of the formula (20) as in the existing Standards of Stability. Then the conventional

roll calculation amplitude of the ship with bilge keels may be determined by the formula:

(36)

iSk

where is obtained from the formula (34) and(7-(<-::-/

from the graph in Fig. 13 or from the Table

5.

5,K is

underdlod-thetOtal area of bilge keels. As regards the last relation it should be obsegst*d that when_

Ar

is noticeably lower, than 1% the effect of bilge keels becomes-insignificant9 but such values for

71

are rarely: en -countered in practice,therefore assuming, for the

simpli-fication, 0998 at

Ak_4-one

should bear in mind. thatz_z? -Couid-be_only a little-lower-than 1%.-The ratio

-- considerably greater by 4% is also not encountered in modern passenger-ships as this may lead' to a noticeable in-crease of resistance to translationary motion of the ship. The'ealculation amplitude for an acute bilge ship can be de-termined by analogy with the existing Standards in accordance with the formula

76),

₍₃₇₎

though such hull forms are rarely encountered in modern chant ships. The calculated amplitude of rolling of any mer-chant ship is determined by formulae (34),

(36)

and

(37)

and according to the graphs in Fig, 119 13 (or Tables 3, 4,

5).

1,0 and lower _

195

290

295 3,0-3,5

-490

and

more . .

0,98

0,93

0,77

1 0,69 --0465 . 1 0,62 0960

A-,

a S. The calculation results of roil

ampli-tudes and. reserve stability coeffi-, cients of the M.S.F. transport ships, in'accOrdance with the proposed met hods, and their analysis

As it followil

from the above-mentioned the proposed

method: of determining calculation. amplitudes contains a

number.of'conditionalities, which 'in

generall-are.ineVit-able in the'process'of

the stability standardization. There-fore -the fitness of this method for practical APlication _must be Checked

up by

_{a great number of roll and dynamic stability} 'calculations of the M.S.F. transport Ships both designed and

in'

service. Such calculations were 'madefor 26 types of pas-senger Ships and for 30 types of cargo ones, most of which are serial. Roll 'amplitudes were calculated for two Variants of loading; one-was.for the greatest amplitude, the other was

for the least stability reserve

_{cOefficient of a ship under}

the Standards in action. For the _{second Variant the stability} reserve coefficients were calculated as well

MG2s.

Nheee

-42-3 Fig 13 (38)

-43

While the amplitude calculations were aimed at evaluating the new interpretation of calculated roll intensity, the calcu-lations of reserve

stability

coefficient were made to prove the acceptability of the proposed calculation scheme for the stabi-lity standartization of the transport fleet as a whole.

- Calculation amplitudes of rolling on proposed method's

al-ways appear to be greater than in the active Standards. 1911le (if) in the active Standards the amplitudes were of 10-20°9 in the pro-posed methods they have increased up to

15-30°.

The direct

calcu-latian with the help of formula (6) of the Standards often re sults in amplitudes, less than 100 (such amplitudes were in 8

ships out of 56calculated)4 the proposed methods only in one case -("The Abehasia") resulted in the amplitude

air,

It mist be

ment-ioned that thie case is an exception. "The Abchasia" is a big pas-senger ship of the second category of sailing only; the ship has ratio --7.4>,3 untypical for modern passenger ships; she is

sup-blied

with large bilge keels. It is supposed that the increase of the calculated roll amplitudes in the limits mentioned proves the advisability of the proposed methods, since it brings the calcula-ted scheme of the Standards to the real conditions of sailing which are most dangerous with'regard to the dynamic stability, and, be-sides, in the process of designing, is the supplementary Stimulus for the improvement of ship's sea worthiness,

There arises a natural question whether this increase of the calculated amplitude will bring to excessive strictness of the Standards to great difficulties in fulfilling these requirements. Calculations of stability reserve coefficients for the worst case of ships loading give us the possibility to negatively answer this question, In fact, not standing the, reduction of the stability re-serve factor, its value. is still greater than 1,00 (Evidently only in the case of its valueL being greater than 1,00 according to the existing Standards). Cargopassenger ships _the steamship "Kulu" and the motorship "Smolqy" and cargo ships s/s type "Khasan" and die type "Dneproges" make an exception, "K" in all four cases being only a little less than 1900. It should be noted that all these ships have certain defects as regards stability. For instance s/s "Kulun built in. 1919, was later converted from a cargo ship into a. d'argo;-passenger ship,s/s"Kulu"has a capsizing angle(Reed's diagram) less than 60and doesn't meet additional requirements of the Stan-dards to the angle of heel from crowding of passengers and an

on gyration. The motorship "Smolny" built in 1929 has a sta-bility-reserve factor equal to 1,00, according to the exist-ing Standards, only in case of takexist-ing on board liquid ballast. The ships of series building type "Khasaa" don't meet the re-quirements of the existing Standards to the greatest arm of Redi's diagram. Finally, the ships of the "Dneproges" type' hardly meet this requirement. It should be noted that the

installation of bilge keels in the steamship "Kulu" and the

in-crease of bilge keels areaon the dieselelectric ship

"Dnepro-ges" from 1,46 to 3%

of LB

increase the stability reserve fac-tora of these ships to 1900.

The above mentioned confirms the acceptability of the pro-posed scheme for the determination of rolling amplitudes as it meets the requirements of Standards without prejudice to econo-mic and working qualities of modern carriers even if conditio-nal designed wind pressures are subjected to some small correct-ions.

Conclusions and recommendations

10, In this paper a new scheme for the determination of the calculated rolling amplitude of carriers in the Standards of Stability is exposed. This scheme is based on principles

es-sentially differing from those used in the existing Standards of Stability of the USSR Shipping Register.

2. The characteristics of rolling are determined in the statietde meaning, on the base of the spectral method of roll theory in irregular waves.

3.

The calculation scheme is worked out with the use of new theoretical and experimental data on hydromechanic para-meters of rolling, based on special series model tests of sea

cargo carriers.)

4.

The analysis and average results of roll calculations for ships withcharacteristic ratios of chief dimensions, block coefficients and natural

Oscillation

periods made it possible to get a simple final calculation scheme for the determination

Of roll amplitudes in the Standards of Stability. The use of this scheme in practice is bound &either with difficult cal-culations nor with any other difficulties.

The rolling amplitudes and stability reserve factors for passenger ships of 26 types Lind cargo ships of 30 types of M.S.F. (Ministry of Sea Fleet) calculated with the' help

of the proposed scheme proved the fitness of this scheme for stability standardizing.

The method of the determination of the conditional calculated rolling amplitude is given in

§§ 9-and

10 of the active Standards of Stability. The

Central-Scietific-Re-n

search Institute of Sea Fleet (Merchant Marine) and the Le-ningrad'Shipbuilding Institute workedout -anjanalogic

met-,

hodic for the calculation of rolling of fishing vessels and tugboats,

taking

into account particular forms of hull li-nes, load distribution and special features in service of ship's of these types. This methodic was made in order to replace completely

§§ 9

and 10 by new paragraphs, based an the proposed calculation. scheme.