Tank size and dynamic loads on bulkheads in tankers

DET NORSKE VERITAS

P. 0. BOX 82, OSLO

TANK SIZE AND DYNAMIC LOADS

ON BULKHEADS IN TANKERS

By

E. ABRAHAMSEN

REPRINTED FROM

TANK SIZE AND DYNAMIC LOADS

Introduction

The general tendency to build oil refineries in the oil consumption areas has resulted in a great

demand for very large ships which for the greater

part of their life carry crude oil to the refineries.

Improved storage facilities for refined oil products and vastly increased production and consumption rates have made it possible and usual to distribute refinery products as one grade cargoes in what is usually called «handy size» tankers, but which are quite often tankers of 32,000 t.dw.

From the point of view of tankers being built to accommodate many grades of oil products

simultaneously, it is obvious that only some

smal-ler tankers need have the fine subdivision

com-monly required to-day. For the majority of the

larger tankers other considerations than the

multi-grade cargoes must be deciding for the subdivision

requirements for tankers. Among such

considera-tions may be mentioned standing waves and

agitation in slack tanks, stability, flooding due to

collision or grounding, and structural strength.

These problems are

discussed here in greater

detail, and it is shown that from rational

considera-tions it should be possible to increase the tank size

in proportion to the increment in ship size. This means that substantial savings of steel weight,

piping and valves may be made for larger size

tankers in comparison with present practice. The necessity to consider in detail structural problems

resulting from the increased tank dimensions is emphasized.

Based on this discussion some proposed recom-mendations for the arrangement of cargo oil tanks

and the maximum distances between transverse

and longitudinal oil-tight bulkheads and wash

bulkheads are given in relation to ship dimensions.

1) _{Head of Research Department, Det norske Ventas,} Orlo, Norway.

ON BULKHEADS IN TANKERS

By E. Abrahamsen')

Flooding and Stability in Damaged Condition

The fine subdivision of conventional tankers

provides a very good safety margin for the vessels when they are subjected to collision or grounding causing flooding of compartments forward of the

engine room bulkhead. Flooding of the engine

room of conventional tankers may, however, prove

disastrous when the ship is in a fully loaded

con-dition.

When considering an increase in tank length,

the problem of loss of buoyancy due to bottom or side damage should be considered rationally. To

provide a background for such discussions, flooding

calculations vere carried out for a tanker with the

following characteristic dimensional ratios:

B/L 0.1440

D/L = 0.0724

d/L 0.0537

CB 0.800

L length between perpendiculars

B breadth mouded

d draught

and

CB block coefficient.

For the flooding calculation a computer

pro-gramme worked out by Ström-Tejsen [1] was used

and results obtained for the permeability factors

u. 0.2, 0.4, 0.6, 0.8 and 1.0. For _{0.2 the}

floodable lengths proved to be greater than the

ship length. Curves for floodable lengths with the other permeability factors are shown for the fully loaded ship with zero trim in Fig. 1.

The floodable lengths shown apply in principle

to flooding across the breadth of the ship. The curves may, however, also be interpreted as

flood-able lengths of an empty centre tank which has a

breadth ratio b'/B' corresponding to the

permea-bility factor p., or as simultaneous flooding of two

wing tanks with a breadth ration 2b'/B'. B' is

Fig. 2. Floodable lengths for ballasted tanker with flooding across the full breadth of the ship.

under consideration; b' is the mean breadth of

the centre tank; b' is the mean breadth of the

wing tank.

Fig. 2 shows the floodable lengths for the same ship in ballast condition with mean draught equal to 51 per cent of full draught, with zero trim and a trim aft corresponding to 0.0092 L respectively. The curves have been drawn for a permeability factor of 1.0 only. It is seen that the floodable

lengths for tankers in such a light ballast condition

constitute no great problem, even if penetration of the hull in the region of the forward engine-room bulkhead might lead to loss of the ship under very

unfavourable circumstances. For our considera-tions penetration of a fully loaded ship will be governing.

If a tanker in a fully loaded condition has empty wing tanks, the loss of buoyancy due to flooding

of such tanks will cause an angle of heel as well as sinkage.

Fig. S shows the angle of heel

in dependence of the length of the wing tank with

the breadth ratio of the wing tank b'/B' as a

parameter.

Fig. 1. Floodable lengths for loaded tanker, with width of centre tank as parameter.

ULL 4 30 'J) w w 20 a D 10 20 30 40

LENGTH 0F DAMAGED REGION OF SIDE

TANKS IN PERCENT OF

Fig. 3. Listing angle of a tanker in relation to the damaged length and the breadth of wing tanks.

If the wing tanks are full of cargo oil, the

per-meability factor for such tanks will

not be far

from zero so that flooding of wing tanks in such

cases will affect draught, trim and heel to a small

extent only. This means that from the point of

view of flooding, centre tanks only should be kept

empty when the full capacity of all cargo tanks

is not needed. Such loading may cause rather high

tension loads on the cross tie, web and stiffener connections in the wing tanks outside the empty

centre tanks, but these structural parts are designed to take such loads in general.

If a tanker is to sail with empty wing tanks, the

heeling caused by possible flooding on one side would probably be counteracted by flooding the

intact wing tank on the opposite side. The reason

for this is that the loss of freeboard due to the heeling caused by unsymmetrical buoyancy, might.

as may be deduced from Figs. i and 3, be nearly

as great as the sinkage caused by symmetrical flooding. If two empty wing tanks are required on each side when the tanker is fully loaded, it

would be wise to keep one full wing tank between

the empty ones.

The general remarks about the loading of wing tanks are also applicable in the case of ballast, but

the great reserve buoyancy may make special

precautions of this type less necessary unless the

tank lengths are increased beyond normal practice.

To maintain the inherent safety of the tanker, which is a result

of the fine subdivision and

excellent means of closing deck openings in such

vessels, a requirement should be that any two

tanks within the cargo tank area can be punctured when the permeability factor is 1.0 without

caus-ing the ship to sink. If the punctured tanks are

bio i

0.20-

/

-0.30

0.25)b

0.40-DEC 0.57 AT WATER K E DGE LEVET

a

a

-.

loo n z 's 75 'f) u, Ui 550 o F-(n u .5 25 Ui C-) (n û-2 L,J u .5 .5 1.5 ° z o (n o 1.0 ° S u- >- F-0,5 n o Ui > Ui

Fig. 4. Relative distribution of collision damage along the length of ships, according to Comstock [2].

wing tanks it should also be possible to flood the corresponding wing tanks on the opposite side to compensate for undue list without causing loss of

the ship. These requirements may seem rather strict but, as can be seen from Fig. 1, they are

easily fulfilled with a much smaller set of

subdivid-ing bulkheads than is normal practice today.

When considering the question of floodable length,

the type of damage which a ship can

sustain is of considerable importance. Firstly, it is

interesting to note that for the engine-room area

of a tanker which from the flooding point of view

is most vulnerable, there seems to be less likelihood

of damage due to collision and grounding than for other parts of the ship. This is clearly reflected in

Fig. 4 which shows the distribution of damage

over the ship's length according to Comstock and Robertson [2]. The same authors have also made

a statistical investigation

of damage length and

damage penetration, the results of which are given in Fig. 5.

Considering that the data have been collected

from about 60 collisions between all types of larger

ships, Fig. 5 gives interesting information about

the probable damage due to collisions. It is seen that the median damage length in the material

investigated is 8.0 metres, and the probability that

the damage length will exceed 16.0 metres is about

10 per cent.

The median penetration is 80 per cent of the ship's breadth, with 10 per cent probability that the penetration depth

will be half the

ship's

breadth. Even if penetration depth and damage

length are to a certain extent connected, the

pro-bability that there will be large values for both is much less than the separate probabilities. It

might be added that the investigations described

100 .5 r 60 C-u, 70 (I) 60 50 o I-40 30 .5 20 Ui lo LU o-o

(A) LENGTH OF COLLISION DAMAGE

lO 20 30 40 50M

in [2] mainly cover collisions in American waters and that the findings are not necessarily

represen-tative for the rest of the world.

Owing to the real possibility of collision damage

to a loaded tanker in general leading to flooding

of compartments with a permeability factor close

to zero, it seems that the subdivision of a tanker

such that any two compartments except the engine room may be flooded in the loaded condition will make the tanker an inherently safer ship than other

types of cargo ships.

In the ballast condition

tankers are even safer than in the loaded condition,

especially when the side tanks or every other side tank are used for ballast.

It will be seen from Fig. 1 that a subdivision

factor of 0.5 may be maintained for conventional tankers with tank lengths i given approximately by

the following formulas: For centre tank:

B'

= (0.1 L - 0.2 x)

b'

For wing tanks:

B'

i

(0.1 L - 0.2 x)

where:

x the distance between the half length of

the ship and the centre of gravity of the tank considered. x should not be taken larger than 0.25 L.

-Ship motions

As mentioned in the introduction, the agitation period in tanks should be considered in relation to the period and the amplitude of the ship motions.

A.P 90 80 70 60 50 40 30 20 10 FP

DISTANCE FROM FP PERCENT OF L

(B) PENETRATION DEPTH/ SHIP BREADTH

Fig. 5. Damage length and penetration depth in collisions, according to Comstock [2].

Of the six possible ship motion components we limit ourselves to considering three or four, viz.

rolling, pitching, surging and possibly heaving. With k as the radius of gyration of mass of the

ship plus entrained water about a longitudinal axis through G, the centre of gravity, and GMT

as the metacentric height, the rolling period T r of the ship in still water is:

27rk

Tr =

(1)

g GMT

In this expression g is the gravity constant. If the ship is subjected to an atwarthships wave train of the same period, synchronous rolling will

occur. The rolling amplitude may in such cases be large, dependent on the amount of damping afforded by bilge keels and appendages, wave generation and friction,

and especially on the

magnitude of the metacentric height. The response of the ship to the various wave components in an

irregular

sea may be described by frequency

response functions.

For a range of loaded tankers which we have

investigated, we found that k varied between 0.34 B and 0.38 B, GMT between 0.10 B and 0.17 B, where B is the ship's moulded breadth. If we use

mean values for k and GMT. formula

(1) for

loaded tankers with B in meters reduces to:

Tr 1.91/B seconds. (2)

For light ballast conditions corresponding to a mean draught of 50 per cent of full draught GMT may be in the range 0.2 B to 0.3 B, whilst k may

have a much wider range than indicated above,

dependent on whether ballast is carried in centre-tanks, in wing tanks or both. If we again use mean values for ballasted tankers, we obtain:

Tr 1.41/B seconds. (3)

Rolling periods much less than given by (3) may

be encountered under unfavourable ballasting and

wave conditions.

Pitching motions of the ship are usually cross-coupled with heaving motions due to the lack of symmetry about the centre of flotation. The

corn-hined motions may give the ship an apparent

pitching axis which is a considerable distance from

amidships, usually well aft of the midship point.

The natural pitching period of a ship may be

expressed by:

T = 2

GML

1/SL' +w)

(4) where JL is the mass moment of inertia of the

ship about a transverse axis, GML is the

longitu-o

dinal metacentric height of the ship, w is

the lumped entrained water coefficient, and ¿ is the

displacement of the ship.

For ships of the tanker type which vary little

in arrangement and form with size, we may write

approximately for the longitudinal metacentric

height CML:

L3B CJL L2

GML - CJL = _d (5)

where L is the ship length, d is the draught. CB is the block coefficient and CJL is the coefficient of waterplane moment of inertia. For tankers CJL

0.059.

Further we have approximately according to

Vedeler [3]:

B

(1+w)

(0.6+0.36)

and

JL kL2L2L\ (6)

where kL is the radius of gyration of mass about a transverse axis, through the gravity centre of the

ship with entrained water. For tankers k_L varies

between 0.20 and 0.26 dependent on the load

condition. If we assume CB 0.78, B = 0.143 L,

loaded draugth d 0.0525 L and mean ballast

draught d = 0.03 L we have approximately: Loaded condition: T

_2.lkL\/L

Ballast condition: T 1.95kLVL

For a ballasted tanker kL will usually be some-what larger than for a loaded ship. A reasonable average for our purpose would be to put T O.45VL.

Iii regular waves the ship will pitch in the

ap-parent period of the waves. In irregular waves the

ship will be more strongly excited by the wave

components having a period at or near the natural

pitching periods of the ship than by the other

components. provided that a reasonable amount of the spectrum energy is concentrated near the

natural pitching period of the ship. The response of the ship to the various wave components may be described by frequency response functions.

Investigations by Cartwright et al [10] and

others, for example, show the frequency response

functions for pitching to be rather broad, such that a broad frequency spectrum for the pitching

motion is also obtained in irregular seas. In rolling the frequency response function is comparatively

narrow such that a narrow rolling spectrum may

be expected for a ship in irregular waves.

The angular amplitudes in rolling and in

-J o >-o_z w D o U)

zq

- *! cc z1 -Jo -J z 0< 400. U) o w 300 o, w 200 o D -J Q. 100 B o o 4 2 03 0,6 FREQUENCY 0F ENCOUNTER, A o 0 20 CUMULATIVE 40 60 PERCENTAGE

with the three-dimensional wave spectrum

experi-enced by the ship at any time. To get an idea of the relative magnitudes of the angular motion in

roll and pitch one may compare the pitch

fre-quency-amplitude spectrum for a ship in a fully

developed two-dimensional Neumann-spectrum

with a direction 1800 to the ship's course with the

roll frequency-amp]itude spectrum for the same

ship in the same sea, but with a course 90° to the direction of the wave spectrum. Results from such

an investigation are shown in Fig. 6 for two

dif-ferent tankers in a fully developed Neumann

wave spectrum corrcsponding to 40 knots wind velocity. The relevant data for this investigation

are given in Fig. 6 and are believed to be average figures for modern tankers.

The pitching periods corresponds to natural frequencies of 0.90 for ship A and 0.75 for ship B. In rolling the natural frequencies are

0.61 for Ship A ando, 0.51 for ship B. Even if the rolling amplitude may change con-siderably within the limits of variation of the

me-tacentric height and the damping created by

dif-ferent ships, the general tendency will be as indi-cated in Fig. 6.

The heaving motions of a ship are of less

im-20 o w U) o 15 "L 10 u, o D F- Q--e = O

F-

L-I"

1

SEAWAY: FULLY DVELOPED NEUMANN SPECTRUM, 40 KNOTS SPEED

ROLLING IN BEAM SEAS. PITCI-IING IN HEAD SEAS

portance in connection with surging effects in

tanks, even if they help to augment vertical acce-leration forces in the tanks, especially in the for-ward part of the ship.

Not much information is

obtainable on the

surging motion. It seems that this type of motion

is mainly created by the orbital motions in the

passing waves and by the repeated transformation

of part of the kinetic energy to potential energy as the ship moves from wave troughs to wave

crests. Also the surging is coupled with the heave

and pitch motions. The surging period is gene-rally given more or less by the period of wave encounter. The longitudinal accelerations are, however, generally rather small and of such an

irregular nature that they will usually not build up and maintain a strong standing wave system

in liquid tanks.

Measured values for the surging of a T-2 tanker

model in regular waves indicate a maximum

surg-ing acceleration of 0.05 g in a wave height H

L/30, wave lengths À ranging from 0.75 L to

7.25 L and with speeds varying from O to 16 knots

for the full scale ship. This result agrees well with values given by Denis & Weinblum [9].

SHIP SI-lIP A TP TR V (PITCHING) 217,9 M 66000 TONS 8,35 SEC 12,25 SEC 9,5 KNOTS 153,3 M 22000 TONS 7,00 SEC 10,30 SEC 8,0 KNOTS

Fig. 6. Roll and pitch spectra for two different ships in a fully developed sea corresponding to 40 knots wind speed.

O 03 0,6 0,9 1,2

FREQUENCY OF ENCOUNTER, WE 1/SEC

1,2

09

WE 1/SEC

100 BO

IEASURING CELL

Fig. 7. Arrangement of test set-up.

Fluid Motions in Tanks

If a tank with a free liquid surface is subjected to periodical motions the acceleration of the fluid

particles will create a wave system on the free

liquid surface. Standing waves with considerable amplitudes will build up when the natural periods of oscillation of the fluid happen to coincide with

the period of one or more of the harmonic com-ponents of the tank motions. The standing wave

frequencies will depend on the shape of the tank

and of the free surface and on the distance

between the free surface and the bottom of the tank. The amplitude of the standing waves will

depend on the magnitude of the disturbing force

(the tank motions) and on the fluid damping. At greater amplitudes the free surface will break

down such that non-linear effects are introduced. The natural period of the fluid oscillations in a

rectangular tank may, according to the linear

theory (see Lamb [4]), be expressed by:

1l

1

T-27T 'n7rg

_nrh

(7) tank

i

where,

t the period of oscillations in seconds

n an integer 1, 2, 3

. .

the gravity constant (m/sek2) the length of the tank (m)

h = the depth of the liquid (m)

Now if h is of the same order of magnitude as

/, the period t may be approximately expressed by:

T= 1.13

If the rectangular tank is part of a ship which rolls

or pitches freely such that the periods of rolling Tr or pitching T

are the same as

the natural period of oscillation T, resonant fluid motions

will usually be generated in the tank. According 8

to Yoshiki et al. [5] the fluid motions at the

reso-nance point are

supressed when the

vertical

distance e between the liquid

surface and the

centre of rolling is:

c

g T21/4r

(8)

Further resonance may occur when Tr

2 T,

provided that n is an even number. Our investiga-tions show that it is difficult

to build up heavy

resonant motions when Tr 2T11.

When the ship is heaving and pitching,

the

tanks, especially those positioned away from the apparent pitching axis, will experience both ver-tical and horizontal translations and simultaneous

angular oscillations. In such cases violent fluid

oscillations will result when the pitching period

Tp approaches the standing wave frequency T in

the rectangular tank. Resonant conditions may also

occur when T = 2 T11 provided that n is an odd number, but again the build-up is not so serious as at the fundamental resonance point with T =

T1

In order to verify the theoretical findings and

also to establish figures for the pressure build-up

at bulkheads and tank top. Det norske Ventas

initiated in 1958 a set of experiments on an oscil-lating rectangular tank with dimensions 800 mm

>< 600 mm X 700 mm. The experimental set-up is

shown in Fig. 7. Mainly due to the limited length

of the connecting rod drive the tank oscillations were not strictly sinusoidal, but the deviations

were according to our acelerometer readings not significant.

Fluid pressures were recorded with membrane pressure cells positioned on the tank walls as

indi-cated in Fig. 7. The membranes of the pressure cells which operated with bonded strain gauge

transducers had a natural frequency of more than

4000 sec' such that

the dynamical calibration

factor of the cells was practically 1.0.

As indicated in Fig. 7 the tank was tested with

three different axes of rotation, and the liquid

height h as well as the angular deflections a of the

tank were varied systematically.

Fig. 8 indicates the good correlation found

between the observed standing wave periods T1

and the calculated values. The small systematic

discrepancies may be due to the afore-meritioned

deviations from the true sinusoidal motions as well as to the non-linear effects encountered under resonant conditions.

In Fig. 9 the pressure build up SP/y h at the

position of the bottom pressure cell (No. 4) is shown in dependence of the liquid height - tank length ratio h/i and the period of oscillation of

C 10 .9 .8 7 s 4 .30 .20 .10 00 _{10 20 0}

Fig. 10. Maximum dynamical pressures on the pressure cells in dependence of the liquid depth.

4 £ 2i-68B j1/ I

..O

3í.0.250 3.7.0125

..

POINTS MEASURED

- Yr2/anh(Á)

íìI

Irr

'-I

Ah

h

F

2.0 4. 80 10.0 12.0

Fig. 9. Pressure increment at bottom of tank due to

reso-nant agitation in tank when the angular motions is

_{± 5.}

reduction in dynamical pressure obtained when

the tank is nearly full or when the angular ampli-tude of oscillation is so great that wave resonance

build-up is prevented by the tank top. With

a

rolling or pitching angle of 7,50 which is

reason-able and often experienced at sea, tanks which are

between 70 per cent and 90 per cent full will suf-fer from great resonance forces on the bulkhead

tops. Deck girders, transverses and stiffeners will, however, help to alleviate the resonance build-up

when the liquid level is approaching 90 per cent of the tank height.

0,5 1.0 1,5

Fig. 8. Standing wave periods according to theory and

experiments.

the tank expressed by the

dimensionless ratio

T/Vl/g. In the above expressions

P is the

ad-ditional pressure due to dynamical effects, and y

is the specific weight of the water. We notice that the dynamic pressure build-up in this case seems

to be more or less independent of the liquid depth,

provided that the wave surface is free. We see

that the dynamic pressure peaks at the bottom

are about three times the static amplitude in these

cases when the angular deflection a

_{is ± 5.0}

degrees. The resonance peaks found theoretically

for T = 2T2

are only slightly visible for the smaller liquid depths.

The arrows above the resonance peaks indicate the positions of the theoretical resonance period for the three liquid depths.

The high dynamical pressures obtained in

oscil-lating liquid tanks are mainly restricted to the

regions near the liquid surface. This is clearly demonstrated in Fig. 10 which shows the

maxi-mum pressures measured on the cells in

depend-ence of the liquid depth. This point is amplified

by Fig. 11 which shows measured values for the

dynamical pressure .P/y. h as a function of the

vertical position in the tank and of the rolling or

pitching angle a.

Attention should be drawn to the considerable

1. 3.0 2.0 1.0 6,0 5,0 4,0 3,0 2.0 1,0 o

ay

Fig. 11. Maximum dynamical pressure on the tank wall

for the liquid depth indicated and for 4 different angular oscillation amplitudes.

As is evident from Fig. 8 the standing wave

period is radically increased when the liquid depth becomes small compared with the tank length. It is thus obvious that the liquid in very slack tanks

may come in resonance with the ship motions. Since the lower parts of the tank boundaries are designed to stand up to very high static pressure which is not present when the tanks are very

slack, damage is not likely

to occur unless the

same tanks are repeatedly subjected to this type

of dynamic loading.

The damping of the motions in liquids is

strongly dependent on the viscosity of the liquids.

The dynamic pressure generated in a tank with crude oil will be less than that generated with

water ballast under the same conditions, provided

that also the specific gravity is the same in both cases.

The influence of wash bulkheads was

investi-gated with cut-out areas corresponding to 3.5, 15

and 32.5 per cent of the bulkhead area and

inserted mid-way along the tank. Even with the

largest cut-out area of 32.5 per cent the wash

bulkhead proved to be an efficient reflection

bar-lo

rier for the standing waves such that the resonant

period was reduced corresponding to the reduc-tion in i which may be taken as the distance be-tween the end bulkhead and the wash bulkhead

in these cases.

Partial bulkheads with heights 150 mm and 250 mm protruding from the tank top half way along the tank proved efficient in destroying

re-sonance build up in all cases when the liquid level

was higher than the lower edge of

the partial

bulkhead. Even with small immersions, the partial bulkhead acted as an effective wave reflection

barrier.

In many ships other shapes than the rectangular tanks are used to carry liquids, for instance stand-ing and horizontal cylinders, spheres etc. When

tanks with such shapes become large enough,

resonance between the fluid motions and the ship motions may create large sloshing effects,

depen-dent on the specific gravity and the viscosity of

the fluid carried.

In rocketry the dynamic effects of liquid fuel

motions may cause grave stabilizing problems, for

which reason fluid motions in many types of oddly

shaped tanks have been investigated. Reference

is made to the works of Bauer [6], Abramson [7]

and McCarthy [8]. The curves in Fig. 12 give

mean values of experimental results for the two

lowest frequencies of the fluid motions in the type

of tank indicated on the figure. Resonances of

large tanks of such shapes should be checked

against the periods of ship motions in all cases

when free surface effects are expected for short or prolonged periods when the ship is at sea.

The standing wave period is not dependent on the specific gravity of the liquid. The dynamic

pressure resulting from the standing waves is, however, proportional to the specific gravity. If

standing wave resonance is created, the dynamic

pressure may reach high and unwanted levels,

even if the specific gravity is 0.42 as for liquefied

methane. It is therefore recommended that tanks

for liquefied hydrocarbons should not be built so

that standing wave resonance with the ship

mo-tion may occur.

Since the natural pitching period is proportional

to the square root of the ship length L and the

standing wave period in rectangular tanks is pro-portional to the square root of the free tank length i, it follows that the permissible free tank length i

may increase in

direct proportion to the

ship

length L, without dangerous resonant conditions

occurring.

When estimating how close to the pitching H

:!'

H H H H 1.00 .90 .80 70 60 50 .40 30 .20 .10

0.7 o 0. o 0.4 ori 0.3 0.2 0.1 o h/R

STANDING CYLINDRICAL TANKS

02 0.4 0.6 08 1.0

'2R

HORIZONTAL _{CYLINDRICAL TANKS} WITH _{LONGITUDINAL WAVES}

Fig. 12. Standing wave periods of the first and second order for different tank shapes.

period T we may allow the fundamental standing

wave period in a fluid tank to be, we may make use of many hundreds ship-years _{of successfull} experience with tankers of about 150 metres in

length and free tank lengths of about 11.0 to 12.0 metres. These figures give T(fl1)/Tp 0.68 0.71, and it seems safe to allow free rectangular

tank lengths of 1 0.075 L to 0.08 L when the

tank is reasonably deep, say h _ 0.5 i.

As we have seen above, the fundamental

stand-ing wave period is drastically reduced when the liquid depth is small, or when the tanks have a

spherical or a cylindrical shape. In such cases one

on 0.6 1.4 1.2 1.0 0.8 0.4 0.2 0 o - In

2Tr6n\/'

n=2 02 04 0.6 08 1.0

HORIZONTAL CYLINDRICAL TANKS WITH _{TRANSVERSE WAVES}

02 04 06 08 10

h/2R

SPHERICAL TANKS

should calculate T and T on basis of the mf

or-mation available and keep the ratio T/T

0.70.

According to Fig. 6 the average amplitude in

pitching with a period which is 0.7 of the resonant period under the conditions shown, i. e. for WE = 1.29 for A and c0E = 1.07 for B, will be quite negligible. Even if the longitudinal motions of a

ship in pitching, heaving and surging _aggravate conditions leading to longitudinal agitation in

tanks, the breadth of tanks should be kept so small

that rolling angles at the natural period of the

atwarthships fluid agitation in the tanks do not

0.2 0.4 0.6 08 1.0

1r2_

Tn2TTón,J tanhh,.Er

rn

3.81 _{FOR n1}

-7.02 FOR rir2 -

_26nftarhflh

0.5 0.4 0.3 02 01 0

SECTION 4-A SEC ION B-5 Fig. 13. Proposed arrangement of wash bulkhead designed

to carry large vertical and horizontal reaction forces.

materially exceed the small pitching angles ob-tained at the frequencies above.

It seems, however, that a ratio between the

atwarthships sloshing period and the natural

rolling period Tn/Tr = 0.6 would be reasonable.

This corresponds to 04E 1.01 for ship A,ÛE =

0.85 for ship B. The distribution of roll amplitudes

to be expected in a 40 knots fully developed sea with frequencies in the range oJE = 0.96 - 1.06

for ship A and oSE 0.80 - 0.90 for ship B are

given in Fig. 6. It is seen that a mean rolling angle

of about ± 1.3° is obtained for both ships within the frequency range indicated. Since the ballast condition must be taken into account, Tn/Tr

0.6 means according to (3),

that the

free tank

breadth should not be more than about 60 per

cent of the ship breadth, provided that free

sur-face effects in tanks cannot be avoided.

It should be added that the above treatment is

an approximation. Actually data of the type given in Fig. 9 should be treated as frequency response

spectra together with the input data which are

the pitch and roll spectra for the ship in question.

Fig. 9

indicates, however, that the frequency

response function for reasonable liquid depths will

be comparatively narrow, and that the agitation

energy spectrum with the ratios T/T and

T/

Tr chosen will be moderate. Further work onthis

point has been initiated.

Structural considerations

From the point of view of flooding and of

dyna-mic effects from liquids, tank lengths may be

increased beyond present practice in larger

tankers, especially when efficient wash bulkheads are fitted. It is a question whether such deviations from current practice may be made so that a

say-12

ing in weight can be effected without undue risk

of fractures occurring.

Firstly,

the design of the primary structural

members in the bottom of such large tanks should

be mentioned. Instead of building up the bottom girder system with a high central girder as the

backbone, it will be more efficient to have several longitudinal girders of almost the same scantlings and a set of transverses attached to the

longitudi-nal girders to form an efficient grid system. The

distribution of stiffness in both directions should

be made from optimum weight considerations

within the limits set by the permissible stresses in this part of the ship structure.

A structurally efficient grid system should have

a length and breadth which are nearly equal. If

full advantage is taken of the upper limit of com-municating tank lengths, it will pay to design the transverse wash bulkheads as effective boundary supports for the bottom and deck girder systems. Such wash bulkheads will have to sustain rather large dynamical forces of a repetitive nature. The high stress low cycle fatigue aspect therefore has to be considered in the design of wash bulkheads as well as in the design of ordinary bulkheads.

Since the static head on wash bulkheads is small, the strength of a wash bulkhead structure

need not increase towards the bottom of the ship

as has been the practice up to the present time.

On the contrary, it is the free surface effects which have to be considered, and these have a maximum near the top of the tanks as shown by our experiments. From Fig. 11 we find that for the fluid level giving the highest dynamic pres-. sures in the tank, an angular roll or pitch of 7.5°

in synchronism with the fluid motions will produce

dynamic pressures on the upper part of the bulk-head between 5 and 15 times the change in static

pressure on the bulkhead due to the same angle

of inclination. This means a dynamic pressure head

corresponding to from one third to the full length of the tank at resonance.

Since free surface resonances will usually be

avoided, a design pressure head for the upper third

of the bulkhead corresponding to one half of the free tank length i seems to be reasonable. The

previously applied static head for wash bulkheads corresponding to half the head for oil-tight

bulk-heads could reasonably be substituted by a con-stant static head corresponding to one half the

total static head on the bulkhead. Further

investi-gations are needed, however, in order to clarify

this matter more fully.

In any case, it is essential to take the dynamic

000± COOCO

I

Û 0 j?0 _O

SS4

s

type of loading on the wash bulkheads into account

and design all details very carefully. A general increase in tank lengths will also lead to a higher rate of occasional heavy liquid blows on both oil-tight bulkheads and wash bulkheads and thus

in-crease the tendency for cracks to occur at hard

Strøm-Tejsen, J.: «Damage Stability Calculation

by the Computer Dask». Danish Shipbuilders Computing Office, June 1960.

Comstock, J. and Robertson, J. B.: «Survival of

Collision Damage Versus the 1960 Convention on Safety of Life at Sea'>. Trans. Soc. of Nay. Arch. & Mar. Eng., New York, 1961, advance copy. Vedeler, G.: «Sea going Qualities of Ships». Sixth

International Conference of Ship Tank

Superin-tenderts, Washington, 1951, p. 162.

Lamb, H.: «Hydrodynamics». Dover Publications, New York, Sixth Edition, p. 363.

Yoshiki, M. and Hagiwara, K.: «Experiments on Dynamical Pressure in Cargo Oil Tanks due to Ship Motions». Trans. Soc. Nay. Arch. of Japan,

1961, advanced copy.

REFERENCES:

spots and unsuitable details.

In Fig. 13 a wash bulkhead transversing the

centre tank is outlined. This type of bulkhead will

provide efficient support for the longitudinal girders and simultaneously make a reasonable flow

of water through the bulkhead possible.

Bauer, H. F.: «Fluid Oscillations in a Circular

Cylindrical Tank». Report, No. DA-TR-1-58, Dcv.

Operations Div., Army Ballistic Missile Agency

(Redstone Arsenal, Ala.), April 1958.

Abramson, H. N., and Ransleben, G. E.: «Simulation of Fuel Sloshing Characteristics in Missile Tanks by Use of Small Models», Tech.

Rep. No. 3, (Contract DA-23-072-ORD-1251),

Southwest Res. Inst., March, 1959.

[81 McCarthy, J. L.: _{«Investigation of the Natural} Frequencies of Fluids in Spherical and

Cylindri-cal Tanks», NASA TN D-252, May, 1960. Weinbium, G. and St. Denis, M.: «On the Motions

of Ships at Sea'>. Trans. Soc. of Nay. Arch. &

Mar. Eng., 1950, Vol. 58, p. 184.

Cartwright, D. E. and Rydill, L. J.: «The Rolling and Pitching of a Ship at Sea>'. Trans. R.I.N.A.,