In de eerste heift van 1966 werden door het Scheepsstudie-centrum een tweetal rapporten gepubliceerd, waarin de
grondsiagen van twee typen slingerdempende tanks, respec-tievelijk de U-tank en de vrije oppervlakte tank, behandeld werden.
In deze rapporten, no. 81 S en no. 83 5, werden een aantal aannamen ingevoerd, waarvan het wenselijk leek deze nader te verifiëren door middel van modeiproeven.
Deze verificatie is gekoppeld aan een onderzoek dat tot doel had de werking van de twee typen slingerdempende tanks te vergelijken.
Hiertoe is een model van een schip dat een vrachtschip representeerde in een aantal beladingstoestanden beproefd met een uitvoering van elk van de twee genoemde typen tanks die voor dit schip ontworpen waren.
Het scheepsmodel werd aan het slingeren gebracht, zowel door een oscillator als door dwarsinkomende regelmatige en onregelmatige golven. Behalve voor een onderlinge verge-lijking van de twee tanktypen zijn de verkregen resultaten gebruikt voor een vergelijking met de voor beide tanks door berekening verkregen prognoses van het gedrag; dit be-tekent voor de onregelmatige golven dus ook een verificatie van het superpositiebeginsel.
Ook werd een indruk verkregen omtrent de invloed van het verzetten op het gedrag van een schip met tank.
Een aparte beschouwing is in djt rapport nog gewijd aan het bepalen van de waarschijnlijkheid dat een schip een zekere slingerhoek zal overschrijden, dit met betrekking tot het gekozen spectrum van een onregelmatige zee.
Het blijkt uit dit onderzoek dat de beide tanktypen als middel tot het reduceren van scheepsslingeringen goed
voldoen.
Tevens kan geconstateerd worden dat de toegepaste be-rekeningsmethode, zeker voor zuiver slingeren, goede
resul-taten oplevert.
De invloed van verzetten verdient nog nadere aandacht. Uit het feit dat voor de beide, voor dit onderzoek ont-worpen tanks, al weer verbeteringen aangegeven worden, blijkt dat de ontwikkeling nog niet afgesloten is. Verder onderzoek is dan ook reeds gaande.
Gaarne willen wij hierbij vermelden, dat het hier gepre-senteerde onderzoek tot stand kwam met medewerking van
acht grote rederijen.
In the early part of the year 1966 two reports have been published by the Netherlands Ship Research Centre, in which the principles were treated of two different types of roll-damping tanks,
a U-tank and a free surface tank
respectively.In these reports, no. 81 S and no. 83 5, a few assumptions had to be adopted, of which it seemed to be necessary to verify them by means of model tests.
This verification could be combined with an investigation
to compare the two types of roll-damping tanks. With
this in mind a ship model, representing a cargo ship, was tested in several loading conditions; the two roll-damping tanks, especially designed for this ship, could be built in. The rolling of the ship model was achieved both by using a mechanical excitator and by the action of regular and irregular beam seas.l'he data obtained in this way were used for comparison of the two tank types, but moreover the results were very valuable to compare the motions themselves with the cal-culated prognosis for the behaviour of both tanks; for the irregular waves this means also a verification of the
prin-ciple of superposition.
Of the influence of swaying on the behaviour of a ship fitted out with a tank an impression could be obtained as well.
A further consideration is given in this report to the
determination of the probability that a ship will surpass a certain roll angle in relation with a chosen spectrum rep-resenting an irregular seaway.Following this investigation it appears that both types of tanks give good results in reducing the roll movements of
the ship. Moreover, it can be stated that the developed compu-tational method gives good results, particularly for the pure rolling motion. The phenomena of the influence of swaying deserves closer attention.
It appears that a further development in this field can be expected, looking to the improvements that could be given for both types of tanks.
Further research is already in progress.
Finally the support received from eight important Dutch shipping companies, is gratefully acknowledged.
page
Summary
71
Introduction
72
Model and ship data
72.1 General 7
2.2 Service conditions 8
3 The tank designs
83.1 The U-tank 8
3.2 The free surface tank 9
3.3 Comparison of some particulars of both tanks 10
4 Experiments and results
104.1 Summary of experiments 10
4.2 Results of oscillation tests 10
4.3 Experiments in beam waves 14
4.4 Further consideration of the roll reduction 16
5 On the possible influence of bilge keels
176 Conclusions 18
7
Suggestions for further research
188 Acknowledgement
18B Breadth of ship
D Depth of ship
G Ship's centre of gravity GM Metacentric height
19, Virtual mass moment of inertia with respect to the rolling axis
K General moment producing roll.
K0 Amplitude of rolling moment produced by an oscillator K Rolling moment due to waves
KG Height of ship's centre of gravity above the keel Length between perpendiculars
N9, Damping coefficient against rolling
P Probability that Pa exceeds a given value rpm
R9, Restoring coefficient
S9,(w) Spectral density of rolling motion S(w) Spectral density of wave amplitude
SkC(w) Spectral density of wave slope
T Draught of ship
Tmax Maximum draught of ship
221kg,
-
Natural rolling period g GMU Wind speed
b Breadth of free surface tank measured athwartships
f(9'a) Probability distribution
g Acceleration of gravity
h Height of connecting duct of U-tank
h Water depth in free surface tank at rest
221
k =
Wave number(k1
Significant wave slope1c5, Transverse radius of gyration
n0 Variance of the function rp(t)
s Distance between the centre of gravity of the ship and the bottom of the tank
w Length of connecting duct of the U-tank
w1 Width at bottom of a reservoir of the U-tank
x Height of the reservoirs of the U-tank
y Average fluid depth in the reservoir of the U-tank
a Model scale
= kC, Maximum wave slope at the surface Block coefficient
Weight of displacement
V Volume of displacement
Vmax Maximum volume of displacement
Phase angle between the wave moment and the rolling motion Phase angle between the tank moment and the rolling motion Wave amplitude
Significant wave amplitude
A Wave length
Ng,
=
Non-dimensional roll damping coefficientV IpRg,
vg,(w) Frequency dependent part of v9,
Mass density Roll angle Roll amplitude
Significant roll amplitude Limiting roll amplitude Static angle of heel
Angle between bottom of U-tank and a plane through the middle of the fluid surfaces in both reservoirs
Circular frequency Vg. GM
-
Natural roll frequency of shipON THE EFFICACY OF TWO DIFFERENT
ROLL-DAMPING TANKS *)
by
Jr. J. BOOTSMA and Ir. J. J. VAN DEN BOSCH
Summar,y
Two roll-damping tanks of different type were designed for the same application. One was a U-tank and the other a rectan-gular tank with a free surface. A ship model equipped with these tanks was subjected to a series of rolling tests, viz, by os-cillating the floating model mechanically and by letting the model free to move in beam seas.
The results show the performance of the two tanks and allow some conclusions to be drawn about the relative merits under the given conditions.
1
Introduction
Lately two reports were published by the
Nether-lands Ship Research Centre, on the action of
roll-damping tanks [1, 2]. The first of these papers
re-ported on an elaborate study by STIGTER on the
behaviour of the U-tanks, as originated by FRAHM
[3]. The second paper, by VAN DEN BoscH and
VUGT5 contained results of systematic experiments
on the performance of the free surface tank,
in-vented by WATTS [4, 5].
The U-tank consists of two reservoirs connected
by a duct. The reservoirs are partly filled with a
fluid, e.g. water. When the ship rolls, the water
oscillates in this U-tube. Under the influence of wall
friction and in- and outlet losses a phase difference
between the motion of the ship and the motion of
the water mass is created. If the ship rolls, the
moving water mass produces an alternating
mo-ment on the ship which tends to damp the
rolling
motion.
The free surface tank in its most simple
rectan-gular form acts differently. The damping of the
water motion is caused by the formation of a bore.
The velocity of this wave is determined by the
water depth and the height of the bore.
The object of the investigation was to compare
the efficiency of both types of tank, designed for
the same set of conditions. These conditions were
formulated so that they represented quite ordinary
circumstances, yet provided enough latitude to
judge the influence of a wide range of service
con-ditions.
When formulating the equation of motion of the
ship, both authors introduced a number of
assump-tions, of which perhaps the most far reaching was
the restriction that only the pure rolling motion
was observed while other motions were
neglected.
*) Publication no. 29 of the Shipbuilding Laboratory of
the Technological University at Deift.
A secondary aim of the experiments was to check
the validity of these assumptions.
It should be emphasized from the beginning
that the results of this comparison should be
inter-preted critically. Each case will present its own
difficulties. Often the choice of the type will be
influenced or even completely governed by the
available space or weight. Or the frequency range
which is considered here will be unnecessarily
large for other applications.
Another difficulty is the choice of the capacity
of the tank. Within certain limits a large tank will
act better than a small one, but will its better
ef-ficiency counterbalance the greater loss of
dead-weight?
In this investigation the available space for each
tank was a part approximately amidships,
extend-ing over the full section, with a length of 5 m.
Only one tank should be projected within this
space.
2
Model and ship data
2.1 General
For the experiments a model of the Series-60 with
a block coefficient
= 0.70 was selected. The
model, with a length of about 3 m was available.
To give an idea of the ship which this model
can be thought to represent, the main dimensions
of both are summarized in Table I, for a model
scale a = 50.
Table I Main dimensions of ship and model
Item Unit Ship Model
m 152.40 3.048
B m 21.77 0.435
D m 13.54 0.271
Tmax m 8.72 0.174
2.2 Service conditions
The following loading conditions were considered:
Condition 1Condition 1 represents the ship fully loaded leaving
port. The natural rolling period of the ship is such,
that she will easily meet sea conditions in which
she will exhibit a tendency to roll.
Table II Particulars condition 1
Condition 2
Condition 2 represents the loaded condition on
arrival, when a large part of the fuel and stores
has been consumed. The GM has become
consider-ably smaller and the natural rolling period larger.
Consequently the motion will be more gentle than
in the first case, and especially the angular rolling
accelerations will be considerably less.
Although the need for roll damping will not be
so urgent, this condition is only reached after a
transitionary stage, in which the circumstances
will be somewhere between the conditions 1 and 2.
Table III Particulars condition 2Condition 3
Ship in ballast. The GM/B ratio is high, making
the vessel an uneasy roller.
Table IV Particulars condition 3It is obvious that a considerable variation is
possi-ble between the extreme cases, the conditions 2
and 3. For the determination of the dimensions of
the tanks, emphasis has to be placed on the fully
loaded condition, which is deemed the most
im-portant.
A slighty lower efficiency for this condition can
be accepted if that follows from a better adaptation
to the other conditions.
3 The tank designs
3.1 The U-tankThe basic quantities which figure in the problem,
viz, the dimension of the tank, the rolling angle
q2and the motion of the tank fluid expressed by the
angle
, are shown in figure 1.
y
Fig. 1 Main parameters of the U-tank
For a comprehensive mathematical treatment
of the problem and the influence of all parameters
the reader is referred to the work of STIGTER.
Only the main considerations concerning this
par-ticular case will be mentioned here.
A first approximation of the dimensions
wasmade, based on the condition that the natural
period of the U-tank should be equal to the natural
rolling period of the ship in condition 1. With this
approximation the rolling motion of the ship was
calculated for a large frequency range and for
three different amplitudes of the rolling moment.
After this the most important dimensions were
varied one by one and the roll angles determined
again. All calculations were carried out on a
com-puter.
Table V Dimensions of the U-tank
All dimensions are given in meters.
Item Unit Ship Model
V m3 20228 0.1618 GM m 1.31 0.026 CM/B 0.06 0.06 KG m 7.48 0.150 kg/B
-
0.38 0.38 sec 14.52 2.05sec'
0.433 3.06xT_-!
Item Unit Ship Model
V m3 18205 0.1456 CM m 0.65 0.013 GM/B
-
0.03 0.03 m 8.08 0.162-
0.38 0.38 Tq, secsec'
20.530.306 2.90 2.16Item Unit Ship Model
V m3 12137 0.0971 GM m 2.18 0.044 CM/B
-
0.10 0.10 m 7.10 0.142 /c5,/B-
0.42 0.42 sec 12.43 1.76sec'
0.505 3.57Item Model Ship
h 0.013 0.65 w 0.260 13.00 w1 0.0864 4.32 s 0.0386 1.93 y 0.080 4.00 x 0.160 8.00
-180
0 E GR.
90
ANFLITUDE
o UTANK V172O CC
FREE SURFACE TANK Vb=0036
CONDITION 1
Fig. 2 Amplitude and phase of the tank moment of U-tank and free surface tank calculated for a wave slope of 0.02 rad. Model values.
Observing all information obtained the
dimen-sions were selected which showed the best
perfor-mance for the loading condition 1. The moment
amplitude and phase characteristics are shown in
figure 2; the dimensions are summarized in the
table V.
In this table the meaning of the symbols is
h = height of connecting duct,
w = length of connecting duct,
= bottom width of reservoir,
S
= distance between the centre
of gravity of the
ship and the bottom of the tank,
-3)
= average fluid depth
in the reservoirs,
x = height of the reservoirs.
These symbols are also explained in figure 1.
The calculation of the motion was also carried out
for the two other loading conditions. The
dimen-sions of the tank were not modified to suit either
of these.
In figure 3 the position of the tank as installed
in the model is shown on the right side.
Fig. 3 Dimensions and position of U-tank in the model. Dimensions in mm.
Originally the height of the tank and of the
water column were chosen so that the water level
would never reach the tanktop, and probably
never the upperside of the duct either. New
inves-tigations revealed that this latter condition was
unnecessary, and that the water level could safely
be allowed to run into the duct without impairing
to a marked degree the efficacy of the tank. This
means that for the same effect, both the cubic
capacity and the weight of water can be reduced
substantially.
Also it appears that the influence of the vertical
position of the tank is of minor importance. This
means that the U-tank can be placed on the double
bottom of the ship, which may be advantageous
when planning the accomodation. The left side of
figure 3 corresponds to the tank according to the
new Conception.
3.2 The free surface tan/cThe only dimension which has to be determined
is the waterdepth, because all other dimensions
are in fact fixed. It is known that the highest
posi-tion of the tank is the most effective, the largest
width which is available is chosen and the length
had already been fixed at 0.10 m model value.
The depth of the tank should be approximately
three times the waterdepth, to avoid the water
from slamming against the tanktop.
From the expression which gives the natural
frequency of the tank for small amplitudes, viz.
b
is tankbreadth
h
is waterdepth
£L)
is natural frequency,
the waterdepth is determined on the condition
that the natural frequencies of the ship and the
tank should be equal.
With an eye to condition 3 the tank depth was
chosen. This determined the vertical position of
the tank, which is shown on the right-hand side
of figure 4.
Fig. 4 Dimensions and position of free surface tank in the model. Dimensions in mm.
With the aid of the available diagrams the
waterdepth has been selected. The best "allround"
waterdepth appeared to correspond to h/b = 0.036.
For condition 2 the ratio h/b = 0.025 seemed
slightly better and for condition 3 the ratio h/b =
0.06 seemed preferable; Ii is the waterdepth and
b the tankwidth.
The moment of the free surface tank as regards
amplitude and phase is presented in figure 2,
to-gether with the same data of the U-tank.
On the right hand side of figure 4 the tank is
shown as installed in the model. On the left side
it is shown to which dimensions the tank could
be reduced if it is accepted that for the h/b = 0.06
ratio the tanktop is touched.
3.3 Comparison of some particulars of both tan/cs
In the following table the cubic capacity, the water
volume and the reduction of GM are shown for
Table VI
both tanks. The given values apply to the smallest
designs, as shown on the left-hand sides of the
fi-gures 3 and 4.
4
Experiments and results
4.1 Summary of experimentsThe model, ballasted and trimmed
correspon-ding to condition 1 was given a list and
relea-sed. The free rolling motion was recorded.
The model without the tanks in operation was
forced to roll. The rolling moment was
produ-ced by a gyroscopic oscillator.
The amplitude of the oscillating moment
cor-responded to a static heeling angle of 0.02
radians. The frequency was varied in steps.
The roll amplitude was measured as well as
its phase with the forcing moment.
The data obtained from these tests were used
to determine the in-phase and quadrature
com-ponents of the reacting water moment, often
called the added mass moment of inertia and
damping. This information served as a basis
for the calculation of the rolling motion with
the tanks in operation.
The model was oscillated under the same
con-ditions as summarized in paragraph b, but now
with the two tanks operative in turn.
The measured motion amplitudes and phases
were compared with the calculated values.
The oscillation experiments were also carried
out for the remaining loading conditions except
for the measurement of the phase angles.
In addition the oscillation tests with the free
surface tank were carried out for different
Wa-terlevels in the conditions 2 and 3.
The model, loaded according to condition 1
was placed in regular beam waves. The model
was free to roll, heave and sway.
The wave height and period were measured
together with the rolling amplitude for the
non-stabilized model and for the model with the
tanks operative in turn.
For the same loading condition the model was
placed in irregular beam waves, the model
being free to roll, sway and heave.
The wave spectrum and the roll spectrum were
determined for two values of the height of the
wave spectrum.
4.2 Results of oscillation tests
The first tests, viz, the free and forced oscillation of
the nonstabilized model, revealed that the damping
and the added moment of inertia were highly
de-Item Unit U-tank F.S.-tank
Cu. capacity m3 206 225 Volume of water m3 m 81 84 reduction Condition 1 0.16 0.21 Condition 2 0.18 0.23 Condition 3 0.27 0.35
penderit on the frequency, while the damping was
For the natural roll frequency was
distinctly non-linear
inthe amplitude of the
motion.
75 5N I? 50 25In figure 5 the measured amplitudes and phases
Paare shown. It appears that the natural frequency
(at Ekri, = 90 degrees) was
= 3.12 sec
instead
of 3.06 sec' as intended. This discrepancy is not
thought of importance with regard to the
perfor-mance of the tank.
25Fig. 6 Damping and moment of inerta of the shipmodel excited by a pure sinusoidal rolling moment.
In figure 6 the mass moment of inertia and the
damping of the model hull are given. It appeared
possible to divide the damping into a part which
only depends on the frequency and a part which
depends on the amplitude of the motion, i.e.
= v.p(w) + 0.0095 a (qin degrees)
= 0.0242
With this knowledge the rolling motion of the
model, equipped with a tank, was calculated and
the results were compared with the measurements
of the next test series. These calculations were
carried out, observing the non-linear and
frequen-cy-dependent behaviour of the hull proper and
of the tanks. The results, as presented in the figures
7 and 8, show by their good agreement, that the
mathematical model so far describes the
pheno-mena adequately. Concerning the free surface tank,
of which the moment was determined
experimen-tally, the good agreement shows that scale effects
cannot be of much importance, as the model scale
of the tests under consideration differed
consider-DEGR, 7.5
-25 OAMPLI1UDE -180PHASE ANGLEtTr
EKiA
- SHIP oROLL CONDITION 1 WITH U-TANK V=1720 AMPLITUDE . ANGLE OF ROLLING ___CALCULATED CC. MEASURED VALUE MOTION, MEASURED VALUES -I PHASEVALU1
_iA\
-CONDITION 1 KpcSIN MSEC I..5P_KOCCOSk.. KG.M.SEC1J
-170 CONDITION SHIP ROLL 1WITH FREE SURFACE AMPLITUDE. MEASURED ANGLE OF ROLLING CALCULATED TANK h/bQD36 VALUE PHASE CKCp MOTION,MEASURED VALUE5 VALUE 0 1 2 3 4 W SEC1
Fig. 5 Measured motion characteristics of the model hull.
0 2 4
ti) SEC1
Fig. 7 Rolling motion of the model with U-tank. Forced oscillation test for condition I. Comparison between experiment and calculation.
a 2 3 4
W SEC1
Fig. 8 Rolling motion of the model with free surface tank. Forced oscillation test for condition 1. Comparison between experiment and calculation.
2 3 0.) SEC1 0 4 DEGR
'a
5.0 DEGR10 17.5 Pa 5.0 2.5ably from the model scale at which the original
bench tests were carried out.
The U-tank shows clearly the two peaks
associa-ted with the linear system with two degrees of
DEORfreedom and constant coefficients. The deviations
in the U-tank system are not so serious that this
general picture is altered. The free surface system
is much more complicated. In the first place the
Parelation between the motion and the resulting
moment is not linear, and secondly the coefficients
prove to be strongly dependent on the frequency.
Because of this the peak at the high frequency side
has degenerated into a slight waviness of the curve.
Figure 9 applies to loading condition 2. It should
be noted that the measurement of the phase has
been omitted because of some trouble with the
measuring apparatus. This makes the comparison
between the experiment and the calculation
some-what less accurate, as now the necessary informa-
DEGR75tion about the variation of the hull damping and
added mass moment of inertia is lacking. Still the
agreement is sufficiently good to conclude that the
motion can be predicted with confidence, although
Pa 0in a qualitative sense, as the correct choice of the
hull-damping is still questionable.
The curves show that for all cases the peak at
Z5the high frequency side is insignificant. The free
surface tank shows a somewhat better performance
than the U-tank due to the flatter
phase-versus-frequency slope (see figure 2) which still has some
effect in the low frequency range. Moreover, this
performance can be improved by a simple low-
OEGR5'°ering of the waterlevel in the tank. This is shown
by the figure 9. It should be noted that the static
heeling angle of the model equipped with the tank
25in action is considerably larger than of the
non-stabilized model. This is due to the loss of GM.
Figure 10 applies to the last loading condition:
the ballasted ship. In these series no phase
mea-surements were carried out either. The figure shows
again the two secondary peaks in the case of the
DEGR75U-tank. The distinct peak at the high frequency
side gives rise to high accelerations, which are
proportional to the amplitude and to the square of
the frequency. Still the ship with tank performs
Pamuch better than the ship without tank.
It is remarkable that the free surface tank with
the compromise water depth h = 0.036 b per-
2.5forms so well under these
circumstances. By
increasing the waterdepth the maximum
ampli-tudes are not diminished, but certainly the angular
accelerations are decreased.
So far it can be concluded that for the most
im-portant loading condition there is not much
dif-ference in the degree of the roll reduction which
the two tanks bring about, although the shape of
the curves is quite different.
5.0
2.5
0
W SEC1
U) SEC1
Fig. 9 Results of oscillation tests for condition 2. Compar-ison between experiment and calculation.
CONDITION 2 1
SHIP WITHOUT TANK
-OMEASURED VALUE
f
..._CALCULATEDVALLJE
_J
\_
SHIP WITH FREE SURFACE TANK h/b MEASURED VALUE =0.036 CALCULATED VALUE A
I.
I.
I.
\\
SHIP WITH FREE .MEASURED VALUE - - _CALCUL VALUE SURFACE TANK h/b=0025
----
\
---S'-SHIP WITH UTANK OMEASURED VALUE ___CALCULATED VALUE V=1720C
I
I.
_0
\
-.
,-2 3 1. U.) SEC1 0 2 3 4 U) SECT 0 2 1.For the other service conditions the free surface
tank has a better performance, and it is, moreover,
possible to adapt the tank by a simple action.
Apparently the results of the oscillation tests
correspond quite well with the theoretical
predic-tion of the mopredic-tion under these circumstances. The
DEGR 7.5 (Pa 5.0 2.5 DEGR50 CL) SEC1 0 0 2 3 U) 5EC
Fig. 10 Results of oscillation tests for condition 3. Com-parison between experiment and calculation.
3
U) SEC1
prediction of the rolling motion in beam seas with
no forward speed, if we confine ourselves to this
simple case, is already much more difficult,
becau-se we know too little about the
wave-induced
rol-ling moments and especially about the moments
which are brought forward by sway forces. Also, the
response of the tanks to horizontal
accelerations is
unknown. So, it seems not probable that the results
in waves will be in conformity with the simple
mathematical model which performed so well in
the case of the oscillation tests.
For the comparison of the results, the rolling
amplitudes measured during the oscillation tests
are presented as magnification factors in the
figu-res 11 and 12. This only concerns the service
con-dition 1. The amplitudes measured in the
experi-ments in waves will be presented as their ratio to
the surface wave slope.
7.5
PaJPst
5.0
CONDITION 1
OSHIP WITHOUT TANK
o SHIP WITH UTANK VX72S CC
0 2 3 1.
CL) SEC1
Fig. 11 Magnification factor for the model with U-tank. Oscillation tests.
50
CONDITION 1
OSHIP WITHOUT TANK
SHIP WITH FREE SURFACE TANK h/bSO35
3
U) SEC1
Fig. 12 Magnification factor for the model with free surface tank. Oscillation tests.
CONDITION 3 SHIP WITHOUT TANK OMEASURED VALUE
CALCULATED VALUE \
.1
....
_<
SHIP WITH FREE MEASURED VALUE
- CALCULATED
SURFACE TANK N/bSO36
VALUE
\,
SHIP WITH FREE MEASURED VULUE
_CALCULATED
SURFACE TANK h/bDS6
VALUE
SHIP WITH UTANK o MEASURED VALUE
-
_. CALCULATED V=172SCC VALUEMn.
2 3 I. Cl.) SEC1 0 2 0 2 1a25 DEGR5,0 25 Pa 7.5 DEGR.Ia
50 2.54.3 Experiments in beam waves
In figure 13 the results of the measurements in
regular beam waves are shown. Only the wave
2.5
5
2.5
I.
Fig. 14 RoIl amplitudes related to wave slope. Results of tests in regular beam waves.
11 and 12 it is seen that the curves are
approxi-mately of the same shape but that the response to
regular waves is appreciably lower. This applies
to all the curves. As the rolling amplitudes do not
differ materially if the two test series are compared
this effect can not be due to non-linearity. Also it
is not plausible that the Smith-effect is responsible
for this phenomenon, as the differences are too
large. It seems that the decreased response to waves
must be attributed largely to the interaction of
sway and roll.
The last series of experiments consisted of the
measurement of the wave and roll spectra when
the model rolled in irregular beam seas. Two wave
spectra were used, which only differed in height.
These two spectra are presented in figure 15
to-gether with the derived wave slope spectra.
0 2.5 50
ci)SEC
-.
Fig. 15 Measured wave height and wave slope spectra.
Model values.
The roll spectra are shown in figure 16. When
the results of the two tanks are compared, it is
striking that, at least in these wave spectra, there
is not much difference in the performance of both.
It should be noted, however, that the wave slope
spectra are very low at the frequency range in
which the U-tank shows its low frequency peak.
The significant values of all spectra are
summa-rized in table VII together with the ratios of these
values in the highest and the lowest wave spectra.
It should be noted that the ratio between the two
wave spectra is not reproduced exactly in the roll
spectra. This effect is largest in the case of the
non-CONDITION 1 o SHIP WITHOUT
SHIP WITH FREE
o SHIP WITH UTANK
WAVE SLOPE TANK
SURFACE TANK
V1720CC
h/b0036
...WAVE HEIGHT SPECTR
- _WAVE SLOPE SPECTRA
CONDITION o SHIP WITHOUT
- SHIP WITH FREE
o SHIP WITH UTANK
TANK SURFACE TANK V.1720CC h/N .5536 0 1 2 3 W SEC1 Fig. 13 Results of tests in regular beam waves.
dimensions and the roll amplitudes were measured.
It should be noted that the wave slope increased
with increasing frequency. In figure 14 the ratio
between the amplitude and the wave slope is
pre-sented. If this figure is compared with the figures
0 2 3 (5) SEC' 4 DEOREE
t
a5
degrsec cm2secf
2.0 sk(w)s(w)
1.5 1.0 0.5DEGSEC 50 2.5 D EGR2SEC 10 5.0 2.5
Fig. 16 Measured roll spectra. Model values.
stabilized ship, indicating the non-linearity of the
of the U-tank, and it has nearly vanished in the
case of the free surface tank.
Fable VII Significant valuesIn figure 17 the comparison is given between the
measured roll spectra and the spectra calculated
S(w) 2.5 DEGR2SEc 5.0
s(w)
2.5FREE SURFACE TANK
CALCULATED SPECTRUM FROM RESPONSE TO REGULAR WAVES MEASURED SPECT
/
I ,1 W SEC.hull damping. It is still partly present in the case
Fig. 17 Comparison of measured and calculated rolltra.spec-ROLL SPECTRA FOR WAVE CONDITION 1 SHIP WITHOUT HEIGHT SPECTRUM TANK FREE 1 -__.._SHIP WITH SURFACE TANK _SHIP WITH U -TAN K
rm.
/'\
/
N'\
SpectrumNo.1 Spectrum
No.2
ratio between1 and 2
Wave height 2ai
in cm 6.03 8.30 1.37
Wave slope (kj
I in degr. 2.41 3.35 Roll angle in degr. for hullwithout tank 6.07 7.28 1.20
with U-tank with free surface tank 3.53 3.20 4.49 4.26 1.27 1.33 CONDITION 1 U-TANK CALCULATED SPECTRUM FROM RESPONSE REGULAR WAVES ___MEASURED SPECTRUM TO
A
,1
/
\
/
---/
ROLL SPECTRA FOR WAVE HEIGHT SPECTRUM CONDITION 1 SHIP WITHOUT 2 TANK ___SHIP WITH SURFACE TANK __SHIP WITH U-TANK FREE
I
fi
\\
\
/1'
0 25 50 W 5EC1 -0 25 5.0 Ci.) SEC. 2.5 50 0 25 50 Ci) SEC1 -7.5 s.(w) S?(W) 7.5 DEGRSEC 5.0from the response to regular waves. The agreement
for the case of the free surface tank is acceptable,
especially if it is considered that the determination
of the response to regular waves for the
frequen-cies around and below a
2.5 was not so accurate.
The differences which occur in the case of the
U-tank cannot be accounted for.
4.4 Further consideration of the roll reduction
The improvement effected by a roll damping tank
will be illustrated by the following example.
The loaded ship is assumed to travel with the
waves broadside on in a fully arisen sea
corres-ponding to a windspeed of 19 m/sec, i.e. force 8
of the Beaufort scale.
The wave spectrum which is chosen is the
PIER-SON-M0sKOWITz spectrum which is given by the
expression
S(w) = AeI0'Iw5
A = 8.ll03g2
B = 0.74 g4/U4
U = windspeed at a height of 19.5 m.
The derived wave slope spectrum is
8
l.l0-SkC(w) = e
Ct)
The roll spectra of the ship for the three conditions,
i.e. without tank and with one of both the tanks
in action, are calculated for this wave slope
spec-trum and the estimated frequency response
func-tions. As the response to the regular beam waves
was not clearly defined at low frequencies (see
figure 14) the results derived from the oscillation
tests(see figure
11 and 12) multiplied by the
factor e_/T!2 were used. All calculations were
car-ried out for the full scale ship.
The wave slope spectrum and the frequency
response curves are shown in figure 18, while the
computed roll spectra are presented in figure 19.
Evidently the wave slope spectrum is so small at
frequencies below
0.35 sec' that the rather
pronounced differences which appear between the
frequency response functions at these low
frequen-cies, do not bring about significant differences in
the roll spectra. The significant roll amplitudes in
these cases are
ship without tank
a1/3 = 17.2 degrees
ship with F.S.-tank (Pal/3 = 8.9 degrees
ship with U-tank
a1/3 = 9.9 degrees
In general the Rayleigh distribution adequately
1000 DEGRSEC S 750 500 250 DEGRSEC. A
--20
30Sk)
I,/LJ=19m/sec
10SHIP WITHOUT TANK
SHIP WIIH_EEEVRF.TANK
/
SHIP WITHIANKIlL
U =19 r,/sc.
SNIP.WITHOUT.J,.NK
/
SHIP WITH U-IANj< .sURFACr
SHIP WITH FREE
.d TANK
Fig. 19 Calculated roll spectra for Pierson-Moskowitz wave spectrum.
describes the probability distribution of the roll
amplitudes. This function is given by
f((pa) = (Paelm0/1nO
from which expression follows the probability that
the roll amplitude will exceed a certain value Pm
P(çoa > (Pm) = emIm0
The variance mo is determined from the roll
spec-trum
m0 =/S(w)dw.
0 0.25 0.50 075 1.00
W SEC-1
Fig. 18 Assumed frequency response functions and Pierson-Moskowitz wave slope spectrum.
025 0.50 0.75 W5 SEC. 1.00 10 75 Hk(w) 5.0 25
The Rayleigh distributions for the three conditions
are presented in figure 20. The corresponding
curves of the probability that q
exceeds 9m are
shown in figure 21.
0.20
015
SHIP WITH FREE$4RFA.E TANK
0.05
0 10 20 30
Pa DEGREES
Fig. 20 Rayleigh distributions corresponding to the spectra of figure 19. 1.0 (PPm) a5 WITH U-TANK
ISHIP
WITHGUT TANK Pa 1.0in action this probability is very small indeed,
even though the Rayleigh distribution will
prob-ably not give an accurate prediction in this
region.
5 On the possible influence of bilge keels
It is often asked whether or not bilge keels can be
omitted if the vessel is equipped with an
anti-rol-ling tank. It seems doubtful that a general answer
to this question can be given, but some indication
of the combined effect of the anti-rolling tank and
the bilge keels can be gathered from figure 22. In
2.5 CONDITCN 1 CALCULATED VALUES VALUES . MEASURED
/
SHIP WITHOUT TANK
SHIP WITH U TANK
TANK
0 2 3 4
(4) SEC1
Fig. 22 Influence of hull damping on roll amplitudes. Model with free surface tank.
this figure are shown the computed amplitudes of
the forced rolling motion under the influence of an
alternating moment corresponding to a static heel
of 0.02 radians. The different curves correspond to
different values of v, the non-dimensional damping
coefficient of the hull. The dots represent the
mea-sured results of the oscillation tests presented in
figure 8. It is seen that the hull damping of the
model was rather small compared with the
damp-ing derived from the first tests with the model
without tank. This is due to the non-linear
char-acter of the hull damping. This non-linearity, for
which presumably the bilge keels are responsible,
acts as a safety measure against the development
of too large rolling angles. If, because of the
omit-tance of the bilge keels, the hull damping decreases,
the roll amplitudes increase considerably, as is
shown by the curves. Of course, a larger tank
ca-pacity would prevent most of this, but the use of
bilge keels has the additional advantage, that in
10 20 30
Pm DEGREES
Fig. 21
Probability that q >
corresponding to the spectra of figure 19.From the latter figure it is evident that, although
the reduction of the significant roll amplitude is
moderate, there is a substantial improvement when
the probability that the roll angle will exceed a
given value is considered. Take for instance a
limi-ting angle of 12 degrees. The probability of
ex-ceeding 12 degrees is about 2.6 percent in the case
of the free surface tank, 4.7 percent in the case of
the U-tank and 37.7 percent for the unstabilized
ship.
In the latter case the probability that the roll
amplitude will be larger than 20 degrees is
stillabout 6.7 percent, while for the ship with a tank
fV)
0.10
10
DEGR.
the case of emergency the vessel would riot lie
bereft of most of its roll damping. This can occur
when the reduction of GM is not acceptable, say
e.g., because of a partial flooding.
If no bilge keels are fitted the percentual reduction
of the rolling motion due to the tank action is
in-creased, but that cannot be the aim in itself.
6
Conclusions
The equation of motion considered concerning
only the rotary motion about an axis through the
centre of gravity of the ship fairly describes the
forced rolling, as furnished by the oscillation tests.
In the case of the motion in beam waves only a
qualitative agreement is obtained.
The principle of superposition appears to hold
in the case of the free surface tank; in the case of
the U-tank this is still questionable.
Both types of tanks can give a substantial
reduc-tion of the rolling moreduc-tion, especially if both are
designed and used for a specific service condition.
For a wider range of conditions, causing
consider-able variations of the natural frequency of the
ship, the free surface tank gives better results.
7
Suggestions for further research
It is desirable to extend our knowledge about the
combined motions of the ship in regular and
irreg-ular long-crested beam seas.
Next to this it is desirable to know the response
of the tanks to translations, especially to the
hori-zontal motion, and to investigate the validity of
the principle of superposition for the translatory
and rotary motions.
8 Acknowledgement
The authors are most indebted to Mr. A. P. DE
ZWAAN who not only carried out the major part
of the experiments, but also prepared the drawings.
References
I. STIGTER, C., The Performance of U-tanks as a Passive Anti-Rolling Device. Netherlands Ship Research Centre TNO, Report No. 81 S, February 1966.
BOSCH, J. J. VAN DEN and J. H. VUGTS, Roll Damping by Free Surface Tanks. Shipbuilding Laboratory of the Technological University, Delft. Report No. 134, No-vember 1965 and Netherlands Ship Research Centre TNO, Report No. 83 5, April 1966.
FRAHM, H., Neuartige Schlingertanks zur Abdampfung von Schiffsrollbewegungen und ihre erfolgreiche An-wendung in der Praxis. Jahrbuch der Schiffbautechni-schen Gesellschaft 12, 1911; p. 283.
WATTS, P., On a Method of Reducing the Rolling of Ships at Sea. T.I.N.A. 1883, p. 165.
WATTS, P., The Use of Waterchambers for Reducing the Rolling of Ships at Sea. T.I.N.A. 1885, p. 30.
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IC.-Reports
1 S The determination of the natural frequencies of ship vibrations (Dutch). By prof. ir H. E.Jaeger. May 1950.
3 S Practical possibilities of constructional applications of aluminium alloys to ship construction. By prof. ir H. E.Jaeger. March 1951.
4 S Corrugation of bottom shell plating in ships with all-welded or partially all-welded bottoms (Dutch). By prof. ir H. E.Jaeger and ir H. A. Verbeek. Novem-ber 1951.
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(Dutch). By ir A. Verduin and ir B. Burghgraef. June 1952.
7 M Cylinder wear in marine diesel engines (Dutch). By ir H. Visser. December 1952.
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10 S On collecting ship service performance data and
their analysis. By prof. ir J. W. Bonebakker. January
1953.
11 M The use of three-phase current for auxiliary purposes (Dutch). By irJ. C. G. van Wijk. May 1953. 12 M Noise and noise abatement in marine engine rooms
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14 M The purification of heavy fuel oil for diesel engines (Dutch). By A. Bremer. August 1953.
15 5 Investigation of the stress distribution in corrugated bulkheads with vertical troughs. By prof. ir H. E. Jaeger, ir B. Burghgraef and I. van der Ham.
Sep-tember 1954.
16 M Analysis and testing of lubricating oils II (Dutch). By ir R. N. M. A. Malotaux and drs J. B. Zabel. March 1956.
17 M The application of new physical methods in the
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Some notes on the calculation of pitching and
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December 1955.
23 S Second series of stability experiments on models of lifeboats. By ir B. Burghgraef. September 1956. 24 M Outside corrosion of and slagformation on tubes in
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25 S Experimental determination of damping, added mass and added mass moment of inertia of a
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26 M Noise measurements and noise reduction in ships. By ir G. J. van Os and B. van Steen brugge. July
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28 M Influence of piston temperature on piston fouling and piston-ring wear in diesel engines using residual fuels. By ir H. Visser. June 1959.
29 M The influence of hysteresis on the value of the mod-ulus of rigidity of steel. By ir A. Hoppe and ir A.M.
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30 S An experimental analysis of shipmotions in
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31 M Model tests concerning damping coefficient and the increase in the moment of inertia due to entrained
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32 S The effect of a keel on the rolling characteristics of a ship. By ir J. Gerritsma. July 1959.
33 M The application of new physical methods in the
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34 S Acoustical principles in ship design. By irJ. H. Jans-sen. October 1959.
35 S Shipmotions in longitudinal waves. By irJ. Gerrits-ma. February 1960.
36 S Experimental determination of bending moments for three models of different fullness in regular waves. By ir J. Ch. de Does. April 1960.
37 M Propeller excited vibratory forces in the shaft of a single screw tanker. By dr ir J. D. van Manen and ir R. Wereldsma. June 1960.
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97 S On the efficacy of two different roll-damping tanks. By ir. J. Bootsma and ir. J. J. van den Bosch. July
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98 S Equation of motion coefficients for a pitching and heaving destroyer model. By W. E. Smith. July 1967.
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10 S/M Condensed report of a design study for a 53,000 DWT-class nuclear powered tanker. By the Dutch International Team (D.I.T.), directed by ir A. M. Fabery de Jonge. October 1963.
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