A NOTE ON THE ROLLING OF SHIPS AND STABILIZING SYSTEMS,
PARTICULARLY ANTI-ROLL tANKS
By P. A. Hamill
Ship Section
Division of Mechanical Engineering
1.
INTRODUCTION
.
Perhaps the best way to introduce the subject is by quoting from the
discussion of a paper by Philip Watts on, " The Use of Water Chambers for
Reducing the. Rolling of Ships at Sea", presented to the Institution of Naval
Architects in 1885 (Ref. 1). The discussion was a lively one and was opened by
Mr. H. Liggins asJollows:
.
My Lord, I venture to address the Meeting on this subject because
upwards of twenty, years ago the first introduction of bilge keels in this room was
brought to the notiçe of this Institution by myself in connection with the improvement of the rolling .of one of the largest passenger steamers of. that day. I have
had experience in the Atlantic of travelling in a ship that had the bad reputation of
being the most inveterate roller afloat, so much so that the records of this Institution
will show that the passengers refused if possible to cross in that ship. The result
was that the owners of the ship introduced bilge keels on her, which made her as
perfect and as comfortable a ship as could well be imagined for the convenience of
passengers, but at a loss of speed of, I think, a knot an hour, which was an inconvenience and an. expense which they had to face. This plan now under our notice is,
in my humble. judgment, the most perfect means which I have .ever seen suggested
for mitigating that very great evil and that very serious-danger to passengers in
connection with excessive rolling, and to all those who have to live in ships it is a
particularly disagreeable motion, and upsets occasionally the stomachs of even the
most hardy seamen; but for passenger ships 'it is very important that anything that
can be suggested should be well tried, and if it should prove effective, as I think
this model has clearly proved it to our judgment to be, it ought certainly to be
adopted. It ought to be done, and the public should be made safe and comfortable,
because there is a great deal of danger, particularly in large ships, if excessive
rolling takes place, that the ship might be dismasted, and a dismasted ship is a most
inconvenient thing to be in in the middle of the Atlantic, and therefore I hail with
great satisfaction this most interesting and, what is of more importance., most simple
remedy 'fór preventing the rolling of our ships at séa".
The Watts presentation was made during the period of transition from sail
'to steam. In terms of ship motion this great change brought about a substantial
decrease in roll damping. This was only partially recovered by the use of bilge keels
-2because the structural problems in fixing these to the ship, and the resistance penalty
involved, limited the size of bilge keels that could bé used in practice. Since then, an
incredible diversity of schemes for reducing roll have been proposed and over 350
ships have been fitted with stabilizing devices (Ref. 2). By transfer of solid weight,
fluid transfer in tanks and ducts, gyroscopes, and finally by external fins, torque was,
developed in opposition to the wave torque which provides the roll excitation. Despite
many technical difficulties in their development, all of these systems had some
measure of success and a large number of them performed very well indeed, giving
roll reductions of 50 to 90 percent.,
In recent years, the activated fin stabiliz er has been dominant. The reason.
for this lies in its peculiar suitability to passenger liner applications where abt of
stabilization is needed on, basically, high speed vessels. However, this does not
mean that othér systems are outmoded. With the current knowledge in the fields
related to the roll stAbilization problem such as oceánography, ship hydrodynamics
and servomechanisms, a successful system design based on moving weights, fluid
transfer or gyros coüld be 'made. There is, in faót, a growing demand at the present
time for a type of ship where low speed operation is of major importance.. In this
range, fins, ,which rely on forward speed to develop restoring torques, cannot
compete. It is not surprising then, in view of the increasing number of oceanographic survey vessels, weather ships, icebreakers and missile tracking ships, that
there is a résurgence of interest in alterriätive anti-roll systems. In particular,
Watts' "most simple remedy", invented and re-invented many times would appear,
áfter 80 years,. filially to have come into its own.
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2. SHIP MQTIONS, PARTICULARLY ROLLING
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The fundamental complèxity in any treatment of ship motions lies in the
fact that the 'floating vessel and the surrounding water are a single, mutually
dependent, hydrodynamic system and the ship movement must be examined simultaneously with the movement of the surrounding medium The ship encounters waves
which induce the motions, the moving ship influences the wave structure in its neighbourhOod and changes the fluid pressure field. Thus the changing pressure field of the
water:, which causes the motions, depends, In turn, on the elements of the induced
motions.
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Initial attempts to solve the problem avoid altogether the hydrodynamic
equations and substitute instead rigid body equations with coefficients modified to
accoûnt, at least approximately, for the role of the fluid (Ref. 3). Even then the
equations of motion for a ship, in its 6 degrees of freedom, subject to the random
excitation of a seaway, contain a plethora of terms expressing cross-coupling of
motions and mutual interaction of the vessel and the fluid medium. In certain
isolated, but nonetheless important cases of motion, providence has made some
concession to simplicity and an acceptable description is possible in elementary
terms. It is always wise to remémber, however, that, because of the gross
assumptions necessary to obtain this simplicity and the, often untrustworthy,
(i
-3empirical dala required in itsaplthation, the results of computations from these
eleméntary equations are, at best, only a first approxirnationto reality
The problem, of stabilizing the motions of ocean-going ships is indeed
formidable, as anyone who has ever encountered a storm at sea will confirm There
is an often-repeated story of a hitherto land-locked scientist who had for some time
been experimenting with small ship models in waves, and was persuaded to take
an Atlantic Voyage to meet, at first hand, his full-scale adversary, the sea. I due
course, he had the opportunity to observe the boundless confusion and energy of a
storm. He watched, fascinated, and felt the 20, 000-ton liner shudder and slam its
way through the heavy sea., After perhaps an hour, he was heard to observe In
melancholy disbelief, "I can't do ANYTHING about THESE waves".
The adverse effects of ship motions on the seaworthiness of a vessel .are
well known. It is, however, worthwhile to recall söme of the, consequences that
occasionally result from extreme motions (Ref. 4).
Capsizing because of excessive roiling.
Damage., to the hull orto individual structure because of additional
forces associated with the motions.
Shifting of cargo due to extreme inclination of the vessel and inertial,
forces.
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Deck flooding.
Disturbance of the operation of. ship' s plant as a result of dynamic loads.
Loss of speed because of increased resistance in waves and bad operating
conditions of propellers.
Seasickness.
Decrease in the accuracy of gunnery on warships. The 'impossibility of
torpedo or gun firing in extreme seas was, historically, perhaps 'the most
important stimulus to the development of stabilizing deviôes.
Item 7, 'being familiär ti most people, provides a useful quantitative,
criterion An important role in the incidence of seasickness is played by the equilibrium apparatus located in the organs of hearing (Ref 4) Disturbances of this
apparaüis', as a result of inertial effects öaused by the motions, induce the symptoms
of seasickness., These'have been observed to become particularly pronounced if the
liner accelerations exceed 1/10 the gravitation acceleration Assuming the rolling
oscillation of the vessel is harmomc, the amplitude of the linear accelerations experienced by a persin standing at the rail, a reasonably representative location in this
contêxt ,
iS
.
.
.
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(2)2
.
wheré B is the ship's beam, 4 Is the amplitude and T Is the period of roll.
oi()
.2
For a typical weathership with B = 40 ft. and T = lo sec.
0. 41 radian
The roll, magnification factor defined by
¡A
roll angle.
- a - wave
slope
-
could, for an unstabillzed ship at resonant roll, be expected to be about 10,.
that the wave slope required
= 0.041 radian
=
where h is the wave height and X the wave length. Since, in this. casò
L
x = .27r
.
T2
= 512 ft.
.
.
.
a wave height of 6. 7 ft. or more, of suitable. period1 would produce uesirable
accelerations Typically, a fully arisen sea associated with a 25-knot wind,
described as a strong breeze, has an average wave height of over 8 ft and a
spectrum with maximum energy at a period of 10 sec Conditions sufficient for
seasickness would be a commonplace óccurrence on the vessel under discussion..
It is no wonder thefl that ship stabilizationhas had öontinuous attention
from inventors and scientists for the past 80 years Progress in the reduction of
pitching and heaving motions has been slow, although some notable advances have
been made Improvement in pitch performance has resulted from closer attention
to ship form in the use of finer lines at bow and stern Further reductions have
been achieved with bulbous bows which increase the pitch damping and, in recent
years, anti-pitching fins have had considerable attefltion, at least n the ship research
5
world. However, most of the effort has gone into the roiling problem, in part
because it is the worst motion, but also because it offered the best prospect for
success.
f
The réatively successful progress roll, as compared with pitch or
heave stabilization, may be explained by considering a very simple mathematical
description of the moving ship In any of the 3 modes a first approximation to the
equation of motion is that of a second-order system with linear dampmg, the muchused spring and mass system For forced oscillation at a discrete frequency, i e
the ship in a frain of regular waves of frequency w, the equation Is
+ B4 = Fcoswt
+N
(1)
For t large the Solution is
cos (wt- E)
where
F = ¡.z (w)
B
2
coB)
2
.2
+ IN w
2
The motion is thub an harmonic oscilation which lags the excitation by a phase
angle E (w) given by
e=ta
-4
Nw
2
Mw-
The function p (w), called the magnification factor, and the phase angle
the following values:
For wO
w=4
w
havò
=0
B
Nw
ir
2
= o,
=ir
(resonaùçe)
-6The charactér of the functimi ,. (w) is thus determined largely by the damping
term N. For small damjing, as in the rolling mode, the magnification factor
rises from a value of i at w = O to a sharp peak at resonance , (for an unstabilized ship with no bilge keels p may be as high as 16), thefl falls rapidly with
increasing frequency. The rolling ship is thus seen to act as a -narrow band filter
to the random excitátion of the seaway, responding in la.re theastñe only to wave
components in the neighbourhood of its own resonant frequency This explains the
marked tendency for a ship to roll, "in its own period" whatever the state of the
sea. It follows that any syetem which substantially reduces roll for a narrow band
of frequencies in the resonaùt range will give a good Over-all tabiiization.
The magnification factor at resonance Is seen to bé inversely proportional
to the damping N which, as previously stated, is small for roll. Because little
damping exists on the bare hull a small increase in damping has a marked effect on
the magnification fáctor at resonance and, hence, on the total roll response. This
fact accounts for both the effectiveness and the limitation of bilge keels A&Ied to
the bare hull, bilge keels of resonable size may double the damping and thus reduce
the magnification factor at resònance 1y half. A further reduction by half would
reqúire bilge keels with 3 times the bare hull damping, i. e., they would have to be
much bigger, and the structural problem of attaching them to the ship as well as
the resultant increase in resistance outweighs the marginal gain in roll performance.
Damping is proportional to the wavemaking capacity of the ship in the
particular mode of motion and it is obvious from the hull geometry that the damping
in pitch and heave, compared to that in roll, is very great. Magnification factors
at resonance are 4 or less so that an enormous increase in damping would be
necessary to make any gain in pitch or heave performance. Also, the possibility of
a "tuned" stabilization, even if such a system could be devised, is ruled out because
the magnification factor is a flat curve and the response distributed, over a wide
frequency range.
But it is, above all, the difference in "stiffness" in the systems that makes
the rolling mode amenable and the pitch and heaving modes difficult to 'influence. The
spring term B is smaller by an order of magnitude in roll and, referring again to
the spring and mass analogy, is easier to influence than the other much stiffer systems.
High roll response results from, relatively, low input torques so that opposing torques
of reasonably attainable magnitude may be expected to improve the roll performance.
The' rolling ship is then a lightly damped, highly túnéd system with a low
spring constant. The most elegant stabilization is' then a passive system, tuned to
the ship's resonant frequency, which would develop suitable torques opposing the
wave excitation. It will be seen that the anti-roll tank is just such a system.
3. THE ANTI-ROLL TANK
To ádequately cónsider even this one stabilizing device would need more
detailed treatment and much more space than an article like this alows. An impressive
-7patent literature has accumulated through the years which details a variety of tank
geometries of systems both passive and active (Ref. 5, 6). A passive system relies
only on the ship motion to transfer the tank fluid, in an active system the fluid is,
,in addition, acted upon by pumps, compressed air or similar means 1f consideration
is limited to passive internal tanks, i e , not open to the sea, the system is simply
a pair of tànks, 1. on each side of the ship, connected by a cross-over duct. This
dúct may be either a closed pipe completely filled with water., as in the so-called
U-tube tanks:, ora flume with a freè surface.
-.
-
The dynamics of the tank may, for the purposes of simple. discussion,
also be considered as a damped spring and mass system This is a crude model
since the damping, being largely viscous, is related more closely to velocity squared..
However, experimental tank responses do exhibit many of the characteristics of the
Simple system and equation (1) with , an angular coordinate describing the fluid
motion relative tO the tank, may be usefully employed, 1h particular, the fluid
motion subject to excitation by harmonic oscillation of the tank bas a resonance
where the motion of the fluid lags the excitation by 9 degrees with a magnification
factor of, typically, 2 or 3. The oscillation of the tankfluid produces an out-ofbalance torque equal to the excess fluid on i side over the other multiplied by a
suitable moment arm This torque will, of course, be in phase with the fluid
motion.
The combined wave-ship-tank system, as a very simple approximation,
may be represented by a block diagram
Wave of frequency
Rolling ship »
Tank fluid motion:
cos(wt-E1= Rólling torque
ship
K1 cös wt
cos (wtTank
Excitation
)
Rolling torque
K2:COs (cút
-
)
For the spécial cùe of a wave excitation at the ship' s resönat rolling frequency,
the phase angle E 1 is 90 degrees If, m addition, the tank is so designed that this
frequency is also the tank resonance, then e2 = 90 degrees and the torque produced
by the fluid motion in the tank is opposite in phase to the wave torque. When the
combination, of water transfer and tank moment arm is such that K2 is. a substantial
fraction of Kj the iolling of the ship at resonance will be correspondingly reduced
and an effective over-all stabilization will result.
A good mechanical analogy to the ship-tank system, as demonstrated in
Reference 7, is the double pendulum. Simplified, the fluid may be considered as a
1-dimensional filament. One coordinate describes the fluid motion in the tank and
2 are sufficient to describe the rolling motion of the ship-tank system. Since 1 part
of the system, the tank fluid, is carried by the other, the ship, and because the
essential forces are the gravitational forces, it is not surprising thatthe 2 systems
arecloselyanalogous. Reference 8 recommends, as a useful visual aid, that a
double pendulum model bé made. A single pendulum, representing the ship, is
first swung alone and the free oscillations observed. The "tank" pendulum with
about 1/lo the ship mass and the same length is then attached belOw Both masses
are then swung and the interplay and exchange of energy between tank and ship can
be seen.
The anti-roll tank design problem maybe stated by the following requirements
The tank resonant frequency should be the same as that of the ship.
The fluid transfer, capacity and geometry should be such that substantial
opposing torquès, compared with representative wave torques, are
developed at reson nee.
Quièt operation requires design of suitable nozzles in the cross-over
duct to prevent excessive splash noise of the fluid.
Details of tank design methodS aré available in the reférencè literature
and only a brief discussion will be given here. Recent designs have favoured the
free-surface as opposed to the U-tube tanks. Apparently the additional damping
from wavemaking losses in the open croSs-over duct tends to flatten the frequency
response curve and widen its efféctive band width. Another advantage is that the
free-surface tank may be easily tuned to variations in the ship resonant frequency,
because f changes in loading, by simply changing the depth of the fluid. It is f
passing interest that the original Watts' proposal of 1885 was for free-surface ta.nks
and that he fully appreciated the possibilities for depth tuning Tn 1911, H Biles, in
discussing Reference 5, described a very thorough seriès ,of model tests on various
free-surface tank geometries. Modern developments are given in References 8 and
9. Resonant frequency of a particular tank geometry may be calculated using the
U-tube analogy (Ref. 9). Tn practice, however, a model test is usually made and
the frequency response of the tank determined experimentally by oscillating the
model through a range of frequencies and measuring the water transfer A model
is particularly valuable in determining the effect of nozzles on the tank tuning and
their ability to quiet the flow.
A number of súcceSsfu installations have been ma7e recently with tank
sizes varying from 1 to 2 percent of the ship displacement. Performance of these
tanks has been good and 50 to 60 percent over-all roll reduction can be expected
from such installations With wave conditions in the resonant range of frequencies
roll reductiOn of 60 to 70 percent can be expected (Ref. 8).
4. COÑCLUDING REMARKS
Passive anti-roll tanks offer a good solution to the roll stabilization
problém. This is particúlarly so in the case of ships which must operate at low
speed for long periods. In high speed ships requiring very fine roll control fins
appear to be more attractive,for, although tank capacity can be increased,
effective stabilizing moments are not realized unless the tank is excited by a few
degrees of roll. Fins, on the other hand, can develop stabilizing moments to
maintain a fine control about the zero roll position. In cases, where retraction of
fins would be required, tanks, as an alternative, deserve consideration. They
are cheap to installand, although there is a space and weight penalty, part of this
may be reclaimed by using the tank as a reserve fuel or water storage tank. Finally,
they have the appeal of all simple and elegant solutions.
5. REFERENCES
Watts, P.
The Use of Water-Chambers for Reducing the Rolling
of Ships at Sea.
Trans. Inst. of Naval Architects, Vol. 26, 1885,
pp. 30-49..
4..
Chadwick, J.H.
On thé Stabilization of Roll.
St. Dems, M.
Craven, J. P.
Recent Contributions under the Bureau of Ships
Fundamental Hydroméchanics Research Program.
Blagoveschensky, S. N.
S.N.A.M.E. Trans., Vol. 63, 1955, pp; 237-280.
Pt. 3 - Control.
Jour. Ship Research, Vol. .2, No. 2, December 1958.
Theory of Ship Motions.
Dover Publications Inc., (2 volümes), New York, 1962.
Frahm, H.
Results of Trials of the Anti-Rolling Tanks at Sea.
Minorky, N,
Problems of Anti-Rolling Stabilization of ShipS by the
Activated Tank Method.
Trans. I.N.A., Vol. 53, Pt. 1, 1911', pp. 183-216.
A.S.N.E., Vol. 47, No.. 1., February 1935, pp. 87-119.
7. Chadwick, J. H.
Kiotter,' K.
Vasta, J.
Giddings, A.J., et al.
Giddings, A.J.
¡LES
On the Dynamics of Anti-Rolling Tanks.
Technical Report No. 2, NR 041-113, Stañford Univ.,
February 1953.
Rull Stabilization by Méans of Passive Tanks.
S.N.A.M.E. Trans., Vol. 69, 1961, pp. 411-460.
Progress in Tank Stabilizers.
4th Bi-Annual Seminar on Ship Behaviour at Sea,, June 1962..
Stevens Institute of Technology TM-136, January 1963.