TECHNISCHE HOGESCHOOL DELFT
AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANICARapport No. 439
-
A NOTE ON THE APPLICATION OF SHIP MOTION ThEORY- Prof.ir. J. Gerritsma
- Augus,t 1976
Prepared for Prof. O.Grim - 65 years
I,S
'Uf
Deift University of Technology
Ship Hydromechanics Laboratory Mekelweg 2
DeIft 2208 NetherIiiids
A NOTE ON THE APPLICATION OF SHIP MOTION THEORY
J. Cerritsma, Deif t University of Technology.
The development of methods to calculate ship motions in waves has been greatly stimulated by a more precise knowledge of the hydrodynamic forces, acting on
oscillating cylinders with ship-like cross sections. Methods to determine two-dimensional damping and added mass values became available after the work by
Grim [i] and Tasai [2] , which was based on Ursell's results for oscillating
circular cylinders on the free surface of a fluid [3]
The results of their method's have shown satisfactory agreement with experimental values, although in first instance only the so called Lewis transformation was applied to map the considered cross sections to the unit circle.Porter extended this work to cope with arbitrarily shaped ship cross
sections by using multi coefficient transformations. He also treated the case of finite water depth (4) . Finally, de Jong [s] and Tasai [6] developed
methods for swaying and rolling coefficients, which are important for lateral
motions.
The use of multi coefficient transformations or so called close fit methods, avoids the restrictions imposed by the Lewis transformation. The resulting fit
to actual ship cross sections including extreme shapes is indeed very good. However in many cases the simple Lewis transformation gives already a
satisfactory result, when only damping and added mass are considered. An alternative solution for the iin2ortant determination of added mass and
damping has been given by Frank [ii who used a pulsating source distribution on the cylinder surface on the mean position. The source strength follows from
the boundary condition on the cylinder surface by means of an integral equation. The results of both methods are very close to each other. A third method employs finite element techniques. Opsteegh [81 found a
complete agreement with the results of the close fit method for a rectangular
cross-section of which experimental values were available. The choice of a particular method to determine damping and added mass seems not very critical
and has become more or less a matter of taste or available computer facilitiès. To reduce computertime special transformations may be used in certain cases, for instance, as proposed by Loukakis, for bulbous sections.
The relatively fast development of strip theory methods to calculate ship wace responses is partly due to the fact that viscosity is not a dominant
factor in most of the ship motion problems; therefore numerical methods based on potential theory could be used for many purposes.
But early attempts to correlate experimental and calculated ship reponse
funtions in waves were only succesful, when the already mentioned accurate
values for sectional damping and added mass became available.
To a minor extent the formulation of the equations of motion has also been improved. Since the work by Korvin Kroukovsky and Jacobs [93 some small
additions in the expressions for the coefficients in the equarions of motion were intróduced. [iO, II, 12] . From a theoretical point of view these
additions are important. For example : the mass cross coupling coefficients
in heave and pitch now have the desired symmetry relation. However, the resulting effect of the new formuleation on the motion amplitudes and phases
Strangely enough the more refined equations of motion do not always give a better correlation with experimental values. In particular heave and pitch motion amplitudes atresonance conditions are somewhat overestimated by the new methods, which have the correct symmetry in the equations of motion.
Another point of interest concerns the limits of applicability of the strip theory with regard to ship form. The strip theory ignores infact three dimensional effects, particularly at the bow and the stern of the ship. To analyse the influence of this neglection , the length-beam ratio can be
regarded as an important parameter.
A systematic series of ship forms with a range of LIB values has been analysed, both by experiments and by calculations, to investigate the limiting value of the L/B ratio in this respect. The experimental results agree very satisfactory with strip theory calculations for L/B ratio's as low as 4, which is rather
surprising. [13]
The possibility to evaluate the ship response in regular waves by numerical methods only, and the validity of the superposition principle for the case of a
ship in irregular waves, anables the analysis of several aspects of the seagoing qualities of ship designs or of existing ships. Ship designers could profit from systematic series of ship reponse computations, with variations in the main ship dimensions, Up to now, it seems that the greater part of such applications is carried out for naval ships. In view of the enless variety of sea conditions,
which a ship will meet during its lifetime, alternative designs have to be
compared in corresponding sea conditions, which may be based on ocean wave
statistics or standardized wave spectra. Ïn this respect it should be noted that the choice of relevant wave spectra for design purposes is important : actual
sea conditions may differ considerably from standard sea spectrum formulations. If available, measured spectra of the considered sea area are certainly to be preferred.
Another useful application is the estimation of the ship speed in a seaway,
including the influence of voluntary power reduction, to avoid excessive dynamic phenomena. Such estimations include the calculation of the added
resistance due to waves, the determination of the conditions leading to wetness
and slamming and the determination of vertical acceleration. It is evident that a sustained sea speed estimation can be carried out only when limiting value for these occurences and quantities are given. That includes assumptions concerning power reduction (a human decision) with regard to acceptable shipment of water, slamming, etc, which may vary between different individuals. On the other hand, the inclusion of such empirical data, based on statistics from sea trials, leads to quite acceptable results when compared with actual ship data. Anyhow the results look sufficiently accurate for ship routing problems. A calculation procedure for sustained sea speed, based only on the main dimensions and form of the ship, the maximum available engine power and the main dimensions of the
propeller has been developed for ship routing problems by Journée [14]
Figure 1 gives a result of such a calculation in comparison with ship data from
M.S. Lukuga.
In sustained sea speed calculations the determination of the total resistance, including added wave resistance and wind resistance, is significant.
With increasing ship length the importance of an accurate estimation of added resistance in waves increases, because larger ships reduce power only in more severe weather conditions.
During ship trials on the North Atlantic a large containership (L=196m) could maintain full power in head seas with a significant height of 7 meters, although
the speed dropped from 23 to 17 knots.
The added wave resistance calculation is based on the determination of the radiated damping energy, due to the vertical ship motions 13 . This method
gives satisfactory results. An additional comparison of experiment and theory, including a full load condition as well as a ballast condition is shown in
Figure 2 [15]
For the calculation of power in waves, the propulsion characteristics for the ship performing oscillatory motions have to be known.
Experiments by Goeman [16] ,who used a forced oscillating ship model with a
propeller running at constant speed, have shown that the influence of
frequency of motion on the thrust and power is very small and can be neglected for practical purposes, when the propeller does not suffer from air suction. Thus for the sustained seaspeed calculation only the decrease of efficiency due to the higher loading is of interest, provided that extreme conditions are
excluded.
An early application of ship motion theory concerned the determination of wave bending moments. These calculations have been used in cases where extrapolation
of existing empirical knowledge was sufficient, as in the case of very large
tankers.
More recently the elastic response to waves, which have a frequency of encounter equal to the frequency of an elastic mode of motion, (for instance the two-node vertical mode, or one node torsional mode) has been analysed by several authors. These phenomena became important for very long ships. The determination of the wave excitation forces is essential for a correct analytical treatment of the
subject. Unfortunately the strip theory does not give reliable results for very small wave length ratio's, say A/L<0.5. This is contradictory to expectation because from theoretical considerations, the strip theory should work well for
such small wave lengths.
To investigate the influence of the wave length ratio, Moeyes [17] carried out
vertical wave load measurements on a model of a large tanker divided in 24
sections. The wave length ratio's varied from 0,065 to 1,5. He concluded that the strip theory gives satisfactory predictions of the wave load distribution along the length of the ship, for wavelengths larger than half the ship length. For smaller wave lengths, which are important for springing phenomena, the strip theory breaks down completely,see Figure 3. This may be due to the fact that three dimensional effects, especially at the bow and the stern, are not included in the strip theory. Therefore, a further analysis of springing is only possible when these effects are included in the calculation of the wave excitation.
The sustained sea speed calculation, and the analysis of springing are two
examples which may show the practical usefulness of ship motion theory, but they may also show the necessity for a further continuation of theoretical work. References
[i] 0. Grim
A method for a more precise computation of heaving and pitching motions, both in smooth water and in waves
Third Symposium on Naval Hydrodynamics, 1960.
F. Tasai
On the damping force and addedmass of ships heaving and pitching Research Institute for Applied Mechanics
Kyushu University, 1959 F. Ursell
On the virtual mass and damping of- floating bodies at zero speed ahead
Symposium on the behaviour of ships in a seaway
[4] W.R. Porter
Pressure distribution, added mass and damping coefficients for cylinders oscillating in a'free surface
Institute of Engineering research, University of Calfornia, 1960
[51 B. de Jong
Computation of the hydrodynamic coefficients of oscillating cylinders Deift Shipbuiding Laboratory, Report 174a, 1969
F. Tasai
Hydrodynamic force and moment produced by swaying and rolling oscillation of cylinders on the free surface
Research Institute for Applied Mechanics, 1961 W. Frank
Oscillation of cylinder in or below the free surface of deep fluids Naval Ship Research and Development Center, Report 2375, 1967
J.D. Opsteegh
Berekening van de hydrodynamische coefficienten van lichamen die zich be-vinden in de vrije opperviakte van een uitgestrekt fluidum, met behuip van
de eindige elementen methode; Thesis Delf t University of Technology, 1971
B.V. Korvin Kroukovsky and W.R. Jacobs
Pitching and heaving motions of a ship in regular waves Society of Naval Architects and Marine Engineers, 1957 [1O]H. Sding
Eine Modifikation der Streifen Methode; Schiffstechnik, 1969
[ii]w.w. Semenof-Tjan--Tsanskij et al
Motion of ships (In Russian language) Publishing Office Shipbuilding, 1969
[12]N. Salvesen, B.O. Tuck and O. Faltinsen
Ship motions and sea loads
Society of Naval Architects and Marine Engineers, 1970
[13]J. Gerritsma, W. Beukelman, C.C. Glansdorp
The effect of beam on the hydrodynamic characteristics of ship hulls Tenth Symposium Naval Hydrodynamics, 1974
[14] J.M.J. Journée
Prediction of speed and behavioúr of a ship in a seaway Report 427 Laboratorium voor Scheepshydromechanica, 1976
[15]J.M.J. Journée
Motions, resistance and propulsion of a ship in longitudinal regular waves Report 428 Laboratorium voor Scheepshydromechanica, 1976
[16] A. Goeman
Weerstands- en voortstuwingsproeven met een model van de S.A. van der Stel, oscillerei-id in viak water
Report 402 Laboratorium voor Scheepshydromechanica, 1974
[17]G. Moeyes
Measurement of exciting forces in short waves Report 437
Laboratorium voor Scheepshydromechanica, 1976
20
o
o
Cm)
reduction based on shipping forward
reduction based on slamming forward
200
IiH HiHHII Iii
1W
I!tWII
liii)
o 200 O STRIP THEORY ° r _jo o oLJ
n
F' aLFig.3 Sectional wave forces: ballast AIL = .215
(Tanker L= 310 m. modeiscale 1:67 )
Fig.2 Measured and calculated non-dimensional added resistance in regular waves of a fast cargoship (L= 150 m.,modelscale 1:50)
F .10 F =.15 F =20 o o c=88% c=55% SL c=89°fo SL o c=81% SL 5H '.., c=72% H
FULL W'' CONDITION LIGHT LOA' CONDITION LIGHT LOA' CONDITION
Fn=.15 Fn.2O
FULL LOAD CONDITION
A Fn =25
A
Fn=.30A
j
sL
g
Fn=.15 s Fn=.20 BALLAST CONDITION Fn=.25 s Fn=.30j
s s]
s O ' 0.5 10 1.50'O.S 10 1.50' 0.5 1.0 1.510 ' 0.5 10 1.5 s EXPERIMENT CALCULATEDc= fuel inlet ratio SH= voluntary speed and acceleration SL= voluntary speed and acceleration Fig. O 5 lolo 5 lolo 5 10
I Predicted and measured behaviour of
M.S.LUKUGA (L= 136 m.) in a sea-way ( Head waves ) 15 V 10 (kn) 5 200 o 2 RAW Pg w1 B2/L O 3 2 RAW P9W2.B2/L
hT
A Note on the Application of Ship Motion Theory.
J. G e r r its m a, Deift University of Technology
The development of methods to calculate ship motions in waves has beengreatly stimùlated by a more precise knowledge of the hydrodynamic forces, acting on oscillating cylinders with ship-like cross sections. Methods to determine two-dimensional damping and added mass values became available after the work by
Grim [i] and Tasai [21 which was based on Ursell's results for oscillating circular cylinders on the free surface of a fluid [33 .
The results of their method's have shown satisfactory agreement with experimental values, although in first instance only the so called Lewis transformation was applied to map the considered cross sections to the unit circle.Porter extended this workto cope with arbitrarily shaped ship cross
section by using multi coefficient transformations;. He also treated the case of finite water depth [4] . Finally, de Jong (5] and Tasai [6]. developed
methods for swaying and rolling coefficients, which are important for lateral
mo t i ön s .
The use of multi coefficiént transformations or so called close fit methods, avoids the restrictions imposed by the Lewis transformation. The resulting fit
to actual ship cross sections including extreme shapes is indeed very good. However in many cases the simplé Lewis transformation gives already a
satisfactory result, when only damping and added massare considered.
An alternative solution for the important. determination of added mass and
damping has been given by Frank [7J who ùsed a pulsating source distribution on the cylinder surface on the mean position. The source strength follows from
the boundary condition on the cylinder surface by means of an integrai equation. The results of both methods are very close to each other.
A third method employs finite element ;techniques. Opsteegh [8) found a
complete agreement with the results of the close fit method for a rectangular cross-section of which experimental valueswere available. The choice of a particular method to determine damping and added mass seems not very critical and has become more or less a matter of taste or available computer facilities. To reduce computertime special transformations maybe used in certain cases,
for instance, as proposed by Loukakis, for bulbous sections..
The relatively fast development of strip theory methods to calculate ship wace responses is partly due to the fact that viscosity is not a dominant
factor, in most of the ship motion problems; therefore numerical methods based on' potential theory could be used for many purposes..
But early attempts to correlate experimental and calculated ship reponse funtions in waves were only succesful, when the already mentioned accurate values for sectional damping and added mass became available.
To a minor extent the formulation of the equations of motion has also been
improved. Since the work by Korvin Kroukovsky'and Jacobs [9] some small
additions in the expressions for the coefficients in the equarions of motion were introduced.
jio,.
ii, 1.2) . From a theoretical point of view these.additions are important. For example : the mass cross coupling coefficients in heave and pitch now have the desired symmetry relation. However, the resulting effect of the new formuleation on the motion amplitudes and phases
is quite small, as shown for 'instance for heave and pitch in r131
u1/..rí
,Ñe.. 3c/fcOEÍ3s iJot/&
Strangely enough the more refined equations of motion do not always give a better correlation with experimental values. In particular heave and pitch motión amplitudes at resonance conditions are somewhat oyerestimated by the new methods, which have the correct symmetry in the equations of motion
Another point of interest concerns the limits of applicability of the strip theory with regard to ship form The strip theory ignores infact three dimensional effects, particularly at the bow and the stern of the ship. To analyse the influence of this neglection , the lengthbeam ratio can be
regarded as an important parameter.
A systematic series of ship forms with a range of L/B values has been analysed, both by experiments and by calculations, to investigate thé limiting value of the LIB ratio in this respect. The experimental results agree very satisfactory with strip theorycalculations for,L/B ratio's as low as 4, which is rather
surprising. ,[131 .
The possibility to evaluate the ship response in regular waves by numerical methods only., and the validity of thesuperposition principle for the case of a
ship in irregular waves, anables the analysis of. several aspects of the seagoing
qualities of ship designs or of existing ships. Ship designers could profit from systematic series of ship reponse computations, with variations in the main ship dimensions, Up to now, it seems that the greater part of such applications is carried out for naval ships. In view of the enless variety of sea conditions,
which a ship will meet during its lifetime., alternative des,igñs have to be
compared in corresponding sea conditions, which may be based on ocean wave
statistics or standardized wave spectra. In this respect it should be noted that the choice of relevant wae spectra for design purposes is important : actual sea conditions may differ considerably from standard sea spectrum formulations. If available, measured spectra of the considered sea area are certainly to be
preferred.
Another useful application is the estimation of the ship speed in a seaway, including the influence of voluntary power reduction, to avoid excessive dynamic phenomena. Such estimations include the calculation of the added
resistance due to wayes, the determination of the conditions leading to wetness and slamming and the determination of vertical acceleratidn. It is evident that a sustained sea speed estimation can be carried out only when limiting value for these occurences and quantities are given. That includes assumptions concerning power reduction (a human decision) with regard to acceptable shipment of water, slamming, etc, which may vary between different individuals. On the other hand, the inclusion of such empirical data, based on statistics from sea trials, leads to quite acceptable results when compared with actual ship data. Anyhow the results look sufficiently accurate for ship routing problems. A calculation procedure for sustained sea speed, based only on the main dimensions and form of the ship, the maximum available engine power and the main dimensions of the propeller has been developed for ship routing problems by Journée [i4
Figure I gives a result of such a calculation in comparison with ship data from
M.S. Lukuga.
In sustained sea speed calculations the determination of the total resistance, including added wave resistance and wind resistance, is significant.
With increasing 'ship length the importance of an accurate estimation of added resistance in waves increases, becausef larger ships reduce power only in more severe weather conditions..
During ship trials on the North Atlantic a large containership (L196m) could
maintain full power in head seas with' a significant height of 7 meters, although the s:peed dropped from 23 to 17 knots.
-The added wave resistance calculation is based' on the determination of the
radiated damping energy, due to the vertical ship motions [13 . This method gives satisfactory results. An' additional comparison of experiment and theory,
including a full load condition as well as a ballast condition is shown in Figure 2 115]
For the calculation of power in waves, the propulsion characteristics for the ship performing oscillatory motions have to be known.
Experiments by Goeman [16] ,who used a forced oscillating ship modeiwith a propeller running at constant speed, have shown that the influence of
frequency of motion on the thrust and power is very small and can be neglected
for practical purposes, when the propeller does not suffer from air suction. Thus for the sustained seaspeed calculation only the decrease of efficiency due
to the higher loading is of interest,, provided that extreme conditions are excluded.
An early application of ship motion theory concerned the determination of wave bending moments. These calculations have been used in cases where extrapolation of existing empirical knowledge was sufficient, as in the case of very large
tankers.
More recently the élastic response to waves, which have a frequency of encounter equal to the frequency of an elastic mode of motion, (for instance the two-node vertical mode, or one node torsional mode) has been analysed by several authors. These phenomena became important for very long ships The determination of the
wave excitation forces is essential for a correct analytical treatment of the
subject. Unfortuna'tely.thé strip theory does not give reliable results for very
small wave length ratio's, say A/L<0..5.. This is contradictory to expectation
because from theoretical considerations, the strip theory should work well for such small wave lengths.
To investigate thé Influence of the wave length ratio, Moeyes [17] carried out
vertical wave load measurements on a model of a large tanker divided in 24
sections. The wave length ratio's varied from 0,065 to 1,5. He concluded that the strip theory gives satisfactory predictions of the wave load distribution along
the length of the ship, for wavelengths larger than half the ship. length. For
smaller wave lengths, which are important for springing phenomena, the strip
theory breaks down completely,see Figure 3. This may be due, to the fact that
three dimensional effects, especially at the bow and the stern, are not included in the strip theory. Therefore, a further analysis of springing is only possible when these effects are included in the calculation of the wave
excitation.
The sustained sea speed calculation, and the analysis of springing are two examples which may show the practical usefulness of ship motion theory, but they my also show the necessity for a further continuation of theoretical work.
References
O. Grim
A method for a more precise computation of heaving and pitching motions, both in smooth water and in waves
Third: Symposium' on Naval Hydrodynamics, 1960. F. Tasai
On the damping force. and' added mass of ships heaving and pitching
Research Institute for Applied Mechanics Kyushu University, 1959
F. Ursell . .
On the virtual mass and damping of floating bodies at. zero speed ahead
Symposium on the behaviour of ships in a seaway
Wageningen, .1957
[4] W.R. Porter
Pressure distribution, added mass and damping coefficients for cylinders oscillating in a free surface
Institute of Engineering research, University of Calfornia, 1960
[5) B. de Jong
Computation of the hydrodynamic coefficients of oscillating cylinders
Deift Shipbuiding Laboratory, Report 174a, 1969
-[6] F. Tasai
Hydrodynamic force and moment produced by swaying and rolling oscillation of cylinders on the free surface
Research Institute for Applied Mechanics, 1961 W. Frank
Oscillation of cylinder in or below the free surface of deep fluids Naval Ship Research and Development Center, Report 2375, 1967
J.D. Opsteegh
Berekening van de hydrodynamische coefficienten van lichamen die zich be-vinden in de vrije opperviakte van een uitgestrekt fluidum, met behuip van de eindige elementen methode; Thesis Delft University of Technology, 1971 LV. Korvin Kroukovsky and W.R. Jacobs
Pitching and heaving motions of a ship in regular waves Society of Naval Architects and Marine Engineers, 1957 [1O]H. Sding
Eine Modifikation der Streifen Methode; Schiffstechnik, 1969 [i i] w.w. Semenof-Tjan-Tsanskij et al
Motion of ships (In Russian language) Publishing Office Shipbuilding, 1969
[12]N. Salvesen, B.O. Tuck and O. Faltinsen
Ship motions and sea loads
Society of Naval Architects and Marine Engineers, 1970
[13]J. Gerritsma, W. Beukelman, C.C. Glansdorp
The effect of beam on the hydrodynamic characteristics of ship hulls Tenth Symposium Naval Hydrodynamics, 1974
[14] J.M.J. Journée
Prediction of speed and behaviour of a shipin a seaway Report 427 Laboratorium voor Scheepshydromechanica, 1976
[15]J.M.J. Journée
Motions, resistance and propulsion of a ship in longitudinal regular waves
Report 428 Laboratorium voor Scheepshydromechanica, 1976 4;
[16] A. Goeman
Weerstands- en voortstuwingsproeven met een model van de S.A. van der Stel, oscillerend in viak water
Report 402 Laboratorium voor Scheepshydromechanica, 1974
[17]G. Moeyes
Measurement of exciting forces in short waves Report 437
Laboratorium voor Scheepshydroinechanica, 1976
Schiffstechnik Bd. 23 1976 184
20 15 '1 (kn) RAW pgw2B/L RAW pg B2/L 3 o Cm)
c = fuel inlet ratio
SH= voluntary speed reduction based on shipping
and acceleration forward
SL= voluntary speed rethiction based on slaimning and acceleration forward
Fig. 1 Predicted and measured behaviour of M.S.LUKUC4 (L= 136 m.) in a sea-way.
(Headwaves )
185 -200-I1'1WH
STRIP THEORY 200Fig.2 Measured and calculaed non-dimensional added resistance in regular waves of a fast cargoship (L 150 rn.,rnodelscaie 1:50)
F'
Fig.3SectiOflàl wave forces: ballast AIL = .215 (Tanker L 310 rn. modeiscale 1:67 ) Schifistechnik Bd..23 - 1976 n..10 .15 =20 FULL WAD D
CONDITION LIGHT LOA i CONDITION LIGHT LoAD CONDITION
Fn=.15 Fn.20
FULL LOAD CONDITION
Fn..25
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