R74R7
LABORATORIUM VOOR SCHEEPSHYDROMECHANICA
PRACTICAL USE OF SHIP MOTION
CALCULATIONS FOR DESIGN AND OPERATION OF SHIPS
Prof.ir. J.Gerritsma
610 - A mel 1984
Deift University of Technology Ship Hydromechanics Laboratory Mekelweg 2
2628 CD DELFT
The Netherlands Phone 015 -786882
Practical use of ship motion calculations for the design and operation of ships.
Prof.ir. J. Gerritsma, Delft University of Technology Summary.
Ship motion calculation methods are reviewed and discussed from a practical point of view.
Some examples are given of the use of these methods in ship design procedures and for operational applications.
1. Introduction.
For more than twenty five years ship responses in a seaway can be calculated with sufficient engineering accuracy. This applies to normal ship forms, moderate ship speeds and mode-rate responses, excluding extreme motions such as capsizing. The calculation methods are mainly based on the assumption of potential flow and the use of a linear strip theory, ne-glecting the influence of three dimensional flow patterns. The effects of viscosity, for instance in rolling, are esti-mated by using empirical data.
From theoretical considerations the use of strip theory
methods should be restricted to slender shipforms, low Froude numbers and high frequencies of encounter, but in many cases these restrictions appear to be very flexible, as shown by the results of model experiments.
The resulting wide applicability is one reason why the strip theory method can be regarded as a valuable design tool. A similar remark applies to linearity: although the
assump-tion of linearity restricts the moassump-tion amplitudes, moderate to severe responses in an irregular seaway can be determined with sufficient accuracy using linear superposition.
In the strip theory the hydrodynamic forces on two dimensio-nal cross sections of the ship are integrated over the ship length to determine the total forces and moments acting on the ship.
This applies to the forces due to the motions of the ship, as well as to the wave forces acting on the ship. The strip theory methods are similar to the slender body techniques as used in aeronautical engineering, except for the important free surface effects.
The equations of motions are linear and contain first order variables only to represent displacements, velocities and
accelerations and the wave forces are a linear function of the wave-amplitudes.
From the equations of motion the amplitude and phase response characteristics can be determined as a function of ship speed,
wave dimensions and wave direction. These in turn are the
basis for a determination of the ship response in a given wave spectrum.
The correlation of ship motion calculations with full scale motion measurement results is difficult due to the complex nature of the seaway.
Consequently only a very few satisfactory comparisons of measured and calculated full scale motions are available. Therefore model experiments have been very important in sea-keeping research to develope and to check ship motion calcu-lation methods. In particular forced oscilcalcu-lation model tech-niques have been most useful in this respect to compare for instance calculated hydrodynamic mass and damping with expe-rimental values.
A wide variety of model motion experiments in regular, irre-gular and oblique waves has been carried out, confirming in general that the existing calculation methods are indeed
use-ful.
In seakeeping problems a reasonably accurate calculation method is a must because a large number of variables plays
a role.
A complete model experiment to determine the seakeeping be-haviour of a given hull would be unacceptable from an econo-mic point of view, because it would be extremely time consu-ming.
The application of ship motion calculations to optimize the seakeeping behaviour of ships started quite recently. In the
early 1970's Capt. J.W. Kehoe draw the attention to the poor performance of U.S. destroyers in head seas as compared with USSR ships of similar type:
"The Soviet Kotlin-Class destroyer operating "in close proximity to the carrier tast group "appeared to be taking no water over the bow "and only occasionally raised spray above the "fo'c's'le deck edge. U.S. sailors wore foul "weather gear and stayed off the fo'c's'le; "Soviet sailors paraded on the fo'c's'le in
"their shirt sleeves.
Kehoe's report in 1973
[iJ
gave a large impact to the design of optimum hull forms in seawaves. In these design procedures a measure of seakeeping merit is maximized by proper selection of geometric hull characteristics within practical designli-mits. Optimum hulls designed in this way showed remarkable
improvements compared with existing ships.
The methods require a multitude of seakeeping calculations. Linear strip theory methods seem to satisfy the requirements for such optimization procedures for only moderate computer time costs.
This is also the case for the determination of the effectivi-ness of a ship carrying out a certain task in a seaway. Degra-dation of the operability of the ship, consisting of many
subsystems (crew, hull, propulsion, air capability etc.) can be determined by using limiting criteria with regard to motion amplitudes, accelerations etc. in waves. In combination with the statistics of the wave climate in the considered sea
area the effectiviness of alternative ship designs may be compared on the basis of such seakeeping calculations. Ship response calculations based on predicted wave spectra are used for optimum routing purposes, but only recently it has been proposed to analyze the sea spectrum and the
ship responses on board of the ship for operational purposes. 2. Calculation of ship motions.
A few remarks will be made on the practical applicability of current methods to calculate ship motions in waves.
in-resulted in a rather fast development of ship motion theory. In the past three decades a fast amount of literature on this subject has been published including a further development and rationalism of strip theory methods and their
experimen-tal verification.
Also three-dimensional methods have been developed in parti-cular to cope with non slender floating structures, such as used in the offshore techniques.
In strip theory methods the calculation of the hydrodynamic forces (added mass and damping) of shiplike cross-sections is important. These calculations are usually carried out using Lewis form cross sections or multi parameter conformal trans-formations in combination with multipole expansion techniques
[2, 3, 4
] . Also Frank's close-fit method using a distribution of sources on the contour of the cross section found wide
application [5} . Using the first method the accuracy of the transformation with regard to the geometrical features of the cross sections is not too critical for the determination of added mass and damping. In many cases the simple Lewis forms, defined only by the beam-draught ratio b/T and the area
coefficient of the cross section A/2bT give a satisfactory result.
In Figure 1 a comparison is made between Lewis forms and an eleven parameter close fit approximation for a Sixty Series CB = .70 hull form.
The transformation is based on: N
z = (2n-1)
n=0
a21
with N = 2 for the Lewis transformation N = 11 for the close fit approximation
However the difference in the calculated damping and added mass as given in the Table in Figure 1 is very small.
Special families of conformal mapping functions have been de-veloped for bulbous sections and for hard chine cross sections. An interesting extended Lewis form family, using additionally the vertical position of the centroid of the cross section
5
I
(N = 3) has been used to show the influence of the vertical position of the center of buoyancy on the seakeeping response of a ship[61
Bulbous cross sections and cross sections as used in SWATH's have a relatively small intersection with the free surface. The resulting small damping for vertical motions and the small wave excitation forces require an accurate numerical treatment
to determine the hydrodynamic forces.
Frank's close fit method is a reliable tool to determine the two-dimensional hydrodynamic forces in strip theory methods. "Irregular frequencies" where discontinuities in the calcula-ted hydrodynamic coefficients occur may be faired in a plot on a base of oscillation frequency as a practical solution. According to Ursell an analytical solution of the irregular frequency problem is the addition of a source in the origin within the contour [7]
Finite element techniques are a third method to determine the hydrodynamic forces on oscillating cylinders. In Figure 2 one result is given for a shiplike cross section in compari-son with a multipole expansion method as well as an experi-mental result, showing excellent agreement [8] . The finite element methods require more computer time, but this method may be used in cases where complicated boundaries, such as
sea bottom configurations or/and walls have to be taken into account.
In general strip theory methods are applicable for length-beam ratio's larger than 4, excluding very blunt bow forms, but in a few cases even smaller ratio's did not seem prohi-bitive.
For a range of L/B ratio's, covering L/B = 4 to L/B = 20 model experiment results and calculations have been compared to in-vestigate the applicability of strip theory methods
[J
.Theprogram included the measurement of added mass and damping of vertical motions, using forced oscillation techniques, the motion response and the added resistance in waves. A very
Experiments in relatively short waves to analyse the elastic response of a ship in head waves have shown that strip theory
I
found in the considered range of length-beam ratio's, exceptfor relatively high frequencies in combibation with small length-beam ratio' s.
As an example a typical result is given in Figure 3.
For very small length-beam ratio's three-dimensional effects at the bow and the stern of the ship cannot be neglected. An extreme case in this respect is an offshore barge with L/B = 1.5, which cannot be regarded as a slender ship form. Apparently the strip theory overestimates the pitch damping, resulting in an underestimation of the pitching amplitudes, see Figure 4, as reported by Kaplan [io] . In this particu-lar case frequency dependent three-dimensional correction factors have been used that multiply the two-dimensional strip theory damping coefficients. These correction factors were based on three dimensional solutions for thin ships by Haskind in comparison with corresponding two dimensional calculations.
In following waves very low frequencies of encounter may occur and in these conditions strip theory methods fail for instance in the calculation of wave bending moments. This is partly due to the divergence of two-dimensional added mass for frequencies approaching zero.
Takezawa used three-dimensional corrections for added mass and damping, based on a revision of the slender body theory by Maruo, which may be regarded as an interpolation between the
slenderbody theory, valid at low frequencies,and the strip theory. [11]
By applying this method a satisfactory agreement between ex-perimental and calculated vertical beding moments has been found, although discrepencies still exist for the vertical shear forces at or near zero encounter frequency.
For the calculation of ship motion amplitudes at very low frequencies pragmatic and sometimes rather intuitive correc-tions to the strip theory methods are used. For instance the added mass may be taken equal to zero below a certain frequency or the amplitude response functions are extra-polated to known values at zero frequency of encounter.
7
calculations do mtpredict the wave forces correctly when A/L < 0.5.
The experiments were carried out with a model divided in 24 separate sections to determine the distribution of the wave forces along the length of the model [12]
A result for AlL = 0.215 is given in Figure 5.
It could be assumed that three-dimensional methods would give a better estimate, because for the considered tankermodel the form of the bow is rather blunt.
In the last few years considerable progress has been made in the solution of the three-dimensional linear ship motion pro-blem at forward speed, also including finite depth. The three dimensional calculation methods make use of panel source
distributions or finite element techniques.
In offshore engineering three-dimensional methods (zero speed) are commonly used to cope with the shape of large floating structures, where two-dimensional calculations would give wrong results. For ships with non zero Froude number these methods are an improvement for the small frequency range and for blunt ship forms, as compared with the use of two-dimensio-nal methods.
However the thb.ee-dimensional numerical calculations are very time consuming and are not yet suited for routine calculations, as used in ship design work.
There is no doubt that with the rapid development of computers this situation will change in the future.
A comparison of calculated damping and added mass for vertical and horizontal harmonic motions of a tanker in shallow water with forward speed has been carried out using the two-dimen-sional strip theory and Lewis cross section forms, a two-di-mensional diffraction method (source distribution) and a three-dimensional diffraction method. The results have been compared with model experiments using a segmented force-oscillated model
in shallow water (H/T = 1.5 and H/T = 1.15), see Figure 6 and 7. The agreement between the three methods is very satisfactory and surprisingly enough there seems to be no preference for one of the three methods. Also the experimental values corre-late well with the calculations [13] . The investigation has been carried out to study allowable keel clearances of large ships.
Viscous effects are important for the rolling motion of a ship. Extensive use has been made of experimental methods for the determination of roll damping. In particular Japanese
investigators have been carried out systematic roll experiments, using forces roll and roll decay tests with ship models.
Roll damping can be split up in components resulting from skin friction, wave energy dissipation eddies, dynamic lift of the hull and appendages, normal pressure on bilge keels and the
influence of pressures due to bilge keels on the hull.
A recent non linear roll damping model by Ikeda contains second and third order wave components as well as a third order eddy component.
It is common practice to use empirical linearized roll damping
I
data in the current strip theory methods to calculated theship motions. However the rolling motion of a ship is a compli-cated and sometimes highly non linear phenomenon: there is
still a need for further investigation. Ikeda stresses the importance of a rational non-linear roll damping model to investigate the various damping components in detail, using forced roll techniques. [14J
The assumption of linearity for the other modes of motion is the basis for the determination of the ship responses in a wave spectrum, using the superposition principle. Model expe-riments in irregular and regular waves have been used to
check the assumptions. The co- and quadrature spectra of vertical motions and the waves enabled the determination of the amplitude-and phase response characteristics, which could be compared
with corresponding runs in regular waves.
Figure 8 shows the very close agreement as found for an eight feet Series Sixty CB = 0.70 ship model [15]
In general a similar full scale experiment cannot be carried out with comparable accuracy because the measurements of the directional spreading of the wave energy is difficult and existing directional wave buoys only provide a rough estimate of the wave energy spreading function. In exceptional cases a reasonable long crested sea has been encountered and amplitude response functions derived from such tests showed an acceptable accuracy as compared with model experiments and strip theory calculations [16]
9
the well known spectrum formulations, because two or more wave systems with different main directions may be
super-imposed. A directional wave buoy recording (WAVECbuoy) as made during the 1982 "Tydeman" trials (see Figure 9) shows a double peaked spectrum with two very different main directions [17] For the calculation of the sustained speed of a ship in a sea-way the added resistance in waves has to be known in addition to the limitation of the ship speed due to shipping of green water, large vertical accelerations and slamming.
A simple but fairly accurate estimate of the added resistance can be made by relating the dissipated damping energy due to the shipmotions, to the energy necessary for the extra resis-tance [18] . For normal shipforms the results are acceptable for practical use, see Figure 10.
Very little systematic research has been carried out to the influence of shipmotions on the propulsive efficiency of a
ship. Model experiments in waves suggest that the increased loading of the propeller is the main cause of the decreased efficiency, as long as the propeller remains immersed for
most of the time. The vertical and horizontal oscillatory
motions of the propeller have little influence on the effi-ciency, as shown by forced oscillation of model propellers and by running propellers under a wave surface. Also in this case excessive motions leading to ventilation etc. are excluded.
3. Application of ship motion calculations in the design and operation of ships.
The relation between the form of a ship and the responses in a seaway can be determined by calculation of the significant motion amplitudes and related phenomena, such as slamming, shipping of water and added resistance. Systematic work in this field has been carried out by Beukelman and Huijser for Series Sixty hull forms in head seas, corresponding to sea states 5, 7 and 9 [19]
As an example Figure 11 gives the influence of ship length and the vertical prismatic coefficient on the response, charac-terized by the significant amplitudes of heave, pitch, accele-ration and relative motion of the bow, the added resistance
5
in waves and the occurrence of slamming. Also the influence of the block coefficient, the longitudinal position of the centre of buoyancy and the gyradius has been investigated. Similar work has been published by various authors [20, 21] and the results may be used to obtain some insight in the effects of form, size and weight distribution on the sea-keeping behaviour of ships.A systematic approach to optimize one particular ship type in waves has been carried out by Bau et al [22] . In this parametric study hull form variations of a fast displacement ship have been analysed to optimize the sustained sea speed. The following hull form parameters have been considered:
CBF CWLI L/V , B/TI LCB, as well as the pitch gyradius kyy/L Sea states 3, 4, 5 and 6, with significant wave heights
up to 3.9 m, have been chosen in accordance with the ITTC 1978 recommendation.
Speed limiting criteria, as used in the analysis to determine
In Table 1 an example is given of the calculated sustained
sea speed in sea state 6 (Hy= 3.9 m, T1 10,6 s) as a
function of CBI CWL and L/VV3
Table 1: Sustained speed in seastate 6 CB 0.44 0.48 0.52 CWL WL CWL 0.73 0.76 0.78 0.73 0.76 0.78 0.73 0.76 0.78 7.50 16.2 19.7 20.9 15.5 17.6 19.7 14.9 17.0 18.6 8.00 17.5 21.0 22.3 16.6 18.7 20.8 16.0 18.1 19.7 8.50 18.7 22.4 23.7 17.9 20.2 22.2 17.2 19.2 21.0
the sustained sea speed are as follows:
Significant amplitude vertical acceleration FPP < 0.4 g
Probability of deck wetness at bow < 7%
Probability of slamming at 3/20 L fwd < 3%
S
The combination CB 0.44, Cw 0.78 and L/V' = 8.5 results in the highest sustained sea speed. The analysis showed that slamming is important only in sea state 6, but the vertical acceleration forward causes the largest limita-tion of the sustained speed of the ship. In a similar way the influence of the other parameters has been investigated and it could be concluded that large values for CWL and
L/V and a small pitch gyradius are favourable. Although a large B/T ratio increases the damping for vertical motions, it is not recommended to choose the beam larger than neces-sary for stability reasons, to avoid a large increase in the still water resistance.
An interesting and more direct method to optimize the hull form with regard to seakeeping behaviour has been published by Bales [23] . Bales developed an analytical model to re-late hull form parameters to an index of seakeeping merit, by using the geometrical data of 20 existing destroyer hull forms, scaled down to a uniform displacement.
The seakeeping index, as used by Bales, was an unweighted average of analytically computed ship responses in head seas (pitch, heave, relative vertical motions and accelera-tion and a slamming indicator) and five forward speeds, nor-malized to a seakeeping rank factor R for each of the 20 hulls. This index was assumed to have a simple linear relation with
only a few hull form parameters:
R=a +aC +aC
0+a (T
1 WE' 2 WA 3 /L) + a4(C/L) + aSCVPF+ a6CVPA
(1)
where: - waterplane coefficient
C - vertical prismatic coefficient C/L - keel length ratio
Subscripts F and A indicate forward and aft.
With a linear regression technique the coefficients,,a"in the equation have been determined using the geometrical data of the 20 hulls.
De R-values as computed from equation (1) correlated very well with the corresponding values as computed for each indi-vidual hull. With (1) the quantative influence of the various
form parameters can be determined and the seakeeping index R can be optimized for a particular design. The analysis indi-cates that CWF and should be as large as possible and T/L, CVPA and CVPF should be as small as possible. The effect of C/L is very small. Bales designed an optimum hull (no. 21) using this method and compared the resulting responses with
the best (no. 06) and the worst (no. 13) ship of the
20 hull form series. Figure 12 gives a typical result to show the improvement in comparison with the existing ships. Model experiments confirmed the superior seakeeping behaviour, but there was a small increase 'in still water resistance.
McCreight extended Bales method by using a larger number of hull coefficients and including the effects of varying dis-placement[24] . His resulting regression equation for the seakeeping rank is given by:
R=a +aBMV+aC
+aC
+aBM/(BL)3 +
o 1 L
2VPF
3VPA
4 L+ a5L + a6T/B + a7AWA/V'+ a8(LCF-LCB)V +
+ a9LCB/V+ a10L2/(BT).
(2)To optimize the seakeeping behaviour of a hydrographic research vessel van Wijngaarden applied the Bales method and compared the result with the behaviour of the existing vessel. [25J . He uses a different formulation for the seakeeping index:
R = a + a C1 + a2LCB + a3C + a4(L/B) +
0
1P
+ a5(L/T) + a6 LCF (3)
The behaviour of the ship in waves was characterized by heave, pitch, absolute vertical acceleration and relative vertical motion at the bow in longcrested ITTC 1978 wave spectra with
average periods ranging from 3 to 8 seconds, which are consi-dered as typical for the North Sea.
Also a regression equation with respect with the calm water resistance has been used in the optimization process:
S
-
13-R =b +bC +bL/V'+b3B/T+b4LCB
T o
ip
2The resulting optimized hull form has an almost equal calm water resistance and improved seagoing qualities at the same
displacement (V= 1014 m3; L = 54 m, LOPT = 50.70 m).
Van Wijngaarden concludes that for this particular case the seakeeping responses are mainly influence by the prismatic co-efficient and the longitudinal location of the centre of buoyancy LCB.
The seakeeping index is only an average indication of the seagoing qualities of a ship. A more detailed analysis is needed when a ship or an other floating structure has to perform a certain task in seawaves for instance a rescue
operation using a ship born helicopter, the use of an offshore crane ship - or the take-off and landing of an aeroplane.
When limiting criteria are known for a particular mission of a ship in a swaway, course and speed combinations for which the mission can be executed define an area or "window" in the speed-polar diagram.The ratio of this window to the area of the full speed polar plane defines an operability index for the considered ship, mission and seaway.
Figure 13 gives the windows for the take off and landing of a VTOL in sea states 4, 5 and 6. The criteria may refer to maximum allowable pitch and roll angles, as well as to the occurrence of wetness and slamming. This method has been used by Comstock et al to compare the seakeeping performance of air capable ships of different type, such as monohulls, cata-marans, SWATH's [261 . In this study the operability indices have been averaged, using statistical data of the considered wave climate. These averages define a so called performance index, which can be used for comparison purposes.
For a range of displacements Bales used his optimization tech-niques to design ship hulls with optimum seakeeping quali-ties, but also antioptimum seakeeping hull forms, to obtain envelopes of attainable performance as a function of the size of the ship (displacements) [27]
Three sets of limiting criteria were used for the analysis of the capability of supporting combat operations in the North Atlantic, as given in Table 2.
Table 2
Limiting criteria
SSA = significant single amplitude.
Criteria set A bounds the ability to full support of combat operations, admitting full mobility. Criteria set B bounds limited combat support and full mobility and set C defines the threshold of seaway survivability conditions.
In Figure 14 the "operability index" using the criteria C in sea states 6 and 7 have been given for three existing hull forms and for the optimum and anti-optimum designs. In Figure 15 the performance index for operation on the North Atlantic is given for each of the three sets of criteria, indicating the dominant influence of size, as
well as the ranges of attainable performance.
Implicitly it is assumed in this analysis that the perfor-mance degradation of subsystems such as the hull, the pro-pulsion, the crew is included in the limiting criteria.
A more systematic treatment of the problem of subsystem degradation has been proposed by Hosoda et al [28]
For the determination of the effectiveness of a ship, the mission in the considered sea area and the degradation of the subsystems due to the ship responses have to be known.
When the subystems are independent of each other with res-pect to their performance in a seaway the shipsystem has
Limiting response A B C
SSA of pitch 3 3 8
SSA of roll 5 10 30
Deck wetness incidence sta 0; No/hr 30 30 50
Bottom slamming inc. sta 3; No/hr 20 20 50 SSA of vertical acc.bridge; g's 0.4 0.4 0.8
SSA of lateral acc. bridge; g's 0.2 0.2 0.4
Sonar dome emergence; No/hr 24 -
-SSA of vertical velocity sta 4;m/s 2 -
--
15-a series structure -and the perform-ance effectiviness e5 of the system can be given by:
n
e .11 e.
S 1=1
where e is the effectiviness of subsystem i in the considered seaway.
In a parallel system the subsystems are complementary to each other, which means that the system does not fails when one of the subsystems breaks down.
For a parallel system the performance effectiviness e is given by:
m
e = 1 - .11 (1 - e.)
p j=1 :i
where e is the performance effectiviness of the j'th subsystem.
Apparently equations (5) and (6) are used in reliability engineering.
An example of a combination of a series- and a parallel
structure is givenin Figure 16 for the case of a patrol
vessel, equipped with a helicopter for rescue operations. As an example the degradation of the performance of a num-ber of subsystems due to ship responses is given in
Figure 17. This concerns the performance of the crew in ad-verse conditions (roll and pitch angles, vertical and
hori-zontal accelerations), the sustained sea speed (hull and propulsion) as well as the take off and landing of the helicopter (relative wind, roll and pitch angles).
According to the equations (5) and (6) the integrated effect of the degradation of subsystems can be important although the individual effects for each subsystem may be small.
In Figure 18 the performance degradation of a patrol boat crew due to pitch, roll, vertical and horizontal accelera-tion is given to show the effect of integraaccelera-tion.
Similar diagrams may be constructed for the total system ship, which provides the possibility to compare the effec-tiviness of alternative designs.
Also in this case the statistics of the wave climate of the considered sea area or sea route may be used for "a long termt' analysis of the effectiviness of the ship in carrying out a
e
specified mission.The results of such investigations reveil significant dif-ferences in the performance of conventional mono-hulls and the advanced SWATH's for patrol and rescue missions.
Figure 19 gives the long term mission effectiviness on a base of Beaufort number for six different ships in short crested head seas. The effects of ship type and ship size are clearly illustrated in the Figure.
In the last decade strip theory methods have been used to compute the speed loss in a seaway for optimal routing pur-poses. For routine computation of the speed loss Journée developed a program which needs only the main data of the ship and the propulsion as input to determine the sustained ship speed as a function of wave height, wave period and main wave direction speed limiting criteria with respect to
slamming, shipping of green water and vertical accelerations according to Ochi and Motter [29] are used:
Fully loaded:
p [ green water and/or
S.S.A.
acceleration fwd > 0.4 g]L
Ballast:
p [ slamming and/or
S.S.A.
acceleration fwd > 0.4 g] <3%
The added resistance is computed according to [18] and appro-ximations are used for the determination of the still water resistance, the propulsive efficiency, steering resistance and the influence of fouling.
The wave spectra, as used in these calculations, are based on the predicted significant wave height, wave period and wave direction on the considered route [30] . Only recently possibilities exist for the detailed prediction of wave directional spectra and these would increase the accuracy of the computed ship responses and the resulting speedloss.
Due to the rapid development of computers which are suited for use on board ships, operational use of calculated ship responses seems possibile.
In theory it would be possible to determine the wave spectrum
par-S (w ) =
r e
17
-ticular motion component (for instance pitch), the calculated amplitude response function and the equation:
Y (w
)2
S (wr e e (7)
However, (7) assumes that the average wave direction as well as the directional spreading of the wave spectrum are known.
In general this information is not available and complex sea conditions consisting of sea and swell, with different direc-tions could be met as remarked before.
In a few favourable cases it has been possible to determine with reasonable accuracy the significant wave height by using measured ship responses.
Conolly used this method to analyse full scale trials with fregates in head seas, using the computed relation:
ry3 f(H31 Fn) (8)
where ry3 stands for pitch, heave or vertical acceleration for-ward.
In this case it was assumed that the seaway could be des-cribed with sufficient accuracy by a unidirectional, one parameter Pierson Moscowitch spectrum [31J . The resulting significant wave height was used to reduce measured ampli-tude responses to unit wave ampliampli-tudes for the comparison of different ships running in close proximity in the same
sea-way.
The Delft Ship Hydromechanic Laboratory assisted Lloyds Register of Shipping to develope an onboard system to deter-mine the significant wave height and the average wave period
by using monitored response data (pitch, heave, vertical acce-leration forward, midship bending stress) and a calculated data base of ship responses. In the data base the significant responses of the ship are stored as a function of wave height, wave period and wave direction can by means of a search pro-cedure the signficant wave height and period can be determined using the measured significant response amplitudes and average periods as an input [32].
re-/
suiting wave heights and periods canbë compared, see
Figure 20.
Also in this case the ship is used more or less as a wave buoy, assuming that the average wave direction can be es-timated visually with sufficient accuracy and the direc-tional spreading of the wave spectrum (cos2) is known.
Corresponding wave buoy measurements have been carried out. The wave height and wave period determined in this way may be used to calculate ship responses for a different course and ship speed and this information may be used to judge the new situation with regard to safety of the construction
(a "hull surveyance system") or from a navigational point of view.
In a complicated seaway consisting of sea and swell with dif-ferent directions this method may not be reliable.
A proposal to analyse in a similar way the power and the fuel consumption in a seaway has been published by Journée
[331 These methods may be regarded as a possibility for optimal routing on board of the ship, using computed ship responses. The reliability of such methods would increase considerable when a more precise measurement of the seaway is available for instance using satellites.
An interesting application of predicted motions based on measured and predicted waves in the Euro-channel leading to Europort is used to allow ships with a draught up to 70 ft. For the category of 67 - 70 ft draught a tidal window and a cr1-terium based on the low frequency content of the wave
spec-trum is used, using a combination of measured and predicted tides and waves. To this end wave measurement devices in the North Sea, in combination with wave and swell prediction methods are employed to predict the low frequency energy content in the Euro-channel 3 - 6 hrs in advance.
The low frequency energy content criterium is defined by: 0.10
l.f.e.<
f
S(f)df , l.f.e = 150 cm2 (9)0.03
because large ship responses are important for frequencies lower than 0.1 Hz in the Euro channel.
Using the tidal window and the l.f.e. criterium an extra permissible draught of about 3 ft could be obtained, which
19
-$
corresponds to a saving of f. 100 - 150 million in construc-tion costs of the channel [34]It may be expected that the practical use of ship motion calcu-lations for the design and operation of ship will increase in the near future, in particular when more precise information of the actual seaway becomes available.
References.
i] Kehoe, J.W.,
Destroyer Seakeeping: Ours and Theirs,
Proceedings U.S. Naval Institute, Vol. 99, November 1973.
Tasai, F.,
On the damping force and added mass of ships heaving and pitching,
Reports of Research Institute for Applied Mechanics, Kyushu University, Japen, 1960.
Grim, 0.,
A method for a more precise computation of heaving and pitching motions, both in smooth water and in waves,
Third Symposium of Naval Hydrodynamics, Scheveningen, 1960.
Ursell, F.,
On the virtual mass and damping of floating bodies at zero speed ahead,
Symposium on the behaviour of ships in a seaway, Wageningen, 1957.
Frank, W.,
Oscillation of cylinders in or below the free surface of deep fluids,
Naval Ship Research and Development Center, Report 2375,
1967.
Athanassoulis, G.A., and T.A. Loukakis, National Technical University of Athens,
Department of Naval Architecture and Marine Engineering Report 12 - 1983.
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Short surface waves due to an oscillating immersed body, PRS, A220, 90.103, 1953.
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Berekening van de hydrodynamische coëfficienten van lichamen die zich bevinden in de vrije oppervlakte van
21
-een uitgestrekt fluidem met behuip van de eindige elementen methode,
Thesis Deift University of Technology, 1971.
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The effect of beam on the hydrodynamic characteristics of ship hulls,
10th Symposium on Naval Hydrodynamics 1974.
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Hydrodynamic analysis of barge-platform systems in waves,
RINA 1982.
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van schepen op ondiep water,
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Ikea, y,
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Ship motions in longitudinal waves,
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Analysis of the resistance increase in waves of a fast cargo ship, International Shipbuilding Progress, 1972.
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Variation of parameters determining seakeeping, International Shipbuilding Progress, 1977.
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The effect of speed, forebody shape and weight dis-tribution on ship motions, RINA 1967
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Dynamics of Marine Vehicles,
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A systematic study about the effect of the main non-dimensional parameters on the seakeeping behaviour of slender fast ships,
Proceedings 5th Polish-Italian Seminar, Gdansk 1981.
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ASNE Day, 1981.
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Estimating the seakeeping qualities of destroyer type hulls,
David Taylor Naval Ship Research and Development Center, SPD-1074-01,January 1984.
-
23 -A.M. van Wijngaarden,Optimization of a hull form with respect to her seakeeping qualities, Dipl. Thesis DUT, 1982.
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Seakeeping performance comparison of air capable ships, Naval Engineers Journal, 1982.
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Optimizing the seakeeping performance of destroyer-type hu 1 ls,
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b
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Brandstofbesparing door bewaking en simulatie van de prestaties van het schip,
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ACTUAL SECTION LEWIS FORM CLOSE FIT
F = .15 = 2.258 m
J2
Figure 1: Lewis form and close fit approximation of Series Sixty CB = .70 cross sections.
N
-
(2n-1)Z=
a r =Q 2n-1 (2) rad/s a / d e A B D E Lewis transformation 4 6.74 31.7 1.08 -6.94 1.71 8.35 -0.32 2.58 6 5.25 26.2 0.34 -6.30 1.17 7.68 -0.18 1.12 8 5.41 16.9 0.10 -6.53 1.10 5.84 -0.09 1.11 10 6.04 9.5 0.02 -6.77 1.18 4.02 -0.04 1.75 12 6.60 5.1 0.00 -6.77 1.29 2.70 -0.03 2.55Eleven parameter transformation
4 6.73 31.4 1.10 -6.83 1.68 8.21 -0.28 2.66 6 5.27 26.0 0.36 -6.30 1.14 7.61 -0.15 1.14 8 5.44 16.9 0.13 -6.651 1.07 5.92 -0.06 1.03 10 6.05 9.8 0.07 -7.01 1.15 4.27 0.00 1.54
pA 1.00 Q25 050 0.75 1.00 1.25 1.50 x 025 0.50 0.75 1.00 125 1.50 1.75 2g
CALCULATED BY USING CONFORMAL TRANSFORMATION.
CALCULATED WITH FINITE ELEMENT METHOD.
X EXPERIMENTAL RESUIrS.
Figure 2: Hydrodynamic mass and damping coefficient calculated with a finite element technique for a rectangular cross-section B/T = 2.
Fn=.20 0 C 1 S experiment old method
new method} calculation
Figure 3: Pitch amplitude characteristics for five
length-beam ratio's. Series Sixty C3 = .70 Fn=.30 L B
1u
11
ic
J2
1 -0 0.5 10ic
7n 2L4
B 10 20 0 05 1 Ts 2.0 Oa K a 23.5 3.0 -2.5 2.0 LP (d CD 1.0 0.5 0 0 2
o
experiment - - - strip theorystrip theory + 3-dim. factors
Figure 4: Pitch amplitude characteristics of a barge with L/B = 1.5, calculated with three-dimensional corrections.
4 6 8
200 200 200 0 F =10 = .15
F =20
Figure 5: Distribution of vertical wave force amplitude along the length of a tanker. X/L = 0.215
0 STRiP THEORY 0
0000000000000
0 0 0 0 0 0 0 0000000000 oo° 0
0 0Ns2 033 N512 0 0 100 C 100 0 SECT NA 2d multi poles - - 2d source distribution 3d source distribution
o
experimentFigure 6: Calculated and measured distribution of hydrodynamic mass and damping of heave in shallow water;
h/T = 1.50 and 1.15; Fn = 0.2. Series Sixtie CB = 0.70. w4 w6 w8 w10 wt. w6 w8 w-10 500 500 N S/m2
to
500 b33 500 SEC 1. NR 0 I 4 2 SECT.NR 5 w 10 w 4 w .8 w.10U
o:J
6 7 SEC 1. NA200 Ns' m 150 Ns'm 22 100 50 50 0 2 4 6 8 10 12 0 0 200 N s'm 150 Ns/m ict 50 50 22 0 0 2 4 6 8 10 12 HEAVE Ns/m 1500 11000 b33 Ns/m b22 500 0 0 2d multi poles
-
2d source distribution 3d source distributionC
experiment -4 I j f G NS/500 b33 500 0 Ns/m 500 b22 0Figure 7: Calculated and measured hydrodynamic mass and damping for sway and heave in shallow water;
h/T = 1.50 and 1.15; Fn = 0.1. Series Sixty CE = 0.70.
U) U) U) U Fn = 0.1 SWAY h U) U) (A) 0 0 0 6 8 2 4 10 12 4 6 8 10 12 2 /. 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 500 0 2 4 6 8 10 12
(A)
-__j 180° N 900-90
o 1,0 NJ 0,5 0 0 -n 0,5 0 0,5Experiment in
regular waves 10 Phase angle 1,5'VL
Experiment in irregular waves Heave Pitch Sixty Series 6=0.70 Fn= .20 2,0Figure 8: Amplitude- and phase characteristics of heave and pitch obtained from cross-spectral analysis of an irregulare wave test and from a regular wave test.
6 U) w
rj
60 r1 w U) 20 0 0 i . .1 .2 .3 .4 .5 I I I .1 .2 .3 .4 .5 frequency in Hz 80 I I 1 .1 .2 .3 .4 .5 frequency in HzFigure 9: Wave spectrum measured with the WAVEC - directional buoy during the 1982 11Tydeman" trials.
frequency in Hz 360 S C') w rTj e 270 0 -ii S 55S 180 90
0 ' 0.5
EXPERIMENT
1.0
1.50 '
0.5CALCULATED
1.0 1.510 0.5 1.0 1.5 0 0.5
Figure 10: Comparison of calculated and measured added resistance in waves for a fast cargo ship.
1.0 1.5
Fn=.15 Fn=.20
FULL LOAD CONDITION
Fn=.25
A
Fn=.30All
-Fn=.15&
Fn=.20 BALLAST CONDITION Fn=.25 Fn=.301.
i.
3 2 RAw pg BYL 1 0 3 2 RAW pg 2 B2/L 1 0rn Za, I. 2 20 P[sammng] 10 0 60 100 0 60 100 30 0 60 100 sea state a-L L 5 200 -- -Vsectiorè' -- - UVsections -Usections_ m rn Cg:0.60, Fn:0.20, K025L, LCB -2 % 300 N degrees /3 8 1. 0 rn/sec2 ava 0 15 0 L m I rn 300
Figure 11: Ship responses in sea states 5, 7 and 9 as a function of ship length, ship speed and cross sectional form.
Series Sixty CB = 0.60. ---V sectionsI ea state 9
\\
---UVsect --Usect;ons - - -Vsections --UVsection ---Vsectis- sea state 9 ----UVsections
-Usectiorts
Iui
ea stte 9 ---Vsections - - -UVsections -U sections L rn L m 300 200 60 100 80 ton RAW 40 300 200 60 100 200 300 10 m fp.05 200 60 100 300 2000.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 _.1,1' I I I I (Two) ,sec 0.9
0.8
0.7
-0.6 0.5 0.4 0.3 0.2 0.1 0.0 0o
Hull 06
o
Hull 13
LHull 21 optimum
---Data base envelope
Figure 12: Optimized seakeeping behaviour of a destroyer hull form.
(1 )
wo sec1.0 > 0.8 U) 0.6 >1 4) H 0.4 Ship's Heading to the Seas PORT BEAM 2700 SEAS 315 225 0 0 HEAD SEAS 0° Ship's Speed (0 to 30, 5 Knot Increments) 45° 1800 FOLLOWING SEAS 135° DInoperableRegion
SEA STATE 4 SEA STATE 5 SEA STATE 6
Figure 13: ,,Windows" for an air capable ships in three sea states. 0 5 10 15 20 25 30 35 1 .0 >< 0.8 U) 0.6 >1 0.4 '-4 -4 -Q (ti 0.2 U) o 0 Optimum Hull STBD 90° BEAM SEAS
- -
Antioptimum Hull0 Existing Hull Design
Figure 14: Operability indices for patrol vessels. (Criteria C, see table 2)
0 5 10 15 20 25 30 35
0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 1.0 0 0 0.8 0 0 0.6 H 0 4-4 0.4 C) .,- 0.2 U) 0 0 0 0 0 , , / /
'0
/ Criteria Set A ("Combat") 5 10 15 20 25 30 35displacement, metric tons/1000
5 10 15 20 25 30 35
displacement, metric tons/1000
0 5 10 15 20 25 30 35
displacement, metric tons/1000 Optimum Hull
- Antioptimum Hull
0
Existing Hull DesignFigure 15: Ship performance indices for patrol vessels on the North Atlantic on a base of displacement.
i0
Criteria Set B ("Mobility")
PERSONNEL
k=1
H
i=3
PERSONNEL
Figure 16: Series and parallel structure of a patrol vessel. PERSONNEL k=2 PROPULS ION i=4 j=1 PERSONNEL RADAR HULL MAIN-ENGINE COMMUNICATION i=1 i=2 HELICOPTER
100 w L) 50 D 10 00
/
a) personnel (a) PM-2 ACCELERATIQt 5 8 10 15 20SIGNIFICANT ROLL AMPLITUDE (DEG)
SIGMIF{CAUT PITCH AMPLITUCE (DEG)
3 5 7.5 10
SIGNIFICANT AMPLITUDE OF PITCN & ROLL (0E0
(c) ACCELERATION IN STIUWATR L2J2 kt) MEACING AftGLE 30 - .-... 0, 60 90 20 150 180
c) sustained sea speed
100 50 20 CD . 15 50 ELET1VE %' END EtI'E1 OIE 0 IN-0PFRAL 40kt ieo U 00 3 4 5 75 b) helicopter (b) ssc-2 114 TIt1 WATER (18.0 kt) HEAi: ANGLE 180
Figure 17: Performance degradation due to ship responses in a seaway.
50
SIGNIFICANT AMPLITUDE OF ACCELERATION (g) 100 L) 50 10 z 23 15 5 6 7 8 9 BE.AUFORT NtRIBER 3 4 5 6 7 8 9 BEAUFORT NUMBER 3 50 10 0 0.1 0.2 0.5
-)
90
PM-i PERSONNEL EFFECTIVENESS BEAUF. NO. = 6 BEAUF. NO. 8
180
90
Figure 18: Performance degradation of patrol boat crew due to pitch, roll, vertical and horizontal acceleration.
100_.
50_
IN STILL WATER PM-4 PM-3 PM-i SSC-i 5 6 7 BEA[IFORT NUMBER IN SHORT-CRESTED HEAD SEASSSC-2
Figure 19: Mission effectiveness of six different patrol vessels. PM-i PM-2 PM-3 PM-4 SSC-i
SSC-2
L (m) 100 90 73 63 31.5 65 B (m) 14.6 11.6 9.6 7.9 17.1 35.3 T (m) 4.9 3.8 3.3 2.7 3.2 5.5 A (ton) 3643 2081 1237 666 340 2000 V (kn) 22 21 21 19 24 18S
(m)
2($ec)
I5
0i8o
1(70001
1 I-P WAVE V2
1800 1400LEA 51ATE. ERIVE
r'oM:
W I4EAVE. P PITCN V VERTICAL 4CC. FORWARc Q M:csP BE4%NC
TIES
P 14I ,-.I WAVE\JOY
L)OYFigure 20: Determination of the significant wave height and average wave period from measured ship responses.
ikoo
I5oo
7:oo5.00 i6.00 17.00
