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VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR 82
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WAVES
Validation of Time-Domain Prediction of Motion, Sea Load, and
Hull Pressure of a Frigate in Regular Waves
W.Qiu, H.Peng and C.C.Hsiung
(Centre for Marine Vessel Development and Research, Dalhousie University, Canada)
ABSTRACT
A time-domain code, SEALOADS, has been developed to predict ship motion, sea load and hydrodynamic pressure
distribution of ship. The theoretical background of SEALOADS is outlined. Computations were carried out for a frigate in
regular waves at various wave headings and steepnesses for different forward speeds. The predictions of heave, roll, pitch,
shear force and bending moment, and pressures at several locations were presented. The validation study of computed
results was carried out by comparing with experimental data from a hydroelastic model of the frigate.
INTRODUCTION
The predictions of ship motions, sea loads and hydrodynamic pressure distribution over a ship hull are essential
components of ship design. Strip theory has been used as a practical prediction method, but it gives unsatisfactory
predictions at low frequencies and at high forward speeds. As well, the strip-theory approach is not able to compute the
hydrodynamic pressure distribution over the hull surface except on sections. Some of the deficiencies of strip theory can be
removed by three-dimensional theory. Several researchers, such as Chang (1977), Inglis and Price (1982) and Guevel and
Bougis (1982), have used three-dimensional panels to obtain solutions of ship motion in the frequency domain. The
frequency-domain panel method has been employed for ship seakeeping analysis using zero-speed Green function with a
“speed correction”, since the frequency-domain Green function containing the velocity term is complicated to handle. An
alternative approach is to formulate the ship motion problem directly in the time domain. When the forward speed is
involved, the time-domain Green function is in a simpler form and requires less computational effort than does the
frequency-domain counterpart.
The concept of direct time-domain solution is based on the early work of Finkelstein (1957), Stoker (1957) and
Wehausen and Laitone (1960). Cummins (1962) and Ogilvie (1964) discussed the use of time-domain analysis to solve
unsteady ship motion problems. The zero forward speed problem has been discussed in detail by Wehausen (1967, 1971).
In the linear time-domain formulations, the time-dependent Green function is applied to derive a boundary-integral
equation at the mean wetted surface of the body under the assumptions of small motion and small amplitude incident
waves. The linearized radiation and diffraction forces acting on the body can be expressed in terms of convolution integrals
of the arbitrary motion with impulse functions. These methods have been developed by Liapis and Beck (1985), Beck and
Liapis (1987), Beck and King (1989), Beck and Magee (1990) and Lin and Yue (1994).
Efforts have been made to directly incorporate the nonlinearity into time-domain formulations. One extension of the
linear time-domain model is to impose the body boundary condition on the instantaneous wetted surface of the body. The
free surface boundary condition remains linear so that the time-dependent Green function can still be applied. The body-
exact problem has been solved with various degrees of success by Lin and Yue (1990), Magee (1994) and Danmeier
(1999). Huang (1997) combined the exact body boundary condition with a free-surface condition linearized about the
incident wave profile. In the results of these studies, the application of the exact body boundary conditions showed promise
of improvement for cases of computations dealing with large-amplitude motions.
The computer program SEALOADS was devel
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WAVES
oped at the Centre for Marine Vessel Development and Research (CMVDR), Dalhousie University for predictions of ship
motions, sea loads, and hydrodynamic hull pressure in the time domain. The linear time-domain model is applied to
compute the radiation and diffraction forces. The Froude-Krylov forces and restoring forces are computed on the
instantaneous wetted surface under the incident wave profile. The other nonlinear forces such as viscous damping forces
and maneuvering forces are also taken into account. The nonlinear equations of ship motion in SEALOADS can be solved
in the time-domain either by the fourth-order Runge-Kutta technique or the Extrapolation Method (Magee, 1994). The
uniqueness of the code is that a direct solution approach (Cong et al., 1998) is applied to solve the impulse response
function, and the analytical solution (Qiu and Hsiung, 1999) of the time-dependent Green function is computed by solving
an ordinary differential equation (Clement, 1998).
Ship motions, sea loads, and hull pressures predicted by the computer program SEALOADS for the Canadian Patrol
Frigate (CPF) in regular waves at various wave headings, steepness, and forward speeds were validated against the test data
with a 1/20-scale hydroelastic model of the CPF.
THEORETICAL ANALYSIS
Equations of Ship Motion
Three right-handed coordinate systems (as shown in Figure 1) are employed for the ship motion analysis. A space-
fixed coordinate system, OXYZ, has the OXY plane coinciding with the undisturbed water surface and the Z-axis pointing
vertically upward. In the steady-moving coordinate system, omxmymzm, the omxmym plane coincides with the calm water
surface and omzm is positive upward. The third coordinate system, osxsyszs, is fixed on the ship, and os is at the point of
intersection of calm water surface, the longitudinal plane of symmetry, and the vertical plane passing through mid-ships.
The osxsys plane coincides with the undisturbed water surface when the ship is at rest. The positive xs-axis points toward the
bow and the ys-axis to the port side.
Denoting a column vector by braces {}, ship motions in the omxmymzm system are represented by the vector
in which are the displacements of the center of gravity (CG), and
are the Eulerian angles of the ship. The Eulerian angles are the measurements of the ship's rotation about
the axes which pass through the CG of the ship. The instantaneous translational velocities of ship motion in the directions
of osxs, osys and oszs are and the rotational velocities about axes parallel to osxs, osys and oszs and passing
through CG are The equations of ship motion are
Figure 1: Coordinate systems
(1)
F is the external force vector, and
where
(2)
(3)
where m is the ship mass and Iij is the moment of inertia.
The total external force acting on the ship is
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(4)

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WAVES
where and are the radiation and diffraction forces, respectively; the are the nonlinear Froude-Krylov
forces; the are the restoring forces; the are the viscous forces; and the are the miscellaneous forces which
include the propeller thrust, the maneuvering forces, and the rudder forces.
The velocities of motions in the omxmymzm system are related to those in the osxsyszs system as follows:
(5)
where represents the ship perturbation velocities in the steady-moving coordinate system. The transformation
matrix T is
(6)
where
(7)
and
(8)
where ci=cos(xi), si=sin(xi) and ti=tan(xi) for i=4, 5 and 6.
Ship motions in the steady-moving coordinate system can be solved from Equations (1) and (5) either by the Runge-
Kutta scheme or by the extrapolation method.
External Forces
The boundary integral equation of linearized radiation and diffraction problem can be expressed by the source
distribution and then solved by the panel method (Liapis and Beck, 1985). The oscillatory part of the time-dependent Green
function and its derivatives can be solved from the fourth-order ordinary differential equations by using a Runge-Kutta
scheme (Clement, 1998). In the computer program SEALOADS, a series expansion method is used to achieve an analytical
solution of the ordinary differential equations (Qiu and Hsiung, 1999).
The linearized radiation force at time t can be obtained from
(9)
Here, and are the added-mass, the damping coefficient and the coefficient of the restoring force of the
ship in the time domain, respectively, and is the impulse response function. This function can be solved from Eq.(9)
In SEALOADS, a direct solution scheme (Cong et al.,
by substituting for a non-impulsive input
1998) is applied to solve the response function instead of using Fourier transformation. The total radiation force is obtained
from
In a similar way, the diffracted wave forces can be computed from
(10)
is the impulse response function for the diffraction force in the ith mode and η0(t) is the free surface
where
elevation of the incident wave at the origin of the steady-moving coordinate system.
The Froude-Krylov forces and restoring forces were computed on the instantaneous wetted surface under the incident
wave profile. The rudder forces, maneuvering forces and viscous forces have been discussed by Huang and Hsiung (1996).
Pressure
The pressure at a point P(x, y, z) on the mean wetted hull surface can be expressed as
(11)
where pR (P; t), pD(P; t) and pI(P; t) are the pressures due to the radiated, diffracted and incident waves, respectively,
and δ pst(P; t) is the hydrostatic pressure fluctuation due to the oscillatory ship motion. The pressures due to the radiated
waves and diffracted waves are obtained from
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(12)

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VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR 85
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WAVES
(13)
is the pressure response function due to the kth mode of motion and
where is the pressure
response function due to diffracted waves.
If a point is below the incident wave profile, the nonlinear pressure due to the incident waves is directly computed by
(14)
where Φ0(P; t) is the velocity potential of the incident wave.
Sea Loads
The sea load acting on a cross section xc can be expressed as
(15)
where Vk(t) is the total sea load in the kth mode of motion; The terms on the right-hand side are the forces acting on
the body forward of station xc. and are the forces due to the radiated and diffracted waves, respectively;
and are the Froude-Krylov forces and the restoring forces, respectively, and represents the inertial forces.
Equations for computing sea loads caused by radiated and diffracted waves are similar to Eqs.(9) and (10). Sea loads
at the section xc caused by incident waves are obtained by directly integrating pI(P; t) over the wetted surface forward of the
station xc .
VALIDATION
An effort was made to validate the ship motions, sea loads, and hull pressures computed by SEALOADS for a
Canadian Patrol Frigate in regular waves in the deep departure condition. This took about 25 minutes to compute using
10,000 time steps (∆t=0.02 sec.) for a single speed and wave condition on a Pentium III 700MHz PC.
Figure 3: Backbone foundations and superstructure
Figure 2: Model frigate body plan (dimensions in full
profile.
scale).
Model Test
Experiments with a self-propelled 1/20-scale model of the CPF were conducted in both regular and irregular waves in
the towing tank (200 m×12 m× 7 m) and the Offshore Engineering Basin (75 m× 32 m×3.5 m) at the Institute for Marine
Dynamics (IMD) in St. John's, Newfoundland, Canada. The steepness, H/λ, of the regular waves ranged from 1/50 to 1/15,
where H is the wave height and λ is the wavelength. Wavelength was varied from 0.5L to 1.6L (the model length between
perpendiculars L=6.225 m). Smaller wave amplitudes were used to measure linear response, while large amplitudes were
for investigation into nonlinear responses. Built with solid fiberglass, the model was segmented into 5 sections with a
continuous backbone to enable the measurement of bend
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WAVES
ing moments and shear forces on the hull girder. The model and the earlier tests were described by McTaggart et al.
(1997). Pressure sensors were deployed in the later tests (Ando, 2000). Table 1 gives the particulars of the ship and the
model. The model was equipped with a hull-mount sonar dome, a rudder, and propeller brackets, but no bilge keels. Table 2
gives the locations of the 11 transducers (Ando, 2000). Figures 2 and 3 show the body plan and the backbone foundations
and superstructure profile. In Fig. 2, the positions of pressure transducers are also indicated. The model was fitted with twin
five-bladed, highly skewed propellers. Figure 4 shows the stern profile. The shallow draft near the stern is notable. Wave
height was measured by a resistor-type wave probe attached to the carriage at 7.84 m forward of the forward perpendicular.
All pressure transducers were zeroed at rest in calm water. The hydrostatic pressure was balanced out initially in the
transducer-bridge monitoring circuit. The recorded quantity was therefore the periodic variation of pressure about the
average hydrostatic value.
Table 1: Hydrostatic particulars of ship and model in deep departure condition.
Designation Ship Model
water salt fresh
Scale ratio 1 1/20
Length overall(LOA ) 134.7m 673.5cm
Length between perpendiculars (Lpp) 124.5m 622.5cm
Length of waterline (LWL) 124.91m 624.6cm
Beam (B) 14.88m 74.4cm
Draft (T) 4.97m 24.9cm
Maximum section abaft amidships 3.73m 18.7cm
59.48m2 0.149m 2
Area of midship section
0.149m 2
Area of maximum section 59.66m
Centre of buoyancy abaft amidships (LCB) 2.46m 12.3cm
Centre of buoyancy above the baseline 3.06m 15.3cm
4548m3 0.568m 3
Volume of displacement
1992m2 4.979m 2
Wetted surface area
Displacement (∆) 4665ton. 567.8kg
Centre of flotation abaft amidships (LCF) 8.02m 40.1cm
1442m2 3.604m 2
Area of the waterplane
Figure 4: Stern profile of CPF.
Motions, Sea Loads and Pressures
Selected predictions of motions, sea loads, and hull pressures together with the experimental results in regular waves
at the deep departure condition are presented below. Predicted heave, roll, and pitch motions are compared with
experimental results. For sea loads, vertical shear forces and bending moments at stations 2.5, 5.0, 7.5 and 10.0 are given.
Pressures are given at sensors 5, 6, 8, 9, 10 and 11 (see Table 2). The matrix of validation work is summarized in Table 3
where Fn and β denote the Froude number and heading, respectively. A heading of 180 degree corresponds to head seas.
The experimental data on pressures are available only for head seas at Fn=0.05, 0.12 and 0.18. The measured pressures at
Fn=0.12 are chosen to validate the computational results. Amplitudes ξa of the incident waves corresponding to H/λ=1/30
and H/λ=1/20 are listed in Table 4, where ω denotes the wave frequency.
Table 2: Location of pressure sensors (in full scale).
Sensor No. Station Distance from CL(m) Height above BL(m)
1 1.0 4.6 11.5
2 1.0 3.3 9.70
3 1.0 2.0 7.0
4 1.0 0.7 3.0
5 1.0 0.0 0.0
6 3.0 0.0 0.0
−1.75*
7 3.8 0.0
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8 7.2 0.0 0.0
9 9.5 0.0 0.0
10 13.0 0.0 0.0
11 18.5 0.0 3.3
* sonar-dome bottom

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WAVES
Motions, sea loads and pressures are nondimensionalized as follows:
(16)
(17)
(18)
(19)
(20)
where k is wave number; is nondimensional motion amplitude; is nondimensional load amplitude; and p′ is
nondimensional pressure amplitude.
In Figure 5, the nondimensional heave and pitch in head seas at Fn=0.06 are given along with vertical shear forces and
bending moments at stations 2.5, 5.0, 7.5 and 10.0. The responses were computed for two wave steepnesses (1/30 and 1/20)
and 7 wavelengths (λ/L from 0.70 to 1.37) for each wave steepness. As shown in figures, the predicted heave and pitch
agree well with experimental results. Predicted sea loads show correlation with test data.
Figure 6 presents the predicted ship responses in oblique waves (β=165°) at Fn=0.06. The predictions for heave, roll
and pitch in oblique waves are generally in good agreement with test data. Predicted sea loads agree well with test data.
Figure 7 gives the computed heave, pitch and sea loads in head seas at Fn=0.12. The corresponding pressures at six
sensor locations are also presented in Figure 8. The predicted pitch agrees well with the experimental results, whereas
heave is over-predicted when 1.0<λ/L<1.6. The predicted bending moments at four stations show reasonable agreement
with experimental results. The shear forces are however over-predicted. The predicted pressures at sensor 5, 6, 9 and 10 are
in general agreement with model test results for cases of H/λ=1/30. The discrepancies between the predictions and test
results for the case of H/λ=1/20 may be due to the assumption of linear radiation and diffraction. Figure 9 shows predicted
time series of heave, pitch, and pressures at sensors 6 and 11 for λ/L=1.01 and H/λ=1/30. Compared with responses of
heave, pitch and pressure at sensor 6, spike-like responses are shown at sensor 11. This could be because sensor 11 is
located close to the stern and the pressure due to incident waves was computed on the instantaneous wetted surface. The
wetted surface could change drastically due to the shallow draft at the stern of CPF.
Table 3: Summary of the validation matrix
β (deg.) H/λ
Fn Ship Speed (knot)
0.06 4.1 180, 165 1/30, 1/20
0.12 8.2 180, 165, 135 1/30, 1/20
0.20 13.6 180, 165, 135 1/30, 1/20
0.25 17.0 180 1/30
Table 4: Amplitudes of regular waves in head and oblique seas.
λ/L ω (rad/s) ξa (m)
H/λ=1/30 H/λ=1/20
0.59 0.92 1.224 1.836
0.70 0.84 1.453 2.179
0.80 0.79 1.660 2.490
0.89 0.75 1.847 2.770
1.01 0.70 2.096 3.144
1.09 0.67 2.262 3.393
1.19 0.64 2.469 3.704
1.36 0.60 2.822 4.233
1.57 0.56 3.258 4.887
1.94 0.51 4.026 6.038
Figure 10 presents the computed motions and sea loads in oblique waves (β=135°) at Fn=0.12. Predicted heave, pitch
and sea loads show reasonable agreement with test data. Predicted roll is smaller than experimental results. This indicates
that the viscous roll damping coefficients might be over-estimated.
Motions and sea loads are also given in Figure 11 for the case of head seas and Fn=0.20. It is shown that motions and
sea loads are in good agreement with experimental results.
Numerical simulations were also conducted in oblique seas (Fn=0.2) and head seas (Fn=0.25). It was found that
irregularities were observed in the time series of ship responses as ship speed increased. This suggests that the assumption
of linear radiation and diffraction might not be valid for these cases, where the wetted surface changed significantly due to
shallow draft and large waves. This applied to very long waves as well as to very short waves.
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WAVES
experimental, H/λ=1/20; — SEALOADS, H/λ=1/30; – – SEALOADS, H/λ=1/20).
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
Figure 5: Predicted motions and sea loads in regular waves, β=180°, Fn=0.06 (Legend: o experimental, H/λ=1/30; ×
88

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WAVES
Figure 6: Predicted motions and sea loads in regular waves, β=165°, Fn=0.06.
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
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WAVES
experimental, H/λ=1/20; — SEALOADS, H/λ=1/30; – – SEALOADS, H/λ=1/20).
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
Figure 7: Predicted motions and sea loads in regular waves, β=180°, Fn=0.12 (Legend: o experimental, H/λ=1/30; ×
90

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WAVES
experimental, H/λ=1/20; — SEALOADS, H/λ=1/30; – – SEALOADS, H/λ=1/20).
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
Figure 8: Predicted pressures on six sensor locations in regular waves, β=180°, Fn=0.12 (Legend: o experimental, H/λ=1/30; ×
91

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WAVES
Figure 9: Predicted time series of heave, pitch, and pressures at sensors 6 and 11 (λ/L=1.01, H/λ= 1/30, β=180°, Fn=0.12).
CONCLUSIONS
Validation of the computer program SEALOADS on ship motions, hydrodynamic pressures and sea loads has been
carried out for CPF. The ship motions, sea loads and hydrodynamic pressures predicted by SEALOADS, in general, agree
well with experimental results under the following conditions: a) up to medium speed (Fn=0.20); b) medium waves (0.7<λ/
L<1.6); and c) wave steepness up to 1/20.
Some of the differences between the computed sea loads and test data may be due to the fact that the physical model
was flexible whereas the SEALOADS computations were based on the assumption of a rigid ship.
The computed results show deviation from measured data as forward speed increased, especially in short waves: λ/
L≤0.59, long waves: λ/L≥1.94, and steep waves: H/λ≥1/20. Also as expected, computed pressures show peculiarities at
locations near the stern.
Since the draft of CPF is very shallow at the stern, i.e., the instantaneous wetted surface can change drastically during
ship motion, the assumption of mean wetted-surface would be no longer valid, especially for large waves. As a step further
to improve the current code, the varied added mass, damping and restoring forces, and the response functions should be
taken into account for the varied wetted surfaces. The effect of varied added mass is being examined by the CMVDR
research group and has shown promising improvement to the current code for ship seakeeping computations. Stokes waves
should be used for the computation of ship responses in steep large waves in order to examine the nonlinearity in
responses.
ACKNOWLEDGMENTS
The authors are grateful for the research support from the Defence Research Establishment Atlantic, Canada. The
useful discussions with Mr. Sam Ando and Dr. Xin Lin are very much appreciated.
REFERENCES
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the authoritative version for attribution.
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WAVES
Figure 10: Predicted motions and sea loads in regular waves, β=135°, Fn=0.12.
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
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WAVES
experimental, H/λ=1/20; — SEALOADS, H/λ=1/30; – – SEALOADS, H/λ=1/20).
VALIDATION OF TIME-DOMAIN PREDICTION OF MOTION, SEA LOAD, AND HULL PRESSURE OF A FRIGATE IN REGULAR
Figure 11: Predicted motions and sea loads in regular waves, β=180°, Fn=0.20 (Legend: o experimental, H/λ=1/30; ×
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DISCUSSION
D.Murdey
National Research Council/Institute for Marine Dynamics, Canada
The authors are to be congratulated for making progress in the very complex and difficult task of improving and
validating numerical prediction methods to assess operational performance and loads imposed on new ship designs in
various environmental conditions. We would like to make three observations, each leading to a question.
The first concerns the range of conditions under which the time-domain predictions were validated. In validating their
SEALOADS time domain code the authors have selected responses in regular waves with moderate wave heights and low
Froude numbers. While such validation demonstrates the performance of the program for much of the operational range for
the ship, it does not exceed the prediction expectations of a linear strip theory based program. We wonder if the authors
have tried to validate their code for predictions of performance in irregular waves, for higher Froude number and possibly
extreme sea conditions? The necessary experiment data are available from tests carried out at IMD with the same frigate
model used by the authors.
Our second observation concerns the use of qualitative validation criteria. The majority of the validation studies, such
as that presented in this paper, have used qualitative nouns such as: good, satisfactory, fair and so on to describe goodness
of fit between the numerical simulation and the experimental results. We would like to ask the authors if they have
considered the use of quantitative validation criteria when judging the comparison of the numerical and experimental
results? A key practical issue is to decide how close the numerical and experimental results need to be for the agreement to
be considered, from a ship designer's perspective, “satisfactory”. For example, although the small scale of figures 5 to 8
makes it difficult to make a precise quantitative evaluation of the differences, it appears that predicted and measured loads
close to amidships differ, by as much as 100%. Should this be considered fair, satisfactory or unsatisfactory, important or
unimportant?
Thirdly, We would like to briefly address the issue of uncertainty. The result of any experiment or simulation is not a
unique value, but rather a range within which the real value is located with a defined level of confidence. While it is well
known that all measurement and calculation are subject to uncertainly, this knowledge is not often used in assessing
comparisons of numerical simulations and results of experiments. An uncertainty analysis is especially important in any
process for validation of new simulation methods. A formal uncertainty analyses would also present an opportunity to
evaluate quality of the data, to identify the biggest sources of error and give direction for future improvements in
experiment techniques or numerical methods. We wonder if the authors have carried out such an analysis or if they have
plans to do so in future?
In conclusion, we would like to acknowledge the importance of the work being carried out by ITTC committees to
develop guidelines and procedures for experiments and numerical code validation, including uncertainty analysis and
publishing benchmark model and full scale data. This work is an essential foundation for ensuring that theoretical and
experimentally based predictions of ship performance may be used with confidence to meet the needs of practical ship
designers and ship operators.
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WAVES
AUTHOR'S REPLY
First of all, we would like to thank all discussers for their thoughtful remarks and comments.
In reply to questions raised by Mr. Murdey: (1) one of the goals of SEALOADS time-domain code is to predict the
ship motion responses under extreme sea conditions. We are in the process of extending the validation to extreme seas and
irregular waves. (2) We have considered the use of a quantitative validation criterion, the total-factor-error (TFE) (Ando,
1998). The TFE analysis has been used to validate our frequency-domain code, WAVELOAD (Qiu, et al, 1999). Although
we did not apply it when examining the numerical and experimental results at this time, it is our intention to carry out TFE
analysis for further validation. Sea loads close to the midship section are important, but the computed results as shown in
Figures 5 to 8 are unsatisfactory, and the reason for this will be investigated. We are continuing to refine the program to
increase its efficiency and accuracy. (3) We have not considered uncertainty analysis yet, but would like to in the future.
DISCUSSION
M.Tulin
University of California, Santa Barbara, USA
I wonder whether you thought about studying the motion of ships in wave groups (modulating waves) where there is in
the ocean a considerable accumulation of energy at the peak of the wave group. It is not difficult to create wave groups in
towing tanks and test ships in them.
AUTHOR'S REPLY
We agree with Professor Tulin that wave groups could be considered and incorporated into the code
ADDITIONAL REFERENCES
Ando, S. (1998). Quantification of correlation of predicted and measured transfer functions for ship motions and wave loads. RINA International
Conference on Ship Motions and Maneuverablity, London.
Qiu, W., Ando, S. and Hsiung, C.C. (1999). Applying the TFE analysis to validate the software WAVELOAD. 22nd International Towing Tank
Conference, Soul, Korea and Shanghai, China.
the authoritative version for attribution.