Proceedings of the ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering
OMAE2016
June 19-24, 2016, Busan, South Korea
OMAE2016-54542
ANALYSIS OF VARIANCE TO DETERMINE THE EFFECT OF HULL FORM PARAMETERS
ON RESISTANCE AND SEAKEEPING PERFORMANCE FOR PSV HULLS
Nicholas Boyd
Memorial University of Newfoundland
St. John’s, Newfoundland and Labrador, Canada
David Molyneux
Memorial University of Newfoundland
St. John’s, Newfoundland and Labrador, Canada
ABSTRACT
analyzed to determine their contributions to the overall model of
the data.
Throughout the world many Platform Supply Vessel
designs have been proposed as the optimal form for their given
operating environment, but evaluating these claims has been
difficult due to a poor understanding of the relationships between
hull form shapes and performance for these vessels. This paper
presents the results of analysis aimed at determining these
relationships.
The results have found the relationships between the hull design
parameters and the Effective Horespower/tonne, heave, and
pitch response of the vessel, indicating which factors provide the
largest contribution to minimizing each response. The interaction
effects between factors were also examined to allow for a
generalized understanding of the resulting effect of selecting one
hull parameter over another. A numerical model combining all
significant factors was fitted to the data, allowing for multiple
objective optimization to determine which hull forms provide the
most desirable performance for each response.
Results of CFD calculations to determine the Effective
Horsepower/tonne for a series of PSV designs were presented in
the paper A step towards an optimum PSV Hull form. This paper
presents results for 16 separate hull forms, which were designed
as each possible combination of four two-level hull form
parameters. The hull form features considered were bow shape
(vertical stem or bulbous), flat of bottom (flat or deadrise), length
of parallel mid body (short or long), and stern shape (convention
or integrated); resistance was calculated at two typical operating
speeds (10 and 14 knots). This set of results was favourable for
analysis using the statistical design of experiments technique:
analysis of variance, which was used to determine the
relationship between the hull and resistance performance.
INTRODUCTION
Offshore Support Vessels are an essential link the
infrastructure required for offshore oil development. The ships
have a variety of roles to play, which include delivering cargo to
and from offshore oil installations, as well as anchor handling,
standby and tanker assistance. Even though the majority of these
ships are under 90m length, they have sophisticated requirements
for powering and station keeping. The nature of the vessel’s
operational profile requires the ship to have minimized power
and fuel consumption at transit speeds (typically between 10 and
16 knots) and low levels of motion at zero speed for effective
cargo transfer.
The same hull form series was used to study the effects of the
hull form parameters on motions in head waves. A 2 level
factorial experiment was designed based on the hull parameters
with the heave and pitch response calculated using the potential
flow ship motion prediction code Shipmo3D, for each of two
representative wave conditions (summer light seas and winter
heavy seas) at the zero speed and 10 knot operating speed.
Analysis of variance was used to analyze the heave and pitch
responses measured, and was used to determine the relationship
between each hull parameter and each response.
In both cases a 5% F-test was used to determine the significance
of each parameter studied, and the significant effects were
There have been recent advances in the design of these ships,
which include specialized bow shapes, such as the Sea Axe bow
developed by Damen Shipyard [1] and the X bow developed by
Ulstien [2], but very little specific information has been provided
to help ship designers and operators select the optimal hull form
proportions and design features for a particular installation and
1
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required mission profile, based on the possible trade-offs in
performance.
runs required to determine a specific level of accuracy in the
results. This method varies parameters in combination with
others to allow for determination of the combined effects of
variables and interactions. Each test run is given a treatment
combination where each level of a variable is prescribed for the
test run.
In light of recent discoveries of oil further offshore and in harsher
environments than previously developed, it is necessary to
develop a design for PSVs that are optimized for these unique
and new environments. [3] This paper aims to define the
relationships between hull design parameters and vessel
performance, to assist in determining the optimal design for this
new environment.
The resistance performance was evaluated by conducting
ANOVA on the data presented in the paper A step towards the
optimum PSV hull form. The ANOVA used an alpha value of 0.05
for significance, and model coefficients were estimated.
Using the experimental design an analysis technique Design of
Experiments (DOE) the effects of hull form parameters were
studied on the resistance and seakeeping performance of PSV
hulls. This powerful technique uses statistical analysis to
perform efficient experiments which capture the nature of
physical systems effectively, including the conditional effects of
parameters on one another, a physical phenomenon which cannot
be modeled using traditional One Factor at a Time Methods.
ANOVA works by comparing the change in a measured response
to the varying of 1 or more parameters. The amount of change in
response is then divided by the Mean Square Error of the Data,
to give a ratio, called the F-Value. This F-value is then assigned
a statistical probability of occurrence due to error based on the
degrees of freedom in the data. This probability is then compared
to the chosen alpha value, to determine whether the change in
response is statistically likely to be due to the change in the
parameters. In this way, all the statistically significant parameters
in an experiment can be identified.
The DOE technique has been used successfully previously in the
naval architecture field, first being shown to be useful when
combined with dimensional analysis techniques for
hydrodynamic experiments [4], and has since been used in
propeller performance prediction experiments [5], as well as ship
motions experiments [6].
To evaluate seakeeping performance, an optimal design 2 level
factorial experiment was conducted using the 16 hull forms used
in the resistance experiment, at speeds representing a normal
forward speed (10 knots), and 0 speed, in wave heights
representative of the expected wave height and period in summer
(1.5m Hs and 8.5 s) and winter (4.5m Hs and 11.5 s) for the
Flemish Pass Basin. Data was collected for heave and pitch,
assuming head seas using the potential flow solving code
ShipMo3D.
METHODOLOGY
The basis for the analysis described in this paper are
numerical predictions of the performance of a series of OSV
hulls forms. The hull parameter effects were evaluated first for
the resistance performance and then the seakeeping performance
for 16 unique hull forms, each a combination of 2 levels of 4
factors: Bow Shape (Vertical or Bulbous), Bottom Shape (Flat or
Deadrise), Midbody Length (Short or Long), and Stern Shape
(Conventional or Integrated).
ANOVA was conducted on this data, with each response (heave
and pitch) having a separate mathematical model to represent the
data. Using an alpha value of 0.05, the significant parameters
were found and the model coefficients were estimated.
The resistance analysis was described by A step towards an
optimum PSV Hull form [7] where resistance per tonne
displacement was calculated using the CFD code Numeca [8].
The numerical predictions of the motions of the same series of
ships in waves were calculated using Shipmo3D [9].
RESULTS
The relationships between parameters and performance were
evaluated by developing a mathematical model for resistance
and motions data using the statistical Design of Experiments
(DOE) method, Analysis of Variance (ANOVA), to determine the
significance of parameters and their equation coefficients. This
method uses statistical analysis to determine the important
parameters in an experiment, comparing the effect of varying a
parameter relative to the noise of experimental error to find a
probability of the effect occurring due to noise. [10]
For the relationship between speed and resistance, a square root
transform was required for the data to fit a model. Following this
a model was developed including the significant terms, as well
as those required to maintain hierarchy in the model, as
summarized in Table 1 below.
After conducting ANOVA on all the data, a model was
fitted which represented the data statistically, these models are
summarized in the tables below.
Table 1, Resistance ANOVA Table
Source
Sum of df
Mean
Squares
Square
The DOE method is an approach to experimental design, where
the variation of parameters is chosen to minimize the number of
Model
2
0.91
12
0.075
F Value
5222.53
p-value
Prob >
F
<
0.0001
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ABottom
B-Bow
CMidbody
D-Stern
E-Speed
AB
AE
BC
BE
CE
DE
BCE
Residual
Cor Total
4.264E004
1.426E003
2.291E003
4.364E004
0.89
1
7.413E005
1.818E004
5.625E004
9.317E003
3.745E005
1.445E004
4.543E004
2.745E004
0.91
1
1
1
1
1
1
1
1
1
1
1
19
4.264E004
1.426E003
2.291E003
4.364E004
0.89
7.413E005
1.818E004
5.625E004
9.317E003
3.745E005
1.445E004
4.543E004
1.445E005
29.52
ESpeed
F-Sea
State
AB
5.13
<
0.0001
<
0.0001
<
0.0001
<
0.0001
<
0.0001
0.0354
12.59
0.0021
BC
38.94
CD
2.59
<
0.0001
<
0.0001
0.1239
ABC
10.00
0.0051
ACD
31.45
<
0.0001
Residual
98.71
158.59
30.21
61607.76
644.93
AC
AD
AE
EF
Cor Total
1
1
1
1
1
1
1
1
1
1
26
3.28819
1
89.9928
8
0.03126
5
0.00563
6
0.00122
4
0.00888
9
0.00490
5
0.00262
9
0.26982
9
0.01581
4
0.00639
2
0.00120
9
2720.14
8
74446.3
9
25.8642
5
4.66197
9
1.01250
4
7.35364
8
4.05724
6
2.17474
4
223.215
7
13.0819
7
5.28777
9
<
0.0001
<
0.0001
<
0.0001
0.0402
0.3236
0.0117
0.0544
0.1523
<
0.0001
0.0013
0.0298
41
Another model was fitted to represent the data for pitch found in
the experiment. The significant terms and those required for
hierarchy are summarized in Table 3 below.
Table 3, Pitch Motion ANOVA Table
Source
Sum of df Mean
Squares
Square
The relationships between parameters and heave were found and
a model was fitted for the data found through experimentation.
A model was fitted, using the significant terms as well as those
needed for hierarchy, summarized in Table 2 below.
Table 2, Heave Motion ANOVA Table
Source
Sum of
df Mean
Squares
Square
A-Bow
Shape
BBottom
Shape
CMidbody
Length
D-Stern
Shape
96.0198
2
1
31
The data in the paper did not have full factorial results for Speed
and Trim, trim was part of a separate model. As this paper is
concerned with understanding the general relationships between
factors for vessels in their normal operating condition, the effects
of trim were excluded from this study.
Model
3.28819
1
89.9928
8
0.03126
5
0.00563
6
0.00122
4
0.00888
9
0.00490
5
0.00262
9
0.26982
9
0.01581
4
0.00639
2
0.03143
95.9883
9
0.02864
7
0.04927
15
0.28267
7
0.01976
5
F Value
p-value
Prob >
F
<
0.0001
<
0.0001
<
0.0001
6.39922
6
0.02864
7
0.04927
5293.74
4
23.6980
2
40.7584
5
1
0.28267
7
233.844
<
0.0001
1
0.01976
5
16.3508
0.0004
1
1
3
F Value
p-value
Prob > F
Model
89.63329
12
7.469441
5020.805
< 0.0001
A-Bow
Shape
BBottom
Shape
CMidbody
Length
D-Stern
Shape
E-Speed
0.021913
1
0.021913
14.72969
0.0006
0.008049
1
0.008049
5.410365
0.0272
0.287899
1
0.287899
193.5196
< 0.0001
0.016483
1
0.016483
11.07928
0.0024
5.391042
1
5.391042
3623.747
< 0.0001
F-Sea
State
AB
83.6061
1
83.6061
56198.3
< 0.0001
0.004044
1
0.004044
2.718
0.1100
AC
0.001505
1
0.001505
1.011571
0.3228
AE
0.007847
1
0.007847
5.274827
0.0290
AF
0.012758
1
0.012758
8.575596
0.0066
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BC
0.003365
1
0.003365
2.261819
0.1434
ABC
0.008248
1
0.008248
5.543985
0.0255
Residual
0.043143
29
0.001488
Cor Total
89.67644
41
The bottom shape was also involved in a significant interaction
with the speed effect. This interaction can be seen when
comparing the results in Figure 2.
Interaction
Resistance (EHP/Te)
0.5
Once a model was fitted to the data, it was then possible to
examine the effect of each parameter which was significant. The
effect of choosing each parameter on the corresponding
performance metric is summarized in the sections below.
14 Knots
0.3
0.2
0.1
0
Flat Bottom
RESISTANCE DISCUSSION
Figure 2, Bottom-Speed Interaction Plot
It can be seen from this figure that although the interaction
between the bottom shape and speed was a weak interaction, the
benefit offered by using a deadrise bottom is more evident at
higher speed than at lower speed.
The next significant factor was factor B, the bow shape. Bow
shape was found to depend on a 3 factor interaction between bow
shape, midbody length and speed. As there was a strong
interaction between the bow shape and other factors, it is not
possible to make a generalized statement about the effect of bow
shape, without first accounting for what the other factor
conditions are. These interactions are explained with their
corresponding figures in Figure 3 and Figure 4 below.
The factor A, Bottom was found to have significant interactions
with speed, and bow shape of the vessel. When examining each
of these interaction plots, we see that the nature of the bottom
shape factor was that for a vessel which had a dead rise bottom
shape, there was a general decrease in required power to operate
at speed. This can be demonstrated in each of the interaction
plots below. The specific nature of each interaction is
summarized along with its interaction plot.
Interaction
First of all there was found to be a significant interaction between
the bottom shape and the bow shape, this interaction is
demonstrated by examining the interaction in Figure 1.
0.14
Short Midbody
Resistance (EHP/Te)
0.12
Interaction
0.6
Vertical Bow
0.5
Deadrise Bottom
Bottom Shape
In the results of each ANOVA, it can be seen that each
of the parameters of the experiment were found to significantly
impact the predicted resistance. To gain an understanding of the
relationships between choosing each parameter, it is necessary to
determine what effect varying a parameter has on the predicted
outcome. To best understand the outcome, it is best to examine
each factor along with its interactions.
Resistance (EHP/Te)
10 Knots
0.4
Bulbous Bow
0.08
0.06
0.04
0.4
0.02
0.3
0
Vertical Bow
0.2
Long Midbody
0.1
Bulbous Bow
Bow Shape
Figure 3, Bow-Midbody Length Interaction at Low Speed
0.1
0
Flat Bottom
Deadrise Bottom
Bottom Shape
Figure 1, Bottom-Bow Interaction Plot
In this figure we can see there is a weak interaction effect
between the bottom shape and bow shape, with a deadrise bottom
offering a slightly larger performance increase for vessels with a
bulbous bow as opposed to vessels with a vertical bow.
4
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Interaction
Interaction
0.5
0.6
Short Midbody
Long Midbody
Resistance (EHP/Te)
Resistance (EHP/Te)
0.5
0.4
0.3
0.2
0.1
0
Vertical Bow
10 Knots
14 Knots
0.4
0.3
0.2
0.1
0
Conventional Stern
Bulbous Bow
Bow Shape
Integrated Stern
Stern Shape
Figure 4, Bow-Midbody Length Interaction at High Speed
Figure 6, Stern-Speed Interaction Plot
As can be seen from these figures, the interaction is rather
complex, first of all, it can be seen that at low speed, the vertical
bow shape was shown to have a lower resistance, but at higher
speed, the bulbous bow offers a benefit. This effect can be
explained by the fact that the bulbous bow is optimized for
operating at higher speed, but adds additional frictional
resistance to the vessel, creating extra resistance at low speed.
There appears to be very little interaction between bow and
midship length at low speed, but this interaction is quite apparent
at higher speed, where the bulbous bow was seen to have a much
larger effect for short mid sections as opposed to large sections.
In this figure we can see that although there is a weak interaction,
it is quite clear that the integrated stern offers a greater
performance increase when operating at higher speed.
The final factor considered in this experiment was that of speed,
which as expected results in a higher resistance when operating
at higher speed.
Once all the factors have been accounted for, a mathematical
model is fitted which can be used to predict resistance for vessels
with the corresponding combinations of hull forms. For
resistance, this formula is found to be:
Following bow shape, the effect of the length of the midbody
was examined. The results showed that in general, a longer
midbody section resulted in a performance increase, the
interaction between midship length and speed was determined to
be significant and is presented in Figure 5.
√𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 0.50 − 0.00365 𝐴 − 0.00676 𝐵 − 0.00846 𝐶
− 0.00369 𝐷 + 0.17 𝐸 − 0.00152 𝐴 𝐵
− 0.00238 𝐴 𝐸 + 0.00493 𝐵 𝐶 − 0.017 𝐵 𝐸
− 0.00108 𝐶 𝐸 − 0.00213 𝐷 𝐸
+ 0.00377 𝐵 𝐶 𝐸
Interaction
Resistance (EHP/Te)
0.5
The Parameters for coded value of factors are provided in Table
4 below:
10 Knots
14 Knots
0.4
0.3
Table 4, Resistance Equation Parameters
Value A BCD - Stern
Bottom
Bow
Midbody
-1
Flat
Vertical Short
Conventional
0.2
0.1
0
Short Midbody
Long Midbody
1
Midbody Length
Deadrise
Bulb
Long
Integrated
ESpeed
10
Knots
14
Knots
Figure 5, Midbody Length - Speed Interaction Plot
Using this mathematical model, it is possible to predict what hull
form would provide the greatest efficiency for a specific
operating condition. The optimum hull forms are presented in
Table 5 below.
This interaction is clearly a weak interaction effect, however, the
nature of this interaction is that the effect of midbody length is
slightly higher at high speed.
The final hull parameter to be examined was the stern shape
parameter. Analysis of this factor showed that in general, using
an integrated stern resulted in a performance increase. This can
be observed by examining Figure 6.
Table 5, Optimized Resistance Hull Forms
Speed
(Knots)
10
14
5
Bottom
Shape
Deadrise
Deadrise
Bow
Shape
Vertical
Bulbous
Midbody
Length
Long
Long
Stern
Shape
Integrated
Integrated
Resistance
(EHP/Te)
0.096
0.399
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HEAVE DISCUSSION
The next factor, the bottom shape, showed that a deadrise bottom
generally resulted in increased motions for the vessel, one
significant interaction was found with the midbody length,
shown in Figure 9.
For heave response, Factor A was the bow shape
studied. In this experiment the results showed that in general
using a bulbous bow had a corresponding increase in heave
motion when compared with a vertical bow. This factor has
several interactions, including the Interaction with bottom shape,
midbody length, stern shape, and speed.
Heave (m)
Interaction
The first interaction is the ABC interaction, and is presented in
Figure 7 and Figure 8.
Heave (m)
Interaction
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Vertical Bow
Flat Bottom
Deadrise Bottom
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Flat Bottom
Long Midbody
Deadrise Bottom
Bottom Shape
Figure 9, Bottom-Midbody Length Interaction Plot
This interaction shows that the effect of midbody length on
performance is greater for flat bottoms than for deadrise bottoms.
Bulbous Bow
The midbody length factor C was found to have a performance
increase corresponding to an increase in length, this interacted
significantly with the stern shape of the vessel, presented in
Figure 10.
Bow Shape
Figure 7, Bow-Bottom Interaction Low Midbody Length
Interaction
Interaction
1.2
Flat Bottom
1
0.9
Deadrise Bottom
Conventional Stern
0.8
0.8
Integrated Stern
0.7
0.6
0.6
Heave (m)
Heave (m)
Short Midbody
0.4
0.5
0.4
0.3
0.2
0.2
0
Vertical Bow
0.1
Bulbous Bow
0
Short Midbody
Bow Shape
Long Midbody
Midbody Length
Figure 8, Bow-Bottom Interaction High Midbody Length
Figure 10, Midbody Length-Stern Interaction Plot
It can be seen in this graphic that for vessels with a long midbody
length, the AB interaction is very weak, showing that although
the bulbous bow increases the motions, it appears to have little
interaction with the shape of the vessel bottom.
It is clear from this interaction plot that the stern shape of the
vessel has little effect on performance for short midbody vessels,
but does offer an effect for long midbody vessels.
However, when comparing this with vessels with a short
midbody, we see that for bulbous bows, the bottom shape does
not influence the motion response, however for vertical bows,
the flat bottom offered a performance increase over a deadrise
bottom.
The effect of factor D stern shape was such that a conventional
stern offered slightly better motion performance than an
integrated stern in heave. All interactions with this factor are
described above.
The effect of vessel speed factor E was found that in general
increased speed resulted in reduced vessel heave. This
experienced an interaction with the sea state, as shown in Figure
11.
The ACD and AE interactions, though statistically significant
showed very weak interaction effects with no particularly
impactful consequences on the effect of the bow shape on
performance.
6
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PITCH DISCUSSION
Interaction
4.5
Similar to heave, pitch data was collected in a numerical
simulation for the 16 hull forms, and analyzed, the factors for
pitch are identical to those used in heave.
Summer Low Seas
4
Winter High Seas
3.5
Heave (m)
3
2.5
Factor A, the bow shape, showed that in general, a vertical bow
offered better motion performance in pitch, but was subject to a
significant interaction effect along with bottom shape and
midbody length. As well as the interaction with speed and sea
state.
2
1.5
1
0.5
0
0 Knots
10 Knots
Speed
This interaction, ABC, is demonstrated in Figure 12 and Figure
13.
Figure 11, Speed-Sea State Interaction Plot
It is clear from this figure that the effect of speed on motion
response is more significant when operating in higher sea states.
The final factor, Factor F indicates that the motions in heave
increase when the sea state is more severe, as expected.
Interaction
1.4
Flat Bottom
1.2
Deadrise Bottom
Pitch (Deg)
1
Using the significant parameters of this experiment, a equation
was fitted to represent this data, this model is presented below in
coded numbers:
0.8
0.6
0.4
0.2
𝐻𝑒𝑎𝑣𝑒 = 2.15 + 0.027 𝐴 + 0.035 𝐵 − 0.084 𝐶 + 0.022 𝐷
− 0.29 𝐸 + 1.49 𝐹 − 0.028 𝐴 𝐵 − 0.012 𝐴 𝐶
− 0.0055 𝐴 𝐷 − 0.015 𝐴 𝐸 + 0.011 𝐵 𝐶
+ 0.0081 𝐶 𝐷 − 0.086 𝐸 𝐹 − 0.020 𝐴 𝐵 𝐶
− 0.013 𝐴 𝐶 𝐷
0
Vertical Bow
Figure 12, Bow-Bottom Interaction Low Midbody Length
Interaction
Pitch (Deg)
The coded numbers for each factor are provided in Table 6
Table 6, Heave Equation Parameters
Value
-1
A - Bow
Vertical
B - Bottom
Flat
C - Midbody
Short
D - Stern
Conventional
E - Speed
0 Knots
F - Seas
1.5 m Hs at 8.5s
+1
Bulbous
Deadrise
Long
Integrated
10 Knots
4.5 m Hs at 11.5s
Bottom
Shape
Flat
Flat
Midbody
Length
Long
Long
Stern Shape
Conventional
Conventional
Flat Bottom
1.2
Deadrise Bottom
1
0.8
0.6
0.2
0
Vertical Bow
Bulbous Bow
Bow Shape
Figure 13, Bow-Bottom Interaction High Midbody Length
It can be seen in this figure that the nature of the interaction is
for a long midbody, the bottom shape has no effect of
performance, but for a short midbody and a vertical bow, the flat
bottom has a slightly better pitch performance.
Table 7, Heave Optimized Hull Form
Bow
Shape
Vertical
Vertical
1.4
0.4
Using this mathematical model, an optimum hull form can be
selected which offers the lowest heave performance, assumed at
the higher sea state, and is summarized in Table 7.
Speed
(Knots)
0
10
Bulbous Bow
Bow Shape
Heave
(m)
3.75
3.04
The interactions with speed and sea state, though statistically
significant have too small an effect to noticeably impact the
motions of the vessel.
Factor B the bottom shape was shown to in general offer a
slightly better performance for flat bottoms as opposed to
deadrise bottoms.
7
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Factor C showed that in general an increase in midbody length
resulted in a corresponding decrease in pitch motion.
The hull analysis has shown that in general, using a long
midbody, deadrise bottom, and integrated stern results in reduced
resistance, with the effect of using a bulbous bow being
dependent on the speed, with low speed favoring vertical bows
and high speeds favoring bulbous bows. Conversely, the
seakeeping performance of vessels is generally better for vessels
with vertical bows, flat bottoms, long mid sections, and
conventional sterns, suggesting there is an inverse relationship
for tradeoffs between resistance and seakeeping performance.
Factor D showed in general that conventional sterns offered
slightly better motion characteristics than the integrated stern.
Factor E showed that operating at a higher speed resulted in a
great reduction in measured motions.
Factor F sea state showed that motions increased with worsening
sea states as expected.
Further analysis is required to investigate the trade-offs in
performance, between the hull shapes needed for minimum
resistance and minimum motions in waves. An optimization
function should be developed based on the combined responses
of multiple variables. A further discussion on the selection of
waves is required. The waves used were for a single height and
frequency (regular waves) in head waves. Other headings could
be considered, especially for the ship with forward speed, and
realistic irregular sea states could be included in further analysis.
Using the significant parameters of this experiment, an equation
was fitted to represent this data, this model is presented below in
coded numbers:
𝑃𝑖𝑡𝑐ℎ = 2.40 + 0.023 𝐴 + 0.014 𝐵 − 0.084 𝐶 + 0.020 𝐷
− 0.36 𝐸 + 1.43 𝐹 − 0.010 𝐴 𝐵
− 0.0061 𝐴 𝐶 − 0.014 𝐴 𝐸 − 0.018 𝐴 𝐹
+ 0.0091 𝐵 𝐶 − 0.014 𝐴 𝐵 𝐶
All of the design of experiments methodology was based on
numerical predictions of ship performance. In the case of the
resistance predictions, a state of the art commercial RANS CFD
code was used. In the case of the ship motions a 3-dimensional
potential flow code was used. In all cases, it was assumed that
there was a linear reaction between the low and high levels, and
that a peak or trough did not occur between the two selected
values. This assumption should be checked, with additional
simulations at intermediate points between the selected levels.
There are design of experiment techniques that could be used to
include these additional points. Also the accuracy of the
numerical predictions should be checked against model
experiments, or the performance of full-scale ships.
The coded numbers for each factor are provided in Table 8.
Table 8, Pitch Equation Parameters
Value
-1
A - Bow
Vertical
B - Bottom
Flat
C - Midbody
Short
D - Stern
Conventional
E - Speed
0 Knots
F - Seas
1.5 m Hs at 8.5s
+1
Bulbous
Deadrise
Long
Integrated
10 Knots
4.5 m Hs at 11.5s
Using this mathematical model, an optimum hull form can be
selected which offers the lowest pitch performance, assumed at
the higher sea state, and is summarized in Table 9.
ACKNOWLEDGMENTS
Table 9, Pitch Optimized Hull Form
Speed
(Knots)
0
10
Bow
Shape
Vertical
Vertical
Bottom
Shape
Flat
Flat
Midbody
Length
Long
Long
Stern Shape
Conventional
Conventional
Pitch
(Deg)
4.03
3.33
The authors would like to thank Peter Van Diepen and Ross
Titman at Naviform Consulting and Research Ltd. who drew our
attention to the work they were doing on OSV hull form design
and its suitability for this type of analysis. They also generously
provided us with the hull form geometry files that allowed us to
carry out the motion predictions.
CONCLUSIONS AND RECOMMENDATIONS
REFERENCES
The work presented in this paper has shown that the
design of experiments methodology can be successfully applied
to numerical predictions of the resistance and motion in waves
for a series of Offshore Supply Vessel hull forms. The number of
significant terms in each case is considerably less than the
number of possible terms, and the most significant parameters in
each case were successfully identified against an assumed level
of statistical significance. The resulting equations can be used to
determine the factors that result in the minimum resistance per
tonne displacement, or the minimum motion (heave and pitch) in
waves.
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