i OPTIMIZATION OF SHIP HULL PARAMETERS BASED ON REGRESSION BASED RESISTANCE ANALYSIS
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OPTIMIZATION OF SHIP HULL PARAMETERS BASED ON
REGRESSION BASED RESISTANCE ANALYSIS
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OPTIMIZATION OF SHIP HULL PARAMETERS BASED ON REGRESSION
BASED RESISTANCE ANALYSIS By
Asim Kumar Sarker
Department of Naval Architecture and Marine Engineering
Bangladesh University of Engineering and Technology.
2011.
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CERTIFICATE OF APPROVAL
The thesis titled “OPTIMIZATION OF SHIP HULL PARAMETERS BASED ON REGRESSION BASED RESISTANCE ANALYSIS” Submitted by ASIM KUMAR SARKER, Roll no: 040812003F, Session: April, 2008 has been accepted as satisfactory in partial fulfillment for the requirement for the degree of Master of Science in Engineering (Naval Architecture and Marine) on January 9, 2012.
BOARD OF EXAMINERS
1.Dr. Goutam Kumar Saha Chairman
________________
Associate Professor (Supervisor) Department of Naval Architecture and Marine Engineering, BUET, Dhaka. 2.Dr. M. Rafiqul Islam Member
________________
Professor & Head (Ex-Officio) Department of Naval Architecture and Marine Engineering, BUET, Dhaka.
3.Dr. Gazi Md. Khalil Member
_______________
Professor Department of Naval Architecture and Marine Engineering, BUET, Dhaka. 4.Dr. Md. Refayet Ullah Member
________________
Professor Department of Naval Architecture and Marine Engineering, BUET, Dhaka.
5.Prof. Dr. M. H. Khan Member
________________
Ex-Vice-Chancellor, BUET (External) Professor, Department of Mechanical and Production Engineering Ahsanullah University of Science & Technology (AUST) 141 &142, love Road,Tejgaon Industrial Area, Dhaka-1208.
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Declaration
I do hereby declare that, this thesis has not been submitted elsewhere for the award of any degree or diploma.
_____________________
Asim Kumar Sarker
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ACKNOWLEDGEMENT
The author is grateful to almighty God for showing him the right path at the right moment, giving him the strength to carry out the work. The author wishes to expresses his deepest gratitude to his supervisor, Dr. Goutam Kumar Saha, Associate Professor, Department of Naval Architecture and Marine Engineering for his valuable guidance and suggestion throughout this study. The author gives special thanks to Engr. Kho. Akther Hossain (Commander, Bangladesh Navy) & Engr. Tasnova Anam (Lieutenant, Bangladesh Navy) for advices and other cordial helps.
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Table of Contents
Acknowledgement ……………………………………………………………… v Table of Contents ……………………………………………………………… vi List of Tables ……………………………………………………………… viii List of Figures ……………………………………………………………… ix Abstract ……………………………………………………………… xi Nomenclature ……………………………………………………………… xii
Chapter 1. Introduction …………… 1 1.1. Research Background …………… 6 1.2. Research Objectives …………… 7 1.3. Methodology …………… 7 1.4. Problem Statement …………… 7 1.5. Expected Outcomes …………… 8
Chapter 2. Theory and Literature Review …………… 9 2.1. Resistance Theory …………… 9 2.2. Component of Total Resistance …………… 10
2.2.1. Frictional Resistance …………… 10 2.2.2. Wave Making Resistance …………… 12 2.2.3. Eddy Resistance …………… 14 2.2.4. Air Resistance …………… 15
2.3. Other Types of Resistance not included in total hull resistance
…………… 16
2.3.1. Appendage resistance …………… 16 2.3.2. Steering resistance …………… 16 2.3.3. Wind velocity and water current resistance …………… 17 2.3.4. Added resistance due to waves …………… 17 2.3.5. Increased resistance in shallow water …………… 17
Chapter 3. Prediction of ship resistance …………… 19 3.1. Resistance calculation methods …………… 20
3.1.1. Holtrop method …………… 20 3.1.1.1. Calculation for viscous resistance …………… 20 3.1.1.2. Calculation for wave resistance …………… 21 3.1.1.3. Calculation for bulbous bow resistance …………… 22 3.1.1.4. Calculation for transom resistance …………… 23 3.1.1.5. Calculation for model ship correlation resistance …………… 23
3.1.2. Hollenbach method …………… 24 3.1.2.1. Typical resistance …………… 25 3.1.2.2. Minimum resistance …………… 25
3.1.3. Oortmerssen method …………… 27 Chapter 4. Effect of hull parameters and form parameters on ship
resistance …………… 31
4.1. Effect of ship hull parameters and empirical formulae …………… 31
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4.1.1. Length …………… 31 4.1.2. Breadth …………… 33 4.1.3. Draught …………… 33 4.1.4. Speed …………… 33
4.2. Effect of hull form parameters on resistance and empirical formulae
…………… 33
4.2.1. Block coefficient …………… 34 4.2.2. Mid ship coefficient …………… 34 4.2.3. Prismatic coefficient …………… 35 4.2.4. Water plane coefficient …………… 35 4.2.5. Longitudinal distance of center of buoyancy …………… 36
Chapter 5. Optimization technique …………… 37 5.1. Optimization problem …………… 37 5.2. SQP algorithm …………… 38 5.3. Steps in SQP algorithm …………… 39
Chapter 6. Result and discussion …………… 42 6.1. Optimization of hull parameters …………… 42 6.2. Optimization of Wigley hull parameters …………… 43
6.2.1.1.Optimization of Wigley Hull parameters within displacement (1400 < < 1500) by Holtrop method
…………… 46
6.2.1.2.Optimization of Wigley Hull parameters within displacement (1400 < < 1500) by Hollenbach method
…………… 48
6.2.1.3.Optimization of Wigley Hull parameters within displacement (1400 < < 1500) by Oortmerssen method
…………… 50
6.3. Optimization of Wigley hull shape …………… 53 6.3.1.1.Influence of water line shape factor α …………… 53 6.3.1.2.Influence of water line shape factor β …………… 55 6.3.1.3.Influence of frame line shape factor γ …………… 57 6.3.2.1.Optimization of Wigley hull shape within specific range
of displacement (1400< <1500) by Holtrop method …………… 59
6.3.2.2.Optimization of Wigley hull shape within specific range of displacement (1400< <1500) by Hollenbach method
…………… 61
6.3.2.3.Optimization of Wigley hull shape within specific range of displacement (1400< <1500) by Oortmerssen method
…………… 63
6.4. Optimization of Wigley hull parameters and shapes. …………… 66 6.4.1.1.Optimization of Wigley hull parameters and shape
within displacement (1400< <1500) by Holtrop method …………… 66
6.4.1.2.Optimization of Wigley hull parameters and shape within displacement (1400< <1500) by Hollenbach method
…………… 68
6.4.1.3.Optimization of Wigley hull parameters and shape within displacement (1400< <1500) by Oortmerssen method
…………… 70
Chapter- 7. SWOT analysis of the optimization process …………… 73 Chapter- 8. Conclusion and future works. …………… 74
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Table 1.1 List of Tables:
Waterways of Bangladesh ……………… 1 Table 3.1 Value of C ……………… Stern 21 Table 3.2 Coefficient for Wetted Surface by Hollenbach’s
Method ……………… 24
Table 3.3 Coefficient for Typical Resistance by Hollenbach’s Method
……………… 26
Table 3.4 Standard deviation for Typical Resistance by Hollenbach’s Method
……………… 26
Table 3.5 Coefficient for minimum resistance by Hollenbach’s method
……………… 27
Table 3.6 Range of validity for minimum resistance, Hollenbach’s method
……………… 27
Table 6.1 Table for Hull Parameter Optimizations ……………… 43 Table 6.2 Optimized WigleyHull parameter at different speeds
by Holtrop methods ……………… 46
Table 6.3 Optimized WigleyHull parameter at different speeds by Hollenbach methods
……………… 48
Table 6.4 Optimized WigleyHull parameter at different speeds by Oortmerssen methods
……………… 50
Table 6.5 Optimized WigleyHull shape at different speeds by Holtrop methods
……………… 59
Table 6.6 Optimized WigleyHull shape at different speeds by Hollenbach methods
……………… 61
Table 6.7 Optimized Wigley Hull shape at different speeds by Oortmerssen methods
……………… 63
Table 6.8 Optimized Wigley Hull parameter and shape at different speeds by Holtrop methods
……………… 66
Table 6.9 Optimized Wigley Hull parameter and shape at different speeds by Hollenbach methods
……………… 68
Table 6.10 Optimized Wigley Hull parameter and shape at different speeds by Oortmerssen methods
……………… 70
Table 7.1 SWOT Analysis ……………… 73
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Figure 2.1 List of Figures
Typical curve of total hull resistance ……………… 9 Figure 2.2 Component of total hull resistance ……………… 10 Figure 2.3 Boundary layer around ship hull at LWL ……………… 12 Figure 2.4 Lord Kelvin wave pattern ……………… 13 Figure 2.5 Schematic diagram of typical ship wave system ……………… 14 Figure 3.1 Pressure distribution around a ship hull ……………… 28 Figure 3.2 Wave system at fore and aft shoulder ……………… 28 Figure 4.1 Parametric study methodology ……………… 32 Figure 5.1 SQP optimization process ……………… 41 Figure 6.1 History of hull parameter optimization process of different
methods of resistance ……………… 43
Figure 6.2 Coordinate system in Wigley hull ……………… 44 Figure 6.3 Different views of Wigley hull ……………… 45 Figure 6.4 History of optimization of Wigley hull parameters for
different speeds in Holtrop methods ……………… 47
Figure 6.5 Views of parameter optimized Wigley hulls at different speeds by Holtrop method
……………… 47
Figure 6.6 History of optimization of Wigley hull parameters for different speeds in Hollenbach methods
……………… 49
Figure 6.7 Views of parameter optimized Wigley hulls at different speeds by Hollenbach method
……………… 49
Figure 6.8 History of optimization of Wigley hull parameters for different speeds in Oortmerssen methods
……………… 51
Figure 6.9 Views of parameter optimized Wigley hulls at different speeds by Oortmerssen method
……………… 51
Figure 6.10 Comparison of reduction of resistance at different speeds for hull parameter optimization
……………… 52
Figure 6.11 Effect of waterline shape factor “α “in Wigley Hull equation
……………… 54
Figure 6.12 Effect of waterline shape factor “β “in Wigley Hull equation
……………… 56
Figure 6.13 Effect of frame line shape factor “γ “in Wigley Hull equation
……………… 58
Figure 6.14 History of optimization of Wigley hull shape for different speeds in Holtrop methods
……………… 60
Figure 6.15 Views of shape optimized Wigley hulls at different speeds by Holtrop method
……………… 60
Figure 6.16 History of optimization of Wigley hull shape for different speeds in Hollenbach methods
……………… 62
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Figure 6.17 Views of shape optimized Wigley hulls at different speeds by Hollenbach method
……………… 62
Figure 6.18 History of optimization of Wigley hull shape for different speeds in Oortmerssen methods
……………… 64
Figure 6.19 Views of shape optimized Wigley hulls at different speeds by Oortmerssen method
……………… 64
Figure 6.20 Comparison of reduction of resistance at different speeds for hull shape optimization
……………… 65
Figure 6.21 History of optimization of Wigley hull parameter and shape for different speeds in Holtrop methods
……………… 67
Figure 6.22 Views of parameter and shape optimized Wigley hulls at different speeds by Holtrop method
……………… 67
Figure 6.23 History of optimization of Wigley hull parameter and shape for different speeds in Hollenbach methods
……………… 69
Figure 6.24 Views of parameter and shape optimized Wigley hulls at different speeds by Hollenbach method
……………… 69
Figure 6.25 History of optimization of Wigley hull parameter and shape for different speeds in oortmerssen methods
……………… 71
Figure 6.26 Views of parameter and shape optimized Wigley hulls at different speeds by Oortmerssen method
……………… 71
Figure 6.27 Effectiveness of research for hull parameter and shape optimization
……………… 72
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Abstract
This research represents a numerical optimization method based on regression resistance analysis for ship hull parameters. Two different ideas; non-linear optimization technique and ship hull resistance are used. The optimal hull form design enables the designer to include advance resistance performance predictions at early stage of design process, allowing a systematic evaluation of the resistance characteristics as a function of hull geometry.
The resistances are calculated by well known regression based Holtrop, Hollenbach and Oortmerssen method. This in turn is linked to the non-linear optimization procedure of Sequential Quadratic Programming (SQP) technique. Non-linear optimization procedure is used because the relation between the ship hull resistance and the ship hull parameters are non linear. An optimal hull form is obtained through a series of iteration, subject to some design constraints.
The optimizations were carried out by selecting a mathematical hull named Wigley at different speeds.In the first steps only the hull parameters such as length, length-breadth
ratio, and breadth-draught ratio are optimized. In the second step the hull form parameters such as block coefficient, prismatic coefficient etc. are optimized by modifying water line shape and frame line shape. Finally both the hull parameters and hull form parameters are optimized. Optimization is carried out at a particular Froude number (Fn = 0.22). The resistance of the ship hull is taken as objective function and ship hull parameters such as length, breadth, draft etc. are taken as constraint that satisfying design constraint of SQP process. The optimized hull resistance is compared to the original ones and also the optimized ship hull parameters and form parameters.
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NOMENCLATURE A Area A BT Bulbous bow transverse area A T Transom area A WP Water plane area A M Mid ship area B Breadth BIWTA Bangladesh Inland Water Transport Authority C Coefficient for similar kind of vessels C A Model ship correlation coefficient C B Block coefficient C F Frictional coefficient C P Prismatic coefficient C M Mid ship coefficient C WP Water plane coefficient CFD Computational Fluid Dynamics d Diameter D P Propeller diameter F n Froude number F ni Froude number for bulbous bow F nT Froude number for transom g Gravitational acceleration g i Inequity constraints h B Height at bulbous bow h i Equity constraints IWT Inland water transport ITTC International Towing Tank Conference i E Entrance angle k Surface factor K Rudd Rudder surface K Brac Bracket surface K Boss Bossing surface L Length LAD Least available depth L CB Longitudinal distance of center of buoyancy L D Displacement length L OS Length of operation L PP Length between perpendiculars L R Length of reflection L WL Length of water line m Wave function N BOSS Number of bossing N BRAC Number of bracket N RUDD Number of rudder P B Coefficient for measuring bow emergence
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r Penalty parameter R A Model ship correlation resistance R AA Resistance caused by still air R APP Appendage resistance R F Frictional resistance R n Reynolds number RT, R Total Total resistance OR Total Total resistance of original hull R TR Transom resistance R V Viscous resistance R W Wave resistance R W-A Wave resistance at FnR
<0.4 W-B Wave resistance at Fn
S >0.55
Surface SQP Sequential quadratic programming S Total Total wetted surface T Draught T F After draught V Velocity V K Velocity at knots α, β Water line factor γ Bodyline factor ρ Density of water γ Kinematic viscosity of water V Displacement l Wave pattern Ø Penalty term ω Step length parameter
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Chapter- 1. Introduction Bangladesh is a riverine country and has about 24,000 km. of rivers, streams and canals that
together cover about 7% of the country's surface. Most part of the country is linked by a complex
network of waterways which reaches its extensive size in the monsoon period. Some major
rivers flow through this country and finally discharge into the Bay of Bengal which surrounds
the southern part. Out of 24,000 km. of rivers, streams and canals only about 5,968 km. is
navigable by mechanized vessels during monsoon period which shrinks to about 3,865km during
dry period. The IWT sector carries over 50% of all arterial freight traffic and one quarter of all
passenger traffic.
Present information and status of inland waterways of Bangladesh. (BIWTA)
● Length of inland waterways : 24,000 km. ● Length of navigable waterways Monsoon : 5968 km. Dry season : 3865 km. ● Least available depth range : 3.90 m to 1.50 m.
The waterways of Bangladesh have been classified into four categories depending on least available depth (LAD) ranging from 3.90 m to 1.50m.
Table-1.1: Waterways of Bangladesh
Name of Route Minimum Depth of Water (m)
Length of Route and Percentage (Km)
Minimum Vertical Clearance (m)
Minimum Horizontal Clearance (m)
Class- I 3.66 683 (11.39%) 18.30 76.22 Class- II 2.13 1027 (17.13%) 12.20 76.22 Class -III 1.52 1885 (31.44%) 7.62 30.48 Class -IV Less than
1.52 2400 (40.04%) 5.00 20.00
Total 5995 (100%) Sources:
River craft, big and small play a very important role in the transportation of goods and
passengers in the country. There is no doubt that the rivers and the Bay of Bangle are very
significant in relation to the economic development. The Inland Water Transport (IWT) vessels
of Bangladesh are mainly divided into three classes, namely tanker, self-propelled vessel and
non-propelled dumb craft. The typical types of the vessel are as follows:
http://www.biwta.gov.bd/about_us.htm
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• Coaster : Conventional, self-propelled vessel with cargo. Some vessels have steel hatch covers. The vessels are authorized to make the coastal voyage between Rangoon and Kakinada within a distance of 20 km from the coast throughout the year.
• Cargo vessel : Smaller version of the coaster and is authorized to make the coastal voyage between Chittagong and Mongla only during fair weather season (November-February).
• Bay crossing flat : Non-propelled, ship shaped barge with up to five holds. • Bay crossing barge : Small non-propelled ship shaped craft. • Towing vessel : Seagoing type of up to1000 BHP, Pusher of similar Horse Power and
inland Tugs of 500 BHP. • Tankers : Oil Tankers operating in Chittagong-Dhaka and Chittagong-Mongla
route having design draughts from 3 m to 4.3 m.
Navigation route of Dhaka to/from Chittagong (Class – I) is through the Meghna River which is
deep and wide enough though there are some sand bars at the upstream of the river which is
dredged seasonally. In the Buriganga River toward Dhaka, the river is also stable but it is
reported that, in the vicinity of Fatulla-Hariharpara-Ganpe, there is river bends at 90 degrees or
more with very narrow point of 90-100m where ship maneuvering will be difficult. At the area of
upstream of the Buriganga river from the confluence of Lakya river, many cargo vessels,
passenger boats and small country boats navigate and cross the river. Crew shall be very careful
in navigating in this area. As for river flow, observation records of speed at Demra on the Lakya
River shows the flow speed of 0.6-0.8m/sec with a maximum of about 1.20m/sec (2.3 knots)
assumed for Dhaka port. On the route between Dhaka and Chittagong, there is the coastal
channel across sandbars from Sandwip to South Hatia, where the shallowest part in the channel
is deeper than 4.7m. Wave height is estimated at the coastal area from 2.0m to 4.4m.
Taking account of the river current, bends , lateral winds, turning area at Dhaka port, and
according to BIWTA investigation at the site, the maximum navigable ships’ size for the river in
Bangladesh is to be;
Maximum length over all 70.0 – 80 m (230-260')
Maximum breadth 12.0 – 15.0 m (40-50')
Maximum draught 3.66m (12')
.
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The overall length of inland vessels should not be more than 80 m. Ship’s overall length of 75m
will necessitate the compensation for ship’s structural strength for both longitudinal and torsional
strength. Such a long cargo hold vessel has not sufficient torsional strength for which means an
additional reinforcement of strength members on scantling of ship will be required including
additional transverse bulkhead which divide the hold into two holds system. Keeping this view in
mind, the length of the vessel should be within the range of 70 m to 80 m.
From the view point of ship’s maneuvering, an excessive ship’s breadth will cause a stability
problem of ship in general. Another problem of excessive breadth is that the inadequate ship’s
proportion of length/breadth will cause an increase of resistance for propulsion which means an
increase of horse power of the main engine to keep the specified speed. Again, it will be very
difficult to keep the ship having breadth of 15 m or more on a proper course especially during the
navigation of the bends of a river. So the range of the breadth of the ship is considered from 12m
to 15m for this research.
Depth does not directly affect the navigation and maneuverability of the ship. The selection of
the depth of a ship is quite important since excessive depth will cause a rise of center of gravity
which will be important to keep a proper stability.
According to BIWTA recommendation the maximum draught of 12ft (3.66m) for ship is taking
into account of draught increased by fresh water and ship’s trim. It is necessary to consider a
ship’s rolling or heel for lateral strong wind and furthermore, fore draft sinkage due to the
shallow water effects when navigating with insufficient bottom clearance to river bed. Heel of 3
degrees corresponds to 0.3m actual draft increase for this ship’s breadth and also 0.3m of fore
draft sinkage is anticipated when ship’s speed is high. From the reasons mentioned above, it
requires that the ship should have an allowance enough of under keel clearance for safety in river
navigation. However, in order to get the satisfactory deadweight of ship for loading cargoes,
adequate draft will be required, to the contrary. Again from the study of hydrographic charts of
BIWTA over the routes (Dhaka-Chittagong and Dhaka-Mongla), it is found that in many areas
there is deposit of plenty of silt over the last 5 years in spite of the fact that BIWTA has been
carrying out routine dredging. So the maximum draft of the ship may not exceed 4.0 m and
range of draft from 2.0 m to 4.0 m may be considered for the present work. A striking feature of
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many rivers of Bangladesh is the vast shallow water areas, which necessitate strict draft
requirement for ship.
When ship’s speed exceeds 12 knots, wave making resistance theoretically increases rapidly.
Moreover an excessive ship speed will not only make ship’s maneuvering difficult when turning
and emergency stopping, but also shallow water effects will be significant by high ship’s speed.
So it is considered that ship speed should be below 12.0 knots and for the purpose of reducing
fuel oil consumption by main engine, the vessel shall have 8.0- 12.0 knots service speed which
will be enough and appropriate for domestic navigation.
Naval architecture’s task is to ensure that, within the bounds of the other design requirement, the
hull form will be the most efficient in terms of hydrodynamics. The final test of the ship will be
conducted at the required speed with minimum of shaft power, and the objective is to achieve the
best combination of low resistance and high efficiency propulsive. Generally, this can only be
achieved by matching precisely the hull and propeller. In general, the basic contractual
obligations are placed on the dock that ship must reach or achieve a certain speed with particular
strength in the good weather on trial and for this reason smooth water performance or still water
is very important.
Forecasting the resistance of vessel is fundamental topic of interest to naval architects.
Hydrodynamics deals with the laws of physics related to the ship resistance and speed
characteristic. Due to the complicated nature of flow around the ship hull, a satisfactory
analytical method relating speed and powering requirement to hull form has not yet been
developed.
In design stage of ship, there are a number of important disciplines that need to be addressed in
detailed. Basically with one aim is to get an optimum performance of the ship. For this particular
project, one of the disciplines that will be focused and discussed in deeper is the ship resistance.
Ship resistance study is one of the essential parts in ship design in order to determine the
effective power, PE required by the ship to overcome the total resistance, RT at certain speed, VS.
5
From there, total installed power then can be calculated and determined for that ship. Prediction
in preliminary design stage is one of the important practices in ship design.
Considering the rise of fuel prices, the requirement increases for the study at the design stage to
get a minimum ship resistance. To evaluate the resistance of a ship, in practice, designer has
several options. Generally, many methods can be used to determine the ship’s resistance. These
methods can be divided into four groups which are:
Model experiments
Traditional Standard series method
Regression based methods
Computational Fluid Dynamics (CFD)
The choice of method basically depends not only on the capability available but also on the
accuracy desired, the fund available and the degree to which the approach has been developed.
Other than that, types of the ship and the limitations are also taken into account.Model testing is
still the most accurate and reliable method but the others may only be used to predict ship
resistance between certain limits. These methods are:
1) Holtrop and Mennen method
2) Hollenbach method
3) Oortmersen method
Hull form optimization is a process that involves changing a given ship or vessel hull in order to
improve performance. The hull is a fundamental component of the vessel and this structure has
the most significant influence on the performance and success of the design. The concept or
initial design stage affects the design such that in the first few weeks of designing the hull takes a
shape and the hull influences the final cost of ship to a great extent. Therefore optimization of the
hull form can be of considerable benefit.
Usually hull parameters and hull form optimization consist of changing parameters and
offsets of an already suitable hull in order to minimize hydrodynamic resistance. At the
preliminary design stage the focus on the parameters of the vessel. These are more often
determined through database analysis of known designs. This represents a search to find the
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principal parameters corresponding to the design requirements or owners’ requirements. In an
optimization process the purpose is to maximize or minimize an objective function here cost
function, while satisfying constraints representing the design requirements. Using a function
representing the cost function, which may not be the cost of the vessel, but is an objective
function to be minimized, an optimal design can be obtained.
The cost function is normally based on a functional representation of the ship. These are usually
in the form of regression-based equations that describe the displacement, form parameters and
other factors that describe the hull. They may also contain regression-based equations to
evaluate the design. These may include regression equations for sea-keeping, resistance,
stability, and design requirements such as the hold volume or cargo deadweight
There are many methods for carrying out numerical optimization in the field of hydrodynamics.
Sequential Quadratic Programming (SQP) has arguably the most successful method for solving
nonlinear constraint optimization problems. The SQP is a general method for solving nonlinear
optimization problems with constraints.
1.1 Research Background
The main objective of this project is to work on the optimization of ship hull parameters
and form parameters with respect to hull resistance satisfying the design constraints imposed by
BIWTA. The ship resistance is normally determined by using model test in a towing tank or
circulating water channel. However in the preliminary stage the ship resistance is determined by
using empirical formula or statistical data. Prediction in the preliminary design stage is one of the
important practice and research in ship design. Several methods can be used in the ship
resistance prediction depending on the type of the ship and the limitation of the methods. For the
hull parameters and hull form optimization process nonlinear method is chosen to carry out the
optimization because the relation among ship resistance (objective function), hull parameters and
form parameters are nonlinear.
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1.2 Research Objective
The objectives of the present study are:
i. To determine the ship hull parameters and form parameters using empirical formula
considering design constraint imposed by BIWTA.
ii. To predict the ship resistance by using regression method.
iii. To optimize hull parameters and form parameters to attain minimum hull resistance
using nonlinear optimization method
iv. To compare the result of optimised hull parameters with the original ones.
1.3 Research Methodology
i. Literature review on ship hull parameters, form parameters, ship resistance theory,
ship resistance prediction method and optimization method.
ii. Study several resistance prediction methods.
iii. Develop computer program for calculation of the ship hull parameters, ship
resistance etc.
iv. Develop resistance prediction equation based on available methods i.e. Holtrop and
Mennen.
v. Develop computer program to correlate the ship hull parameters, ship resistance
prediction and nonlinear programming (Sequential Quadratic Programming – SQP)
method.
vi. Optimize the ship hull parameters and shape
vii. Make a comparison between the computed results of optimized ship hull parameters with the initial hulls.
1.4 Problem Statement
In carrying out the hull optimization process using regression method for resistance
calculation, empirical formulae for hull form parameters and optimization programming
method, several issues will be addressed as fallow:-
i. How accurate is the present empirical method for ship hull parameters prediction? Is
it reliable?
ii. How accurate is the present method of resistance prediction? Is it reliable?
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iii. How accurate is the present nonlinear optimization method? Is it reliable for this
present study?
iv. If not? Why it is not reliable at first place? What are the factors contributing to the
reliable of these predictions?
v. What are the limitations?
vi. Which method can be used to get reliable and accurate results with limit for a
particular study?
1.5 Expected Outcome
i. Comparison between Optimized hull parameters and form parameters with real ones
and the optimised hull parameters can be selected in the preliminary stage.
ii. Identify suitable resistance methods that can be applied to predict ship resistance
more accurately.
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Chapter- 2. Theory and Literature review
This chapter will give an overview of about the methods to achieve the objectives of trawler
resistance prediction using regression method.
2.1. Resistance Theory
When a body moves through a fluid it may experiences forces opposing the motion. As a ship
moves through water and air it experiences both water and air forces. This force is the water’s
resistance to the motion of the ship, which is referred to as “total hull resistance” (RT
). This
resistance force consequently is used to calculate a ship’s effective horsepower. A ship’s calm
water resistance is a function of many factors, including ship speed, hull form (draught, breadth,
length, wetted surface area), and water temperature. Total hull resistance increases as speed
increases as shown below in Figure 2.1. Note that the resistance curve is not linear. The water
and air masses may themselves be moving, the water due to currents and the air as a result of
winds. These will, in general be of different magnitudes and directions. The resistance is studied
initially in still water with zero wind velocity. Unless the winds are strong the water resistance
will be the dominant factor in determining the speed achieved. Separate allowances are made for
wind and the resulting distance travelled corrected for water.
Figure 2.1: Typical curve of total hull resistance
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2.2. Components of Total Hull Resistance
As a ship moves through calm water, there are many factors that combine to form the total
resistance force acting on the hull. The principle factors affecting ship resistance are the friction
and viscous effects of water acting on the hull, the energy required to create and maintain the
ship’s characteristic bow and stern waves, and the resistance that air provides to ship motion. In
mathematical terms, total resistance can be written as:
(2.1)
Other factors affecting total hull resistance will also be presented. Figure 2.2 shows how the
magnitude of each component of resistance varies with ship speed. At low speeds viscous
resistance dominates, and at high speeds the total resistance curve turns upward significantly as
wave making resistance begins to dominate
Figure 2.2: Components of Total Hull Resistance
2.2.1. Frictional Resistance
As a ship moves through the water, the friction of the water acting over the entire wetted surface
of the hull causes a net force opposing the ship’s motion. This frictional resistance is a function
11
of the hull’s wetted surface area, surface roughness, and water speed. Viscosity is a temperature
dependent property of a fluid that describes its resistance to flow. Although water has low
viscosity, water produces a significant friction force opposing ship motion. Experimental data
have shown that water friction can account for up to 85% of a hull’s total resistance at low speed
(Fn
≤ 0.12 or speed-to-length ratio less than 0.4 if ship speed is expressed in knots), and 40-50%
of resistance for some ships at higher speeds. Naval architects refer to the viscous effects of
water flowing along a hull as the hull’s frictional resistance (Bertram, 2000).
The flow of fluid around a body can be divided into two general types of flow: laminar flow and
turbulent flow. A typical flow pattern around a ship’s hull showing laminar and turbulent flow is
shown in Figure 2.3. Laminar flow is characterized by fluid flowing along smooth lines in an
orderly fashion with laminar boundary layer. For a typical ship, laminar flow exists for only a
very small distance along the hull. As water flows along the hull, the laminar flow begins to
break down and becomes chaotic and well mixed. This chaotic behavior is referred to as
turbulent flow and the transition from laminar to turbulent flow occurs at the transition point
shown in Figure 2.3 (Harold, 1957).
Turbulent flow is characterized by the development of a layer of water along the hull moving
with the ship along its direction of travel. This layer of water is referred to as the “boundary
layer.” Water molecules closest to the ship are carried along with the ship at the ship’s velocity.
Moving away from the hull, the velocity of water particles in the boundary layer becomes less,
until at the outer edge of the boundary layer velocity is nearly that of the surrounding ocean.
Formation of the boundary layer begins at the transition point and the limit of the boundary layer
increases along the length of the hull as the flow becomes more and more turbulent.
For a ship underway, the boundary layer can be seen as the water next to the hull. Observation of
this band will reveal the turbulent nature of the boundary layer, and perhaps one can see some of
the water actually moving with the ship. As ship speed increases, separation of the boundary
layer will increase, and the transition point between laminar and turbulent flow moves closer to
the bow, thereby causing an increase in frictional resistance as speed increases.
12
Mathematically, laminar and turbulent flow can be described using the dimensionless parameter
known as the Reynolds Number to the study of hydrodynamics (Harold, 1957). For a ship, the
Reynolds Number is calculated using the equation given:
(2.2)
For external flow over flat plates (or ship hulls), typical Reynolds number magnitudes are as
follows:
Laminar flow:
Turbulent flow:
Values of between these numbers represent transition from laminar to turbulent flow.
Figure 2.3: Boundary Layer around Ship Hull at LWL
2.2.2. Wave Making Resistance
A ship moving through still water surface will produce a very specific pattern of waves. There
are essentially two primary points of origin of waves, which are at the bow and at the stern.
13
However the bow wave train is more significant, because the waves generated here persist along
the ship's hull. Generally the bow waves also larger and more predominant. These wave systems,
bow and stern, arises from the pressure distribution in the water where the ship is acting and the
resultant of net fore-and-aft force is the wave making resistance. Wave making resistance is the
result of the tangential fluid forces. It’s depends on the underwater shape of a ship that moves
through water. The size of wave created shows the magnitude of power delivered by the ship to
the water in order to move forward.
Figure 2.4: Lord Kelvin Wave Pattern
Kelvin (1887) has illustrated a ship’s wave pattern in order to explain the features. He considered
a single pressure point at the front, moving in straight line over the water surface. The generated
wave pattern consists of a system of transverse wave following behind the pressure point and a
series of divergent waves radiating from the same pressure point. The envelope of the divergent
wave crests makes an angle of 19° 28' for a thin disturbance travelling in a straight line,
regardless of the speed. Figure 2.4 shows the wave pattern illustrated by Kelvin (Edward, 1988).
14
Furthermore, the actual ship’s wave system is more complicated such that in Figure 2.5. A ship
can be considered as a moving pressure field located near the bow and moving suction field near
the stern. The bow produces a series of divergent wave pattern and also the transverse wave in
between on each side of the ship. Similar wave system is formed at the shoulder, and at the stern
with separate divergent and transverse pattern.
In the case of a deeply submerged body, travelling horizontally at a steady speed far below the
surface, no waves are formed, but the normal pressures will vary along the length. The
magnitudes of the resistance reduce with increasing the depth of a submerged body. This force
will be negligible when the depth is half-length of the body.
Figure 2.5: Schematic Diagram of Typical Ship’s Wave System (Edward, 1988).
2.2.3. Eddy Resistance or Viscous Pressure Resistance
In a non-viscous fluid the lines of flow past a body close in behind it creating pressures which
balance out those acting on the forward part of the body. With viscosity, this does not happen
completely and the pressure forces on the after body are less than those on the fore body. Also
where there are rapid changes of section the flow breaks away from the hull and eddies are
15
created. The effects can be minimized by streamlining the body shape so that changes of section
are more gradual.
However, a typical ship has many features which are likely to generate eddies. Transom sterns
and stern frames are examples. Other eddy creators can be appendages such as the bilge keels,
rudders and so on. Bilge keels are aligned with the smooth water flow lines, as determined in a
circulating water channel, to minimize the effect. At other loadings and when the ship is in
waves the bilge keels are likely to create eddies. Similarly rudders are made as streamlined as
possible and breakdown of flow around them is delayed by this means until they are put over to
fairly large angles. In multi-hull ships the shaft bracket arms are produced wider streamlined
sections and are aligned with die local flow. This is important not only for resistance but to
improve the flow of water into the propellers.
Flow break away can occur on an apparently well rounded form. This is due to the velocity and
pressure distribution in the boundary layer. The velocity increases where the pressure decreases
and vice versa. Bearing in mind that the water is already moving slowly close into the hull, the
pressure increase towards the stern can bring the water to a standstill or even cause a reverse
flow to occur. That is the water begins to move ahead relative to the ship. Under these conditions
separation occurs. The effect is more pronounced with steep pressure gradients which are
associated with full forms.
2.2.4. Air Resistance
Air resistance is the resistance caused by the zero wind velocity when ship moves with still
water. This component of resistance is affected by the shape of the ship above the waterline, the
area of the ship exposed to the air, and the ship’s speed through the water. Ships with low hulls
and small sail area will naturally have less air resistance than ships with high hulls and large
amounts of sail area. Resistance due to air is typically 4-8% of the total ship resistance, but may
be as much as 10% in high sided ships such as aircraft carriers. Attempts have been made to
reduce air resistance by streamlining hulls and superstructures, however; the power benefits and
fuel savings associated with constructing a streamlined ship tend to be overshadowed by
construction costs.
16
2.3. Other Types of Resistance Not Included in Total Hull Resistance
In addition to frictional resistance, wave making resistance, eddy resistance and air resistance,
there are several other types of resistance that will influence the total resistance experienced by
the ship.
2.3.1. Appendage Resistance
Appendage resistance is the drag caused by all the underwater appendages such as the propeller,
propeller shaft, struts, rudder, bilge keels, pit sword, and sea chests. Appendages will primarily
affect the viscous component of resistance as the added surface area of appendages increases the
surface area of viscous friction. Appendages include rudders, bilge keels, shaft brackets and
bossing, and stabilizers. Each appendage has its own characteristic length and therefore, if
attached to the model, would be running at an effective Reynolds' number different from that of
the main model. Thus, although obeying the same scaling laws, its resistance would scale
differently to the full scale. That is why resistance models are run naked. This means that some
allowance must be made for the resistance of appendages to give the total ship resistance. The
allowances can be obtained by testing appendages separately and scaling to the ship. Fortunately
the overall additions are generally relatively small, say 10 to 15% of the hull resistance, and
errors in their assessment are not likely to be critical.
2.3.2. Steering Resistance
Steering resistance is added resistance caused by the motion of the rudder. Every time the rudder
is moved to change course, the movement of the rudder creates additional drag. Although
steering resistance is generally a small component of total hull resistance in warships and
merchant ships, unnecessary rudder movement can have a significant impact. Remember that
resistance is directly related to the horsepower required to propel the ship. Additional
horsepower is directly related to fuel consumed (more horsepower equals more fuel burned). A
warship traveling at 15 knots and attempting to maintain a point station in a formation may burn
up to 10% more fuel per day than a ship traveling independently at 15 knots.
17
2.3.3. Wind Velocity and Water Current Resistance
The environment surrounding a ship can have a significant impact on ship resistance. Wind and
current are two of the biggest environmental factors affecting a ship motion. Wind resistance on
a ship is a function of the ship’s sail area, wind velocity and direction relative to the ship’s
direction of travel. For a ship steaming into a 20-knot wind, ship’s resistance may be increased
by up to 25-30%. Ocean or river currents can also have a significant impact on a ship’s resistance
and the power required maintaining a desired speed. Steaming into an opposing current will
increase the power required to maintain speed.
2.3.4. Added Resistance Due to Waves
Added resistance due to waves refers to ocean or river waves caused by wind and storms, and is
not to be confused with wave making resistance. Ocean waves cause the ship to energy
increasing the wetted surface area of the hull (added viscous resistance), and to expend
additional energy rolling, pitching, and heaving. This component of resistance can be very
significant in high sea states.
2.3.5. Increased Resistance in Shallow Water
Increased resistance in shallow water (the Shallow Water Effect) is caused by several factors.
i. The flow of water around the bottom of the hull is restricted in shallow water, therefore the
water flowing under the hull speeds up. increases the viscous resistance on the hull.
ii. The faster moving water decreases the pressure under the hull, causing the ship to “squat”,
increasing wetted surface area and increasing frictional resistance.
iii. The waves produced in shallow water tend to be larger than do waves produced in deep water
at the same speed. Therefore, the energy required to produce these waves increases, (i.e. wave
making resistance increases in shallow water). In fact, the characteristic hump in the total
resistance curve will occur at a lower speed in shallow water.
The net result of resistance for ship traveling in shallow water is that it takes more horsepower
(and fuel) to meet the required speed. Another more troublesome effect of high speed operation
in shallow water is the increased possibility of running aground. Just as shallow water will
adversely affect a ship’s resistance, operating in a narrow waterway such as a canal can produce
18
the same effect. Therefore when operating in a canal, the ship’s resistance will increase due to
the proximity of the canal walls and the decrease in pressure along the ships sides is likely to pull
the ship towards the edge of the canal. The prudent mariner is advised to operate at moderate
speeds when steaming in shallow and/or narrow waters (Harvald, 1983).
19
Chapter- 3. Prediction of Ship Resistance
In the design s tage, particularly at the preliminary stage, early estimation of total resistance of
the s hip contributes a n important pa rt. It is imp ortant to predict the tot al r esistance o f a s hip
during design stage for used of determination the installed power. Regression based method or
also known is a prediction method that base on the statistical analysis of resistance results from
ad-hoc testing of models in the towing tank. The standard series prediction method is
based on t he t esting of series of m odel t hat c arried out f or t he r esistance pr ediction pur poses.
However t hese m ethods onl y a pplicable t o be us ed f or s hip ha ving s imilar c haracteristics. It
should be emphasized that resistance prediction is not an exact science and that the algorithms
implemented in this program, while they are useful for estimating the resistance of a hull, may
not provide exact results (Carlton, 1994). Since early 1900s, number of studies onto prediction of
ship r esistance w ere c arried out a nd publ ished. V arious methods a nd a pproaches ha d be en
and a part f rom t hat, t his de velopment pr ocess i s s till for be tter
. Particularly for the preliminary stage in ship design process, number of prediction
methods f or s hip r esistance ha d be en de veloped. T hese basically appl icable t o
various families of hull shape. For example, some of the algorithms are useful for estimating the
resistance of hull , while others are useful for estimating the resistance of sailing boat hulls.
Prediction m ethods s uch a s H oltrop & M ennen’s m ethod, H ollenbach’s m ethod and
Oortmersen’s method are among the useful methods in the ship resistance prediction. As
a s ummary, most of t hese m ethods ba sically c onsider s everal el ements contribute t o the
prediction of total resistance of the ship. From the basis theory of ship resistance, as discussed
previously, elements such as frictional resistance, wave making resistance and other components
of r esistance s uch as vi scous pressure r esistance and air r esistance ar e viewed as major
elements in and de velopment of s hip r esistance pr ediction. All of t hese e lements
mainly c ontribute as and factors t o correlate ship r esistance pr ediction .
The relationship of those factors is applied differently for each type of prediction methods and is
discussed the next .
20
3.1. Resistance Calculation Method
This pa rt w ill f ocus on methods us e to calculate t he r esistance. Details of the se resistances will also show with mathematical formulation.
3.1.1. Holtrop Method: Holtrop Mennon (1984, 1982, 1978) a power prediction method which was based on a regression analysis of random model and full-scale test data. For several combinations of main dimensions and form coefficients the method had been adjusted to test results obtained in some specific cases.
According t o Holtrop (1984, 1982, 1978) formula t he t otal r esistance of a s hip has b een
subdivided into:
(3.1)
3.1.1.1.Calculation for Viscous Resistance
One has only to look down from the deck of a ship at sea and observe the turbulent motion in the water ne ar t he hul l, i ncreasing i n e xtent f rom bow t o s tern, t o r ealize t hat e nergy i s be ing absorbed i n f rictional r esistance. E xperiments ha ve s hown t hat e ven i n s mooth, ne w s hips i t accounts f or 80 t o 85pe rcent of t he t otal r esistance i n s low-speed s hips a nd a s m uch a s 50 percent in high-speed ships. Any roughness of the surface will increase the frictional resistance appreciably over that of a smooth surface, and with subsequent corrosion and fouling still greater
will . N ot onl y do es t he na ture of t he s urface a ffect t he dr ag, but t he wake and propulsive performance are also changed. Frictional resistance is thus the largest single component of the total resistance of a ship, and this accounts for the theoretical and experimental research that ha been devoted to it over the years. The c alculation of w etted s urface a rea w hich i s r equired f or t he calculation of t he f rictional resistance is discussed below. Viscous resistance,
Viscous Coefficient,
Reynolds Number, From ITTC 1978 form of the hull is described as
(3.2)
21
where, (3.3)
Coefficient is used for stern shape where
After body form Pram with gondols -25 V-shaped sections -10 Normal section shape 0 U-shaped sections with Hogner stern 10
Table-3.1: Value of
3.1.1.2.Calculation for Wave Resistance The wave-making resistance of a ship is the net fore-and-aft force upon the ship due to the fluid pressures acting normally on all parts of the hull, just as the frictional resistance is the result of the tangential fluid forces. In the case of a deeply submerged body, travelling horizontally at a steady s peed far b elow the s urface, no w aves are f ormed, but t he nor mal pr essures w ill va ry along the length.
(3.4)
where
when L/B < 12
when L/B > 12
d = -0.9
22
when
when 1726.91 512
when > 1726.91
(3.5)
when < 0.11
when 0.11 < < 0.25 when > 0.25
when CP
when C
< 0.80
P
> 0.80
for Fn
for F
< 0.4
n
for 0.4 < F
> 0.55
n
< 0.55 (3.6)
3.1.1.3.Bulbous Bow Resistance Calculation Bulbous bow resistance is the additional resistance due to the presence of a bulbous bow near the surface and is determined from:
(3.7)
where
23
and
3.1.1.4.Transom Resistance Calculation
Transom resistance is an additional pressure resistance due to immersed transom and calculated from:
(3.8)
Coefficient c6
when
is related with Froude number based on the transom immersion:
when 5
is defined as:
3.1.1.5.Model ship co-relation Resistance Calculation
The model ship correlation resistance R A
(3.9)
is supposed to describe primarily the effect of the hull roughness and the still-air resistance. From an analysis of result of speed trials, which have been corrected t o i deal t rial condition, t he f ollowing f ormulas a re us ed t o c alculate m odel s hip correlation resistance.
Correlation allowance coefficient CA
where
as follows:
when TF/L ≤ 0.04 when TF
/L > 0.04
Application of Holtrop Approach: Commercial and naval vessels.
Limitation of Holtrop Approach:
Prismatic coefficient (CP
L/B ratio : 3.9 ~ 14.9
): 0.55 ~ 0.85
24
B/T ratio : 2.1 ~ 4.0
Speed range (Fn
3.1.2. Hollenbach Method:
) : 0.10 ~ 0.80
From H ollenbach a nalysis of model t ank t ests f or 433 s hips pe rformed by V iena S hip M odel Basin dur ing t he p eriod f rom 1980 t o 1995 t o i mprove t he r eliability of t he pe rformance prognosis of m odern c argo s hips i n t he pr eliminary d esign s tage. T he f ormulae w as given b y Hollenbach for t he ‘ best-fit’ c urve, but a lso a c urve de scribing t he l ower e nvelop, i .e. t he minimum a de signer ma y hope to achieve a fter extensive opt imization of the s hip lines if its design is not subject to restrictions. In a ddition t o L = LPP and L wl, which are d efined a s us ual, Hollenbach us es a ‘length ove r surface’ LOS
• For design draft; length between aft end of design waterline and most forward point of ship below design waterline.
which is defined as follows:
• For ballast draft; length between aft end and forward end of ballast waterline (rudder not taken into account).
Hollenbach gives the f ollowing e mpirical f ormulae to estimate the w etted surface inc luding appendage:
(3.10)
(3.11)
With according to table 3.2
Table 3.2: Coefficient for wetted surface in Hollenbach’s method
Single-screw Twin-screw Design draft Ballast draft Bulbous bow No bulbous bow
-0.683 -0.8037 -0.4319 -0.0887 0.2771 0.2726 0.1685 0.0000 0.6542 0.7133 0.5637 0.5192 0.6422 0.6699 0.5891 0.5839 0.0075 0.0243 0.0033 -0.0130 0.0275 0.0265 0.0134 0.0050 -0.0045 -0.0061 -0.0006 -0.0007 -0.4798 0.2349 -2.7932 -0.9486 0.0376 0.0131 0.0072 0.0506
0.0131 0.0076 -0.0030 -0.0036 0.0061 0.0049
The Froude number in the following formulae is based on the length, :
25
(3.12)
The residual resistance is given by
(3.13)
Note that (BT)/10 is used instead of S as reference area. The non-dimensional coefficient C R
where,
is generally expressed as
(3.14)
3.1.2.1.Typical Resistance The typical residual resistance coefficient is then determined by the coefficients in Table 3.2. the range of validity is given by Table 3.3. Table 3.4 gives the range of the standard mean deviation of the database considered. Within this range, the formulae should be reasonably accurate, but values outside this range may also be used.
3.1.2.2. Minimum Resistance Very good hul ls, not subject t o s pecial d esign constraints enforcing h ydro d ynamically suboptimal hull forms, may achieve the following residual resistance coefficients:
(3.15)
26
Table 3.3 Coefficients for typical resistance in Hollenbach’s method
Single-screw Twin-screw Design draft Ballast draft
-0.3382 -0.7139 -0.2748 0.8086 0.2558 0.5747 -6.0258 -1.1606 -6.7610 -3.5632 0.4534 -4.3834 9.4405 11.222 8.8158 0.0146 0.4524 -0.1418 0.0 0.0 -0.1258 0.0 0.0 0.0481 0.0 0.0 0.1699 0.0 0.0 0.0728 -0.57420 -1.50162 -5.3475 13.3893 12.9678 55.6532 90.5960 -36.7985 -114.9050 4.6614 5.55536 19.2714 -39.721 -45.8815 -192.3880 -351.483 121.820 388.3330 -1.14215 -4.33571 -14.3571 -12.3296 36.0782 142.7380 459.254 -85.3741 -254.7620 0.854 0.032 0.8970 -1.228 0.803 -1.4570 0.497 -0.739 0.7670 2.1701 1.9994 1.8319 -0.1602 -1.446 -0.1237
Table 3.4: Standard deviation of database for typical resistance, Hollenbach’s method Single-screw Twin-screw Design draft Ballast draft
4.490-6.008 5.450-7.047 4.405-7.265
0.601-0.830 0.559-0.790 0.512-0.775
4.710-7.106 4.949-6.623 3.960-7.130
1.989-4.002 2.967-6.120 2.308-6.110
1.000-1.050 1.000-1.050 1.000-1.050
27
1.000-1.055 0.945-1.000 1.000-1.070
0.430-0.840 0.655-1.050 0.495-0.860
Table 3.5: Coefficient for minimum resistance in Hollenbach’s method
a a1 a2 a3 4 Single –screw ship -0.3382 0.8086 -6.0258 -3.5632 Twin-screw ship -0.2784 0.5747 -6.7610 -4.3834 For single-screw ships
a -0.9142367 00 a 4.6614022 10 a -1.1421462 20 a 13.389284 01 a -39.720987 11 a -12.329636 21 a 90.596041 02 a -351.48305 12 a 459.25433 22
For twin-screw ships
a 3.2727938 00 a -11.501201 10 a 12.462569 20 a -44.113819 01 a 166.55892 11 a -179.50549 21 a 171.69229 02 a -644.46500 12 a 680.92069 22
Table 3.6: Range of validity for minimum resistance, Hollenbach’s method.
Single-screw Twin-screw Fn, min, CB 0.17 ≤ 0.6 0.15 Fn, min, CB 0.17+0.2 (0.6- C> 0.6 B 0.14 )
Fn 0.614-0.717 C, max B+0.261 CB0.952-1.406 2
B+0.643 CB2
3.1.3. Oortmerssen Method:
In this method, the derivation of formula by Oortmerssen is based on t he resistance and
propulsion of a ship as a function of the Froude number and Reynolds number. The constraint of
this formula is also based on ot her general parameters for small ships such as trawlers and tugs
that are collected from random data. The method was developed through a regression analysis of
data from 93 models of tugs and trawlers obtained by the Marine Research Institute, Netherlands
(MARIN). Besides, few assumptions were made for predicting resistance and powering of small
craft such as:
1. According to t he F igure 3.1 t here are pos itive a nd ne gative
hull surface .
28
Figure 3.1: Pressure distribution around a ship hull
2. Small s hip can be s aid to have a cer tain characteristics s uch as t he abs ence of a
parallel middle body, so the regions of low pressure and the wave system of fore and
after shoulder coincide and consequently the pressure distribution is illustrated as in
figure 3.2.
Figure 3.2: Wave system at fore and aft shoulder
3. The s ummation of vi scous r esistance a nd w ave-making resistance r epresenting the components of the total resistance.
The basic expression adopted for the residual resistance was derived from wavetwo –dimensional pr essure di sturbance, ha ving pe aks a t t he e quivalent
29
stem and stern positions and a minimum pressure in between, such as occurs for vessels with no parallel middle body. The range of parameters for which the coefficients of the basic expressions are valid, are as follows:
Waterline length between 8 to 80 meters; Displacement volume between 5 and 3000 cubic meters; Length-beam ratio between 1.9 and 4.0 Prismatic coefficient between 0.50 and 0.73 Mid ship section coefficient between 0.70 and 0.97 Longitudinal center of buoyancy between -7%L and +2.8%L forward of 0.5L; Half angle of entrance of design waterline between 10o and 46o
.
The speed range covered by the 970 data points lie in the Froude number range between and 0.50 (equivalent to a range of to 1.70). Some extrapolation to higher s peeds i s pe rmissible, because of t he n ature of t he ba sic ex pression. The num erical expression is as follows:
(3.16) In which
30
In the formulas for 1000C1, 1000C2, 1000C3, 1000C4, the value of CWL is based on the value of iE
In the a bove e xpressions, where i in degrees.
E is t he ha lf an gle of entrance of the de sign waterline. The va lues o f L/B and B/T c an be b ased on the w aterline v alues of L, B a nd T , although Oortmerssen used the displacement length LD rather than the waterline length, where LD
was defined as half the sum of the length between perpendiculars and the waterline length.
Application of Oortmerssen approach: Small ships, tugs, trawlers.
31
Chapter - 4.Effect of hull parameters and form parameters on ship resistance: Ship dimension, block coefficient, and speed changes a ffect hul l r esistance, fuel consumption, and operating costs as well as vessel capital cost so a complete assessment needs to consider how the Required Freight Rate (RFR) would be affected by these changes. Effects of these parameters are described below.
4.1. Effect of ship hull parameter and empirical formulae: A recommended approach to obtain an initial estimate of vessel length, beam, depth, and design draft is to use a dataset of s imilar vessels, if feasible, to obtain guidance for the ini tial values. This can be done simply by inspection or regression equations can be developed from this data using pr imary functional r equirements, s uch as cargo d eadweight and s peed, a s i ndependent variables. Development of these equations will be discussed further.
In ot her s ituations, a s ummation of l engths f or va rious vol ume or w eather d eck n eeds can provide a s tarting point for vessel length. Since the waterline length at the design draft T is a direct f actor i n the di splacement and resistance of t he ve ssel, LWL (Length of W ater Line) is usually the most useful length definition to use in early sizing iterations.
4.1.1. Length (L): Length is the most influential dimension in ship design. Roy and Gee (2001) has shown that, it has a s ignificant i mpact on e conomics, s ea keeping, resistance and pow ering. P revious parametric studies of high speed slender vessels have shown that a longer vessel will require a lower installed power for a constant displacement due to a higher length displacement ratio and lower Froude number. Those papers presented the results of a parametric study undertaken to investigate t he ef fects o f ve ssel s ize on the po wer requirement. T he pa rametric study w as undertaken to establish the l ikely change i n displacement w ith changes i n vessel l ength and hence determine if larger vessels have a significant power advantage or if the increase in weight is such that the advantage is small. The influence of design parameters on ship are as follows.
Roy and Gee (2001) also showed that, for a constant displacement, a 7% increase in LWL will lead to an increase i n speed of app roximately 1 knot f or a cons tant pow er or a d ecrease i n installed power demand of approximately 12% at 40 knots.
Molland et a l. (1994) a lso f ound t hat t he l ength/displacement r atio w as a pr edominant hull parameter.
32
Figure 4.1 – Parametric Study Methodology
A number of empirical equation exits in the literature for estimating vessel length from other ship characteristics. In Posdunine’s formula,
(4.1)
An estimating vessel length is Schneekluth’s (1998) formula,
(4. 2) The formula is applicable for ships with Δ ≥ 1000 tonne and 0.16 ≤ Fn ≤ 0.32.
Various non -dimensional r atios of hul l di mensions c an be used t o guide t he s election of hul l dimension or alternatively used as a ch eck on the dimension chosen based upon s imilar ships, functional requirements etc. Each designer develops his or her own preferences, but generally the length-breadth ratio L/B, and the breadth-draught ratio B/T, are found to be most useful.
Requirements
Initial Platform Size Estimates Length and Weight
Matrix of Ships Weight Prediction
Matrix of Required Power
Constraint Weights Variable Weights
Hull Structure Wt Variation with Length
Ship Wt Variation Vs Length
Available Machinery
Available Power
Ship Speed Variation Vs Length
Is Bigger Ship Better?
33
4.1.2. Breadth (B):
The l ength-breath r atio c an be us ed t o c heck i ndependent c hoices of l ength a nd breadth with initial length, a choice of L/B ratio can be used to obtain an estimated breadth . The L/B ratio has significant influence on hull resistance and maneuverability (both the ability to turn and directional stability). With the primary influence of length on capital cost, there has been a trend toward shorter wider hulls supported by design refinement to ensure adequate inflow to the propeller. From Watson and Gilfillan (1977) recommendation,
L/B = 4.0 for L ≤ 30 m
L/B = 4.0 + 0.025 (L – 30) for 30 ≤ L ≤ 130 m
L/B = 6.5 for 130 m ≤ L (4. 3)
4.1.3. Draught (T): The t hird m ost i mportant non di mensional ratio is the br eadth-draught r atio B /T. T he br eath-draught r atio is p rimarily important th rough its inf luence on residuary r esistance, transverse stability, and wetted surface. In general, va lues range between 2.25 ≤ B/T ≤ 3.75. The breath-draught r atio correlates s trongly w ith residuary resistance, w hich increases for l arge B/T. Roseman (1974) recommendation for maximum breath-draught ratio,
(B/T) max = 9.625 - 7.5 CB
4.1.4.
(4. 4)
4.2. Effect of hull form parameters on resistance and empirical formulae: The choice of primary hull form coefficient is a matter of design style and tradition. Generally, commercial s hips t end t o be de veloped us ing t he bl ock c oefficient C B as the pr imary form coefficient, w hile f aster m ilitary v essels t end t o be de veloped us ing t he C P as t he f orm coefficient of greatest i mportance. Through the ir lon gitudinal pr ismatic coefficient CP definitions, the form coefficients are related by dual identities, one for the longitudinal direction
34
and one for the vertical direction. A designer cannot make independent estimates or choices of the coefficients in either identity. The influences of form factors on resistance are described below.
4.2.1. Block coefficient (CB
Block Coefficient (C
):
B) is the volume (V) divided by the multiplying product of Length, Breadth and Draught (L x B x T). If a box is drawn around the submerged part of the ship, it is the ratio of the box volume occupied by the ship. It gives a sense of how much of the block defined by the LPP, beam (B) and draft (T) is filled by the hull. Full forms such as oil tankers will have a high CB where fine shapes such as sailboats will have a low CB
.
The bl ock coefficient C B
Well-known Alexander’s formula for block coefficient, C
measures t he f ullness of t he s ubmerged hul l, t he r atio of t he hul l volume to i ts surrounding pa rallelepiped L x B x T. Generally, it is economically efficient to design hulls to be slightly fuller than that which will result in minimum resistance per tonne of displacement.
(4. 5)
B
(4. 6)
is given by
where,
4.2.2. Mid ship coefficient (CM
Mid ship Coefficient (C):
m or Cx) is the cross-sectional area (Ax) of the slice at mid ships (or at the largest section for Cx) divided by beam x draft. It displays the ratio of the largest underwater section of the hull to a rectangle of the same overall width and depth as the underwater section of the hull. This defines the fullness of the underbody. A low Cm indicates a cut-away mid-section and a high Cm indicates a boxy section shape. Sailboats have a cut-away mid-section with low Cx whereas cargo vessels have a boxy section with high Cx to help increase the Cb
Mid ship coefficient C
.
(4. 7)
M is determined from Schneekluth and Bertram’s (1998) formula
35
(4. 8)
The mid ship and maximum section coefficient CM ≈ CX
4.2.3. Prismatic coefficient (C
can be estimated using generalizations developed from existing hull forms or from systematic hull series. For most commercial hulls, the ma ximum s ection includes a midships. For f aster hul ls, the ma ximum s ection may be significantly aft of amidships.
p ) :
Prismatic Coefficient (C
p) is the volume ( ) divided by Lpp x AM. It displays the ratio of the immersed volume of the hull to a volume of a prism with equal length to the ship and cross-sectional area equal to the largest underwater section of the hull (mid ship section). This is used to evaluate the distribution of the volume of the underbody. A low or fine Cp indicates a full mid-section and fine ends, a high or full Cp indicates a boat with fuller ends. Planning hulls and other high speed hulls tend towards a higher CpFroude number
. Efficient displacement hulls travelling at a low will tend to have a low Cp
(4. 9)
Prismatic coefficient from empirical relation of parameter
.
(4. 10)
The design of faster military and related vessels typically uses the longitudinal prismatic coefficient CP, rather than CB, as the primary hull form coefficient. The longitudinal prismatic describes the distribution of volume along the hull form. A low value of CP
4.2.4. Water plane coefficient (C
indicates significant taper of the hull in the entrance and run.
WP
Water plane C oefficient ( C ):
WP) is the water plane area di vided b y LPP x B . The w ater plane coefficient ex presses t he f ullness of t he water plane, or t he r atio of t he water plane area t o a rectangle of the same length and width. A low CWP figure indicates f ine ends and a high C WP figure indicates fuller ends. High C WP
(4. 11)
improves stability as well as handling behavior in rough conditions.
Water plane coefficient from Schneekluth’s (1998) formula
(4. 12)
And from Riddlesworth’s (1998) formula
(4. 13)
36
The water plane coefficient CWP is usually the next hull form coefficient to estimate. The shape of the design water plane correlates well with the distribution of volume along the length of the hull, so C WP can usually be estimated effectively in early design from the chosen CP, provided the designer’s intent relative to hull form, number of screws, and stern design is reflected. A n initial estimate of C WP used to estimate the transverse and longitudinal inertia properties of the water plane needed to calculate BMT and BML
4.2.5. Longitudinal Center of Buoyancy (LCB):
, respectively.
Longitudinal Centre of Buoyancy (LCB) is the longitudinal distance from a point of reference (often mid ships) to the centre o f the di splaced volume of water when the hul l i s not moving. Note that the Longitudinal Centre of Gravity or centre of the weight of the vessel must align with the LCB when the hull is in equilibrium.
Longitudinal Center of Buoyancy from Schneekluth and Bertram’s (1998) formula
(4. 14)
37
Chapter- 5. Optimization Technique
Optimization mig ht be defined as the s cience of de termining the be st s olutions to certain mathematically defined problems, w hich a re o ften m odels of physicals r eality (Saha, G . K., 2004). It involves the study of optimality criteria for problems, the determination of algorithmic methods of solution, the study of the structure of such methods, and computer experimentation with methods both under frail conditions and on real life problems. There is an extremely diverse range o f practical a pplications. The a pplicability of opt imization methods is widespread, reaching into almost e very a ctivity in w hich numerical inf ormation is processed (Science, Engineering, Mathematics, Economics, Optimization techniques, is used effectively, commerce, etc.), can greatly r educe the engineering de sign time a nd yield i mproved, e fficient, a nd economical design. Numerical opt imization techniques of fer a lo gical a pproach to design a utomation, and many algorithms h ave b een p roposed in recent years. Some of t hese techniques, such as linear, quadratic, dynamic, and geometric programming algorithms, have been developed to deal with specific classes of optimization problems. A more general category of algorithms referred to as nonlinear pr ogramming has e volved f or t he s olution of general op timization problems. A s i s frequently the case with nonlinear problems, there is no single method that is clearly better than others. Methods for n umerical opt imization are r eferred to col lectively as mathematical programming techniques.
5.1. Optimization Problem Formulation of an optimization problem involves taking statements, defining general goals and requirements of a given activity, and transcribing them into a series of well-defined mathematical statements. More precisely, the formulation of an optimization problem involves:
1. Choosing an objective function, and 2. Selecting one or more optimization variables, 3. Identifying a set of constraints.
The obj ective function a nd t he c onstraints m ust all be f unctions of on e or m ore opt imization variables. For a naval architect, to design a ship following operation has to be performed.
Objective Function: The s tated design objective is to minimize s hip resistance. Assuming the cost of s hip is proportional to the resistances, the objective function can be stated as follows:
Minimization of ship resistance, i.e. F(x) =
Constraints
All optimization variables are not independent. Since the length is related with displacement and shape of ship. Breadth is related with length and draught for stability. And power is related with displacement.
38
5.2. SQP Algorithm
Sequential Quadratic Programming (SQP) is the most successful method for solving nonlinearly constrained opt imization pr oblems. The S QP is a g eneral method f or solving nonlinear optimization problems w ith c onstraints. The m athematical formulation of the pr esent d esign oriented (SQP) program or algorithm, which finds an optimum shape of the ship with minimum resistance subject to geometric constraints can be expressed as Minimize f (x) (5.1) Subject to hi
g(x) = 0, i = 1……. N
i
Where x is a vector representation of design variables defining the hull parameter and hull form characteristics. The s hip wave m aking r esistance is us ed a s a n obj ective f unction f. The geometrical and geometrical design constraints about the hull surface are contained in both the equality (h
(x) ≠ 0, i = 1……. M
i) and inequality (gi
) constraints, N is the number of equality constraint and M is the number of inequality constraints respectively.
At first this design-constrained problem is converted to an unconstrained one associating penalty for any constraint violation. Thus the Equation (5.1) is transformed into the following function
(5.2) Where N TC is the total number of constraint, di is the penalty coefficients for cons traint i a nd Øi(x) is a penalty term related to the ith
constraint.
F is a nonlinear optimization problem since the objective function, the wave making resistance of ship and the constraints are implicit, non-linear functions of the design variable x. F is in many cases non -convex and ha s o ften m ultiple m inima. In fact, there i s no general reliable optimization method available to find a global minimum and no general agreement on t he best approach to solve non-linear multivariable constrained problems. A method that works well on one problem may perform very poorly on another problem of same kind. Given the penalty parameter r (r =1) and step length parameter ( = 0.5)
39
5.3. Steps in SQP algorithm Step l. Set an iteration counter k = 0.
Starting initial estimates x0, u0, v0 and a symmetric positive definite matrix H0
Step 2. Solve the problem
.
Minimize
Subject to
Solving Kuhn-Tucker conditions for the original problem using Newton’s method for solving nonlinear equations directly leads to above form in which matrix H represents the Hessian of the Lagrangian
Where u = ( T and v = ( T are the Lagrangian multipliers for equality and inequality constrains, respectively. The Lagrangian function is defined in terms of variables x, and Lagrangian multipliers (u, v), so a feature of the resulting methods is that a sequence of approximations x(k), u(k), and v(k)
Step 4. Update the penalty parameter r
to both the solution vector x and the vector of optimum Lagrange multipliers (u, v) is generated.
(i) Set
(ii) need to restart, go to step 1. Otherwise go to step 5.
Step 5. Compute the step length using approximation line search as follows:
(i) Compute
40
(ii) Set i = 0.
(iii)Set
(iv) Compute
(v) If then accept . Otherwise i = i+1 and go to step (ii)
Step 6: Set the new point as X(K+1) = X(K)
Step 7: Check for convergence. If
(a small number), then stop. Otherwise go to step 8.
+
Step 8: Update the Hk in such a way that H(k+1)
The Hessian matrix is updated by using the BFGS (Broyden, Fletcher, Goldfarb and Shanon) method as follows:
remains positive definite. Then set k =K+l and go to Step 2.
Where
The method of finding a form with lower resistance is described below. Optimization is carried out s o a s t o yield t he hull f orm w ith l ower resistance. T he obj ective f unction i s t he total resistance or residual resistance coefficient.
41
Figure 5.1: SQP Optimization Process.
Objective Function (Resistance
Minimization)
Design Constraints
Resistance Optimizer
Alternate Hull Parameters
Problem Solver
Optimized Ship Hull
42
Chapter- 6. Result & Discussion This research represents a study of the optimization of hull parameters and hull form parameters
with r espect t o s hip r esistance a t di fferent c onditions. F or t he c alculation of hul l pa rameters,
some empirical formulae are used for calculation of hull parameter and for the calculation of ship
resistance, statistical m ethods ar e us ed. Firstly, a ge neral hul l pa rameters are optimized with
respect to hull r esistance. After tha t, mathematical well know n Wigley hull pa rameters a re
optimized and finally Wigley hull shape and parameters are optimized.
6.1. Optimization of Hull Parameters: Ship hull are optimized with respect to minimum resistance calculating Holtrop, Hollenbach and
Oortmerssen m ethod considering hul l parameters and form pa rameters. Hull pa rameters were
changed w ithin s ome r anges, like a s le ngth is v arying within 70 to 80 meters, length-breadth
ratio is varying within 4.66 to 6.66, breadth-draught ratio is varying within 2.4 to 5.0 and speed
is va rying w ith 8.0 t o 12.0 knot s. Detailed of cons idering t hese limita tions a re de scribed in
section introduction.
In the optimization of ship hull parameters a typical ship hull is selected that hull parameters are
similar to a ship operating in inland waterways of Bangladesh. Detailed of this hull parameters
are ex plained i n T able 6.1. Variation of t hese hul l pa rameters a re de scribed i n T able 6.1 a nd
design constraints. Some of these hull parameters and displacement are set as design variables.
These variations of pa rameters ar e s elected from t he condi tion of inland water ways of
Bangladesh. C omparison of t hese di fferent opt imum hul ls a re pr esented i n T able 6.1. T he
convergence history of optimization process explained in Figure 6.2.
From Figure 6.1 and from Table 6.1, it is observed that the optimized hull by Holtrop method is
to have found higher displacement which is very near to upper limit of displacement constraints
where as the other two methods showed that the opt imized hul l t ends to be towards the lower
limit. In case of length parameter, Holtrop and Oortmerssen method showed higher length and
lower breadth- draught ratio. Hollenbach method showed few variations in length, length-breadth
ratio a nd br eadth- draught r atio and other p arameters. In case o f s peed parameter, t he hul l i s
optimized b y H oltrop method a t hi gher s peed w hich di ffers f rom others H ollenbach and
Oortmerssen methods, where they optimized at lower limit of speed constraint.
43
Figure 6.1: Hull parameter optimization process of different methods by resistance calculation.
Table 6.1: Table for hull parameter optimizations
Ship Parameter
Original Hull
Range of Parameters Optimized Hull Parameter Holtrop method
Hollenbach method
Van Oortmerssen
method Length (m) 80.0 70 < L <80 80.0 79.57 80.0
Length Breadth Ratio (L/B)
5.33 4.66 < L/B < 6.66 6.66
6.38
6.66
Breadth Draught Ratio (B/T)
3.75 2.4 < B/T <5.0 2.4 3.04 2.4
Speed (Knots) 10.0 8 < Speed < 12 8.873 8.0 8.0 Block Coefficient 0.783 0.828 0.862 0.863
Mid ship Coefficient
0.995 0.998
0.999
Prismatic Coefficient
0.787 0.830
0.863
Longitudinal Position of Center of Buoyancy (LCB
1.616
)
1.612 1.616
Displacement (m3 3759 )
0.93x < <1.06x (3500< <4000)
3500
6.2. Optimization of Wigley Hull Parameters Only: A mathematical Wigley hull is chosen for optimization. Resistance calculations are done using
relation of hull parameters. Resistances of two selected hulls are compared and the hull of lower
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30
Rto
tal /
Ort
otal
No. of Iteration
HOLTROP
HOLLENBACH
VAN-OORTMERSSEN
44
resistance is selected for comparison with the next selected hull resistance. In this way finally a
hull is selected, which has the lowest resistance within the described constraints.
Wigley hul l pa rameters ( Length, L/B r atio, B/T r atio) a re opt imized ba sed on resistance
minimization keeping the displacement variation within (1400<V<1500).
The mathematical Wigley hull is defined by following equation:
(6.6) Co-Ordinate system of Wigley Hull:
Figure 6.2: Coordinate system in Wigley hull.
45
TOP VIEW BODY PLAN
SIDE VIEW PERSPECTIVE VIEW
Figure-6.3: Different views of Wigley hull
46
6.2.1.1. Optimization of Wigley Hull parameters within displacement (1400 < < 1500) by Holtrop method.
Optimum hull parameters are found for each optimization at different speeds. From Table 6.2 it
is f ound t hat i n opt imization pr ocess a t di fferent s peed, l ength and l ength-breadth ratio a re
almost in ma ximum limit of c onstraint. Whereas, breadth-draught r atios a re ne ar to minimum
limit of constraints. In every case, displacement is found to be at the lower limit of displacement
constraint for optimization process.
Figure 6.4 s hows that, resistance reduction of the opt imization increase with speeds. Table 6.2
shows tha t, optimum hul l pa rameters a re a lmost s ame at all s peeds. Figure 6. 5 s hows t he
differences among optimum hulls at different speed by Holtrop method.
Table-6.2: Optimized Wigley Hull parameter at different speeds by Holtrop method.
Ship Parameter
Original Hull
Constraints Optimized Hull Parameter Holtrop method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 79.8 80.0 79.9 80.0 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 9.09
9.09 9.09
9.09 9.09
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.95 1.96 1.96 1.96 1.96
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1400 1400 1400 Initial Resistance
(KN) 10.426 at 8 10.169 13.673 19.875 26.132 38.059
14.173 at 9 20.816 at 10 27.606 at 11 40.393 at 12
Resistance Reduction (%)
2.52 3.65 4.73 5.64 6.13
47
Figure-6.4: Optimization of Wigley hull parameters for different speeds by Holtrop methods.
Figure-6.5: Views of parameters of optimized Wigley hulls at different speeds by Holtrop method.
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 5 10 15 20 25 30
OR
Tot
al /
Rto
tal
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
48
6.2.1.2. Optimization of Wigley Hull parameters within Specific range of displacement (1400 < < 1500) by Hollenbach method.
Optimum hull parameters are found for each optimization at different speeds. From Table 6.3 it
is f ound t hat i n opt imization pr ocess a t di fferent s peed, l ength a nd l ength-breadth ratio a re i n
highest limit of c onstraint. W hereas, br eadth-draught r atios ar e ne ar t o lowest limit of
constraints. In every case, displacement is found to be lower limit of displacement constraint for
optimization process.
Figure 6.6 shows that, resistance reduction of the opt imization increase with speeds. Table 6.3
shows tha t, optimum hu ll pa rameters a re same at al l s peeds. F igure 6. 7 shows t he di fferences
among optimum hulls at different speed by Hollenbach method.
Table-6.3: Optimized Wigley Hull parameter at different speeds by Hollenbach method.
Ship Parameter
Original Hull
Constraints Optimized Hull Parameter Hollenbach method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 80.0 80.0 80.0 80.0 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 10.0
10.0
10.0
10.0
10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.62 1.62 1.62 1.62 1.62
Displacement (m3 1419.4 )
(1400< <1500) 1400 1400 1400 1400 1400
Initial Resistance (KN)
0.078 at 8 0.077 0.142 0.237 0.366 0.539 0.145 at 9 0.241 at 10 0.373 at 11 0.548 at 12
Resistance Reduction (%)
1.28 1.65 1.65 1.66 1.64
49
Figure-6.6: Optimization of Wigley hull parameters for different speeds by Hollenbach methods.
Figure-6.7: Views of parameter optimized Wigley hulls at different speeds by Hollenbach method.
.
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
1.002
0 1 2 3 4
ORT
otal
/ R
Tota
l
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
50
6.2.1.3. Optimization of Wigley Hull parameters within Specific range of displacement (1400 < < 1500) by Oortmerssen method.
Optimum hull parameters are found for each optimization at different speeds. From Table 6.4 it
is f ound that in opt imization process le ngth a nd length-breadth r atio are i n upper limit of
constraint at different s peed. W hereas, br eadth-draught r atios a re ne ar t o lowest limit of
constraints. In every case, displacement is found to be lower limit of displacement constraint for
optimization process.
Figure 6.8 shows that, resistance reduction of the opt imization increase with speeds. Table 6.4
shows tha t, optimum hu ll pa rameters a re s ame at al l s peeds. F igure 6. 9 shows t he di fferences
among optimum hulls at different speed by Oortmerssen method.
Table-6.4: Optimized Wigley Hull parameter at different speeds for Oortmerssen method.
Ship Parameter Original Hull
Constraints Optimized Hull Parameter Oortmerssen method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 80.0 80.0 80.0 80.0 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 10.0
10.0
10.0
10.0
10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.62 1.62 1.62 1.62 1.62
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1400 1400 1400 Initial Resistance (KN) 0.213 at 8 0.206 0.393 1.486 7.227 26.647
0.405 at 9 1.516 at 10 7.335 at 11 27.021 at 12
Resistance Reduction (%)
3.28 2.96 1.97 1.49 1.40
51
Figure-6.8: Optimization of Wigley hull parameters for different speeds in Oortmerssen method.
Figure-6.9: Views of parameter optimized Wigley hulls at different speeds by Oortmerssen method.
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4
OR
Tot
al /
RT
otal
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
52
Figure-6.10: Comparison of reduction of resistance at different speeds for hull parameter optimization.
From Figure-6.10 it is found that the resistance reduction increases almost linearly with speeds in
Holtrop method. Hollenbach method shows a slow rise of resistance reduction and Oortmerssen
method shows a drop of resistance reduction with speeds.
0
1
2
3
4
5
6
7
7 8 9 10 11 12 13
Res
ista
nce
Red
uctio
n (%
)
Speed (Knots)
Holtrop
Hollenbach
Van-Oortmerssen
53
6.3. Optimization of Wigley Hull Shape: In t his pa rt a W igley h ull i s c hosen f or opt imization ba sed on r egression ba sed r esistance
calculation, where α, β represents water line shape factor and γ represents frame line shape
factor. Initially influence of the water line and frame line factors are described, then constraints
are set for these factors. Resistance calculations are as before given in section6.2.
The ma thematical formulation of the modified Wigley hull f orms including w aterline s hape
factor (α, β) and frame line shape factor (γ):
(6.7) The influence of waterline shape factor (α, β) and frame line shape factor (γ) on regression based resistance are described below.
6.3.1.1. Influence of water line shape factor α:
Body plan Top View
( ) ( )
( ) ( )
54
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Figure -6.11: Effect of waterline shape factor “α “in Wigley Hull equation.
55
From Figure-6.11, it is shown that, mid section area is less than stern and bow area. Negative
values of waterline shape factor “α “result in impractical ship.
6.3.1.2. Influence of water line shape factor β:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
56
( ) ( )
( ) ( )
Figure-6.12: Effect of waterline shape factor “β “in Wigley Hull equation.
From Figure-6.12, it is observed that, mid section area of ship is less than stern and bow area.
Negative value of waterline shape factor “β “also result in unrealistic ship.
57
6.3.1.3. Influence of frame line shape factor γ:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
58
( ) ( )
( ) ( )
Figure-6.13: Effect of frame line shape factor “γ “in Wigley Hull equation.
On the other hand, from Figure -6.13 it is clear that, mid ship area is larger than stern and bow
area. Moreover, negative value of waterline shape factor “γ “result in impractical ship.
From the above di scussions it is cl ear that va lue of α, β, γ must be l arger t han zero (i.e. non-
negative constraints).
Wigley hull shapes (α, β, γ) are optimized based on resistance minimization considering
displacement variation within (1400<V<1500).
59
6.3.2.1. Optimization of Wigley hull shape within specific range of displacement (1400< <1500) by Holtrop method.
Optimum hul l shapes are found for each opt imization a t di fferent speeds. From Table 6.5 it is
found t hat i n opt imization pr ocess a t di fferent speed, waterline shape factors (α, β) are in
minimum limit of constraints. Frame line shape factor (γ) is almost in lowest limit of t he
constraints. In every case, displacement is found same as original except at 8 knot.
Figure 6.14 shows that, resistance reduction of the optimization decrease with speeds. Table 6.5
shows t hat, opt imum hu ll shapes which are al most s ame at al l s peeds. Figure 6.15 s hows t he
differences among optimum hulls at different speed by Holtrop method.
Table-6.5: Optimized Hull shape at different speeds by Holtrop method.
Ship Parameter
Original Hull
Optimized Hull Parameter Holtrop method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33
Water Line (α) α ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Water Line (β) β ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Frame Line (γ) γ ≥ 0.0 0.178 0.0 0.0 0.0 0.0
Water Plane Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Block Coefficient 0.444 0.437 0.444 0.444 0.444 0.444 Mid ship
Coefficient 0.667 0.652 0.667 0.667 0.667 0.667
Prismatic Coefficient
0.665 0.670 0.665 0.665 0.665 0.665
Displacement (m3 1419.4 ) (1400< <1500) 1400 1419.4 1419.4 1419.4 1419.4 Initial Resistance
(KN) 10.426 at 8 10.392 14.173 20.816 27.606 40.393
14.173 at 9 20.816 at 10 27.606 at 11 40.393 at 12
Resistance Reduction (%)
0.32 0.0 0.0 0.0 0.0
60
Figure-6.14: Optimization of Wigley hull shape for different speeds by Holtrop method.
Figure-6.15: Views of shape optimized Wigley hulls at different speeds by Holtrop method.
.
.
0.9965
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
0 1 2 3 4 5
OR
Tot
al /
RT
otal
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
61
6.3.2.2. Optimization of Wigley hull shape within specific range of displacement (1400< <1500) by Hollenbach method.
Optimum hul l shapes are found for each opt imization a t di fferent speeds. From Table 6.6 it is
found that in optimization process at different speed, waterline shape factors (α, β) are in
minimum limit of constraints. Frame line shape factor (γ) is almost in lowest limit of the
constraints. In every case, displacement is found to be lower limit of displacement constraint for
optimization process.
Figure 6.16 shows that, resistance reduction of the optimization decrease with speeds. Table 6.6
shows t hat, opt imum hu ll s hapes w hich a re a lmost s ame a t a ll s peeds. Figure 6.17 shows t he
differences among optimum hulls at different speed by Hollenbach method.
Table-6.6: Optimized Hull shape at different speeds by Hollenbach method.
Ship Parameter
Original Hull
Constraints Optimized Hull Parameter Hollenbach method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33
Water Line (α) α ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Water Line (β) β ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Frame Line (γ) γ ≥ 0.0 0.178 0.178 0.178 0.178 0.178
Water Plane Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Block Coefficient 0.444 0.438 0.438 0.438 0.438 0.438 Mid ship
Coefficient 0.667 0.652 0.652 0.652 0.652 0.652
Prismatic Coefficient
0.665 0.671 0.671 0.671 0.671 0.671
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1400 1400 1400 Initial Resistance
(KN) 0.078 at 8 0.077 0.143 0.238 0.369 0.543
0.145 at 9 0.241 at 10 0.373 at 11 0.548 at 12
Resistance Reduction (%)
1.282 1.31 1.244 1.018 0.912
62
Figure-6.16: Optimization of Wigley hull shape for different speeds by Hollenbach method.
Figure-6.17: Views of shape optimized Wigley hulls at different speeds by Hollenbach method
.
.
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
1.002
0 20 40 60 80 100 120
OR
Tot
al /
RT
Ota
l
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
63
6.3.2.3. Optimization of Wigley hull shape within specific range of displacement (1400< <1500) in Oortmerssen method.
Optimum hul l shapes are found for each opt imization a t di fferent speeds. From Table 6.8 it is
found that in optimization process at different speed, waterline shape factors (α, β) are in
minimum limit of constraints. Frame line shape factor (γ) is also in lowest limit of the
constraints. In every case, displacement is found same as original.
Figure 6.18 shows that, resistance reduction of the optimization decrease with speeds. Table 6.8
shows t hat, opt imum hu ll s hapes w hich a re a lmost s ame a t a ll s peeds. Figure 6.19 shows t he
differences among optimum hulls at different speed by Hollenbach method.
Table-6.7: Optimized Hull shape at different speeds for Oortmeressen methods.
Ship Parameter Original Hull
Constraints Optimized Hull Parameter Oortmerssen method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33
Water Line (α) α ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Water Line (β) β ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Frame Line (γ) γ ≥ 0.0 0.0 0.0 0.0 0.0 0.0
Water Plane Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Block Coefficient 0.444 0.444 0.444 0.444 0.444 0.444 Mid ship
Coefficient 0.667 0.667 0.667 0.667 0.667 0.667
Prismatic Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Displacement (m3 1419.4 ) (1400< <1500) 1419.4 1419.4 1419.4 1419.4 1419.4 Initial Resistance
(KN) 0.213 at 8 0.213 0.405 1.516 7.335 27.021
0.405 at 9 1.516 at 10 7.335 at 11 27.021 at 12
Resistance Reduction (%)
0.0 0.0 0.0 0.0 0.0
64
Figure-6.18: Optimization of Wigley hull shape for different speeds by Oortmerssen method.
Figure-6.19: Views of shape optimized Wigley hulls at different speeds by Oortmerssen method
.
.
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2
OR
Tot
al /
RT
otal
No. of Iteration
8 Knots
9 Knots
10 knots
11 Knots
12 knots
65
Figure-6.20: Comparison of reduction of resistance at different speeds for hull shape optimization
From Figure-6.20 it is found that rate of resistance reduction decreases with speed in Hollenbach
method and only at 8 knots in Holtrop. Oortmerssen method shows no change in resistances with
speed.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
7 8 9 10 11 12 13
Resi
stan
ce R
educ
tion
(%)
Speed (Knots)
Holtrop
Hollenbach
Van-Oortmerssen
66
6.4. Optimization of Wigley Hull Parameter and Shape: In this pa rt a W igley hu ll is c hosen for opt imization of hul l pa rameters a nd s hapes based on
regression based resistance calculation, where α, β represents water line shape factor and γ
represents frame line shape factor. Resistance calculations are as before in section 6.2.
Wigley hull parameters (Length, L/B ratio, B/T ratio) and shapes (α, β, γ) are optimized based on
resistance minimization considering displacement variation within (1400<V<1500).
6.4.1.1. Optimization of Wigley hull parameters and shape within displacement (1400< <1500) by Holtrop method.
Optimum hull parameters are found for each optimization at different speeds. From Table 6.8 it
is f ound t hat i n opt imization pr ocess a t di fferent s peed, l ength and l ength-breadth ratio a re
almost in ma ximum limit of c onstraint. Whereas, breadth-draught r atios a re ne ar to minimum
limit of c onstraints. Shapes do not c hange in t he opt imization pr ocess. In every case,
displacement is found to be lower limit of displacement constraint for optimization process.
Table-6.8: Optimized Hull parameter and shape at different speeds by Holtrop method.
Ship Parameter
Original Hull
Constraints Optimized Hull Parameter Holtrop method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 79.88 80.0 79.98 80.0 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 9.091 9.091 9.091 9.091 9.091
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.955 1.963 1.962 1.963 1.963
Water Line (α) α ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Water Line (β) β ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Frame Line (γ) γ ≥ 0.0 0.0 0.0 0.0 0.0 0.0
Water Plane Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Block Coefficient 0.444 0.444 0.444 0.444 0.444 0.444 Mid ship
Coefficient 0.667 0.667 0.667 0.667 0.667 0.667
Prismatic Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1400 1400 1400 Initial Resistance
(KN) 10.426 at 8 10.169 13.673 19.875 26.130 37.536
14.173 at 9 20.816 at 10 27.606 at 11 40.393 at 12
Resistance Reduction (%)
2.52 3.65 4.73 5.646 7.61
67
Figure 6.21 shows that, resistance reduction of the optimization increase with speeds. Table 6.8
shows that, optimum hull parameters which are almost same at all speeds. Figure 6.22 shows the
differences among optimum hulls at different speed by Holtrop method.
Figure-6.21: Optimization of Wigley hull parameter and shape for different speeds by Holtrop method.
.
Figure-6.22: Views of parameter and shape optimized Wigley hulls at different speeds by Holtrop method
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 20 40 60 80
OrT
otal
/ R
Tot
al
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
68
6.4.1.2. Optimization of Wigley hull parameters and shape within displacement (1400< <1500) in Hollenbach method.
Optimum hull parameters are found for each optimization at different speeds. From Table 6.9 it
is f ound t hat i n opt imization pr ocess a t di fferent s peed, l ength and l ength-breadth ratio a re
almost in ma ximum limit of c onstraint. Whereas, breadth-draught r atios a re ne ar to minimum
limit of c onstraints. Shapes changes f rom V s hape t o U s hape with increase of s peeds in t he
optimization pr ocess. In e very case, di splacement i s f ound t o be lower l imit of di splacement
constraint for optimization process.
Figure 6.23 shows that, resistance reduction of the optimization increase with speeds. Table 6.9
shows that, optimum hull parameters which are almost same at all speeds. Figure 6.24 shows the
differences among optimum hulls at different speed by Hollenbach method.
Table-6.9: Optimized Hull parameter and shape at different speeds by Hollenbach method.
Ship Parameter Original Hull
Constraints Optimized Hull Parameter Hollenbach method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 80.0 80.0 80.0 79.62 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 10.0 9.99 10.0 9.99 10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.625 1.708 1.671 2.765 2.081
Water Line (α) α ≥ 0.0 0.013 0.229 0.132 0.671 1.197 Water Line (β) β ≥ 0.0 0.005 0.096 0.054 0.128 1.219 Frame Line (γ) γ ≥ 0.0 0.018 0.007 0.007 0.035 0.729
Water Plane Coefficient
0.665 0.667 0.700 0.685 0.760 0.890
Block Coefficient 0.444 0.444 0.467 0.457 0.506 0.569 Mid ship
Coefficient 0.667 0.665 0.666 0.666 0.664 0.606
Prismatic Coefficient
0.665 0.668 0.700 0.685 0.762 0.939
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1400 1400 1400 Initial Resistance
(KN) 0.078 at 8 0.076 0.140 0.234 0.342 0.461
0.145 at 9 0.241 at 10 0.373 at 11 0.548 at 12
Resistance Reduction (%)
1.666 3.379 2.904 9.061 18.87
69
Figure-6.23 Optimization of Wigley hull parameter and shape for different speeds by Hollenbach method.
Figure-6.24: Views of parameter and shape optimized Wigley hulls at different speeds by Hollenbach method
.
0.8
0.85
0.9
0.95
1
1.05
0 20 40 60 80 100
OR
Tot
al /
RT
otal
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
70
6.4.1.3. Optimization of Wigley hull parameters and shape within displacement (1400< <1500) by Oortmerssen method.
Optimum hul l parameters a re f ound f or e ach s peeds. F rom T able 6. 10 it is f ound t hat i n
optimization process at different speed, length and length-breadth ratio are in maximum limit of
constraint. Whereas, breadth-draught ratios are near to minimum limit of constraints. Shapes do
not change in the optimization process. In every case, displacement is found to be at lower limit
of displacement constraint for optimization process.
Figure 6.25 shows that, the resistance reduction in the optimization increases with increases in
speeds. Table 6.10 shows that, opt imum hul l parameters are almost same at al l speeds. Figure
6.26 shows that the differences among optimum hulls at different speed by Oortmerssen method
are negligible.
Table-6.10: Optimized Hull parameter and shape at different speeds by Oortmeressen method.
Ship Parameter Original Hull
Constraints Optimized Hull Parameter Oortmerssen method
Speed (Knots) 8.0 9.0 10.0 11.0 12.0 Length (m) 80.0 70 < L <80 80.0 80.0 80.0 80.0 80.0
Length Breadth Ratio (L/B)
5.33 7.0 < L/B < 10.0 10.0 10.0 10.0 10.0 10.0
Breadth Draught Ratio (B/T)
3.75 1.6 < B/T <3.33 1.622 1.622 1.622 1.622 1.622
Water Line (α) α ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Water Line (β) β ≥ 0.0 0.0 0.0 0.0 0.0 0.0 Frame Line (γ) γ ≥ 0.0 0.0 0.0 0.0 0.0 0.0
Water Plane Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Block Coefficient 0.444 0.444 0.444 0.444 0.444 0.444 Mid ship
Coefficient 0.667 0.667 0.667 0.667 0.667 0.667
Prismatic Coefficient
0.665 0.665 0.665 0.665 0.665 0.665
Displacement (m3 1419.4 ) (1400< <1500) 1400 1400 1419.4 1419.4 1419.4 Initial Resistance
(KN) 0.213 at 8 0.206 0.393 1.486 7.226 26.647
0.405 at 9 1.516 at 10 7.335 at 11 27.021 at 12
Resistance Reduction (%)
3.28 2.96 1.97 1.499 1.40
71
Figure-6.25: Optimization of Wigley hull parameter and shape for different speeds by Oortmerssen method.
Figure-6.26: Views of parameter and shape optimized Wigley hulls at different speeds by Oortmerssen method
.
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 5 10 15 20 25 30
OR
Tot
al /
RT
otal
No. of Iteration
8 Knots
9 Knots
10 Knots
11 Knots
12 Knots
72
Figure-6.27: Comparison of reduction of resistance at different speeds for hull parameter and
shape optimization
From Figure-6.27 i t i s found that r esistance reduction i s i ncreased with speeds i n Holtrop and
Hollenbach m ethod. Whereas, Oortmerssen m ethod s hows fall of resistance reduction w ith
speeds.
0
2
4
6
8
10
12
14
16
18
20
7 8 9 10 11 12 13
Res
ista
nce
Red
uctio
n (%
)
Speed (Knots)
Holtrop
Hollenbach
Van-Oortmerssen
73
Chapter- 7. SWOT (Strength Weakness Op portunity Threa t) analysis of t he optimization process:
SWOT analysis to evaluate t he strengths, weaknesses/limitations, opportunities, a nd threats involved i n this r esearch. It i nvolves s pecifying t he obj ective of t he research work and identifying t he i nternal and external f actors t hat ar e f avorable and unfavorable to achieve t hat objective.
The objective should be done after the SWOT analysis has been performed. This would a llow achievable goals or objectives to be set for the organization.
• Strengths: characteristics of the research work that gives an advantage over others • Weaknesses (or Limitations): are characteristics that place the team at a
disadvantage relative to others • Opportunities: external chances to improve performance (e.g. make greater
profits) in the environment • Threats: external elements in the environment that could cause trouble for the
business or project
Table-7.1: SWOT Analysis of this research work.
Internal Origin of the Process
Strength Opportunities
Hel
pful
• This procedure gives a quick calculation. • Different types of hull could be
optimized through this process. • Different methods could be verified with
this process. • This research may be used in initial
design stage
• For quick calculation any designer can take decision easily.
• Different types of can be justified through the optimization procedure.
External Origin of the Process
Weakness Threats
Har
mfu
l • Selection of e mpirical formula f or the calculation of hull f orm a nd pa rameter are not always exact.
• Only one obj ective f unction ( resistance) is used in this method.
• Justification of hull parameters with real values.
74
Chapter-8. Conclusion and future work: An i ntegrated m ethodology f or t he ba sic pr eliminary s hip hul l pa rameter e valuation a nd optimization of t hese pa rameters ha s be en pr esented. T he m ain di fficulty of t he num erical optimization lies in formulating the objective function, design variables and all the constraints. The opt imization pr oblem ha s be en c arefully f ormulated t o g ive a s table i nspection of e very approach. T he constraints a re b ased on t he d esign p arameter requirements. T he obj ective function is normalized with respect to its ini tial value. For the opt imization process, empirical formulae for the calculation of design parameter were used. Stability criteria’s did not include in the opt imization pr ocess. For m ore accurate o r de tailed optimization, require a m ore s eparate work. T he m ethodology m ay be us ed i n t he pr eliminary de sign s tages f or s electing hul l parameter of inland vessel. Finally this research conclude with these
Combination of optimized hull pa rameters (L, L/B andB/T) with s peed s hows l ower resistance with original values.
Holtrop method is more suitable than other methods such as Hollenbach and Oortmerssen method. Because c alculation b y H oltrop m ethod us ed m ore hul l pa rameters a nd f orm parameters than others.
This m ethodology m ay be us ed i n t he pr eliminary d esign s tages f or s electing hul l parameters of inland vessels.
Following works are commented as future works:
Optimization based on total resistance, ship stability and building cost.
Optimization imposing more than one objective functions.
Comparison of thi s opt imization me thod with o thers optimization t echniques (genetic algorithm, simulated annealing method etc.).
75
References: ASNOP (1991) Research Group: Application Systems for Non Linear Optimization Problems,
Nippon Kogyo Shimbun (In Japanese).
Bertran, V. (2000) Practical Ship Hydrodynamics, pp. 65-66.
Bhatti, M. Asghar, (2000)Practical optimization methods: with Mathematical applications, Dover
publications, New York.
Carlton, J. S. (1994) Marine propeller and propulsion, Cahpter-12, pp.-285.
Edward, V. (1988) Principles of Naval Architecture (2nd
Gammon, M A . (2004) Ship Hull F orm Optimization by E volutionary Algorithm, Yildiz
Technical University, Istanbul.
Revision), Vol. II, Resistance,
Propulsion and Vibration.
Harold, E. (1957) Hydrodynamic in ship design, Vol. I and II.
Harvald, S. A. (1983) Resistance and propulsion of ships, Chapter-xii, pp. 353.
Harries, S. (1998)Parametric D esign and Hydrodynamic O ptimization of S hip Hull F orms,
Dissertation, TechnischeUniversität Berlin; Mensch &BuchVerlag.
Hino, T. (1996) Fluid Dynamic Shape Optimization using Sensitivity Analysis of Navier Stokes
Solutions, Journal of Kansai Society of Naval Architects, Japan.
Hino, T ., K odama, Y . and H irata, N . ( 1998) H ydrodynamic s hape opt imization of s hip hul ls
forms using CFD, Proceedings of the 3 rd
Hollenbach K.U, (1998) Estimating resistance and propulsion for s ingle screw and twin screw
ships, Ship technology research.
Osaka Colloquium on A dvanced CFD Application to
ship Flow and Hull Form Design, Japan, pp. 533-541.
Holtrop, J and Mennen, G.G.J (1984)A statistical re-analysis of resistance and propulsion data
International Shipbuilding Progress.
Holtrop, J a nd M ennen, G .G.J (July, 1982 )An a pproximate pow er pr ediction m ethod.
International Shipbuilding Progress, Vol. 29.
76
Holtrop, J a nd M ennen, G .G.J.(October,1978), A s tatistical pow er pr ediction method.
International Shipbuilding Progress, Vol. 25.
Kelvin, L. (1887) Long Ship Waves in Shallow Water Bodies, pp. 197.
Molland A. F., Wellicome J. F. and Couser P. R. (1994) Resistance experiments on a systematic
series of H igh speed displacement C atamaran forms: V ariation of Length- Displacement r atio
and Breadth- Draught ratio.’ Ship Science Report 71, March.
Oortmerssen, G. va n, (1971)A pow er pr ediction m ethod a nd its a pplications to small s hips,
International Shipbuilding Progress, Vol. 19.
Oortmerssen, G. van, (1971) A power prediction method for Motor Boats, 3rd
Oosterveld, M.W.C. and Oossanen, P. Van, (July, 1975) Further computer analyzed data of the
Wageningen B-screw series, International Shipbuilding Progress.
Symposium Yacht
Architecture, The Netherlands, also NSMB publication 429.
Peri, D ., R ossetti, M . a nd C ampana, E .F. (2001) D esign opt imization of s hip hul ls V ia C FD
technologies, Journal of ship research, vol. 45, No. 2, pp. 140-149.
Roy, J., Gee, N.,(2001) The Effects of Length on the Powering of Large Slender Hull Forms.
Proceedings 15th ITTC (1978) The Hague.
Reynolds O. (1883)An experimental investigation of the circumstances which determine whether
the motion of water in parallel channels shall be direct or sinuous and of the law of resistance in
parallel channels. Philos. Trans. R. Soc. 174:935–82
Robert L. Daily,(December 16, 2005) Thesis Abstract Optimization of Hull Shapes For Water-
Skiing and Wakeboarding, Auburn, Alabama.
Robert, W., John, D. a nd Ryan, B.(2004) Ship de sign us ing h euristic optimization m ethods.
Massachusetts Institute of Technology, USA.
Roseman, D. P., Gertler, M., and Kohl, R. E., (1974) Characteristics of Bulk Products Carriers
for Restricted-Draft Service, Transactions SNAME, Vol. 82.
Saha, G . K .,(2004) Numerical O ptimization of S hip Hull F orms f rom V iew P oint of Wave
Making Resistance Based on Panel Method, Yokohama National University, Japan.
77
Schneekluth, H . a nd Bertram, V . (1998) Developments i n t he D esign f or E fficiency and
Economy, Second Edition, Butterworth-Heinemann, Oxford, UK.
Skalna, I. a nd P ownuk, A , ( 2008) On us ing global opt imization m ethod f or a pproximating
interval hul l solution of pa rametric line ar s ystems, Reliable E ngineering C omputing ( REC),
USA.
Tahara, Y. and Himeno, Y. (1998) An Application of Computational Fluid Dynamics to ship hull
optimization problem,Proceedings of the 3rd
Watson, D .G.M., and Gilfillan, A .W., (1977)Some Ship Design Methods, T ransactions R INA,
Vol.119.
Osaka Colloquium on Advanced CFD Application
to ship Flow and Hull Form Design, Japan, pp. 515-531.
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