LOW WAKE WASH USING DIFFERENT HULL SHAPES

ACADEMY OF MARITIME EDUCATION AND TRAINING
To Study the effect of Resistance & Wake distribution in Catamaran made from a Monohull {NPL}
A PROJECT REPORT
On
“To Study the effect of Resistance & Wake distribution in Catamaran made from a
Monohull {NPL}”
Submitted in partial fulfillment of the requirement for the award of degree
Of
Bachelors of Engineering in Naval Architecture
By
Jeet Banerjee
Under the guidance of
Asst. Prof. Himanshu Uppal
NAVAL ARCHITECTURE AND OFFSHORE ENGINEERING
CHENNAI CAMPUS

CERTIFICATE
This is to certify that the project entitled “To Study the effect of Resistance & Wake
distribution in Catamaran made from a Monohull {NPL}" submitted by JEET BANERJEE
to the Dept. of Naval Architecture & Offshore Engineering, AMET University, Chennai is a
bonafide record of work carried out by him under my supervision.
Signature Signature
Mr. Prem Anand Mr. Himanshu Uppal
(Asst. Professor) (Asst. Professor)
Department of Naval Architecture Department of Naval Architecture
& Offshore Engineering & Offshore Engineering

SHIP DESIGN PROJECT
To Study the effect of Resistance & Wake distribution in Catamaran made from a
Monohull {NPL}

PREFACE
Practical knowledge means the visualization of the knowledge, which we read in our books. For
this, we perform experiments and get observations. Practical knowledge is very important in
every field. One must be familiar with the problems related to that field so that he may solve
them and become a successful person.
After achieving the proper goal in life, an engineer has to enter in professional life. According to
this life, he has to serve an industry, may be public or private sector or self-own. For the efficient
work in the field, he must be well aware of the practical knowledge as well as theoretical
knowledge.
To be a good engineer, one must be aware of the industrial environment and must know about
management, working in the industry, labor problems and many, so he can tackle them
successfully.

ACKNOWLEDGEMENT
This project was a part of the curriculum of our 6th semester of B.E (NA&OE). Doing this
project over the past 5 months has been absolutely enriching experience not to mention the vast
amount of knowledge I gathered via experiencing some of the real time difficulties in the field of
Naval Architecture.
I would thank my project guide Asst. Prof. Himanshu Uppal for his constant guidance and
overwhelming support throughout my project.
I also wish to express thanks to our seniors and the staff of AMET for their help during the
project.
.
AMET-Chennai Jeet Banerjee
(ANA15026)

TABLE OF CONTENTS
S.NO TOPIC
PG-
NO
1 INTRODUCTION 6
2 LITERATURE SURVEY 9
3 OBJECTIVES 12
4 MAIN DIMENSIONS OF BASIS SHIP 13
5 LINES PLAN- GENERAL OVERVIEW 15
6 OFFSET TABLE 18
7 MAXSURF MODELER FOR MONOHULL 20
8 MAXSURF RESISTANCE CALCULATION FOR MONOHULL 24
9 MODEL MAKING- RHINOCEROS 27
10 MAIN DIMENSIONS OF CATAMARANS 31
11 LINES PLAN OF CATAMARANS 33
12 CFD ANALYSIS { WAVE PROFILE GENERATION} 35
13 RESISTANCE COMPARISON FOR FSI & FSO (BY CFD & MAXSURF) 49
14 CONCLUSION 51
15 REFERENCES 52

INTRODUCTION
WAKE
In fluid dynamics, a wake may either be:
 The region of recirculating fluid immediately behind a moving or stationary blunt
body, caused by viscosity , which may be accompanied by flow separation and
turbulence.
 The wave pattern on the water surface downstream of an object in a flow, or
produced by a moving object (e.g. a ship), caused by pressure differences of the
fluids above and below the free surface and gravity (or surface tension), or both.
Wake effects caused by viscosity: The wake is the region of disturbed flow
(often turbulent) downstream of a solid body moving through a fluid, caused by the flow
of the fluid around the body. For a blunt body in subsonic external flow, for example
the Apollo or Orion capsules during descent and landing, the wake is massively separated
and behind the body is a reverse flow region where the flow is moving toward the
body. This phenomenon is often observed in wind tunnel testing of aircraft, and is
especially important when parachute systems are involved, because unless the parachute
lines extend the canopy beyond the reverse flow region, the chute can fail to inflate and thus
collapse. Parachutes deployed into wakes suffer dynamic pressure deficits which reduce

their expected drag forces. High-fidelity computational fluid dynamics simulations are
often undertaken to model wake flows, although such modelling has uncertainties
associated with turbulence modelling (for example RANS versus LES implementations), in
addition to unsteady flow effects. Example applications include rocket stage separation and
aircraft store separation.
Kelvin wake pattern : Waterfowl and boats moving across the surface of water produce a
wake pattern, first explained mathematically by Lord Kelvin and known today as the
Kelvin wake pattern.
This pattern consists of two wake lines that form the arms of a chevron, V, with the
source of the wake at the vertex of the V. For sufficiently slow motion, each wake line
is offset from the path of the wake source by around arcsin(1/3) = 19.47° and is made up
of feathery wavelets angled at roughly 53° to the path.
. This pattern is independent of the speed and size of the wake source over a significant
range of values.
However, the pattern changes at high speeds (only), viz., above a hull Froude number of
approximately 0.5. Then, as the source's speed increases, the transverse waves diminish
and the points of maximum amplitude on the wavelets form a second V within the wake
pattern, which grows narrower with the increased speed of the source.
The angles in this pattern are not intrinsic properties of merely water: Any isentropic
and incompressible liquid with low viscosity will exhibit the same phenomenon.
Furthermore, this phenomenon has nothing to do with turbulence. Everything discussed
here is based on the linear theory of an ideal fluid, cf. Airy wave theory.

Parts of the pattern may be obscured by the effects of propeller wash, and tail eddies
behind the boat's stern, and by the boat being a large object and not a point source. The
water need not be stationary, but may be moving as in a large river, and the important
consideration then is the velocity of the water relative to a boat or other object causing
a wake.
No wake zones " may prohibit wakes in marinas, near moorings and within some distance
of shore in order to facilitate recreation by other boats and reduce the damage wakes
cause. Powered narrow boats on British canals are not permitted to create a breaking
wash (a wake large enough to create a breaking wave) along the banks, as this erodes them.
This rule normally restricts these vessels to 4 statute miles per hour or less.

LITERATURE SURVEY
The Port of London Authority is the navigational authority for the tidal river Thames,
from the outer limit inland to Teddington, which lies upstream of this capital. Throughout
the stretch of water as defined by the (MSA’s) & (MCA’s) many regulations and tidal
river conditions vary considerably. Despite mariners qualitative approach there were
certain hull-forms which showed or resulted in substantial wave wake- up to 1.2m high,
measured between trough & crest. This is certainly enough to cause distress to rowers &
small boat operators. It was decided, therefore, to commission scientific research into the
effect of shallow water upon the wash of a variety of typical hull forms. The theoretical studies
and practical trials were commissioned by the PLA to optimise the design for a
replacement class of patrol launch, where the operational environment has constraints
(depth and width of the river; type and inclination of riverbanks, etc.) that affect the wave
wake developed by the craft and its impact upon that environment.
It was intended that the research and trials should follow a phased programme, seeking
consistency of the theory and results, throughout:
• Computational modelling, using existing theoretical models and specialist understanding;
• Practical tank tests of suitably scaled physical models; and
• Near full-scale trials, using available prototype vessels of each hull form, in the real
river environment, measuring wash height with a Wavetector buoy.

WAVE WASH: When a ship travels through the water, it creates divergent waves and
transverse waves. Wave wash refers to the wash caused by ship generated waves on shore and
disturbance created by ship generated waves. It is a hydrodynamic tool which explains wave
impacts on shore. Many researchers have identified it as a potential reason of shore erosion. The
wave impacts created by marine vessel in inland waterways and coastal areas are known as wave
wash. In some papers, it was termed as wake wash too. However, some authors have considered
it as ship generated wave itself. Ship-generated waves or boat wash or wave wash can have
significant impacts on natural and artificial features and structures. Wave formation in
waterways occurs due to wind wave and ship generated wave. Wave wash is of significant
importance at many locations like rivers, lakes, canal, coastal waters where ship generated wave
heights are greater than wind generated wave heights. That is why wave wash is mainly of
concern of safety in coastal waters as normal wind wave conditions are moderate to severe there.
At sheltered locations such as small lakes, rivers and channels ship generated waves become
dominant mode of wave generation. Murphy et al. Found characteristics of these waves to be
similar as wind generated waves once they move away from the vessel. Thus, ship generated
wave can have negative effects. These are shore erosion, damage shoreline structures when ship
or boat passes close to the shore banks, damaging moored vessels or other marine structures,
threatening people travelling in small vessels near shores or people living nearby shores,
negative impacts on flora and fauna and so on. This paper describes that wave wash is an
important factor to impose ship speed restriction for any shallow and narrow waterway.
This paper investigates the relationship of wave wash with different wave and waterway
parameters in a shallow waterway named Buriganga River on the basis of data collected,
empirical formulae collected from previous literatures, site investigation and CFD
simulation which has been given later. Finally, a model has been proposed to determine
maximum permissible ship speed in a waterway.
WAVE PATTERN : Though the wave pattern generated by a vessel is largely
independent of vessel form, it is greatly affected by water depth and vessel speed. Vessel wave
wake is dependent on vessel speed and water depth. The defining parameter is depth Froude
number, F, a non-dimensional relationship between vessel speed and water depth, which is
defined by Fh = V √ gL When the water depth is less than about one-quarter the vessel’s

waterline length, then Depth Froude number has its greatest effect. And Fh has moderate
influence at depths up to one-half the waterline length. Again, it has little influence at depths
greater than the waterline length. The water depth limits the speed at which a wave can travel
in shallow water, such that the maximum speed will be reached when the depth Froude number
equals the value of unity. From this point of view there are four categories- Sub-Critical (Fh <
0.75), Trans-Critical (0.75 < Fh < 1.0), Critical (Fh = 1.0) and Super-Critical (Fh > 1.0).The
position of the trans-critical range can vary according to vessel and waterway. Sub-Critical (Fh <
0.75): Short-crested divergent waves and transverse waves are seen. This is well-known as
Kelvin wave pattern. Trans-Critical (0.75 < Fh < 1.0): Divergent wave angle increases with Fh.
Period of leading waves also increases. Waves tend to flow approximately at right angle with
sailing line.
WAVE WASH CRITERION: Wave Wash Criterion Time period, . Where, V is ship speed in
knots. It was proposed by Kirkegaard et al. (1998).He developed a wake wash criterion
formula for a channel in Denmark having depth of 3 m. where, Hh is the maximum wave
height of the long-periodic waves. Hh ≤ 0.5 0.45 this is known as Wave Wash Criteria.
SIMULATION : CFD Simulation is the fourth step of the model. The CFD result showed that
wave patterns created by this vessel are in consistent with Kelvin’s wave theory. It also shows,
with the increases in vessel speed (when, Fh < 1) the divergent wave angle increases too. Wave
heights have been found from the elevations and coordinates of free surface and wave contours
of the CFD results. Maximum wave heights from CFD results are in close harmony with wave
heights calculated by Blaauw’s method at 1m distance away from ship’s side.

OBJECTIVES
• To design an npl hull as a reference or basis hull for the study.
• To cut it into two parts and create a catamaran with FSI & FSO.
• To compare the resistances for monohull, catamaran at different (S/L) ratios.
• To create wave profiles for different (S/L) ratios. ( By CFD Analysis).

MAIN DIMENSIONS OF BASIS SHIP {NPL}

LBP (m) 40
BREADTH (m) 6.66
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.397

LINES PLAN {General Overview}

BODY PLAN
Look at the body plan. The cross sections are laid out on a grid. On the right side we have the
cross sections from the forward part of the hull back to the midsection. On the left side we have
the cross sections in the aft part of the hull going forward to the midsection. Now, note the
horizontal lines in the grid. The bottom line is the base line. You will see the base line drawn on
the sheer profile. This is the line from which all vertical measurements are taken. Above that you
will see other evenly spaced horizontal lines. These are the waterlines we saw as straight lines in
the sheer profile and as curved lines in the half breadth. There are also the vertical lines to be
noted. The one in the middle is the centre line we saw in the half breadth, from which all
horizontal measurements are taken. Out from the centre line, we see evenly spaced vertical lines.
These are the buttock lines we saw as curved lines in the sheer profile and straight lines in the
half breadth. You will also see curved lines running along the cross sections giving you the line
of the deck and the line of the railing.
HALF BREADTH PLAN
Look at the half breadth. You will see a centre line, from which all horizontal measurements are
taken. Out from the centre line you will see a series of curved lines. These are those same
waterlines we saw in the sheer profile, they are just seen from the bottom up rather than from the
side. In the half breadth, you will also see some straight lines that are placed out from the centre
line at even spacing. These are those same buttock lines we saw as curved lines in the sheer
profile. Again, we are seeing them from a different aspect. Also, in the half breadth, the line of
the deck and the line of the railing will show up as curved lines, almost like waterlines. These are
important for developing the cross section shapes in the upper part of the hull.

PROFILE PLAN
Look at the sheer profile. This side view gives you the general outline of the hull, but there are
also some other important architectural lines to address. There are the waterlines (not to be
confused with the hull's load waterline) that run along the hull horizontally. These are sometimes
referred to as level lines or, in the case of a solid hull model, lift lines. Then there are some
curved lines that run along the length of the hull called buttock lines. The key to a drawing like
this is that these lines appear in each of the three drawings, they just look different because of the
different aspect of each drawing.

OFFSET TABLE

Maxsurf Modeler {For Monohull}

 Firstly markers are selected on Maxsurf for creating curves.
 After that curves are formed.
 After formation of the curves, skin surfaces are done by taking 3(linear); and
after doing that all the surfaces are joined accordingly.

 The views accordingly will be showcased like this :
 Correction of Frame Of Reference according to vessel’s draft must be done once
the surfacing is fully complete and proper joining is done.

 Once reference frame is set, checking of sectional area curve should be done since
if the curve does not follow a proper slope then there might be some mistakes in
the designing.
 After proper checking of the sectional area curve, Hydrostatics should be checked
whether it is matching the particular model’s block co-efficient or not.
 {For my vessel block co-efficient as mentioned earlier is 0.397, which is
exactly matching the modeler’s hydrostatic value}.

Maxsurf Resistance Calculation {For Monohull}

 Firstly we have to open the respective design that we are going to analyze on
Maxsurf Resistance Modeler.
 Then select the methods accordingly for which the analysis should be done for the
respective model.

 Before starting the analysis, we have to specify the vessel’s service
speed, for my basis ship it is 4kn.
 After setting up the speed, we can run the analysis; once analysis is
done we have to check the graphs for the respective methods.
 After analyzing the graphs, now it is time for the values; If not by graphs we can
identify the suitable method for our vessel with the calculated data’s from the
software.

MODEL MAKING- {RHINOCEROS}

 Rhinoceros (Typically abbreviated Rhino or Rhino3D) is a commercial 3D computer
graphics and computer-aided design (CAD) application software developed by Robert
McNeil & Associates, an American, privately-held, employee-owned
company founded in 1980. Rhinoceros geometry is based on
the NURBS mathematical model, which focuses on producing mathematically precise
representation of curves and freeform surfaces in computer graphics (as opposed
to polygon mesh-based applications).
MODEL CREATION
 Firstly the basis model for the study is imported from Maxsurf to Rhino.
 Then the model is separated from mid section at a distance of 4m.
 Then accordingly model for 4m FSI is made by putting planes on both sides of the
surfaces, after that surfaces are joined/merged and imported back to Maxsurf.

 Similarly we will find out for 8m FSI & 6m FSI.
6m
8m
 Now for FSO or flat side outward the demihull orientation is changed.

 For 4m FSO the model looks like this:
 Similarly for 8m FSO & 6m FSO models are made.
 6m
8m
 {After creating model in Rhinoceros all are exported back to Maxsurf
modeller for Resistance Calculation}.

MAIN DIMENSIONS OF CATAMARAN
{MODELS}

1) For Flat Side Inward at S/L = 0.10
LBP (m) 40.748
BREADTH (m) 10.68
DEPTH (m) 5
DRAFT (m) 2.224
DISPLACEMENT (tonnes) 577.9
Cb 0.337
2) For Flat Side Outward at S/L = 0.10
LBP (m) 40.748
BREADTH (m) 10.68
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.394
LBP (m) 40.748
BREADTH (m) 12.66
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.30

LBP (m) 40.748
BREADTH (m) 12.66
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.332
LBP (m) 40.748
BREADTH (m) 14.66
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.287
LBP (m) 40.748
BREADTH (m) 14.66
DEPTH (m) 5
DRAFT (m) 2.224
Cb 0.255

LINES PLAN {MONOHULL &
CATAMARAN}

CFD ANALYSIS {for catamaran}

GENERAL OVERVIEW
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical
analysis and data structures to solve and analyze problems that involve fluid flows. Computers
are used to perform the calculations required to simulate the interaction of liquids and gases with
surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can
be achieved. Ongoing research yields software that improves the accuracy and speed of complex
simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such
software is performed using a wind tunnel with the final validation coming in full-scale testing,
e.g. flight tests.
 During preprocessing
 The geometry and physical bounds of the problem can be defined using computer aided
design (CAD). From there, data can be suitably processed (cleaned-up) and the fluid
volume (or fluid domain) is extracted.
 The volume occupied by the fluid is divided into discrete cells (the mesh). The mesh
may be uniform or non-uniform, structured or unstructured, consisting of a combination
of hexahedral, tetrahedral, prismatic, pyramidal or polyhedral elements.
 The physical modeling is defined – for example, the equations of fluid motion
+ enthalpy + radiation + species conservation
 Boundary conditions are defined. This involves specifying the fluid behaviour and
properties at all bounding surfaces of the fluid domain. For transient problems, the initial
conditions are also defined.
 The simulation is started and the equations are solved iteratively as a steady-state or
transient.
 Finally a postprocessor is used for the analysis and visualization of the resulting solution.

METHODS
Discretization methods
Further information: Discretization of Navier–Stokes equations
The stability of the selected discretisation is generally established numerically rather than
analytically as with simple linear problems. Special care must also be taken to ensure that the
discretisation handles discontinuous solutions gracefully. The Euler equations and Navier–Stokes
equations both admit shocks, and contact surfaces.
Some of the discretisation methods being used are:
Finite volume method
Main article: Finite volume method
The finite volume method (FVM) is a common approach used in CFD codes, as it has an
advantage in memory usage and solution speed, especially for large problems, high Reynolds
number turbulent flows, and source term dominated flows (like combustion).[40]
In the finite volume method, the governing partial differential equations (typically the Navier-
Stokes equations, the mass and energy conservation equations, and the turbulence equations) are
recast in a conservative form, and then solved over discrete control volumes.
This discretisation guarantees the conservation of fluxes through a particular control volume.
The finite volume equation yields governing equations in the form,

Finite element method
Main article: Finite element method
The finite element method (FEM) is used in structural analysis of solids, but is also
applicable to fluids. However, the FEM formulation requires special care to ensure a
conservative solution. The FEM formulation has been adapted for use with fluid dynamics
governing equations. Although FEM must be carefully formulated to be conservative, it is
much more stable than the finite volume approach. However, FEM can require more
memory and has slower solution times than the FVM.
Finite difference method
Main article: Finite difference method
The finite difference method (FDM) has historical importance and is simple to program.
It is currently only used in few specialized codes, which handle complex geometry with
high accuracy and efficiency by using embedded boundaries or overlapping grids (with
the solution interpolated across each grid).
Spectral element method
Main article: Spectral element method
Spectral element method is a finite element type method. It requires the
mathematical problem (the partial differential equation) to be cast in a weak
formulation. This is typically done by multiplying the differential equation by an
arbitrary test function and integrating over the whole domain. Purely mathematically,
the test functions are completely arbitrary - they belong to an infinite-dimensional
function space. Clearly an infinite-dimensional function space cannot be represented
on a discrete spectral element mesh; this is where the spectral element discretisation

begins. The most crucial thing is the choice of interpolating and testing functions. In
a standard, low order FEM in 2D, for quadrilateral elements the most typical choice
is the bilinear test or interpolating function of the form . In a spectral element
method however, the interpolating and test functions are chosen to be polynomials of
a very high order (typically e.g. of the 10th order in CFD applications). This
guarantees the rapid convergence of the method. Furthermore, very efficient
integration procedures must be used, since the number of integrations to be
performed in a numerical code is big. Thus, high order Gauss integration quadratures
are employed, since they achieve the highest accuracy with the smallest number of
computations to be carried out. At the time there are some academic CFD codes
based on the spectral element method and some more are currently under
development, since the new time-stepping schemes arise in the scientific world.
Boundary element method
Main article: Boundary element method
In the boundary element method, the boundary occupied by the fluid is divided into a
surface mesh.
High-resolution discretisation schemes
Main article: High-resolution scheme
High-resolution schemes are used where shocks or discontinuities are present.
Capturing sharp changes in the solution requires the use of second or higher-order
numerical schemes that do not introduce spurious oscillations. This usually
necessitates the application of flux limiters to ensure that the solution is total
variation diminishing.

 At first we have to open the star ccm+.
 Then we have to select the EHP module setting for estimating hull performance in
calm water.

 After that we have to import our geometry and set the draft lever for our ship.
 After that specify the values , base size, speed range & select the typeof motions to
simulate : For my ship {heave and pitch} are not required .
Volume mesh will be created after the setup is done.

 After creation of volume mesh scalar scenes are created. Two scalar scenes were
needed for my study :
1) Velocity
2) Position {along z}
 Scalar scenes are made so that to identify the changes happening to the hull
due to the flow of fluid. {output file location should be selected from the
scalar scene window}

 After scalar scenes are made accordingly for the model ITERATIONS are started for
the vessel. Iterations are processes that generate a series of approximated solution
which will converge to the exact solution.
 The residuals plot describes or depicts the number of iterations that the vessel
has run for a certain time step.

 Simulation should continue till the graph/plots come constant. For me, it was
Resistance Vs Time plot.
`
 After running for certain Iterations the graph will eventually come constant and the
simulation can be stopped and report can be calculated.
 For my study the vessel that I have taken at different S/L ratios 2000 iterations are
made to run. After 2000 iterations the plot was constant and the process was stopped
eventually. Following are the scalar scenes of different vessels at different S/L ratios:

1) S/L = 0.10 {FSI & FSO}
FSI
FSO

2) S/L = 0.15 {FSO}

3) S/L = 0.20 {FSI & FSO}
FSI
FSO

 PLOTS FOR DIFFERENT S/L RATIOS :
o For S/L = 0.10
o For S/L = 0.15
o For S/L = 0.20
 After the Plots are checked perfectly, the total resistance report is obtained
and they are compared in Excel accordingly.

RESISTANCE COMPARISON OF MODELS
{BY CFD & MAXSURF}

 On basis of the values obtained from the Star CCM+ software and the
Maxsurf resistance software, values are accordingly compared and graphs are
plotted on basis of it.
S.NO SPEED
FROUDE
NUMBER
S/L
Ratio
knots v/root g.L
Maxsurf(KN) CFD(KN)
Percentage
Variation
Maxsurf(KN) CFD(KN)
Percentage
Variation
1 4 0.10 2.866 1.967 31.4 2.423 2.11 12.9
0.15 2.466 1.968 20.2 2.445 2.073 15.2
0.20 2.488 2.088 16.1 2.468 2.057 16.7
FSI FSO
Hull Types

CONCLUSION
 From the study I found out the model which could provide the
least wake with maximum safety and less resistance.
 Based on the analysis done in CFD and also in Maxsurf it is
clear that the model Flat Side Outward has better resistance
characteristics
 For Flat Side Inward the resistance is increasing with the
separation which is against the motive of the study.
 So according to the findings by CFD and by the wake profile
generated by it FLAT SIDE OUTWARD model is suitable for
the study.
 Since comparison is done only based on same speed at
different S/L ratios the findings are limited, for different
Speeds the model might show different characteristics.
 Hence, to conclude FSO is the best model to work on with
while dealing with wake distribution from CFD analysis point
of view.

REFERENCES
1. SOLAS, International Convention on Marine Pollution, 2003
Watson D.G.M. 2.Gilfillan A.W; Some Ship Design Methods,
RINA 1976.
3. H.Schneekluth; ‘Ship design for Efficiency and Economy’.
4. Taggart R; ‘Ship Design and Construction’, SNAME
Publications, New York, 1980.
5. Harvald; Resistance and Propulsion of ships.
6. www.marinewikki.com.
7. www.wikipedia.com.
8. www.shipinfo.com.
9. Papers on “Hull Form Configuration Study Of A Low Wake
Wash Catamaran” By Omar Yakoob, Mohd. Afifi.
10. Fluid Mechanics by CENGEL.
11. NPTEL lectures {video & audio} about CFD.

LOW WAKE WASH USING DIFFERENT HULL SHAPES

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to LOW WAKE WASH USING DIFFERENT HULL SHAPES

Similar to LOW WAKE WASH USING DIFFERENT HULL SHAPES (20)

Recently uploaded

Recently uploaded (20)

LOW WAKE WASH USING DIFFERENT HULL SHAPES