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TABLE OF CONTENTS
Page
... ..................................................................................................... Table of Contents III
List of Figures ........................................................................................................... vi
... List of Abbreviations and Symbols Used ................ ... .......................................... VIII
.................................................................................................. Acknowledgernents bc
..................................................................................................................... Abstract x
Chapter 1 . 0 The Purpose Of The Project ............................................................... 1
...................................................... Chapter 1 . 1 Background ......... ...... -2
........................................ Chapter 1 -2 The FulCScale Vessel ............... .. -5
Chapter 1.3 A Case Study Of Broaching ........................... .... ...................... 7
..................................................................................... Chapter 2.0 Water Waves 1
......................................................................... Chapter 2.1 Waves at Sea -11
................................................................... Chapter 2.2 Trochoidal Waves 13
........................................................... Chapter 2.3 Waves Used in Testing 15
................................................... Chapter 3.0 The Full-Scale Vessel ................. .. 17
............................................................... Chapter 3.1 Measuring the Mold -17
................................ Chapter 3.2 Recreating Lines on AutoShip ........... .. -20
......................... Chapter 3.3 How the Full-Scale Vessel was Measured ..... 21
.............................................................. Chapter 4.0 The Theory of Model Scaling 23
.................... ............................................. Chapter 4.1 Model Scales .... 23
.............................................................................. Chapter 4.2 Hull Scaling 24
Chapter 4.3
Chapter 4.4
Chapter 4.5
Chapter 4.6
Chapter 4.7
Chapter 4.8
Chapter 4.9
Chapter 4.10
Chapter 4.1 1
..................................................................... Propeller Scaling -28
Propeller Shroud Scaling ................... ... .......
................................................................ Propeller Cavitation -36
Rudder Scaling ........................................................................ 39
....................................................................... Rudder Stalling -40
...............*....... ....,................................... Rudder Cavitation .. -42
....................................................................... Rudder Aeration 43
............................. Overall Strategy For Modelling The Rudder 44
.......................................................................... Wave Scaling -46
................................. Chapter 5.0 Building And Instrumenting The Scale Model -49
............................................................................ Chapter 5.1 Model Scale -49
Chapter 5.2 Model Hull Construction ......................... .. ................................ 49
..................................................................... Chapter 5.3 Model Hardware -53
..................... Chapter 6.0 Development Of Systems For Measuring Model Action -55
............................. Chapter 6.1 Six Degrees Of Freedom Of A Rigid Body -56
Chapter 6.2 Methods For Detenining The Motion Of A Model .................. 57
..................... Chapter 6.2.1 The Strapdown Accelerometer Method -57
.................. Chapter 6.2.2 The Manual Optical Triangulation Method 60
.......................................... Chapter 6.2.3 The OPTOPOS Method -61
................. Chapter 6.3 Determining The Model Motion ................ .... -61
.......................................................... Chapter 6.3.1 One Shot Mode -65
.................................................. Chapter 6.3.2 Circular Buffer Mode -66
...................................................................... Chapter 6.4 Model Control 67
..........*.... .......*...... Chapter 6.5 Locations For Testing The Model .. .... .. -67
Chapter 6.6 The Wave Basin At The InstiMe of Marine Dynamics ............ -68
................................................................................................. Chapter 7.0 Testing -70
........................................................................ Chapter 7.1 Test Conditions -70
........................................................................... Chapter 7.2 Modal Testing 71
........... .......... Chapter 7.3 Expected Model Behaviour During Broaching .. -74
References and Bibliography ..................................................................................... -75
LIST OF FIGURES
Page
Figure 1.1 A Destroyer Broaching ........................................................................... 3
Figure 1.2 The Navigable Semicirde For Vessels North Of The Equator ............... 4
Figure 1.3 The Fisheries Patrol Vessel Tuebor, Front View .................................... 6
Figure 1.4 The Fisheries Patrol Vessel Tuebor, Oblique View ................................ 6
Figure 1.5 Map of Wedgeport, N.S ......................................................................... -8
Figure 2.1 Profile of an lrregular Wave .............. ... ............................................ 11
Figure 2.2 Creation Of A Trochoidal Wave ...................~.......................................... 13
Figure 2.3 Wave Particle Motion ............................................................................. -14
Figure 2.4 Wave Makers at The lnstitute of Marine Dynarnics in
..................................................................... St. John's, Newfoundbnd - 3 6
Figure 2.5 General Tank Layout at The lnstitute of Marine Dynamics in
. ....................................................................... St John's, Newfoundland 16
Figure 3.1 The Mold Of The Tuebor. Bow View ...................................................... 17
....................................................... Figure 3.2 The Mold Of The Tuebor, Side View 18
.......................... Figure 3.3 The Mold Of The Tuebor, Oblique View ................. .. 18
...................................................... ................... Figure 3.4 Measuring A Station .. -19
Figure 4.1 Propeller Shroud . Oblique View ....................... .... .............................. 34
.................................................................. Figure 4.2 Propeller Shroud . Side View -34
Figure 4.3 The Effed of Reynolds Nurnber on Stall Angle ......................... ... ...... 41
Figure 4.4 Rudder Geometry .................................................................................... 45
Figure 5.1 Ships Lines as created on AutoShip ............................. ..... ............. 5 0
Figure 5.2 Buttock Boards For One Side Of Model .................................................. -51
Figure 5.3 Assembled Bottock Boards For Port Side Of Model Hull ......................... 51
Figure 5.4 Assembled Bottock Boards For Entire Model Hull ................................ - 5 1
Figure 5.5 Ternplates For Ensuring Model Hull Shape ............................................. -52
Figure 5.6 Rudder Geornetry As Built By The Center For Marine Design
.......................................................................................... And Research -53
Figure 5.7 Model outfiecl with moton and power supply ........................................ -54
Figure 6.1 The Six degrees Of Freedom Of Motion Of A Rigid Body ....................... -56
Figure 6.2 The Six Accelerometer Method Setup ........................ ... ...................... -58
Figure 6.3 The Seven Accelerorneter Method Setup ................................................. 59
List of Abbreviations and Symbols Used
Note: The subscripts 'm' and 's' are used extensively throughout this text to denote properties of the model and full-scale vesse1 respectively
SYMBOL L Ta H 113
R R o
e k z T R P v 9 L v f Co 7cH T v a D Q J-P P J O LCG VCG LED DC PC Hz IMD
MEANING average apparent wavelength average apparent period significant wave height radius of a circle radius of the motion of a particle at the water surface natural logarithrn unknown constant depth below water surface wave penod hull resistance density of the fluid velacity of the hull acceleration due to gravity length of the body kinernatic viscosity of the fluid unknown mathematical function drag coefficient hull scaling factor speed of rotation of propeller speed of advance of the propeller diameter of the propeller torque on the propeller propeller scaling factor pitch of propeller advance ratio angle of encounter with waves longitudinal center of gravity vertical center of gram light emitting diode direct current persona1 computer hertz lnstitute of Marine Dynamics
The author wishes to acknowledge the following people for their contributions
to this thesis;
Dr. Orest Cochkanoff for being my supe~*sor. for his guidance and patience
during the many drafts of this paper as well as help securing financial support
men the 'chips were down',
Dr. Charlie Hsiung for his help and financial support,
Brian Liekens for his insight into the electronics,
Gordon Lacy for his help with AutoShip, and
Howard Blinn and David Fraser for their time and photographs
When a vessel runs before the sea at a speed comparable to the wave speed,
it cornmonly experiences a reduction in its directional control. ln severe cases, the
vesse1 rnay begin ta yaw uncontrollably, swing broadside to the waves and heel to
leeward at a large angle. This is broaching. In some cases, extrerne heel angle rnay
cause the vessel to capsize.
Testing a free-ninning scale model for its broaching characteristics is not
straight-fonrvard. There are many conflicting scaling requirements that must be
reconciled to pmperly model the full-scale vessel's behaviour. All aspects of the
scaling requirements for the hull, propeller, nidder, and test environment are
exarnined and rnethods for reconciling conflicting requirements are given.
Chapter 1 .O The Purpose Of The Proiect
The objective was to develop a model useful for measuring broaching
behaviour of a specific vessel. Broaching is the inability of a ship's nidder to control
yawing in following or quartering seas. This results in the loss of direaional stability.
The project required developing a model to properly reflect the vessel's broaching
characteristics The project began with aie measurement of the existing vessel to
determine its geornetry. Then methods for scaling the model to accurately reflect the
vessel's handling characteristics were developed. The areas considered when
scaling were the vessel's hull. propeller, rudder, and wave environment These four
areas were examined using standard dimensional analysis. For the propeller, the
effects of the shroud and propeller cavitation were also considered. For the rudder,
the effects of stalling, rudder cavitation, and aeration were considered.
As will be seen. it is not always possible to accurately scale all aspects of a
vessel. There were confiicting requirements for the construction of the model.
Suggestions are given to rewncile these requirements so as to minimize the
detrimental effects on the modelling of the behaviour of the full-scale vessel.
The methods for measuring and constnicting an accurate, sale
representation of the full-scale vessel were discussed. The projed was concluded
with a discussion of the wave conditions and test proceedures required to determine
the broaching characteristics of the model.
The premise of this project is that the results of broaching tests on a mode1
constructed and tested in a manner consistent with the theory of this paper can be
applied to the full-scale vessel.
Chapter 1.1 Backaround
When a vessel nins before the ssa at a speed comparable to the wave speed,
it commonly experiences a reduction in its directional control. This becomes more
pronounced as wave height and wind speed increase. At some point, the vessel may
begin to yaw uncontrollably. and swing broadside to the waves. It also heel to
leeward at a large angle. It has lost its directional stability. See figure 1.1 This
process is defined as 'broaching' or 'broaching-to'. In extreme cases, when the angle
of heel and the wave heights are large enough, the vessel can capsize.
Figure 1.1 A Destroyer Broaching [ I l
It would seem obvious that the easiest way to avoid the significant danger
posed by the broaching phenornenon would be to avoid mnning before the sea under
rough conditions. However. this is not always feasible. The standard procedure for
avoiding a tropical s t o n as defined by the 'Admiralty Manual Of Navigation' is to
avoid the center of the stom and head for the 'navigable semicircle'. See figure 1.2.
This course of action places the predominant wave direction on the quarter [Il. Also.
when a vessel is attempting to enter a safe harbor or estuary in a stom. the vessel
may be required to run before the sea. As the vessel entes the shaflower waters. the
waves will become higher and steeper. thus increasing the chance of broaching.
Even if the vessel does not capsize. the loss of control may cause the vessel to fun
aground in the restricted waterway [Z].
Figure 1 2 The Navigable Semicircle For Vessels North Of The Equator
There is still some debate over the exact causes of broaching. There are
conditions that are cornmonly accepted as contributing factors. Conolly (11
summarizes the conditions under which broaching is likely to occur. 'The
predominant direcüon of the waves must be on the quarter; and although wind may
aggravate the situation. it is not a necessaiy constituent. In moderate sea States a
ship may broach-to if its speed is high and comparable with the speed of advance of
the waves; in severe conditions, however, a ship may broach-to when its speed is
much lower. A clear distinction can rarely be drawn between loss of directional
control caused by speed being too high and loss of control because speed is too low.
In al1 cases, the phenornenon is characterized by the inability of the rudder to control
the yawing motions of the ship". Broaching is also more likely to occur on the
"forward edge" of a wave. A possible explanation for this is given in ChapteR.2.
If the wdder is not manned, and the ship does not have an adequate autopilot,
broaching may occur under conditions that are not as severe. The capsizing of the
Angie Derek II discussed later in Chapter 1.2 is a prime example of sud, an event.
In this project. the effects of wind speed on the broaching of the model will not
be considered.
Chaoter 1.2 The FullScale Vessel
The vessel chosen for testing was a 42 faot, D'€on class. Fisheries Patrol
vessel, the Tuebor, Reg M08729. See figures 1.3 and 1.4. This was chosen for a
number of reasons. The mold oflginally used to produce the vessels' fibreglas hulls
was available for study and measurement. The Department of Fisheries and Oceans
was willing to provide free time on the vessel for testing. They had also expressed
concem with the handling characteristics of this class of patrol vessel in following
seas. The results of the broaching tests would be useful to them in detennining
operational safety parameters.
Figure R View
The patrol vessel is a Capdsland type vessel and it is similar in size and
shape to many small vessels used in the Maritimes for fishing. This allows the tmng
methods, and possibly the results, to be applied easily to many other vessels.
Several different variations of the D'Eon dass patrol vessel were produced, al1
with the same basic hull. There were a number of variations on the superstructure
layout. The particular vessel that was tested for this report was the Tuebor, stationed
in Wedgeport, Nova Scotia. If was the first of the D'Eon class that was produced, and
it has been repaired since construction. The vessel had fun aground and suffered
keel darnage. During these repairs, a large quantity of Sand was added to the keel as
ballast. The basic shape of the vessel, however, was not altered during these
repairs.
Since 1975, more than 25 fishing vessels between 12m and 15m have
capsized or foundered in Canadian waters. The Transportation Safety Board of
Canada maintains a database on aIl such incidents. The Board does extensive
investigations on these incidents, but it is not always possible to determine the exact
causes of an accident.
It is possible that a large percentage of these losses are due to broaching.
We may never know for certain because there are usually very few s ~ ~ v o r s . Most of
the vessels were lost in weather conditions that are similar to those under which
broaching wmmonly occurs.
Chapter 1.3 A Case Studv Of Broaching
The rnost dangerous aspect of broaching is that it happens very rapidly, in a
few seconds, and that there are no set conditions to determine when broaching will
ocwr and Men it will not A good example of such an incident is the capsking of the
Angie Derek II, a 12.8rn dragger. On November 15, 1982, the Angie Derek II
capsized duting a voyage between Yarmouth and Wedgeport, N.S., resulting in Me
death of her sole crewrnan, Mr. A. Boudreau. See figure 1.5. While Mere were no
s u ~ v i n g witnesses, the Canadian Coast Guard detemined that broaching was the
probable cause of the accident. [3]
Figure 1.5 Mâp of Wedgeport, N.S.
The incident o m m d during conditions that are not usually associateci with
broaching. The weather was relatively good. with good visibility, winds of 20-25 knots
and wave heights of 0.9rn. However, there were a number of reasons why broaching
was probable.
a) Them were no hash marks on the hull to indicate a collision.
b) The vessel nomally camed a cargo of ice on voyages. However, there was none
present in the hold at the time of the accident.
c) The vesse1 was canying heavy dragging gear and nets on its deck of a type
usually camed by vessels over 20m in length.
d) The lack of ballast and the load on the deck would have degraded the stability of
the V ~ S S ~ well below that nomally expected of the Angie Oerek II.
e) The operator was most likeiy below deck when the vessel broached. Shortly prior
to the incident, he had radioed ashore and indicated that he was going below to
sewïce the engine because it was speeding up and slowing down. This was
supported by the fact that his body was found in the engine roorn, and the
autopilot was found in the 'onJ position. Since he was not at the helm, he would
not have been able to use the mdder to counter the slew of the ship as she began
to broach.
f) The autopsy of Mr. Boudreau's body showed that he had died instantly from
drowning and that there were no signs of a struggle or foul play. This is consistent
with the vessel suddenly broaching and capsizing.
g) lnclining experiments and stability calculations were conducted on the Angie
Derek II after the incident and it was concluded that the stability of the vessel was
deficient at a large angle of heel, when compared to other vessels in its class.
h) The wind direction at the time of the incident was Southeasterly, which would have
put the waves on the stem or on the quarter of the vessel. This is the relative
wind direction that is most commonly associated with broaching.
It was concluded thaï the loading condition of the vessel and its inherent lack
of stability at high angles of heel. cornbined with a lack of hand steering resulted in
the broaching of the vessel. P]
If the broaching characteristics of the vessel had been more fully understood,
the operator would likely have been able to recognize that setting his vessel on
autopilot under the prevailing conditions was a dangerous decision.
As fish stocks decrease and as fishing seasons become shorter, fishermen are
more often tempted to venture out in fou1 weather in an attempt to catch what fish
remain. This puts thern in situations where broaching is likely ta occur. The results of
broaching tests would be useful to them in detemining operational safety parameters
for their craft.
Chapter 2.0 Water Waves
The follawhg discussion on waves is meant as a &nef background to help the
reader understand the role of waves in testing a model for broaching. More detail can be
found on the theory of water waves in any one of a large number of texts.
Chapter 2.1 Waves at Sea
The waves encountered by a vesse1 at sea are flot of a regular or predictable
nature. The wave amplitude along a straight Iine drawn in any direction through the
waves would resemble figure 2.1.
Figure 2.1 Profile of an lnegular Wave
These waves are cornplicated and not easily dealt with from a mathematical
perspective. A simple way to deal with these irregular waves is through statistical
descriptions. A sea state can be described using terms such as the 'average apparent
period (TJ and "significant wave height (Hl& Ta is the tirne required for a wave crest to
advance a distance equal to the average apparent wavelength (h). It is also possible to
describe the irregular wave profile shown in Figure 2.1 as the sum of an infinite number
of Sine waves of different amplitudes, periods and directions.
12
The sea-state in a given area çould then be described by its energy spectrurn.
This spectrum shows the relative amount of energy in each of the regular waves that
combine to fom the irregular sea-state.
The fact that an irregular sea state can be described by an infinite nurnber of
regular sinusoïdal waves makes it relatively easy to create a desired irregular sea state in
a controiled environment such as a wave tank. In practice, it is not practical to create an
infinite number of Sine waves. It is usually considered suffÎcient to combine 15 to 20
regular Sine waves to reasonably mode1 a given sea-state.
These 15 to 20 regular waves can easily be generated on a cornputer, combined.
and sent to the wave makers in a wave basin or towing tank. By changing the relative
energy given to each of these regular waves, the characteristics of the resultant irregular
sea state can be changed.
It is usually desirable to test a model of a vessel in wave conditions that the full-
scale vessel would encounter during operation. This can be achieved by recording the
actual wave spectnim in the vessel's future area of operations using a wave buoy or
similar recording apparatus. Depending on the areas of operation in question for the full-
sale vessel. it is possible that this information has already been recorded. The
observed sea-state can then be duplicated in a wave basin by combining the regular
Sine waves with the appropriate relative energy levels.
The model is wnstructed such that it will behave similady to the full-scale vessel.
Therefore, testing the model in a "scaled sea-state" should provide an accurate
13
representation of how the full-scale vessel will behave in Mat sea-state. The method for
testing the mode1 in a wave tank is described in chapter 7.
Chapter 2.2 Trochoidal Waves
To understand what effect waves have on the broaching of a vessel, it is
necessafy to develop an idea of how water particles behave in a wave. A simple. yet
relatively acwrate means of describing a wave uses Me trochoidal approach. The
surface of a trochoidal wave is defined by a point on a mlling Urcle as shown in figure 2.2
F rgure 2.2 Creation Of A Trochoidal Wave
This creates a wave profile that is very close to the second otder Stoke's wave. Partides
in the wave follow a circular path about a fixed center with a constant angular velocity.
The radius (R) of these circles decays exponentially with depth.
or:
R = R, *e-"
Where z is the depth below oie surface. k is an unknown constant and R. is the radius of
the circular motion of a particle at the surface.
The motion of particles at or near Me surface of the wave are s h o w in figure 2.3.
Figure 2.3 Wave Particle Motion
Each pacticle in the wave completes one revolution along its circular path during
the petiod of the wave. For a given wave period 0. the greater the wave height. Me
greater the distance each particle must travel in its orbit. This requires a particle in a
large wave to rnove pmportionally faster Vian a particle in a small wave.
As a vessel travels through waves, the velocity of the water flowing past the
nidder changes. Consider a vessel traveling at a constant velocity in the sarne general
direction as the waves. The flow past the rudder will increase when the nidder is located
in the trough of the wave because the water particle motion and the vessel motion are in
opposite directions. The flow past Me nidder will decrease m e n the rudder is located on
the crest of the wave because the particle motion and the vessel motion are in the same
direction. This decrease in flow past the rudder on the crest of the wave will reduce the
ability of the nidder to control the direction of the vessel. The greater the wave height.
the greater the water particle velocity. and hence the greater the reduction of flow past
15
the rudder. For sufficientiy high waves, this reduction of flow may reduce the ability of
the nidder to control the direction of the vessel to such a point that broaching will occur,
as discussed in Chapter 1 .O.
Chapter 2.3 Waves Used in Testing
Trochoidal waves provide a simple model for explaining the motion of fluid
particles in a wave. However, it is highly unlikely that a vessel wilI encounter a çea state
that closely resembles trochoidal waves. A vessel operates in irregular seas similar to
that shown in figure 2.1.
Fortunately, it is not overly diffïcult to produce an irregular sea state in a controlled
environment. The lnstitute of Manne Dynamics in St. John's, Newfoundland has a
M~l t id i re~onal Wave Basin equipped with hydraulic wave makers. Software currently
exists that c m create irregular waves by combining a large number of regular sine
waves. This software is used to drive the wave makers. The result is an irregular sea
state with almost any desired average apparent period and average apparent wave
height. The operator enters the desired values into the cornputer and the machinery
produces the desired sea state. The scaling of waves for model tests is discussed in
Chapter 4.1 1. The wave makers at The lnstitute of Manne Dynamics are shown in figure
2.4. The general tank layout for this facility is shown in figure 2.5.
Figure 2.4 Wave Makers at The InstiMe of Marine Dynamio in St John's, Nwfoundland
Figure 2.5 General Tank Layout at The Instihite of Marine Dynamio in St John's, Newfoundland
Chaoter 3.0 The Full-Scale Vessef
Chaoter 3.1 Measuring the Mold
The first step in the project was to determine the exact shape of the hull of the
patrol vessel. Unfortunately. there were no existing Iines plans of the vessel.
Tharefore, it was necessary to construct a new set of lines plans. The most
convanient way to do this was to take measurernents direcüy off the original rnold.
This mold is located at the Bedford InstiMe of Oceanography in Dartmouth, NOM
Scotia. See figures 3.1. 3.2, and 3.3.
Figure 3.1 The Mdd Of The Tuebor, Baw View
Figure 3.2 The Mold Of The Tuebor, Side View
Figure 3.3 The Mold Of The Tuebor, Oblique View
The mold was measured in the following rnanner. A cord was sûung tightly
along the centerline of the upnght mold and divided into stations approximately one
metre apart At each station, a crossbar was placed across the top of the mold.
perpendicular to the centerline. A vertical post was then attached to the centre of the
crossbar. A plumb bob was attached to the aossbar and used to mark points on the
inside of the mold. This ensured that al1 of the points at that station were 'in plane'
and that the plane of the station was perpendicular to the centerline. Nails were
driven into the vertical post at known locations. The distances between two different
points on the vertical post and each of the points marked on the mold were measured
and recorded. Approximately twenty points were marked on the hull at each station.
The density of these points was greatest in areas with small radii of curvature to
ensure accuracy of measurement.
Figure 3.4 Measuring A Station
The procedure can also be used to measure the hull of an existing vessel with
only slight modifications in method. The vessel would have to be out of the water.
The vertical post would be on the outside of the vessel and the distances from known
points on the post to points on the hull could be measured. The results could be
reconstnicted as above.
Chapter 3.2 Recreatin~ Lines on AutoShiv
The information taken from the mold was then transferred to the AutoShip
program. AutoShip is a cornputer program that can create fair, three dimensionai
lines plans of a hull from two dimensional hull cross-sections at known locations.
Before the lines plans could be generated, the curves from each station were
recreated using the distances recorded from the mold and the cornputer program
Autocad. Plots of these curves were then digitized using the AutoShip procedure
'SEC'. Lines plans were then generated using standard AutoShip methods.
Unfortunately, the resulting lines were not completely fair. This posed a
problem. In order to ensure that there had been no error in measuring the lines from
the mold, certain stations in areas of concem were measured again. The results were
consistent with the original measured values. This suggested that either the mold had
settled and changed shape slightly since constniction, or the original mold had not
been fair. By visual inspection of the rnald, and by cornparing the shape of both sides
of the mold at several stations, it was concluded that very little settling had occurred.
The settling that was apparent was judged to be smaller than the error involved in
measunng the shape of the stations, and was therefore negligible.
Since it is unlikely that the lack of faimess was due to the design of the vessel,
it was assumed that it was due to the construction techniques used in the construction
of the mold or the slight errors involved in measuring the mold. Some of the lack of
hull faimess would be corrected in the final stages of construction by workmen when
they sanded and painted the hull after it had been removed from the mold. It should
be noted that numerous flat spots were apparent on the hull of the actual vessel, the
Tuebor. It would be neariy impossible to duplicate the exact shape of the vessef's
hull, including fiat spots. Therefore, the hull lines in AutoShip were made as fair as
possible without significantly changing the shape of the hull envefope. The mode1
was constmcted to be as fair as possible. The minute differences, including flat
spots, should not create any appreciable errors.
Chaoter 3.3 How the Full-Scale Vessel was Measured
In addition to the hull lines, obtained from the mold, and in order to ensure that
the model provides an accurate representation of the full-scale vessel, it is necessary
to examine the vessel to detemine its characteristics.
The following characteristics of the full-scale vessel should be measured;
1.The location of the vertical centre of gravity (KG)
P.The location of the longitudinal centre of gravity (LCG)
3.The vesse1 displacement
4.The location and geometry of the nidder
5.The location and geometry of the propeller
6.The polar moment of inertia
7.The transverse moment of inertia
8.The location and geometry of the superstructure
Due to time constraints, it was not possible to perform standard inclining tests
on the full-scale vessel. Therefore, the method described by Maritime Marine
Consultants [4] should be used. This method gives a good approximation of the
location of the VCG for inshore vessels less than eighty feet in length.
To detemine the position of the LCB and the displacernent of the vessel, it is
necessary to measure the position of the wateriine on the bow and stem. When this
information is used in conjunction with the cornputer program AutoHydro, it will
calculate the location of the LCG and the displacement of the vessel.
The vessel was examined while it was still in the water. This created difficulty
in exarnining the rudder and propeller. The position of the rudder stock was
rneasured frorn the inside of the hull. The remainder of the measurernents were
determined from information and photographs provided by the ship's captain and
engineer.
The transverse and polar moments of inertia are detemined by measuring the
location and weight of al1 the major items on the vessel. i.e. fuel tanks. engine.
batteries, anchor, water tanks, etc.
The geometry of the superstructure was detemined with a tape measure.
This was necessary to give the model 'stand-off scale appearance.
Chapter 4.0 The Theorv of Model Scaling
When using a model to test the characteristics of a full-scale vessel, it is
necessary to scale the hull, propeller and rudder geometries in such a manner as to
ensure that its behaviour will accurately refiect that of the full-scale vessel. lt is not
sufficient to sirnply reduce the size of the vessel and al1 of its cornponents by a
geometric scale factor. This will only produce a model that looks like the real vessel.
Other factors must be considered if the rnodel is to accurately sirnulate the behaviour
of the full-scale vessel. The factors that dorninate scaling rnay be different for each
part of the vessel. This rnay result in different parts of the vessel being scaled by
different factors.
Chapter 4.1 Mode1 Scales
When scaling a model, it is desirable to choose a sa le that is an adequate
compromise between ease of use and errors caused by using a model that was much
smaller s a l e than the original. For this model, a scale of 117 was chosen for the hull.
Reasons for this are further discussed in Chapter 5.1. Choosing a scale for a mode1
is not always a straight-forward decision. There are four different parts of the vessel
that must be considered when scaling; the hull, the propeller, the rudder, and the
protective wire shroud around the propeller. The standard methods of dimensional
analysis and similitude as well as physical considerations are used to determine the
scale for each part.
Chapter 4.2 Hull Scaling
In order to scale the hull, we must consider behaviour in the sea. Hull
resistance is often taken as the important factor. The following variables are
considered to be significant:
Hull resistance, Fi
Density of the fluid, p
Velocity of the hull, V
Acceleration due to gravity, g
Length of the body, L
Kinematic viscosity of the fiuid. v
Applying the Buckingham Pi theorem of dimensional anaiysis. we arrive at the
well known expression for hull resistance in deep water;
Deep water is defined as water deeper than the length of the hull.
The three terms in the above equation are known as dimensionless PI ternis.
Since the fom of the function f is not known, it is not possible to solve the nght-hand
side of the equation explicitiy. However. only the relationship between the model and
vessel properties is required. Therefore, dividing the vessel equation by the model
equation , we get.
If the tems of the function are selected such that
Then the right-hand side of the equation equals one, or,
Rs
or reducing, we get,
If the properties of the model are constrained such that the dimensionless Pi tems for
the model and the vesse1 are equal. then the drag coefficient of the model will be
scaled properiy. The drag coefficient (Co) is defined as.
The first Pi term,
is defined as the Froude number. The Froude number is the ratio of inertiai forces to
gravitational forces. It is the dominant factor in hull resistance for surface piercing
bodies at high speed, such as the hull being modelled. It is also significant in dealing
with the response of a ship in waves. If the mode1 hull length is scaled from the full-
scale vesse1 by a factor of AH, where
then the above Froude Law of Similitude becomes,
The second Pi terni, equation 4,
r?
is defined as the Reynolds number. The Reynolds number is the ratio of inertial
forces to viscous forces. lt is the dominant factor in hull resistance for plates or
deeply submerged bodies.
The Reynolds Law of Similitude is,
or, if we again introduce the scale factor An, then Reynolds Law can be wntten as
If both the Reynolds Law of Similitude and the Froude Law of Similitude are satisfied,
then it follows that the Ieft-hand side of equation 1 will be scaled properly.
However, it is obvious that it is not possible to satisfy both the equations for
Reynolds law and Froude law for the hull. Nomally, in a towing tank model test, the
Froude Law is applied to ensure that the wave resistance coefficients are equal for
both the model and the full-scale vessel. The viscous effects are then taken into
account by corrections.
In the usual case of models tested in a towing tank, the well known procedures
descnbed below are used. Consider the case of the vessel being tested at a top
speed of 8.5 knots(4.4 m/s). Scaling the velocity by Froude law gives a maximum
required mode! velocity of 1.65 mis, based on a length scale of 7 for the model. This
velocity is easity obtainable in a tank environment.
When scaling the velocity by Froude law, the Reynolds number of the vessel
will be A'-' tirnes smaller for the model than for the ship. In this case, it would be 18.5
tirnes smaller. Thus the viscous flow condition would not be met by the model. The
resultant achieved Reynolds number for the model implies that the flow would be less
turbulent than required. The effects of this can be minimized by placing turbulence
generaton on the hull of the modei to induce a realistic turbulent flow. This causes
the flow condition to act in a manner that is similar to the higher Reynolds Number
flow expenenced by the full scale vessel. This approach is based on well
docurnented expenrnental procedures but nevertheless should be carefully monitored
to established suitable conditions as rnuch as possible.
For the case of broaching conditions for modeling we would scale acwrding ta
the Froude Law. In this case the turbulence stimulation would not be easily designed.
as the exact flow directions or patterns along the hull during broaching are not known.
A model hull surface that is relatively rougher than the full scale vessel might be
useful in this case.
Cha~ter 4.3 Proneller Scalinq
In order to scale the propeller, we consider thmst. Using the standard
techniques of dimensional analysis, we amve at the well known expression for
propelter ttirust in open water;
where: T is the propeller thnist
n is the speed of rotation
p is the density of the fluid
Va is the speed of advance of the propeller
O is the diameter of the propeller
g is the acceleration due to gravity
v is the kinematic viscosity of the fluid
Q is the torque on the propeller
The same argument used in Chapter 4.2 c m be used here. The fom of the
function f is not known. Dividing the equation for the vesse1 by the equation for the
model, we get,
If the dimensionless Pi ternis of the function f are selected such Mat.
If the properties of the model are constrained such that the dimensionless Pi ternis for
the model and the vesse1 are equal, then the thnist coefficient of the rnodel will be
scaled properiy. The thnist coefficient is defined as,
For the following discussion, it is useful to define the length scale ratio for the
propeller, as h, where,
The propellers have similar geometry and due to the lirnited space available for
mounting the propeller, it is convenient to choose & such that &, =AH. Or.
os = A , U m [25]
In order for the first terni of the expression. the Advance ratio,
to be the same for the model propeller and the full-scale propeller, the speeds of
rotation must be related by the following equation.
This results in a slip ratio for the model that is A, times higher for the model propeller
than for the full-scale propeller. Slip Ratio is cornmonly defined as
where Pm is the mode1 propeller pitch. The slip ratio is one minus the ratio of actual
propeller advance distance per revolution to the theoretical maximum propeller
advance distance per revolution. This higher model slip ratio means that the mode1
propeller must rotate at a speed that is &ln times faster than the full-scale propeller
speed.
The second tenn of the expression,
defined as the propeller Froude number, will have the same value for the vesse1
propeller and the model propeller if,
D, - &Dm [30] and V , = &Y, [31]
The fint condition is satisfied because L,, =&. The second condition is satisfied
because the propeller and the hull have the same Froude speed of advance.
The third tenn,
is defined as the propeller Reynolds number. It will not be the same for the mode1
propeller and the full-sale propeller because the hull speeds and propeller speeds
follow the Froude law. Reynolds Law deals with the frictional resistance on the
propeller blades. This is considered to be small compared to other forces on the
blades and in any case it is not possible to scale this effect in detail.
To minimize the error caused by the unequal Reynolds nurnbers, it is
sometimes possible to use a mode! propeller that is larger than hull scale. In this
case, the size of the propeller is limited by the geometry of the shaft and hull. The
largest propeller diameter usable on the model (Dm) corresponds roughly to D A .
The fourth terni,
can be satisfied if
where J is defined as the advance ratio,
For best results, the model propeller geometry will be scaled by Froude Law
and the propeller will be operated at a higher slip ratio. This will result in a model
propeller that satisfies the following equations;
The mode1 propeller wili not be operated at the proper Reynolds nurnber. However.
the evor introduced by this is expected to be srnall.
Cha-r 4.4 Pronelier Shmud Scalinq
The D'Eon dass patrol vessels are equipped with a wire shroud just forward of
the propeller. See figures 4.1 and 4.2. The shroud is designed to prevent trap lines
and nets from becoming fouled in the propeller.
Figure 4.1 Propeller Shroud, Oblique View
.. - Figure 4.2 Propiler Shroud, Side View
There are several factors which rnuch be considered M e n scaling the shroud.
It is completely submerged and hence its resistance is due primarily to viscous forces.
Therefore, scaling should be done using Reynolds Law. This is not possible however
because the model, and therefore the shroud, are constrained to move at the Froude
speed of advance. The shroud diameter is also limited by the vessel geometry. Its
minimum diameter is lirnited by the propeller and its maximum diameter is limited by
interference with the bottom of the hull. Thus for practical reasons, the propeller
shroud is scaled by Froude Law.
Scaling the propeller shroud by Froude Law results in a Reynolds number that
is 1'" (or 18.5) times smaller for the model shroud than for the full-scale shroud. This
could result in the flow through the full-scale shroud being turbulent and the flow
through the model shroud being laminar. However, this is not expected because the
flow that enters the shroud on both the model and the full-scale vessel should already
be turbulent. This turbulence is generated by flow past the hull for flow from the bow
of the vessel. For flow from the stem of the vessel, the water will be turbulent after
passing the spinning propeller. The fiow will not be turbulent if it enten the shroud
from the side.
The flow pattern past the stem of the hull during broaching is not fully
understood. Hence the direction from which the flow wili enter the shroud is not
known. Therefore, it is not known whether the disproportionate difference in
Reynolds number will have a significant effect on the behaviour of the model.
Chapter 4.5 Propeller Cavitation
Scaling the propeller shroud by Froude Law instead of Reynolds Law also
increases its blockage effects. This means that the relative torque actually required to
tum the model propeller at a desired speed will be greater than the torque predicted
by the theory in Chapter 4.3. The pressure difference across the model propeller will
be greater than predicted by theory. This increases the possibility of the model
propeller cavitating.
Cavitation is an important phenornenon that must be wnsidered when
modelling a propeller on a free-running rnodel. Cavitation occun, in theory. when the
pressure on the low pressure side of the propeller is less than the vapor pressure of
the water. This causes the water to "boiIn and f o m bubbles. These bubbles impede
flow and cause a reduction in propeller performance. In practice. cavitation occurs
when the pressure on the low pressure side of the propeller falls to a point somewhat
larger than the vapor pressure of the water. This is due to the presence of dissolved
gases and other impurities in sea water. The mode1 is tested in fresh water that
presumably has less impurities and this reduces the probability of the model
cavitating. This may lead to cases where the rnodel propeller will produce relatively
more thnist than the vesse1 propellet.
The presence of cavitation is easily discernable. The bubbles are observable
with the naked eye. These bubbles generate a signifiant amount of noise and
vibration. Over an extended petiod of time, cavitation will cause serious erosion of
the propeller blades, leading to a further reduction in propeller performance.
Cavitation is most Iikely to ocwr on propellers that are near the surface and
are tuming at high speed or on propellers that are under a high load. The vessel
being tested in this program operates at relatively low propeller speeds. The model
propeller mtates times faster than the full-scale propeller. However, even this rate
of rotation is relatively slow. Any cavitation that occurs would be due to the propeller
being under a heavy load.
The vessel being tested could be considered to be "loaded" if it were towing
another vessel, or if it were experienung severe weather conditions. Although towing
a stranded vessel is part of the Tuebof s duties, it is a rare occurrence and it is not
considered in this projeb. Severe weather conditions would contribute ta cavitation if
the wind and the waves were acting against the motion of the vessel. However.
broaching occurs when the wind and waves are in roughly the same direction as the
motion of the vessel. This reduces the chance of propeller cavitation occuning under
the conditions that will be tested.
Propeller cavitation is a dimcult phenomenon to rnodel. In addition to the
scaling criteria mentioned in Chapter 4.3, there is an additional condition which must
be met. The atmosphenc pressure and the vapor pressure must be scaled for the
model. This is very difficult to achieve in free-ninning rnodel tests as it would require
the model test basin to be operated with a significantly lower atrnosphetic pressure.
The mode1 basins that are available for testing the model of the Tuebor do not have
this capability.
Discussions with the Tuebots Captain and Chief Engineer. Howard Blinn and
David Fraser reveal that there is no apparent evidence of cavitation on the full-scale
vessel. It is assumed that the full-scale propeller does not cavitate under any of the
conditions that will be tested.
The blockage effect of the shroud may increase the risk of cavitation but, even
so. the model propeller is not expected to cavitate. This would be easily verified by
visual inspection of the model from undewater or through a side window of a towing
tank.
Chapter 4.6 Rudder Scaling
Modetling the rudder of a vessel poses several problems. The rudder is
cornpletefy submerged and should be scaled by Reynolds law. However. the rudder
is constrained to move at the huli's Froude speed of advance. Therefore, in order to
satisfy Reynolds Law, the rudder rnust satisfy the relationship
This would result in a rudder that is larger than the fulCscale rudder and it would be
much too large to attach to the model.
Another problem is caused by the unequal propeller slip ratios. The model is
operated at a much smaller Reynolds number than the ship. and consequently its
propeller must operate at a much higher slip ratio than the ship propeller. The rudder
of the vessel being tested is located aft of the pmpeller and in its slip stream.
Therefore, 'Yhe velocity of the rnodel propeller race relative to the free-stream velocity
is larger than that of the ship propeller race" [5]. This would cause the model to be
conservative when predicting the tuming ability of the ship.
Ships with a single propeller and a single nidder that is located aft of the
propeller. such as the patrol vessel being studied. have an additional problem which
must be considered. The boundary layer of the rnodel is relatively thicker than that of
the ship because the model operates at a lower Reynolds number. This causes the
flow velocity to the propeller and to the rudder relative to the free-stream velocity to be
reduced more in the model than in the ship. This would cause the model to over
predict the maneuvering ability of the ship.
Fortunately, the change in velocity due to the thicker boundary layer is
opposite to that caused by the increased propeller slip ratio. These effects are not
necessatily of the same magnitude but for the vesse1 being studied, these two
problems wilt tend to cancel each other 151. Depending on the experiment being
conducted, it may be desirable to more cfosely model the tuming ability of the rudder.
Methods for achieving this are discussed in Chapter 4.1 0.
Chapter 4.7 Rudder Stalling
An aspect of nidder behaviour that rnust be considered when conducting
broaching tests is stalling. Stalling is defined as an "abrupt discontinuity in the lift
venus anglcof-attack curve. As the angle of attack on a rudder is increased, the
point where the flow separates on the downstrearn side of the nidder moves forward
along the chord of the rudder. As the extent of the region of flow separation
increases, the dope of the lift curve with respect to the angle of attack begins to
decrease" [5]. As the angle of attack continues to increase, it reaches a critical value
known as the stall angle. At this point, there is a sharp discontinuity in the lift force.
As the angle of attack continues to increase, the lift on the rudder begins to decrease.
The stalling characteristics of the rnodel should ideally be identical to the
characteristics of the full-scale rudder. However, since the Reynolds number of the
model rudder is A'.' times smaller than the Reynolds number of the full-scale nidder,
this is not the case. From figure 4.3, it c m be seen that the different Reynolds
numbers seriously affect the maximum lift and the stail angle of the rudder. Figure
4.3 shows Reynolds numbers appropriate for the full-scale vesse1 (2.2~10~). The
model has Reynolds numbers less than 0.2~10~. This value is not covered in the
chart. It is assumed that the Cumes will be the same general shape in the region for
the mode1 propeller.
Figure 4.3 The Effect of Reynolds Number on Stall Angle [5]
The maximum lift coefficient increases with Reynolds number. This is due to
the delay of stall angle with increasing Reynolds nurnber. This means that the mode1
rudder develops relatively less tuming force than the full-scale nidder.
When a vessel begins to broach, the helmsman attempts to counteract the
yawing of the ship by tuming the nidder and it is possible that the nidder may exceed
the stall angle. Thus the nidder force rnay be insufficient to counteract the yawing of
the ship, and the ship will broach. Therefore, the mode!, with its correspondingly
lower Reynolds number, will be less likely to be able to use its rudder to avoid
broaching than the full-scale vessel.
A method is discussed at the end of this chapter that compensates for the
inaccuracies in modelling the rudder.
Chapter 4.8 Rudder Cavitation
Cavitation occurs on the low pressure side of a rudder when the total pressure
is less than the vapour pressure of the water. The total pressure is the sum of the
maximum negative pressure, the hydrostatic pressure. and the atmospheric pressure.
Cavitation, "reduces the rate of increase of l i f t as the angle of attack is increased at
any given speed .....[ but] cavitation alone does not stop the growth of the l i f t curve with
angle of attack; it only slows growth." [5] For moderate speeds, the effeds of
cavitation an nidder performance are not considered as important as the effects of
stalling.
Cavitation occurs on the full-scale rudder before it occurs on the model rudder.
The rnodel is scaled according to Froude law. This means that the negative pressure
and the hydrostatic pressure on the low pressure side of the rudder are properly
scaled. The vapour pressure and the atmospheric pressure are not properîy scaled.
They are relatively farger for the model than the full-scale vessel. The atmospheric
pressure is the largest of the two pressures. This delays the beginning of cavitation in
the rnodel until a larger nidder angle is reached.
Cavitation on the low pressure side of the rudder is not expected to be a
problem in this expen'ment. The full-scale vessel is operated at the relatively low
speed of 8.5 knots (4.4 m/s) and the nidder is restrided to a maximum angle of 30'.
Chapter 4.9 Rudder Aeration
Another aspect of rudder behaviour that must be considered when rnodelling
rudder performance is aeration, also known as ventilation. This occurs when air is
drawn from the surface down into the water on the low pressure side of the nidder.
Aeration reduces the performance of the rudder.
The pressure difference between the atmosphere and the low pressure side of
the nidder must be suffkiently large for aeration to occur. Larger vessel speeds and
nidder angles increase the magnitude of this pressure difference and make it more
likely for aeration to occur. The vessel geornetry also has a great effect on aeration.
Vessels with mdders that pierce the surface are rnuch more likely to experience
aeration than vessels that have deeply submerged mdders. This is due to the much
srnaller resistance to the air being drawn down under the free surface for the case of
a piercing rudder.
Aersltion is not a factor in the broaching tests of the Tuebor. The fudder is
completely subrnerged and well isolated from the free surface by the hull. Also, the
vesse13 maximum rudder angle is 30' and its maximum speed is 8.5 knots (4.4 mis).
Aeration will not occur under such conditions. Even under the weather conditions that
the vessel is likely to be experiencing when it is in danger of broaching, the mdder will
likely remain submerged, and aeration will not occur. The nidder would only be
exposed in extrerne conditions and its exposure would occur when the vesse1 was
experiencing rnuch greater problems that aeration.
Chapter 4-1 0 Overall Stratew For ModeIlincl The Rudder
It is evident from the discussion in previous chapten that it is not possible to
accurately rnodel al1 aspects of the rudder. However, it is possible to create a mode1
that will duplicate the broaching characteristics of the vessel without exactly matching
every aspect of the nidder. The most important factor for the mode1 rudder in this
projed is that it provide the same relative maneuverability as the full-scale rudder. If
the mode1 wuld be made to maneuver similarly ta the full-size vessel, then the results
of the broaching tests could reasonably be expected to be accurate.
A reasonable rnethod for modelling the mdder is to scale the chord (1) and
thickness by Froude law. This ensures that the geometry of the forces acting on the
mdder remains sirnilar ta the full-scale vessel and that the rudder can easily be
attached to the hull. The depth of the rudder can then be changed to compensate for
the errors introduced by scaling in this rnanner. The 'depth' is the vertical dimension
of the rudder. See figure 4.4.
l
Figure 4.4 Rudder Geametry
Maneuverability tests can be conducted on the mode! for different values of
nidder depth. This will detemine the depth of the rudder required to accurately mode1
the vessel's rnaneuverability. From experience, it is expected that the resultant mode1
rudder depth will be greater than if the depth had been scaled by Froude law. If the
mode1 does have a mdder that is relatively deeper than the rudder of the full-scale
vessel, then a greater proportion of the model rudder will not be in the propeller
sfipstream. However, since the resultant mdder will accurately model the vessel's
rnaneuverability, it will be appropriate for this project.
It is proposed that the tests be conducted in the following manner. Test nins
will be conducted to measure the time required for the model to complete a 360" tum
at different speeds and nidder angles in calm water for each of a series of wdders of
different depths. The results of these tests will be plotted on a graph and compared
to similar full-scale results to detennine which rudder depth most accurately dupiicates
full-scale rnaneuverability. In this way the mdder required for the broaching tests c m
be selected.
This method of selection is based on the assumption that rnodelling the tuming
capabilities of the vessel under steady flow conditions will provide adequate results for
broaching tests. It is realized that this assumption rnay not be entirely valid for
broaching tests where the flow is not necessarily a steady flow. However, it would not
be feasable to atternpt to test the vessel under the unsteady flow conditions that could
be expected during broaching.
Chapter 4.1 1 Wave Scaling
There are four independent variables that must be considered when scaling
waves in deep water;
Hln Significant wave height
Ta Average apparent period
O Angle of Encounter
v vesse1 speed
Deep water for waves is defined as water deeper than half the wavelength of the
wave.
When scaling waves, Froude law is used. This means that the values of HIi3,
and Ta of the waves used to test the model are scaled by a factor of 1. ln equation
fom,
H, = ÂH, [43]
The relationship between model wave period and full-scale wave period is not
as simple. If we equate the Froude ternis,
Substituting,
yields,
Substituting,
yields a final result of,
When scaling waves, the wave height should be scaled by a factor of ;C and
the wave periods should be scaled by the above equation.
Chapter 5.0 Building And lnstrumentinn The Scale Model
Chapter 5.1 Model Scale
The 1:7 scale for the model hull was chosen as a compromise between ease
of use and erron caused by using a model that was much smaller scale than the
original. The resulting hull is large enough (1.8m long and 55kg displacement) so that
it can easily carry the required equipment (batteries, motors. electronics) and errors
introduced by scaling are relatively small. The model is also small enough so that it
can be easily transported and the required testing speeds can be achieved with an
inexpensive efectric motor.
Chapter 5.2 Model Hull Construction
The lines plans created by the AutoShip program were plotted at a scale of
117, the aduaî size of the mode!. The buttock lines were spaced so that they would
19mm apart on the scale plot. See figure 5.1.
Figure 5 1 Ships Lines as created on AutoShip
The plotted buttock lines were traced on to 19mm thick pine boards using a
small. spiked, tracing wheel. These 'buîtock boards' were Men cut out and Me pieces
were glued together, producing a 'stepped' hull. See Figures 5.2 through 5.4.
Figure 5.2 Buttock Boards For One Side M Ailodei
A spoke shave, gouge, and plane were used to smooth out the hull.
Templates at stations at six indi intervals were used to ensure that the hull
maintaineci its proper shape. See Figure 5.5. The inside edge of the template was
placed on the outside of the hull at appropriate locations. The hull was then sanded
or filled at that location until the hull shape exactly matched the shape of the template.
The mode1 was slightiy modified by memben of the Center For Marine Design
and Research. One inch was added to the freeboard height, and the transition from
hull bottom to skeg was 'sharpened'. This was done to correct perceivecl errors
created by the AutoShip software. There was no propeller shroud added to the model
because a shmud is not typical of a Cape-Island type vesse!. For the sarne reason,
the model ~ d d e r used was a simple rectangle rather #an a true scale version of the
nidder. A readily amilable propeller was used instead of a pmperiy scaled propeller
for mnvenience. The propeller used was a 114mm diameter, four bladed propeller
wiai a pitch of 137mm. The stem gear geometry is show in figure 5.6.
Figure 5.6 Rudder Geometry As Buiit By The Center For Marine Design And Research
The hull was kept relatively thin to reduce weight. A combination of crack filler
and enamel paint were used, in conjunction with wet sanding, to fiIl in and srnooth any
slight imperfections of the hull surface. The stem of the model was constmcted from
a piece of 6mm plywood. The skeg of the model was wnstnicted of pine and added
to the model. The entire model was then covered with West brand epoxy to make it
waterproof.
Chapter 5.3 Model Hardware
The electronics unit is powered by two 12 volt, 6.5 amp-hour gel-pack
batteries. This provides up to thirteen hours of operating time for the electronics. Any
auxiliary sensors added to the model would use this power supply and would reduce
the maximum operating time.
The model is powered by two bmshless, high torque, 24 volt electric motors.
See Figure 5.7. Electricity is supplied by four 12 voit, 10 amp-hour Dryfi batteries.
The positioning of these batteries is a convenient way to adjust the LCG and VCG to
the desired values.
The entire model has been made water-tight This is to protect the electronics
and moton from damage in the likely event of the rnodel overtuming. The model is
being tested in relatively high waves and is likely to experience a great deal of spray
and green water as well.
Figure 5.7 Mode1 outfitted with mators and power supply
Chapter 6.0 Development.Of Svstems For Measun'nn Model Action
8roaching is characterized by the inability of the rudder to control the yawing
motions of a ship. This does not necessarily result in the vessel coming broadside to
the waves and capsizing, but it is a possible occurrance. The process of broaching is
not instantaneous. Hence there may not be sufficient time during the relatively short
run in the wave tank for broaching to develop to the point where the model capsires.
Different cnteria are Iikely to be necessary to detemine if the model is
beginning to broach under given conditions. The two criteria that should be used are
the force on the model nidder and model yaw . If the force on the nidder drops
dramatically, it is assumed mat maneuverability has been lost and the model has
begun to broach. Also, if yawing occurs in the model and it cannot be corrected with
the model's wdder, then it may be considered that broaching has occured. Obviously,
the ability of the helmsman to respond to changing conditions will also be a factor
here.
The response time of the helmsman must be conectly scaled to successfully
model the broaching characteristics of the full-scale vessel. The tirne scale defived in
Chapter 4.1 1 must be used to scale the response of the helmsrnan.
This results in the requirement that the model nidder respond 2.6 times faster than
the full-scale rudder. The servos in the remote control unit used in the model are very
fast, and could easily be adjusted to approdmate the response times required.
In order to detemine if yawing occurs, it is necessary to quantify the motions
of the model and the force on the mdder under test conditions. This can be
accomplished using a variety of electronic senson and recording instrumentation.
The methods for achieving this that are described below quantify the force on the
rudder and the entire motion of the vessel. The full motion of the model is not
specifically required for this project, but it will provide data that might be useful for
studying other phenornena.
Chapter 6.1 Six Dearees Of Freedom Of A R i ~ i d Body
The model is a ngid body and hence has six degrees of freedom of motion,
three rotational and ttiree translational. The three rotational motions about the X,Y,
and Z axes are roll, pitch and yaw. The three translational motions in the X. Y. and Z
directions are known as surge sway and heave. See figure 6.1.
, - 7
_ - .. ,.
Figure 6.1 The Six degrees Of Freedom Of Motion Of A Rigid Body
Two rnethods for deteminhg the motions of the model were considered for
use in this expenment, an opticaf system and an accelerometer system.
Cha~ter 6.2 Methods For Determinina The Motion Of A Model
Chapter 6.2.1 The Strapdown Accelerometer Method
One method of determining the motion of a model uses accelerometers. The
simplest configuration of accelerometers is shown in figure 6.2. This setup uses six
accelerometers, two on each axk. The two accelerometers on the X-axis (1 and 2)
rneasure motion in the Y direction and motion about the Z - a s . The motion about the
z axis is derived from the difference in the motions of the two accelerorneters while
the motion in the Y direction is derived from the motion that is cornmon to the two
accelerorneterç.
Figure 6.2 The Six Accelerometer Method Setup
In a similar fashion, the accelerometers on the Y-axis (3 and 4) are used to
determine roll and heave, and the accelerometers on the 2-axis (5 and 6) are used to
detemine pitch and surge.
The above system uses the minimum number of accelerometers required to
measure al1 six motions of the model, but requires that they be rnounted in a 'three
dimensional" fashion. Another method of mounting the accelerometers is shown in
figure 6.3. It requires 7 accelerometers. but they can ali be mounted in the same
plane. This is often more convenient for rnounting in a cramped model and reduces
the effect of the instrumentation on the vertical mass distribution of the mode!. As
before. the accelerometers on the X-axis (1 and 2) measure yaw and surge. and the
accelerometers on the Y-axis (3 and 4) measure roll and heave. The difference in the
motions of accelerometen 5 and 6 produces pitch. The motion of accelerometer 7
gives surge.
Figure 6.3 The Seven Accelerorneter Method Setup
An accelerometer system has the added benefit of being portable. It can
easily be installed on another model or fulCscale vessel. Since it is a "stand-alone"
system, it can be used to test a vessel in the open ocean. However, testing a vessel
in the open ocean. or in any environment where the sea state was not artificially
created would require the use of a wave buoy or similar equipment to determine the
prevailing sea state.
The Strapdown Accelerometer Method for detemining the motions of a model
was used successfully by Myles (61. However, this method was found to be
unacceptable for peak mll angles over socty degrees. For angles greater than sixty
degrees. such as those encountered during extreme conditions like broaching, the
numerical integration techniques used by Myles failed to converge. The details of the
FFT-based integration technique used to solve for the motions of the model are given
in detail by Myles. The mathematics of this technique is not within the sape of this
thesis.
Chanter 6.2.2 The Manual Optical Trianaulation Method
Another rnethod that could be used to detennine the motion of the rnodel is the
manual optical triangulation method. Two sighting devices with swivel bases are
located at fwed. known locations on the edge of the test area. During testing, the
sighting devices are continuously aimed at a cornmon point on the model. Sensitive
potentiometen in the bases of the sighting devices are used in wnjunction with a
recording device. Simple triangulation can then be used to detenine the position of
the model at any given time. The system is inexpensive, and easy to use.
The are disadvantages to an optical triangulation system. The sighting
devices are operated by people and may not be aimed at the exact same spot at any
given time. This source of error increases dramatically at high speeds and
pmnounced rotational motion. This system only provides information on the position
and speed of the model. Another systern is required for information on the rotational
motions of the model.
Chapter 6.2.3 The OPTOPOS Method
The OPTOPOS system is a variation of the optical triangulation system that
uses five video cameras and six LEDs to determine the motion of a ffoating body.
The LEDs are positioned on the body and are pulsed sequentially. The cameras
digitize the position of each LED and send the information to a central computer.
Knowing the location of the cameras and the positions of the LEDs on the model, the
six degrees of motion c m be wmputed. With the software available, the computer is
theoretically capable of determining the position of an object with an accuracy of less
than 1 mm in an area 50 m long by 50 m wide by 4 m high (Sullivan p.2 #15). The
system requires very litde extra weight in the model.
Chapter 6.3 Determinina The Model Motion
The method selected for detemining the motion of the mode1 is a combination
of the two methods descnbed in Chapters 6.2.2 and 6.2. 'l. The optical triangulation
method is used for detemining the position and speed of the model. A srnail
electronics package containing accelerometers and a heading sensor is used to
detemine the remaining motion.
The ideal electronics package for recording the motions of the model would
meet several criteria. It would be compact and light enough so that it could be easily
mounted inside a relatively srnall model. It would be capable of recording reiatively
quick changes in motion. Also, voltage and current requirements would be such that
common portable power supplies would be adequate. Six, Twelve, or twenty four
volts DC would be best. A low arnperage draw would allow for reasonable battery life
and would reduce the need for a cooling system.
The electronics package should be capable of handling at least twelve data
channels. This allows eight channels to be used for motion sensors. The extra
channels a n be used for any other sensors that may be required.
A small electronics package for measuring and recording the motions of the
mode1 was designed and built at the Technical Univenrty of Nova Scotia. The unit is
120mm high by 200mm wide by 375mm long, weighs 5kg, and is fully portable. The
unit consists of a microprocessor, 3 accelerometers, a vertical reference sensor, and
an autopilot heading sensor. The autopilot sensor is capable of measuring changes
in orientation of 100 degrees per second. The senson provide information on the
rotational and translational motion of the vesse1 as well as pitch rate, yaw rate and
magnetic compass heading. The small size and Iight weight enable the unit to be
used in reiatively srnall models as well as full-scale vessels.
The electronics package records up to 16 channels of analog input. The
sensors for the first 9 channels are contained within the unit. The other 7 channels
are accessed through a teminal block on the side of the unit. Sensors for these
channels can be added as required. Currently, one of the extra channels is used to
wllect data from a load cell on the mode1 rudder. This load cell measures side thrust
on the rudder. The side thnist on the rudder is an indication of the lift generated by
the rudder to control the motion of the model. It is expected that this side thrust will
be greatiy reduced at or near broaching conditions. A CB9 connecter provides serial
InlOut connection to a PC or a radio modem. The small, 5 key, keypad and a two-line
liquid crystal display on the top face of the unit provide for set-up and control of the
unit's program.
The unit's program is resident in E-PROM in a microprocessor circuit board.
Once the program is set up, data acquisition start, stop, and download can be
controlled from the keypad or via the extemal PC or modem. This allows the unit to
be installed on a model and data can be logged on a shoreside PC via radio modem.
If installed on a large vessel, the unit can be diredy wired to a PC.
The built-in sensors for the first nine channels are configured for data
acquisition using the left hand nile. The left hand rule was used because it was flot
possible to adjust the heading sensor to use the right hand nile. Al1 other sensors
were adjusted to match the sign convention of the heading sensor. The sensors
operate on positive voltage with the mean voltage being neutral.
The nine channels record the following information.
Channel: 1 Surge output = negative = forward
The sensor is a Sundstrand QA-700 Accelerorneter
Channel: 2
Channel: 3
Channel: 4
Channel: 5
Channel: 6
Channel: 7
Channel: 8
Sway output = negative = port
The sensor is a Sundstrand QA-700 Accelerorneter
Heave output = negative = up
The sensor is a Sundstrand QA-700 Accelerometer
Roll Output = negative = port up
The sensor is a Watson Industries ADS-C232-?A
Roll Angle limits I 30 deg
Roll Rate
The sensor used is the channel4 accelerometer
Pitch Output = Negative = bow down
The sensor used is the channel4 accelerometer
Pitch Rate
The sensor used is the channel4 accelerometer
Heading
The sensor is a Watson Industries FGM-G1 00HS autopilot
sensor.
Channel: 9 Yaw Rate Output = Negative = bow to port
The sensor used is the channel8 sensor
The unit requires a 12VDC supply and draws 1 amp. Intemally, the 12 volt
supply is converted to 5 volts and k15 volts as required by the vanous wmponents.
The rnicroprocessor used is a Freedom 16 v1.12. It is powered by 5 volts DC.
None of the inputs must exceed this voltage or damage will occur. As some of the
sensors have outputs of I 5 V and 110V. signal conditioning is required. This is done
using two LT1007 low noise, high speed precision op-amps per channel. The fint o p
amp brings the input voltage down to I2.5V. The second ogamp uses a 2.5V
precision reference voltage as an offset, raising the output to 5V maximum. This
voltage is fed to two CD4051 eight channel analog multiplexers. The program
switches the two multiplexers, which in tum connects the 16 channels in sequence to
the microprocessor board.
Two modes of data logging are availabie with the cuvent setup. They are One Shot
Mode and Circular Buffer Mode.
Chapter 6.3.1 One Shot Mode
In this mode, data is collected and stored in a buffer until it is full. then data
acquisition stops. (509 seconds at 60Hz) The data has to be downloaded and the
buffer cleared before new data can be logged. This method of data collection would
be used when it was not practical to connect the electronics package to either a radio
modem or PC. This may be caused by weight or space restrictions in the model or
excessive radio interference.
Chapter 6.3.2 Circular Buffer Mode
In this mode, the program uses two buffers to store data. During setup, a data
acquisition time is set. The default is 2 seconds. Data is continuously collected and
stored in the first buffer. When the preset data acquisition time is reached, the
program switches ta the second buffer for storage. The first buffer is now
autornatically downloaded and w'll be ready for the next switch-over. The only limit to
the duration of data acquisition with this method is the amount of hard disk space on
the PC being used. The data logger can continue switdiing and downloading
indefinitely.
During program setup, any of the channels can be turned on or off. When
data is being acquired, al1 of the channels are scanned. However, only the 'on'
channels are downloaded.
The unit has extemal channel connections:
Channels 10, i i,12 allow for -1 0,0,+10 volt input
Channels 13,14,75,76 allow for û-5 volt input.
The terminal block also has a +5V output which is 'on' during data acquisition and 'off
when not logging. This permits a srnall L.E.D. or other device to be connected so a
visual signal from the model can indicate the status of the data logger.
Chanter 6.4 Model Control
As discussed. it is not sufficient sirnply to record the six motions of the model
during testing. To adequately test the handling characteristics of the model, it is
necessary to be able to maintain a given course and speed. To mntrol the rnodel
heading, a standard radio control unit is installed in the model. The radio control gear
used on the model is a Futaba SP-T4NBL AM75 digital proportional radio control unit.
It has four channels and operates at 75 rnegahertz in the AM band. It is assumed that
the operator of the radio contml unit will posses piloting skills comparable to the
operator of the full-scale vessel. The speed is controlled using an electronic speed
control connected to the radio unit
Chapter 6.5 Locations For test in^ The Model
After the model is instmmented, it must be tested. There are several places
the model c m be tested. There are essentially two types of testing facilities, indoor
and outdoor. Each has its own advantages and disadvantages. To test a mode1 for
its broaching characteristics, the body of water in which it is tested must be of
sufficient width and length to allow the model to experience quarteflng seas for a
significant period of time. The ease of data acquisition, the cost of the facilities, ease
of testing, operator comfort and cost must also be considered.
The University of Washington tests their models in a nearby freshwater lake.
The University of British Cotumbia tests their rnodels in a long, narrow wave basin on-
site. For this project, the most feasable location for mode1 testing is The lnstitute of
Manne Dynamics in St. John's, Newfoundland.
Chapter 6.6 The Wave Basin At The lnstitute of Marine Dynamics
The lnstitute of Manne Dynamics (IMD) ir! S t John's, Newfoundland has a
Multidirectional Wave Basin that is of sufficient length and width to test the mode1 for
its broaching charactenstics in quartering seas. The basin was designed and
equipped primarily for testing bottom-mounted structures, but it has a nurnber of
features that make it ideal for broaching tests. The basin is 50m long by 30m wide by
3m deep. It is equipped with National Research Council designed, vertical wave
absorbers that have an average reflection coefficient of less than ten percent.
There are two types of wave generaton installed in the basin," ... a segmented
wave maker, consisting of sixty. 0.5m wide by 2m high wave boards. to generate
short-crested (multidirectional) sea States and a 1 Sm wide wave rnaker to provide
irregular, long-crested waves (swell)." m These wave generaton are controlled by
comprehensive wave generating programs. They can provide a simulation of most of
the features of a natural sea state in both shallow and deep water conditions. The
generators can generate waves with a maximum height of 0.75m. The basin is also
equipped with mobile wind fan arrays if the effects of wind on broaching are to be
studied.
After the model is wnstmcted and outfïtted, it must be tested. The results
can then be cornpiled to create a database of information about the broaching
cha~cterïstics of the vessel.
Chanter 7.1 Test Conditions
The first step in testing is to determine the sea-states under which the full-
scale vessel is likely to operate. Some vessels, such as the Tuebor, cover a
relatively wide area during the course of operations. The Tuebor patrols coastal
waters, estuaries, and may even venture several miles off-shore. The area covered
extends from the Bay of Fundy to Halifax. It is necessary to take data from each of
these areas to detemine the types of sea-states the full-scale vessel will encounter.
The characteristics of the sea-states encountered by the vessel will also
change throughout the year. Some vessels operate only during relatively short tirne
frames dunng the year. These times of operation are dependent on the type of
catch for which the captain is fishing. The Tuebor is operated as a search and
rescue, as well as a fisheries patrol vessei. Therefore, it is at sea for the majority of
the year and hence it operates in ail the types of weather in which a Cape-Island
type fishing vessel would be operated.
A simple method for detennining the characteristics of the sea-states encountered
by the vessel is to place a wave buoy or similar instrument package in the ocean in
the area of vessel operations. However, it would be a lengthy and expensive
7 1
project to place wave buoys in the entire area of vessel operation for a complete
year. Fortunately, it is likely that information on the sea-sbtes likely to be
encountered already exists. The Department of Fishedes and Oceans has been
collecting this type of information al1 along the eastem seaboard for many years.
The data from the wave buoys provides a range of sea-states for which the model
should be tested.
Chapter 7.2 Model Testinq
Once the requirements for the testing environment have been detenined,
the model can be tested. There are four independent variables that are being
considered; Average Apparent Wave Height (H.), Average Apparent Period (T,).
Angle of Encounter (O), and vessel speed (v). The first two values are varied using
the wave generation hardware and software particular to the testing facility being
used.
The values of Ha and Ta generated by the wave rnakers in the wave basin
are detemined by the range of values selected for the operating conditions. They
are scaled as descnbed in Chapter 4.1 7 .
The model should be tested for different values of Ha and Ta ranging from
the scaled maximum to the scaled minimum of the values recorded.
The values by which Ha and Ta are incremented during testing should be
small enough that it is possible to obtain a good idea of exactly when the flsk of
72 broaching occurs. However, the interval should also be large enough that it
represents a measurable or noticeable difference to the pilot of the vessel.
Using a relatively large increment also decreases the number of data points
that have to be recorded.
The third variable, the angle of wave encounter, can be varied in one of two
ways. The model can be nin in a constant direction in the wave tank and the
direction of the generated waves can be varied. The degree to which the angle of
wave encounter c m be varied depends on the equipment in a given wave basin.
IMD has the capability to change the direction of the generated waves.
The angle of wave encounter c m also be varied by changing the direction of
the model in the tank. The waves woutd be generated in a constant direction and
the operator of the model would steer the rnodel at a given angle to the waves.
This method reduces the sophistication of the equipment required to test the model.
It is also the method that would be used to test the model in a natural environment
where the experirnenter has no control over the direction of the natural woves.
The drawback to using the model direction to change the angle of wave
encounter is that the length of the 'run' will decrease with increasing angle. For a
narrow rectangular basin. the direction of wave propagation is generally parallel to
the long dimension of the tank. This yields the greatest 'mn' length when the model
is travelling parallel to the wave direction (Le. O=oO or 0-90' ). As O approaches
90' (or 270'). the run length decreases until it is equal to the width of the tank. This
73
makes a long, skinny tank impossible to use at angles of O other than 0' and 180'.
This is not a problem at IMD due to their relatively wide tank.
The final parameter to be varied is the model speed. This is easily achieved
using an eleçtronic speed control hooked into the throffle channel of the remote
control for the model. The hrottle control would have to be calibrated using the
rnodel motion sensing equiprnent. The OPTOPOS System at IMD could be used
for this purpose. The model of the Tuebor would have a speed that ranges from O
to 1.65 mls. This is easily obtained with a small OC motor.
For each set of values of v, O, ha, and Ta, the mode1 should be tested for a
sufficiently long period of time to allow broaching to occur. Exactly what length of
time constitutes a "sufficiently long" period of time is not known. It will Iikely Vary
with the values of the independent variables being tested.
When testing a model in some facilities, it rnay not be possible to have a
continuous test that lasts for the required time. Therefore, the model should be fun
for a nurnber of Mals for each set of values of test data. The combined time for this
set of trials should equal or exceed the required test time. For tests with high model
speeds in short tanks, there is another factor which also must be considered.
Broaching is not an instantaneous process and hence there may be a time lag
between the point broaching begins and when it is recognizable to the
expenmenter. In general. care should be taken that the 'run' time is significantly
larger than the amount of time between the point broaching actually begins and the
point where the model is seen to slew sideways.
It is also important to note that for a given test, it rnay take several seconds
for the model to accelerate to the desired velocity and direction at the beginning of
the test fun. A test run that lasts hnrenty sewnds rnay only have ten seconds of
useful data at the correct speed and direction.
It is also useful to repeat certain tests to detemine the probability of
broaching ocwmng. For example, if a test is conducted 5 times for a given set of
conditions and the model broaches once, the nsk of broaching may be consideted
moderate. If the rnodel broaches in each of the five tests, the risk of broaching
should be considered extreme.
Chanter 7.3 Expected Model Behaviour Durina Broachinq
It is expected that when the model begins to broach, the force on the nidder
will drop, indicating a reduction in steeiing ability. Then, the mode1 will begin to
yaw. This yaw may increase to the point that the model overtums. The entire
model has been sealed so that, if it overtums, it will not swamp. The fact that
broaching has occurred should be readily apparent from the data.
References and Biblio~ra~hy
(11 Conolly. J.E. (1972), Paper 26. Stability and Controt in Waves: A Survey of
the Problern. Journal of Mechanical Engineering Science. p l 86-193
(21 Admiraltv Manual of Navigation, Vol. II. London, 1960. Her Majesty's
Stationery Office. pp. 203-205
[3] Canadian Coast Guard Marine Casualty Investigations. Report No.262:
Report of Investigation lnto the Cirwmstances Attending the Capsizing With
the Loss of One Life of the F.V. "Angie Derek II" on November 15, 1982 Off
Wedgeport. N.S.
[4] Report of an Investigation of the Stability Characteristics of New Brunswick
lnshore Fishing Vessels Less Than 80' -0" Length Overail For Department of
Fisheries. Maritime Marine Consultants, Saint John, N.B. 1976.
[5] Cornstock, John P. (Editor) (1 967), Principles of Naval Architecture (Revised
1980) The Society of Naval Architects and Marine Engineers. New York.
~494,495,491,492, 491.
[6] Miles. M.D., Measurement of Six Oegrees of Freedorn Model Motions Using
Strapdown Accelerorneters. Hydmulics Laboratory. National Research
Council, Ottawa, Canada.
m National Research Council, (brochure, 1993), Coastal and Multidirectional
Wave Basins.
IMAGE NALUATION TEST TARGET (QA-3)
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