Model Testing and Computational Analysis of a
High Speed Planing Hull with Cambered Planing
Surface and Surface Piercing Hydrofoils
by
Matthew Joseph Williams
B.S. Nuclear Engineering, Oregon State University (2006)
Submitted to the Department of Mechanical Engineering
and
Sloan School of Management
in partial fulfillment of the requirements for the degrees of
Naval Engineer
and
Master of Science in System Design and Management
at the
ARCHNES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
@Massachusetts Institute of Technology, 2015.
Signature redacted
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INSTITUTE
OF EECHNOLOLGY
MASsACHUSETTC
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JUL 3 0 2015
LIBRARIE
. of. Mechanical Engineering
b 1tment
and
Sloan School of Management
May 7, 2015
Certified by..........
Signature redacted
Stefano Brizzolara
Research Scientist and Lecturer
Assistant Director foflesearch, MIT Sea Ppant
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Certified by..... ..
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Accepted by ....
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atrick Hale
m Director
Supervisor
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David E. Hardt
Chairman, Department Committee on Graduate Students
Model Testing and Computational Analysis of a High Speed
Planing Hull with Cambered Planing Surface and Surface
Piercing Hydrofoils
by
Matthew Joseph Williams
Submitted to the Department of Mechanical Engineering
and
Sloan School of Management
on May 7, 2015, in partial fulfillment of the
requirements for the degrees of
Naval Engineer
and
Master of Science in System Design and Management
Abstract
As part of a 2014 thesis, the MIT Innovative Ship Laboratory (iShip) designed a
high-speed planing hull form that was based on the Model Variant 5631 developed at
the US Navy's David Taylor Model Basin [7] [3] [5]. This model was a variant of the
parent hull 5628. The 5631 variant was a model of the 47 foot Motor Lifeboat of the
US Coast Guard, which was a hard chine, deep-vee vessel.
Model 5631 had no step, with a 20 degree dead rise angle. The Clement method [4]
was used in order to design a cambered planing surface that would generate dynamic
lift and support most of the weight of the vessel. A second cambered step was
designed using an in-house lifting surface program. The step was designed such that,
at top speed, the entire hull aft of the step would be ventilated. To accommodate this
effect, the aft underbody design departed from the conventional dead-rise. Directional
stability of the model in the pre-planing regime was increased by incorporating three
vertices at the design dead-rise angle.
A set of super-cavitating, surface-piercing hydrofoils were designed to be attached
aft of the vessel transom in order to provide support and prevent re-wetting of the
afterbody. The constructed hydrofoils were positioned in a vee configuration, differing
3
from the anhedral design in the Faison thesis. A support manual control system for
the hydrofoils was designed as part of this thesis.
Known as Model 5631D, this dynaplane model underwent a series of tests at the
380 foot towing tank at the United States Naval Academy in Annapolis, Maryland,
over the course of several days. Several parameters were varied during the tests: the
cambered step (via the wedge insert), the carriage speed, and the model longitudinal
center of gravity (LCG). In this thesis, data from the series of tests of Model 5631D
will be compared to that of the tests of Model 5631 by combining methods from
Savitsky [15] and Faltinsen [8] for data scaling of planing vessels. Both models were
scaled to the same static waterline length in order to determine the efficacy of the new
design changes of Model 5631D in reducing total drag. Additionally, comparisons of
the test data were made to computational fluid dynamics models conducted under
the same conditions in the virtual environment.
An introduction and motivation for the thesis is presented in Chapter 1. Half and
full factorial statistical analysis was performed on the testing data and presented
in Chapter 2, along with the results of data scaling and comparison of Hull 5631D's
performance to the parent hull. Results of the CFD simulations along with calculation
of model stability is presented in Chapter 3. Conclusions and opportunities for future
work are given in Chapter 4. A full catalogue of the testing data is given in Appendix
A.
Thesis Supervisor: Stefano Brizzolara
Title: Research Scientist and Lecturer
Assistant Director for Research, MIT Sea Grant
Thesis Supervisor: Patrick Hale
Title: SDM Program Director
4
Acknowledgments
I would like to thank the US Navy for granting me the opportunity to pursue my
education at MIT, and Dr. Stefano Brizzolara for his enthusiasm, encouragement,
and expertise. Special thanks go to my mother Connie, my father Greg, and my sister
Kristi for their unconditional love and support, and to my girlfriend Kate for enduring
the long nights of only having HGTV as a companion while I toiled seemingly without
end at the office and in front of the computer.
5
6
Contents
1
2
3
15
Introduction
1.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
1.2
Planing Hull Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
Thesis Work
21
2.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2
M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.3
Hydrofoil Support System . . . . . . . . . . . . . . . . . . . . . . . .
24
2.4
Testing Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.5
Test Procedure
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.6
Analysis of Testing Data . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.6.1
2k
Factorial Design . . . . . . . . . . . . . . . . . . . . . . . .
34
2.6.2
Comparison To Parent Hull . . . . . . . . . . . . . . . . . . .
47
53
CFD Simulations
3.1
Introduction to Computational Fluid Dynamics
. . . . . . . . . . . .
53
3.2
Hull 5631D Simulation Set-Up . . . . . . . . . . . . . . . . . . . . . .
57
3.3
Simulation Validation . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
3.4
Longitudinal Stability Margin Computation
. . . . . . . . . . . . . .
75
4 Conclusions and Future Work
81
A Testing Data
85
7
A .1 Run 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
86
A.2 Run 14 ........
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87
A.3 Run 15 ........
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88
A.4 Run 16 ........
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89
A.5 Run 17 ........
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A.6 Run 18 ........
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A.7 Run 19 ........
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A.8 Run 20 ........
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A.9 Run 21 ........
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A.10 Run 22 ........
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95
A.11 Run 23 ........
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A.12 Run 24 ........
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A.13 Run 25 ........
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98
A.14 Run 26 ........
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99
A .15 R un 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 100
A .16 R un 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 101
A .17 R un 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 102
A .18 R un 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103
A .19 R un 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
A .20 R un 33 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. 105
A .21 R un 34 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . ... 106
A .22 Run 35 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . ... 107
A.23 Run 36 ...... ..
...........
....................108
A .24 Run 37 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . ...
..
109
A .25 Run 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A .26 Run 39 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 111
A .27 Run 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A .28 Run 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A.29 Run 42.. .......
...................................
114
A .30 R un 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8
A.31 Run 44.
116
A.32 Run 45.
117
A.33 Run 46.
118
A.34 Run 47.
119
A.35 Run 48.
120
A.36 Run 49.
121
A.37 Run 50.
122
A.38 Run 51
123
A.39 Run 52.
124
A.40 Run 53.
125
A.41 Run 54.
126
A.42 Run 55.
127
A.43 Run 56.
128
A.44 Run 57.
129
A.45 Run 58.
130
A.46 Run 59.
131
A.47 Run 60.
132
A.48 Run 61
133
A.49 Run 62.
134
A.50 Run 63.
. . . 135
A.51 Run 64.
. . . 136
A.52 Run 66.
. . . 137
A.53 Run 67.
. . . 138
A.54 Run 68.
. . .
139
A.55 Run 69.
140
A.56 Run 71
141
A.57 Run 72.
. . .
142
A.58 Run 75.
. . .
143
A.59 Run 78.
. . .
144
A.60 Run 79.
. . .
145
9
A .61 R un 80 . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 146
A .62 R un 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A .63 R un 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
A .64 R un 83 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
A .65 R un 84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
A .66 Run 85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
A .67 R un 86 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A .68 R un 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
A .69 R un 91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
A .70 R un 92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
A .71 Run 93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
10
List of Figures
1-1
Pressure Distribution of a Flate Plate at an Angle of Attack . . . . .
18
2-1
Design of Cambered Step . . . . . . . . . . . . . . . . . . . . . . . . .
22
2-2
Plate Inside Model For Towing Carriage Attachment
. . . . . . . . .
23
2-3
Model With Static Waterline Shown
. . . . . . . . . . . . . . . . . .
24
2-4
Model Inverted, Step Removed, Stations and Waterline Shown . . . .
24
2-5
Photograph of Hydrofoils and Control System . . . . . . . . . . . . .
25
2-6
CAD Model of Hydrofoils and Transverse Support Plate
. . . . . . .
27
2-7
CAD Model of Hydrofoil Support System Bracket . . . . . . . . . . .
28
2-8
CAD Model of Hydrofoil Support System Tie Rod . . . . . . . . . . .
28
2-9
CAD Model of Hydrofoil Support System Hinge . . . . . . . . . . . .
29
2-10 CAD Model of Hydrofoil Support System . . . . . . . . . . . . . . . .
29
2-11 Underwater Photo Captured During Model Testing, Annotations Added 33
2-12 Savitsky and Morabito Spray Pattern Predictions . . . . . . . . . . .
33
2-13 Normal Probability Plot with Hydrofoil Effects Aliased . . . . . . . .
38
2-14 Normal Probability Plot with Interaction Terms and Hydrofoil Effects
A liased . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2-15 Normal Probability Plot, 23 Full Factorial Design . . . . . . . . . . .
42
2-16 LCG Main Effect Plot on Trim Fluctuations, Full Factorial Design . .
42
2-17 Normal Probability Plot, Drag Half Factorial Design, Hydrofoils Aliased 43
2-18 Normal Probability Plot, Drag Full Factorial Design, No LCG . . . .
46
2-19 Wedge Main Effect Plot . . . . . . . . . . . . . . . . . . . . . . . . .
46
2-20 Hydrofoil Main Effect Plot . . . . . . . . . . . . . . . . . . . . . . . .
46
11
47
2-22 Normalized Resistance for 5631D and Parent Hull . . . . . . .
51
3-1
Overset Mesh Data Transfer Schematic . . . . . . . . . . . . .
.
61
3-2
Truncated Test Data, 42% LCG, Hydrofoils at -2, +2.5 position.
64
3-3
Pitch, 42% LCG, Hydrofoils at -2, +2.5 position.
. . . .
. . . . . .
64
3-4
Heave, 42% LCG, Hydrofoils at -2, +2.5 position.
. . . .
. . . . . .
65
3-5
Resistance, 42% LCG, Hydrofoils at -2, +2.5 position. . .
. . . . . .
65
3-6
Simulation Mesh on a Longitudinal Cross-Section
. . . .
. . . . . .
66
3-7
Simulation Trim Plot . . . . . . . . . . . . . . . . . . . .
. . . . . .
67
3-8
Simulation Results, Total Model . . . . . . . . . . . . . .
. . . . . .
68
3-9
Simulation Results, Hydrofoils . . . . . . . . . . . . . . .
. . . . . .
68
3-10 Simulation Results, Afterbody . . . . . . . . . . . . . . .
. . . . . .
69
3-11 Simulation Results, Forebody . . . . . . . . . . . . . . .
. . . . . .
69
3-12 Run 19 Underwater Photo . . . . . . . . . . . . . . . . .
. . . . . .
70
3-13 View of Simulation Underhull and Free Surface
. . . . .
. . . . . .
70
3-14 Simulation Volume of Fluid on Hull Bottom . . . . . . .
. . . . . .
71
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2-21 Speed Main Effect Plot . . . . . . . . . . . . . . . . . . . . . .
3-15 Simulation Volume of Fluid on Cambered Surface with Strain Rate
.
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3-16 Simulation Volume of Fluid on Hydrofoil Upper Surface Showing Ven72
3-17 Simulation Pressure Coefficient on Hull Bottom . . . . . . . . . . .
73
.
.
tilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-18 Simulation Pressure Coefficient on Cambered Surface with Strain Rate
.
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
3-19 Zero DOF Simulation Cambered Surface Cp, 2.250 Degrees Trim by
the Stern.......
..................................
78
3-20 Zero DOF Simulation Cambered Surface Cp, 2.75' Degrees Trim by
.
the Stern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
3-21 Zero DOF Simulation Cambered Surface Cp, 3.25' Degrees Trim by
.
the Stern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
79
List of Tables
2.1
Hull 5631Specifications . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.2
Speeds Used During Testing . . . . . . . . . . . . . . . . . . . . . . .
31
2.3
24-1 Half Factorial Alias Structure
. . . . . . . . . . . . . . . . . . .
36
2.4
Table of Contrasts, Hydrofoil Aliased . . . . . . . . . . . . . . . . . .
36
2.5
Table of Effects and Coefficients, Hydrofoil Aliased
. . . . . . . . . .
37
2.6
Table of Contrasts, Hydrofoil Aliased, Interaction Terms Included . .
39
2.7
Table of Effects and Coefficients with Interaction Terms, Hydrofoil
A liased . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
. . . . . . . . . . . . . .
41
. . . . . . . . .
41
2.8
Table of Contrasts, 23 Full Factorial Design
2.9
Table of Effects and Coefficients, 23 Factorial Design
2.10 Table of Effects and Coefficients with Interaction Terms, Hydrofoil
Aliased, Drag Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
. . . . . . . . . . .
44
2.11 Table of Contrasts, 23 Full Factorial Drag Design
2.12 Table of Effects and Coefficients with Interaction Terms, Full Factorial
D rag D ata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
. . . . . . . . . . . . . . . . . . . . . . . .
70
3.1
Initial Simulation Results
3.2
Second Simulation Results, Pre-Positioned Heave
. . . . . . . . . . .
74
3.3
Fixed Draft, Zero DoF Simulation Data . . . . . . . . . . . . . . . . .
77
13
14
Chapter 1
Introduction
1.1
Background
In the early days of the Naval Architecture discipline, vessel speeds were thought to
be limited to what was called hull speed. As a displacement vessel travels through
the water, the high pressure area at the bow produces a bow wave crest.
At a
certain speed, the so-called hull speed, the wave system was such that the midships
region of the boat appeared to be trapped in a bow wave trough. This corresponded
to a large increase in drag due to the wave system.
The additional drag created
by increasing speed beyond hull speed was largely an insurmountable task by the
propulsion standards of the time. Hull speed, in today's nomenclature, corresponds
to a Froude number of approximately 0.43.
Traditionally, the Froude number is a non-dimensional quantity defined by the vessel
length:
(
FrL =
SLLW L
where LWL is the length of the water line, v is the vessel speed, and g is the gravi-
15
tational constant. This parameter is a ratio of the vessel speed to the characteristic
wave speed, and its primary purpose is to compare the wave-making resistance of
vessels of various sizes. The empirical formula for hull speed 116] is
Vhull
=1.34
(1.2)
LWL
Inserting Equation 1.2 into Equation 1.1 gives
FrL
1.34 LWL
Ag LW L
0. 43
(1.3)
V
At hull speed, large values total resistance occurred due to an increased wave-making
resistance from the interaction of the bow and stern waves. Displacement vessels
have a large wetted area, and this area creates surfaces for frictional drag as the
water moves from a region of zero speed at the hull to the free-stream velocity at
the outer edge of the boundary layer. The combination of these resistances presented
quite a challenge for propulsion technology of the period.
The advent of planing
technology sought to drastically reduce the frictional resistance component of vessel
drag.
The earliest documented use of planing technology was an 1898 sailboat, said to be
capable of twice hull speed. Initially, beyond-hull-speed vessels maintained the roundbilge form of their displacement counterparts, and, instead of reducing the frictional
drag through the hydrodynamic lift development in planing vessels, reduced the pressure drag on the hull through controlling streamlines, which will be discussed in
Section 1.2. Since then, planing vessels have become ubiquitous, and the features
of planing vessels have become more sophisticated. At the turn of the century, investigations into planing technology increased, witha peak in interest corresponding
to the outbreak of World War II. The National Advisory Committee for Aeronautics (NACA), the predecessor to the National Aeronautics and Space Administration
16
(NASA), began research into planing technology specifically for application to sea
planes. Eventually this interest trickled into marine applications. Daniel Savitsky
published the seminole article Hydrodynamic Design of Planing Craft in 1964, which
continues to influence the design of planing vessels today. During this time, many
models were developed and tested at the US Navy's David Taylor Model Basin in
Bethesda, MD. Current planing technology owes much to the researchers involved in
this testing and development.
1.2
Planing Hull Theory
Traditional displacement vessels rely entirely on the buoyancy force to support the
weight of the craft and to keep it afloat. As the vessel is propelled through the water,
some hydrodynamic lift is developed, however most of the weight of the boat is still
supported by buoyancy. Displacement-type vessels have round bilges, which were
designed in order to prevent flow separation to minimize residual drag [161. With
a properly designed hull, as speed is further increased, more hydrodynamic lift is
developed, and the vessel's center of gravity begins to rise which, in turn, reduces the
buoyant force on the hull. Once the hydrodynamic lift is supporting the majority of
the weight of the vessel, the boat is said to be planing.
The simplest form of a planing hull is the flat plate. Several experiments performed by
Savitsky identified the pressure distribution on a flat plate at an angle of attack to the
incoming flow [7]. A generalized pressure distribution is shown in Figure 1-1.
Round-bilge hulls were capable of exceeding hull speed by taking advantage of streamline curvature, which allows for some control over the pressure distribution on the hull.
Streamline effects on a round-bilge hull operating at "displacement speeds" will be
discussed below.
A streamline is a line to which velocity vectors in a uniform flow field are tangent. In
order for a three-dimensional infinitesimal fluid parcel to travel along a streamline,
17
._...
..........
...
PRESSURE DISTRIBUTION
I
2
2-pv
LEVEL WATER
SPA SURFACE
8= SPRAY TWtCKNESS
SPRAY ROOT
STAGNATION LINE
Figure 1-1: Pressure Distribution of a Flate Plate at an Angle of Attack
it must be subjected to a pressure differential that balances the centripetal force
experienced as the parcel travels on a curvilinear path. From classical mechanics,
this centripetal force is
PV dxdydz
r
(1.4)
where r is the radius of curvature. Assume this force to be acting in the positive
y direction in an inertial cartesian coordinate system that is attached to the fluid
parcel. If the bottom of the parcel is subjected to a pressure p, then due to the
pressure differential, the top is subjected to p+ -Pdy. If the particle is not accelerating,
summing the forces in the y-direction yields
Fy = 0 = pdxdz -
pdxdz +
dxdydz
+
dxdydz
(1.5)
and therefore
Op
Oy
pV 2
r
18
(1.6)
The solution of Equation 1.6 shows that pressure increases with increasing streamline
radius of curvature [11]. That is, if the ship hull is on the convex side of a streamline's
curvature, a positive pressure gradient results. Simultaneously, the rate of change of
pressure decreases with increasing radius. Conversely, if the hull is on the concave
side of a streamline's curvature, a negative pressure gradient results. Therefore, it
can be seen from Equation 1.6 that the convex surface of a round bilge hull at normal
operating speed will lie in an area of decreasing streamline radius of curvature, that is
on the concave side of a curvilinear streamline. Negative pressures will result on the
hull, but these effects are relatively small when compared to the residual resistance
component of flow separation that they are designed to prevent [16].
Ultimately, however, the frictional component of total resistance from the boat's
wetted area limited the top speed. A planing craft looks to greatly reduce the wetted
area by having a large portion of the boat come out of the water during high-speed
operation. As previously discussed, the vessel's center of gravity will begin to rise
when hydrodynamic lift is generated. If the vessel can be supported by the small area
producing the lift, then the viscous drag can be greatly reduced. As planing vessels
operate at different speeds, the amount of hydrodynamic lift varies, and therefore
the corresponding LWL varies.
For this reason, use of the waterline length as a
defining parameter in the Froude number for planing vessels is inappropriate. Instead,
defining the planing vs. non-planing flow regime uses the volumetric Froude number
(FV):
V
FnV
(1.7)
where v is the vessel speed, g is the gravitational constant, and the cubic root of V,
the vessel's static displaced volume, has replaced the waterline length. Displacement
vessels operate at volumetric Froude numbers < 1.3. [2], which roughly corresponds
to the length Froude number definition of the subcritical flow regime (F < 1).
19
The flat plate, while the simplest planing surface, is also capable of producing the
most lift. However, this design is impractical, due to the large accelerations produced
when the flat plate is subjected to slamming forces, such as would be experienced
after a broaching event at high speed. This effect is mitigated by a dead rise bottom.
Dead rise is the angle formed by the hull bottom with a horizontal plane. Modern
planing boats have a constant dead rise angle until the bow region, referred to as
a warped hull. Increasing the dead rise will decrease slamming accelerations, but
in turn will decrease the hydrodynamic lift developed at a given volumetric Froude
number. Additionally, the dead rise prevents convex hull shapes aft of the bow. As
shown previously, convex streamline curvature causes a negative pressure gradient in
the direction of decreasing radius of curvature, which would be detrimental to the
hydrodynamic lift on the underhull.
Besides dead rise, there are other essential features of a planing monohull. To prevent
negative pressures with respect to atmospheric pressure, and to further reduce the
frictional resistance, there must be flow separation at the stern and along the sides
[8].
The former is accomplished by a transom stern, and the latter by spray rails and hard
chines. Hull steps are another common feature of planing vessels, and are a creature of
great variability regarding their orientation. Most commonly, steps occur transversely
and are such that the "ledge" faces away from the incoming flow. The purpose of a
step is to further decrease the hull wetted area by creating full flow separation and a
region of ventilation aft of the step. For boats without some type of hydrofoils or other
lifting surfaces near the transom, the hull body aft of the step will be rewetted in order
to provide support. This aft rewetting can be avoided if lifting surfaces are provided
near the transom. This was included in the design of the 5631D dynaplane.
20
Chapter 2
Thesis Work
2.1
Background
The basis of the Dynaplane design that was tested at the US Naval Academy is the
parent hull of series 5631, which underwent a number of tests at the David Taylor
Model Basin (DTMB) in Bethesda, Maryland. The parent hull had a dead rise of 20
degrees, a pair of longitudinal spray rails, and no step. Brizzolara and Faison (2014)
aimed to improve upon the parent hull by applying Clement's dynaplane method.
The parent hull specifications are shown in Table 2.1.
Model 5631
LBP
B
T
L/B
B/T
Deadrise [deg]
Displacement
10 ft [3.05 m]
2.24 ft [0.683 m]
0.510 ft [0.155 ml
4.47
4.39
20
375 lb [170 kg]
Table 2.1: Hull 5631 Specifications
Unique features added to the Dynaplane model were a cambered planing surface and
aft hydrofoils. A swept-back step was included at the trailing edge of the cambered
21
surface. The hydrofoils' vertical position and angle of attack are adjustable via a
system designed by the author. Designing a cambered planing surface was intended to
increase the developed lift force over a flat-bottom design. The 5631 Dynaplane design
used a swept-back design, shown in Figure 2-1. Two cambered surfaces were designed,
one by Leon Faison and the other by Giuliano Vernengo, the former using the method
of Clement [4], and the latter using a self-developed lifting surface program.
605.35,
1979
-
-
-
57.66
Figure 2-1: Design of Cambered Step
2.2
Model
The model was designed in Rhinoceros 5.0. An STL file was created and sent to
a private company for construction. The model was made from wood, with a layer
of paint placed over the underhull, side hull, and transom. The top of the model
was designed to be open, and a metal plate was placed inside the model to provide
an attachment point for the towing carriage. A photograph of the plate is shown
in Figure 2-2. The open top of the model also allowed for control of LCG through
the placement of weights. The model was 1.5 m long overall, and 0.315 m at the
beam.
The model was designed to have two separate cambered surfaces, the trailing edge of
which forms a transverse, swept-back step. These surfaces were designed to be held in
place by an interference fit only. That is, there were no features for attaching the cambered surface to the model hull. Instead, the tight tolerances and the pressure from
the generated lift were used to keep the cambered surfaces in place. This eliminated
the use of bolts and corresponding drilled holes. The underhull aft of the step had a
22
Figure 2-2: Plate Inside Model For Towing Carriage Attachment
tri-vertex design, with each having the designed deadrise angle. Although completely
ventilated at design speed, this afterbody design increased directional stability in the
pre-planing regime, and during times when the afterbody was wet, as when operating
at lower FV.
Upon completion, the model was shipped to the USNA Hydrodynamics Laboratory.
Station markings were drawn on the hull, and the model was placed in the tank in
order to note the static waterline. This waterline was also drawn on the hull. Both
of these can be seen in Figures 2-3 and 2-4.
After initial placement in the towing tank, it was noted that some water was entering
the model through imperfections, particularly at the vertex of the cambered surface
insertion point, and the trailing edge of the cambered surface. These areas were
sanded and epoxied. With the cambered surface inserted, the leading edge was treated
with a layer of putty in order to fair the edge and prevent unwanted flow disturbances
due to the discontinuity. To prevent further issues with water logging, the model was
23
Figure 2-3: Model With Static Waterline Shown
Figure 2-4: Model Inverted, Step Removed, Stations and Waterline Shown
removed from the water after testing was complete each day. A layer of plastic was
placed over the top of the model at the bow region to prevent taking on water from
spray during testing.
2.3
Hydrofoil Support System
Since the portion of the hull aft of the cambered step was intended to be completely
ventilated, hydrofoils were designed to provide lifting force for the boat at the transom. Non-stepped planing hulls rely on a rewetted portion of the underhull near the
transom to provide this support. At full speed, the step was designed to support 90%
24
of the weight of the boat, while the hydrofoils were designed to carry the remaining
10%. It was therefore necessary to design a system that would support the hydrofoils
while simultaneously allowing for their adjustment. A picture of the manufactured
system, out of the water and inverted, is shown in Figure 2-5.
Figure 2-5: Photograph of Hydrofoils and Control System
As designed, the lift generated by the hydrofoils were sensitive to the angle of attack
and vertical submergence. The nominal testing condition was to pre-adjust the hydrofoil angle such that zero angle of attack existed while the boat was operating at
design trim conditions. Vertical positioning was also available to increase or decrease
the lift produced in order to achieve the design trim of 3.5'. From these requirements,
two explicit and one derived design objectives existed:
1. The hydrofoil vertical position must be adjustable.
2. The hydrofoil angle of attack must be adjustable.
3. The system must be mianufacturable.
25
The support system was required to meet all of these objectives, while also remaining
clear of the water to prevent parasitic frictional drag.
In order to meet the first
and second objectives, the system had to be designed such that there were only two
degrees of freedom, namely vertical translation and rotation about a transverse axis.
Additionally, these motions needed to be decoupled, so that rotation does not result
in vertical translation, and vice versa.
The hydrofoil configuration was that of a "vee." The lower sections of the hydrofoils
near the trailing edge were very thin, and therefore the support system needed to also
be designed to provide structural support for the hydrofoils, specifically to prevent
excessive bending moments at the hydrofoil vertex from generated lift. Rhinoceros 5.0
was the CAD tool used to design the hull, hydrofoils, and support system. To provide
structural support, a transverse plate was connected to the upper regions of the
hydrofoils. To ensure that this plate remained clear of the water, the non-functional
upper section of the hydrofoils were extended. With this configuration, the transverse
plate would absorb some stress in compression, and also change the bending mode of
the hydrofoils. Without the transverse plate, the hydrofoils would have structurally
behaved similar to a "fixed-free" cantilevered beam, with the very thin hydrofoil
vertex providing all counter forces and moments to maintain the system in equilibrium
in the presence of lifting forces. With the transverse plate, the hydrofoils became
"fixed-fixed," with the plate available to provide counter-moments at its connection
to the hydrofoil, and to provide a larger footprint for reaction force distribution in
response to the lift force. A view of the hydrofoils and transverse plate CAD model,
viewed from the trailing edge, is shown in Figure 2-6.
This hydrofoil and transverse plate system was then needed to have the capability
to be rotated as a rigid body to provide angle of attack adjustment.
To simplify
construction, the system was to be designed such that the rotation and translation
components were integrated, while simultaneously providing the desired motion decoupling. The guiding principle of this design process was to start with simple systems and components, and to add complexity where needed to achieve the system
26
Figure 2-6: CAD Model of Hydrofoils and Transverse Support Plate
goals.
A bracket was designed to provide vertical positioning of the hydrofoils via a pin
connection.
For additional stability, and to prevent undesired transverse motion,
vertical positioning was accomplished by two brackets, positioned near the extremities
of the transverse plate.
The bracket and holes were designed for manufacturing;
that is, they were made large enough to allow them to be machined or 3D printed
accurately. The dimensions were 4.4 cm wide and 7.2 cm tall, with a series of seven
holes, 6.4 mm in diameter and equally spaced at 1 cm, center-to-center. The smallest
dimension on the brackets was the backplate width of 5 mm, which provided the
connection point to the boat transom. A slot in the center of the brackets allowed
for a moveable piece to translate. The CAD model of the bracket is shown in Figure
2-7
The translatable tie-rod had a section which mated, via pins, to the inside of the
brackets in order to fix the hydrofoil vertical position, shown in Figure 2-8.
The
rectangular cross-section of the tie-rod prevented rotation about the pin connector.
The rounded end of the tie rod was designed to fit inside a hinge, shown in Figure
2-9, in order to control the hydrofoil angle of attack.
Rotation of the of the hydrofoils and transverse plate was prevented by a friction
27
Figure 2-7: CAD Model of Hydrofoil Support System Bracket
Figure 2-8: CAD Model of Hydrofoil Support System Tie Rod
connection. The hinge pin had a threaded end, where a nut was tightened against
the hinge surface. The entire hydrofoil support system is shown in Figure 2-10.
Measurement of the hydrofoil angle of attack during the tests was performed by use
of a bevel protractor, using the transom as a reference. Positive angles were defined
as rotation that increased the hydrofoils angle of attack, or counter-clockwise rotation
when viewed from the starboard side. This is the opposite of the sense of angles in the
computational fluid dynamics simulation, as will be discussed later. The definition
of the y-axis in the simulations resulted in negative angles orienting the model in a
"bow-up" configuration.
28
Figure 2-9: CAD Model of Hydrofoil Support System Hinge
Figure 2-10: CAD Model of Hydrofoil Support System
2.4
Testing Facility
The model was tested at the US Naval Academy Hydrodynamics Laboratory. The
tank used for testing measured 380' long, 26' wide, and 16' deep. At the starting end
29
of the tank was a "wave beach," specifically designed to reduce the time required for
waves in the tank to dissipate. A wave maker existed at the south end of the tank,
but was not used for the calm water testing.
A high-speed carriage was used for towing of the model. A stand-alone computer
on the carriage collected and stored information from the sensors, and mirrored this
data to a computer in the control room. The carriage was towed by cables that were
wound by two 400 HP motors. The stopping point of the carriage was an input to
the control system, and was decided by the operator ahead of time. The carriage was
stopped at 0.25G.
Attachment of the model to the carriage allowed it to heave and pitch freely, and to be
constrained in the other degrees of freedom. During initial trial runs, the test engineer
William Beaver noted that the model tended to a bow-down configuration until it was
on the trim and heave stops. As a correction, the model was pre-positioned to be
close to its operating heave and to have a slight initial trim. Additionally, the trim
was limited to be bow-up by attaching a string to the bow that was taught in an even
keel condition.
2.5
Test Procedure
The model variables during the test runs were speed, cambered step (one of two
different designs were inserted at a time), hydrofoil vertical position, hydrofoil initial
angle of attack, and longitudinal center of gravity. The two step inserts were held
in place by friction, reinforced by generated lift. In order to avoid undesirable flow
separation due to non-flush fitting between the step and the hull, putty was used as
a leveling agent. Speeds used during the testing and their corresponding volumetric
Froude numbers are shown in Table 2.2.
An underwater camera was positioned at the bottom of the tank to capture still
images of the vessel as it passed on the surface. Photos were automatically timed
30
Speed [fps]
Speed
31.137
28.541
25.939
23.339
20.739
18.136
9.465
8.676
7.885
7.095
6.304
5.513
FnV
[mps]
6.005
5.505
5.003
4.501
4.000
3.498
Table 2.2: Speeds Used During Testing
based on the carriage speed. Images were sent to a monitor in the control room.
These images played an important role in the testing process. At a given carriage
speed, the model wedge and LCG were held constant. The process could be thought
of as an embedded "for" loop used in many computing languages. For a given step
insert, an LCG was selected. For this LCG, a particular carriage speed was run. For
this particular carriage speed, the hydrofoil angle and vertical position were adjusted
to achieve the desired trim. Variables were iterated from inside the "for loop" to the
outside. That is, the hydrofoils were adjusted until the trim condition was satisfactory,
and then the speed was changed. Once all the speeds had been run, the LCG was
adjusted, and all of the speeds run again for this LCG, adjusting the hydrofoils as
necessary for trim. Once all LCG positions were tested at all speeds, the wedge was
changed and the process repeated. Considering the number of speeds, LCG locations,
and step inserts, the minimum number of testing runs required was 36.
In reality, the number of runs was much more, due to duplicate runs at different
hydrofoil configurations. The design trim at full speed was 3.5'. During testing, the
image from the underwater camera was consulted to determine hydrofoil positioning.
The leading edge of the step was visible on the image, as was the stagnation line and
whisker spray line. It was desired to have the stagnation line correspond with the
leading edge of the cambered surface. The hydrofoils were adjusted to generate more
or less lift depending the trim of the model. Additionally, trim and heave data were
available in the control room to assist in this process.
31
A typical underwater image is shown in Figure 2-11, with annotations added by the
author. Testing conditions in this photograph were Wedge B, 42% LCG, hydrofoils at
pin 2 (2 cm down from the top position), -4' initial angle of attack, carriage speed
18.133 fps. Both the spray root line and stagnation line are clearly visible in the
image. The region between the two lines, most readily seen on the port side, is the
whisker spray while attached to the hull, and the main spray blister once separated
from the hull. These images were available to the testing team immediately following
a run, and were used to help guide the hydrofoil configuration to achieve the desired
trim.
32
Figure 2-11: Underwater Photo Captured During Model Testing, Annotations Added
water intersection
r
b
stagnation line
chine
~
keel
spray root Iine
1-----.1
1
main spraY-
blister
Figure 2-12: Savitsky and Morabito Spray Pattern Predictions
The underwater photo is shown compared to the underhull spray conditions analyzed
by Savitsky and Morabito in Figure 2-12 . [17]
The model was accessible while attached to the carriage via an inflatable raft , and
hydrofoil position was adjusted at the highest speed in order to achieve the desired
stagnation line position with respect to the cambered surface leading edge. Data
33
collected during the tests were recorded using MATLAB and exported to an Excel
spreadsheet and then manually truncated to eliminate the beginning and end of the
runs when the carriage was accelerating. The truncated data was then averaged.
In order to aid in CFD simulation of the current model and future models, it was
desired to know which factors had the greatest effect on drag and on the the dynamic
instabilities observed during some of the test runs. These dynamic instabilities manifested themselves primarily as "porpoising," where the model never reached a stable
trim angle, but instead experienced trim oscillations that persisted throughout the
entire run.
The truncated and averaged data for each run is presented in Appendix A. In order to
monitor for whether or not a test run experienced trim oscillations, the standard deviation of the trim data for the truncation period was calculated. The trim fluctuations
then served as an output for statistical analysis of the data.
2.6
2.6.1
Analysis of Testing Data
2k
Factorial Design
The variables available during the test runs, as stated previously, were cambered
surface insert (or wedge), LCG, hydrofoil vertical position, hydrofoil angle of attack,
and speed. Most of these variables lend themselves well to a
2k
factorial statistical
analysis, with the exception of the hydrofoil. Although the hydrofoil vertical position
is a discrete variable, the angle of attack is a continuous variable due to the design
of the hydrofoil support structure. Furthermore, since the hydrofoil was adjusted ad
hoc in order to achieve the desired full-speed trim angle, there is not repetition in the
hydrofoil configuration across the other variables. It was desired, therefore, to treat
the hydrofoils differently.
34
To perform the analysis, two levels of each variable were selected. In the case of the
cambered surface insert, there were only two levels, since there were only two inserts.
Two LCG's were selected that had similar hydrofoil configurations at each speed, and
the speeds selected were full and one sub maximal speed. This led to the following
level selection:
1. Wedge: A and B.
2. LCG: 42% and 44%.
3. Speed: 31.1 fps and 23.3 fps.
If the hydrofoils were included as a single variable, the number of treatment combinations would be 24
=
16. However, due to the large variability in hydrofoil configura-
tion, this type of treatment was not supported. Analysis of the data could continue,
however, using a half-factorial model with an aliasing structure.
Assigning letters to the design variables:
1. Wedge type = A
2. LCG = B
3. Speed = C
4. Hydrofoil configuration = D
Modulo 2 arithmetic yields the alias structure for the 24-1 half factorial shown in
Table 2.3
"I" is the regression intercept, and is typically estimated using an interaction of all
main design variables, as is the case here. The main design variables, A, B, C, and
D, are aliased with the 3-term interaction variables. Specifically, the term ABC will
be used as a stand-in for the variable D, hydrofoil configuration. The alias structure
reveals that a model can be generated with terms for the intercept and each main
35
I = ABCD
A
B
C
D
AB
AC
AD
BCD
ACD
ABD
ABC
CD
BD
BC
Table 2.3: 24-1 Half Factorial Alias Structure
effect. The two-factor interactions are aliased with each other.
The table of contrasts is constructed by renaming the variables to x1 for the wedge, X
2
for LCG, x 3 for speed, and X4 for the hydrofoil. Per the alias structure, the hydrofoil
variable is computed by multiplying the other three. Taking X 4 = -(X
1 *
x 2 * X 3 ), the
table of contrasts is shown in Table 2.4
I
1
1
1
1
1
1
1
1
xl
-1
1
-1
1
-1
1
-1
1
x2
-1
-1
1
1
-1
-1
1
1
x3
-1
-1
-1
-1
1
1
1
1
x4
1
-1
-1
1
-1
1
1
-1
d
a
b
abd
c
acd
bcd
abc
y
1.05
1.46
0.07
0.218
0.2
0.1
0.25
0.044
Table 2.4: Table of Contrasts, Hydrofoil Aliased
The first column of Table 2.4 represents the intercept. "-1" represents a design variable
in its low state, and "1" is the high state. The sixth column shows the letter(s) of the
design variables in their high state. The last column, labeled "y," is the experimental
yield, which in this case is the standard deviation of the trim angle for the testing run
represented in that row of Table 2.4. For example, the first row of Table 2.4 indicates
that design variable d, also called 4, which represents the hydrofoil configuration, is
the design variable in its high state. The other design variables are all in their low
states. The standard deviation of the trim data from the model tests corresponding
to this condition is 1.05'.
36
The effect of each design variable is calculated by performing the vector multiplication
of the corresponding transposed column from the table of contrasts with the column
of yield, or:
Effect =
4
(2.1)
where 4 is half of the total treatment combinations. Dividing Equation 2.1 by the total
number of treatment combinations yields the regression coefficient for each design
variable. Performing these calculations gives the following results:
Design Variable
Wedge
LCG
Speed
Hydrofoil
Intercept
Effect
0.063
-0.557
-0.551
-0.039
0.848
Regression Coefficient
0.0315
-0.2785
-0.2755
-0.0195
0.424
Table 2.5: Table of Effects and Coefficients, Hydrofoil Aliased
By inspection, the hydrofoil has the smallest effect in terms of coefficient absolute
value. To determine which design variables indeed have the largest effect on the trim
oscillations, a normal probability plot was constructed. A normal probability plot
shares similarities to a global F-test in regression analysis [10]. If the regression model
was constructed reasonably, then the effects sizes would follow a normal distribution.
The global F-test null hypothesis is that all effect sizes are zero. Constructing a
normal probability plot allows those effects whose value is close to zero to define
a straight line, and any effect that falls far from the straight line is an important
effect.
The first step in constructing the normal probability plot is to determine the estimated
cumulative probability point, P. This process is straightforward, and depends on the
rank of each particular data value, i. The effects, excluding the intercept, are ranked
from the lowest value, 1, to the highest value, n, which is equal to the number of
treatment combinations. Pi is then calculated for each effect by:
37
i
Pi
-
(2.2)
0.5
n
From these values, the normal quantile for each effect is determined using a table of
Cumulative Distribution Function for the Standard Normal Distribution, often called
the Cumulative Z-Table. The resulting plot of effect vs. normal quantile is shown in
Figure 2-13.
Normal Probability Plot, Hydrofoils Aliased
1.5*
0.063
1
Os
-0.039
T
-0.6
Speed
*
-0.5
-0.4
-0.1
-0.2
-0.3
0
OA
-0.551
-0.557
LCG
Standardzed Effect Value
Figure 2-13: Normal Probability Plot with Hydrofoil Effects Aliased
Both the hydrofoil and wedge effects appear to lie closest to the regression line representing the normal distribution. The other effects carry more importance, with LCG
,
and speed carrying nearly equal importance. The coefficient of determination, R2
was calculated in order to determine how much of the variance is described by the
statistical model.
R2 =
SSre
-
"_S(2.3)
sstot
In Equation 2.3, SS,, is the residual sum of squares, or the sum of squares of the
error, and SStat is the data sum of squares. Subtraction of the regression sum of
squares from the data sum of squares yields the residual sum of squares. Application
38
of this to Equation 2.3 yields an R 2 value of 0.631, meaning the model does not do
well explaining the variance in the data. However, the two-factor interaction terms
are not included. Incorporating these terms will likely improve the R 2 value, however
since they are aliased with other two-factor interaction terms, it will not be possible
to discern which factor is being truly represented by the model.
To include the two-factor interaction terms, the table of contrasts must be expanded.
The expanded table of contrasts is shown in Table 2.6.
I
1
1
1
1
1
1
1
1
x1
-1
1
-1
1
-1
1
-1
1
x2
-1
-1
1
1
-1
-1
1
1
x3
-1
-1
-1
-1
1
1
1
1
x1x2
1
1
-1
-1
-1
-1
1
1
-1
1
1
-1
1
-1
-1
1
x4
x1x3
1
-1
1
-1
-1
1
-1
1
x1x4
-1
-1
1
1
1
1
-1
-1
d
a
b
abd
c
acd
bcd
abc
y
1.05
1.46
0.07
0.218
0.2
0.1
0.25
0.044
Table 2.6: Table of Contrasts, Hydrofoil Aliased, Interaction Terms Included
It is worth noting that although the interaction term xx2 is shown in the table of
contrasts, this term is identical to -x3x4, per the alias structure. It is also worth noting that the main design variables x1, x2, and x3 are, like x4, aliased with third-order
interaction terms. However, a first order term is much more likely to be dominant
than a third order term, so it can be said with confidence that the first order terms
are truly represented. Since the second order interaction terms are aliased with each
other, discernment is not possible.
Using Equation 2.1 again to calculate the effects and coefficients of the variables gives
the results in Table 2.7.
Performing normal quantile calculations again and constructing the normal probability plot gives the results in Figure 2-14.
From Figure 2-14 it is clear that the hydrofoil effect sits directly on the regression line
and has little effect on the trim oscillations. Other effects that appear to lie within a
39
Design Variable
Wedge
LCG
Speed
Hydrofoil
Intercept
x1x2 (-x3x4)
xlx3 (-x2x4)
x1x4 (-x2x3)
Regression Coefficient
0.0315
-0.2785
-0.2755
-0.0195
0.424
-0.046
-0.108
-0.277
Effect
0.063
-0.557
-0.551
-0.039
0.848
-0.092
-0.216
-0.554
Table 2.7: Table of Effects and Coefficients with Interaction Terms, Hydrofoil Aliased
Normal Pmbability Plot with Interaction Terms, Hydrofoil
Allased
0.5
U2.
*6
a
-0.6
Speed
_05
-0.4
-0.3
-02%2
-0.1
0
01
0.5
xOSx1
*
Cf
LCG
*0.5-7
-2
Standardized Effect Value
Figure 2-14: Normal Probability Plot with Interaction Terms and Hydrofoil Effects
Aliased
"fat pencil line" of the normal distribution are the three interaction terms. The effects
with the most influence are LCG and speed. The sum of squares for this regression
is equal to the data sum of squares, so R 2 = 1, and the regression fully explains the
variance of the data.
If the hydrofoils have little to no effect on the trim oscillations, then it is possible
to exclude them from the regression design and perform a full
2k
factorial analysis,
including all two and three factor terms. The table of contrasts for the full 2' factorial
design is shown in Table 2.8.
For this design, x is the wedge, x2 is LCG, and x3 is speed. Correspondingly, xx2
is the interaction of the wedge and LCG, et cetera. The full factorial design includes
40
I xl
1T -1
1 1
1 -1
1 -1
1 1
1 1
1 -1
1 1
x2
-1
-1
1
-1
1
-1
1
1
x3
x 1x2
-1
-1
-1
1
-1
1
1
1
1
-1
-1
1
1
-1
-1
1
xlx3
x2x3
1
-1
1
-1
-1
1
-1
1
1
1
-1
-1
-1
-1
1
1
xlx2x3
-1
1
1
1
-1
-1
-1
1
1
a
b
c
ab
ac
bc
abc
y
1.05
1.46
0.07
0.218
0.2
0.1
0.25
0.044
Table 2.8: Table of Contrasts, 23 Full Factorial Design
the three-factor interaction term as well. Performing all effects calculations as before
results in:
Design Variable
Wedge
LCG
Speed
Wedge/LCG
Wedge/Speed
LCG/Speed
3-Factor
Intercept
Effect
0.063
-0.557
-0.551
-0.092
-0.216
0.554
0.039
0.848
Regression Coefficient
0.0315
-0.2785
-0.2755
-0.046
-0.108
0.277
0.0195
0.424
Table 2.9: Table of Effects and Coefficients, 23 Factorial Design
Removing the hydrofoil from the analysis shifts some of the effect values, while others
remain unchanged. As before, in order to determine design variable significance, the
normal probability plot was constructed.
From Figure 2-15, it appears that the three main design variables are the most significant, and that all interactions are insignificant. Contrasting Figure 2-15 with Figure
2-14, it appears that the speed has lost some of its effect, while the wedge has gained
some effect. Of the three main variables, LCG has the strongest effect on trim instability, having a negative correlation. That is, as LCG goes from its high to low
value, or as LCG moves forward, the fluctuations in trim data subsides, or the model
becomes more stable. This effect is visualized by constructing the LCG main effect
plot, as shown in Figure 2-16. Therefore, it can be concluded that LCG has the
41
Normal Probability Plot, Full Factorial Design
LCGISpOed
10.06 3
z
WedQG/C
C
-0.6
I-1
0.039
3-Factor
w
Speed
4 -0.55
0.4
0.2
-0.A4
0.6
01B
V-.216
Rtm"-.
a
LCG
- ----- -
Standardized Effect Value
Figure 2-15: Normal Probability Plot, 2' Full Factorial Design
largest effect on the stability of the model test runs. The slope of the main effect
plot regression is not the same as the LCG regression coefficient since the main effect
plot considers each effect in isolation. Speed also has a negative regression coefficient,
meaning that the trim oscillations subsided as the speed increased, which is what was
observed during testing.
LCG Main Effect Plot
Y
1.6
1A
1.2
0.8
* LCG Data
0.6
0.4
0.2
0
-1
-0.5
0
0-5
1
1.5
X2
Figure 2-16: LCG Main Effect Plot on Trim Fluctuations, Full Factorial Design
As in the half factorial with interaction terms, the full factorial regression sum of
squares is equal to the data sum of squares, and the model fully explains the variance
in the data. It was also desired to analyze the design variables' effects on drag. As
42
before, the hydrofoils were initially aliased, and a half-factorial design was analyzed
with interaction terms. The effects and coefficients now took on different values, along
with the effect rankings. This changed the nature of the results considerably. As with
the analysis of variance for the trim data, there was not enough data to perform a
full 2' factorial design. Therefore, the half-factorial was constructed to determine if
any of the main effects could be eliminated from a 2' full factorial design.
Design Variable
Wedge
LCG
Speed
Hydrofoil
Intercept
xlx2 (-x3x4)
xlx3 (-x2x4)
x1x4 (-x2x3)
Effect
-0.14
0.0615
0.931
-0.2145
16.5445
0.294
0.0645
-0.34
Regression Coefficient
-0.07
0.03075
0.4655
-0.10725
8.27225
0.147
0.03225
-0.17
Table 2.10: Table of Effects and Coefficients with Interaction Terms, Hydrofoil
Aliased, Drag Data
Normal Probability Plot with Interaction Terms, Hydrofoil
Allased
0.93n g
1.5
-1
-0.6
-0.4
-0.2WdgO
LCG
0.2
0*904
0.6
0.8
-0.5
xlxx
Standardized Effect Value
Figure 2-17: Normal Probability Plot, Drag Half Factorial Design, Hydrofoils Aliased
The normal probability plot for the half factorial design with the hydrofoils aliased
is shown in Figure 2-17, and the effect values and regression coefficients are shown
in Table 2.10. In this instance, it appears that wedge and LCG have less of an effect
than the interactions. Speed appears to have a significant effect. The greatest effect
43
belongs to the third interaction, which is either wedge/foil or LCG/speed. The most
insignificant effect is LCG, and therefore LCG is a candidate for elimination from the
full factorial design. Of course, LCG is not eliminated per-se, however data will be
selected in order to achieve a high and low state for the other three design variables
without regard to LCG.
The data available presents a challenge for selecting a high and low state for the
hydrofoils. It was decided to allow the hydrofoil angle of attack to be the driving factor
for selection. Hydrofoil prepositioning that created a larger positive angle of attack
at design trim was selected to be the high value. Conversely, hydrofoil prepositioning
that created a lesser angle of attack at design trim was the low value. There was not
enough duplicity in hydrofoil prepositioning to allow for identical states. Therefore,
the "high" state was, in the hydrofoil positioning notation, f2+2.5 and f2-0 for wedge
A and B respectively, where f2+2.5 represented a hydrofoil position that was 2 cm
down from the top position and had a positive 2.50 initial angle of attack. The "low"
state was fl-0 and f2-4 for wedge A and B respectively. The table of contrasts is
shown in Table 2.11. The resultant effects and coefficients are shown in Table 2.12.
The residual sum of squares for the model is zero.
I
1
1
1
1
1
1
1
1
x1
-1
1
-1
-1
1
1
-1
1
x2
-1
-1
1
-1
1
-1
1
1
x3
-1
-1
-1
1
-1
1
1
1
xlx2
1
-1
-1
1
1
-1
-1
1
x1x3
1
-1
1
-1
-1
1
-1
1
x2x3
1
1
-1
-1
-1
-1
1
1
xlx2x3
-1
1
1
1
-1
-1
-1
1
1
a
b
c
ab
ac
bc
abc
y
7.263
7.804
8.638
8.138
8.245
7.605
8.87
8.528
Table 2.11: Table of Contrasts, 23 Full Factorial Drag Design
In Table 2.11, the "1" in the 9th column of the first row represents only the intercept in
the high state, or conversely that all design variables are in their low state. The normal
probability plot was again constructed in order to determine to importance of the
effects. The normal probability plot for the full factorial drag design is shown in Figure
44
Design Variable
Wedge
Speed
Hydrofoil
Intercept
Wedge/Speed
Wedge/Foil
Speed/Foil
3-Factor
Effect
-0.18175
0.86775
0.29775
16.27275
-0.18575
-0.25575
-0.04025
0.28125
Regression Coefficient
-0.090875
0.433875
0.148875
8.136375
-0.092875
-0.127875
-0.020125
0.140625
Table 2.12: Table of Effects and Coefficients with Interaction Terms, Full Factorial
Drag Data
2-18. The main effect plots for wedge, hydrofoils, and speed are shown in Figures 2-19,
2-20, and 2-21. From Figure 2-18, the 3-factor interaction is the least significant, lying
directly on the normal distribution line. The wedge/speed interaction is next in terms
of the least amount of significance. The wedge/foil interaction is the most significant
effect on model drag, with the remaining effects sharing nearly equal significance.
From the main effect plots, the wedge and hydrofoils individually have very small
effects, with the speed having the largest effect of the three design variables. The
positive slope of the speed main effect plot is congruent with expectations, that the
model drag will increase as speed increases. The wedge/foil interaction has a negative
slope, which means that the drag decreases as the interaction goes from its low value
to its high value. Therefore, lower drag is achieved with wedge A using the higher
foil angle of attack pre-positioning value and with wedge B using the lower foil angle
of attack pre-positioning value. Drag increases as speed increases, as expected. LCG
and selection of the wedge alone had little impact on the drag.
The wedge and hydrofoil interaction is likely significant due to the shaping of the
free surface. Each cambered surface creates a different free surface at the hydrofoil.
The shape of the free surface at the hydrofoil will impact the lift developed and the
moment contribution, which will impact the equilibrium trim and therefore both the
frictional and wave-making resistance.
45
Normal Probability Plot, Full Factorial Drag
12
OmJS
speamous3-Factor
-0.4
-0.2
-0.1
05
0.2
0.4
0.6
08
1
-0.5
Spie d-.1
Wedge
0
C
Wedgu/FoIla
-2
Standardized Effect Value
Figure 2-18: Normal Probability Plot, Drag Full Factorial Design, No LCG
10
Wedge Main Effect Plot
V
987-
6
5
4-
-
3
2
1
0
-1.5
-1
-0.5
0
0.5
1
1.5
x
Figure 2-19: Wedge Main Effect Plot
Hydrofoil Main Effect Plot
Y
10
9-
7-
6
43'
210
-1.5
-1
-0.5
0
0.5
x3
Figure 2-20: Hydrofoil Main Effect Plot
46
1.5
10
Speed Main Effect Plot
Y
4
3
2
0
-1.5
-1
-0.5
0
0.5
11.5
Figure 2-21: Speed Main Effect Plot
2.6.2
Comparison To Parent Hull
It was desired to compare the drag performance of Hull 5631D with Hull 5631. Testing
data for the parent hull is available in Reference 1131.
For comparison purposes,
data from the 375 lb model with 42% LCG was used. Models 5631D and 5631 are
geometrically dissimilar, and therefore the data from each needed to be scaled to the
same LOA. Both models were scaled to a length overall (LOA) of 60 feet.
Wetted area information was readily available for model 5631, but needed to be
calculated for 5631D. In order to determine the wetted area, the CAD model in
Rhino was used. The CAD model was oriented to have the average pitch and heave
for each run for the model with wedge A, 42% LCG, and foil orientation f2+2.5.
The underwater photo for that run was imported into Rhino and aligned with the
underhull of the CAD model. The stagnation line from the underwater photo was
traced on the CAD hull, along with the hydrofoil waterline and any stagnation line
resulting from rewetting of the underhull. Wetted area measurements were then taken
on the CAD model. Characteristic length measurements were also taken by averaging
the longest and shortest longitudinal lengths of each wetted section of the CAD hull
(hydrofoils, afterbody wetted area, forebody wetted area).
Data scaling was performed using some of the methods of Savitsky [15]. The procedure
is outlined below. The subscripts 7a and s refer to the model and the full-scale ship
47
respectively.
1. Calculate the scaling factor A:
LOAs
(2.4)
LOAm
2. Calculate the volumetric Froude number
FnV =
(2.5)
Vm
g V 1/ 3
3. Calculate the total resistance coefficient CR:
CR
(p/2)Vm( E Sai)
(2.6)
Where Sai is the wetted area of a section of the hull.
4. Calculate the mean dynamic pressure of the hull Pm:
P_
_
(A)(g)(0.9)
(2.7)
Safwd
Where the factor 0.9 is derived from an assumption that the cambered surface
will generate 90% of the dynamic lift, and Safwd is the wetted area of the hull
forebody.
5. Calculate the model median velocity, Vmed.
V.
Vmed
2Pm
P
(2.8)
The median velocity is computed in order to calculate the Reynolds number on
the hull. This is used instead of the model velocity because the flow velocity
on the model underhull varies from zero at the stagnation line to free stream
velocity at the transom.
48
6. Calculate the hydrofoil Reynolds number.
Rei Ref~=
1
-
VmLk
__P_
(2.9)
Since the hydrofoils existed aft of the transom, they experienced free stream
flow velocity, and so the model velocity Vm is used.
7. Calculate the hull Reynolds number.
RentI, = PVmedLk
(2.10)
This wetted length Lk is for the hull, and differs than that of the hydrofoils.
8. Calculate the frictional resistance coefficients of the hull and hydrofoils.
0.075
(log(Re) - 2)2
(2.11)
9. Calculate the frictional resistance of the hydrofoils and the hull.
Rf = (Cf)(p/2)(V
)(Sai)
(2.12)
Vi is either Vmr or 1Vmed and Sa is for the hydrofoils or hull depending on which
resistance is being calculated.
10. Calculate the total frictional resistance.
Rft
=
Rff 0 1i + Rf hull
(2.13)
11. Calculate the residual resistance R,:
Rr = Rt - Rft
49
(2.14)
Rt is the measured resistance from testing.
12. Calculate the full scale ship velocity V:
(Vs/Vm)(1/
3
)
Vs = V.
(2.15)
where V is the displaced volume.
13. Calculate the full scale wetted areas.
2
Sas = SamA
(2.16)
14. Calculate the full scale residual resistance.
Rrs = RrmA 3
(2.17)
where Rrm was calculated in Equation 2.14. Due to model/ship Froude similitude, the residual resistance is able to scale as the cube of the scaling factor.
15. Calculate the full scale mean dynamic pressure as in Equation 2.7.
16. Calculate the median full scale hull velocity as in Equation 2.8.
17. Calculate the full scale characteristic lengths.
Lks - LkmA
(2.18)
18. Calculate the full scale Reynolds numbers as in Equations 2.9 and 2.10.
19. Calculate the full scale frictional resistance coefficients as in Equation 2.11.
20. Calculate the frictional resistances as in Equation 2.12.
21. Calculate the total resistance by summing the results of Equation 2.17 and Step
50
20.
The resistance data for both the dynaplane and parent hull was normalized by dividing
by displacement, Rt/A. The results are plotted against volumetric Froude number in
Figure 2-22
Figure 2-22: Normalized Resistance for 5631D and Parent Hull
5631D outperforms the parent hull at higher speed, beginning around a volumetric
Froude number of 4.5. Because it was not designed for lower speed operation, the
Dynaplane has a higher resistance than the parent hull at low Froude numbers. With
both models scaled to a length overall of 60 feet, the dynaplance achieves a 12.6%
reduction in drag at full speed.
51
52
Chapter 3
CFD Simulations
3.1
Introduction to Computational Fluid Dynamics
Much of the design work prior to the testing of Model 5631D involved simulation predictions using STAR CCM+ CFD software by CD-Adapco. It was therefore desired
to perform validation of the software using the data from the tests.
The discipline of Computational Fluid Dynamics seeks numerical solutions to the
Navier-Stokes equations [19] using a time-averaged turbulence model [14]. Software
providing this capability allows the engineer to simulate real world problems with a
high degree of accuracy that would be impossible to perform otherwise.
From conservation of mass and the transport theorem, we have the continuity equation:
(3.1)
6x
or, writing Equation 3.1 in vector form,
53
-pi u+P(
+6u)
V-V=O
(3.2)
which is a condition applicable to any material volume of viscous fluid.
The Euler Equations are obtained by applying the transport theorem to the conservation of momentum:
6 (pui)
+
6 (puiuj)
] dV =
[
+ F)dV
(3.3)
Since Equation 3.3 applies to an arbitrary fluid volume, then the equation must hold
for the integrands alone
[14].
Using the requirement that the shear stress tensor 'ri
is symmetric and of the form
+
ij
(3.4)
where 6,j
1 for i
=
j
and 0 for i
$
p
6xi
j, we arrive at the Navier-Stokes equations:
6us
6un
6 +u 6 -=
6xj
6t
where v =
6xj
1 6p
--- +v
p6xi
62ui
1
2i+-FI.
p
6xj6xj
(3.5)
Written more succinctly in vector form, the Navier-Stokes equations
become:
6V
+ (V - V)V
1
1
-- Vp + vV 2 V + -F
(3.6)
[14]
In many CFD applications, flow in the turbulent regime will be desired for study and
modeling. In order to properly capture behavior of turbulent flow, the Navier-Stokes
equations must be modified. Following Newman [14], we can separate the velocity
54
into an averaged component and an unsteady component:
U-= U7 + u'
(3.7)
where the overline denotes the average and the prime notation indicates the fluctuating component. The average applies to time or space. Noting that the average of
an oscillatory term is i = 0, and that the average of a derivative gives the relationship
6U
6xj
= &6xj
(3.8)
the substitution of Equation 3.7 can be made for ui in the Navier-Stokes equations.
Doing so yields the turbulent Navier-Stokes equations:
&ur
6t
6-i
+ Vj-
oxj
6
1 6P
= --
p 6xi
6 2;
6xj6xj
()
6uiu'
6xj
3
(3.9)
Comparing Equation 3.9 to Equation 3.5 shows a different term at the end of the
right-hand side. The term -pu'u
is referred to as the Reynolds stress, and is related
to momentum transfer from the unsteady component of velocity. The Reynolds stress
will be important in the CFD flows of concern except within the viscous sublayer close
to boundary walls.
The CFD simulation uses the turbulent Navier-Stokes equations and the continuity
equation as the governing physics for the determination of flow behavior.
Using
initial conditions supplied by the user, STAR CCM+ solves Equations 3.1 and 3.9 for
velocity and pressure within each mesh cell for a given time-step, also defined by the
user. Once the simulation is initiated, the cells interact by transferring velocity and
pressure data at their interfaces, each adjacent cell face essentially passing boundary
condition data.
55
The turbulence model selected for simulation of Hull 5631D is the k - E model, which
is widely used in CFD software, first introduced in Reference 112]. In this model, k is
the turbulent kinetic energy and E is the dissipation rate of k. The turbulent viscosity pt is determined as a function of k and E, which are further determined through
partial differential equations involving coefficients determined through experimentation [11.
While it seems that k and e aren't of immediate use to the CFD user, tracking their
normalized values over time during the development of a CFD simulation is valuable in
troubleshooting a divergent solution. STAR CCM+ allows plotting of the residuals of
various parameters. A residual is the absolute error of the discretized solution within
a particular cell. For plotting, the root mean squared value of residuals of a particular
parameter for all cells is taken. In a perfectly converging solution, the residuals will
rapidly decay towards a machine-error value. Near a wall where a zero-slip boundary
condition applies, the so-called low-Re k - e model is invoked. Using this model, the
velocity in the boundary layer is assumed to increase logarithmically for y+ > y+,
where both y+ and y+ are non-dimensional distances from the wall. Noting that
(3.10)
y+
it can be seen that the turbulent viscosity is part of the input, but also part of the
solution. It therefore cannot be known ahead of time, except through experience
developing simulations, whether or not the cells close to the wall are appropriately
sized to capture boundary layer phenomena. If this is not occurring, it will usually
manifest itself as unbounded growth of the turbulent kinetic energy and turbulent
energy dissipation rate residuals.
Situations like this result in non-physical solutions developing within the simulation.
That is, the software is unable to properly apply and solve the Navier-Stokes equations
in large portions of cells. When this occurs, the non-physical solution will tend to
56
Ill
M 111
11oil" MI
cascade through the cells comprising the fluid domain, since the cells interact by
passing data to adjacent cells. Judicious construction of the simulation environment
is required to ensure that the real-world physics are properly captured. One of the
most important parameters to ensuring a simulation's success is the Courant number,
which is a measurable manifestation of the Courant-Friedrichs-Lewy (CFL) condition
[6].
For a cell within the fluid domain whose dimensions are Ax, Ay, and Az, and subjected to a flow of velocity V = (u, v, w], the simulation time step At, or the cell
dimensions must be selected such that:
C
uAt
vLAt
A + A
To illustrate, in a 1-dimensional flow, Cmax
wAt
Az
Cmax
(3.11)
1. If the value of the Courant number
exceeds Cmax, then the distance traveled by a fluid particle in the given time step is
greater than the spatial dimension of the cell, and numerical instability will result.
Larger values of
Cmax
can be tolerated in 3-dimensional flows, and software using
implicit solvers. It is therefore useful, when first initializing a simulation, to display
the range of Courant numbers present in the fluid domain. Excessively large values of
the Courant number will likely result in solution divergence, and need to be addressed
prior to running the simulation.
3.2
Hull 5631D Simulation Set-Up
Hull 5631D was designed using the Rhinoceros 3-D CAD program. This software
would therefore provide the underlying CAD geometry for STAR CCM+. The hydrofoil support system was not needed for simulation, so the hull and hydrofoils were
the only items to be imported.
The design in Rhino was converted into a stereolithography file for import. Due to
57
some fine geometric features of the hull and hydrofoils, such as the spray rail vertices,
a high mesh density was required. Without a large number of cells in the STL mesh,
fine geometry will tend to get blended and lost by the internal STAR CCM+ CAD
engine.
For a simulation to be able to initialize in STAR CCM+, the underlying CAD geometry must be properly groomed to have no naked edges, and no non-manifold edges
or vertices. While these problems can be addressed in the software, it is easier to
ensure the imported geometry is free of these issues. A naked edge is any non-vertex
edge; it is an edge of a surface that is disconnected from an adjacent surface.
A
CAD object must be free of all naked edges before the software will consider it to
be a solid, and therefore an STL file cannot be generated if naked edges are present.
Despite this, CAD solids can have naked edges upon import into STAR CCM+ if
the underlying STL mesh is not fine enough. The condition of being manifold has a
rigorous mathematical definition which can be simplified for the purposes of designing
CAD geometry. For an edge to be manifold, it must be formed by the intersection of
two surfaces. An edge where three (or more) surfaces intersect is non-manifold. Nonmanifold vertices are more abstract, and are formed when the neighborhood topology
surrounding the vertex is not homeomorphic with Euclidian space. For example, a
circle is a manifold ID shape, but a lemniscate (figure-eight) is not. The vertex of a
lemniscate is a non-manifold vertex. Also, consider a pyramid. The apex of a pyramid
is a manifold vertex, as it is fully defined by the surfaces below it. However, if two
pyramids, one inverted and one not, are joined at this same vertex, the vertex now
becomes non-manifold.
Non-manifold geometry is unlikely to appear while designing in CAD. Issues can
arise, however, when importing into STAR CCM+ due to the underlying mesh. A
tessellated mesh, if not exactly imported, can result in undesired mesh surface overlaps
and gaps, and these can lead to non-manifold geometry.
It was desired to measure the forces and moments on the hydrofoils, aft underhull,
58
and cambered surface separately. In order to do so, STAR CCM+ must recognize
these regions as separate parts of the CAD object. Since the hydrofoil support system
was not included in the simulation geometry, the hydrofoils were imported as their
own separate part. For the hull itself, STAR CCM+ was instructed to create separate
parts for hull geometry that was separated by an edge. This allowed separate parts
to be created for the aft underhull and the forward underhull. Since the dimensions
of the hydrofoils, particularly near the leading edge, were small compared to the hull
mesh base size, the hydrofoil surface mesh was treated separately and made smaller
than the hull base size.
Once the geometry was imported, the fluid domain must be created. The computational environment cannot cover the entire fluid domain. As a result, areas where
the computational domain end serve as artificial boundaries. A rectangular computational environment was selected. Dimensionally, the grid extended twice LOA aft
of the transom and below the bottom of the model in order to allow for full wake
development and to avoid shallow water effects. The grid extended one LOA to the
port side and in front of the bow. The computational grid intersected the model
down the longitudinal axis. This would act as a symmetry plane in order to save
computational expense.
In addition to the parts already mentioned, several other parts were created that
would act as volume refinements during the meshing operation. Volume refinements
provide a method to contain a more refined mesh in a particular area of interest where
more flow detail is required. The mesh for the background fluid domain was more
coarse than is practicable to capture important flow phenomena. For the Hull 5631D
simulation, the areas of interest were the free surface far field, the free surface near
field, the wake of the step, and the hydrofoil wake.
On the contrary, some areas of the fluid domain were of less interest. In particular,
the six boundaries of the background did not require the same mesh refinement as
the rest of the domain. Similar to the hydrofoil surface mesh control, a boundary
59
surface control was also established as part of the automated mesher. The boundary
cells were set at 1600% of the base cell size, and allowed to shrink to the base cell
size within a short distance into the fluid domain.
The main physics environment for the simulation was the Volume of Fluid (VOF)
solver. This is a multiphase model that allows for dynamic fluid body interaction
(DFBI) between a translatable solid and one or more fluids. To allow for appropriate
application of the VOF physics solver, the newly created mesh objects had to be assigned to physics regions. For the Hull 5631D simulation, two separate regions were
created; one region contained the bulk of the fluid domain, and the other contained
the hull and the associated volume refinements. The boundary conditions had to be
assigned within the regions. In the translatable region, the hull and hydrofoils were
defined as wall boundaries, and the longitudinal plane was defined as a symmetry
boundary. For the background fluid domain region, there was a symmetry boundary,
four velocity inlet boundaries, and one pressure outlet boundary. The latter boundary
was the aft-most vertical plane, whose initial condition was defined to be the hydrostatic pressure of the fluid. The four velocity inlet boundaries had the velocity of the
fluid, defined by the simulation volumetric Froude number, as their initial condition.
Additionally, each region applied a volume fraction initial condition which defined
the multiphase fluid region. The initial position of the free surface was also defined
by the user.
The inertial reference frame of the simulation, where the hull and hydrofoils will be
rotating and translating relative to the fluid domain, presented a unique computational problem. In past versions of the software, cell morphing was the method to
address this. As the name implies, cells near the DFBI body changed shape as the
body moved, in order to maintain continuity of physics between adjacent cells. More
recently, a feature called overset meshing was included in the software. This feature
was designed to handle large relative motions.
A separate volume was defined where the hull and the surrounding cells would move
60
as a rigid body. Defining the boundaries of this region as the "overset mesh" created
an overlap between these cells and the background cells. A layer of cells near the
overset boundary actively solved the governing equations.
These cells overlapped
with the active cells of the background mesh. Deeper into the overset mesh overlap,
the background region contained a layer of acceptor cells, inside of which all other
cells were inactive.
By contrast, all cells within the acceptor layer in the overset
mesh were active cells. In this way, the background and overset meshes interacted by
passing information from active cells to the acceptor cells.
A visualization of this process using linear data interpolation is shown in Figure 3-1,
taken from a CD-Adapco training presentation.
I
I
II
u
/
I N
WSL
A
-
I
-u
I 1j'N' 2
/
J
X-
Nr
I
N
I
N3
1
4
N6
N2
/
PN
14
1
MT
S
171
Figure 3-1: Overset Mesh Data Transfer Schematic
Two meshes are shown, one in red, one in blue.
An active cell near each mesh
edge is marked with a "C". For each case, the center value for cell C is determined
by calculating a weighted sum of neighboring cells in the same mesh: N1, N2, and
N3. In 3D, a fourth cell will contribute to the weighted average. Acceptor cells are
shown with dotted lines. The center values for the acceptor cells are calculated using
neighboring donor cells from the opposite mesh: N4, N5, and N6. This way, acceptor
61
cells for a particular mesh are virtual cells, or ghost cells, and receive their data
from the other mesh. This allows data transfer at the overset boundary, allowing the
background mesh to pass data into the overset mesh, and the overset mesh to pass
data out to the background mesh, providing continuity of data during large relative
motions.
There must exist at least 4 - 5 overlapping cells between the overset boundaries
and any wall boundaries inside the overset region, in order to allow the program to
establish the network of active, donor, and acceptor cells. Initially, this condition
could not be met due to the relatively large size of the background cells compared to
the dimensions of the overset region. Although the automated mesher does taper cell
size as cells approach a wall or a region with a smaller cell base size, this transition
was not happening rapidly enough to satisfy the overlap requirement. The overset
region would have to be made undesirably large in order to allow 4 - 5 background
cells to fit inside, which would greatly increase the total cell count and carry a heavy
computational price tag. The solution to the problem was adding a third rectangular
volume encompassing the overset region, approximately 20% larger than the overset
region in all directions. The base cell size for this transition region was the average of
the background and overset base sizes. The presence of this transition region forced a
reduction of the background mesh cell sizes earlier, resulting in a smaller background
cell size at the overset region boundaries, and ultimately the fulfillment of the 4 - 5
cell overlap inside the overset region.
And additional user input to the program was the body moments of inertia. Moments
of inertia for the vessel were estimated using:
mR 2=
where i =
[y,
zi, m is the model mass, and Rei is the radius of gyration.
(3.12)
Due
to hull symmetry, cross-inertia terms were zero. The radii of gyration about the
62
",
.....
.9..........
principle axes were measured in CAD, and were taken about the volumetric center of
the model.
In order to improve simulation accuracy, the turbulent boundary layer must be modeled as accurately as possible. For turbulent flows, y+ values in the range of 30-300
are generally acceptable. Lower y+ values, in the range of 1 - 5, require a larger
amount of cells in order to resolve the flow. A special type of cell, called a prism cell,
was used to analyze the boundary layer. A prism cell is a high rectangular aspect
ratio cell compared to those cells in the bulk flow. Several of these cells were stacked
to form a layer, called the prism layer. Varying the thickness of the cells in the prism
layer as it grew out towards the bulk flow created proper resolution and modeling of
the velocity gradient near the wall. The goal was to create a velocity gradient that
closely modeled theoretical gradients. To properly create a velocity gradient, the
prism cells decreased in aspect ratio as they approached the bulk flow. Good velocity
resolution was generally achieved with a prism cell growth rate that increased by 1.5
times the thickness of the adjacent cell. For low wall y+ values (1 - 5), a prism layer
of 10 - 20 cells was needed.
The thickness of the prism layer was selected to be the same magnitude as the boundary layer. Boundary layer thickness was estimated by:
0.382x
6 ~l.'Re'/5
Re
(3.13)
From Equation 3.13, the boundary layer grew from zero to approximately two centimeters thick near the transom. However, this was not strictly correct in the case of
5631D, since the afterbody was ventilated. It did, however, provide an estimation of
the order of magnitude of the boundary layer thickness.
63
3.3
Simulation Validation
A simulation was created that modeled a full-speed test run (9.4955 m/s) with the
hydrofoils at the second position (2 cm down from top) with a positive 2.5' angle
of attack, with cambered surface A (designed using the Clement method) and LCG
position at 42%. The hydrofoil position was shorthanded as f2+2.5. The dimensions
of the fluid domain were created using the guidelines in Reference
[7].
Truncated test data is shown in Figure 3-2. Absolute trim differs from measured trim
due to 0.82' of model pre-positioning. The data is plotted in Figures 3-3 through
3-5
GAMWaO
S
9
a
I.5
1175
6
is
16
23.339
20.739
18.136
0.:1&0
U.la0O
4.501467
3.999919
7.914 0.217784
7.394 0.203466
7.605 0.209277
8.019 0.220678
3.497872
0.22316
5.504853
25.939 5.002832
3.16
2.67
3.98
4.12
2.52
2.32
2,01
4.94
5.13
5.72
5.95
6.54
Figure 3-2: Truncated Test Data, 42% LCG, Hydrofoils at -2, +2.5 position.
PItch, 42% LCG, f2+2.5
7.0
6.0
5.0
.
J3.0
,
,
14.0
2.0
1.0
0.0 1
0
20
10
30
MOd" Speed p)
Figure 3-3: Pitch, 42% LCG, Hydrofoils at -2, +2.5 position.
64
Heave, 42% LCG, f2+2.5
3.5
3.0
4*
2.5
2.0
1.5
1.0
0.5
0.0 +0
20
10
Model
30
Speed (fpsj
Figure 3-4: Heave, 42% LCG, Hydrofoils at -2, +2.5 position.
Resistance, 42% LCG, f2+2.5
9.0
S4
8.0
7.0
so.
140
3.0
2.0
1.0
0.0
0
to
20
30
Model Speed ItpS
Figure 3-5: Resistance, 42% LCG, Hydrofoils at -2, +2.5 position.
65
A simulation was developed to study the model at full speed with cambered surface A,
42% LCG, and hydrofoils at the f2+2.5 position. A view of the mesh on a longitudinal
cross-section of the fluid domain is shown in Figure 3-6. The innermost rectangular
domain containing the vessel is the overset mesh, which rotated and translated with
the vessel itself. The areas of finer mesh density are volumes whose purpose was to
provide flow refinement in regions of interest, such as at the hydrofoil and at the
cambered surface.
=......3===:====:=:=enmeamnmnmeee
: th me :no trim=until 0:: seconds had elapsed,
As +!e=:rpreviously II descr:be
+=,H+ iu~gnnunnnnn==============
+amannuuu~~
4-
! =i:=:== i=:== == == ===. + H4+-+mmmm em mm
+
3= ==
+==i:=
:= = :=
:=
=== = = := =
+e=:==:=========n==:=====
+:===:===============::m
====
4 +m
_+ __-+
4
mmmmmmmmmmmmmmmmnmeaeammma4
X
mensomnomemmenanemamennoeneommenonomaneno
m
a
= :=
momnensmamms
nomemama
mepmof 5E-4 smecns No
meo
o
o
m
oe
m
ooom
em
fH H
eavoe or trime-pstinngocrean
hefe
ahsmlto
was at theeevmenkemel"ndiin
vertexof the traensom m
ed satineeary for te first 0.3 emsens withno degee o freom inre
initisall
a
Figure 3-6: Simulation Mesh on a Longitudinal Cross-Section
Trie=:nm
dayed =erioic osillains= of about:0.:-0.25 secons, as seen i Figure 3-7
The simulation was allowed to run until equilibrium conditions were exhibited with
a time-step of 5E-4 seconds. No heave or trim pre-positioning occured, and the free
surface was initally placed at reference level (z =-0), which corresponded to the lowest
vertex of the transom. Trim was at the "even keel" condition. Each simulation was
initially held stationary for the first 0.3 seconds with no degrees of freedom in order
to allow the flow domain to accelerate to full speed and to allow the physics time to
develop. After 0.3 seconds, the virtual model was allowed to heave and trim freely.
Model trim was monitored to determine when the equilibrium state was reached.
Trim displayed periodic oscillations of about 0.2 - 0.25 seconds, as seen in Figure 3-7.
As previously described, the model was not free to trim until 0.3 seconds had elapsed,
66
at which point the model achieved a negative trim angle, which corresponded to a
bow-up configuration based on the sense of the y-axis (positive y-axis lies on the port
side of the model). The model overshot its steady state trim condition and briefly
hunted until it began the periodic oscillations seen from approximately 1.1 seconds
on. In addition to the trim data, the plots for the drag, lift, and moment on the
total body, hydrofoils, aft body, and forward body are shown in Figures 3-8 through
3-11. The afterbody was defined as the portion of the model aft of the step until
the transom, and the forebody was that portion of the model forward of the step.
Sharp peaks in the graphs are points where the simulation was stopped and then
restarted.
Trim Monotr Plot
-
1.5
-2
-3
01
0
.2 0..
0'4
05
0:6
07
08
0
1 1
2
m3
14
f5
16
17
18
19
2.1
2.2
2.3
2.4
PhoIcal Time MS
-
Trim Monitar
Figure 3-7: Simulation Trim Plot
A summary of the simulation's results are given in Table 3.2. Since the parameters
measured were oscillatory, averages were taken from 1 second until the end of the
simulation.
Graphics taken from the simulation were available only at the most recent time-step.
A comparison of the underwater photo from the test and the simulation at the final
time-step is shown in Figures 3-12 and 3-13.
The underwater photo displays a cambered surface that appears to be fully wetted.
67
.........
....
.
..
....
..
.......
.....................
.............
.
200
180
160
140
120
100
..80'
60o
40-
20
-20.,
-40'
-60-100-0.1
02
03
0:4
06
0.5
0.7
0:8
1.1
1
09
1.2
1.4
1.3
(s)
1.5
1.6
1.7
18
19
2
21
2.2
2.3
2.4
PhMiclal TIme
-
Drag-lot Monitor -
Ufn-Tot Monitor
-
Moment-tot
Monitor
Figure 3-8: Simulation Results, Total Model
Hd~o
80
75
70,
65
550
8
-
050-
45
Z40
33.
-
30
20
10-
01
02
03
04
05
0:
07
08
-
09
Hdrofoil Drag
1
11
12
13
Physical Time (3)
Monitor
Hydrofoil Lift Monitor -
14
1f1
H-10rofolI
18 192 21222.3 2.4
17
Moment Monitor
Figure 3-9: Simulation Results, Hydrofoils
The whisker spray region is also clearly visible. The simulation snapshot shows a
cambered surface that appears to not be fully wetted, which is confirmed when viewing
the volume of fluid condition on the hull bottom, shown in Figure 3-14. An additional
view of the volume of fluid condition on the bottom of the cambered surface with
strain rate vectors is shown in Figure 3-15.
68
..' - 11- - 11
7 ...
---------
Mt
30-
Body
20
10
3-1
-20
-40
-30-
-80-70-
0.2
0.1
03
04
0.5
0.6
0.8
0.7
09
1
11
1'2
Phyical
-
Aft
Underhul Moment Montor -
At(
1.3
Time (s)
1.4
Underlil Dra Mentor
16
05
-Mt
17
1.8
19
2
2.1
2.2
23
2.4
Underhil Uft Monftor
-
Figure 3-10: Simulation Results, Afterbody
Forward Body
200-
180
-
160
140
120-
7ni
100'
P
Ti
606
40-
20
0-'
-20-40-
-801
0,2
03
0.4
03s
o7
0ll
0. 0.0911.1
21.3
.
'
0
--- FwdBody Drag
P"yIcal Time (s)
Monitor 2 - FwdBodL~ft Monitor 2 -Fwd~odvMoment
Monitor 2
Figure 3-11: Simulation Results, Forebody
69
Parameter
Average Value
Standard Deviation
Trim
2.580
0.3410
Heave
Drag
Lift
Hydrofoil Drag
Hydrofoil Lift
Aft Body Drag
Aft Body Lift
Forward Body Drag
Forward Body Lift
2.19 cm
34.52 N
164.42 N
7.26 N
22.63 N
-0.45 N
-13.32 N
25.85 N
151.26 N
0.25 cm
3.00 N
32.50 N
0.58 N
2.23 N
0.096 N
2.85 N
3.08 N
32.32 N
Table 3.1: Initial Simulation Results
Figure 3-12: Run 19 Underwater Photo
Figure 3-13: View of Simulation Underhull and Free Surface
70
.g
Volume
Fraction of Water
Figure 3-14: Simulation Volume of Fluid on Hull Bottom
Figure 3-15: Simulation Volume of Fluid on Cambered Surface with Strain Rate
Vectors
71
Viewing the volume of fluid of the hydrofoil from the top confirms that the upper
surface is ventilated aft of the leading edge as expected. This condition is shown in
Figure 3-16.
0.
0.1
01
0.2
0.
Volume Fraction of Water
06
0.5
4
0.8
09
1.
Figure 3-16: Simulation Volume of Fluid on Hydrofoil Upper Surface Showing Ventilation
Figures 3-17 and 3-18 show the pressure coefficient on the entire underhull, and
a zoomed view on the cambered surface with strain rate vectors respectively.
In
the latter, the strain rate vectors show the stagnation line, which separates the low
pressure portion of the forebody shown in blue and light blue from the cambered
surface where dynamic lift is developed, represented by regions of the color bar from
green to red.
Forward of the stagnation line is a spray region.
Aft of the step,
which coincides with the trailing edge of the cambered surface, is a region of negative
pressure on the hull bottom.
Simulation instability affects the solution's ability to correctly converge. In this case,
the drag predicted by the simulation differed from the testing data by approximately
9%. Since the simulation trim oscillations were not observed during model testing,
the simulation was re-run in order to attempt to achieve better stability. The average
heave value was used to pre-position the simulation model for the second iteration.
72
-0.010
0.00067
0.011
0 022
0.033
0.043
0.054
Pressuire Coefficient
0.075
0.086
0.06S
0.097
0.11
0.12
0.13
0.14
015
..X *z
Figure 3-17: Simulation Pressure Coefficient on Hull Bottom
-0.010
0.00067
0.011
0.022
0.033
0.043
0.054
Pressure Coefficient
0.075
0.086
0.065
0.097
0.11
0.12
0.13
0.14
0.15
Figure 3-18: Simulation Pressure Coefficient on Cambered Surface with Strain Rate
Vectors
Simulation pre-positioning attempted to place the virtual model in a condition that
was as close to its steady state orientation as possible prior to running the program.
The heave pre-positioning for the second iteration was very close to the true equilibrium, with the simulation heave changing by an average of -0.356 millimeters from
the pre-positioned value of 2.2 cm below baseline. Trim was not pre-positioned, but
73
an improvement in performance was observed. The average trim became 2.75' with
a standard deviation of 0.29'. The drag during this second simulation was 35.3 N, a
difference of -7.14% from the testing drag.
Parameter
Trim
Heave
Drag
Lift
Hydrofoil Drag
Hydrofoil Lift
Aft Body Drag
Aft Body Lift
Forward Body Drag
Forward Body Lift
Average Value
2.760
-.036 cm
35.3 N
161.82 N
7.68 N
23.77 N
-0.49 N
-13.96 N
26.12 N
147.87 N
Standard Deviation
0.290
0.2 cm
2.86 N
26.90 N
0.67 N
2.55 N
0.12 N
2.76 N
2.58 N
26.54 N
Table 3.2: Second Simulation Results, Pre-Positioned Heave
A very likely culprit for the difference in the simulation drag versus the testing drag
was the modeling of the free surface. In order to properly capture the wave-making
resistance and, to a lesser degree, the frictional resistance, the part of the fluid domain containing the free surface must be properly refined. The CFD software cannot
mesh a free surface refinement that exists simultaneously in the moveable mesh region
and the stationary mesh region; the free surface refinements for each region must be
created and meshed separately. As a result, the free surface refinement within the
overset region rotated and translated with the virtual model. For refinements that
capture flow details of the hydrofoils and cambered surface, this type of behavior
was desirable. However, the free surface was relatively stationary compared to the
virtual model, and therefore much of the flow detail of the free surface near the hull
was lost as the refinement volume moved out of alignment. This likely resulted in
a loss of data regarding hull resistance, causing the simulation to under-predict the
actual resistance. The simulation drag can be separated into the wave-making and
frictional components. When compared to the testing data, the simulation frictional
resistance differed from the test by 45%! Contrast this with the wave-making resistance, which saw only a 2.3% difference between the simulation and testing data. A
74
lack of refinement where the free surface contacts the hull clearly resulted in errors in
the frictional resistance computation, likely due to the VoF model underestimating
the wetted area. This is corroborated by returning to Figures 3-12 and 3-13. Although the free surface shown in both figures is a snapshot, and not representative
of the average condition during the test and simulation respectively, the data in each
case leads one to believe that the free surface is not being modeled in the simulation
with adequate resolution, and as a result the wetted area, and therefore the frictional
resistance, was under-computed.
Future work regarding simulation validation would require correcting this condition,
however the process is iterative. Another simulation should be run with the free
surface refinement pre-positioned such that at equilibrium it will be aligned with
the actual free surface. Recapturing the flow detail will, however, likely result in new
equilibrium heave and trim values, which will require a new pre-position for the model
and free surface refinement.
3.4
Longitudinal Stability Margin Computation
A means of determining the model stability was to compute the Longitudinal Stability
Margin (LSM). The major contributors to the vertical forces on the hull were the
hydrofoils, the cambered surface, and the ventilated underbody of the hull aft of
the step, the latter contributing negative lift.
The coordinate convention applied
to the CFD simulations was such that the positive y-axis pointed outwards from
the model's port side, therefore a positive moment tended to orient the model in a
"bow-up" configuration. Using the vertical forces mentioned before and summing the
moments about the model center of gravity yields:
ZM
= Ffo
0 ilxfoils + FaftXaft + Fcsxcs
75
(3.14)
where cs is the cambered surface, and x in each instance represents the distance from
the center of force to the center of gravity. Setting xcg = 0, Xfoils was less than zero,
creating a negative moment as expected. Similarly, the cambered surface was forward
of the center of gravity, creating a positive moment and tending to orient the model
bow-up. The moment contribution of the afterbody depended on whether or not the
center of force was forward or aft of the center of gravity.
If the forces are summed into one vertical component acting through a single center
of force h, then Equation 3.14 becomes
E M = h(Ffo
0 il + Faft + Fes)
(3.15)
As in Reference [71, quasi-static measurement of the Longitudinal Stability Margin h
required the derivative of Equation 3.15 with respect to trim. The simulations were
held with zero degrees of freedom and changes in the total moment and vertical forces
measured as the trim was varied. The reference condition for the LSM measurements
was the steady-state trim and heave conditions from the previous 2 DOF simulation.
Calculation of the LSM becomes:
am
h
6Ff
-
9Faft _
_F__
a-r
aT
QF(3
(3.16)
49r
The partial derivatives in Equation 3.16 were computed using zero DOF simulations.
The reference conditions were the steady-state heave and trim from the second 2DOF simulation, that is a free surface position of -2.2 cm and a trim of -2.75'. Trim
was varied by
0.50 from the reference trim, and the changes in total moment and
vertical forces were calculated using a center difference:
df
dh
_
f(x+h)-f(x-h)
2h
76
(3.17)
For small h, a centered difference is more desirable than forward or backward differences since the center difference error is O(h2 ), whereas the forward and backward
differences are O(h) [18]. The averaged results for the vertical forces and total moment
for the zero DOF simulations are shown in Table 3.3.
Trim Angle (Deg by Stern)
2.25
2.75
3.25
Fwd Body Lift (N)
60.97
70.17
77.23
Afterbody Lift (N)
-14.27
-13.22
-11.56
Foil Lift (N)
18.20
23.05
30.64
Moment (N-m)
-4.03
-0.59
9.00
Table 3.3: Fixed Draft, Zero DoF Simulation Data
Computing the center differences using Equation 3.17 from these averages yields:
Or
OFf"'
16.26 N/deg
=9f 2.71 N/deg
= 12.45 N/deg
am= 13.03 N-m/deg
Substituting these values into Equation 3.16 gives h = 0.414. This means that the
effective vertical force acted through a position forward of the center of gravity, resulting in a positive moment and model stability. It is also worth noting that the
reference orientation with the free surface at -2.2 cm and a trim angle of 2.75' by the
bow gave a total moment that was near zero, indicating that this is in fact a proper
choice for the equilibrium condition.
A comparison of the pressure coefficients on the cambered surface with the strain rate
vectors is shown in Figures 3-19 through 3-21.
77
-0.010
0.00067
0.011
0.022
0.033
0.043
0.054
Pressure Coefficienr
0.086
0.065
0.075
0.097
0.11
0.12
0.13
0.14
0.15
Figure 3-19: Zero DOF Simulation Cambered Surface Cp, 2.250 Degrees Trim by the
Stern
-0.010
0.00067
0.011
0.022
0.033
0.043
0.054
Pressure Coefficient
0.086
0.065
0.075
0.097
0.11
0.12
0.13
0.14
0.15
.xx
Figure 3-20: Zero DOF Simulation Cambered Surface Cp, 2.75' Degrees Trim by the
Stern
78
-0.020 0.00067
0.011
0.022
0033
0.043
0.054
Pressure Coefficient
0.065
0.075
0086
0.097
0.11
0.12
0.13
0.14
0.15
Figure 3-21: Zero DOF Simulation Cambered Surface Cp, 3.250 Degrees Trim by the
Stern
Perturbing the trim angle away from the equilibrium conditions resulted in a more
irregular pressure distribution than at the reference trim. The stagnation line swept
back at a greater angle from the transverse plane than in the reference condition, as
observed by the strain rate vectors. As a result, the stagnation line did not extend
to the edge of the hull, and therefore this region was a spray region.
79
80
Chapter 4
Conclusions and Future Work
The 5631D dynaplane model with cambered planing surface designed using Clement's
method outperformed the parent hull for the condition analyzed at high speeds (FnV
> 4.5) by approximately 12.6%. Through statistical analysis it was found that the
interaction between the cambered surface and the hydrofoils had the largest effect on
the model drag. This was likely an indirect effect. The cambered surface strongly
influenced the shape of the free surface at the hydrofoils, which influenced the lift
produced by the hydrofoils.
The hydrofoils produced a moment on the order of
50% of that from the cambered surface, and therefore had a strong influence on the
equilibrium trim angle. As the trim angle changes, both the frictional and wavemaking resistances will change.
Simulation drag tended to under-predict that which was seen during testing. Specifically, drag was under-predicted by 7.14%. This difference could likely be attributed
to a lack of free surface resolution inside the movable overset mesh region of the simulation. The free surface refinement within the overset region rotated and translated
as a rigid body with the virtual model, and therefore came out of alignment with the
actual free surface. This misalignment resulted in a free surface that had areas where
its resolution was as course as the bulk domain cells. Loss of data likely occured in
the free surface near field, where the free surface was close to the model hull. This
81
lead to errors in the resistance computations, causing the computed drag to be less
than the testing drag, as was seen during the course of simulations for this thesis, and
resulted in underestimation of the frictional drag as discussed in Chapter 3. A large
error in the frictional resistance was seen compared to the testing data. The frictional
resistance represented 35% of the total resistance, and therefore reducing this error
will cause the simulation drag to converge to the testing drag. Future work in simulation validation could converge on the testing drag through an iterative process of
pre-positioning not only the hull, but the free surface refinement as well. Additional
simulations that were not included in this thesis showed that, although the simulations responded well to pre-positioning of the model in heave, trim pre-positioning of
the model had little effect on the results. Therefore, future simulations should aim
to pre-position a simulation in heave and to pre-position the free surface refinement
such that it will be close to zero degrees when the model reaches equilibrium. The
free surface refinement should therefore be pre-positioned to the equilibrium trim,
but in the opposite sense, that is for an equilibrium trim of -2.75', the free surface
refinement should be pre-positioned to +2.50. It is likely that as the refinement becomes more and more aligned with the actual free surface, new equilibrium heave and
trim orientations will result, requiring additional simulation iterations. Ultimately,
however, the simulation will likely converge to values nearing the testing data.
An additional consequence of improving the accuracy of the simulation will be the
ability to improve the accuracy of the data scaling used to compare Hull 5631D
with the parent hull. For this thesis, the wetted area for Hull 5631D was estimated
using the CAD model and the underwater photographs. When the free surface is
properly refined along the model hull, the simulation can be used to give a wetted
area measurement, thereby improving the accuracy of the scaled data. Uncertainties
in the current wetted area estimations exist in the hydrofoils, the afterbody when
rewetting occurs, and the area of the forebody between the cambered surface leading
edge and the stagnation line. In each testing case, the cambered surface itself was
fully wetted, and so the value of this wetted area was constant and exact. In the full82
speed case, the exact cambered step wetted area represented 77.8% of the estimated
total wetted area.
More testing data exists with the need to be compared to the parent hull, although it
stands to reason that the same drag improvements seen in this thesis will exist in the
other cases as well. However, further optimization of the cambered surface is needed,
and a validated simulation will prove an invaluable tool to assist in design and analysis
efforts. Additionally, the model has yet to be tested in waves. The dynamic instability
known as porpoising was seen during several testing runs, with a statistical analysis
showing that the model LCG was the main contributing factor to the inception of
these instabilities which, like the wedge/foil interaction, is likely an indirect effect.
The direct effect is most likely the equilibrium trim angle of the model, which is
affected by the LCG. Simulations in waves could help predict under which conditions
the physical model will experience stability and instability, and could assist in saving
valuable testing time by focusing the efforts of the research group. Although methods
exist for predicting the porpoising inception of conventional planing hulls [91, a similar
method does not exist for non-conventional planing hulls such as 5631D. Simulating
the tests prior to actual model testing could help aid in instability prediction.
83
84
Appendix A
Testing Data
This appendix contains all testing data from the model tests of Hull 5631D, along with
all available photographs. Testing runs are catalogued by their number. Calibration
runs and other runs not involved in data collection received a catalogue number,
but are not included in this appendix, and therefore gaps may occur in the number
sequencing.
85
A.1
Run 13
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
42%
fO-O
28.5
5.21
0.034
2.84
8.276
86
A.2
Run 14
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
42%
fO-O
31.1
5.09
0.176
2.96
9.087
87
A.3
Run 15
Wedge
LCG
Foil Position
A
42%
f 1-0
Speed (fps)
28.5
Avg Trim (Deg)
4.70
No underwater pic available
88
Trim Std Dev
0.109
Heave (In)
2.83
Drag (lbs)
8.085
A.4
Wedge
A
Run 16
LCG
42%
Foil Position
f3-0
Speed (fps)
28.5
Avg Trim (Deg)
2.55
89
Trim Std Dev
0.051
Heave (In)
2.71
Drag (lbs)
7.587
. .............
A.5
Run 17
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
A
42%
f2-0
28.5
4.22
No underwater pic available.
90
Trim Std Dev
0.112
Heave (In)
Drag (lbs)
2.81
7.954
A.6
- ---
--- -------------
Speed (fps)
Avg Trim (Deg)
28.5
3.73
Run 18
Wedge
LCG
A
42%
Foil Position
f2+2.5
91
Trim Std Dev
Heave (In)
0.06
2.8
Drag (lbs)
7.914
A.7
Wedge
A
Run 19
LCG
42%
Foil Position
f2+2.5
Speed (fps)
31.1
Avg Trim (Deg)
3.61
92
Trim Std Dev
0.055
Heave (In)
2.87
Drag (lbs)
8.528
A.8
Wedge
A
Run 20
LCG
42%
Foil Position
f2+2.5
Speed (fps)
Avg Trim (Deg)
3.98
25.9
93
Trim Std Dev
Heave (In)
Drag (lbs)
0.271
2.67
7.394
A.9
Wedge
A
Run 21
LCG
42%
Foil Position
f2+2.5
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
23.3
4.94
0.218
94
Heave (In)
2.52
Drag (lbs)
7.605
A.10
Run 22
Wedge
LCG
A
42%
Foil Position
f2+2.5
Speed (fps)
20.7
Avg Trim (Deg)
5.95
No side picture available.
95
Trim Std Dev
0.475
Heave (In)
2.32
Drag (lbs)
8.019
A.11
Run 23
Wedge
LCG
Foil Position
A
42%
f2+2.5
Speed (fps)
18.1
Avg Trim (Deg)
6.54
96
Trim Std Dev
0.106
Heave (In)
2.01
Drag (lbs)
8.109
.
. .........
.
A.12
Run 24
Wedge
LCG
A
40%
Foil Position
f3-0
Speed (fps)
28.5
Avg Trim (Deg)
3.19
97
Trim Std Dev
0.302
Heave (In)
Drag (lbs)
2.53
7.498
A.13
Run 25
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
A
40%
f2-0
28.5
3.79
98
Trim Std Dev
Heave (In)
Drag (lbs)
1.639
2.49
8.955
A.14
--
-- -------------- ----
-
Run 26
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
A
40%
fl-0
28.5
4.71
99
Trim Std Dev
3.84
Heave (In)
2.82
Drag (lbs)
9.241
-~
A.15
Wedge
A
Run 27
LCG
40%
Foil Position
f4-0
Speed (fps)
28.5
Avg Trim (Deg)
2.41
100
Trim Std Dev
0.061
Heave (In)
2.56
Drag (lbs)
7.482
A.16
Run 28
Wedge
LCG
Foil Position
A
40%
f3-0
Speed (fps)
28.5
Avg Trim (Deg)
3.10
101
Trim Std Dev
0.035
Heave (In)
2.61
Drag (lbs)
7.468
A.17
Wedge
A
Run 30
LCG
40%
Foil Position
f3-1.5
Speed (fps)
28.5
Avg Trim (Deg)
3.34
102
Trim Std Dev
0.194
Heave (In)
2.60
Drag (lbs)
7.443
A.18
Wedge
A
Run 31
LCG
40%
Foil Position
f3-1.5
Speed (fps)
31.1
Avg Trim (Deg)
3.16
103
Trim Std Dev
0.229
Heave (In)
2.65
Drag (lbs)
8.114
A.19
Wedge
A
Run 32
LCG
40%
Foil Position
f3-1.5
Speed (fps)
Avg Trim (Deg)
25.9
3.78
104
Trim Std Dev
0.471
Heave (In)
2.49
Drag (lbs)
7.150
A.20
Wedge
A
Run 33
LCG
40%
Foil Position
f3-1.5
Speed (fps)
23.3
Avg Trim (Deg)
3.88
105
Trim Std Dev
0.352
Heave (In)
2.31
Drag (lbs)
6.754
A.21
Run 34
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
40%
f3-1.5
20.7
5.50
0.406
2.10
7.395
106
A.22
Run 35
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
40%
f3-1.5
18.1
6.85
0.061
1.83
8.627
107
A.23
Wedge
A
Run 36
LCG
40%
Foil Position
f3-1.5
Speed (fps)
23.3
Avg Trim (Deg)
4.16
108
Trim Std Dev
1.142
Heave (In)
2.30
Drag (lbs)
7.124
A.24
Wedge
A
Run 37
LCG
40%
Foil Position
f 1-0
Speed (fps)
28.5
Avg Trim (Deg)
3.65
Side and rear pictures not available.
109
Trim Std Dev
0.07
Heave (In)
2.84
Drag (lbs)
7.563
A.25
Run 38
Wedge
LCG
Foil Position
A
40%
f 1-0
Speed (fps)
31.1
Avg Trim (Deg)
3.57
Side and rear pictures unavailable.
110
Trim Std Dev
0.10
Heave (In)
2.91
Drag (lbs)
8.245
A.26
Wedge
A
Run 39
LCG
40%
Foil Position
f3-1.5
Speed (fps)
25.9
Avg Trim (Deg)
4.00
111
Trim Std Dev
0.75
Heave (In)
2.70
Drag (lbs)
7.399
A.27
Run 40
Wedge
LCG
Foil Position
A
44%
fl-0
Speed (fps)
23.3
Avg Trim (Deg)
4.92
112
Trim Std Dev
1.46
Heave (In)
2.53
Drag (lbs)
7.804
A.28
Run 41
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
44%
fl-O
20.7
5.79
0.11
2.38
7.913
113
A.29
Run 42
Wedge
LCG
Foil Position
A
44%
f 1-0
Speed (fps)
18.1
Avg Trim (Deg)
Trim Std Dev
6.63
0.09
114
Heave (In)
2.06
Drag (lbs)
8.016
A.30
Wedge
A
Run 43
LCG
44%
Foil Position
Speed (fps)
Avg Trim (Deg)
f 1-0
28.5
3.63
115
Trim Std Dev
0.04
Heave (In)
2.85
Drag (lbs)
7.552
A.31
Run 44
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
44%
fl-O
28.5
3.65
0.29
3.65
7.470
116
A.32
Run 45
Wedge
LCG
Foil Position
Speed (fps)
A
44%
fl-O
28.5
Avg Trim (Deg)
3.63
117
Trim Std Dev
Heave (In)
Drag (lbs)
0.09
3.63
7.515
A.33
Run 46
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
A
44%
fl-O
28.5
3.59
0.001
2.80
7.529
118
A.34
Wedge
A
Run 47
LCG
44%
Foil Position
Speed (fps)
Avg Trim (Deg)
f1-0
28.5
3.62
119
Trim Std Dev
0.27
Heave (In)
2.83
Drag (lbs)
7.524
A.35
Run 48
Wedge
LCG
B
44%
Foil Position
fl-0
Speed (fps)
28.5
Avg Trim (Deg)
2.78
120
Trim Std Dev
0.42
Heave (In)
2.72
Drag (lbs)
8.082
A.36
Wedge
B
Run 49
LCG
44%
Foil Position
fO-O
Speed (fps)
28.5
Avg Trim (Deg)
3.83
121
Trim Std Dev
0.29
Heave (In)
2.84
Drag (lbs)
8.204
A.37
Wedge
B
Run 50
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
44%
fO+2
28.5
3.71
0.08
2.82
8.102
122
A.38
Run 51
Wedge
LCG
Foil Position
B
44%
f0+2
Speed (fps)
31.1
Avg Trim (Deg)
3.54
123
Trim Std Dev
0.20
Heave (In)
2.86
Drag (lbs)
8.829
A.39
Run 52
Wedge
LCG
Foil Position
Speed (fps)
B
44%
fO--2
25.9
Avg Trim (Deg)
4.26
124
Trim Std Dev
0.82
Heave (In)
2.70
Drag (lbs)
8.206
A.40
Run 53
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
44%
fO- 2
23.3
4.93
1.05
2.55
8.088
125
A.41
Run 54
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
44%
fO+2
20.7
5.69
0.09
2.37
8.230
126
A.42
Wedge
B
Run 55
LCG
44%
Foil Position
fO+2
Speed (fps)
18.1
Avg Trim (Deg)
5.74
127
Trim Std Dev
0.06
Heave (In)
1.82
Drag (lbs)
8.459
A.43
Wedge
B
Run 56
LCG
44%
Foil Position
fO+2
Speed (fps)
15.6
Avg Trim (Deg)
-0.44
128
Trim Std Dev
0.04
Heave (In)
1.18
Drag (lbs)
16.047
A.44
Wedge
B
Run 57
LCG
44%
Foil Position
f0+2
Speed (fps)
15.6
Avg Trim (Deg)
-0.61
129
Trim Std Dev
0.06
Heave (In)
1.18
Drag (lbs)
16.237
A.45
Wedge
B
Run 58
LCG
40%
Foil Position
fo-0
Speed (fps)
28.5
Avg Trim (Deg)
5.50
130
Trim Std Dev
0.11
Heave (In)
2.74
Drag (lbs)
9.304
A.46
Wedge
B
Run 59
LCG
40%
Foil Position
f2-0
Speed (fps)
28.5
Avg Trimi (Deg)
3.51
131
Trim Std Dev
0.35
Heave (In)
2.74
Drag (lbs)
8.308
A.47
Run 60
Wedge
LCG
Foil Position
B
40%
f2-0
Speed (fps)
31.1
Avg Trim (Deg)
3.24
132
Trim Std Dev
0.18
Heave (In)
1.84
Drag (lbs)
8.870
A.48
Wedge
B
Run 61
LCG
40%
Foil Position
f2-0
Speed (fps)
25.9
Avg Trim (Deg)
4.02
133
Trim Std Dev
1.01
Heave (In)
2.58
Drag (lbs)
8.211
A.49
Run 62
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
B
40%
f2-0
23.3
5.36
0.35
134
Heave (In)
2.46
Drag (lbs)
8.138
A.50
Run 63
Wedge
LCG
Foil Position
Speed (fps)
B
40%
f2-0
20.7
Avg Trim (Deg)
6.12
135
Trim Std Dev
0.08
Heave (In)
2.29
Drag (lbs)
8.064
A.51
Wedge
B
Run 64
LCG
40%
Foil Position
f2-0
Speed (fps)
18.1
Avg Trim (Deg)
6.67
136
Trim Std Dev
0.07
Heave (In)
1.96
Drag (lbs)
8.411
A.52
Wedge
B
Run 66
LCG
42%
Foil Position
fl-O
Speed (fps)
28.5
Avg Trim (Deg)
4.32
137
Trim Std Dev
0.06
Heave (In)
2.73
Drag (lbs)
8.550
A.53
Wedge
B
Run 67
LCG
42%
Foil Position
f2-0
Speed (fps)
28.5
Avg Trim (Deg)
2.87
138
Trim Std Dev
0.43
Heave (In)
2.66
Drag (lbs)
8.041
A.54
Wedge
B
Run 68
LCG
42%
Foil Position
f2-0
Speed (fps)
31.1
Avg Trim (Deg)
2.83
139
Trim Std Dev
0.25
Heave (In)
2.75
Drag (lbs)
8.722
A.55
Wedge
B
Run 69
LCG
42%
Foil Position
f2-0
Speed (fps)
25.9
Avg Trim (Deg)
3.82
140
Trim Std Dev
0.84
Heave (In)
2.58
Drag (lbs)
8.120
A.56
Wedge
B
Run 71
LCG
42%
Foil Position
f2-0
Speed (fps)
23.3
Avg Trim (Deg)
4.28
141
Trim Std Dev
0.07
Heave (In)
2.42
Drag (lbs)
7.730
A.57
Run 72
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
42%
f2-0
20.7
5.46
0.42
2.26
7.961
142
A.58
Wedge
B
Run 75
LCG
42%
Foil Position
f1+2
Speed (fps)
28.54
Avg Trim (Deg)
4.04
143
Trim Std Dev
0.03
Heave (In)
2.72
Drag (lbs)
8.440
A.59
Run 78
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
42%
f2-2
28.2
3.07
0.27
2.66
7.996
144
A.60
Wedge
B
Run 79
LCG
42%
Foil Position
f2-3
Speed (fps)
28.5
Avg Trim (Deg)
3.10
145
Trim Std Dev
0.17
Heave (In)
2.66
Drag (lbs)
7.917
A.61
Run 80
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
42%
f2-4
28.5
3.37
1.06
2.64
8.410
146
A.62
Wedge
B
Run 81
LCG
42%
Foil Position
f2-4
Speed (fps)
31.1
Avg Trim (Deg)
3.35
147
Trim Std Dev
0.14
Heave (In)
2.73
Drag (lbs)
8.638
A.63
Run 82
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
42%
f2-4
25.9
3.38
0.30
2.51
7.629
148
A.64
Wedge
B
Run 83
LCG
42%
Foil Position
f2-4
Speed (fps)
23.3
Avg Trim (Deg)
3.47
149
Trim Std Dev
0.30
Heave (In)
2.30
Drag (lbs)
7.263
A.65
Wedge
B
Run 84
LCG
42%
Foil Position
f2-4
Speed (fps)
20.7
Avg Trim (Deg)
4.17
150
Trim Std Dev
0.18
Heave (In)
2.08
Drag (lbs)
7.024
A.66
Wedge
B
Run 85
LCG
42%
Foil Position
f2-4
Speed (fps)
18.1
Avg Trim (Deg)
1.48
151
Trim Std Dev
0.05
Heave (In)
1.47
Drag (lbs)
13.994
A.67
Wedge
B
Run 86
LCG
42%
Foil Position
f2-4
Speed (fps)
18.1
Avg Trim (Deg)
6.13
152
Trim Std Dev
0.05
Heave (In)
1.87
Drag (lbs)
7.757
A.68
Wedge
B
Run 90
LCG
42%
Foil Position
f2-0
Speed (fps)
28.5
Avg Trim (Deg)
Trim Std Dev
Heave (In)
2.76
0.66
2.63
153
Drag (lbs)
8.843
A.69
Run 91
Wedge
LCG
Foil Position
Speed (fps)
Avg Trim (Deg)
Trim Std Dev
Heave (In)
Drag (lbs)
B
42%
f2-0
28.5
3.57
0.24
2.71
8.395
154
A.70
Wedge
B
Run 92
LCG
42%
Foil Position
f2-0
Speed (fps)
31.1
Avg Trim (Deg)
3.32
155
Trim Std Dev
0.18
Heave (In)
2.78
Drag (lbs)
8.986
A.71
Wedge
B
Run 93
LCG
42%
Foil Position
f2-0
Speed (fps)
25.9
Avg Trim (Deg)
3.33
156
Trim Std Dev
1.06
Heave (In)
2.48
Drag (lbs)
8.196
Bibliography
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Eugene P. Clement. A configuration for a stepped planing boat having minimum
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[5] Eugene P. Clement and Donald L. Blount. Resistance tests of a systematic series
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R. Courant, K. Friedrichs, and H. Lewy. On the partial difference equations
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[9]
Tullio Celano III. The prediction of porpoising inception for modern planing
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