.1
Flapping Foil Propulsion for Cruising and
Hovering Autonomous Underwater Vehicles
by
Victor Polidoro
Submitted to the Department of Ocean Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Ocean Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 2003
Massachusetts Institute of Technology 2003. All rights reserved.
A uthor ...... .
...............
Department of Ocean Engineering
May 22, 2003
/7
Certified by.........
II
- ..
rlichael S. Triantafyllou
Professor of Ocean Engineering
Thesis Supervisor
Accepted by .............
....
M e...
Michael S. Triantafyllon
Chairman,Departmental Committee on Graduate Students
INSTITUTE
MASSACHUSETTS
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
BARKER
AUG 2 5 2003
LIBRARIES
-;
2
Flapping Foil Propulsion for Cruising and Hovering
Autonomous Underwater Vehicles
by
Victor Polidoro
Submitted to the Department of Ocean Engineering
on May 22, 2003, in partial fulfillment of the
requirements for the degree of
Master of Science in Ocean Engineering
Abstract
This thesis describes the design, construction, and testing of an autonomous underwater vehicle capable of high precision positioning and hovering using flapping foils
as actuators. The vehicle is 2 m long with an approximate displacement of 157 kg.
Four flapping foils, each actuated by two motors, performing a two degree of freedom
angular motion (roll and pitch motion) provide the necessary forces for maneuvering
and propulsion. The design of the actuators is based on an extensive hydrodynamic
database for two and three dimensional foils developed at the Testing Tank and the
Propeller Tunnel facilities. The foils have dimensions 0.4 m span and 0.1 m chord
and are capable of producing peak lift forces up to 100 N, peak thrust forces up to
70 N, and mean thrust forces up to 37 N. Flapping foils can provide large forces (up
to an order of magnitude larger than steadily translating foils) very rapidly.
Experiments were performed with an individual foil actuator over a range of foil
sizes (s/c = 6, 5, 4, 3) and wake widths (1.4 < ho/c < 6.3). Planform area thrust
coefficients of 7.2 were recorded at a Strouhal number of 1.2. The coefficient of thrust
was found to be a strong function of the Strouhal number and maximum angle of
attack and a weak function of the wake width in this regime. The size of the foil was
the primary factor controlling the trade off between the magnitude and bandwidth
of the thrust forces produced.
Thesis Supervisor: Michael S. Triantafyllou
Title: Professor of Ocean Engineering
3
4
Acknowledgments
I would like to thank my advisor Professor Michael Triantafyllou for his generous
support and his kind words of encouragement. His insight into hydrodynamics and
controls have changed my perspective of physics. His curiosity and foresight have
provided the direction and motivation for this work.
I would like the thank Dr. Franz Hover for introducing me to the Towtank and getting
me involved with this vehicle. If I had never met Franz, I definitely would not have
attended MIT. Throughout this project Franz has always taken the time to discuss
every problem and idea.
All the design and fabrication work for this vehicle was accomplished as a collaborative effort with Stephen Licht. I could not have asked for a better partner on this
project. I would have been overwhelmed without him to lean on. Anyone reading
this thesis must also read his.
Dave Beal was a great friend and an excellent source of advice. I asked Dave more
questions than anyone.
I would like to thank Melissa Flores for the countless hours she worked at the water
tunnel gathering data that directly contributes to this vehicle. Be sure to read her
thesis as well.
I would like to thank Fred Cote for teaching me nearly everything I know about machining. Fred offered advice and hands on help for almost every part on the vehicle.
I would like to thank Tom Consi for his valuable advice on electronics and for the
fabrication materials and computer he contributed to this vehicle.
5
I would like to thank Jim Bales for his advice on batteries and power management.
I would like to thank Jeff Stettler for his help with the dynamometer and calibration
rig.
I would like to thank Justin Manley for his advice on vehicle maintenance and deployment.
I thank Karl McLetchie for his foil molds and his help with I4TEX2E
6
Contents
List of Figures
13
List of Tables
15
Nomenclature
17
1
Flapping Foil Propulsion and Biomimetic Design
19
1.1
20
1.2
2
Hydrodynamics and Mechanics ......
.....................
1.1.1
Wake Structure ..........................
24
1.1.2
Kinematics .......
26
1.1.3
Dynamics .......
1.1.4
C ontrol
............................
.............................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Previous Work with Flapping Foil Robotics
32
34
. . . . . . . . . . . . . .
37
1.2.1
Autonomous Vehicles . . . . . . . . . . . . . . . . . . . . . . .
37
1.2.2
Externally Propelled Robotic Platforms . . . . . . . . . . . . .
46
Design and Fabrication of AUV
51
2.1
Purpose of Vehicle
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.2
Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
2.2.1
Mission Length and Location
. . . . . . . . . . . . . . . . . .
54
2.2.2
Depth Rating . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
2.2.3
D im ensions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
2.3
Vehicle Layout
2.3.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
Modularity and Scalability . . . . . . . . . . . . . . . . . . . .
55
7
2.3.3
Mass, Hydrostatic Stability and Net Buoyancy .
.
56
2.3.4
Added Mass and Drag Considerations . . . . . .
.
57
57
2.4.1
Single Board Computer Running Linux . . . . .
57
2.4.2
Distributed Motion Control on Ethernet Network
59
.
.
Control and Communication . . . . . . . . . . . . . . .
60
2.5.1
Inertial Measurement Unit . . . . . . . . . . . .
60
2.5.2
Three Axis Magnetometer
. . . . . . . . . . . .
61
2.5.3
Leak Detectors
. . . . . . . . . . . . . . . . . .
62
Batteries and Power Management . . . . . . . . . . . .
62
.
.
.
.
Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diodes for Preventing Accidental Charging or Di scharging
of
. . . . . . . . . . . . . . . . . . .
. . . . .
63
2.6.2
.
2.6.1
Voltmeter on Batteries . . . . . . . . . . . . . .
. . . . .
63
2.6.3
Ammeter on Power Supply to Each Foil Actuator
. . . . .
63
2.6.4
Digital I/O and Relays . . . . . . . . . . . . . .
. . . . .
63
2.6.5
Magnetic Switches and LEDs
. . . . . . . . . .
. . . . .
64
.
the Batteries
Design of Foil Actuators
65
Single Housing Design
. . . . . . . . . . . . . . . . . . . . . . . . .
68
3.2
Two Housing Design . . . . . . . . . . . . . . . . . . . . . . . . . .
74
.
3.1
.
3
.
56
.
2.6
. . . . . . . . . . . . . . .
.
2.5
Planes of Symmetry
.
2.4
2.3.2
4 Force Measurements
4.2
. . . . . . .
84
4.1.1
Setup
. . . . . . . . . . . .
. . . . . . .
84
4.1.2
Sensors and Calibration
. .
. . . . . . .
85
4.1.3
Data Acquisition and Control
. . . . . . .
88
4.1.4
Sources of Error . . . . . . .
. . . . . . .
88
4.1.5
Testing Procedure . . . . . .
. . . . . . .
90
4.1.6
Postprocessing
. . . . . . .
. . . . . . .
92
Cruising Data . . . . . . . . . . . .
. . . . . . .
93
.
.
.
.
.
.
Description of Tests . . . . . . . . .
.
4.1
81
8
4.3
5
Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design Recommendations
108
109
A Cruising Forces in Time
115
9
10
List of Figures
Diagram of a reverse von Kirmin vortex street
. . . .
.
1-1
.
1-2 Flow visualization of a wake behind a flapping foil . . .
Distance from center of roll axis to the root of the foil, ro
1-4 Angle of attack diagram
. . . . . . . . . . . . . . . . .
.
1-3
Angle of attack distribution over span . . . . . . . . . .
1-6
Periodic lift and thrust forces . . . . . . . . . . . . . .
1-7
Tail Section of the RoboPike -
1-8
John Kumph and the RoboPike. . . . . . . . . . . . . .
1-9
Draper Laboratory free swimming robotic tuna. . . . .
.
.
1-5
.
.
.
John Kumph. . . . . .
Draper Laboratory . .
.
1-10 Drawing of the Draper tuna. -
.
1-11 Draper tuna at Nickerson State Park. . . . . . . . . . .
.
1-12 Robotic fish with 3DOF pectoral fins. - Naomi Kato .
1-13 The first generation robotic dolphin with pneumatics.
-
Motomu
.
N akashim a . . . . . . . . . . . . . . . . . . . . . . . . .
1-14 The first generation robotic dolphin with pneumatics.
-
Motomu
.
N akashim a . . . . . . . . . . . . . . . . . . . . . . . . .
1-15 The second generation robotic dolphin with batteries and an electric
.
motor. - Motomu Nakashima . . . . . . . . . . . . . . . . . . . . .
1-17 RoboTunall -
.
Dave Barrett. . . . . . . . . . . . . . . . . . . . . . .
Dave Beal, Mike Sachinis, Mike Jakuba .
. . . . . .
.
1-16 RoboTuna -
.
1-18 SeaLion - Craig Martin .. . . . . . . . . . . . . . . . . . . . . . . .
AUV in the sea turtle configuration .. . . . . . . . . . . . . . . . . .
.
2-1
11
AUV power, control, and communication schematic
58
3-1
Single housing foil actuator. . . . . . . . . .
69
3-2
Single housing foil actuator. . . . . . . . . .
. . . . .
69
3-3
Drawings of single housing foil actuator.
. .
. . . . .
70
3-4
Inside of single housing foil actuator.
. . . .
. . . . .
71
3-5
Drawings of the bellows. . . . . . . . . . . .
. . . . .
72
3-6
Drawings of the bellows assembly . . . . . .
. . . . .
73
3-7
Two housing foil actuator. . . . . . . . . . .
.
. . . . .
75
3-8
Drawings of the two housing foil actuator.
.
. . . . .
75
3-9
Inside the two housing foil actuator. . . . . .
. . . . .
76
3-10 Close up of the roll shaft coupling . . . . . .
. . . . .
77
3-11 Drawings of the pitch seal boot. . . . . . . .
. . . . .
78
3-12 Drawings of the pitch seal assembly with shaft seal.
. . . . .
79
Two housing foil actuator mounted to the six axis dynamometer. . .
85
4-2
Calibration rig used to apply force at the 70% span, ro.7 . . . . . . .
.
86
4-3
Calibration curve for thrust axis.
. . . . . . . . . . . . . . . . . . .
87
4-4
Calibration curve for lift axis. . . . . . . . . . . . . . . . . . . . . .
87
4-5
Calibration curve for ammeter.
. . . . . . . . . . . . . . . . . . . .
88
4-6
Spectrum of mechanical vibrations and line noise
4-7
A typical case: St = 0.6, amax = 40 deg, s
4-8
A high thrust case: St = 1.2, ama = 40 deg, s = 0.40 m, q0 = 60 deg
4-9
A high efficiency case: St
deg......
=
.
.
.
4-1
.
.
.
.
.
.
.
.
.
.
.
2-2
.
#0
0.40 m,
= 40 deg .
.
=
. . . . . . . . . .
91
95
96
1.0, ozy, = 30 deg, s = 0.40 m, 0 = 60
..........
...........................
97
99
= {60,40,20}
100
#0 = {60,40,20}
101
{60,40,20} . .
102
4-14 Summary of contour plots for coefficient of thrust CT . . . . . . . .
103
4-15 Summary of contour plots for mean thrust F, [N], with St . . . . .
104
=
0.60,
4-11 Contour plots for coefficient of thrust CT: s = 0.50,
4-12 Contour plots for coefficient of thrust CT: s
=
0.40,
=
.
.
4-13 Contour plots for coefficient of thrust: s = 0.30, #o
0
.
# 0 = {60,40,20}
4-10 Contour plots for coefficient of thrust CT: s
12
4-16 Summary of contour plots for operational efficiency rTop, with St
4-17 Summary of contour plots for mean thrust Fx [N], with
f
. . .
105
. . . . . . .
106
4-18 Summary of contour plots for operational efficiency rop, with
13
f
. . . .
107
14
List of Tables
2.1
Mass and buoyancy of major components . . . . . . . . . . . . . . . .
56
3.1
Specifications of roll and pitch motors . . . . . . . . . . . . . . . . . .
67
3.2
List of variables for program running on motion control card. . . . . .
68
4.1
Force and moment capacities for six axis dynamometer . . . . . . . .
86
15
16
Nomenclature
c
foil chord [m]
s
foil span [in]
U
steady vehicle forward velocity, steady towing speed in experiments [rn/s]
p
fluid density [kg/m3 ]
V
fluid kinematic viscosity
Rec
chord Reynolds number, Uc/v [-]
0
maximum angle of attack
'max
[m 2 /S]
[radians] in equations, [degrees] in text
00
amplitude of sinusoidal pitch motion 0(t) [radians] in equations, [degrees] in text
00
amplitude of sinusoidal roll motion
V)
phase between roll and pitch [radians]
ro
distance from center of roll axis to root of the foil [m]
rO.7
distance from center of roll axis to 70% of span, ro + 0.7s [m]
ro.7 /ro
a measure of the range of the angle of attack distribution over span [-]
2ho
wake width at rO.7 (arclength), 2ro.7#0 [M]
ho/c
normalized wake width [-]
f
frequency of foil motion
T
period of foil motion [s]
W
frequency of foil motion [radian/s]
St
Strouhal number, 2ro.7 q#of/U
Fx(t)
thrust force; mean value Fx [N]
[s-1]
[-]
17
#(t)
[radians] in equations, [degrees] in text
Fy(t)
lift force; mean value Fy [N]
CT
mean thrust coefficient, 2FX/pU2cs
CL
mean lift coefficient, 2FY/pU 2cs
V
voltage of power supply (always 24 volts) [V]
I
24 (t)
[-]
[-]
current supplied to actuator at 24 volts; mean value I 24 [A]
P(t)
electrical power supplied to actuator, VIA 24 (t); mean value P [W]
770P
operational efficiency, FxU/P [-1
18
Chapter 1
Flapping Foil Propulsion and
Biomimetic Design
Considerable theoretical, numerical, and experimental work has been done to investigate the physics of swimming and flying [19] [24] [12] [4] [7] [5] [21] [14]. The success
of this body of work has greatly improved the general understanding of the hydrodynamics of fish swimming. One of the prime motivations for this body of work was to
provide an understanding of hydrodynamics that could be used to improve the design and performance of underwater vehicles. A man-made machine that successfully
exploits the hydrodynamics of fishlike swimming could have greatly improved maneuvering and hovering capabilities, while maintaining the ability to cruise efficiently. A
simple and robust vehicle of this nature could serve as an extremely powerful mapping
and surveying tool for oceanographers and underwater archeologists. Improved maneuvering and hovering capabilities would enable the vehicle to operate in confined
spaces, at low speeds, near the surface, and in unsteady flow conditions. Existing
AUVs are incapable of operating in such conditions due the limited maneuvering
capabilities of vehicles with propellers and conventional lifting surfaces.
The goal of the work presented in this thesis is to apply this knowledge of hydrodynamics to the design of an autonomous underwater vehicle (AUV). Knowledge
gained from the design and implementation of this AUV will help transition flapping
foil propulsion from the laboratory to the ocean. One of the major hurdles remain19
ing in developing this form of propulsion into a technology that can be implemented
in the ocean is to find a mechanical design that is simple and robust enough to be
useful. Most of the previous work in designing autonomous flapping foil vehicles [17]
[3] has strived to exactly replicate the morphology of a particular species of living
fish. While these robots were extremely well designed and well built, they were also
too complicated and had too little room for payload instrumentation to be used as
a piece of laboratory equipment for oceanography. The focus of the current vehicle
was to strive for the simplest design possible to minimize the time and cost for fabrication and maintenance. While the design of this vehicle was not based directly on
any particular animal, the location and motion of the foils are similar to a sea turtle.
It has a rigid frame to simplify the sealing problems and to make it easier to leave
room for payload sensors. This vehicle has four flapping foils that each move with
two degrees of freedom.
1.1
Hydrodynamics and Mechanics
Flapping foil propulsion is a common mode of locomotion in nature. Birds, flying
insects, fish, and cetaceans move with grace and agility. These animals are capable
of maneuvers that are currently impossible for machines.
Some of these animals
are optimal for straight line cruising, while others have an astounding capability to
accelerate and turn. Dolphins and tuna are capable of high cruising efficiency [23]
[10]. Hummingbirds and dragonflies have stellar hovering capabilities. Sharks and
pikes are highly agile and maneuverable predators. All of these animals use some form
of flapping foil propulsion. From the perspective of hydrodynamics, aerodynamics,
and biology, the investigation of flapping foil propulsion is well justified.
Similarities in the morphologies of various species of fish and cetaceans indicate
there is something fundamental in the hydrodynamics of swimming. It was noted
that shape and motion of the lunate caudal fin of dolphins and tuna were remarkably similar [19]. The convergence to similar optimal solutions from substantially
different initial conditions indicates that there is something universal about these
20
particular geometries and kinematics. Purely from the perspective of hydrodynamics
the optimal design should be expected to be independent of the mechanical means
of actuation.
However, this view completely disregards the complexities and effi-
ciency losses within the body itself. While there are notable differences between the
biomechanics of mammals and fish, these differences are very subtle compared to the
differences between machines and animals. Given that the initial conditions for the
design of mechanical fish are so drastically different from the initial conditions of
animals, it is not safe to assume the design will again converge to the same optimal
solution. If this convergence does eventually occur, there will first need to be great
advances in artificial muscles.
While it is easy to draw inspiration from the wonders of nature, it is important
to remember that animals are made of very different materials than machines. There
is certainly no reason to expect that the optimal design in nature will be manifested
in the identical form as a machine. The dynamic characteristics of muscles are far
different from those of electric motors, combustion engines, and hydraulic pistons.
Currently available artificial muscles are very limited by either low bandwidth, low
displacement, or low efficiency.
The sealing and elastic properties of skin are far
superior to the material properties of flexible rubbers and composites. Even primitive
animals have a brain and nervous system that is capable of producing highly robust
and adaptive behavior. Tissues that are grown can be far more complex than parts
that are machined or molded. It is also important to consider that the morphology and
behavior of animals are subject multiple evolutionary forces [9]. The aerodynamics
of a bird's tail may not be optimal if the size and shape of the tail is also used for
attracting a mate
[1].
A successful strategy for designing a biomimetic robot should acknowledge the
key differences in the fundamental building blocks. A mechanical design that strives
to exactly replicate an animal will not be optimal if the properties of the components
are drastically different. Design of biomimetic robots is a constrained optimization
problem. While the constraints on the biological solutions are far different from the
constraints on the mechanical solutions, the optimal design should be expected to
21
differ.
While evolution produces extraordinary solutions, there is no planning or
insight in the process. Designers are limited only by their available materials and
understanding of physics. Changes between generations of complex machinery are
not random, they are the result of deliberate attempts at improving performance or
reducing complexity.
The idea of exploiting the hydrodynamics of fishlike swimming to improve the
performance of underwater vehicles
[24]
has been introduced at a time when the req-
uisite technologies for robotics are immature. The performance of future generations
of flapping foil vehicles will greatly depend on advances made in artificial muscles, batteries, flow sensors, and controls. The design process is strongly time variant. Clearly
the selection of components depends on the availability of materials. Acknowledging
the limits on the availability of actuators and materials, the focus of future hydrodynamic research should include a search for kinematics that will be easier for machines
to achieve. In order to simplify the mechanical aspects of the problem it is necessary
to search for the simplest kinematics with the fewest degrees of freedom that will still
result in optimal hydrodynamic forces. Complexity in mechanical design does not
scale linearly with the degrees of freedom of motion.
There are many similarities between the current state of flapping foil vehicles and
helicopters in the 1920's. The performance of early helicopter designs were greatly
limited by the available engines and structural materials. As knowledge of rotary
wing aerodynamics rapidly progressed, the performance was restricted mostly by the
mechanics. Igor Sikorsky had limited success with his early helicopter designs due to
current state of technology in the components. Early helicopters were plagued by lack
of power and vibration. Progress depended strongly on the general understanding of
metallurgy and combustion. Now, in retrospect, Sikorsky's designs were remarkably
modern and sophisticated. He was on the right path and he has received universal
recognition as a visionary. There are similarities between the kinematics of rotary
wing aerodynamics and flapping foil hydrodynamics.
Many of the lessons learned
in the design, control, and maintenance of helicopters will provide insight into the
design of flapping foil vehicles. There are many ideas in the designs of cyclic and
22
collective pitch control mechanisms on helicopters that could be applied to flapping
foil actuators.
Due to the tremendous success of previous research in the hydrodynamics of flapping foil propulsion, the performance of flapping foil vehicles is now mostly limited
by the general understanding of the mechanical and control aspects of the problem.
Some of the most daunting tasks in the mechanics and controls could be simplified
through research in hydrodynamics. There are certainly many issues that remain to
be explored in hydrodynamics. These areas involve three dimensional flow effects,
the geometry and compliance of the foil, methods for manipulating upstream vorticity, and cavitation. In addition to these areas, the direction for future research into
the hydrodynamics of flapping foil propulsion should be directed towards reducing
the complexity of the kinematics and finding regimes with the greatest forgiveness
to errors in the angle of attack profile. Due to the necessity of the flow velocity in
calculating the kinematics, the performance of flapping foil propulsion will be highly
sensitive to the accuracy of the estimated or measured value of the incoming flow
velocity upstream of the foils. Flapping foil propulsion could be applied to a much
wider variety of vehicles if this knowledge of the incoming flow velocity was not necessary. The technological impact of flapping foil propulsion would be much greater
if flapping foil actuators could effectively be used for propulsion and maneuvering
without knowledge of the local flow velocity.
Progress in flapping foil propulsion will depend on the availability of advanced
artificial muscles, batteries, and velocimeters.
Specifically we need batteries with
greater power density and actuators with dynamic characteristics like fast twitch
muscles. In order to take full advantage of the potential of flapping foil propulsion,
the powertrain needs to be able to deliver rapid bursts of energy. Fast starts require
large forces quickly. The majority of muscle tissue in fish is only used for quick bursts
of energy to rapidly accelerate or turn [25], while a very small portion of the muscles
have the endurance for cruising. A highly advanced flapping foil vehicle would have
two types of artificial muscles or motors in parallel.
One type of actuator would
deliver the explosive power for rapid starts and aggressive maneuvers and the other
23
Cylinder
Von Karman Vortex Street
DRAG
mean
velocity
deficit
U
THRUST
mean
(4k'
~
velocity
excess
Flapping Foil
Reverse Von Karman Vortex Street
Figure 1-1: Diagram of a reverse von Kairmain vortex street. The foil motion repositions the vortices in the wake to form a thrust jet.
would be used for cruising with high efficiency.
1.1.1
Wake Structure
One of the major hydrodynamic benefits of flapping foil propulsion is that the wake
structure is very simple and natural, it is the reverse of a common drag wake known
as a von Kairmain vortex street. In a von Karmin street the vortices are shed in an
alternating pattern that results in a mean velocity deficit behind the body. For a
steady upstream flow, this velocity deficit is manifested as a reduction of the momentum flux in the streamwise direction. By conservation of momentum, a decrease in
the streamwise momentum of the fluid must result in a net drag force on the body.
The beauty of flapping foil propulsion is that the motion of the foil is simply
reversing the shedding pattern of the vortices in the von Kairmain street to result in
a net velocity excess behind the body. As the foil imparts additional downstream
momentum into the fluid, there is a net thrust force on the body. This is a very
simple and elegant means of transforming drag into thrust.
24
Figure 1-2: Flow visualization of a wake behind a flapping foil -Oyvind Haugsdal [14]
One of the major benefits of a simple wake structure is that it now becomes
possible to devise control strategies to superimpose existing upstream vorticity with
the downstream wake in such a way that the foil can recover energy from the flow
[2] [8]. With existing upstream vorticity in the flow, a flapping foil actuator could
achieve hydrodynamic efficiency greater than 100% by extracting some of the existing
kinetic energy from the flow. This is how rainbow trout are able to swim upstream
so efficiently [18]. The ability to manipulate upstream vorticity gives flapping foil
propulsion enormous potential for improving the efficiency of underwater vehicles.
While this aspect of flapping foil propulsion is too complicated to implement on a
vehicle in the short term, a vehicle that is able to manipulate upstream vorticity
will have greatly improved efficiency in the wake of another vehicle. This strategy
could give AUVs the ability to exhibit schooling to cruise to a survey sight. The
net efficiency of the group of vehicles could be greatly improved if the downstream
vehicles could recover energy from the wakes of upstream vehicles.
Manipulating
upstream vorticity may also give AUVs the capability of operating in the surf zone.
25
The most common form of propulsion in marine applications is obviously the
The wake structure of a propeller is far more complex than the wake
propeller.
behind a flapping foil. The geometry of a propeller is more complex and difficult to
manufacture than a foil. The major advantage that propellers currently have over
flapping foils is that the drivetrain supplying power to the propeller is drastically
simpler and more efficient than the existing designs for drivetrains of flapping foils.
The drivetrain is defined to be every component that transfers either electrical or
mechanical energy.
Engines and electric motors perform best when turning at a
constant speed, which makes them ideally suited to supply energy to a propeller.
The other advantage that propellers currently have is that their performance for
straight cruising is not as sensitive to the knowledge of the incoming flow.
1.1.2
Kinematics
In this work foils are moved with two rotational motions. The large displacement
flapping motion of the wing is refereed to as the roll motion. The twisting or feathering
of the wing is referred to as the pitch motion. The terms roll and pitch were selected
to be consistent with conventional ship and vehicle notation. Linear motions and the
yaw rotational motion are not used to minimize the complexity of the mechanical
design.
Equations of motion for three dimensional kinematics
The roll and pitch motions of the foil are both sinusoidal, and this is sometimes referred to as simple harmonics.
The roll position of the foil is defined as,
0(t) =
where
#o is
#osin(ot) +
/bN.,
(1.1)
the roll amplitude in radians and L is the frequency of the foil motion in
radians per second.
#bias
is a static roll bias used to change the mean roll position
26
of the foil.
#bia, is
normally zero, but may be used, for example, to prevent a down-
stream foil from intercepting an upstream wake.
The pitch position of the foil is defined as,
0(t) = 0o sin(wt +
) + Obias
(1.2)
where 00 is the pitch amplitude in radians and V) is the phase angle between pitch
and roll in radians.
Obia,
is a static pitch bias used for maneuvering, and is normally
equal to zero. For this work the phase angle
4'
is always 7r/21 and we can therefore
write 0(t) as,
0(t)
= 0o cos(Wt)
+ Oias
(1.3)
A rolling and pitching foil is referred to as having three dimensional kinematics
because the angle of attack varies over the span of the foil, refer to Figure 1-5. The
heaving and pitching kinematics used in previous work [21] [14] is referred to as two
dimensional because the angle of attack is constant over the span of the foil. The
three dimensional (rolling and pitching) kinematics are collapsed to two dimensions
(heaving and pitching) at one span location on the foil. This location was selected
to be 70% from the root of the foil. This location was selected because it is close to
the effective center of hydrodynamic force on the foil and also to be consistent with
conventional propeller notation. This location is referred to as rO.7 , and is defined,
To.7
=
ro + 0.7s
(1.4)
where ro is the distance from the center of the roll axis to the root of the foil, and s
is the span of the foil, refer to Figure 1-3.
'This phase angle was selected based on the results of Doug Read's experiments with a heaving
and pitching foil.[21]
27
Figure 1-3: Distance from center of roll axis to the root of the foil, ro
The amplitude of heave motion (arclength) at rO.7 is referred to as ho, and is defined,
ho- rO. 7 0
(1.5)
h(t) = ho sin(wt)
(1.6)
The heave motion is defined as
a(t)=-arctan
( h(t)U
)
For two dimensional kinematics the angle of attack is defined as,
+9(t)
(1.7)
where U is the forward speed of the foil, and h is the heave velocity,
h(t) = who cos(wt)
Using our definition of ho,
28
(1.8)
Angle of
incoming fluid
velocity
Angle of
Heave velocity
I
Attack
Pitch angle
Forward velocity of vehicle
Figure 1-4: Angle of attack at one span location - The angle of attack has two components, one due to the ratio of two velocities, and another due to the instantaneous
pitch position of the foil.
h(t)= wro.7#o cos(Wt)
= ro.7q$(t)
(1.9)
Now for three dimensional kinematics we can express the angle of attack as,
a(t)
-
arctan
(wro.
7 0 COS(Wt
U
+ 00 cos(Wt) + Obias
(1.10)
pitch induced
roll induced
Note that for positive 00 the pitch motion is selected to reduce the maximum angle
of attack, which is the case for vast majority of the motions that produce thrust.
In these cases the leading edge of the foil is rotated towards the direction of incoming flow.
Obias
is used to make the mean angle of attack nonzero, and therefore the
mean lift force nonzero.[21] Nonzero lift forces allow for the thrust vector to be rotated out of the surge direction in order to produce maneuvering forces on the vehicle.
,
The maximum angle of attack is calculated at rO. 7
Cmax
=
max[a(t)]
29
(1.11)
Dimensionless parameters in kinematics
In order to make the knowledge gained from experiments as general as possible, scaling analysis is applied to the results. Scaling analysis involves finding dimensionless
numbers through Buckingham 7r theory. The relationships between the correct dimensionless parameters reveals fundamental aspects of the physics.
The most important dimensionless parameter in flapping foil propulsion is the
Strouhal number [23].
The Strouhal number, St, can be thought of in two ways.
The Strouhal number is the normalized heave velocity.
The Strouhal number also
describes the geometric spacing of the vortices in the wake.
For three dimensional kinematics, the Strouhal number is defined,
(1.12)
St = 2ro.7q 0 f
U
Since a radian is dimensionless, the maximum angle of attack is also a dimensionless
parameter. For a particular geometry, the St and amax together capture the physics
of the foil motion.
(1.13)
amax
The wake width is determined mostly by the amplitude of the heave motion.
The
amplitude of heave motion is nondimensionalized by the chord of the foil,
-o
(1.14)
c
The distribution of the angle of attack profile, as seen in Figure 1-5, could be described
by the ratio of the heave velocities at two locations.
Likewise it could simply be
described by the ratio of two radii,
O. 7
TrO
30
(1.15)
Angle of attack distribution over span with simple harmonics: a
60---;..Y
30
= 50 degrees
.j
6-
-
---.
-tip
0
-6
R 0.70
-
0.50
-
-30 -
-
0
0.5
1
1.5
Angle of attack distribution over span with simple harmonics: a
2
= 40 degrees
-
60
-60
----
- ------
~
~ ~~
0
0.5
~
-
0
-30 -
-
-
---
- -
~
..-.
30 -.-
--
tip
R 0.70
-0.50
0.25
root
1.5
1
2
Angle of attack distribution over span with simple harmonics: amax = 30 degrees
-
60
-
tip
-
-
30
-
root j
-60
0
0.5
1
Angle of attack distribution over span with simple harmonics:
60m30 --
0
1.5
a
~-
-C--S
2
= 20 degrees
-R
-- ----
-30
-60
.70
0.25
-30-
i
R-
0
0.5
1
1.5
tip
0.70
0.50
0.25
root j
2
Time [period]
Figure 1-5: Angle of attack distribution over. span. The only parameter that changes
between these four plots is the amplitude of pitch motion. Lower amax correspond to
larger pitch motions. Note that amax is always computed at ro. . Simple harmonics
is referring to the sine in the roll motion and the cosine in the pitch motion. Heave
velocity increases with radius because it is proportional to the arclength. Locations
near the tip of the foil are farther from the centerline of the roll axis, so the heave
velocity is higher near the tip. The angle of attack is larger near the tip of the foil due
to the increased heave velocity. The pitch motion is constant over the span. For low
Ozmax the large pitch motions cause the the local angle of attack to be negative near
the root of the foil. An analysis from the 2D perspective would indicate that a change
in the sign of the angle of attack in the spanwise direction would degrade thrust. This
problem is fully 3D and this 2D analysis may not be valid. A compliant foil may allow
the sign of the angle of attack to be constant over the span. Actively twisting the
pitch of the foil over the span would allow for better control of this distribution. This
is similar to the reason helicopter rotor blades are twisted. The orientation of the
twist for a helicopter rotor blade is fixed because there is a preferred direction for lift.
For a flapping foil the orientation of the twist would need to flip every half cycle.
31
Force Vectors for 2D Kinematics
0.4 --------------------------------------
.
E
----------
0.2 -------------
-- --------------
------
0
0
0
-------------------
>-0.3 ----------------------------
-0.4
1
1.2
1.4
1.6
1.8
Horizontal Position of Foil [m]
Figure 1-6: Periodic lift and thrust forces. Figure made with Doug Read's data [21].
1.1.3
Dynamics
Considerable experimental work has been done to map foil motions to forces [21] [14]
[11]. Experimental force data is presented in Chapter 4.
The hydrodynamic forces produced by flapping foils are periodic. For most kinematics used there are either two or four vortices shed per cycle of foil motion. The
lift force varies at the frequency of foil motion, and the thrust force varies at twice
that frequency. Typically the magnitude of the lift force is higher than the thrust
force. For symmetric geometries and kinematics the mean lift force over an integer
number of cycles is zero and the mean thrust force is nonzero.
Thrust vectoring is
achieved by breaking the symmetry in the kinematics. This is normally accomplished
by adding a static DC offset to the pitch motion.
Flapping foils need reciprocating motions with coordinated velocity trajectories
32
on multiple axes. In order to achieve oscillatory motion, energy must be spent to
accelerate the mass of the solid moving parts. Passive mechanical springs or magnets
may be used to minimize the energy spent on inertial forces of the solid moving parts,
at the cost of added complexity in the mechanics and controls. If the stiffness of the
spring or magnet results in a fundamental resonant frequency of vibration that is
coincident with the desired frequency of motion, the motors and active control will
only need to supply energy to offset the damping in steady state. The closer the
passive dynamics of the system are to the desired motion, the lesser the energy that
will be required by active control. The biomechanics of animals take great advantage
of this. There are passive elastic materials at the base of the wings of dragonflies.
When they are not gliding, some species of dragonflies (e.g. Sympetrum sanguineum)
flap their wings within a very small range of frequencies centered about 39 Hz, which
suggests they are storing the inertial energy in the elastic structures. [26] [27] In
this case the desired frequency of the flapping wings is coincident with the natural
frequency of the wing mass and elastic structure.
There is another strategy that does not require a spring. Some insects, for example
some butterflies and some Drosophila species, have no elastic structures and spend no
net energy on inertia [27]. This is a special case of insect flight where the net inertial
power is less than the aerodynamic power. These cases correspond to relatively large
wings and low wingbeat frequencies. The net inertial power is zero for these insects
because the energy required to accelerate during the beginning half-stroke will be
recovered when the fluid is used to decelerate the wing at the end half-stroke [27].
The kinetic energy stored in the solid material is transferred to the fluid during the
deceleration phase. If it is determined that the hydrodynamic power is greater than
the inertial power (which will be the case for a substantially large foil), then perhaps
commanding a small or zero torque for a portion of the cycle of motion would enable
our flapping foil actuators to achieve zero net inertial power. For a heavy actuator
design, the zero torque strategy would only work for a relatively large foil, and the
frequency of foil motion would be low, resulting in a low thrust vectoring bandwidth.
In light of the knowledge gained from these insects, one of the considerations for
33
selecting an appropriate foil size should be that the hydrodynamic power is greater
than the inertial power in order to allow for control strategies to recover energy spent
on solid mass in the absence of a spring.
1.1.4
Control
There are nontrivial control problems to be solved on the lowest level.
There is
typically a large inertial term in the solid dynamics of the foil actuator and a large
damping term in the hydrodynamics. As the desired frequency of motion is increased,
the torque on the roll motor will saturate in the acceleration phase or the velocity
phase, depending on the foil size and amplitude of motion. A PD controller with
velocity feed forward is sufficient to track the requisite sinusoidal velocity trajectories.
With a spring, a higher level controller could be used to slide the desired frequency
to lock onto the resonant mode.
The physical constraints on the frequency of foil motion limit the frequency of
thrust vectoring bandwidth. Lags at the low level will contribute to phase loss in the
higher body level control. There will be additional lags at the foil level due to the
hydrodynamic and mechanical constraints on the rate of transition between velocity
profiles. Discontinuities in the velocity trajectories will likely cause unfavorable vortex
shedding and will certainly cause large inertial forces. There are physical constraints
on the rate at which the desired thrust vectors can be updated. The bandwidth on
the thrust vectoring rate will be key in determining the maneuvering capabilities of
the vehicle.
High bandwidth, low magnitude forces may be achieved with high frequency pitch
motions and chordwise flexibility. This style of motion would be useful for hovering
and making minor adjustments in the body position at low speeds. The two degree of
freedom large amplitude flapping foil motion will be used for accelerating the vehicle
and cruising at moderate to high speeds.
Once the foil motion control has been pushed to the highest bandwidth possible
(currently in the absence of a spring), the next major control problem will be to find
paths in the kinematics parameter space to scale the magnitude of the thrust force for
34
a given geometry and vehicle speed. There is redundancy in the kinematics, which will
allow for a constrained optimization problem. Certainly the most desirable parameter
to optimize will be efficiency. So the problem will be to find paths in the kinematics
parameter space that will satisfy a specific coefficient of thrust while maximizing the
operational efficiency. It may be possible that the frequency of foil motion always
remains the same to simplify the central body motion control. As larger forces are
needed the amplitude of motion could be increased.
In order to implement flapping foil propulsion on a vehicle there need to be sensors
that measure the incoming velocity upstream of the foil, or this velocity must be
estimated with a mathematical model running in real time on the vehicle control
system. Errors in the measured or estimated fluid velocity will translate directly to
errors in the foil kinematics, and therefore into the hydrodynamic forces and body
dynamics.
For this reason, regimes with great forgiveness to errors in the angle
of attack profile are desirable to minimize the effect of error in the fluid velocity.
These errors in the fluid velocity will also effect the hydrodynamic efficiency. If the
kinematics are incorrectly computed, the forces may deviate from the plateau of high
hydrodynamic efficiency. While accurate high bandwidth velocimeters are available,
they consume power and space, and add to the cost of the vehicle.
One of the unique control problems for flapping foil vehicles will be to develop an
algorithm that accepts as inputs the desired thrust vectors and the measured or estimated local flow velocity, and outputs the necessary kinematics for the foils to achieve
the desired forces. The algorithm must be robust in the presence of uncertainties in
the upstream velocity, uncertainties in the hydrodynamic interactions between individual foils and interactions between the foils and the body, and constraints of the
motions attainable by the machine. The robustness of this algorithm will be fundamental in determining the performance of this and future vehicles. This is at the core
of the control problem for flapping foil propulsion, and this vehicle will provide the
opportunity begin developing this algorithm.
Beyond vehicle body motion control, there are higher level control problems that
must be solved to obtain a robust and useful tool for oceanography or deep water
35
archeology. This is a very rough overview of the control hierarchy for an flapping foil
AUV that is to be deployed in the ocean:
1. Start with high level mission objectives such as building a map of the ocean
floor, or locating an object within a search area, or sampling temperature,
salinity, and chemistry of the water column. Simultaneously perform high level
error handling in regard to the vehicle status involving leaks, battery capacity,
collisions, etc. Perhaps given robust machine vision algorithms and hovering
capability, a higher resolution map could be made in the vicinity of a potential
object of interest. Likewise if the payload sensors detect other events such as
the presence of a particular chemistry in the water, a large disturbance in the
magnetic field revealing the presence of a metal object, or particular sound
pattern, other high level mission objectives could occur.
2. Perform concurrent mapping and localization to navigate the vehicle along a
desired trajectory to meet the objectives.
3. Given the desired vehicle body position, measure linear accelerations and angular velocities of the body. Additional orientation information will be available
from a magnetometer. Additional body and fluid velocity information may be
available from a doppler velocity log. Additional position data may be available
from a sonar, digital camera, or perhaps laser. Using a Kalman Filter estimate
the vehicle body velocity and position, and the hydrodynamic and hydrostatic
forces on the body.
4. Given the full vehicle state, calculate the desired thrust vectors for each foil
given the estimated hydrodynamic, hydrostatic, and solid dynamic forces.
5. Given a desired thrust vector at each actuator, the velocity of the vehicle body,
and possibly the local velocity of the fluid, calculate the necessary kinematics
for the foils to result in the desired thrust vector at each actuator. Command
velocity trajectories for each axis of foil motion.
36
6. Given desired velocity trajectories for the foils, implement closed loop motion
control locally at each foil.
1.2
Previous Work with Flapping Foil Robotics
Flapping foil propulsion is very attractive in terms of hydrodynamics, but it presents
great difficulties in the mechanics and controls. Previous work with robotic fish [3]
[6] [17] has resulted in extraordinarily complex and beautiful machines with limited
performance compared to the animals on which they were based. While these machines have provided further insight in the hydrodynamic and mechanical aspects of
the problem, they have also served as an indication that the elegant solutions that
exist in nature will be extraordinarily difficult to implement as machines. In order
to simplify the mechanical aspects of the problem it is necessary to search for the
simplest kinematics with the fewest degrees of freedom that will still result in optimal
hydrodynamic forces. Complexity in mechanical design does not scale linearly with
the degrees of freedom of motion.
1.2.1
Autonomous Vehicles
RoboPike
The RoboPike was the first autonomous robotic fish built at MIT [17]. It was designed
and fabricated by John Kumph in 1994. This robot is remarkably small with a length
of 0.81 meters and a displacement of 3.6 kilograms. The depth rating is approximately
2 meters. The top speed is approximately 0.2 body lengths per second. This robot
has five degrees of freedom. Two servomotors control the curvature of the body and
tail sections, and a third servomotor controls the angle of the caudal fin. The two
pectoral fins are each controlled by another servomotor.
The frame is made of links of Delrin. The links are connected by stainless steel
ball bearings that are direct contact with water. There are two helical springs made
of fiberglass and epoxy that surround the body of the vehicle. The skin is made of
37
Figure 1-7: Tail Section of the RoboPike - John Kumph.
Lycra. With the exception of the head, the rest of the vehicle is flooded. Buoyancy is
obtained with small pieces of PVC foam that are placed to trim the vehicle and provide
a small hydrostatic righting moment. Each of the motors are individually sealed with
a butyl rubber coating. There are a small pack of nickel cadmium batteries that give
the vehicle a mission life of less than an hour.
There is a small dry volume in the head that contains an Onset model 8 computer.
This computer has a 32 bit processor that runs a C program that sends pulse width
modulation signals to each of the servos. Each servo receives a square wave signal.
The duty cycle of the square wave determines the position of the servo. All commands
are sent open loop. This robot is simply running a predetermined set of kinematics
that have been hard coded by the user.
In the past nine years a series of modifications have been made to the RoboPike
to incorporate a wireless modem, three axis magnetometer, and two pressure sensors.
The wireless modem was used to communicate with a laptop on the bench, but
it has recently been removed to make space in the head for new sensors. The two
pressure sensors measure depth and approximate forward velocity. Once incorporated
38
Figure 1-8: John Kumph and the RoboPike.
into a vehicle body control system, the three axis magnetometer and two pressure
sensors will, give the robot the ability to maintain a heading and to navigate by dead
reckoning. The RoboPike is not currently operational, but is being worked on by
Cosimo Malesci, an undergraduate at MIT.
Draper Laboratory Robotic Tuna (VCUUV)
The Vorticity Control Unmanned Underwater Vehicle (VCUUV) is a free swimming
robotic tuna fish that was designed and fabricated by Jamie Anderson and her colleagues at Draper Laboratory [3] in 1997.
This robot is near the practical upper
limit of what is currently possible for a flexible hull free swimming robotic fish given
the constraints on available batteries and actuators. The vehicle has a length of 2.4
meters and a displacement of 136 kilograms. It has a 10 meter depth rating and a
top speed of 0.5 body lengths per second with a tailbeat frequency of 1 Hertz.
This robot has maneuvering capabilities that far exceed traditional cylindrical
shaped AUV's. While a typical cylindrical AUV has a turning radius of 3.5 body
lengths, this vehicle has a turning radius of 0.5 body lengths. This vehicle has a
maximum yaw velocity of 30 degrees per second, in comparison to a typical value of
39
Figure 1-9: Draper Laboratory free swimming robotic tuna.
7 degrees per second for a cylindrical vehicle. This yaw rate enables the vehicle to
make a full 90 degree turn every 10 seconds.
This robotic fish has a total of six degrees of freedom, four in the tail section and
two in the pectoral fins. The tail section and caudal fin are actuated by hydraulics
and rigid links. The hydraulic pump is powered by an electric motor that is connected
to 29.5 kilograms of sealed lead acid batteries. There is a total of 800 watt-hours of
battery capacity that result in a mission life of 3 hours. The pectoral fins are driven
by servomotors.
The Draper tuna is capable of closed loop body control with a six axis inertial
navigation unit, three axis magnetometer, and depth sensor. The body motion control system receives feedback from the drivetrain in the form of force and positions
of the hydraulic pistons, electric motor speed, and pressure in the hydraulic reservoir. The error handling algorithm is aided by measurements from leak detectors and
thermocouples.
The design of VCUUV has been demonstrated to be mechanically robust and
reliable, with over one hundred deployments in swimming pools and fresh water ponds.
40
Figure 1-10: Drawing of the Draper tuna. - Draper Laboratory
Figure 1-11: Draper tuna at Nickerson State Park.
41
Figure 1-12: Robotic fish with 3DOF pectoral fins. - Naomi Kato
Bass Robot at Tokai University
Naomi Kato and his colleagues at the Department of Marine Design and Engineering
at Tokai University built two generations of robotic fish with two pectoral fins. Each
pectoral fin is driven by three servos. The fins are moved to perform a drag based
form of propulsion, similar to rowing. The vehicle is 2 m long and has a displacement
of 105.7 kg. This vehicle is capable of cruising and turning in the horizontal plane.[16]
Robotic Dolphins at Tokyo Institute of Technology
Motomu Nakashima and his colleagues at Tokyo Institute of Technology have built
two robotic dolphins. The first design was powered by a pneumatic motor attached
a crankshaft and spring mechanism in the tail section.
The robotic dolphin was
propelled by a caudal fin that moved with two degrees of freedom. The robot was
constrained to operate at the free surface due to the large buoyancy resulting from
the pneumatics. The mission life was on the order of one minute due to the limited
compressed air in the tank. The second design incorporated motors and batteries to
enable the vehicle to be submerged and achieve a substantially longer mission life.
42
Figure 1-13: The first generation robotic dolphin with pneumatics.
Nakashima
Motomu
175015
1312.5
Air Tank
437.5
Gear
Air
Motor
& Crank
Top view
Caudal -Fin
2nd Joint
Joint
Exhaust SAirIst
RubenS[i
Air Tark
Gear
Air
Motor r-& Crank
Soft Rubber
Srn
Side View
Figure 1-14:
Nakashima
The first generation robotic dolphin with pneumatics.
43
-
Motomu
1887
I
1887
115.5
1I~115.5
1595
11
Frame
Battery
Motor
LO
Gear & Crank
Rod
CaudaI Fin
Spring
77--F,"
1000
Figure 1-15: The second generation robotic dolphin with batteries and an electric
motor. - Motomu Nakashima
44
Figure 1-16: RoboTuna
45
Dave Barrett.
1.2.2
Externally Propelled Robotic Platforms
RoboTuna
The RoboTuna was designed and constructed by Dave Barrett at MIT in 1994. [6] [7].
The RoboTuna was a robotic platform for investigating the hydrodynamics of fish
swimming. The body had six degrees of freedom that were actuated with cables and
pulleys connected to motors above the water. This apparatus demonstrated drag
reduction on an undulating body.
The RoboTuna was externally mounted to an overhead carriage system that contained the motors, amps, power, and control. The hull was flexible and flooded. There
was no dry space underwater for sensors, electronics, motors, or batteries. However
the nose cone was rigid and water tight, and could have been sealed with a bulkhead.
Actuation was achieved through cables and pulleys. These cable tendon drives
drastically simplified the design by enabling the motors to be removed from the flexible
submerged body. This offered a nice simple solution for keeping the electronics and
motors dry and out of the way of moving parts. The cable tendon drives had relatively
low backlash and the forces in individual cables could be measured with strain gauges,
which enabled measurement of the power input with the known velocities from the
servomotors. The drive ratio for the cable tendon drives could be easily modified by
changing the diameter of the drums. The cables could deliver very large forces into
small places. This cable tendon drive arrangement also allowed the mechanical fish
to be removed and replaced by another body with a different geometry or design.
RoboTuna II
RoboTuna II was the next generation, constructed by Dave Beal, Mike Sachinis, and
Mike Jakuba in 2000. [8] [22] [15] As with the first tuna, it was mounted to a carriage
with external power and control. One of the major improvements for this generation
was that the cables and pulleys were arranged to decouple the motion of the links
which simplified the control.
The goal of RoboTuna II was to use pressure sensors along the lateral line of the
46
Figure 1-17: RoboTunaII -
Dave Beal, Mike Sachinis, Mike Jakuba.
flexible body as input to a control system that could manipulate upstream vorticity
being generated by a half cylinder ahead of the body. Results from those experiments
were published by Mike Sachinis [22].
47
SeaLion
The SeaLion was constructed by Craig Martin at MIT in 2001 [20].
This robot
was also carriage mounted and received external power and control. There was a
considerable dry volume underwater for motors and sensors. There was a single foil
that was moved with two degrees of freedom.
The purpose of this apparatus was to measure hydrodynamic forces on a rolling
and pitching foil. There are two motors with collinear centerlines. Power is transmitted from the motors to the foil through bevel gears. When the motors are turned the
same direction roll motion is achieved, when they are turned in opposite directions
pitch motion is achieved. Linear superposition of these two modes allows for combined rolling and pitching motions. This design allows the centerline of the motors to
be close to the root of the foil, which decreases the radius of the body. If the backlash
in the bevel gears could be eliminated, this design certainly has potential that should
be explored.
48
Figure 1-18: SeaLion
49
Craig Martin.
50
Chapter 2
Design and Fabrication of AUV
2.1
Purpose of Vehicle
This AUV will be a platform for research in hydrodynamics and controls. The design
and fabrication of this vehicle serves as an opportunity to identify and address the key
design considerations for rigid hull, flapping foil, autonomous underwater vehicles.
Knowledge gained from the major problems in the mechanics and controls of this
vehicle will provide feedback for the direction of future hydrodynamic research that
will help maximize the performance and minimize the complexity of flapping foil
propulsion.
There is considerable knowledge to be gained from the design process, the dynamic
characterization of the foil actuators, and data from the navigation sensors on the
vehicle. Individual foil actuators are useful for flow visualization, hydrodynamic force
measurements, and testing motion control algorithms. Four foils on a vehicle with
sensors and data acquisition, will serve as a valuable test platform for hydrodynamics
and controls research.
The acceleration of the vehicle and good estimates of the
hydrodynamic coefficients of the vehicle body will give insight into the forces produced
by the foils in unsteady or accelerating flow. This AUV will be useful for testing body
motion control strategies for a vehicle with highly unsteady propulsive forces.
The open loop dynamic characterization of the vehicle will help in the design of the
closed loop foil and body control systems. The closed loop dynamic characterization
51
/
Figure 2-1: AUV in the sea turtle configuration.
52
will provide quantitative estimates of the capabilities of a next generation vehicle.
If this vehicle has far better hovering than cruising capabilities, the next generation
design should be specifically tailored for missions that require mostly hovering. Likewise if this vehicle has a far superior ability to cruise than hover, the next generation
design should be highly streamlined.
Ultimately the goal will be to develop a vehicle that has superior hovering agility
and cruising efficiency. It is not crucial for the current vehicle to obtain these capabilities. The purpose of the current vehicle is to provide information to make the
ultimate goals more obtainable, and also to demonstrate that two degree of freedom
flapping foil propulsion can be used to propel and control a vehicle. As the development of the mechanics and controls becomes more advanced, it will become more
evident which aspects of flapping foil propulsion can be leveraged to provide new
capabilities for oceanographic research.
Knowledge gained in hydrodynamics will endure. Knowledge gained in mechanical
design will need to be adapted to developments in materials, fabrication techniques,
and actuators. Likewise the knowledge gained in the controls that is particular to
physics will persist, and knowledge that is particular to hardware and software will
need to be adapted to the advancements in the available computers, solid state memory, sensors, motion control cards, digital I/O and data acquisition cards, servomotors,
amps, waterproof cables and connectors, wireless and underwater modems, and batteries. Advances in electronics occur at a fast rate, and each new generation vehicle
should take full advantage of the components that become affordable and practical
to implement.
2.2
Design Criteria
This vehicle was designed to primarily operate in confined shallow water spaces such
as swimming pools, large tanks, and perhaps in a small pond or quarry. The first
deployments of this vehicle will be with open loop body motion control. For these
initial runs the vehicle will not have the capability of navigating or performing high
53
level error handling and behaviors such as collision avoidance. With such limited high
level control functionality the vehicle must be confined to protected waters where there
will be no chance of the vehicle becoming lost or sunk.
One of the highest priorities in the design was modularity.
A highly modular
design minimizes the cost and difficulty in changing the location and number of foils.
For this modular design, all the electronics, motors, and mechanical components
required to add a foil to the vehicle are contained in a single, stand alone module.
These individual foil modules receive power and communication, and are capable of
operating independently from the rest of the vehicle. Any individual foil module can
be operated with a 24 volt power supply and any computer with an Ethernet card.
These individual foil modules can be operated in a variety of testing facilities such as
a propeller tunnel or towing tank, which makes them very valuable for hydrodynamic
force measurements and flow visualization.
2.2.1
Mission Length and Location
The two 12 volt sealed lead acid batteries have a total capacity of 31.3 amp-hours at
24 volts.1 With all four foils moving continuously and aggressively, this would result
in approximately 2 hours of battery life. For the preliminary open loop runs, battery
life will not be the limiting factor on mission life. Without the ability to navigate or
perform collision avoidance, the preliminary open loop mission life will be limited by
the size of the pool or tank and the commanded open loop kinematics.
The first several deployments will be used to characterize the open loop dynamics
of the vehicle. With short bursts of acceleration on each linear and rotational axis,
the vehicle will not travel any considerable distance. The first test will be done at
the MIT Towing Tank.
'For these batteries, the amp-hour capacity is a function of the discharge rate. This calculation
was made iteratively so that the discharge rate was equal to the battery life. The final amp-hour
value used was taken as an average of the capacity ratings for the 3 hour discharge rate and the 1
hour discharge rate.
54
2.2.2
Depth Rating
This AUV was designed for 30 meter depth rating, however there are custom seals
that have an uncertain depth rating.
The safe operating depth will be limited to 5 meters for initial tests. The shaft
seals need to be tested in order to give an accurate depth rating. The shallow depth
rating will not substantially inhibit the functionality of the vehicle, given its intended
purpose.
The shaft seals could be replaced with magnetic couplings in order to eliminate
all dynamic seals. With only static seals at the lids and end plugs the depth rating
would be drastically increased. The next weakest link on the depth rating will be due
to the structural integrity of the housings.
2.2.3
Dimensions
The vehicle is 2.0 m long without a fairing. The fairing will be approximately 2.5 m
long and 0.5 m in diameter.
2.3
2.3.1
Vehicle Layout
Modularity and Scalability
The location and number of foils may be changed easily. The communication and
power hardware have a capacity for six foil modules with relatively minor changes in
the wiring.
As the development of the vehicle advances it may eventually be desirable to add
payload instrumentation. There will be room on the frame to add small electronics
housings. There will be additional communication ports, power capacity, and data
acquisition channels to accept several payload sensors.
55
2.3.2
Planes of Symmetry
Modularity enables to vehicle to be reconfigured with different planes of symmetry.
Symmetry in the geometry and kinematics will increase the open loop stability of the
vehicle. The foils may be arranged so that the net unsteady lift components will be
cancelled by symmetry in order to eliminate the cyclic roll and pitch moments on
the vehicle body. Asymmetries in the foil motions could result in large pitch and roll
moments for maneuvering.
Initially the vehicle will be configured like a sea turtle. This configuration results
in two strong planes of symmetry and one weak plane of symmetry. Weak symmetry
simply means that the center of buoyancy will be placed above the center of gravity
to result in a net hydrostatic righting moment. The sea turtle configuration should
provide control of five degrees of freedom on the body (surge, heave, pitch, roll, yaw).
A static roll bias can be used to change the orientation of the lift vector on a foil, and
this may enable control of the full six body motions with the sea turtle configuration.
Another useful four foil configuration for the vehicle would be similar to a boxfish,
with two pectoral fins near the front of the vehicle and a vertical anal and dorsal fin
near the rear of the vehicle. The boxfish configuration may allow control of all six
degrees of freedom. The disadvantage of this configuration would be less open loop
stability, resulting in more complex body dynamics and thus more closed loop body
control activity.
2.3.3
Mass, Hydrostatic Stability and Net Buoyancy
[Net Buoyancy
Mass
Component
1.0 kg (2.2 lbs)
157 kg (345 lbs)
Total Vehicle (Approximate)
4 X [27.4 kg (60.5 lbs)] 4 X [-9.3 kg (-20.5 lbs)]
Two Housing Actuator
2 X [-9.0 kg (-19.8 lbs)]
2 X [17.1 kg (31 lbs)]
Lead Acid Batteries
-5.0 kg (-11 lbs)
7.1 kg (15.6 lbs)
Frame (Approximate)
12.5 kg (27.5 lbs)
Electronics Housings (Approximate) 6 kg (13.2 lbs)
48.7 kg (107.1 lbs)
_
Flotation Required (Approximate)
Table 2.1: Mass and buoyancy of major components
56
There is a trade off between passive stability and maneuverability. Many fish are
passively unstable in order to perform quick starts and turns. A low or negative
hydrostatic righting moment allows the body to be rolled or pitched rapidly. The
location of the batteries and electronics housings can be adjusted to trim the vehicle
and to adjust the hydrostatic stability.
The vehicle will always be trimmed a few kilograms positively buoyant so that
the vehicle will rise to the surface in the event of a power failure or small leak. A
large leak could certainly be catastrophic. One strategy for recovering from a large
leak would be to carry dead weight that could be dropped with a magnet. Another
strategy would be to attach a piston to a pin on a CO 2 canister to inflate a small
volume.
2.3.4
Added Mass and Drag Considerations
In order to retain the ability to quickly and easily relocate the foils for the open loop
runs, there will initially be no external fairing on the vehicle. Without a fairing, the
bluff body drag on the batteries and housings will be very high the added mass of
the batteries and housings will be slightly increased. This will greatly decrease the
speed of the vehicle and will only be the case for the initial runs.
Once a foil arrangement has been settled upon, a highly streamlined fairing will
be fabricated. Ideally the fairing would be modular to retain the ability to relocate
the foils. A simple fairing shape (elliptical or cylindrical) is desirable to simplify the
computations to estimate the hydrodynamic coefficients.
2.4
2.4.1
Control and Communication
Single Board Computer Running Linux
The single board computer is the Octagon Systems model PC680. This computer is a
state of the art embedded PC made for vehicles operating in extreme environments.
This computer fits the EBX form factor, which simply means that the size of the
57
LEGEND
I I FUSE
POWER
-
INFORMATIC)N
------
o.
HOWER
SUPPLY
POWWR
SUPPLY
SUPPLY
HOWER
SUPPLY
TCF/IF
RS 232
DIGITAL
ETHERNET
SINGLE BOARD
SERIAL
C:OMMUNiCATCON
COMPUTER
COMMUNICATION
-------------------------------------RUNNING
W
LINx
(D
-
-----------------------
CDt
DMC 1425
DMC 1425
2-Axis MOTIoN
:
PWM
*a l
PWM
AMP
--
PITCH
FQ"l MODULEF
CONTROL CARD
PlWM
AMP
L---
CONTROL
*g
CARD
PWM e-
PWM
AMP
S
e
e
7,4
*
PlWM
AMP
ROLL
ROLL
MOTOR
2AXIS MOTIONI
b
--
AMP
MC 142L'
UMC 'I42b
CONTROL CARD
t
CONVERTER
2,Axis MoT1ot4
b
l
U
Ic-D
DC
...C-C
2-AXIS MOTIOIJN
CONTROLCARD
i'
TCP/IP ETHERNET
RL COMMUNICATION
p CONVERTER
CONVERTER
CONVERTER
lal
,
-------
----------------------
I
jI
,
4
A
24 VOLT DC POWER
-
01
00
,
,
7.2
VOLT9
WIRELESS
ET14ERNET FOR
SIURFACE
COMMUNICATION
8 PORT
ETHERNET ----------Hua
I
FOIL
MDLFOLM
FOI MODlULE
ROLL
ROLL
MOTOR
MOTOR
PW~M
e
PITC H ~
Amp
--
AMP
a
IC
Rw
WM
W
AMP
m
FOIL MODULE
UE
---
---
PMOCHDU
FOIL MODULE
board is 14.6 cm x 20.3 cm. It has a Intel Pentium 166 MHz processor with 32 MB of
SDRAM. There are two two operating systems loaded on the computer. The primary
operating system is Red Hat Linux 7.2, which is installed on a 20 GB IDE hard drive.
The secondary operating system is Datalight ROM-DOS v.6.22, loaded onto a 32
MB solid state Flash memory chip. The BIOS is loaded onto 512 KB of solid state
EEPROM memory. There is a programable watchdog timer that can automatically
reboot the computer and execute a program in the event of a system lock up.
This computer has 6 serial ports, 2 parallel ports, 2 USB ports, a 10T/100Tx
Ethernet card, 32 channels of 32 bit digital I/O, PCI and ISA bus. It has a built in
video card and support for PS-2 keyboard and mouse, so it can function as a normal
desktop PC. It supports all 8 and 16 bit PC/104 expansion boards, so it should be
completely compatible with the hardware used on the Odyssey class AUVs.
All components except the hard drive can withstand -400 to 85 0 C operating temperature, 5% to 95% relative humidity, 40g shock, and 6g vibration. It has onboard
support for up 128 MB of solid state memory, so the hard drive could be completely
removed.
The power supply accepts 10-36 volt DC power. The operating voltage of the
vehicle is 24 volt, so it is extremely unlikely that a voltage dip on the batteries caused
by a draw from the foil actuators, could reboot the computer.
Software and technical references for this computer are available at
http : //www.octagonsystems.com
2.4.2
Distributed Motion Control on Ethernet Network
There is a two axis motion control card located within each foil module. Each motion
control card has a processor with solid state memory and an Ethernet card with a
unique IP address. There is a simple program running locally on each motion control
card. This program executes closed loop motion control for sinusoidal velocity trajectories and computes transitions between desired motions. Kinematics commands
are sent from the single board computer in the form of amplitudes, phases, and frequencies. Refer to Table 3.2 and Figure 2-2.
59
In the center of the Ethernet network is a hub. A laptop could be connected to
this hub either directly or via a wireless Ethernet modem. The laptop would enable a
user to communicate with the single board computer, or directly with one of the foil
modules. This communication setup will enable a user to change the gains, torque
limits, or error limits for an individual foil without communicating with the single
board computer.
The motion control cards are the Galil Motion Control model DMC-1425.
Software and technical references for the motion control cards are available at
http: //www.galilme.com
2.5
Sensors
Data will be logged with through serial ports and a data acquisition card. The data
acquisition card will connect to the single board computer on either the PCI bus or
on one of the USB ports.
2.5.1
Inertial Measurement Unit
The inertial measurement unit is a Crossbow IMU VG300CB-100. It measures three
linear accelerations on orthogonal axes and three angular rotations rates about orthogonal axes. The range on the acceleration measurement is
on the rotation rates is
2g and the range
100 degrees/second. This sensor has an RS232 serial link
and 10 analogue outputs. It has an onboard CPU with solid state EEPROM memory
that executes a calibration algorithm. This sensor does not require calibration after
shipment from the factory.
The data from this sensor will be the most crucial in determining the dynamics of
the vehicle body. This sensor will provide the most valuable data and it is critical to
thoroughly understand its output. Once a closed loop body motion control system is
implemented, the inertial measurement unit will be used to measure the vehicle body
60
attitude and short term perturbations.
Factory Calibration Data for IMU
Serial Number: 111278
Current firmware version: DMU VGX REV.B.04
Accelerometer Calibration Data:
Axis
Range (g)
Sensitivity (g/V)
Null Offset (V)
X
2.000
1.037
2.584
Y
2.000
0.981
2.599
Z
2.000
1.008
2.547
Gyro Calibration Data:
Axis
Range (deg/sec)
Sensitivity (deg/sec/V)
Null Offset (V)
X
100.000
49.847
2.525
Y
100.000
50.077
2.519
Z
100.000
49.847
2.520
Software and technical references for the IMU are available at http : //www.xbow.com
2.5.2
Three Axis Magnetometer
The three axis magnetometer is a Precision Navigation model TCM2. It has built in
tilt and roll sensors to correct the compass heading for tilt. This sensor communicates
via RS232 on a serial port.
Dimensions
6.35 cm X 5.08 cm X 2.79 cm
Heading
0 - 359.90
0.10
Tilt
500
Magnetic Field
80pT t 0.2pT
Sampling Rate
0.40
16 to 30 Hz
61
Technical references for the magnetometer are available at
http: //www.pcweb.com/pni/TCAM2.HTAM
2.5.3
Leak Detectors
There will be leak detectors in every electronics housing and foil actuator. The leak
detector simply measures the resistance between two probes. In the event of a leak,
the water will provide a current path between the two probes and the detector will
sound an alarm or alert the central control system. The design for these leak detectors
is the simple flood alarm from the Encyclopedia of Electronic Circuits Volume 5. The
design consists of two 2N3904 transistors and two 1 kQ resistors.
2.6
Batteries and Power Management
The operating voltage for the vehicle is 24 volts. There are two sealed lead acid 12
volt batteries, MK Systems model 8G22NF. The mass of each battery is 17.1 kg. At a
2 hour discharge rate the batteries have 31.3 amp-hours of capacity. These batteries
can be deep cycled (100 % discharge) 500 times, a lower discharge will greatly increase
the cycling capacity.
These batteries would never be used on an ocean going vehicle. They have a large
block shape (23.8 cm x 14.0 cm x 23.5 cm) that will be difficult to incorporate into a
streamlined fairing. Compared to state of the art AUV battery technology, they have
low power density 22 watt-hour/kg (vs. 150 watt-hour/kg for state of the art).
These batteries were selected as a temporary solution because they are very cheap
and can sustain a massive current draw (120 amp) with a low voltage dip. As the
central control system becomes more advanced, these batteries will eventually be
replaced with a pack of nickel metal hydride or lithium ion batteries.
Technical references for the batteries are available at
http : //www.mkbattery.com
62
2.6.1
Diodes for Preventing Accidental Charging or Discharging of the Batteries
There will be two diodes to ensure that the batteries will not be accidentally charged
while connected to shore power, and also to guarantee the user will not be shocked
while connecting shore power. The voltage drop across these diodes will consume
battery power. While these diodes waste approximately 5 % of the battery power,
they provide a crucial safety measure.
2.6.2
Voltmeter on Batteries
In order to monitor the remaining battery life, a voltmeter will be installed in parallel
across the two batteries in series. As the batteries are discharged the voltage will drop.
When the remaining battery life reaches a critical value the vehicle will surface.
2.6.3
Ammeter on Power Supply to Each Foil Actuator
There will be an ammeter monitoring the electrical current delivered to each individual foil actuator. With an estimate of the thrust produced by a foil, this will provide
an estimate of the operating efficiency of the actuators on the vehicle. Conversely
with an estimate of the operational efficiency, the power consumption will provide a
measure of the thrust produced by a foil. If the foil actuators are retrofitted with
springs, these ammeters will enable a low level control system to sweep the frequency
of foil motion to lock onto the resonant mode.
2.6.4
Digital I/O and Relays
The digital I/O and relays enable each of the foil actuators to be individually powered
on by a program running on the single board computer. Individual power control will
enable the vehicle to conserve power in a dormant state during shore communication
or as part of mission objective that requires idling. If one of the foil actuators is
leaking or overheating, it can be powered down in an effort to protect the electronics.
63
Powering on individual foil actuators may be useful for debugging. Power control and
wireless Ethernet will enable a user to communicate directly with an individual foil
actuator, independently of the single board computer.
2.6.5
Magnetic Switches and LEDs
The magnetic switches will enable a user to power on the vehicle without opening
an electronics housing. This will greatly simplify the deployment and operation of
the vehicle. There could be multiple switches to define a vehicle power state, such
as computer and sensors on with all foil actuators off. The LEDs would be used to
indicate the vehicle power state and status. Individual foil actuators could have red
and green status LEDs for leaking, overheating, and communication.
64
Chapter 3
Design of Foil Actuators
The foil actuators make this AUV unique. Most of the design effort for the vehicle was
concentrated on the foil actuators. In order to maximize the reliability of the vehicle,
more emphasis was placed on simplicity and robustness than on performance. To
achieve a modular design, a single foil actuator contains all the components necessary
to add one foil to the vehicle. There are two DC brush motors, a two axis motion
control card, two PWM amps, gears, bearings, and frame enclosed in waterproof
plastic housings.
There are two generations of foil actuator designs. In the first design, all the
components were placed in a single housing. While the mechanical actuation and
wiring were simple with a single housing, the sealing was complex. The dynamic seal
between the foil and housing limited the depth of operation, range of motion, and the
fatigue life.
The first design was improved to increase the depth rating of the actuator and
the range of roll motion of the foil. The design was changed to be contained in two
independently sealed housings, one that remains stationary with respect to the vehicle
and a second that rotates about one axis with respect to the other housing. Having
two independently rotating housings drastically simplified the sealing problem, which
improved the robustness of the seals and the range of motion on the roll axis. The
major problem with the second design is that the mass of the solid moving parts
is relatively high, which increases the energy wasted on inertia and decreases the
65
bandwidth of thrust vectoring.
A future design should be substantially smaller and lighter. Smaller amps and
motion control cards should be available. Two smaller motors on the roll axis could
be used to completely eliminate the backlash and to increase the torque. A passive
mechanical spring on the roll axis would improve the operational efficiency and bandwidth. Direct drive on the pitch axis would decrease the size of the pitch housing,
and enable higher frequency motions on the pitch axis. Currently the torque on the
pitch axis is limited by the shaft couplings and not by the power of the motor.
There are two rotational motions about orthogonal axes. One motor is dedicated
to each axis so the motions are decoupled. The roll motor is a Litton Polyscientific
model C34-L60-W10, with the HEDS 5600-500 rotary encoder. The pitch motor is a
Litton Polyscientific model C13-L19-W20, with the HEDS 5500-500 rotary encoder.
Refer to Table 3.1 for more detail.
Technical references for these motors are available at http : //www.polysci.com
There is a two axis motion control card located within each foil module. Each
motion control card has a processor with solid state memory and an Ethernet card
with a unique IP address. There is a simple program running locally on each motion control card. This program executes closed loop motion control for sinusoidal
velocity trajectories and computes transitions between desired motions. Kinematics commands are sent from the single board computer in the form of amplitudes,
phases, and frequencies. Refer to Figure 2-2 for a power, communication, and control
schematic.
The motion control cards are the Galil Motion Control model DMC-1425.
Software and technical references for the motion control cards are available at
http: //www.galilmc.com
The PWM amps are Advanced Motion Controls series 25A model 12A8. They
accept a reference voltage from the motion control card and output a current to the
66
ROLL MOTOR
PITCH MOTOR
Rated Terminal Voltage
12-30 V
6-24 V
Rated Current
Torque Sensitivity
Back EMF
Terminal Resistance
Terminal Inductance
Rotor Inertia
Stiction Torque
Damping
8.20 A
0.08 N-m/A
0.08 V/rad/s
0.43 Q
0.90 mH
2118.45 g-cm 2
0.11 N-m
0.02 N-m/KRPM
ROLL GEARHEAD
two stage 25.01:1
75%
1.8 A
0.0242 N-m/A
0.0242 V/rad/s
2.30 Q
0.84 mH
18.4 g-cm 2
0.01 N-m
0.001 N-m/KRPM
PITCH GEARHEAD
three stage 50.89:1
70%
1.50
2.50
Gear Reduction
Efficiency
Maximum Backlash
Shaft Inertia
Maximum Torque
Maximum Axial Load
Maximum Radial Load
Operating Voltage
Maximum Continuous Current
Maximum Peak Current (<2.0s)
PWM Switching Frequency
__
Resolution
(including quadrature,
excluding gear reduction)
0.125 g-cm
60 N-m
120 N
600 N
ROLL PWM AMP
24 V
6.0 A
12.0 A
36 kHz
ROLL ENCODER
1.49 g-cm 2
4.5 N-m
30 N
100 N
PITCH PWM AMP
24 V
6.0 A
12.0 A
36 kHz
PITCH ENCODER
2000 counts/revolution
2000 counts/revolution
2
Table 3.1: Specifications of roll and pitch motors
motors that is linearly proportional to the reference voltage. The PWM switching
frequency is 36 kHz.
Technical references for the PWM amps are available at
http: / /www.a - m - c.com
67
Variable
AMX
AMY
PHIX
PHIY
FR
TRNRATE
BIASX
BIASY
CHANGE
STOP
Description
Roll Amplitude [deg]
Pitch Amplitude [deg]
Roll Phase [deg]
Pitch Phase [deg
Frequency [Hz]
Number of Cycles to Transition Motion
Static Roll Bias (Relative Adjustment) [deg]
Static Pitch Bias (Relative Adjustment) [deg]
Set value to 1 to update motion
Set value to 1 to stop motion
Default Value
0
-90
2
0
0
0
0
Table 3.2: List of variables for program running on motion control card.
3.1
Single Housing Design
The single housing design is very simple. There is an aluminum frame inside a Lexan
housing. The roll motor is face mounted to a bulkhead, as seen in Figure 3-3. The
pitch motor and the pillow blocks constraining the foil are attached to a plate. Refer
to Figure 3-4. That plate is cradled between the shaft on the roll motor and large
double roller taper bearing. The PWM amps and the motion control card are mounted
beside the roll motor.
There is one dynamic seal and four static seals in this design. The dynamic seal
is a large flexible cone shaped bellows, as seen in Figure 3-5. The bellows forms a
rotary shaft seal at the base of the foil and a static o-ring seal at the side of the Lexan
housing. There is an o-ring seal at the lid of the housing.
Power and communication are sent to the module through two waterproof cables
and connectors. These cables and connectors were purchased from Impulse Electronics, as seen in Figure 3-2
Closed loop foil motion control is achieved with two servomotors and a two axis
motion control card. There is a program running locally on the motion control card,
which minimizes the communication required to operate the module.
This actuator was used by Melissa Flores for measurements of hydrodynamic
force data and flow visualizations. The results of those experiments are detailed in
her thesis [11].
68
Figure 3-1: Single housing foil actuator.
Figure 3-2: Single housing foil actuator.
69
Figure 3-3: Drawings of single housing foil actuator. The center line of the roll axis
crosses the center line of the pitch axis. There are radial ball bearings in the pillow
blocks that constrain the shaft attached to the foil. There are set screws on the inner
collar of the radial ball bearings that constrain the shaft in the axial direction. The
large bearing attached to the vertical plate at the far end is a double roller taper
bearing. This bearing can take large radial and axial forces, and large moments
about the pitch and yaw axes. This design is highly over constrained, which allows
no motion on axes other than pitch and roll. The range of motion on the pitch axis
is 360 degrees. The total range of motion on the roll axis is 26 degrees due to the
stiffness of the bellows. The limited range of motion on the roll axis and the poor
robustness of the bellows were the major problems with this design.
70
Figure 3-4: Inside of single housing foil actuator. The pitch actuation is achieved
with a small DC brush motor with a three stage gear reduction, resulting in a drive
ratio of 50.89:1. Power is transmitted from the pitch motor to the shaft through
two stainless steel anti-backlash gears. The anti-backlash gears are actually two pairs
of gears with a very fine teeth that are loaded against each other with two pairs of
springs. As the pitch motion is reversed the torque that is immediately transmitted
is proportional to the tension in the springs. The gears are attached to the shafts
with set screws on a flat and a spring pin. While these anti-backlash gears did have
near zero backlash, they were only capable of transmitting about 1.5 newton-meters
of torque.
71
Figure 3-5: Drawings of the bellows. The bellows is made of a flexible urethane and
Kevlar composite. The urethane has a Shore A hardness of 30. The Kevlar was cut to
form overlapping triangular sheets. This cross-section made the bellows much stiffer
in compression than in tension. A better design would a cross-section more like a
sine wave with a duty cycle of 0.5, however a mold for that design would be very
complicated to machine or very expensive to buy. The fatigue life of this design was
measured to be about 60,000 cycles. This fatigue life would need to be increased by
at least a factor of 10 to be useful on a vehicle.
72
Figure 3-6: Drawings of the bellows assembly with shaft seal and retaining rings. The
shaft seal has two buna-n o-rings and two teflon bushings. The larger inner retaining
ring bolted to the side of the Lexan housing, and mated with an o-ring on the inner
radial face. The smaller outer retaining ring compressed the bellows on the outermost
planar surface to form a gasket seal.
73
3.2
Two Housing Design
In order to eliminate the bellows seal the pitch motor and pillow blocks were moved
into a separate housing. With two housings there are two dynamic seals that function
as conventional rotary shaft seals, and nine static seals. Refer to Figure 3-8.
The roll motor and electronics are contained in a PVC tube. The roll motor is face
mounted to a bracket attached to a circular plate. Refer to Figure 3-10. The PWM
amps and motion control card are mounted to an L bracket that is cantilevered from
the same base circular plate. Power and communication are sent through Impulse
cables penetrating the end plug on the PVC housing.
The pitch motor and pillow blocks are housed in a cylindrical block of Delrin, as
seen in Figure 3-9. Power and communication for the pitch motor are received via
two waterproof cables connecting the housings. The pitch motor is connected to the
foil shaft with sprockets and chains. The sprockets and chains have zero backlash and
can transfer 2.5 N-m of torque. The sprockets and chains were purchased from W.M.
Berg. Refer to http : //www.wmberg.com for more detail on these components.
The two housing actuator is mounted to the vehicle frame with a large aluminum
C bracket. There is a wet bearing at one end of the C bracket that constrains the
pitch housing. The wet bearing is made of a composite material called Rulon, and
has low friction and high strength. The other end of the C bracket is attached to the
circular plate that constrains the roll motor, electronics, and PVC tube.
Torque is transmitted from the roll motor to the pitch housing through a stainless
steel bracket bolted to the Delrin housing. This bracket is clamped to the shaft on
the roll motor with a large shaft coupling, as seen in Figure 3-10.
74
Figure 3-7: Two housing foil actuator.
Figure 3-8: Drawings of the two housing foil actuator.
75
Figure 3-9: Inside the two housing foil actuator.
76
Figure 3-10: Close up of the roll shaft coupling and one of the PWM amps in the two
housing actuator
77
Figure 3-11: Drawings of the pitch seal boot. The large lift and thrust forces cantilevered out on the foil result in radial deflections of the shaft attached to the foil.
In order to prevent these radial deflections of the shaft from transmitting large loads
to the shaft seal, this seal boot allows the shaft seal to ride on the shaft and the
deflections are taken up in the compliance of the boot. These deflections are on the
order of several millimeters. While these deflections may seem small, o-ring seals need
tolerances on the order of 0.01 millimeters. These seal boots are made of a flexible
urethane with a Shore A hardness of 70. The depth rating for this seal has not been
measured, but it will be on the order of 10 meters. Fatigue is not an issue with these
seals because the small motions of the boot.
78
Figure 3-12: Drawings of the pitch seal assembly with shaft seal. These shaft seals
are identical to the shaft seals used in the bellows. There are two buna-n o-rings and
two teflon bushings. The purpose of the teflon bushings is to transmit radial loads
and to prevent compression set from occurring in the o-rings. There is an aluminum
ring that is used to hold the seal boot to the Delrin pitch housing. There is a gasket
seal formed between the planar surface of the seal boot and a planar surface on the
pitch housing. The compliance in this boot also allows the dimensional tolerances on
the location and alignment of the pillow blocks to be drastically relaxed. Reducing
these tolerances greatly simplified the fabrication and assembly of the actuator.
79
80
Chapter 4
Force Measurements
There were six reasons for taking force data with one of the two housing foil actuators:
1. To make a preliminary map of the hydrodynamic forces over a broad range in
the parameter space for a rolling and pitching foil.
2. To determine how sensitive the scaling analysis is to perturbations in geometric
similarity.
3. To determine how well the spanwise distribution of the angle of attack profile
predicts thrust.
4. To find an appropriate foil size for this particular actuator design.
5. To determine how large the inertial forces are compared to the hydrodynamic
forces for this design.
6. To run an actuator for enough time to identify any major problems in the design
before assembling the vehicle.
Experimental hydrodynamic force data will always contain some artifacts, however
small, of the mechanical apparatus used to make the measurements. These artifacts
will be manifested as boundaries in the parameter space of the kinematics, mechanical
vibration, and electrical noise. In order to predict the performance of future designs,
it will be necessary to understand the interactions between the water and machine.
81
The boundaries of the parameter space are due to the torque limits of the motors
and the strength of the components in the power transmission such as the chains,
sprockets, gears, shaft couplings, and shear pins. Signals from most sensors are on
the order of millivolts. These low level signals are corrupted by the magnetic fields
surrounding motors, amps, and power supplies. There is an additional component in
the electrical noise due to the fluctuations in motor torques in response to the inertial
forces of the vibrating solid parts, refer to Figure 4-6.
Highly unsteady hydrodynamic forces excite structural modes in the rig containing the sensors. Given that the sampling frequency is higher than twice the lowest
structural mode, which should be the case in order to prevent aliasing in the absence
of an analogue filter, there will be certain regions in the spectrum of the force data
that are highly dependent on the machine used to measure the forces. This component of the signal is normally filtered in order to generalize the knowledge beyond the
specific experimental apparatus. The strong presence of these mechanical vibrations
in hydrodynamic force data for flapping foil propulsion serves as an indication that
mechanical vibrations will be a serious design consideration for flapping foil vehicles.
Great care must be taken by the designers of flapping foil vehicles in order drive the
lowest frequency of the structural modes well above the excitation frequency of the
propulsion forces. Data from accelerometers will be highly sensitive to vibrations in
the frame. For a high performance design, the bandwidth of thrust vectoring may be
limited by structural vibrations in the frame.
Flapping foil propulsion has the potential to improve both the maneuverability and
the efficiency of AUVs, this work is focused on maneuvering rather than efficiency.
Previous work [21] [14]
[4]
has shown that flapping foil propulsion may have the
potential to exceed the hydrodynamic efficiency of screw propellers, but this aspect
of the propulsion is much more difficult to exploit in practice. The only useful measure
of efficiency on a vehicle must include all losses of energy from the batteries to the
water. Hydrodynamic efficiency only accounts for the losses in the water. There are
losses in the drivetrain for existing designs of flapping foil actuators that do not exist
for screw propellers.
For the two housing actuator design, a typical value for the
82
operating efficiency,
(4.1)
= -
vILQ24
was 10%, with a maximum of 20%.
This measure of efficiency is different from
the hydrodynamic efficiency, and these findings do not conflict with the any of the
previous work cited in this thesis. Operational efficiency includes all the losses in the
machine, and therefore will enable designers to benchmark the efficiencies of various
flapping foil actuator designs. This is a necessary metric to optimize the performance
at the vehicle level.
A design that incorporates mechanical springs and a higher
operating voltage could drastically improve these values. The springs would be used
to minimize the energy spent on inertial forces and the increased voltage would reduce
the losses due to the impedances in the electronics. Magnetic couplings could be used
to eliminate the need for dynamic shaft seals, thus removing the high damping in
the seals due to the necessary o-ring squeeze and resulting friction. These magnetic
couplings would also enable the vehicle to operate to much greater depths.
Measuring hydrodynamic efficiency is extremely desirable, but it was not possible
to measure directly with this experimental setup.
In order to make an accurate
measurement of the hydrodynamic efficiency there must be an accurate measure of
the power input into the water. Normally this power is calculated using torques,
forces, and velocities measured directly at the foil. There were no torque sensors
available for these experiments. In these experiments the power input was calculated
using the voltage and current delivered to the actuator. The hydrodynamic efficiency
can not be directly computed using this data, but an approximation could be found
with good estimates of the mechanical and electrical losses in the actuator.
The
mechanical losses are due to the inertia of solid moving parts, friction in the seals,
gears, and bearings, and impedances in the amps, wires, connectors, and motors, and
the power consumption of the motion control card and encoders.
The thrust coefficient was calculated using the projected area of the foil,
83
CT
= -2F2
pU cs
(4.2)
Description of Tests
4.1
Cruising tests were done at a forward speed, U, of 0.5 m/s. Data was taken over a
wide range, with large steps, in the parameter space. Measurements were taken at St
= (0.2, 0.4, 0.6, 0.8, 1.0, 1.2}, amax = {50, 40, 30, 20}, s = {0.6, 0.5, 0.4, 0.3}, and
<o =
{60,
40, 20}. In all of the previously cited work, data was taken over a smaller
range in the parameter space with higher resolution. This is a preliminary mapping
of the parameter space for a rolling and pitching foil. Future work should certainly
be done to map out the details of the space where the best performance was found.
Measurements were done over a variety of spans and wake widths. This data could
also be used to determine how well scale analysis and nondimensional parameters are
able to capture the physics of flapping foil propulsion when geometric similarity is
not maintained. This data will help determine how well the measured thrust and lift
coefficients from one design can applied to a design with different ro and s.
4.1.1
Setup
Description of Tank
Tests were performed at the MIT Towing Tank in March 2003. The tank is 30 meters
long, 2.5 meters wide, and 1.1 meters deep.
Description of Foil
The distance between the centerline of the roll axis and the root of the foil, ro was
0.178 m. The foil was a NACA 0012 with (0.6, 0.5, 0.4, 0.3} m span and 0.1 m chord.
The foil was made of a rigid Shore D 50 urethane. There was a 1 cm x 3 cm aluminum
frame inside the foil. The frame was not precisely located in the center of the foil,
which resulted in a slight asymmetry of the bending stiffness of the foil. This may
84
have caused some asymmetry in the lift force under heavy loading.
Figure 4-1: Two housing foil actuator mounted to the six axis dynamometer.
4.1.2
Sensors and Calibration
Forces were measured with a six axis strain gauge dynamometer. The dynamometer
is an Advanced Mechanical Technology Inc. model MC3A-6-100. This sensor had an
appropriate linear force capacity for these tests, but the moment capacity was an order
of magnitude too small, refer to Table 4.1. In order to use this sensor it was necessary
to constrain the roll and pitch moments about the sensor. To protect the sensor on
the moment axes, there were two plates with four threaded rods used to constrain the
sensor. Basically the idea is that the threaded rods are compliant in bending and stiff
in tension. The rods are placed were in tension to prevent buckling. The nuts on the
threaded rods were very tight to prevent slipping and friction. The deformation of
the rods was nearly linear elastic, so the sensor could be calibrated with a linear curve
fit. Constraining the dynamometer resulted in a slight nonlinearity, refer to Figure
85
.
Figure 4-2: Calibration rig used to apply force at the 70% span, ro. 7
4-3 and 4-4. It would not have been possible to use this sensor without constraining
the moments.
Axis
Fx and Fy
Fz
Mx and My
Mz
Capacity
220 N (50 lbs)
440 N (100 lbs)
11 N-m (100 in-lbs)
5.6 N-m (50 in-lbs)
Table 4.1: Force and moment capacities for six axis dynamometer
Technical references are available for the dynamometer at
http: //www.amtiweb.com
The electrical current delivered to the actuator was measured with a hall-effect
current sensor. The sensor was an F.W. Bell model BB-25/100 type 155150. This
sensor has a +25 amp range and outputs a signal in the +1 volt range.
Technical references are available of this sensor at
http: //www.fwbell.com
86
Calibration of x axis in positive direction
50
o Actual Load
- - Measured Force (slope = 32.7021 NewtonsNolt)
-
45
40
3530-
z
250
o1
0L
20-
.1
-
15
0o
10
5
0
0.2
0.4
0.6
0.8
Signal Voltage [Volts]
1
1.2
1.4
Figure 4-3: Calibration curve for thrust axis. The slight nonlinearity of the sensor is
due to the rig used to reduce the roll and pitch sensitivity.
Calibration of y axis in positive direction
Sn
454035CD,
30-
z
25/
0~
/
0
LL
2015
0/
10
-
/
[
o
-
Actual Load
Measured Force (slope = 44.3839 Newtons/Volt)
/
5
0
0.2
0.4
0.6
0.8
Signal Voltage [Volts]
1
1.2
1.4
Figure 4-4: Calibration curve for lift axis. The slight nonlinearity of the sensor is due
to the rig used to reduce the roll and pitch sensitivity.
87
7
o
6
-
o
Actual Current
Measured Current (slope =25.2431)
-
0.5-
E
0
4--
@3
0
0
0.05
0.15
0.1
Signal Voltage
0.2
0.25
Figure 4-5: Calibration curve for ammeter.
4.1.3
Data Acquisition and Control
Data was logged at a sampling rate of 100.040 Hz using a 16 channel 12 bit data
acquisition card. The input range on the data acquisition card was set to
10V on
every channel. 1 The foil was controlled with a program running on the motion control
card in the foil actuator. The amplitudes, phases, and frequency were input by the
user with a laptop via Ethernet. The forward motion of the foil was achieved with a
servomotor pulling a carriage along a rail down the tank.
4.1.4
Sources of Error
1. Wave action and free surface effects were present. Instead of using a streamlined
fairing, the foil actuator was mounted above the water to avoid the bluff body
drag on the housings. The root of the foil was approximately 5 cm below the free
surface of the water. Substantial wave action was observed for high Strouhal
'The firmware for this data acquisition card forces every channel to have the same range. The
resolution is inversely proportional to the range. Ideally the ranges could be set independently to
maximize the resolution for the output of each sensor.
88
numbers.
2. Structural vibrations in the rig containing the dynamometer were present, refer
to Figure 4-6. The motions due to vibration were on the order of 1 mm.
3. Asymmetry in the frame of the foil may have resulted in asymmetry in the lift
and thrust forces.
4. The projected area of the foil was rectangular. The sharp corners on the foil
reduced the hydrodynamic efficiency and thus the operational efficiency.
5. The actual position of the foil was not recorded. The position data was not
used for any calculations, but the actual foil position could have varied from
the desired foil position by several degrees for highly aggressive kinematics. The
error on the axes was queried regularly during the runs. The error on the pitch
axis was typically on the order of 0.1 degrees (not including backlash), and the
error on the roll axis was on the order of 2 degrees (not including backlash).
6. Each measurement was repeated twice. The contour plots were made with the
mean of the two runs. In the majority of the test matrix the values would vary
by less than 7%. For kinematics with large St and large amax the values varied
by as much as 12%.
7. The water was allowed to settle while the carriage returned to the starting end
of the tank. The total time between consecutive runs was about three minutes.
It takes fifteen minutes for the tank to completely settle. The shorter settling
time was used to enable the full test matrix to be completed in one week.
8. The rig used to constrain the moments on the dynamometer resulted in a slightly
nonlinear response, refer to Figure 4-3 and Figure 4-4.
9. The voltage of the power supply was not measured. The power supply had
a maximum power output of 500 watts. The foil actuator never drew more
than 200 watts and would typically draw 50 watts, so a substantial voltage dip
89
is unlikely. An unmeasured voltage dip would result in an apparent decrease
in the operating efficiency.
For example, if the voltage of the power supply
dipped by one volt under a heavy load and the measured operating efficiency
was 10%, the actual operating efficiency would be 10.4%. This error is always
conservative.
10. The actual forward velocity of the carriage was not recorded. There is a closed
loop motion control system with a tachometer used to control the forward velocity of the carriage. The user would not include the regions of acceleration or
deceleration in the region of data points used to compute means.
11. The pitch position was zeroed at the beginning of every day by repeatedly
running the carriage down the tank and searching for the position resulting in
minimal mean lift. The zero position was checked again at the end of the day.
A typical minimum mean lift value obtained corresponded to a lift coefficient
of 0.2.2
4.1.5
Testing Procedure
The dynamometer and current sensor were calibrated at the start of every testing
day. The natural frequencies in the structure were measured at the beginning and
end of every day to determine if any screws had worked loose during testing. The
pitch position was zeroed at the beginning of every day and checked again at the end
of the day.
For a given foil size two measurements were taken at every Strouhal number,
maximum angle of attack, and roll amplitude. The following day the foil was removed
from the actuator, cut to the next span length, and the new sharp edges were slightly
2
This nonzero value for lift is likely due to the interaction between the backlash on the pitch axis
and the munk moment on the foil. This interaction between the backlash and munk moment would
be very sensitive to the stiction in the pitch seal. It is also important to consider that very small
forces are difficult to measure due to electrical noise, and the resolution of the dynamometer and
data acquisition card.
90
Spectrum of Structural Natural Frequencies: PSD = Power Spectral Density
10
80
6-
-c
42--
0t
0
5
10
15
20
25
30
35
40
45
50
30
35
40
45
50
i
I
I
25
30
35
45
50
Frequency [Hz]
10
80
U)
642
0
0
5
10
15
20
25
Frequency [Hz]
0 .1
I
I
0.08C')
Q-
0.06-
C
( 0.040.02I-
0
.
- I- - .. .
5
A.
10
.
.
.
.I
I
I
15
20
'a.,do"e-1
40
0
1,I .-.d
A--11
Frequency [Hz]
Figure 4-6: Spectrum of mechanical vibrations and line noise. The natural frequencies
were measured by repeatedly jarring the structure constraining the dynamometer,
with the motors and sensors on. The motors were commanded to maintain a zero
position. The structure was hit in many different directions, with forces of varying
magnitude. Data from the dynamometer and current sensor was logged at 100.040
Hz for several minutes, while the structure was perturbed approximately every 10
seconds. The dominant structural mode (7 - 10 Hz on the lift axis) was due to the
cantilevered mass of the actuator, refer to Fig 4-1. The mechanical vibrations on the
thrust axis were at a higher frequency because the structure has a greater stiffness in
that direction. The magnitude of the defiections due to vibration were on the order
of 1 mm. The motion of the foil in the water was minimal due to the backlash on
the roll axis. The backlash on the roll axis minimized the effect of the added mass
of the water on the foil, and as a result the frequencies of these vibrations were not
effected by the size of the foil. The two sharp peaks in the current signal are due to
aliasing of electromagnetic interference from 60 Hz 120 volt AC power and 180 Hz
three phase 220 volt power. In postprocessing the hydrodynamic force data, the raw
data was filtered by convolution at 6 Hz on the lift and current axes, and 8 Hz on the
thrust axis. The current signal was filtered at 6 Hz because in some runs there was
a strong 7 - 10 Hz component in the current signal due to mechanical vibrations on
the lift axis. Means were computed with both the filtered and unfiltered data, and
values were consistent within 1.5%, typically varying by 0.5%.
91
rounded (approximately 2 mm radius round on the edges near the tip of the foil).
The sensors would be calibrated and the next block of experiments were conducted.
The forward speed of the carriage was 0.5 m/s and the return speed was 0.2 M/s.
The return speed was selected to allow for a moderate settling time between runs.
The carriage would be stationary for less than 10 seconds between runs.
In order to find the boundaries of where the actuator could operate in the kinematics parameter space, increasingly aggressive (higher Strouhal number) kinematics
were attempted until the saturation of roll torque resulted in a position error on the
roll axis greater than approximately ten degrees, or the spring pin would shear on
the pitch axis. There was no torque limit enforced on the roll axis. The torque limit
on the pitch axis was lowered three times in an effort to increase the fatigue lifetime
of the spring pin. The final torque limit used on the pitch axis was 0.9 V (voltage
of command sent from motion control card), which corresponds to approximately 1.3
N-m of torque after gear reduction. The design has since been retrofitted with substantially stronger pins, which will enable the full 2.5 N-m to be transferred on the
pitch axis. If the two housing actuators are routinely operated at Strouhal numbers
greater than 1.0, there will be fatigue problems on the pitch axis. No problems were
ever encountered on the roll axis in over 110 hours of testing.
4.1.6
Postprocessing
All postprocessing was done in Matlab. The file used to process the data was called
postcruise.m and is located on the Towtank server at /Vic/Documents/Matlab/.
To remove the effect of the structural vibrations and electrical noise, the data was
filtered at 6 Hz on the lift and current axes and 8 Hz on the thrust axis, refer to
Figure 4-6. The filtering was done by convolution, which resulted in zero distortion,
attenuation, or phase shift in the pass band.
Means were computed over an integer number of cycles. The number of data
points for the integer cycles was computed using the period of foil motion and the
sampling rate. The user was prompted to visually inspect the data and select the
zero region and load region. For every run the means were computed with both the
92
filtered and unfiltered data, and the values were consistent within 1.5%, typically
varying by 0.5%.
4.2
Cruising Data
Figure 4-7 represents a typical case for the time history of the forces and current
recorded. The lift force varies at the frequency of foil motion and is very nearly symmetric about zero. The thrust force varies at twice the frequency of foil motion, and
the mean is positive. For good thrust producing kinematics, the current is qualitatively similar to the thrust. In regimes with useful thrust kinematics, the measured
current may provide a good estimate of the thrust produced on a vehicle given an
estimate for the operational efficiency. The distribution of the angle of attack profile
is calculated analytically using the commanded motion of the foil and is not synchronized with the measured data. The distribution of the angle of attack profile is
presented to enable the reader to make a qualitative assessment of the dependency of
the hydrodynamic forces on the spanwise distribution of the angle of attack profile.
Figure 4-8 is a time trace of the maximum thrust force encountered in the test
matrix, at St of 1.2, amax of 40 degrees, and a span of 0.40 m. The mean thrust
force was 37 N, which corresponds to a thrust coefficient of 7.2. The maximum lift
force for this run is 100 N. These kinematics correspond to the condition where the
mean of the angle of attack at r0 7 over a half cycle of motion is nearly maximum.
The angle of attack profile at r07 is qualitatively similar to a low order Fourier series
approximation of a square wave.
Under these heavy loading conditions there are
substantial cantilevered deflections of the foil. The asymmetry in the thrust force is
likely due to the asymmetry in the bending stiffness of the foil due to an asymmetry
in the frame. For this run it is notable that the current is qualitatively similar to the
thrust.
Figure 4-9 is a time trace of the run with the maximum operational efficiency,
20%. The high operational efficiency corresponds to a mean thrust force of 22 N, and
a thrust coefficient of 4.8. These kinematics correspond to the condition when the
93
angle of attack at the root of the foil is nearly zero for the full cycle of motion.
94
INPUT: U 0.5 [m/I, span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 40 [deg], run2 OUTPUT: Ct 1.6, efficiency 009
20-
W5
II
T
thrust
__
0
.. \... ..... ..
_10
....
U)
0
..\...
.........
A.... .........................
entrs
A
2
4
6
10
8
12
14
Time [seconds]
lift
-... i- mean
lift
50 -\
-5
0 --
0.
0
2
4
6
8
Time [seconds]
10
12
14
E
CoJ
4-1
....
It
current
mean currn
C\1
0
2
4
6
10
8
12
14
Time [seconds]
Angle of Attack Distribution Over Span
-o
40
1
--
-I-4 0
-
-.
-
. -.
N
-
-.
-~
-
. -.
-
. -
-
. -
C,
0
-
.
. -.
-
-
0 -40
-
-
N
0.5
1
1.5
Time [period] (not synchronized with forces and current)
Figure 4-7: A typical case: St = 0.6, ama= 40 deg, s = 0.40 m,
95
#o
tip
R 0.70
0.50
0.25
root j
2
= 40 deg
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 1.20, MaxAoa 40 [deg], run2 OUTPUT: Ct 7.2, efficiency 0.13
0.
80
1
-
6040
.
thrust
m ean thrust I
..
...I..
.. .......
.......
. ..
...
4 A
V
rA
.A
V
A
.
VI
V
V
V
2
-20
4
..\IVVU
8
6
10
14
12
Time [seconds]
0
l~
mean lift
-- 100-
0
2
4
8
6
10
14
12
E
.3-
current
8
6
4
2
0
CI
C
U)
0
.
.
Time [seconds]
.... mean current
0
2
4
6
8
10
14
12
Time [seconds]
Angle of Attack Distribution Over Span
v40
~
-R
S-40-a,
C
0
-
-
tip
0.70
root
1.5
1
0.5
Time [period] (not synchronized with forces and current)
Figure 4-8: A high thrust case: St = 1.2, amax = 40 deg, s = 0.40 m, 00 = 60 deg
96
F
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 1.00, MaxAoa 30 [deg], run1 OUTPUT: Ct 4.8, efficiency 0.20
40
thrust
mean thrust
_
0
5
10
15
Time [seconds]
20
20
lift
.
.
.
.......
.
..
.
.
.
.
mean lift
.
-20-40-
0
5
10
15
Time [seconds]
4
-current
... mean current
01
0
5
10
15
Time [seconds]
Angli of Attack Distribution Over Span
P
30
-
N __
~
0 -30a)
0
x-.
-
-30
-
-
0.5
1
1.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
-
0.50
0.25
root j
2
Figure 4-9: A high efficiency case: St = 1.0, amax = 30 deg, s = 0.40 m, 00 = 60 deg
97
Figures 4-10 through 4-13 are contour plots of CT as a function of St and camax.
Each figure represents one foil size. There are three contour plots in each figure, each
contour plot corresponds to a roll amplitude, 0. Higher St could be achieved at
larger
#o because
these runs correspond to a larger wake width, when the machine
has greater time to accelerate to the maximum velocity.
Larger 0 correspond to
lower frequencies of foil motion, and therefore lower bandwidth of thrust vectoring
capability.
Figure 4-14 is a summary of all 12 coefficient of thrust contour plots on one
page. Each column corresponds to a foil size and each row corresponds to a roll
amplitude.
It is evident from these 12 contour plots that the scaling analysis is
robust to perturbations in geometric similarity. The aspect ratio of the foil s/c varies
from 6 to 3, while ro is held constant. These geometries and kinematics cover a large
range of wake widths (1.4 < ho/c < 6.3) and a large range of spanwise angle of
attack distributions (2.18
ro 7/ro < 3.36). This is a indication that a designer may
apply the nondimensional data from one design to make accurate predictions of the
hydrodynamic loads for a future design with a substantially different geometry.
The previous summary of contour plots includes a range of foil sizes, Figure 4-15
provides the same 12 contour plots with the dimensional mean thrust. The dimensional force data is used to find the maximum thrust in the test matrix. The 0.40 m
span foil provided the largest thrust forces.
Contour plots of operational efficiency as a function of St and amax are presented
in Figure 4-16. The 0.40 m span foil provided the largest operational efficiency. The
operational efficiency was highest when amax is close to 30 degrees.
In order to demonstrate the effect of foil size on thrust vectoring bandwidth, the
dimensional thrust and operational efficiency are plotted as a function of frequency
in Hertz and amax, as seen in Figures 4-17 and 4-18. The 0.6 m foil and 60 degree roll
amplitude correspond to a low frequency of motion, in the 0 to 0.4 Hz range. The
0.3 m span foil with 20 degree roll amplitude corresponds to a frequency range of 0.7
to 1.5 Hz.
98
Coefficient of Thrust: span = 0.60 [m], roll
=
60 [degree], ho/c
=
6.3
50
40
E
:3
E
*0s
LO,
0
302.5
iA\
2
0.2
0.4
0.6
0.8
1.2
1
Strouhal Number
Coefficient of Thrust: span = 0.60 [m], roll = 40 [degree], ho/c = 4.2
50
0
19
'0
E0
:3
C
E 3
2.5
\---
.2
-----
0.4
0.6
0.8
1
1.2
Strouhal Number
Coefficient of Thrust: span = 0.60 [m], roll = 20 [degree], ho/c = 2.1
W
0
E0
E
2.5
0
U1.)
'6.2
0.4
0.6
0.8
Strouhal Number
1
1.2
Figure 4-10: Contour plots for coefficient of thrust CT: s = 0.60,
99
#o
={60,40,20}
Coefficient of Thrust: span = 0.50 [m], roll = 60 [degree], ho/c = 5.5
II
40
C
.. .
...
.
. ..
. ..
..
.
.
C~j
. ..
'
E 30
E
0.6
0.8
Strouhal Number
Coefficient o f Thrust: span = 0.50 [m], roll
50 I
'b.2
0.4
1
=
1.2
40 [degree], h0/c = 3.7
0
CV
16
C
E 30
E
x
1.2
0.6
0.8
1
Strouhal Number
Coefficient of Thrust: span = 0.50 [m], roll = 20 [degree], ho/c = 1.8
0.4
I
iI I
/
2 .2
a)
40
0V
70
.
..........
E 30
E
'6.2
0.4
0.8
0.6
Strouhal Number
1
1.2
Figure 4-11: Contour plots for coefficient of thrust: s = 0.50, qOo = {60,40,20}
Note: The actuator could have operated up to St 1.0, the data is missing due to over
conservative torque limits
100
Coefficient of Thrust: span = 0.40 [m], roll = 60 [degree], ho/c = 4.8
50
/
/ C"4
a)
CV
43
0)
(D
~ ~/.........
.~~
....
....
0
4)$
C
E 30
E
2.5-n
V?
0.4
0.6
0.8
1
1.2
Strouhal Number
Coefficient of Thrust: span = 0.40 [m], roll = 40 [degree], ho/c = 3.2
/C
,'
CS
.
...
.....
.......
.......
....
S40
0
;C~
tn
LO
.
....
...
E0
Mu
E:
(CA)
*~~~~
.5
M
~
2)
-.2
W
0.4
0.6
0.8
1
1.2
Strouhal Number
Coefficient of Thrust: span = 0.40 [m], roll = 20 [degree], ho/c = 1.6
C\,
CC4)
0
Cn
E30
E
... .\....
.~
"b.2
0.4
<
0.6
0.8
Strouhal Number
1
1.2
Figure 4-12: Contour plots for coefficient of thrust CT: s = 0.40, #o = {60,40,20}
101
Coefficient of Thrust: span
=
0.30
IF
(D
[m], roll = 60 [degree], ho/c = 4.1
L)
40
(O
Cj
0)
C
E 30
E
(U
1
0.6
0.8
1.2
Strouhal Number
Coefficient o f Thrust: span = 0.30 [m], roll = 40 [degree], ho/c = 2.7
.2
0.4
40
CV
(D
40
U
LO
E0
. ....
..
. ....
. .
.
E3
E
(a
1
1.2
0.6
0.8
Strouhal Number
Coefficient of Thrust: span = 0.30 [m], roll = 20 [degree], ho/c = 1.4
'6.2
0.4
(U
0)
C;c
~0
E0
C
E3
6.2
0.4
0.6
0.8
Strouhal Number
1
1.2
Figure 4-13: Contour plots for coefficient of thrust: s = 0.30,
102
0
= {60,40,20}
I.;
0)
0)
C:
S:
Cz
)
0.6
1.2
0.2
0.8
7
/
0.2
20
ts=0
1
0.4 0.6 0.8
Strouhal Number
C.:
0.6
0.8
1
1.2
0.2
2On
0.4
o--
'
1.2
0.2
0.4
0.6
--
-/
0.8
1
-
-
1.2
0.2
30
40
0.4
0.6
-.
..-.-.
0
0.6
1
1.2
0.2
30
40
0.4
-
0.6
0.8
ii6>
C-
1
iii
1.2
(..
=60, h 0/c = 4.1
0.8
1
1.2
0.2
eu.
30
40
50
0.4
0.6
0.8
4--
1
1.2
= 40, h 0/c = 3.2 CT: s =0.30, 0= 40, h0/c = 2.7
0.8
4
=60, h0/c = 4.8 CT: s = 0.30,
50
/ - ---
0
1 .2
0.6
0.8
1
1.2
Strouhal Number
0.2
20
0.4
200.2
1.2
20
0.2
30
40
30
40
50
30
1
0.4 0.6 0.8
Strouhal Number
/\
50
1
0.4 0.6 0.8
Strouhal Number
r')
1.2
h/c = 2.1 CT: s = 0.50, $ = 20, h /c = 1.8 CT: s =0.40, $ = 20, h0/c = 1.6 CT: s = 0.30, $0 = 20, ho/C = 1.4
1
30
40
50
40
0) 3m
')
0.4
0
30
- -.-.-.-.-/
30
2
40
.-
CT: s=0.40,
50
0-.
.-..
40
0.6
1
0 = 60, ho/c = 5.5
40
50
0.4
0
!.cv
0.8
C/
CT: s = 0.50,
50
= 40, h 0/c = 4.2 CT: s =0.50, $ = 40, h /c = 3.7 CT: s=0.40,
.
$0 = 60, h 0/c = 6.3
CT: s =0.60, $0 = 20,
50
0.2
2
40
E0
0)
0.4
0
-
s = 0.60,
CT: s=0.60, 0
50
0.2
2
z30
-640
50
CT:
B
'-1
0
cj~
0
'-1
0
0
0
S
S
U)
C;'
'-1
~TJ
-
LU
0.2
20
co
E0
0.6
0.8
cc
0.4
-
0.6
1
0.8
VV
1
40
'
1.2
1.2
-----
0.60,00 =
20
1
0.4 0.6 0.8
Strouhal Number
C,
'
1.2
Mean Thrust [NJ: s = 0.60, 0 = 20
20
0.2
40
50
-6'40
0.4
Mean Thrust [N]: s =
0.2
LU
~E 3 0
0
ci)
Mean Thrust [N]: s = 0.60, $0 = 60
0.4
-- .
-
0.6
U
0.8
1
1.2
. . .. . .
0.2
2on
30
40
50
.
1
1.2
0.4
0.6
0.8
1
1.2
0.6
0.8
Ov
Strouhal Number
0.4
. . .. .
....
...
.
1
1.2
0.4
0.6
..... ...
.......
0.2
20
30
40
0.8
to
Ln
1
1.2
......
NIO
0.4
0.6
0.8
1
1
1.2
0.2
20
30
40
- .
-
0.4
.
0.6
0.6
0.8
Strouhal Number
0.4
1
1.2
0.8
1
1.2
0.2
20
30
40
50
(0
1
0.4 0.6 0.8
Strouhal Number
1.2
Mean Thrust [N]: s = 0.30, 00 = 20
0.2
20
30
40
1......
!
Mean Thrust [N]: s = 0.40, 0 0 = 20
50
0.2
20
2U
4U
c
50
0.8
.7
C
,
Mean Thrust [N]: s = 0.30, $ = 40
0.6
.,
c
Mean Thrust [N]: s = 0.40, 00 = 40
0.4
V6
f
VV (0
Mean Thrust [N]: s = 0.30, $0 = 60
50
rln
0.2
eu
20'
40
c
Mean Thrust [N]: s = 0.40, $0 = 60
rln
(....U.
ca
Mean Thrust [N]: s = 0.50, 00 = 20
0.2
2- v
30
40
Mean Thrust [N]: s = 0.50,00 = 40
0.2
-
20'-
30
40
Mean Thrust [N]: s = 0.50, 00 = 60
01
CD
Cr2
C-
CD
7
0.6
0.8
1
1.2
0.6
o
20
0.2
~E30
0.4 0.6 0.8
1
Strouhal Number
cv.
1.2
0.6
0.8
1
1.2
0.2
20
u
30
I
4z5*
0.6
0.8
Strouhal Number
0.4
C
.
: s = 0.50, $ = 20, h 0/c = 1.8
0.4
op s
0.2
200
1
1 .2
20
0.2
30
40
40
Ti
20
0.2
30-
40
-.-.
.
.........
2.1
1.2
-
-6)40
1
-
. ..
50
50
20
0.8
-
0.4
- --
0.6
4
0.6
1.2
1
.
1.2
- -
.
1.2
20, h 0/c =1.6
0.8
=
1
--
40, h/c = 3.2
0.8
- -
0.4 0.6 0.8
1
Strouhal Number
0=. 0, $
0.4
-
I1: s =0.40, $=
0.2
20
30
40
CI
ri : s = 0.40, $ = 60, h /c = 4.8
50
I
0.60,
0.4
c
40n
40
5.5
1.2
=
40, h/c =3.7
- -
0.6 0.8
40: s =0.50, $
500
30
30
0.2 0.4
200
1
,: s =0.50, $ = 60, h /c
50
4En
E30
20
0.2
30
20
50
0.4
: s =0.60, 00 = 40, h0/c = 4.2
20
0.2
E
0
-.
...
.--.
--.
.4 0 - . .. ..-.-
6.3
40 - -.
=
50
s= 0.60, $0 =60, h 0/c
Il:
50
0.6
0.4
gi
'
2u.
0.2
30
40
0
0
1
1.2
1
1.2
00
1 .2
= 20, h /c = 1.
0.8
X.
7
4
= 40, h /c = 2.7
0.8
0.4 0.6 0.8
1
Strouhal Number
/
0
0.6
0.30,
.1
:s=
0.4
i : s = 0.30,
50
0.2
20-
30
40
50
20
0.2
30
40 -...
ro : s =0.30, $0 = 60, h /c =4.1
50
..
.......
'-1
SCD
0
i-I
0
0
CD
0
S
S
U)
CD
~1
0.1
*0
0.2
0.6
20
30
40
50
0.6
0.8
50
0.4
=
0.60, 00
0.8
f [Hz]
0.6
1
/Cvi
Mean Thrust [N]: s
f [Hz]
0.4 0.6 0.8
cv\
1
1.2 1.4
20
30
0.5
1
f [Hz]
cA-
'C(0
1.5
20.
30
0.8
1
f [Hz]
1.2
0.7
1.4
20
0.4
0.6
20
20
0.2
0.5
30
=
20
0C
CDv
0.4
E30
0.6
30
40
0.3
20
Mean Thrust [N]: s = 0.30, 0 = 40
20
40
0.4
-/-.
0.6
> (....
40
0.2
30'
-
0.4
30
CD- ..
40
20.
40
50
0.2
Mean Thrust [N]: s = 0.40, $ = 40
50
20
V6
40
40
20
'
30
co
Mean Thrust [N]: s = 0.30, $
0.5
.
0.4
Mean Thrust [N]: s = 0.50, $o = 40
0.3
Iv
00.
40
50
0.4
. .. .
40
0.2
.
jC
Ct2
Mean Thrust [N]: s = 0.30, $0 = 60
50
Mean Thrust [N]: s = 0.40, $0 = 20
0.3
.. .
=
0.1
0o
:7-/
Mean Thrust [N]: s = 0.40, $0 = 60
50
50
0.2
40 .
(0
cv~cQD
=0.60,
0.3
30
40
50
Mean Thrust [N]: s = 0.50, $0 = 60
Mean Thrust [N]: s = 0.50, $0
50
20
x
Mean Thrust [N]: s
50
20
20
(40
Mean Thrust [N]: s = 0.60, $0 = 60
50
-KI
CD
-1-
C)
00
CD
0.3
0.2
C,)
0.3
0.4
0.5
oo5
: s= 0.60, 0 = 40, h0/c = 4.2
A
0
20
0.4
0
0.8
f [Hz]
0.6
0
1
0.1-2
Tjop s = 0.60, $0 = 20, ho/c = 2.1
30
40
~E3 0
CD
0D
'7'40
'f
rj
50
0.2
0
Co
0)
0.
0*
020
00
0
0.3
~o
0
0.4
0.6
-
400
300
20
30
40
f [Hz]
0.4 0.6 0.8
(00
..
('2
1
1.2 1.4
a : s = 0.50, $ = 20, h 0/c = 1.8
0.2
20
30
40
50
f
0.4
-
0.6
0.6
0
40, h/c= 3.2
0.4
40.18
-
0.4
0.6
C).
0.8
1
f [Hz]
1.2
: s = 0.40, $= 20, h0/c= 1.6
201
0.2
0.4
.
20
--
.
0.2
: s =0.40, $=
30
-
/
50
I
20
30
40
50
ro :s=0.40, 00=60, h/c =4.8
30
40
50
1p: s = 0.50, $ = 40, h /c = 3.7
0.1
20
0.2
.
-.-..
40
20
'
30
0.1
Co_
/
r, :s=0.50, 0 =60, h/Ic = 5.5
50
t30
a)
40
50
lop:s=0.6 0 , 0 = 60, h/Ic = 6.3
0.4
0.5
20
30
40
50
0.8
0.6
0.7
=60,h0 /c=4.1
0
0.6
'0
1
1
1.2
f [Hz]
co
0;
1.4
0c0
20, h0 /c = 1.4
0.8
= 0.30, $= 40, h/c =2.7
20'
0
s
0.4
:
0.3
-
0
i 4 : s =0.30, $=
30
40-
50
T
20
30 - -
40
ro :s=0.30,
50
4.3
Discussion of Results
The scaling analysis was found to be robust to perturbations in geometric similarity.
The coefficient of thrust is a strong function of the Strouhal number and maximum
angle of attack, and weak function of the wake width in this regime.
The 0.40 m span foil performed best in terms of thrust and operational efficiency.
This foil size may have performed best simply due to the constraints of the kinematics
parameter space attainable by the machine. However these findings may point to a
more general result, which is that the optimal aspect ratio (s/c) for a flapping wing
is near 4.
Geometric similarities exist between various species of flying animals. [13] For many
species of birds, the relationship between wing area and wing length is remarkably
consistent. For an enormous variety of birds with wing spans ranging from 0.16 m
to 2.4 m, the wing length squared divided by wing area is consistently near 3.86.[13]
For a rectangular foil this would result in an optimal aspect ratio of 3.86. The work
in this thesis found the optimal aspect ratio to be 4. The similarity between these
optimal wing aspect ratios may be an indication that there exist three dimensional
flow effects that are optimal when the aspect ratio of the foil is near 4. More work
should be done to investigate the relationships between the geometry and aspect ratio
of the foil and three dimensional flow effects.
108
Chapter 5
Design Recommendations
Future flapping foil actuator designs should be smaller, lighter, and have a much
greater depth rating. Minimize the mass of the solid moving parts. Do not rush the
design in early stages. Hold design reviews early and often to discuss multiple strategies for the design. Think the design through to the end before starting fabrication.
Be sure all the components and materials will be available. Include long lead times
for purchasing in the planning.
Maximize the performance with two degrees of freedom per foil before considering
more complicated designs. Avoid extremely complex designs that will be expensive
to fabricate and difficult to maintain. A vehicle should be practical and relatively
easy to use and maintain.
Consider both the magnitude and bandwidth of the thrust produced. Massive
forces delivered at a very low bandwidth are useless. Foil size is the primary factor
controlling the trade off between magnitude and bandwidth. A light and powerful
design should be able to achieve a thrust vectoring bandwidth of at least 4 Hz. Be
sure the pitch axis is powerful enough to use single degree of freedom propulsion
kinematics with a flexible foil.
Incorporate a spring or magnet on the roll axis to minimize the inertial power. If
incorporating the spring into the design will lead to substantially increased mechanical
or fluid damping, the net effect of the spring may decrease efficiency. Simulate the
109
solid dynamics, hydrodynamics, and control to select an optimal spring stiffness. 1
A large range of motion on the roll axis has many practical benefits in regard to
wake interactions and during the deployment and recovery of the vehicle. A low
level control system could be used to sweep the frequency and roll amplitude to lock
onto the resonant mode. Be sure to consider the interaction between the backlash
on the roll axis and the spring. Discontinuities in the velocity trajectory may lead to
unfavorable vortex shedding.
Maximize the power density of the motors. Considering the cost of the sensors,
custom machined parts, and waterproof cables, additional money spent on extremely
high performance motors is well justified. There is a point of diminishing returns
on increasing motor size. Multiple small powerful motors in parallel may provide
more power density. Think in terms of delivering rapid bursts of energy through the
drivetrain. Minimize or eliminate the gear reduction. There has been a recent move
in robotics towards high torque direct drive motors to eliminate the backlash and
efficiency losses. Investigate advanced servomotors that have the motor, amp, motion
control card, and encoder packaged in a single unit. A foil module could consist almost
entirely of one or two of these small servomotor packages in waterproof housings.
The rest of the design would simply consist of bearings, couplings, and a frame. Be
wary of artificial muscles. Rigorously test the actuators before incorporating them
into a design. All the artificial muscles available today are seriously limited by the
bandwidth, displacement, efficiency, or required operating voltage.
Give sealing a high priority in the design. Consider using magnetic couplings and
wet bearings to eliminate the shaft seals. It is very difficult to make reliable dynamic
seals on rotating and bending shafts. The friction in the seals wastes considerable
amounts of energy. Radial deflections of shafts cause rapid o-ring wear. Buna-n orings have good resistance to creep (called compression set in the sealing industry),
but they absorb water and swell. Ethylene propylene o-rings are ideal for static seals.
Avoid excessive o-ring squeeze in dynamic seals. Read the Parker O-ring Handbook.
'There is Matlab code of a preliminary simulation for this purpose on the Towtank server at
\Vic\Documents\Matlab\2165\project\
110
Teflon and nylon bushings should be used to protect the o-rings from large radial
deflections. Pressure compensation should be avoided on a prototype design. The oil
adds considerable weight and makes maintenance more difficult.
Give maintenance serious consideration, especially in a prototype design. Make
all the housings easy to open and have clear lids if possible. Make all the parts interchangeable. Keep extra fasteners, hardware, electrical connectors (signal, power,
communication), o-rings, and fuses organized and on hand. Try to minimize the variety of machine screws in the design. Maintaining a stock of a large variety of screws
is very tedious and expensive. Always use a course thread in aluminum and plastic.
Avoid threading holes into brittle plastics. Avoid helical threaded inserts, they gall
and work loose. Always use a copper based lubricant when threading stainless steel
screws into stainless steel parts.
Use a higher operating voltage (at least 48 volt) to minimize losses due to impedance.
Use more sophisticated batteries (nickel metal hydride or lithium ion). Be aware
there are numerous fire and explosion hazards with batteries. Never charge batteries
while sealed in housings. Use diodes to guarantee the batteries will not accidently
be charged while connected to shore power. Use diodes to protect the user while
wet plugging shore power. Consider using over pressure relief valves in battery housings. Avoid placing switches and relays that spark in the same housings as batteries.
Flammable gasses can be trapped in sealed housings with batteries while they are in
storage. Manufacturers rarely approve of using batteries in sealed housings.
Teflon and composite materials such as Rulon work well for wet bearings. The
dimensional tolerances on conventional packaged bearing units, such as pillow blocks,
are very loose. These loose tolerances cause great alignment difficulties with seals
and couplings.
The strength of the shaft couplings has been the weakest mechanical component
in every design. Consider milling the shafts to have square ends. Coiled spring pins
take some effort to replace, but they have worked very well. Clamps have worked well
in some applications. Set screws often vibrate loose when there are high derivative
gains in the motion control. If set screws are used, drive a cone point into a deep
111
pocket on the shaft. Use two short set screws in the same hole and drive one into
the other. Avoid taper pins. Parts joined with taper pins are not interchangeable
because of the tapered reamer. Taper pins vibrate loose very easily.
Sprockets and chains (with two stainless steel cables and urethane coating from
W.M. Berg) have worked very well on several designs. Fatigue, strength, and stretching concerns for chains are relatively minor on this scale. Chains rarely break and
are very easy to replace. Cable drives have tremendous potential in biomimetic design, but they can be very difficult to adjust and maintain. The cables often slip
and break. It is difficult to get the cables in enough tension. Pneumatic pistons are
totally impractical for an underwater vehicle. Hydraulics are complicated and have
many stages of efficiency losses.
Incorporate an absolute position reference on every axis, (potentiometer, halleffect, mechanical or optical switch) for homing the foil. It is very important to be
able to zero the pitch axis on the foil repeatably. Make sure the pitch axis can rotate
a full 3600. One of the major advantages of flapping foil propulsion is that there could
potentially be no preferred direction for thrust.
Make the foils easy to detach and replace. Do not make the foil detachment point
inside a housing. Magnetic couplings would be very convenient for detaching the foils
and providing a safety measure. Make all the foils and couplings interchangeable.
A foil crash is inevitable.
Use torque limits and error limits in the control.
Be
absolutely sure to include a shear pin, or design failure point to protect the motors
and structure. Sharp rigid foils can be dangerous. Flexible foils have many practical
benefits as well as hydrodynamic benefits. Foils that bend before they break will be
much more robust. It is almost impossible to maintain a pristine trailing edge on a
rigid foil once the actuator is getting some serious use.
Give major consideration to the number of waterproof cables and connectors when
deciding which components will reside in which housings.
Waterproof cables and
connectors are very expensive and unreliable. Do not send the encoder signal for
the roll axis through a waterproof cable without a limit switch. Encoder signals are
routinely lost and a crash on the roll axis could cause major damage.
112
The least
reliable components have always been the custom cables and connectors. This is true
in many robotics applications. Communication problems are almost always due to a
faulty connector. Take the extra time to make extremely high quality cables. Always
dispose of faulty cables, never return them to storage.
Make the housings easy to open and have clear lids if possible. Nearly every time
there is a communication or mechanical problem the housings must be opened. Count
on opening the housings several times a day when using the vehicle. End plugs on
tubes can be difficult to remove, but this can be avoided with a strong protruding
lip on the end plug that can be tapped with a mallet. Be sure that the cables and
connectors are not stressed when housing is opened. Use wireless communications
between the laptop and vehicle.
Use heat sinks for all the electronics and motors. Be sure to consider the melting
temperature of plastic housings. Aluminum or titanium housings would certainly
certainly conduct heat into the water much more effectively than plastic housings.
Use corrosion resistant materials. Be aware that anodized parts can be scratched
easily. Get samples for any new materials (especially flexible rubbers and composite
materials) that are being considered for the design and leave them underwater for
several months to observe the rate of deterioration.
Take design measures to minimize structural vibrations in the frame of the vehicle.
Make a stiff frame for the vehicle in order to drive the lowest mode well above the
excitation frequencies of the highly unsteady hydrodynamic forces. Every flapping
foil test rig has experienced heavy mechanical vibrations (normally in the range of 7
to 30 Hz). These test rigs were deigned to be very rigid, with size and weight limits
that far exceed the constraints for a vehicle frame.
Consider exploiting symmetry in the vehicle design to increase open loop stability.
Make the vehicle small and light to ease deployment. Make a modular design and
exploit economies of scale in the fabrication. Consider making a prototype for any
actuator design before making the full set.
113
114
Appendix A
Cruising Forces in Time
The data contained in this appendix covers this range in the test
matrix:
span
= {0.6, 0.4}
roll
= {60,
St
= {0.4, 0.6, 0.8}
MaxAoa = {50,
run
40,
40,
20}
30, 20}
= {1 or 2}
These figures, and the remainder that are not published here, are
located on the Towtank server at \Vic\Thesis\Latex\Figures\Matlab\
in *.eps,
*.fig, and *.jpg format.
The distance from the centerline of the roll axis to the root of
the foil for these tests was
rO = 0.178 m
The other dimensions and relevant values needed for calculations
are all given in the title of each figure.
115
All the data presented in these plots was filtered using ifilt.m at
6 Hz on the lift and current axes
8 Hz on the thrust axis
All of the raw data and calibration data is located on the Towtank server
at \Vic\Thesis\Data\
The data is organized by day.
The calibration
files always reside in the same folder as the raw data.
The
calibration data is also loaded into *.mat files in the same directory.
The calibration files (cal-dyno-x-pos.m,
cal-dyno-y-pos.m,
calammeter.m)
and postprocessing files
(postcruise.m,
ifilt.m, notch.m, notch2.m, parsedl2.m, postcruise combo.m,
plot-specral-analysis-dyno.m) are located
on the Towtank server at \Vic\Documents\Matlab\
Refer to cruiseHELP.txt for a complete explanation of the file
naming conventions and specifics of the raw and summarized data
files.
All of the mean filtered cruising data (operational efficiency,
coefficient of thrust, mean thrust, max thrust, mean current, max
current, frequency of foil motion, integer number of cycles used
to compute mean, pitch amplitude) is stored in a large data
structure called cruising-testmatrix() written in
cruisematrixmat.mat on the Towtank server at \Vic\Thesis\Data\
There is a help file called cruiseHELP.txt in that directory to
explain the arguments and output of the data structure.
additional help files located with the raw data.
116
There are
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 50 [deg], run2 OUTPUT: Ct 0.1, efficiency 0.01
C
6-
-
thrust
-mean thrust
4
-
0
2
I-
0
2
4
2
CD
6
Time [seconds]
8
10
50
12
__n
0-
lift
-.-.
m ean uift
0
2
-
0
0
2
4
6
Time [seconds]
8
10
12
E
4
C~
-current
mean current
T.m.
50-R07
2
a,
0
S 0
2
a,
50
4
6
Time [seconds]
8
<
5 0
12
Angle of Attack Distribution Over Span
.-.
I7
..--
tip
0.2
root.z:*
_-.
ca50
a)
10
~05
0.5
1
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 40 [deg], run2 OUTPUT: Ct 0.3, efficiency 0.03
S 8-C
6
0
64+=3
-
...
......
... .........
thrust
mean thrust
2
I
....
0
40
+
6
Time [seconds]
4
2
I
I
2
00.............
-20
12
10
8
Ilift
......
............
-40
mean lift
......... .............................
I
0
6
Time [seconds]
4
2
12
10
8
00D
E
4-
current
11-
> -... mean current
-
2 Cj2
4.
CD
0
0
3
12
10
8
6
4
2
Time [seconds]
Angle of Attack Distribution Over Span
40
.
40
a) 0
.i
ii<N-
tip
----------
-40 -a)
5
<
0
R 0.70
-
0.50
root
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 60 [deg], St 0.40, MaxAoa 30 [deg], run2 OUTPUT: Ct 0.6, efficiency 0.06
10
thrust
-II
0-
C
mean thrust
'5
CAA
0
AA
V
I
VV
I
0
8
6
4
2
V
AA
JAA
AAN
Vvy
'V
V,
A
'I
I
14
12
10
18
16
Time [seconds]
lift
20
0
-20
-40
mean lift
0
8
6
4
2
14
12
10
18
16
Time [seconds]
I'a
0
current
mean current
3
2
........... .......... .... .. .......I..........
1
0
4
6
2
0
................ ........... .......... ..
8
Angle of Attack Distribution Over Span
a)
30
-
-.
-
\
-- 300
0
N
N
-~
-
-
-.
-
-
-
-
*/
---
tip
N
-
N
--
-
"i
-a
18
16
Time [seconds]
(>
-(
14
12
10
.......
.
E
Co
1.5
1
0.5
Time [period] (not synchronized with forces and current)
- -
R 0.70
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 20 [deg], run2 OUTPUT: Ct 0.6, efficiency 0.09
10
.
0
\
.- %
'IV
....
........
2
,v
thrust
..... mean thrust
~~AA
jA
-
4CD 0 5 ........... . ........ ........
...
I. .....................
........
............
1.C
. . .
I
v~II
4
6
8
10
I
12
Time (seconds]
2C
C
0
.... -mrean lift
0.............................
4,
-20[I
I
0
Er
2
I
4
6
Time [seconds]
-
I
I
L
8
10
12
I
-
IVA
1:
Z
........
..
..
C
20
I
0
I
V
2
current
mean current
........
V
4
V
4
6
U)
8
10
12
Time [seconds]
Angle of Attack Distribution Over Span
0-0.51-1
0- 20C
C>
-- - - - 0
.5-2
~
0.5
~
---
. . .-1
R 0.70
root
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 50 [deg], run2 OUTPUT: Ct 1.0, efficiency 0.05
0
15
10
5
0
I
....
I
0
thrust
-e
2
4
6
8
10
12
I
V -
I
I
I
V
II
-V
thrust
mea thrust....
14
I
16
Time [seconds]
C,
50
lift
0
C:
.-. mean lift
0
-50
0
2
4
6
8
Time [seconds]
10
12
14
16
E
--
4
current
.
...
I.
...
...
..
....
m.
.n
I.u
rr...
...n..
..
..........
I..
......
Co
2 --
0 1II|
0
2
6
4
8
10
14
12
16
Time [seconds]
C-)
Angle of Attack Distribution Over Span
50
tip
. . .- .-.-.--. . . . . .
--
R 0.70
0
-.
-50
a),
-a
<C
0
-.
A
--
0.5
1.5
1
Time [period] (not synchronized with forces and current)
-
0.50
0.25
-
0
root 0
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 40 [deg], run2 OUTPUT: Ct 1.5, efficiency 0.08
C:
0
thrust
mean thrust
20
10
C
......
0
0
2
A
...
8
6
4
C,)
C
50
4a)
r)
AA
A
14
12
10
Time [seconds]
.
-
lift
-- mean lift
----------
- - - -- -........
I
20
18
16
0
A
-500
CL
2
8
6
4
12
10
Time [seconds]
14
16
20
18
E
current
- mean current
4
-
2-
C
0
2
10
8
6
4
12
14
16
20
18
Time [seconds]
Angle of Attack Distribution Over Span
)
a)
)IZII~.tip
-5 4(
-
--
0)
a
- -----
-4
0
-- - ~-
1.5
1
0.5
Time [period] (not synchronized with forces and current)
--------.
~--- -
R 0.70
5-0.25
root _
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 30 [deg], run2 OUTPUT: Ct 1.7, efficiency 0.11
a
1
-
C: 10
-
---..............................................................
A
UI
I
0
2
I-
I
-VI
-
-I
6
4
..................................
8
thrust
. mean thrust
I
I
10
12
Time [seconds]
50
0
-
1
1
1
lift
0
mean lift
-50
1
0
C-
2
4
I'4
6
Time [seconds]
12
10
8
E
W
4 _current
C1
0
a,
S.... mean
I
II
0
2
4
6
Time [seconds]
I
I
8
10
a)
-5 30
--
0
a
I
12
-~---,-
------
current
Angle of Attack Distribution Over Span
0)
-30
)
H
020
-
30 -
-
-
-----1.5
1
0.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
o0.5
root j
2
IN PUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 20 [deg], run2 OUTPUT: Ct 1.5, efficiency 0.15
20--
2...
C
4-
1010....... ............ ........... ....... ........... /^\......
............-.
0
6
Time [seconds]
4
2
C:
20
0..............................
C:
thrust
mean thrust
..... ......
12
10
8
mean lift
. .................. ............
enlf
-20
0
-40
E
0
2
4-
I
1
6
Time [seconds]
4
12
10
8
current
mean current
2 ...... ... .. ......... .........
....... ...
....... ...
...... ..
CZ)
... ....
........
V
0
2
4
6
Time [seconds]
V4
8
12
10
20
/
Angle of Attack Distribution Over Span
- -tip
-
1.---.~.
R 0.70
-
0 -20
C
-
1.5
1
0.5
Time [period] (not synchronized with forces and current)
-
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 50 [deg], run2 OUTPUT: Ct 1.8, efficiency 0.07
30
20-
thrust
mean thrust
-
0
0
0
-
-10 -
6
4
2
8
12
10
Time [seconds]
- -
W 50 Cmean
0 +-
lift
-m- --..
lift
C
-50
0
6
Time [seconds]
4
2
8
12
10
E
.........
S
.......................................................
4mean
... ... ..... ... ..... ... .............. ... .... ..... ....- m
current
current
2-
0
0
2
6
Time [seconds]
4
8
12
10
Angle of Attack Distribution Over Span
'
-o 50
-
--
0
7 L7
50
M
<
'-
tip
-- R 0.70
0.50
0.25
root
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 40 [deg], run2 OUTPUT: Ct 2.6, efficiency 0.10
40
thrust
..... . -m ean
thrust
0, 20 -- .... --- --.-.---.-- .---.NC
0
Co
0
50
-(1
C
00
2
4
I
I
6
Time [seconds]
8
10
12
lift
mean lift
...
-.1
............
..
-..
.....
C
"=-j -50
II
0
II
2
4
6
Time [seconds]
8
10
12
E
current
>.4
S
.....
mean
current
2-
CS 0
0
2
4
6
8
10
12
Time [seconds]
(D
Angle of Attack Distribution Over Span
S40
0
/~~.
0
Z-40
C
0
-- ------- --
I
-I -1
1.5
0.5
Time [period] (not synchronized with forces and current)
--
R 0.70
root Lj
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 30 [deg], run2 OUTPUT: Ct 3.3, efficiency 0.15
thrust
40
mean thrust
20
C
0
5
0
0
10
15
Time [seconds]
zu
lift
n~r lift
..
..
.
.
..
.
.
C
-50n
t'Q
10
5
0
U)
15
Time [seconds]
a-
-KJ
CD
6
current
mean current
4
a)
2
-
C
Ui
U
0
15
10
5
Time [seconds]
0
Angle of Attack Distribution Over Span
/
-
30
0
-
.
-
-30
J-*
-
.
K.
0
Rtip
-
N
-
R0.70
1.5
1
0.5
Time [period] (not synchronized with forces and current)
--
--
-.
R
0.50
.0.25
root
2
INPUT U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 20 [deg], run2 OUTPUT: Ct 1.8, efficiency 0.18
5 30
thrust
20
- mean thrust
0
C10
S0
15
10
5
0
Time [seconds]
10-1
W 10C_
lift
0 0
...
-10...
..- m ean lif
.. ....
C
-20
-30
15
10
5
0
Time [seconds]
a.
E
3
-
C
2
current
> - mean current
-
00
0
15
10
5
0
Time [seconds]
Angle of Attack Distribution Over Span
v
20-
tip
X/..N<*.
R 0.70
--
->
C:
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
-.-
root -i
2
6 422...............................................
04
-
.............
-
=3-2
thrust
-
-
C
0
1
2
4
6
8
10
12
Time [seconds]
-
S50
1
1
1
lift
11
-
S 0
. .1 rf ean lift
+-
C
--
50 L
0
2
4
6
Time [seconds]
8
10
12
0.
4
C\
....
--...-.. .. .......... ......
....-----..---I--.-----------..-I-.
-----.---..
-.
.-.
-..
.....
2 -------- ..-.. ..
.
W,
- current
-.-.mean current
-
0
0
0
2
6
Time [seconds]
4
8
10
12
Angle of Attack Distribution Over Span
a
-a_CD, 0 50
*
-
tip
R 0.70
N.
-~--
CZ
0
0-- 50
a)
)
....
mean
thrust
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.40, MaxAoa 50 [deg], run2 OUTPUT: Ct 0.2, efficiency 0.01
*-*
0.50
0.25
root
0.5
1
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.40, MaxAoa 40 [deg], run2 OUTPUT: Ct 0.3, efficiency 0.03
10
c
-- thrust
mean thrust
.
5-A
.
0V 'V\V
)
I
2
\
IV
A
4
6
Time [seconds]
8
12
10
50
lift
C
/ *1-
mean lift
0
-50
)
C)
E
2
4
6
Time [seconds]
8
12
10
4
-
CZJ
current
- mean current
2
C
M)
0
0
=3
2
4
6
8
12
10
Time [seconds]
a)
Angle of Attack Distribution Over Span
-
Z
0
-y
S-40
a5)
C
tip
R 0.70
-- 0.50
-0.25
-root
-
40
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
-
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.40, MaxAoa 30 [deg], run2 OUTPUT: Ct 0.6, efficiency 0.06
10
-thrust
.............
..
mean thrust
.....
C,,
0
2
4
6
8
Time [seconds]
10
12
14
lift
..... mean lift
20-
-
16
-20-40
r
0
2
4
Z
6
8
Time [seconds]
10
12
14
p1
Il
16
-
current
mean current
0
Uf
0
V VI
2
V
I
4
6
10
12
16
14
Angle of Attack Distribution Over Span
(D
30
CZ
8
Time [seconds]
0-
tip
YIN
R 0.70
-
-0.50
0.25
~-30E
C
* 0
-T-r
--
~
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 40 [deg], St 0.40, MaxAoa 20 [deg], run2 OUTPUT: Ct 0.6, efficiency 0.09
thrust
mean thrust
0
U)
y
IVI
I
I
I
I
4
2
0
H
20
0
6
8
Time [seconds]
16
14
12
10
-
_.
._ m e a n lift
0
-
~VVV
v
A
A
C
"
~ 10
-20
4
2
)
6
I,
t'Q
8
Time [seconds]
14
12
10
16
E
-
--
2
C
............. ...... ........ ...... ........................
.. .................
1
0
4
2
0
........ ........ ........
16
14
12
10
8
6
current
mean current
Time [seconds]
0)
a)
a)
a)
Angle of Attack Distribution Over Span
N-
20
0
~---
-20
C>
~~
-
0
'---
.
-
-
--
--N.
1.5
1
0.5
Time [period] (not synchronized with forces and current)
.--
tip
R0.70
0.50
0.25
root j
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 50 [deg], run2 OUTPUT: Ct 1.1, efficiency 0.05
C
0
C:
thrust
.....
thrust
thrust . V . ..... .
-e
V
I
2
4
I
I
6
8
~~~~~~~ma
~
P~~
)
-
U)
IM
15
10
5
0
10
II
12
I
14
16
18
Time [seconds]
C
50
-lift
0
mean lift
0
-50
0)
)
2
4
6
8
10
Time [seconds]
12
14
16
18
0-
E
-current
Co
4
mean current
2
01
0
a)
2
4
6
8
10
Time [seconds]
12
14
18
Angle of Attack Distribution Over Span
0)
50
tip
-0
<.....-
--
-
-
0
Co
16
R 0.70
0.50
0.25
-50
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root j
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 40 [deg], St 0.60, MaxAoa 40 [deg], run2 OUTPUT: Ct 1.5, efficiency 0.08
~ 20-II
cc
thrust
...
mean thrust
........................... ......... ........... ......... ...
S10-..... ..........
0
F-
0
C
0~
II.V41.IY
4
2
0
6
8
Time [seconds]
10
16
14
12
50
-lift
.. mean lift
0
-50
4
2
0
6
8
Time (seconds]
10
16
14
12
E
ucurrent
...
mean current
4
Cj
2
a)
0
0
C-)
4
2
6
10
8
16
14
12
Time [seconds]
Angle of Attack Distribution Over Span
-5 40
~ ~N
:n
0
~N
0-a,-40L0
a)
C
-.
,.
tip
R 0.70
0.50
-
0
-
S
-0.25
- --- root
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 30 [deg], run1 OUTPUT: Ct 1.9, efficiency 0.11
30a
th
Cthrust
20-
... mean thrust
C 10-A
o
n
2
4
.
6
n
8
10
12
Time [seconds]
0
~'50
-lift
0
m ean lift
C)
2
4
6
8
Time [seconds]
CIO
Q1
10
12
E
current
mean current
4
C\j
C
=3
u
0
0-
2
4
6
8
10
12
Time [seconds]
Angle of Attack Distribution Over Span
CD)
30
R 0.70
0
0
(1)
-30
-
0
-
--
.-
-
ro0.25
----------
0.2roo
1.5-
0.5
1.5
1
Time [period] (not synchronized with forces and current)
---
2
2
-
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 20 [deg], run2 OUTPUT: Ct 1.5, efficiency 0.15
1
1
1
1
I
30
C-thrust
20
.... mean thrust
C
10 ............. ......... .........
230
A
...
.............. ..... ....... ..............
A
8
Time [seconds]
6
4
2
0
16
14
12
10
2C
lift
U)
* ....
......... ..
I.......
............... ..................... ..
C
....... ..... m e a n lift
C
V
8
Time [seconds]
6
4
2
)
16
14
12
10
E
-
4
C-)
mean current
2 .....
...
..
.....
....
..
......
....
...
.......
.... ..... ... ........ ....
0
0
16
14
12
10
8
6
4
2
.
.
C
current
Time [seconds]
Angle of Attack Distribution Over Span
0>
a)
aZ
20
/.........
..........
..............
................
--
0
-
-20
C
~
-
0.5
1
-
.5
I
1.5
Time [period] (not synchronized with forces and current)
Stip V
D7A
0.50
0.25
root
2
-
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 50 [deg], run2 OUTPUT: Ct 1.8, efficiency 0.07
1
1
1
S 40--- thrust
8
0
0
-
2
4
6
8
10
12
14
16
18
Time [seconds]
C
50
---
CD
lift
lift
0....................................................mean
a,
C
-50
0
2
4
6
8
10
Time [seconds]
12
14
16
18
E)
urencurrent
2
0
0
2
4
6
8
10
12
14
16
18
Time [seconds]
Angle of Attack Distribution Over Span
50
S-
-
-
-
-
-
-
- -
-
/-.--
0
.... . . .
. . . ..
-50
0
tip
R 0.70
0.5
1
1.5
Time [period] (not synchronized with forces and current)
.
0.50
root j
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 40 [deg], run2 OUTPUT: Ct 2.6, efficiency 0.09
thrust
~~~~~~~ 20.....
8
Time [seconds]
10
~-5
mean lift
0
I
I
..
U
2
0
4
6
8
Time [seconds]
10
current
--
M
4
16
14
12
E
>
16
14
12
0nlift
0
a)
00
6
*
C
4
2
0
....... mentrs
...................................
mean current
C\j
2a)
0
2
0
:
4
6
8
10
12
14
16
Time [seconds]
a)
Angle of Attack Distribution Over Span
0)Z
Co
0.5
'5
<
0
11.5
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 30 [deg], run2 OUTPUT: Ct 3.2, efficiency 0.14
thrust
mean thrust
40
C
20
.
\.)
V.......
.. ... M
.
.
.
.... .......
8
10
12
14
.
.
.
-A
.
.
.... f
.
.
.................
-A
---- [seconds]
-------- Time
.
0
0
2
4
6
U,
---------------C
50
lift
m ean lift
0
-j
-50
0
E
CZ
2
4
6
8
Time [seconds]
10
12
14
6
current
...
mean current
4
2
0
0
C-)
2
4
Co
6
8
Time [seconds]
10
12
14
Angle of Attack Distribution Over Span
30
tip
-0
0
CM
~
3-
0
/
-
R 0.70
0.5
1
1.5
Time [period] (not synchronized with forces and current)
0.50
0.25
root _
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 40 [deg], St 0.80, MaxAoa 20 [deg], run2 OUTPUT: Ct 1.5, efficiency 0.16
W~
30-
I
o
1
Hh
-thrust
... mean thrust
020
A.. .... ............ ..........
1 ...........
0
=3
4
2
10
uc)
V
-v'
0
I-
............ ...........
8
Time [seconds]
6
0 0l\n
10
12
16
14
4
...
lift
mean lift
o: -10S-20
-j-30
I
0
2
4
6
8
Time [seconds]
10
12
16
14
EMT
---
current
-.-mean current
C\i
a)
0
0
2
4
6
8
10
12
14
16
Time [seconds]
=3
Angle of Attack Distribution Over Span
a)
a)
02
0
05
0.70
a)
.Z -2 C
-root0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 50 [deg], run2 OUTPUT: Ct 0.2, efficiency 0.02
C
z
4-
~A
/~hf'lA
C
0
2
4
6
ft
~
8
/
1M~at~
10
~meanA
thhrust
12
14
16
18
Time [seconds]
C:
in(\
5C
0
-A
-
nmean
l i ft
lift.
-50
0
2
4
6
8
10
12
14
16
18
Time [seconds]
4
Co
.current
mean current
2
0
0
(D
4
6
8
10
12
14
16
18
Time [seconds]
Angle of Attack Distribution Over Span
0)
CZ
2
50
tip
R
0.70
0.50
0
-50
-.-0.25
0
-
root 1
0.5
1
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 20 [deg], St 0.40, MaxAoa 40 [deg], run2 OUTPUT: Ct 0.4, efficiency 0.04
thrust
10..
y\At.~V\J~~fl\
thrust
mean
...
18
16
14
12
10
8
6
024
I
Time [seconds]
0
C
-50
V
)
fI\
..'. mean lift
fI\
fI\
.
0
A
II
-
.
5(
I
4
2
8
6
10
Time [seconds]
I
I
12
14
-
18
16
0-
E
I
mcurrent
42- ......
C
CD
C)
....
0.
0
..........................
I
I
I
I
2
4
6
8
12
10
14
I
I
16
18
1
Time [seconds]
a,
Angle of Attack Distribution Over Span
-- ---- -- -
-
40
r
-
---------
-
0S-40
a)
*5
I
V I
0
I
1.5
1
0.5
Time [period] (not synchronized with forces and current)
-
-
tip
R 0.70
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 30 [deg], run2 OUTPUT: Ct 0.7, efficiency 0.07
thrust
...
mean thrust
10
0
A.A
V
)
......
A.
.AA
...........
I
V
2
.........
y
V
V
4
6
I
v
......
V
A A .
.
.A
...
.
5
V%
8
y
y
V
V
10
12
I
V
14
16
Time [seconds]
20
0
-20
-40
- n
0
4-
2
4
6
8
Time [seconds]
.... mean
lift
nlift
10
12
14
I
16
current
mean current
2
0
2
4
6
8
Time [seconds]
10
12
16
14
Angle of Attack Distribution Over Span
30
tip
R 0.70
0
0.50
N
0
*~*
-*-
5
.... .
0.25
.
-30
--
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 20 [deg], run2 OUTPUT: Ct 0.7, efficiency 0.10
h~thrust
10m
.....
0
2
0
0
3:
6
4
8
Time [seconds]
16
14
12
10
0I
V
-2 0
-lift liftiri
mean lift
........ ......
.V .........
V
2
thrust
A'
C
0
mean
6
4
8
Time [seconds]
10
16
14
12
E
-current
... mean current
2
1.
......
. ........ .. .... ... ......... ...
. ........... .... .... .....
....... ........
0
0
0-
2
6
4
8
10
12
16
14
Time [seconds]
2
CZ
a)
Angle of Attack Distribution Over Span
-0
0
0~
0
- R 0.70
---
0.5
-----
0
0 C)
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
----
root
2
-
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 50 [deg], run2 OUTPUT: Ct 1.4, efficiency 0.06
C
0
20 ~ .
10......[~4VV\mean
thrust
thrust
C
D10
0
C
C
0
50
2..
4......1
2
4
6
8
Time [seconds]
10
12
1
1
14
16
lift
III
'
~
0.......................................
.
..
mean lift
........
C
S-50-
E
2
0
-.
6
4
8
10
14
12
16
Time [seconds]
4
mean current
2
C
0
0
2
4
6
8
Time [seconds]
10
14
12
16
Angle of Attack Distribution Over Span
....-.....
50
- -.
-
I
-
0
CD
0>
C
--
50
0
~~
---- - .- ~.-
1.5
0.5
1
Time [period] (not synchronized with forces and current)
tip
R 0.70
0.50
0.25
--
root _
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 40 [deg], run2 OUTPUT: Ct 1.7, efficiency 0.08
thrust
S-
o 0 110
C,,
V0
\
2.IV81
6
4
2
0
8
20..ean
61 IV
16
14
12
10
thrust
4
1
18
Time [seconds]
50
"5 n
mean
lift
..
0
6
4
2
18
16
14
12
10
8
Time [seconds]
E
-current
4
...
mean current
2
0
0
4
2
6
12
10
8
18
16
14
Time [seconds]
Angle of Attack Distribution Over Span
tip
40
_~7
N
-40
.
0
.
.
-
.
0.5
. -.
-
-.
N
-
/
0
R 0.70
0.50
0.25
.
n
lift
I
root
1
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 30 [deg], run2 OUTPUT: Ct 1.8, efficiency 0.11
(
0
0) 20
C10
2
mean thrust
I
0
n
5
10
15
Time [seconds]
5C
lift
0
...
mean lift
C
3,
CD
-5C
15
10
5
)
Time [seconds]
E
CZJ
-current
4
A
2
I
5
0
~mean
current
I
10
I
15
Time [seconds]
C
Angle of Attack Distribution Over Span
Q)
0) 30
a,
-
N
/
.,...
.-.-.-.-..-.-.--..-.-.
-.
-
-
0
tip
N
-
-
-.
N
N
-
N
0O.70
-0.50
----
-30
-
------
-/
0
0.5
.
.0.25
rootj
1
1.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.60 [in], chord 0.10 [in], roll 20 [deg], St 0.60, MaxAoa 20 [deg], run2 OUTPUT: Ct 1.2, efficiency 0.14
a,
(\fl\A lAI\~
120
20
Hc501
Time.
C
a,
C
10
0
-10
-20
-30
[seconds]s
* enlift
A AM AA
10
Time [seconds]
5
)
00
Athrust
Amean
i
20
15
W
E
3
Scurrent
mean currentT
2
0
0
20
15
10
5
Time [seconds]
CD
Angle of Attack Distribution Over Span
.
*-"
tip
0
(D
C
20
--
/
___
-
-
-
0
I-.J
V
0.50
0.25
root
-20
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10
[m],
roll 60 [deg], St 0.40, MaxAoa 50 [deg], run1 OUTPUT: Ct 0.1, efficiency 0.01
C S42
-
thrust
mean thrust
C
4-V
0
|
V
2
6
4
I
12
10
8
14
16
7
-
-2 --
18
Time [seconds]
0
C
20
nlift
-40
......
...............
0 ............................
-20
.........
...
mean lift
.............
IIIII
0
2
6
4
8
12
10
Time [seconds]
14
16
18
@
E
current
2
c\j
mean current
1
......
a)
0
... .V
0
0
4
2
6
10
8
12
14
16
18
Time [seconds]
a)
a)
Angle of Attack Distribution Over Span
(D
Co
Iii~..
0
- -50
a)
.5)
0
tip
-
**-z.
-.
-
-
-
-.
---
-
Z
-
CD,
-.
1.5
0.5
1
Time [period] (not synchronized with forces and current)
R 0.70
0.50
0.25
root W
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 40 [deg], runi OUTPUT: Ct 0.4, efficiency 0.04
6
4
2
U)
C
~
AM~A
~'~AAA
4-1
rVV-V
0
2
4
f~'\A
J~\AX~
A
VyV
6
-thrust
Aftmean
thrust
Y:frM
-]-VV01
y
Vv
10
8
12
14
16
18
Time [seconds]
2C
0
lift
f
- - m e a n lift
C
S-2C
0
2
4
8
6
01
E
-
------------------------
cZ
2
10
Time [seconds]
14
12
current
current
-
-mean
- - ---- -- - -- - -
1
18
16
0
0
2
4
6
8
10
12
14
16
18
Time [seconds]
C
Angle of Attack Distribution Over Span
Tn
0
tip
40
-
7-......
(D
7
N.
*-
-40
7
R 0.70
0.50
0.25
root
0
1
1.5
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 30 [deg], run1 OUTPUT: Ct 0.6, efficiency 0.07
8
-
thrust
~mean thrust
64 _
-C
0
-2 0
W
V
-
8
14
18
16
I
Ilift
20-
C
mean lift
......... .........
..........................
ma
lift-
I
12
-
20
0IV.............
Z I
10
Time [seconds]
20 -
I
AAA*-fV
6
4
2
C
I
\N
Z
6
4
2
0
8
C;'
10
Time [seconds]
12
14
18
16
2-
current
mean current
)
....
C
.
......... ...
1 - ...... --....
......... - -- -........... ....... ....- - -............. ......
U
i
0
i
i
4
2
6
i
I
i
8
10
12
0~
Time [seconds]
CDI
Angle of Attack Distribution Over Span
-a
-+--
14
I
18
16
C
tip
301
R 0.70
--
--
..
. .
. . .
. . .
*
0
-
-,
-30 r
0
I
1.5
1
0.5
Time [period] (not synchronized with forces and current)
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.40, MaxAoa 20 [deg], run1 OUTPUT: Ct 0.7, efficiency 0.08
C
86
thrust
..... mean thrust
C
-V~
Y
0
H
2
V
4
6
8
Time [seconds]
I
I*
10
12
\~
-
S100
14
lift
mean lift
- -~~...
14
10
-20
2
0
Ec 1.5 -
4
6
10
8
Time [seconds]
14
12
1
-
>1......................
.........
......
~~..
........
..
-
current
................ .... .m.......rean
ma urn current
@ 0.50
I
2
0
4
8
6
10
12
14
Time (seconds]
Angle of Attack Distribution Over Span
2
-20
-
-- - -
----.
0
- 1 - - . - -'
1
1.5
0.5
Time [period] (not synchronized with forces and current)
--R 0.70
-- -
ro ot
2
cA
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 50 [deg], run1 OUTPUT: Ct 1.1, efficiency 0.06
15
1
1
1
1
-rthrust
a n th ru st
-me
50
4-
.
5
..
...
0
..
......
........
.....
...........
....
..
.......
10-24681
~ 0
21
2
4
6
8
10
.
.
.
a)
A
AA/
61
12
14
16
18
Time [seconds]
A-
50
-A-
.
lift
I
...
mean lift
S-50
h
0
IV
II
2
4
onr
6
8
10
Time [seconds]
12
14
I
16
18
E
S-
-current
T>me
C\
CD
0I
S0
I
2
4
6
8
10
Time [seconds]
...
.......... ....
I
I
12
14
16
18
Angle of Attack Distribution Over Span
a)
a)
mean current
2 ........................... .......... ........................................
50 :z>.~--tip
CZ0
RJ 0.50ii>1727-27
Q
a)
'5
0
<
-.
-50
-
0.5
1
1.5
Time [period] (not synchronized with forces and current)
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [in], chord 0.10 [in], roll 60 [deg], St 0.60, MaxAoa 40 [deg], runi OUTPUT: Ct 1.6, efficiency 0.09
4-1
100..............................
I-
u)i
00
A
1A
151-
-thrust
mean thrust
...... ...........
AA
1\
4
2
40
8
6
10
Time [seconds]
12
14
16
18
lift
II
0 20 -...
mean lift
-20S-40
I
0
4
2
8
6
10
Time [seconds]
12
14
18
16
Q1L
E
W
>
4-
1current
meancurrent
N~ 2 . .. . . . . ... . . .. . . . . . . . . . . . . .. ... . . ....
. . . . . . . . . . . . . . . .. .. .. ...
. . . . . . . .. . . . . . . . . . .
rn:
. . ...
0
0
C-
2
4
6
8
10
12
14
18
16
Time [seconds]
Angle of Attack Distribution Over Span
Q)
40 -- -CZ
a)
---
0
R .7
0.5
-40-
0
0
0.1.5
1
0.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 30 [deg], run1 OUTPUT: Ct 1.8, efficiency 0.13
0)
C
0,
20
thrust
mean thrust
10
0
A.A
)
2
VA.
4
6
8
10
12
14
16
18
Time [seconds]
20
lift
__
...mean lift
C-20
)
E
C\i
4
2
3
2
1
6
I
8
10
Time [seconds]
14
12
16
I
current
~.. ~~ ~~ ~ ~~~~~~~~~~~~~~~~ma current ..... ..... ....... .............. .... . ....
UI
0
I
VI
2
4
6
18
'I
8
mecurrent
I
I
I
I
I
10
12
14
16
18
Time [seconds]
C
Angle of Attack Distribution Over Span
30
~
0
-
----
tip
K-.-
-
-
-
0.50
._...0.25
-30
CD
R 0.70
-
-
0
root
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.60, MaxAoa 20 [deg], runi OUTPUT: Ct 1.4, efficiency 0.14
C
a,
C
KA
15
10
5
0
.mean thrust
-AV
A
5
)
V
10
15
10
15
Time [seconds]
10
0
n* mean lift
"IJ4
0
-10
-20
I-V
r-
5
0
-
C
Time [seconds]
E
2
current
mean current
1
C:
(D
0
0
15
10
5
Time [seconds]
U
Angle of Attack Distribution Over Span
~0
2C :
*-
*
N
tip
R 0.70
-
C
--
-
C
--
N
-
-
-
-
-
aZ
-
--
-I-
--
-2C
- -
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 50 [deg], run1 OUTPUT: Ct 2.5, efficiency 0.07
0
0
thrust
20
C, 10
mean thrust
C
(0
01N-
0
I
I
A
2
4
6
8
0
12
14
16
18
Time [seconds]
-
U-
C
10
50 -lift
0
mean lift
C:
-50
0
2
4
6
8
10
Time [seconds]
12
14
16
18
E
6
-current
rn man current
4
2
0~
0
2
4
6
8
12
10
14
16
18
Time [seconds]
C
50
-
_--
-
Z
-
0
-
-
-
-
-
-
- -
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
-
-
-
-
-
-50
--
- --
-
tip
R 0.70
-
Angle of Attack Distribution Over Span
0
0.50
0.25
root
2
IN PUT: : U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 40 [deg], run1 OUTPUT: Ct 3.3, efficiency 0. 11
thrust
...
mean thrust
c:30
~0
0
10
Sn
0
I-
2
8
6
4
14
12
10
Time [seconds]
50
lift
-ean
lift
m
0
CD
-50
0-
II
0
Co
2
4
-V
6
....
8
Time [seconds]
V
14
12
10
V1
Go
E
rcurrent
mean current
4
-
r4
C
0)
W
0
2
4
8
6
14
12
10
Time [seconds]
C
Angle of Attack Distribution Over Span
4C
tip
R 0.70
-
---
C
0.50
0
-~--
-4C
C:
0
-~
1
1.5
0.5
Time [period] (not synchronized with forces and current)
-
~
-
.-
r0.25
rootj
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 60 [deg], St 0.80, MaxAoa 30 [deg], run1 OUTPUT: Ct 3.4, efficiency 0.17
A
thrust
C
0
mean thrust
S20
-C
0
2
6
4
8
10
14
12
16
Time [seconds]
20 1
0 ....
-200 -40
I
WV
.........
V
IV IV
'L\V
C/)
C
V
2
0
6
4
8
10
Time [seconds]
c-fl
12
mean lift
16
14
4
-current
C
....
0
2
4
6
5>
12
16
14
-
3
tip
/
-
-
-30
0
10
.
-o30H
ro
8
Time [seconds]
Angle of Attack Distribution Over Span
a)
- -*
mean current
2
0-
7.iJ-
-.
-~
0
1.5
0.5
1
Time [period] (not synchronized with forces and current)
~
*~-*-
~
R 0.70
0.50
0.25
~~
L
2
INPUT: U 0.5 [m/s], span 0.40 [in], chord 0.10 [in], roll 60 [deg], St 0.80, MaxAoa 20 [deg], runi OUTPUT: Ct 1.4, efficiency 0.13
20
c:
-
thrust
00
........ ...................
10. .... ........ .....
U
VV
I
2
0
-
I-I
0 nn
V I
6
4
0
a)
C
V
............
........
VI
V
I~
-V
VI
VII
12
8
10
Time [seconds]
thrust
.ma
I
14
16
lift
-___
lift
IMAnAMmean
*6
-10
q
4
2
0
6
12
10
8
Time [seconds]
16
14
E
2
c
C
0
6
4
2
0
12
10
8
16
14
Time [seconds]
0)
Angle of Attack Distribution Over Span
a)
a0
20
-
.-
0
0
a)
05
C
tip
-.
2
R 0.70
\*N-..
*
-
~
.
0.50
.
-' 0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.40, MaxAoa 50 [deg], run1 OUTPUT: Ct 0.2, efficiency 0.01
C
0
thrust
0
I-
2
-2
4
6
I
I
8
10
Time [seconds]
I
12
14
16
18
I
I
S20
l-ift
~
n if
2
0
0
2
4
O1..................................................
40 L
V
2
I
I
6
8
10
Time [seconds]
I
---
I
12
14
I
I
18
16
current
-.- mean
current
@
0
4
6
8
-
0
2
C~j
0
.......
10
Time [seconds]
12
14
16
18
-. 0 .5 0
.
Angle of Attack Distribution Over Span
U)
50
---
R 0.70
--
-n
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.40, MaxAoa 40 [deg], run1 OUTPUT: Ct 0.5, efficiency 0.05
-
...........
...
.....
....
.......
..
...
.-.-...
.-.------V
..-
C
4-
0~3
C:
8
6
4
2
0
-2
A\
-A
thrust
mean thrust
..... ... .
FI
N.\
1dx
2
4
20
0
-20
6
IIA
I"
10
8
Time [seconds]
I'V
12
Iv~
14
.....ifmean lift
.....................................
E
2
0
CZ
6
4
8
d~v
18
16
10
Time [seconds]
12
14
18
16
2
....
current
me
an current
............................... ................ ..................... ..... ...
.....................
0)
:-
C
0
2
6
4
4
6
8
8
10
10
Time [seconds]
12
12
14
14
16
18
C
Angle of Attack Distribution Over Span
0
tip
40
0
-
-40k
0
0.5
1.5
0.5
1
Time [period] (not synchronized with forces and current)
R 0.50
0.70
-.
0.25
-
root
2
INPUT: U 0.5 [m/s], span 0.40 [in], chord 0.10 [in], roll 40 [deg], St 0.40, MaxAoa 30 [deg], runi OUTPUT: Ct 0.7, efficiency 0.08
Vthrust
10c -III
C
+-
..... mean thrust
0
31
0
-
2
4
6
8
10
Time [seconds]
12
14
16
18
0
men
lift
0
S-200
I
I
I
I
2
4
6
8
2
I
II
II
I
10
Time [seconds]
12
14
16
18
U)
E
>
'JI
0
I
V
'
2
current
.... mean current
1
6
10
8
12
14
I
I
I
4
16
18
Time [seconds]
Angle of Attack Distribution Over Span
tip
0
-30
-
0
-
-
-
-
. -
-
*-.-'--*~*
-
-.
-
V
N
-
-
N
-- -
-
30Q
-
-
CT
1
1.5
0.5
1
Time [period] (not synchronized with forces and current)
-
R 0.70
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [in], chord 0.10 [in], roll 40 [deg], St 0.40, MaxAoa 20 [deg], runi OUTPUT: Ct 0.6, efficiency 0.08
./V\M
MAA
AP~\
Atmeanthrs
..... m e a -n
thrust
I-
I lV
C 111 V
AI
\..................... .................................... ...
..
0
W,
=3
15
10
5
)
Time [seconds]
C
0
10
lift
mean lift
0
0)
-10
Co
-20
15
10
5
0
Time [seconds]
CL
E
1.5--
current
1 ......... ... ....... ... ........... ...... ..... ................... ...... .... ....
ma current.
0.5C
C
15
10
5
0
Time [seconds]
0
Angle of Attack Distribution Over Span
CZ)
2C
/
--
C
0
-----------
-2C
-
0
-
-
..
---
I..--
1.5
1
0.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
0.25
0--
rootj
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 50 [deg], run1 OUTPUT: Ct 1.2, efficiency 0.06
C
0)
C
15
10
5
0
mean thrust
)
2
4
6
8
10
12
14
16
18
Time [seconds]
50
0
...
-50
A-
-A
me..an
......
lift
C
_-50
I
)
2
4
6
8
10
Time [seconds]
I
I
12
14
-----
16
18
Q1
E
4
-current
..
.mean current~
2
C
.. ~~~~~~ ~
0
a3
0
0
2
. ........
4
6
....
... ... 10.
. 8.
8
10
M
....
.... .....14.16.18
.12.......
12
14
curl
7
18
16
Time [seconds]
Angle of Attack Distribution Over Span
50
Ca
-
0
*
%-50
a)
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
...------
tip
R 0.70
r0.50
*0.25
root _
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 40 [deg], run1 OUTPUT: Ct 1.6, efficiency 0.10
- 20
2
1
1
1
12
-0
C
Amen
A
'
: 0
thrust
enthrust
....
C:
-C
0A
F-
0
A
2
A
AV
A
An
Time [seconds]
-C 50 )r
lift
-
0,
.. .
0
4
2
6
.
...mann lift
... ...........
...
.....
8
10
Time [seconds]
12
14
16
CL
E
4
....
2
C
mean
Scurrentcurrent
0
I
(D
0
0
2
I
4
I
I
6
8
V
10
V
12
14
16
Time [seconds]
a)
a)
Angle of Attack Distribution Over Span
v40
CZ
............
N
-
0-
-
a,
C
--
.--
-40F
)
0
- -
0.5
1
1.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
-
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 30 [deg], runi OUTPUT: Ct 1.8, efficiency 0.13
AA.
20
U)
C:
U,
10
thrust
mean thrust
I..
0
2
4
6
8
10
12
14
16
18
20
Time [seconds]
0
c200
-lift
mean lift
_,20
-J
-40
2
4
8
6
10
12
Time [seconds]
14
16
20
18
-
0
E
3
-III
current
2
.. .. . .. ..........
1
mean current
.. ......
....
U
0
2
4
6
8
CD
C)
12
10
Time [seconds]
14
16
20
18
0)
Angle of Attack Distribution Over Span
~iZi
0
---
0
a)
c,)
tip
R 0.70
-
0.50
V
-*- -
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
-
-
-30
-
-
L
/
0
/-----------
-
30
Co
-
c
a)
-a
0.25
--
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.60, MaxAoa 20 [deg], runi OUTPUT: Ct 1.3, efficiency 0.12
0
4-
C
15
10
5
-
thrust
mean thrust
U,
-.
.Ve
=3
0
2
4
6
C
0
C
8
^ VA
...... .....
A,
... .....
...... .... .........
10
Time [seconds]
K)V
....... ..... ......
12
14
A
4
.......
n
18
16
K
'
.......
lift
VA...mean
lift
.... .... ......
-1 C
-2C
0
E)
C
2
4
6
8
10
Time [seconds]
12
14
16
18
00
Icurrent
2
............
C
current
mean current
.
0
0
2
4
6
8
.
10
12
14
16
18
Time [seconds]
20
.
Angle of Attack Distribution Over Span
-
.-. - -
- -
tip
-
.
~
/
1~*-..~
-20
R 0.70
-u
0.50
10 -20
-.
C
0
I
-.
-
/.
-.
0.5
1
1.5
Time [period] (not synchronized with forces and current)
-.-..-
-.
0.25
root
j
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 50 [deg], run1 OUTPUT: Ct 2.6, efficiency 0.07
thrust
C
o 20
10
meanthrust
2
0
10
8 Time[se[nds
6
4
12
18
16
14
Time [seconds]
lift
C50
0
...mean lift
AA
50
2
0
8
6
4
10
Time [seconds]
12
18
16
14
E
6L--
-
C c.I 0I til
.. . ....... ..
2
S 0
0
4
8
6
10
Time [seconds]
12
50
-.
~.-.~~~~~ 00.70i77
0-50
'&
-
9
<
-
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
tip
-
V
C
180
16
14
Angle of Attack Distribution Over Span
a)
a)
current
mean current
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 40 [deg], run1 OUTPUT: Ct 3.3, efficiency 0.12
40
4
1
1
-
nfthrust
mean thrust
0
2
4
~5 5
0
6
8
10
Time [seconds]
12
14
16
18
lift
III
0..............................................mean
lift
C
0
2
4
6
8
10
Time [seconds]
12
14
16
18
E
I
me current
>
...
40
me- current
--...
. .V
.V
VV
2-
-4-50S 0
2
a,
4
6
8
10
Time [seconds]
12
14
16
18
Angle of Attack Distribution Over Span
0
CZ 0 *~-40
a)
"a
<
0
-ROJ0.5
-0.25
I--
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 30 [deg], run1 OUTPUT: Ct 3.3, efficiency 0.16
C:
30
20
10
0
-thrust
mean thrust
02
4
6
8
10
12
14
16
18
20
Time [seconds]
I
0
-J
I
20-
-lift
mean lift
0...........
-20
0
2
4
6
8
10
12
14
16
18
20
Time [seconds]
E
. . . ...............
...
1+
't
a)
I~J
2
current
mean current
.. ..
...
U.
0
0
2
a)
4
6
8
10
12
Time [seconds]
14
16
18
20
Angle of Attack Distribution Over Span
0)
0
-
-30 r
CD
-a
C:
0
-
~0
-
-
30
-
.-
-
-
0.5
1
1.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 40 [deg], St 0.80, MaxAoa 20 [deg], run1 OUTPUT: Ct 1.0, efficiency 0.09
c
thrust
thrust..
J\ AAA
AAA
hA
20-
mean thrust_
10
C
'ki' A
V
0
'V
IV
W
-V
W
2
8
6
4
10
12
14
18
16
Time [seconds]
W
C
I
1C
I
I---Ilift
-. mean lift
C
-ic
[seconds
0~
0
2
6
4
8
10
12
14
18
16
Time [seconds]
--- 1
E
C
2
m
1
0
2
6
4
8
10
12
14
18
16
Time [seconds]
current
vean
Angle of Attack Distribution Over Span
aZ
20
-
--
R 0.70
0
0
-20
root_
0
1.5
1
0.5
Time [period] (not synchronized with forces and current)
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 50 [deg], run1 OUTPUT: Ct 0.2, efficiency 0.02
4
2
-C
0- 0
-2
A
U)
jj~~\IAI~lIV~~A~1A
A' ' AA
IIMA
VV
''UNA-A.A.
A'A ' .' A~h .A
V. AFV
IV,
lV
VR
-Il~
IMP
F-VH
VJ 'WI
W
IW
-IIV
,V
q
0
2
4
6
I
T
'V
.....
mean thrust
A
.
I
'P
8
lt~
lfLAl
10
12
14
16
18
Time [seconds]
40
lift
mean lift
C -20
~-40
2
0
4
6
8
10
Time [seconds]
12
14
16
18
CL
E
Cu
3
2
current
... mean current
-
1
0
I
0
-
I
I
I
I
I
2
4
6
8
10
L
12
14
16
18
Time [seconds]
a)
Angle of Attack Distribution Over Span
4-
tip
50:
0
0
(D
*
-**
-.
-.
-.
-
-
-
R 0.70
0.50
-
*-
N..
*-
-.
S0.25
-50-
--
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 40 [deg], run1 OUTPUT: Ct 0.5, efficiency 0.05
8
C
_0
trs
0
-42
26+Tim
2
0
0121
[eancthdu]
6
4
8
61
14
12
10
Time [seconds]
18
16
20l
0:
-V................mean
0..............................
lift
S-20
I
0I
2
0
6
4
I
I
8
10
I---I
14
12
18
16
Time [seconds]
U)
E
Tm
mean current
'F........................................
77
.......................
crl
0.
Q
Time [seconds]
Angle of Attack Distribution Over Span
0)
z:--.--
-~40
CZ
0
'5
....-
~
tip
... .
--
R.70
--
0
-
40
.
.----
0
<
.
1.5
1
0.5
Time [period] (not synchronized with forces and current)
0.50
rootj
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 30 [deg], run1 OUTPUT: Ct 0.7, efficiency 0.08
A
W
-
10
2
VV
VV
VVI
VV-' VV
V
0
2
(A
T.
VV
thrust
mean thrust
I
4
6
8
10
12
14
16
12
14
16
Time [seconds]
0
2
4
6
8
10
0
Time [seconds]
2
0
4
6
8
10
12
Co~~2cu
C
0)
C)
ren
t
14
--
-~~~~
Time [seconds]
0
16
current0.50I
0
2.41 011416
<
Time [period] (no~~tim [sehonzds]t
ore
ncret
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.40, MaxAoa 20 [deg], run1 OUTPUT: Ct 0.6, efficiency 0.08
10
trust
12
1
24
mean thrust
50....
0)
=3C 0
.
1
.
.....
. . .
.
.
.
.
-
.
.
.
.
.
VVV
.
.
.
.
.. .
.
.
.
.
.
..
VWVV
14
12
10
8
6
4
2
-20
.
.
10-
Time [seconds]
.,0
A
0.
'.
........
A
...
A
lift
mean lift
...............
S-10
-20
I
6
I
2
0
4
8
Time [seconds]
10
14
12
E
1
E>
An>
1f
C\- 20R
> 0.5
A
-current
st b
mean current
.7
n
0T
2
S 0
a)
CZ
0
4
6
8
Time [seconds]
10
Angle of Attack Distribution Over Span
0.515150
Tim [pro](ntsnhonzdwthfre5ndcret
12
14
AANA\AA Ahthrust
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 50 [deg], run1 OUTPUT: Ct 1.3, efficiency 0.06
C:
0
1M
10
0
a)
5
-
C
10
15
Time [seconds]
50
lift
0-50
mean lift
-
W)
CL
E
0
5
10
15
Time [seconds]
-KJ
C
4
mean current
j*k*\............
2
................
a)
0
.. -....
10
5
15
Time [seconds]
a)
5C
tip
-
.
. -
. -.
. -
R
C
-
0
-
-5C
-
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
-
Angle of Attack Distribution Over Span
.
-4
n thrust
m
0.70
0.50
0.25
root j
2
.-.-..-.---.---
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 40 [deg], runi OUTPUT: Ct 1.8, efficiency 0.09
20
0.....
_
0
114.
144
2
0
4
20
fMAAAAAAAAVAA
6
8
thrust
mean thrust
16
14
18
lift
.............................................................
0,
,S-2055 -40
2
0
00
12
10
Time [seconds]
-
4
6
T
mean lift
V
[60-me
[secnds
10
8
Time [seconds]
12
18
16
14
C
E
> ~
current
Z-
.... mean current
00
S 0
2
.........
.. ......
2\
2................................
4
6
8
12
10
Time [seconds]
14
18
16
Angle of Attack Distribution Over Span
-- --- - ---.
-
- R .70
4Z
0
/-.5ti
o
a)
-a
0
-4
0
C
1.5
1
0.5
Time [period] (not synchronized with forces and current)
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 30 [deg], runi OUTPUT: Ct 1.8, efficiency 0.12
AAA
c 20
_
'A
0
0
0
2
A AA k. VOi
thrust
...
mean thrust
4
6
8
10
12
14
Time [seconds]
CD
.V.....V
A , A A , A [A
-200...... T
-401
0
.. mean lift
,
C
Kj' K,...t2
4
..
-4
1
6
8
10
14
12
Time [seconds]
E
-current
... mean current
2
C:
0
2
4
6
8
10
12
14
Time [seconds]
0)
Angle of Attack Distribution Over Span
N-
--
3(
~-
-3
0
--C
.-
-.-
--
---
tip
-~--
......-..
\7
R 0.70
---I-
~.
a)
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
0. 5
..--- --
ro o t
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.60, MaxAoa 20 [deg], run1 OUTPUT: Ct 1.1, efficiency 0.09
T
C
[meannthrust
-
0
-5
0
20
A g
A
16
14
12
10
8
Time [seconds]
6
4
2
stlift
menlift
0
C
0
j
20
II
0
00
6
4
2
16
14
12
10
8
Time [seconds]
U
E
C-
curren
mean current
2-
>
C
a)
0
0
:3
2
6
4
16
14
12
10
8
Time [seconds]
Angle of Attack Distribution Over Span
-
20
-
0
M
-
~-20
)
-
11
-
0.5
1
1.5
Time [period] (not synchronized with forces and current)
tip
R 0.70
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.80, MaxAoa 50 [deg], run1 OUTPUT: Ct 3.2, efficiency 0.07
r
0
0
H
2
4
6
8
10
12
Time [seconds]
14
16
18
C
0
0
2
4
6
8
10
12
Time [seconds]
00
-J
20
lift
....mean lift
50
0
-50
CZ
rusthr
0
14
16
6
18
20
-current
...
mean current
2
0)
I.
0
2
6
4
8
10
12
Time [seconds]
CZJ
14
16
18
20
-
-
- -
-
-
50
.
-
-
0
-R
0N
--
-
. -
. -
. -.
~.-
-
* -.
-
-50
N*
-
CM
0
0.5
1
1.5
Time [period] (not synchronized with forces and current)
tip
0.70
-
Angle of Attack Distribution Over Span
0.50
0.25
root _
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.80, MaxAoa 40 [deg], run1 OUTPUT: Ct 3.7, efficiency 0.11
1
14
1
1
1
4
40
thrust
C
w
0
mean thrust
2
0
8
6
4
12
10
Time [seconds]
14
16
20
18
-0
50
lift
I
lift
0.....................................................mean
1: -50
I
II
I
0
2
4
6
8
12
10
Time [seconds]
14
16
18
20
S 0
2
4
6
8
12
10
Time [seconds]
14
16
18
20
E
c -d
4Z
-- -c~r--e-t
@~~
Angle of Attack Distribution Over Span
2
)
CD
~o40:
CZ
0
tip
20.515150
Time~~~~~~
~[period (not. sycrnzd.ihfre.adcret
-oot
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.80, MaxAoa 30 [deg], run1 OUTPUT: Ct 3.2, efficiency 0.14
AAAAAA!AA!AAAA
me
thrust
40
0
me thrust
20
C
-C,
I
0
2
4
6
8
10
12
14
16
18
Time [seconds]
14u
C
20
0
-20
-40
CL
-lift
mean lift
)
2
4
6
00
E
8
10
Time [seconds]
12
14
16
4
18
current
....
mean curren
2
a)
0
0
2
4
6
8
10
12
14
18
16
Time [seconds]
Angle of Attack Distribution Over Span
30
30
./
.....
0Z
-
---
-~ -30
0,
0
1.5
0.5
1
Time [period] (not synchronized with forces and current)
tip
R 0.70
0.50
0.25
root
2
INPUT: U 0.5 [m/s], span 0.40 [m], chord 0.10 [m], roll 20 [deg], St 0.80, MaxAoa 20 [deg], run1 OUTPUT: Ct 0.6, efficiency 0.03
20
.20
0c2
2..
2040
2
4ea
12
10
8
6
4
thr1u1s1t11
14
16
18
14
16
mean18 t
Time [seconds]
2
S 0
6
4
ANAA
12
10 AAAstrbutAAA.n....
Time [seconds]
8
AAng
k
20 -V
Anl of Atac Ditrbuio Over Spanen
C~
...- .......
*-.
i
-2O7
-
0Z
S-20
a
C
-
-
.N
*.-
I
R0.70
0.50
0.25
root
1.5
1
Time [period] (not synchronized with forces and current)
05
2
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