Sensors 2011, 11, 11168-11187; doi:10.3390/s111211168
Design and Implementation of a Biomimetic Turtle Hydrofoil
for an Autonomous Underwater Vehicle
Davinia Font 1, Marcel Tresanchez 1, Cedric Siegentahler 2, Tomàs Pallejà 1, Mercè Teixidó 1,
Cedric Pradalier 2 and Jordi Palacin 1,*
1 Department of Computer Science and Industrial Engineering, University of Lleida, Jaume II, 69,
Lleida 25001, Spain; E-Mails: email@example.com (D.F.); firstname.lastname@example.org (M.T.);
email@example.com (T.P.); firstname.lastname@example.org (M.T.)
2 Autonomous System Lab, Tannenstrasse 3 CLA E 14, 8092 Zürich, Switzerland;
E-Mails: email@example.com (C.S.); firstname.lastname@example.org (C.P.)
* Author to whom correspondence should be addressed; E-Mail: email@example.com;
Tel.: +34-973-70-2724; Fax: +34-973-70-2702.
Received: 20 October 2011; in revised form: 16 November 2011 / Accepted: 22 November 2011 /
Published: 28 November 2011
Abstract: This paper presents the design and implementation of a turtle hydrofoil for an
Autonomous Underwater Vehicle (AUV). The final design of the AUV must have
navigation performance like a turtle, which has also been the biomimetic inspiration for the
design of the hydrofoil and propulsion system. The hydrofoil design is based on a National
Advisory Committee for Aeronautics (NACA) 0014 hydrodynamic profile. During the
design stage, four different propulsion systems were compared in terms of propulsion path,
compactness, sealing and required power. The final implementation is based on a ball-and-
socket mechanism because it is very compact and provides three degrees of freedom (DoF)
to the hydrofoil with very few restrictions on the propulsion path. The propulsion obtained
with the final implementation of the hydrofoil has been empirically evaluated in a water
channel comparing different motion strategies. The results obtained have confirmed that
the proposed turtle hydrofoil controlled with a mechanism with three DoF generates can be
used in the future implementation of the planned AUV.
Keywords: AUV; DoF; sea turtle locomotion; propulsion system
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An Autonomous Underwater Vehicle (AUV) is a robotic device that operates under water and is
controlled by an onboard computer. The main advantages of the AUV compared with manned
underwater vehicles (MUV) are its reduced size and cost because no human or life-support systems
need to be carried, so the operational time depends mainly on battery life. AUVs have many research,
commercial, and military applications. One of the earliest AUVs, called Special Purpose Underwater
Research Vehicle (SPURV) , was developed by the Applied Physics Laboratory at the University of
Washington in 1957 to study diffusion, acoustic transmission, and submarine wakes. Currently, the
inclusion of specialized sensors in the AUVs has enhanced their ability to perform different applications,
such as applied research in biology , hydrographic , geostatistics  or oceanography , as well
as to detail topological maps of the seafloor [2,6,7] in order to study deep-sea plankton , perform
mine-countermeasures , port protection applications , complementing underwater acoustic
networks [10,11], and to define the source location of chemical plumes .
The most common AUV propulsion system is based on propellers, but they are not a viable solution
for applications which require working under low flow conditions, in confined spaces, near the
surface , and in unsteady flow . The use of fins (hydrofoils) is an alternative propulsion system
used by nature, and one which is currently being considered because it allows stable motion with less
noise, good flexibility, and high maneuverability . In this work, we propose the design and
implementation of a propulsion system for an AUV that is bio-inspired in the turtle’s propulsion (see
Figure 1. (a) Oval path followed by the legs of a freshwater turtle. (b) Figure-of-eight path
followed by the hydrofoils of a sea turtle.
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1.1. Biological Background
The turtle’s anatomy  is the biomimetic inspiration for this work. The turtle’s hydrofoil, which
is also called fin or forelimb, is its principal source of propulsion. The main characteristic of the
skeleton of the turtle’s fin are that the humerus and the radius are very thick but not very long while
the phalanx are comparatively very long . These characteristics generate a streamlined hydrofoil
that is adapted to swim efficiently because it reduces the resistance of hydrofoil dynamic swirl. In
addition, the turtle’s head can also reduce forward resistance by adapting its orientation relative to the
navigation path .
The turtle’s displacement is produced due to a thrust force generated on both lateral hydrofoils
when performing a specific trajectory. Depending on the species of turtle, the trajectory of the
hydrofoils changes . Freshwater turtles’ locomotion depends on drag generating thrust by
paddling, and each leg follows an oval-shaped trajectory [Figure 1(a)]. The trajectory of the hydrofoil
of a sea turtle imitates a trajectory like a figure-of-eight [Figure 1(b)], and both drag and lift forces are
involved . In this case, the path followed by the hydrofoils is split into four different phases called
downstroke, pronation, upstroke and supination [16,19]. The downstroke and upstroke phases are the
most important, whereas pronation and supination are just phases to close the motion cycle with less
1.2. Contributions of This Work
This project is part of a larger study under development at the Autonomous System Lab (ASL),
department at Eidgenössische Technische Hochschule (ETH), Zürich, where the final target is to
develop a turtle-like AUV using hydrofoil propulsion.
To this end, this work proposes the design and implementation of the hydrofoil and the propulsion
system for an AUV taking into account that the final fin prototype must be attached in a robot of 1 m
length working that must operate in depths up to 10 m. During the evolution of the AUV in the water
the assumptions performed were a maximum fluid velocity of 1 m/s and a characteristic hydrofoil
linear dimension of 0.1 m, resulting in a constant Reynolds number of 112,359. Based on this result,
the hydrodynamic profile selected for the hydrofoil was the National Advisory Committee for
Aeronautics (NACA) 0014 because it provided the best relation between lift and drag forces for a
constant Reynolds number. Using a similar approach, this profile was used previously in  to
improve the maneuverability of an AUV.
The selected propulsion path is biomimetically inspired in the sea turtle and will follow a
figure-of-eight shape as a way to generate the maximum forward force during the whole period of the
motion. The mechanism proposed to generate this hydrofoil displacement is based on a ball-and-socket
mechanism with three degrees of freedom (DoF) that is able to replicate any propulsion path for
experimentation purposes. Several propulsion paths were tested in a water channel in order to optimize
the thrust generated. The proposed propulsion system will be included in a planned future AUV design
with turtle-like navigation performances. The external proportions of the different parts of this future
AUV will be also bioinspired in the proportions of the sea turtle.
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1.3. Related Work
The research into AUVs is progressing towards solutions in the commercial, military and research
fields. Some examples are Slocum [21,22], based on a buoyancy engine and Ictineu , that uses
propellers as a propulsion system. In  the proposal was the use of the Slocum as a thermal glider
using the heat flow between the vehicle engine and the thermal gradient of the ocean temperature in
order to propel itself. In this case the control of the pitch and roll was performed by moving an internal
mass and the control of the yaw and heading by the hydrodynamic yawing moment due to the roll.
In  the proposal was the use of an electric glider based on the use of an electromechanical
displacement actuator to change their weight. In this case the roll was set by the position of the glider’s
static center of gravity (CG) and pitch was controlled by moving its internal mass. Yaw and heading
were controlled using the rudder mounted on the vertical tail of the glider. In the case of Ictineu ,
developed by the University of Girona, the AUV prototype was developed to fulfill several aims:
moving the robot from a launch/release point and submerging, passing through a 3 × 4 meter
validation gate, locating a cross situated on the bottom of the pool and dropping a marker over it, and
locating a mid-water target.
Other AUVs, such as Finnegan , Madeleine , AQUA , and NTU turtle robot 
are examples of robots that alternatively use hydrofoils as a propulsion system to improve
maneuverability . Finnegan is a prototype developed by MIT Department of Ocean Engineering
Towing Tank, which uses four fins located symmetrically on each side of the robot to generate thrust
force. Each fin is started by a pair of actuators allowing an unlimited motion in pitch. The main target
of this research was to improve the maneuvering performance of AUVs, while providing the agility to
control six degrees of freedom. Madeleine is a prototype developed in 2005 as a result of the
cooperation between three institutions: Nekton Research, Monterey Bay Aquarium Research Institute
and Vassar College. Like Finnegan, Madeline uses four fins, but in this case, each fin is started by a
single actuator. The motivations of this project were to predict efficient fin pitching operation, and
build a platform for testing the fin’s locomotion. AQUA is the result of collaboration between McGill
and York Universities. This robot is able to swim or walk using six legs, which can be changed
depending on the robot’s function. The vehicle uses a variety of sensors to fulfill a range of real tasks
in applications that require large autonomy. The NTU turtle robot was developed by Nanyang
Technological University. This robot can swim using two fore limbs, which are started by two
actuators, while its two hind limbs are used for steering. Finally, a similar approach was proposed
in  to implement a robotic dolphin.
2. Materials and Methods
The materials and methods used to perform the implementation and validation of the proposal can
be divided into CAD design, motion and control, water channel, and instrumentation.
2.1. CAD Design
Different steps in the work were solved using distinct CAD programs. The JavaFoil platform 
was used to study the characteristics of the selected hydrodynamic profile to understand how it works
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and the effects that it generates in the fluid and on the mechanism. The most important information
extracted was the estimate of the angle of attack and the lift, drag and momentum coefficients, which
allowed the mechanical design to be optimized and the hydrodynamic forces to be calculated. The
potential flow analysis performed with this program was a linear varying vorticity distribution. Taking
the airfoil coordinates, it was calculated the local, inviscid flow velocity along the surface of the airfoil
for any desired angle of attack. First it was calculated the distribution of the velocity on the airfoil
surface which could be integrated to get the lift and the moment coefficient. Then it was calculated the
behaviour of the flow close to the airfoil surface which was used to calculate the friction drag of the
airfoil. Both steps were repeated for the given range of angle of attacks, which yields a complete polar
of the airfoil for one fixed Reynolds number. The estimate of the hydrodynamic forces was performed
applying a quasi-static analysis at three representative positions of the propulsion system along the sea
turtle path and estimating the relative speed at each time.
Working Model (Design Simulation Technologies, Inc., Canton, MI, USA) was used during the
design phase in 2D simulations to estimate the torque of the motors. Unigraphics NX 6 (Siemens PLM
NX, Plano, TX, USA) and AutoCAD 2010 (Autodesk Inc., San Rafael, CA, USA) were used during
the design stage to model the mechanical components. Ansys Workbench 11 (ANSYS, Inc.,
Canonsburg, PA, USA) was used to simulate each component of the assembly taking into account the
maximum equivalent von Mises stress and deformations in order to be sure that all parts were strong
enough to withstand the forces while operating in the water channel. Maple (Maplesoft, Waterloo, ON,
Canada) and Matlab (Math Works, Natick, MA, USA) were used for calculus, solving system
equations and to simulate the displacement of the hydrofoil from the control sequence applied to the
motors used to generate the propulsion path.
2.2. Motion and Control
In the experimental stage, the mechanical motion of the turtle hydrofoil was generated using Maxon
EC 22 50W/167129 (Maxon Motors ag., Switzerland) direct current (DC) motors whose nominal
electrical parameters are 32 V, 2.82 A, 50 W, 37.2 mNm, and 20,200 rpm, used in combination with a
planetary gearhead GP 32C 190:1. The motor feedback is provided by an optical encoder (MR
Encoder 128 CPT) with two channels of 128 counts per revolution and one reference channel.
The control of the absolute angular position of the DC motors was performed by using three EPOS
24/5 from Maxon. The velocity of the DC motors between two angular position points of the defined
trajectory was limited to 10,000 rpm. The sequence of angular positions was sequentially defined by
using custom control software written in Matlab and C++. The timing and angular sequence applied to
the motors was obtained by using a simulation tool written in Matlab that simulates the complete
motion of the hydrofoil and the propulsion system in a three-dimensional space depending on the
angular position sequence applied to the DC motors.
2.3. Water Channel
Experiments were performed at the ETH Zürich in a recirculating water channel 2.5 m long, 0.45 m
wide and 0.64 m deep with a 0.4 m water level high. During the experimental phase, the hydrofoil and
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propulsion mechanism were located at the centre of the water channel whose dimensions were big
enough to operate without colliding with the walls.
The water speed generated on the water channel during the experiments was measured at different
points using a helix based MiniWater 6 Micro Schildknecht Anemometer. This device measures water
speed from 0.5 to 20 m/s with an accuracy of ±1.0% fs and is unaffected by pressure, temperature,
density or humidity. This sensor requires a power supply from 9 to 26 V and its operating range is
from −10 to +80 °C for the electronics and from −10 to +140 °C for the probe.
3. Design and Implementation of the Turtle’s Hydrofoil
This section discusses the biomimetic design and implementation of the hydrodynamic profile of
the turtle hydrofoil.
3.1. Hydrodynamic Profile and Optimal Angle of Attack
Each hydrodynamic profile in motion in a fluid is influenced by drag D and lift L forces, and the
resulting moment M (Figure 2). Lift is defined as the sum of fluid dynamic forces perpendicular to the
fluid direction whereas drag is the force that opposes the fluid direction but appears along that
direction. All these forces are applied at the pivoting point which is located at 25% of the chord.
Equation (1) shows the formulas to compute these forces, which depend on the geometry of the
hydrodynamic profile and the characteristics of the fluid involved:
?· ??· ? · ??· ?
?· ??· ? · ??· ?
?· ??· ? · ??· ? · ?
where V is the speed of the object relative to the fluid; ρ is the density of the fluid; C is the
chord; Cl, Cd and Cm are the lift, drag and momentum coefficients and S is the surface of the
hydrofoil. This surface was computed by multiplying the chord b by the length of the hydrofoil
because the theory of thin profiles can be applied.
Figure 2. Hydrodynamic forces applied at the pivoting point of a NACA 0014
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The hydrodynamic profile selected for the turtle hydrofoil was the NACA 0014 (Figure 2) because,
in simulations with JavaFoil, it provided the best relation between lift and drag forces for a constant
Reynolds number (Re). This can be computed with:
where ρwater is the density of the fluid; V is the fluid velocity; L is characteristic linear dimension of the
profile and μwater is the dynamic viscosity of the fluid.
The most important parameter which defines the orientation of the turtle hydrofoil is the angle of
attack (α), which is optimal when the lift divided by the drag coefficient is maximum (L/D). In this
particular case with a constant speed of the robot of 1 m/s, and 0.1 m as the characteristic linear
dimension of the hydrodynamic profile, a constant Reynolds number of 112,359, the optimal angle of
attack for the turtle hydrofoil estimated with JavaFoil was 8°. This value will be later verified and
optimized experimentally in the water channel.
The values of the hydrodynamic forces applied on the static mechanism analysis, deformational
analysis and the maximum equivalent stress analysis were computed along the path followed by the
sea turtle hydrofoil which has an eight shape. Figure 3 depicts a representation of the trajectory of the
turtle’s hydrofoil with three critical positions labelled.
Figure 3. Body diagram of the hydrodynamic profile located at the most unfavorable
situations through the eight path (M moment, L lift, D drag, R resultant).
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In all cases the profile was titled following the description of the angle of attack. These situations
are the most unfavourable since is when the speed of the profile relative to the water is higher and the
forces were estimated on the tip of the fin taking into account the hydrodynamic Equations (1). The lift
force, drag force and momentum for case 1 are 7.09 N, 0.17 N and −9.3 mNm respectively. For case 2
are 6.88 N, 0.16 N and −9.0 mNm and, for case 3 they are 22.45 N, 0.53 N and −29.3 mNm. Although
at high speeds the lift and drag ratios tend to be higher, for this project the Reynolds number was fixed
because of the operational specifications planned for the AUV robot.
3.2. CAD Design and Implementation
The design of the turtle hydrofoil was defined by the NACA 0014 profile using a characteristic
linear dimension of 100 mm and a profile length of 307 mm, so the aspect ratio of the foil was 3.07.
The functional prototype of the hydrofoil will be implemented using a rapid prototype technique in
plastic FullCure 720 (tensile strength of 60.3 MPa, tensile modulus equal to 2.87 MPa, shore of 83 and
density of 1.094/1.189) by splitting the fin into two parts that will match to become a unique element.
The inner part of the hydrofoil was designed sparse to reduce its weight and the Ansys Workbench 11
program was used to verify that the hydrofoil has minimum weight and enough mechanical resistance
to operate without a break down in the assembly. The best approach that satisfies both objectives was
based on longitudinal strips located at distances of 58, 99.7, 141.4, 183.1, 224.8, 266.5 mm from the
button of the fin (part used to attach the fin with the mechanism) and transversal strips located at 9.8,
37.1, 59.3, 71.9 mm from the right part of the fin. The width of the strips was 2.8 mm in both cases.
Figure 4(a) shows the results of a von Mises stress simulation of the hydrofoil where the maximum
value was 55 MPa, which is lower than the resistance of the material used. Figure 4(b) shows the rapid
prototyping implementation of the design. These results confirm that the design will support all the
mechanical effort performed without a break down in the assembly.
Figure 4. (a) Von Mises stress simulation of the internal structure of the turtle hydrofoil.
(b) Rapid prototype implementation of the turtle hydrofoil.
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4. Hydrofoil Propulsion Mechanism
In this work, four alternative hydrofoil propulsion mechanisms have been considered: four bar
mechanism, differential mechanism, ball-and-socket mechanism, and pulley mechanism. These
mechanisms have been analyzed and compared in order to get the best system for the proposed AUV
design. The selected propulsion mechanism has been designed and implemented to perform
experimental validations in a water channel of the complete hydrofoil propulsion mechanism.
4.1. Four Bar Mechanism
The 4-bar mechanism [Figure 5(a)] has two DoF and consists of four members represented by four
bars controlled by two linked motors [M1 & M2: Figure 5(a)] located inside the fixed parts. The
hydrofoil is attached to an additional motor placed in the middle point of the b bar to change the angle
of attack [M3: Figure 5(a)]. The most important characteristic is that the middle point of the b bar
describes a figure-of-eight trajectory (like the sea turtle). The amplitude of the path depends on the
relations between the lengths of the members [Figure 5(a)]. The mechanism is characterized by four
singular positions defined when the angle for the input and output bar is 45° and −45° with respect to
the d bar. In these situations, the mechanism reaches a limit that makes the final motion uncertain.
Therefore, in this case, the control of the angular orientation of the two linked motors must work
properly to avoid a breakdown in the mechanism.
4.2. Ball-and-Socket Mechanism
The ball-and-socket mechanism [Figure 5(b)] has three DoF provided by three motors located
strategically in the mechanism and can apply any propulsion path to the turtle hydrofoil. In this case,
the horizontal motion is generated by controlling motor M1, motor M2 controls the vertical motion,
and M3 is used to control the hydrofoil angle of attack. This design is very compact and can easily be
integrated into the structure of an AUV. In this case, the control of the three motors is simple but the
generation of the sequence of angular orientations required to generate a figure-of-eight shape trajectory
is complex and may require verification with a simulation tool.
4.3. Differential Mechanism
The differential mechanism [Figure 5(c)] is a compact mechanism with two DoF currently used for
the leg movement in walking robots. In this case, two motors [M1 & M2: Figure 5(c)] feed two bevel
gears, located on the horizontal axis, transmitting the motion to a third gear located on a vertical axis.
This third gear is able to generate rotation and vertical motions in the hydrofoil. In addition, a third
motor [M3: Figure 5(c)] is used to incorporate the third degree of freedom, which corresponds to the
horizontal hydrofoil motion. The main drawbacks of this proposal are the large space required inside
the AUV and the difficulty of sealing the mechanism properly. In this case, the control of the two
linked motors and the generation of the sequence of angular orientation required to control the motors
is very simple.
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4.4. Translational Pulley Mechanism
The pulley mechanism [Figure 5(d)] consists of two pulley transmissions linked by a guide to
transmit the axial motion between the two. Each pulley transmission generates motion through a single
motor located in a pulley. The combination of two motors [M1 & M2: Figure 5(d)] generates the
vertical and horizontal amplitude of the final propulsion path. The hydrofoil is attached to a third
motor [M3: Figure 5(d)] to change the angle of attack. The translational movements generated on the
transmissions are converted to rotational using a free joint, which is located on the same axis where the
hydrofoil is attached. In this case, the main drawback is the flexibility of the ropes that will increase
with wear, generating uncertainty in the position of the hydrofoil thus making the mechanical device
prone to break downs.
Figure 5. Alternatives considered for the hydrofoil propulsion mechanism: (a) 4-bar
mechanism. (b) Ball-and-socket mechanism. (c) Differential mechanism. (d) Translational
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4.5. Selected Hydrofoil Propulsion Mechanism
The proposed propulsion mechanisms were compared by simulations using Working Model,
Unigraphics NX6, Ansys Workbench and Matlab, considering the relative size and compactness of the
different mechanisms, the maximum vertical and horizontal amplitude of the propulsion path achieved,
and the maximum torque requirements of the DC motors during the most unfavorable situations along
the propulsion path. Table 1 gathers the results of the simulations performed to quantify the selection
criteria. Given these requirements, the mechanism selected to propel the hydrofoil was the ball-and-
socket mechanism mainly because it is the most compact with a size of 0.01 m3 and places few
restrictions on the movement of the hydrofoil as it does not have any limitations in the vertical or
horizontal amplitude path either. In addition, it was also taken into account the facility of the sealing of
the propulsion mechanism inside a real AUV which also agrees with this selection.
Table 1. Decision matrix.
Ball and socket
0.012 m3 Size
0.32 m No limit No limit 0.346 m
0.2 m No limit No limit 0.346 m
4.6. Design and Implementation of the Propulsion Mechanism
Figure 6 shows the final design of the components involved in the ball-and-socket mechanism with
the assembly optimized to work together without collisions. Each component was modeled using
Unigraphics NX6 software and the simulations were performed with Ansys Workbench 11. The mesh
generated on each component of the assembly was based on Tetra elements using the maximal nodes
admitted by the simulator. It was chosen the Tetra elements because it was the ones that took full
advantage of object-oriented unstructured meshing technology. The simulation used the CAD
geometry components filling the volume with tetrahedral elements using the Octree approach. Once
the mesh was created, a static analysis was carried out applying the forces previously estimated at its
location. Two additional analyses were performed; a deformational and a maximal equivalent stress
analysis. During the analysis different boundary conditions were considered. Some components were
studied as a solid rigid (a unique element) because there was not relative motion between them. In
addition, in each component analysis a surface was fixed in order to simulate the adequate motion of
each part of the assembly in its environment and a pressure force was applied on the surfaces in order
to simulate the pressure exerted by the water on the parts. This pressure was calculated taking into
account the depth that the robot can reach with:
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P = ρ·L·g (3)
where ρ is the density of the fluid (water = 1,000 Kg/m3), L the depth estimate of the robot (in m), and
g the constant of gravity (9.81 m/s2).
Figure 6. Representation of the hydrofoil and propulsion mechanism. The three motors
used are also labeled.
Figure 7. Images of the static mechanical analysis of the hydrofoil propulsion mechanism.
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Figure 8. (a) Von Mises stress analysis. (b) Deformational analysis.
Figures 7 and 8 show the different simulations carried out during the design stage of the ball-and-
socket mechanism: Figure 7 shows the static mechanical analysis, Figure 8(a) shows the von Mises
stress analysis, and Figure 8(b) the deformational analysis.
Some considerations were made to compute the static mechanical analysis. A rigid solid was
created when there was no relative motion between the parts involved, so a simulation study was
carried out applying the forces as a unique element. For this, the mechanism was split into three
assemblies [Figure 7(a–c)] and the turtle hydrofoil. The first assembly to be studied must be the turtle
hydrofoil since is where the most unfavorable hydrodynamic forces were applied and had effects on
the other components of the mechanism. Another assumption made was that the hydrodynamic forces
were applied to the tip of the hydrofoil.
To ensure that each component will be strong enough to withstand the forces, the maximum von
Mises stress results of the simulations have to be higher than the yield stress of the material used to
manufacture the part. In addition, the deformations have to be within a limited range to verify that the
part will work properly. Figure 8 shows the results of both analyses for one of the assemblies of the
Figure 9. Hydrofoil and mechanical propulsion system.
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Finally, Figure 9 shows the practical implementation of the complete hydrofoil and propulsion
system. Each motor gives a direct vertical, horizontal and rotational movement to the hydrofoil. The
design of the whole mechanism depends on the maximum amplitude of the motion, which was limited
in this case to 60° in both directions.
In this phase, three experiments were carried out in a water channel to validate the complete design.
The propulsion system was fixed in the water channel by a dedicated structure. The main information
extracted from the tests was the instantaneous current of each motor during the propulsion path and the
average water speed at different points of the water channel. Figure 10(a) shows the reference axis
system used in this work and Figure 10(b), an image obtained during the tests.
Figure 10. (a) Water channel with the reference axis system. (b) Water channel facility
during an experiment.
5.1. Experimental Validation of the Optimal Angle of Attack
The first experiment was focused on validating the optimal angle of attack obtained in the design
stage. The methodology used in this experiment consisted of applying a predefined fixed propulsion
path to the hydrofoil in the water channel and modifying the angle of attack. Each case analyzed was
repeated five times and the results were averaged.
The path used was a linear motion where one motor (M1: Figure 6) was activated to generate
the amplitude and another motor (M3: Figure 6) was used to define the angle of attack [(a) in Table 2].
Figure 11 depicts the total average maximum current for different angles of attack measured during the
linear motion. On one hand, the results show that the total current increases as the angle of attack
decreases (increasing the resistance of the water). On the other hand, the maximum water speed in the
channel was obtained with an angle of attack of 12°.
The experimental optimal value of the angle of attack was very similar to the value obtained with
JavaFoil. The small discrepancy is because the assumptions made during the numerical calculations
such as the AUV speed were constant to 1 m/s. In addition, there were some limitations to execute
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JavaFoil because it does not work with accurate results when working with model laminar separation
bubbles and flow separation. Finally, note that this experiment was performed in a water channel
where the hydrofoil mechanism was fixed (very far from real AUV operation), so additional empirical
validation procedures must be prepared for the final implementation in the AUV.
Figure 11. Average maximum current relative to the angle of attack.
5.2. Experimental Validation of the Optimal Hydrofoil Path
In this experiment, several alternative propulsion paths were compared in order to optimize the
AUV’s displacement. Table 2 summarizes the propulsion paths applied to the hydrofoil, the angular
position of the motors, the average current of a complete motion, and the maximum current measured.
The cases analyzed are (a) linear path with a frequency of 0.36 Hz, (b) diagonal path with a constant
angle of attack and a frequency of 0.35 Hz, (c) diagonal path with a variable angle of attack at 0.34 Hz,
(d) symmetric figure-of-eight path with a frequency of 0.38 Hz, and (e) anti-symmetric figure-of-eight
path with a frequency of 0.38 Hz.
The trajectory in case (a) is a linear motion where an up and down movement is generated while the
angle of attack is constant on one way but is changed using the opposite value on the transition
between the up and down motion. The absolute value of the angle of attack used was 12°, which was
extracted from the experimental tests. The second and third cases reproduce a diagonal motion where
the difference was that in case (b) a constant value of the angle of attack of 12° was used whereas in
case (c) the angle of attack varied from −94° during the downstroke phase to +56° during the upstroke
phase. The value of the angle of attack followed the specification of a sinus wave, which was
determined from an analysis of the hydrodynamic forces during a motion cycle in order to optimize the
AUV’s displacement. The trajectory of case (d) is a symmetric figure-of-eight path whereas in case (e)
an anti-symmetric figure-of-eight path was used. In these two cases, the angle of attack was 12° during
the downstroke and upstroke phases but during the pronation and supination phases, this value changed
transiently to adopt the correct values on the up and down movement.
0 20 4060 80
Angle of attack (º)
Average maximal current (mA)