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					Computational Fluid Dynamics
Investigation of Two Surfboard
      Fin Configurations.




       By: Anthony Livanos (10408690)


        Supervisor: Dr Philippa O‟Neil

            Faculty of Engineering
        University of Western Australia
For the fin fanatics of Swaylocks.




                                     2
          Contents Page



 Introduction …………………………………………………………………4

 Hydrodynamic Forces ……………………………………….7

 CFD Analysis Observations .……………………….12

 Conclusion & Review…….…………………………………….18

 Appendix …………………………………………………………………………20

 Bibliography ………………………………………………………………..22




                                            3
                        Introduction
As the sport of surfing is continually evolving, surf riding equipment is
steadily improving. The surfing industry has lead the surfboard to
develop from its origins of tree trunks to highly sophisticated
composite structures.

The professional competitive nature of surfing pushes the performance
limits higher and higher. There are many variables involved with
surfboards and fins in terms of performance such as wave size, board
size and the surfer‟s ability. All components are inter related and must
be optimised as a group, to satisfy the conditions they are being used
in and to reach the desired performance.

All the thousands of variables and the definitions of performance make
the analysis and comparison of surfboards and fin configurations very
difficult. For the purpose of this report, only two different fin
configurations have been investigated, the Thruster setup (three fins)
and the Single fin setup. The two side fins of the Thruster setup were
FCS G5 fins, whilst the rear was an FCS G3000 fin. The fin used for the
single fin setup was the JB2 single fin. Both configurations have been
put under the same flow conditions.

There is limited experimental evidence available for the relative speeds
involved in surfing. For the purpose of this report, a speed of 6 m/s of
water relative to the fin has been used in the analysis. Surfboards
typically encounter large angles of attack and significant change in
directions. This report only simulates straight line flow as the dynamic
simulation of turning and manoeuvres is beyond the scope of this
report. To simulate the presence of the surfboard, the fins have been
modelled in a rectangular domain, attached to a wall surface,
representing the bottom of the surfboard.

Since the fin chords are in the order of 0.1m, consequently chord
calculated Reynold‟s numbers will be in the order of 105 . In this range,
separation and boundary layer effects are known to be significant. It is
expected the flow will be turbulent with vortices present.

The ultimate goal of this report is to qualitatively investigate the
hydrodynamic forces, and fluid behaviour surrounding two different
surfboard fin configurations.


                                                                            4
The fin properties, configurations and dimensions used in the analysis
are as follows:




                   Figure 1. Thruster and Single fin configurations




    Figure 2. Front view of Thruster setup                   Figure 3. Top view of Thruster
                depicting Cant.                                 setup depicting Toe – In.

                                                                                     5
                 Figure 4. Thruster setup analysis domain. Front and Side view.




                 Figure 5. Single fin setup analysis domain. Front and Side view

     Fin:             JB2 Single Fin               FCS G5                   FCS G3000

  Base Chord
                             155                     110                           110
    (mm):
 Surface Area
                           47, 600                 20, 100                     18, 730
   (mm ²):

Volume (mm ³):            235, 380                 53, 800                     51, 180

 Aspect Ratio:               1.88                     1.6                          1.49

      Base
Thickness/Chord
  Length ratio               9.03                    5.45                          6.65
      (%):


                         Table 1. Summary of Surfboard fin properties




                                                                                          6
             Hydrodynamic Forces
Performance in regards to surfboard fins is not easy to define.
Performance is based on a wave-to-wave and surfer-to-surfer basis.
Some fins work well in bigger waves, and some fin properties are good
for beginners rather than professionals. Fundamentally, the purpose of
surfboard fins is to provide greater control over the surfboard.

A greater understanding of the hydrodynamic forces acting on
surfboard fins would provide an insight into how to maximise certain
properties of the fins in order to achieve greater performance levels.
Since fins are foiled bodies, with a large range of angle of attack, they
will experience a lifting force acting perpendicularly to the flow, and a
drag force acting in parallel with the flow. For visualisation purposes,
since the fin is oriented in the vertical plane, the forces will act in
primarily the horizontal planes.

Drag forces:

The total drag force acting on a body
immersed in a fluid is comprised of three
different types of drag: Form (or pressure),
Skin Friction (or viscous), and Induced.

Form drag is a result of the difference
between the high pressure regions at the
leading edge, and the low pressure regions
associated with the trailing edge(s). The
differences in pressures can be reduced
through efficient streamlining of the
immersed fin. Studies have shown
streamlining the leading edge reduces drag
by 45%, whilst streamlining the trailing
edge reduces drag by up to 85%.
Rounded leading edges prevent early flow
separation, as pre-mature flow separation
will lead to the fin stalling and reducing lift
dramatically.

                                                  Figure 6. Lift and Drag forces.



                                                                               7
Skin friction drag is caused by the physical contact between fin and
water molecules. This form of friction is similar to the friction
between two bodies. Since the friction is between a solid and a fluid
the properties of both the solid and fluid will determine the magnitude
of the friction. The surface roughness is a factor affecting friction in
terms of the solid fin, and for the fluid it is the fluid‟s viscosity
dictating the friction. Since the viscosity cannot be changed, changes
to the fin surface such as a matte finish or a gloss finish will alter
performance.

Along the surface of the fin, a low energy flow region exists known as
the boundary layer. The magnitude of skin friction also depends on the
state of the boundary layer. Boundary layer and fluid interactions are
usually beneficial since the friction between boundary layer and fluid is
less than fluid and solid. One method of inducing and retaining
boundary layers would be to roughen the surface of the fin, initiating
turbulent flow, which is less prone to flow separation, consequently
forming a boundary layer.

Induced drag is mainly concerned with the formation of vortices at the
fin tips. Vortices are spiralling bodies formed by the „leaking‟ of
pressures at the tip of the fin. A vortice is formed when the high
pressure underneath the fin curls around the wing tip to the top side of
low pressure. Consequently, the overall pressure above the fin is
reduced, and this dramatically reduces the lift generated.
Vortices can be reduced in a few ways. Shortening the chord length
will reduce vortices as it provides less opportunity for the formation of
vortices. Fins of higher aspect ratios are more efficient because the
load bearing distribution is concentrated further away from the tips.
Since less load is distributed to the tips vortices are reduced. The
introduction of a physical barrier, such as tips on airplane wings also
prevents and interrupts the formation of vortices.

In summation, total drag = parasitic drag (form and skin) + induced.

Ideally total drag must be minimised to increase performance, but
there are other factors to consider. Certain drags contribute directly to
loss of speed, whilst others contribute to fin „stability‟ and „suck‟, which
are responsible for control and responsiveness of the board on the
wave surface. Which drags are positive or negative is another debate
in itself, and subject to opinion without the presence of proper
evidence.




                                                                           8
A qualitative comparison of drag occurring in the two fin configurations
can be done using the information given in Table 1. Since the Thruster
setup consists of two G5 fins and one G3000, the total surface area
and volume is 58930 mm ² and 158, 780 mm ³ respectively. For the
Single fin setup, we have a total surface area of 47, 600 mm ² and
volume of 235, 380 mm ³.

From this data and assuming that all fins have the same surface
roughness, since the Thruster setup has more wetted surface area, it
would possess more Skin friction drag than the single fin setup.

From the data it can be observed that the Single fin occupies a larger
volume compared the Thruster setup. Theoretically form drag relates
to volume but there are other factors involved. The single fin is larger,
but has no Cant or Toe-In to add to drag forces. In the simple straight
line flow analysis, the Thruster setup would have more form drag due
to the side fins being Canted at 4and having a 3.5Toe-In.

In terms of Induced drag, the strength and number of vortices must
be considered. The Thruster setup will generate three vortices as
compared to the single vortice created by the single fin. It can be
assumed that the total induced drag would be more for the Thruster
setup. Further investigation with CFD will clarify this issue later in this
paper.

Lift forces:
There are quite a few explanations of lift published in resources and
available on the internet. Unfortunately, theories are mis-applied and
lead to incorrect theories being widely accepted. Theories of lift have
been the source of many arguments. The primary reason for this is
people choose to believe either a Newtonian point of view, or a
Bernoullian point of view.

Incorrectly applying Bernoulli‟s theory leads us to the theory which is
known as the "equal transit time" or "longer path" theory. This theory
states that foiled bodies are designed with the upper surface longer
than the lower surface in order to generate higher velocities on the
upper surface because the molecules of gas on the upper surface have
to reach the trailing edge at the same time as the molecules on the
lower surface. From Bernoulli, pressure of a fluid is inversely
proportional to velocity. The incorrect theory then invokes Bernoulli's
equation to explain lower pressure on the upper surface and higher
pressure on the lower surface resulting in a lift force.


                                                                              9
The correct theory of lift is based on „flow turning‟ and is actually a
combination of both Bernoullian and Newtonian views. When a body is
immersed in a moving fluid, the fluid flows around it, with varying
velocities depending on shape, size and drag factors. This variation in
flow velocities causes variations in pressures. Integrating the
pressures over the entire body, not just the top side, equates to the
total hydrodynamic force acting on the body. This hydrodynamic force
is comprised of lift, perpendicular to the flow direction, and drag,
parallel to the flow direction. This makes the basis for the Bernoullian
part of lift.

The Newtonian part is based around Newton‟s third law of action and
reaction. Since this hydrodynamic force is acting on the solid body, the
solid body must also be acting on the fluid with the same force. This
force acts to „turn‟ or deflect the fluid. So in essence, both Bernoulli
and Newton are correct.

Factors affecting the generation of lift are grouped into two categories;
Object and Fluid.

In relation to the object, shape and size will affect the generation of
lift. In terms of a fin, this relates to the fin‟s foil, thickness, and
camber. Over all plan form shape will also affect the lift generated.
Plan form of fins can vary in terms of rake and depth. The discussion
of how these factors affect the fin are not relevant as the testing is
only being done on two sets of fins, with shape and size being
constant.
Hydrodynamic forces are definitely proportional to surface area of the
fins.

The Coanda effect is definitely an important consideration in regards to
analysis of forces on foiled bodies. The Coanda effect states that a
moving stream of fluid in contact with a curved surface will tend to
follow the curvature of the surface rather than continue to travel in a
straight line. Relating back to the theory of lift, this effect would
essentially aid in „turning‟ the air, thus creating more lift. Certain foils
would lead to a more pronounced Coanda effect and consequently
more lift.




             Figure 7. Cross section of a foil, depicting Coanda Effect

                                                                          10
With regards to the fluid factors, properties such as viscosity, mass of
fluid and velocity of the fluid relative to the immersed body all
contribute to the generation of lift. The velocity of the fluid is constant
for both trials, but it is known that higher velocities correlate to larger
hydrodynamic forces. Fluid viscosity and velocity in terms of surfing
are all dictated by the waves and oceans. Since these are constants,
other factors must be optimised to achieve greater lift performance.

The Thruster setup derives its name due to the fact it provides a
forward thrust. This thrust comes from the two side fins. The overall
lift force on the fin is biased slightly forward on an asymmetrical fin to
begin with due to the foil. Increasing the Toe-In angle increases
forward thrust to an extent, until the fin reaches a stall angle. At this
point flow separates from the fin and reduces the lift dramatically.

                                             Since the Single fin setup is only
                                             one fin, with no Cant or Toe-In, it
                                             will be producing less lift as
                                             opposed to the Thruster setup.
                                             The Thruster setup will be
                                             providing more lift, but also has
                                             increased drag, consequently
                                             reducing the lift.




  Figure 8. Vector forces of the side fins
      providing the forward thrust.




                                                                              11
                   CFD Analysis Observations
          Computational Fluid Dynamics (CFD) is the of computers to help
          analyse and visualise problems in fluid dynamics. CFD can be used in
          many applications. For the purpose of this report, CFD will provide
          information to help visualise the fluid dynamics involved with two
          different fin configurations.

          A wide range of information can be extracted using CFD, in both
          numerical and graphical data. Caution has to be exercised in order to
          not make first impression assumptions when considering images and
          data because they can be mis-leading. The results of CFD analysis of
          both the Thruster and Single fin configurations are depicted below.

          Form Drag:
          The first set of images is useful to investigate the form drag present in
          both fin configurations. Extreme form drag would be evident with a
          very high pressure at the leading edge of the object, and a very low
          pressure at the trailing edge. From these images it can be seen that a
          concentrated high pressure exists before the single fin.




Figure 9. Single fin plane cut depicting pressures.   Figure 10. Thruster plane cut depicting pressures.


                                                                                          12
      The Thruster setup also has high pressure build up at the leading edge
      of all fins, but it is somewhat larger. The inherit angle of attack of the
      side fins due to their Toe-In could be the contributing factor. Both sets
      of fins do not display obvious low pressures behind the fins. This is
      most likely a result of the fins having an efficient trailing foil, reducing
      the low pressure behind the fin.

      Since the Single fin has a lower average pressure at the leading edge,
      and with both side fins contributing heavily to form dram on the
      Thruster setup, it can be confirmed that the Single fin has less form
      drag.

      Skin Friction and the Boundary Layer:
      Certain Skin friction configurations would lead to types of Boundary
      layers being formed. A rougher skin would induce turbulent flow, and
      consequently reduce the chance of flow separation on the fin. Certain
      Boundary layer configurations have been used to achieve reduced drag
      in similar sports, such as skins on the hulls of yachts racing in the
      America‟s Cup. CFD is able to provide us with physical properties of
      the boundary layer such as fluid velocity within the boundary layer,
      and size of the boundary layer itself.

      Figures 11 & 12 provide us with valuable information in regards to the
      shapes and sizes of the boundary layers of the different fins.




 Figure 11. Single fin plane cut,                  Figure 12. Thruster plane cut, depicting
depicting velocity boundary layer                      velocity boundary layer profile
             profile

                                                                                     13
From Figure 11 it can be seen that the boundary layer exists mainly
the concave formed by the rear half of the fin foil. The Thruster side
fins have a different shape, with the boundary layer being formed
around the outside and inside edges, all over the fin.

CFD would be a useful tool in analysis of boundary layers, because
with the aid of probe lines, the exact profile of the boundary layer can
be seen. This would be beneficial in running one test, then slightly
changing a variable, for example surface roughness, and then running
the same test, and viewing the subsequent profiles.

Probe lines have been placed on the surface of the Single fin, and the
side and centre fins of the Thruster setup. The probe lines extend out
from the fin‟s surface about 10 – 12mm, and the velocity profiles are
depicted in the graphs below.

Graph 1 is a plot of three line probes in the Thruster fin setup. One
exists on the centre fin (dark blue), another on the curved foil of a side
fin (light blue) and the third on the flat side of a side fin (green).
Graph 2 indicates the line probes on the Single fin.


                                        Graph of Probe Line on Centre and Side fin of Thruster Setup

                  7




                  6




                  5
 Velocity (m/s)




                  4
                                                                                                           Centre BL
                                                                                                           Curved Foil Side BL
                                                                                                           Flat Foil Side BL
                  3




                  2




                  1




                  0
                      0   1   2     3       4    5       6     7     8        9   10   11   12   13   14
                                                     Probe Line Length (mm)




                                  Graph 1. Boundary Layer Investigation of Thruster Setup



                                                                                                                           14
                                       Graph of Line probe in Single Fin Boundary Layer

                      7



                      6



                      5
     Velocity (m/s)




                      4



                      3



                      2



                      1



                      0
                          0   1   2   3    4     5       6     7     8        9   10   11   12   13   14
                                                     Probe Line Length (mm)




                              Graph 2. Boundary Layer Investigation of Single Fin Setup

From the graphs it can be seen that the boundary layer profiles are of
similar shape. Boundary layers are zones of flow close to the surface of
bodies where the velocity drops dramatically. The boundary layers
associated with the Thruster setup can be seen to drop dramatically
between 0 and 1mm from the surface of the fins. From Graph 2, the
boundary layer of the Single fin drops dramatically between 0 and 0.5
mm. This data indicates that the boundary layer associated with the
Single fin is only half as thick as the boundary layer of the Thruster
fins.

An interesting result can be seen in the differences between boundary
layer profiles on either side of the side fin in the Thruster setup. It can
be seen that both have a boundary layer thickness of around 1mm,
but the gradient of the lines after this point is different. The gradient of
the flat side of the fin is a lot less, indicating that the velocity of the
flow increases a lot slower as you move away from the fin from the flat
side. The curved foil side has a higher gradient, and reaches a
maximum quicker. This data confirms Bernoulli‟s principle in relation to
speed differences observed over asymmetrically foiled bodies.




                                                                                                           15
Induced Drag (Vortices):

A major part of the control and board stability in relation to fins has to
do with the formation, location and behaviour of trailing vortices.
Through the mapping of particle flow trajectories in CFD we are able to
visualise and gather data on the properties of the vortices formed.
Similar experiments can be carried out in real life, with wind tunnels
and smoke trails.

From suggested theories and knowledge, we expect the formation of
vortices to be located mainly around the tip of the fins. In Figure 13,
we can see the formation of a tip vortice. Since the fin is symmetrically
foiled, two vortices are seen at the tip of the fin, as shown in Figure
14.




   Figure 13. Side view of Single fin flow                Figure 14. Rear view of
 trajectories. Tip vortice highlighted in red.             Single fin tip. Arrows
                                                         indicate vortice rotation.


It is known that the strongest vortices are shed at the tips, but are not
the only place vortices can exist. Figure 15 shows a rather surprising
result. Figure 15 depicts the velocity isosurfaces related to the
Thruster setup. Vortices are shown as the long spikes protruding from
the rear of the fin. The surprising result comes from the fact there is
two major vortices forming on the two side fins, one near the top, and
one near the base of the fins. The centre fin also possesses a vortice,
but it is located at the base, rather than the tip. The centre fin doesn‟t
have the same amount or sized vortices compared to the side fins.




                                                                           16
       Figure 15. Velocity                    Figure 16. Rear view of Thruster
    isosurfaces depicting the                  fins. Flow trajectories map the
  formation of trailing vortices.                rotation of trailing vortices.


From rough measurements of the flow trajectories, it can be seen the
diameter of the tip vortice is around 11 mm for the Single fin, and 40
mm for the side fins of the Thruster setup. The size of the vortice is
proportional to its strength, if measured in the same conditions. Higher
flow rates would pertain to smaller diameters in vortices.

The foil of the fin and its plan form shape, especially at the tip, will
affect the location and strength of vortices. Drag relates proportionally
to the percentage of the fin affected by vortices. Larger fins with
smaller vortices located closer to the tips would have less induced
drag, as opposed to smaller fins with more vortices. Consequently the
Single fin would have less induced drag. Since the Thruster setup
possess stronger and more vortices, it offers more control and hold on
the wave face.

From the above results of CFD, it can be confirmed that the Thruster
setup does possess a higher overall drag force than the Single fin
setup, in a straight line simulation. Whilst this is the case, other
factors complicate the investigation such as lift and angles of attack
during high speed manoeuvres. The real world evidence suggests
there is more to the story since most professionals use a variation of
the Thruster setup during competition. To improve this investigation,
a more quantitative analysis can be done using complex mathematics
and more accurate CFD.



                                                                             17
             Conclusion & Review

Historically, a major part of the development of surfboards and fins
involve the shapers and the feedback received from professional
surfers. A large influence on the design relates to aesthetic
considerations and perceived market expectations. The trial and error
method has yielded impressive results in terms of performance, yet
the introduction of technology and CFD analysis is beginning to be
more widely accepted. Beyond the argument of reality against virtual
simulation, the surfing industry is starting to realise CFD as yet
another tool to investigate and refine the performance variables of surf
craft.

Due to the number of variables involved with fin performance, CFD
becomes extremely useful. The ability to slightly change one variable,
such as foil, and to then run the exact same flow simulation under the
exact same conditions yields more efficient and accurate results,
allowing the user to properly investigate relations between variables.
Combining CFD, and real life experimentation on waves would be an
unstoppable combination on the path to advancing performance in
surfboards and their fins.

This investigation has helped to visualise flow theories and confirm
fluid behaviour surrounding two different surfboard fin configurations.
In my opinion, this method can be improved in a variety ways. Firstly
the modelling method I used was the cross sectional profile and loft
method. More accurate models can be made incorporating NACA
formulas to define the foils entirely. In terms of the CFD software
itself, perhaps using more scenario specific software would be more
appropriate. Using more powerful computers to calculate the
simulation to a higher resolution would also aid in the accuracy of
results. A paper report provides limited information. To fully
understand and visualise the models need to be viewed in 3D and
animations.

For this purpose, I have placed a variety of animations and extra
images on the internet. They are located at the following address:

http://www.iinet.net.au/~livanos/CFD_report/index.html


                                                                      18
My recommendations for future work would revolve around the
dynamic simulation of the surfboard on a water surface, eventually
simulation of a wave. Being able to model real life manoeuvres and not
just straight line flows would be incredibly useful. To model the wave
alone is a massive challenge. On top of this to model the interaction of
a surfboard and its fins, whilst measuring values and calculating flows
is a very difficult task. Similar work has been done with ships and
dynamic simulations of wave impacts and forces, so it is not
completely a pipe dream to envisage dynamic simulation of a
surfboard and wave.




                                                                      19
                          Appendix

Airfoil: An airfoil or aerofoil is a part or surface, such as a wing,
propeller blade, or rudder, whose shape influences control, direction,
thrust, lift, or propulsion.

Angle of attack: The angle between an airfoil or wing and the
direction of the fluid relative to it.

Aspect Ratio: The ratio of the fin depth to the chord length

Bernoulli's Principle: Bernoulli's Principle states that an increase in
the velocity of a fluid is always accompanied by a decrease in
pressure.

Boundary Layer: A layer of static to slow moving fluid adjacent to the
surfaces of a moving body.

Cant: The angle of a surfboard fin in relation to the vertical plane.

Centreline: A line of symmetry along the axis of an object.

Coanda Effect: The Coanda Effect states that a moving stream of
fluid in contact with a curved surface will tend to follow the curvature
of the surface rather than continue to travel in a straight line. „

Computational Fluid Dynamics (CFD): The use of computers to
analyse problems in fluid dynamics.

Cross-sectional area: The area of a two dimensional slice of a three
dimensional object.

Drag: Any force that creates resistance to motion.

Dynamic pressure: The pressure of a fluid in motion, measured by
the pressure it exerts on a flat surface.

Fluid: A liquid or gas that flows and assumes the shape of its
container.



                                                                           20
Foil: A foil is a surface designed to maximize lift while minimizing drag
in a given range of conditions.

Form drag: Form drag, also called profile drag or wind resistance, is
the drag force created on a body as it displaces the fluid through which
it moves. If moving forward, form drag results in greater air pressure
at the front of the body than at the rear.

Isosurface: A type of display that shows a 3D surface for a given
value

Lift: Aerodynamic forces that support a vehicle solely due to airflow or
pressure.

Pressure: The force exerted on a surface per unit area of the surface.

Single fin setup: One-fin surfboard design dating back to the first use
of the fin on a surfboard (by Tom Blake of the USA in the 1930s)

Static pressure: The pressure of a stationary fluid.

Thrust: A force that produces motion. Thrust can result from the
displacement of a fluid.

Thruster setup: Three-fin surfboard design created by Simon
Anderson of Australia in 1980; now the most common fin setup used
by surfers.

Toe-In: The angle of a surfboard fin, in relation to the angle made
with the centre line of the board.

Velocity: The speed in a given direction; a vector quantity.

Vortice: A vortice is a spinning, often turbulent, flow (or any spiral
motion) with closed streamlines.




                                                                         21
                  Bibliography
1. White, F. M 2003, Fluid Mechanics, University of Rhode Island,
   Kingston.

2. Lavery, N. 2005, „Optimisation of Surfboard Fin Design for
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   International Surfing Reef Symposium, Natural And Artificial
   Surfing Reefs, Surf Science, and Coastal Management.
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3. Hendricks, T. 1969, “Surfboard Hydrodynamics, Part I: Drag”,
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4. Hendricks, T. 1969, “Surfboard Hydrodynamics, Part II:
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5. Hendricks, T. 1969 , “Surfboard Hydrodynamics, Part III:
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6. Paine, M. 1974 , “Hydrodynamics Of Surfboards”, Final Year
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   Engineering, University Of Sydney

7. Rosen, B., Laiosa, J. 2000, “CFD Design Studies for America‟s
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8. Benson, T. 2006, Guided tours of the BGA, [Online], N.A.S.A.
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   http://www.grc.nasa.gov/WWW/K-12/airplane/guided.htm

9. Preston, R. 2005, Pressure Drag, [Online], Available from:
   http://selair.selkirk.bc.ca/aerodynamics1/Drag/Page2.html

10.      Lavery, N. 2006, S.U.R.F.S, [Online], Available from:
   http://cetic.swan.ac.uk/surfs/

11.      Paler, M. 2006, How Important is Lift in Fins?, [Online],
   Swaylocks. Available from:
   http://www.swaylocks.com/forum/gforum.cgi?do=post_view_flat
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                                                                    22

				
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