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

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For the fin fanatics of Swaylocks.

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Contents Page

• Introduction …………………………………………………………………4

• Hydrodynamic Forces ……………………………………….7

• CFD Analysis Observations .……………………….12

• Conclusion & Review…….…………………………………….18

• Appendix …………………………………………………………………………20

• Bibliography ………………………………………………………………..22

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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.

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The fin properties, configurations and dimensions used in the analysis

are as follows:

Figure 1. Thruster and Single fin configurations

Figure 3. Top view of Thruster

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

depicting Cant.

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

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

Table 1. Summary of Surfboard fin properties

Fin:

JB2 Single Fin

FCS G5

FCS G3000

Base Chord

(mm): 155 110 110

Surface Area

(mm ²): 47, 600 20, 100 18, 730

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

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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.

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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.

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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.

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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

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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.

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

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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,

depicting velocity boundary layer

profile

Figure 12. Thruster plane cut, depicting

velocity boundary layer profile

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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

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Probe Line Length (mm)

Velocity (m/s)

Centre BL

Curved Foil Side BL

Flat Foil Side BL

Graph 1. Boundary Layer Investigation of Thruster Setup

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Graph of Line probe in Single Fin Boundary Layer

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Probe Line Length (mm)

Velocity (m/s)

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.

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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.

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.

Figure 13. Side view of Single fin flow

trajectories. Tip vortice highlighted in red.

Figure 14. Rear view of

Single fin tip. Arrows

indicate vortice rotation.

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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.

Figure 15. Velocity

isosurfaces depicting the

formation of trailing vortices.

Figure 16. Rear view of Thruster

fins. Flow trajectories map the

rotation of trailing vortices.

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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

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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.

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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.

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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.

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Bibliography

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2. Lavery, N. 2005, ‘Optimisation of Surfboard Fin Design for

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Surfing Reefs, Surf Science, and Coastal Management. Manhattan Beach, California.

3. Hendricks, T. 1969, “Surfboard Hydrodynamics, Part I: Drag”,

Surfer, Vol. 9, No. 6

4. Hendricks, T. 1969, “Surfboard Hydrodynamics, Part II:

Pressure”, Surfer, Vol. 10, No. 1

5. Hendricks, T. 1969 , “Surfboard Hydrodynamics, Part III: Separated Flow”, Surfer, Vol. 10, No. 2

6. Paine, M. 1974 , “Hydrodynamics Of Surfboards”, Final Year

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Swaylocks. Available from: http://www.swaylocks.com/forum/gforum.cgi?do=post_view_flat

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