1. sports
2. surfing and bodyboarding

Surfboard Hydrodynamics
Rowan Beggs – French
The University of New South Wales at the Australian Defence Force Academy
Science and engineering represent an integral part of many sports today with the manufacture of
equipment which aims to enhance athletic performance. One sport which has not yet seen this influence is
that of surfing. Surfing is a unique sport in which riders aim to move powerfully and gracefully along a wave
face, using the energy of a breaking wave to propel them. Little research has been conducted in the field thus
far with design improvements in surfboards occurring through trial and error of shapers, rather than
hydrodynamic analysis. Through flow visualization, this thesis aims to develop a better understanding of the
conditions under which a surfboard operates on an actual wave, extending the current work based on scale
models, and CFD. The first stage of this process is a qualitative look at the flow properties impacting a board
on an actual wave, while the second stage uses video processing to determine typical angles through which the
fins of a board operate. This allows the thesis to examine some design fundamentals and make suggestions for
further development.
Contents
I.
Introduction
A. Background
B. Water wave theory
C. Surfboard Design
D. Aims
II. Previous Research on Surfboard Hydrodynamics
A. Surfboard Hydrodynamics, M Paine 1974
B. Stationary Oblique Standing Wave, H Hornung et al 1976
C. Optimization of surfboard fin design, Brown et al 2004
III. Experimental Methodology
A. Flow Field Properties
B. Fin Angle Measurement
C. Video Processing of Measurements
IV. Results and Discussion
A. Flow Field Properties
1. Results
2. Discussion
B. Fin Angle Measurement
1. Results
2. Discussion
V. Conclusions
VI. Recommendations
Acknowledgements
References
APPENDICES
Appendix A. Definition of angles
Appendix B. Force Balance
Appendix C. MATLAB code for tests
Appendix D. Full numerical results from fin angle testing
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OFFCDT Rowan Beggs - French, School of Engineering and Information Technology. ZACM 4049/4050
Aeronautical Engineering: Project, Thesis & Practical Work Experience A/B.
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Fr
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Vw
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Nomenclature
= Wetted beam to length ratio
= Beam of planning craft [m]
= Celerity, wave speed [m.s-1]
= Drag force [N]
= Water depth [m]
= Froude number
= Acceleration due to gravity [ 9.81 m.s-2]
= Height of board on wave face [m]
= Height of wave, crest to trough [m]
= Lift Force [N]
= Lift due to buoyancy [N]
= Wetted length [m]
= mass [kg]
= Reynolds number
= Side force, perpendicular to velocity [N]
= Period [s]
= Break speed of wave, parallel to bottom contours [m.s-1]
= Speed of surfboard [m.s-1]
= Particle speed of water relative to wave crest [m.s-1]
= Free surface angle with horizontal [degrees]
= Angle of wave with bottom contour [degrees]
= Load [N]
= Density [kg.m-3]
= Wavelength [m]
= Trim angle, board angle of attack relative to the water surface [degrees]
= Yaw angle, wetted area centerline relative to direction of velocity [degrees]
= Roll angle, board base relative to free surface [degrees]
= Dynamic Viscosity [N.s.m-2]
= Surface Tension [N.m-1]
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Final Thesis Report 2009, UNSW@ADFA
I.
Introduction
A. Background
Engineering design and analysis is having an increasingly important role in the development of high
performance sporting equipment, as can be seen in sports such as cycling and sailing. Surfing is a unique sport
where riders use the energy of a breaking ocean wave to propel them. The surfboard, or craft used by a surfer to ride
waves has been developed essentially to its current design over the past sixty years (Carswell, 2004), through the
trial and error of shapers and surfers. There have been three theses that represent the first attempts to apply
Engineering to surfing. Two of these were conducted in the 1970‟s while the most recent was in 2004. This thesis
aims to build upon this knowledge through flow visualisation to provide both qualitative and quantitative data. The
remainder of the introduction will look at the background theory applicable to surfboard hydrodynamics before
examining more closely the research aims.
B. Water Wave Theory
The waves which are used by surfers are water waves on the ocean‟s surface. These are generated by winds
associated with low pressure systems blowing across the water‟s surface in areas known as a fetch (Butt et al, 2008).
The effect of the wind due to viscosity is to create ripples on the surface of the water. These ripples are themselves
water waves, known as capillary waves, due to the restoring force and propagation being driven by the surface
tension of the water (Butt et al, 2008). Over time these ripples merge together forming larger waves, once the wave
height goes beyond 0.02 m they transition from capillary to gravity waves. As the name suggests the restoration
force now becomes gravity, and the surface tension becomes less important in the wave motion. Over the length of
the fetch the small waves will continue to merge forming larger and larger waves, the wave size generated by a fetch
is a function of the wind speed and the length over which it acts; a small fetch and light winds will create small
waves compared to a large fetch with strong winds (Butt et al, 2008).
Figure 1: (a) Deep water wave motion. (b) Shallow water wave motion (Kiss, A., 2008)
The waves once they leave the fetch generally travel a great distance through the open ocean where the water
depth is much greater than the wave height. These deep water waves move sinusoidally as can be seen in figure 1a.
As the wave moves over a section of the ocean‟s surface, the particles will move through a circular path, whose
period is equal to that of the wave and the diameter is the same as the wave amplitude (Stoker, 1957). The particle
speed is much lower than the wave propagation velocity . The equation used to derive the wave velocity, or celerity
for all water waves is:
𝑐=
2 gλ
2π
2𝜋𝑑
tanh⁡
(
𝜆
)
Equation 1
For deep water waves tanh(2πd/λ) approaches 1, simply leaving the wave velocity as a function of the wavelength.
This information is plotted in figure 2, showing the wave speed for given amplitude and period (Kiss, 2008). Wave
period can be related to the wavelength by the equation:
𝜆=
𝑐
𝑇
Equation 2
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Final Thesis Report 2009, UNSW@ADFA
This equation shows that for a given wave length and speed the period is fixed. The straight line that can be seen in
figure 2 with all the other lines emanating from it shows the lower limit for the wave speed given a certain period.
This is a function of the fluid properties and
gravitational constant.
As the wave propagates into shallow water, it begins
to slow, causing the wave to increase in amplitude.
What this means is that the wave front will tend to
follow a coastline, as the section of wave in deeper
water will continue moving at a faster speed (Peachey,
1986). As the wave moves into shallower water the
shape changes from the sinusoidal shape to a peaked
shape that can be seen in figure 1b. As this happens the
water particles themselves go from having small circular
paths to larger elliptical paths. As the paths become
more elliptical the particle velocity increases until the
point at which it equals the wave propagation velocity.
It is at this point that a wave is said to break, with the
top of the wave falling forward. This occurs when the
water depth reaches 78% of the wave height (Kiss, 2008),
Figure 2: Wave velocity for various water depths
and is shown in figure 3 by streak line 1.
and wave periods. Note: h is water depth in this
Waves when they come to the point of breaking can be
plot (Kiss, A., 2008)
incident to the bottom contours at the critical depth through
a wide range of angles, shown as γ in figure 3. This can
theoretically range from 0o through to 90o, which then
affects the rate at which the wave breaks. In practice due to the slowing of waves in shallower water a wave will
never move at 90o to the critical bottom contour (Stoker, 1957). The speed at which a wave breaks is given by the
relationship:
𝑉𝑏 =
𝑐
Equation (3)
sin ⁡
(γ)
γ
As can be seen if the wave makes too smaller angle with
the bottom contours then the break velocity will be very
fast. If the wave is breaking at a speed too high for the
surfer to keep up with, a wave is said to close out (Hendrix,
1969). Generally for surfing γ is between 30o and 60o
(Pattiaratchi, 1999). If we consider a wave incident at 0o
then the wave motion is unsteady. It will rise up and break
all at once, whereas if it makes an angle greater than 0 o it
1
will transition from unbroken to broken wave at a constant
3
vb
2
c
rate of Vb (Hornung et al, 1976). This allows the wave
Figure 3: Diagram of breaking wave, dashed line
breaking to be viewed as a steady event, which makes
analysis of the problem considerably simpler.
indicates critical depth contour causing wave to break
It is in the transition region, just before the wave
actually breaks that surfers ride, as it is the steepest part of the wave allowing the greatest speed to be attained
(Hornung et al, 1976). In order to stay with the point of breaking the rider has to have an average velocity equal to
Vb, however they will often be riding with speeds around 50 percent higher (Brown et al, 2004), but manoeuvring up
and down the wave face.
As was stated earlier at the point of breaking the water particle velocity is equal to the wave propagation
velocity. This is true along the entire breaking streak line, streak line 1 in figure 3 which allows us to plot the water
speed relative to the peak at the point of breaking, shown in figure 4, and the equation for which is:
𝑉𝑤
𝑐
= 2 1−
ℎ
𝐻
Equation (4)
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Final Thesis Report 2009, UNSW@ADFA
Figure 5: Diagram of particle motion at point of
breaking. (Paine, M., 1974)
Figure 4: Velocity profile for water particles
along breaking streak line
This means that water at the base of the wave appear to be moving at twice the celerity, as it is moving at the
same speed as the top of the wave but in the opposite direction. The top on the other hand has the water particles
moving at the same speed and direction as the wave‟s propagation therefore the relative velocity is zero. This can be
seen in figure 5.
C. Surfboard Design
As was discussed earlier the surfboard designs which we see today are the culmination of around sixty years of
trial and error (Brown et al, 2004). The boards which I am concerned with for the purpose of this thesis are modern
high performance short boards. In this section the basics of surfboard motion are outlined along with the basic
design features of a surfboard.
Because surfboards work on the interface between two fluids the non dimensional groups that govern their
motion are the Froude, Weber, and Reynolds numbers (Munson et al, 2006):
𝐹𝑟 =
𝑊=
𝑅𝑒 =
𝑉
𝑔.𝑑
𝜍
𝜌𝑔 𝑙 2
𝜌𝑣𝑠 𝑙
µ
Equation 5
Equation 6
Equation 7
The Froude number is the ratio between the
speed that a craft is moving at and its wetted
length. This is important because it defines the
way that the craft moves through the water. Craft
that operate at low Froude numbers are known as
displacement craft, with the lift coming
predominantly from hydrostatic or buoyant forces
(Hornung et al, 1976). High Froude numbers on
Figure 6: Planing motion of flat plate (Hornung et al,
the other hand indicate that the craft planes along
1976)
the fluid surface, with the lift coming
predominantly from hydrodynamic forces. Surfboards are craft that operate at high Froude numbers, which means
the majority of the lift they achieve is from water rushing along the bottom surface, which is at a small angle to the
water surface (Hendrix, 1969). A diagram of a planning surface is shown in figure 6.
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The Weber number is the relationship between the surface tension and gravitational forces acting on a fluid. This
applies to surfing as the waves ridden are gravity waves, meaning that they have a low Weber number. Capillary
waves, or small waves as discussed earlier have their motion driven by surface tension. This is important in
determining the forces on a board, as the two categories of waves have different affects on the wave drag
experienced by a surfboard (Hornung et al, 1976). Finally the Reynolds number shows the balance between inertial
and friction forces. A low Reynolds number means that the flow is laminar, while high indicates that the flow is
unsteady or turbulent (Munson et al, 2006). This greatly affects the skin friction drag developed on a moving body.
A surfboard on a wave operates at Reynolds numbers around 10 6 which lies in the transition region between laminar
and turbulent flows. It is likely that the flow is often turbulent due to the water that the board is moving over being
turbulent to begin with (Hendrix, 1969).
Figure 7: Example of a rider in trim condition
(Corona, 2009)
Figure 8: Example of a rider turning (Hyatt, 2009)
In order to allow a surfer to effectively ride and
control a board on a wave there are several important
design features of boards which are outlined below:
Bottom surface –The bottom design of a surfboard
is very important as this is the region providing the
planing lift to support the board and rider. The centre
region is generally flat, as water will flow over this
part of the board at a wide variety of angles,
depending if the rider is in trim on the wave face or
turning (Please refer to figures 7 and 8 for conditions).
As we move towards the rear of the board there will be
two shallow concave sections running parallel to the
board centerline which increases the bottom surfaces
Figure 9: Plan of board and side elevation showing basic
lift effectiveness, in a similar way to winglet on an
design features
aircraft (Hendrix, T., 1969). This is the double
concave shown in Figure 9.
Rail Design – There are two predominant types or rails used in surfboards, hard and soft. A hard rail is where the
curved edge of the board has a sharp edge or chine, causing the flow to separate, which reduces drag in the trim
condition (Hendrix, T., 1969). Therefore this is usually used on the rear third of the boards rails, as these are in
contact with the water during the trim condition on a wave face. The rails used mid way down the board are
described as soft. These rails have a rounder profile that can be seen in figure 10, which allows the water to wrap
around them further thereby generating higher lift. The soft rail allows tighter turns due to this higher lift, increasing
board manoeuvrability. They are used further forward on the board . Please refer to Figures 9 and 10.
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Final Thesis Report 2009, UNSW@ADFA
Rocker – Rocker refers to the curve in the board when looked at in
side elevation. Rocker is used to give a board stability, as it acts as a
shock absorber (Hendrix, T., 1969). This allows easier transition to turn
from trim, and also damps the motion of the board over the chop
normally found on the surface of waves. Too much rocker however will
slow a board down due to a larger area being in contact with the water. A
diagram of a standard medium rocker is shown in figure 9.
Fins – The fins in conjunction with the rail give the side force
necessary to hold the board into the wave face. They are a type of
hydrofoil positioned at the rear of the board, and act in much the same
way as the wing of an aircraft to generate lift. The most common fin set
up used is that pictured, the three fin thrusters developed by Simon
Anderson.
Figure 10: Half cross sections
taken at the dashed line in figure
9. Left indicates „hard‟ rail while
right shows a „soft‟ rail
D. Project Aims
The initial project aimed to examine the flow field around a whole surfboard whilst it was riding a wave. Then
with this data the research would be in a position to make recommendations as to the future direction of surfboard
design. This would be done based upon craft which were better understood and were acting under the influence of
similar forces. The first stage of this has been conducted, estimating the force balance based on the theory available
and qualitatively examining the flow properties around a surfboard on a real wave.
Through the literature review conducted and the initial testing the initial aim outlined above became unrealistic
for the following reasons:
- The number of unknowns meant that problem is outside scope of final year thesis
- A surfboard on a wave represents a three dimensional problem on a constantly moving reference plane
- In order to obtain reasonable results a high degree of accuracy is necessary
- Surfboards are very small, lightweight craft. Any test equipment must not interfere with the performance,
and rider use
- Ocean can be very fickle, with unrideable surf for long periods, as has been experienced during research
- Repeatability is hard to achieve given no two waves are the same, let alone can be ridden identically
The culmination of these realisations was that the focus of the thesis need to be narrowed, which yielded the final
aim of the thesis, to examine the performance of the fins on an actual board. As was outlined above, the fins are a
vital part of the surfboard giving the rider the stability and control necessary to turn powerfully on a wave. The more
powerfully and gracefully a rider can manouvre the better in high performance surfing. In competition this leads to
the best results as it demonstrates a riders ability.
The assumption to this point in time has been that because fins are a hydrofoil, they operate under similar
conditions to an aircraft wing, seeing maybe a window of angles between -5 degrees to positive 10 (Brown et al,
2004). As can be seen in figures 12 and 13 there is basis to believe that fins are operating well outside this small
window. If this was the case then it would suggest that a major change in the design direction would be necessary in
order to increase fin performance.
Hence the adjusted focus of the thesis was to perform tests to accurately measure the range of surfboard fin
angles whilst riding waves.
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Final Thesis Report 2009, UNSW@ADFA
Figure 12: Surfer demonstrating the
extreme angles that the fins can go through
whilst riding a wave (Robertson, 2008)
Figure 13: Whilst in trim on the wave face angles
likely small, similar to aircraft wing (Sheffield, 2009)
II. Previous Research on Surfboard Hydrodynamics
A. Surfboard Hydrodynamics, M. Paine 1974
The first Engineering work that was conducted into surfboard
design was that of Michael Paine at the University of Sydney in 1974.
His work was conducted in three parts, measuring the speeds of
actual surfboard on waves, conducting a theoretical force balance
based upon planing craft theory and investigating the creation of a
standing wave to test model surfboards on.
The speed measurement was conducted in two stages, in order to
validate his results. The first method was setting up a pitot static
system on his surfboard with a data recorder, while the second used
triangulation of his position from two traces on the beach. What he
found was that the speed he could go along a wave was directly
proportional to the wave height, with the fastest velocity he attained
being around 12 m.s-1. The results of this can be seen in figure 14.
In his force analysis of the surfboard he applied the basic planing
craft theory which had been developed by NASA in the 1950‟s. He
defined the relevant angles for a surfboard, as can be seen in figure
15, and then simply through geometry determined the forces than
must be generated for a board to be in equilibrium on a wave face. A
Figure 14: Correlation between measured
full definition of relevant angles can be found at appendix 1. He
velocity and wave size (Paine, 1974)
approximated a free surface at the point where the board meets the
water on a wave face, assuming it to be flat (an accurate assumption over the relevant distance, the board width). He
then defined a coordinate system such that the xy plane was the free surface and z was coming vertically out of it:
𝐿 = 𝑊. cos⁡
(𝛼)
Equation 9
𝑆 = 𝑊. sin 𝛼 . cos⁡
(𝛽)
Equation 10
𝐷 = 𝑊. sin 𝛼 . sin⁡
(𝛽)
Equation 11
Finally his work examined the possibility of developing a standing wave for testing surfboard designs, however
due to difficulties encountered this was unable to be fully developed for testing by the conclusion of his thesis.
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Final Thesis Report 2009, UNSW@ADFA
Figure 15: Definition of angles for force balance
B. Stationary Oblique Standing Wave, Hornung, Killen, 1976
Following on from the work of Michael Paine, H.
Hornung and P. Killen completed a PHD developing a
standing wave for the testing of surfboards at the
Australian National University in Canberra. The idea of a
standing wave is similar to that of a wind tunnel. Rather
than having a board moving across the fluid, have the
fluid move across a stationary board in order to create a
dynamically analogous case for ease of testing. They
followed on theoretically from the work of Paine, by
adding the work done by Lueders et al at NASA on force
and moment coefficients for asymmetric planing. This
Figure 16: Transformation of 2D planing motion
allowed them to derive a formula to calculate the lift
to 3D (Hornung et al, 1976)
generated by a flat plate planing asymmetrically, which is
a simplification of a surfboard (see figure 16).
After developing a functioning standing wave, a side elevation of which can be seen in figure 12, they made
model boards, and conducted a force balance in order to establish the important forces acting on a board. They
managed to get successful results by weighting a board accurately, however the model wave was around 18 cm in
height, with surfboards of the same length. What this meant for the results is that there were order of magnitude
differences in all three non dimensional groups applicable, shown below in table 1.
Figure 17: Standing wave developed by Hornung et al
for PHD (Hornung et al, 1976)
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Final Thesis Report 2009, UNSW@ADFA
Coefficient
Fr, 𝐹𝑟 =
Re, 𝑅𝑒 =
W, 𝑊 =
𝑉
𝑔.𝑑
𝜌𝑣𝑠 𝑙
𝜇
𝜍
𝜌𝑔 𝑙 2
Model (orders
of magnitude)
1
Full scale (order
of magnitude)
10
105
106
10-3
10-5
Implications
Relative importance of wave and splash drag is directly
proportional to Fr. The full scale would have a lower
wave drag but higher splash drag. The relative
importance of hydrostatic lift (buoyancy) would be
higher for the model compared to the real board.
Boundary layer laminar for model, transition or
turbulent for actual, effecting viscous and pressure drag.
This means that the viscous drag on the real board will
be relatively higher, while we could expect to see a drop
in the pressure drag.
Importance of capillary waves and gravity waves in the
wave drag varies with W. The model board will have
capillary waves around it, which interact with the board
differently to the gravity waves seen in the full size case.
The implications are what the author of this thesis expected to see when looking at the flow properties on a full
size surfboard. This can be found in the discussion section of this report.
C. Optimisation of surfboard fin design, Brown, Carswell, Foster, Lavery, 2004
The most recent work which has been conducted into surfboard
hydrodynamics is that of Brown et al at the University of Swansea
in England. The work they conducted focused upon was the
development of a Computational program that would allow various
fin designs to be directly imported into the computational fluid
dynamics program Fluent. Once this was achieved they conducted
simulations in Fluent to determine the difference in performance
the blending of fins onto the board made. This is really interesting
and important as there are two predominant designs of fins being
used, fin systems which are removable and not filleted, and glass
on fins which have a shallow blend at the join to the surfboard, a
demonstration of each can be seen in figure 18.
Figure 18: Example of unfilleted (left) and
What the research found was that in filleting the fin base there
filleted (right) surfboard fins (Brown et al,
was a small reduction in interference drag. The research was
2004)
conducted over a wide range of angles, however
the assumption was that the fins would operate
much the same as the aerofoil of an aircraft, not
going beyond angles of around 10o(Brown et al,
2004). They experimented also with various flow
conditions using laminar and turbulent models,
however this work is ongoing. The findings were
that the filleted glassed on fins had less drag,
however the difference was found to be only 3
percent, which when the variability of the forces
that act on a surfboard, and the differing rider
styles is considered, it is not a great deal.
Figure 19: CFD simulation showing leading edge vortex
generation (Brown et al, 2004)
(Brown et al, 2004)
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Final Thesis Report 2009, UNSW@ADFA
III. Experimental Methodology
A. Flow Field Properties
The first stage was to calculate the forces based on the theory developed by Paine and Hornung et al. This
allowed an initial estimate to be made of the forces required to hold a board in the trim condition on a wave face.
The next stage was to examine the flow properties through a form of flow visualisation. This meant examining how
water flowed around a board on an actual wave. In order to do this a waterproof camera was provided by Dr Michael
Harrap. The idea behind this was that if the camera could be mounted on the board whilst it is ridden across waves
then this would allow the flow field to be qualitatively examined as it moved over the various parts of the surfboard.
The requirements of the design were:
- Gave a clear view of the flow field over the board
- Was robust enough to withstand the forces of the ocean
- Had minimal effect on the way in which the board was ridden
- Posed minimal threat if the author fell off and was hit by it
The result of the first design iteration was the mounting
that you can see in figure 20. The ideal place to mount the
camera was on the nose of the board, as it would provide both
the best view of the flow of water over the rail of the board,
and it would be out of the way when the board was being
ridden on a wave. The camera was mounted onto the
aluminium plate shown, which was attached with Velcro to the
board so that if the surfer fell and hit the camera with sufficient
force, the Velcro would release, preventing injury. There was
also a safety leash attached which allowed the camera to be
saved if this did occur, taped to the deck of the board to
prevent it being an extra obstacle. In the first trials the design
was found to be mounted too low. The consequences of this
was that the image was too flat, not giving a good appreciation
of flow over the board, and there was also considerable
splashing of water across the lens obscuring the image.
The next iteration worked on the same principles, however
raised the camera up by 100 mm, as can be seen in figure 21.
This design worked really well, providing some of the images
which can be seen in the results section. It removed both the
problem of splashing and gave a much wider viewing angle of
the flow, allowing more to be viewed. One problem that was
encountered during the testing of this design however was the
safety leash was not strong enough, and that the camera did
not float. This resulted in the safety leash snapping during one
test and a camera being lost somewhere in the ocean on the
South Coast of NSW. This led to the final design which was
the raised mount, with a stronger double safety leash and a
foam block that ensured the camera floated if the cord failed
again.
Figure 20: First camera mount on board nose
Figure 21: Second Aluminium mount,
showing new higher position on nose
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Final Thesis Report 2009, UNSW@ADFA
B. Fin Angle Measurement
After the readjustment of the thesis aims the goal was to accurately measure the range of motion that the fins of a
surfboard go through while riding a wave. For this once again the underwater video camera was employed courtesy
of Dr Michael Harrap.
The design considerations were much the same as for the flow field visualisation, being:
- Gave a clear view
- Was robust enough to withstand the forces of the ocean
- Had minimal effect on the way in which the board was ridden
- Posed minimal threat if the author fell off and was hit by it
The most effective method that was determined to measure the
angles of the fins during riding was to tuft the board, much the same as
the way an aircraft wing is tufted for flow visualisation. The first
experimental design can be seen in figures 22 and 23. The test board
had a 60 mm hole cut through it 50 mm in front of the right hand fin.
This fin was chosen, as the author is a natural foot, and predominantly
rides right hand breaking waves. This means that the right hand fin is
in the water the majority of the time. In order to provide light for the
camera to see the tufts, a Perspex disc was inserted, with light
Figure 22: First mount using foam block
with battery pack and switch to left
emitting diodes mounted around its edges. The Perspex was used as it
would allow the flow along the board to be uninterrupted, was very
clear and easy to mount. A battery pack was mounted further forward
on the board which would allow the author to turn the LED‟s on and
off during surfing, and a charging port so that the batteries did not
require removal from the board once they were mounted in.
The camera itself was then mounted directly above the Perspex
disc, looking down. The method for this was to cut a foam block to the
required shape and glue this, along with the other components to the
board using „sylastic‟ silicon glue. Cotton tufts were finally taped to
the underside of the board. When this design was tested, the first wave
that was ridden managed to knock the foam block clean off the board.
Figure 23: Battery pack, switch and
Luckily lessons learned earlier meant that the safety cord was
charging port
sufficiently strong to prevent loss of the camera. The other problem
found was that the sylastic had not provided a good seal, and the circuit
controlling the LED‟s had become wet, corroding and failing. The final
problem was that the cotton once wet frayed, so was useless in indicating the
fin angle.
In the second design two aluminium brackets were fibre glassed onto the
deck of the board, to provide rigidity to the foam, so that the camera would
stay mounted to the board whilst the waves were ridden. The second design
iteration can be seen in figure 24. The tufts were also waxed so that they would
not fray when they were wet. The testing of this indicated that the tufts worked
more effectively this time, and the camera remained on the board as it was
ridden. The first problem that was encountered here was that the gap between
the Perspex and the camera lens was not water tight, meaning that water got in
and sloshed around making it impossible to get an accurate image of the tufts.
It was also found that under dull light conditions that the white tufts were hard
to distinguish from the background.
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Final Thesis Report 2009, UNSW@ADFA
Figure 24: Second design with
Aluminium brackets
The final design that was reached is what can be seen in figures 25, 26 and 27. Instead of using the flimsy foam
to mount the camera which was not water tight, a design employing plumbing fittings obtained from Bunning‟s
Warehouse was used. The circuit for the LED‟s was glued in using polyester resign, and a male sink fitting was used
to create a water tight seal on the Perspex. The camera was then glued using Sylastic into a piece of PVC tube
attached to the female fitting, which then could be screwed into and out of the board as necessary. Permanent fixing
of the camera was considered, but there were concerns that having an air tight cavity would mean that under certain
conditions the Perspex window or camera lens could fog, obscuring the image.
Figure 25: View of underside
with Perspex window in place.
Tufts held on with tape
Figure 26: View from video
camera perspective. Note 3
LED‟s around edge
Figure 27: Side elevation of final
design, employing plumbing
fittings
The aluminium brackets remained in place, and were used as extra supports by cable tying the camera in place,
as can be seen in image 27. From what was seen in the last tests, red and white tufts as can be seen in figure 26 were
employed. This was to allow the angles to be seen in both very bright light conditions and very dull, a wide variety
of light conditions can be seen in a single surf depending on the time of day, water clarity and cloud cover. In testing
this design proved to be successful, having the strength to withstand the beating a board can receive on a wave,
whilst remaining water tight.
The lighting system used proved to be very effective under all the light conditions encountered. The design used
three 3V LED‟s mounted in series around the circumference of the Perspex disc, as can be seen in figure 26. The
holes were drilled carefully using kerosene as a lubricant in order to get a well polished clear finish. The remaining
edge of the disc had the highly reflective film attached to it as used on road signs, after consultation with Dr Harald
Kleine. This ensured that the maximum light possible was reflected from the walls, improving the visibility of the
tufts.
With the final design testing was ready to be conducted. In order to best appreciate the wide variety of angles
that surfboard fins can go through on a wave, the goal was to ride with the design under the widest range of
conditions. Due to the development time for the design the testing time was seriously limited. Add to this the
difficulties of getting good waves on any day, and getting data becomes quite difficult.
The board and fin system being used are fairly standard for a rider of the authors size. Understandably a larger
rider requires a larger board to provide the floatation to paddle, and a larger fin to generate the necessary lift to hold
the rider on a wave. The board being used is what the author uses for larger waves, being 6‟11” long 18 ½” wide and
2 ¼” thick. The fins being used are the FCS (Fin Control System) G-7000, a standard surfboard fin design being
currently used. The standard fin series are the G-3000, G-5000, and G-7000, all of the same outline and profile just
scaled to suit different rider weights. A photograph of the fins being used can be seen in figure 28. The middle fin is
understandably symmetric with a smooth curve on each face, while the outside fins are cambered on the outer
surface only, with the inner being flat.
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Final Thesis Report 2009, UNSW@ADFA
Figure 28: FCS G-7000 fins as tested
C. Video processing of Measurements
This section will briefly look at the video and image processing techniques which are used to provide the output
data on the tuft angles.
The program was developed by Dr Michael Harrap in 2008 for use with the SEIT Cessna. The purpose of the
program was to effectively give the user a digital wind tunnel. Using video footage of the aircraft in flight with tufts
in place, the program outputs the average angle of attack of the tufts over a pre determined time step.
By changing the filtering levels and identifying the colour intensities the program was able to be applied to the
video analysis of the tufts on the surfboard for this project. The full code can be found in Appendix C, and the rest of
this section will look at the different stages the program goes through to output the data.
Firstly the program imports the data that is to be processed, as is in figure 29. Then the user selects the section of
the video frame to focus on, which is helpful if the tufts only take up a portion of the frame. Next the grid size needs
to be set, if the grid is too fine it will have too much noise, while if too large it will fail to recognise the tufts which
are in each frame. The program then enters the main processing loop where it reads each slide individually. Each
slide is then eroded and dilated to remove the tufts from the background image. This is necessary because the tufts
need to be segregated from the background image which can have many anomalies in it, as can be seen figure 33.
The result is then subtracted from the original slide, which leaves only the tufts. This is helpful if the background
has objects which are of similar brightness to the tufts but different sizes.
Figure 29: Input image, with
selected region for processing
shown by dashed line
Figure 30: Cropped image
ready for processing
Figure 31: Tufts
identified and
converted to Binary
image
Figure 32: Images
overlayed and average
shown for time interval by
green lines
Once this is done the image is converted to a binary image, with the tufts left as white while the rest of the image
is black, as can be seen in figure 31. The program then identifies the tufts, measuring the length and angle that they
are at. A weighted average is then conducted across the slide, to output a single average angle of the tufts for each
grid in each frame. This is done for however many images are in the time step chosen, and the results averaged, with
the average displayed using a green line, as is seen in figure 32. For use with the aircraft the images were averaged
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Final Thesis Report 2009, UNSW@ADFA
over one second intervals. Due to the rapid changes in direction that occur while surfing a time step of 0.2 seconds
has been employed.
This process is then repeated until the video finishes, at which point the results are visually displayed on the
screen with a plot of the average angles, and the average angle is stored in an array as a function of time. This
allowed the time vs. angle plots to be developed for the results of this thesis.
Figure 33: Extreme background noise that program has to remove during processing. All three are from the same
single video clip
IV. Results and Discussion
A. Outline
In this section the results of the thesis are discussed. The two experiments which have been performed will be
examined and the data that was obtained. First the flow field results are presented along with a force balance to
assist in understanding the basic dynamic situation on a wave. After a discussion of these results the fin angle
analysis is presented along with an interpretation of what the results mean.
B. Flow Field Properties
1.
Results
The first results presented here are the initial calculations based on the theory developed by Paine and Hornung et al.
This allowed an initial estimate to be made of the forces required to hold a board in the trim condition on a wave
face. The first result displayed below is the force balance initially conducted to estimate the forces acting on a board
riding a wave.
For this a photograph of a surfer riding an actual wave was used, and from the picture approximated the angles
which were necessary for analysis (please find photograph and full calculations at appendix B):
α
b
τ
ψ
υ
= Free surface angle
= Beam of planning craft
= Trim angle
= Yaw angle
= Roll angle
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Final Thesis Report 2009, UNSW@ADFA
Figure 34: Force balance of a board riding on a wave. Note Q =
side force in this diagram (Hornung et al 1976)
Also approximated were the wave height, based upon the rider size, which allowed based upon the water wave
theory to calculate the water velocities relative to the surfboard. This data was then used to calculate the various
force coefficients found by Savitsky et al in their work done on asymmetric planing in 1958. This allowed the
forces for equilibrium to be calculated and then compared with the theoretical values necessary. The results were:
For W = 883 N, α = 40o, and H = 2 m, using equations 9, 10, and 11 the required forces for balance are:
L = 750 N
D = 300 N
S = 450 N
The next section uses the work of Savitsky et al to calculate the planing forces which would act on a flat plate
operating at the angles from the tabulated coefficients:
Figure 35: Extract of tabulated coefficients for asymmetric planing (Savitsky et al, 1957)
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Final Thesis Report 2009, UNSW@ADFA
For:
ψ = 10o
φ = 15o
τ = 6o
CΔ = Δ/ρ.b3 = 700/ 1030 x 0.33 = 25.17
Cl = 0.215
Cs = 0.0537
CD = 0.046
This then allowed the relevant forces to be calculated by applying the following formulae:
𝐿=
1
𝑆=
1
𝐷=
1
2
2
𝜌𝑣 2 𝑏 2 𝐶𝐿
Equation 12
𝜌𝑣 2 𝑏 2 𝐶𝑠
Equation 13
2
𝜌𝑣 2 𝑏 2 𝐶𝐷
Equation 14
The results of this were that planing forces alone contributed:
L = 700 ± 100 N
D = 150 ± 50 N
S = 150 ± 50 N
The results which were obtained from the flow field looking
back along the rail of the board were very interesting. Figure 36
is from the first camera mount, showing that the image is hard
to distinguish due to the shallow angle. This image is looking
down the right hand rail of the board, whilst riding across the
face of a left hand wave. It can be seen the water that is shooting
out from rail, this jet showing the speed at which the water is
moving.
The next two images are more useful however as they are
using the second mount which has the extra elevation and hence
allows a clearer image. In figure 38 we can clearly see the flow
wrapping around the rail and then shearing to continue up the
wave face to break. The flow in figure 37 is somewhat different
Figure 36: Image taken from tests using
with what appears to be a large pocket of air induced into the
first camera mount, limited field of view
flow , and the water wrapping considerably further around the
rail. One reason why this difference is seen is that the wave
being ridden in figure 37 is considerably smaller that in 38, hence the speed of the board through the water is lower.
This means that a higher lift coefficient would be necessary to maintain the same lift, hence the higher degree of
wrapping.
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Final Thesis Report 2009, UNSW@ADFA
Figure 37: View with final mount design. Note high
degree of wrapping when travelling at slow speed
2.
Figure 38: View with final mount. Note
separation when travelling at high speed
Discussion
As can be seen from the force balance results the forces
calculated by the pure planing theory are within the same
order of magnitude as the forces required by the physical
geometry. The lift result is very similar, which is what we
would expect with the board being in planing motion, and
the majority of its lift being derived from hydrodynamic
force. The Drag and side force calculated are considerably
lower than what is required for equilibrium, however this
analysis does not include the surfboard fins. This indicates
that we would expect around two thirds of the side force to
be from the fins and half the drag. These values seem
reasonable, and demonstrate that the theory for planing is
indeed quite accurate for a surfboard moving along a wave
face, of course neglecting the fins, and approximating the
Figure 39: Plan view of test board on standing
board as a flat plate. It is difficult however to go further with
these calculations, as the complexities of the problem are
wave (Hornung et al, 1976)
immense. Adding the fins to the analysis creates a very
complex interaction of flow properties that would be best analysed through CFD, which is being investigated at
present by a research team at Swansea University in the UK. The degree of uncertainty is also high, stemming from
the fact that a small variation in any of the measured angles will cause a very large change in the force developed,
and the difficulty in getting accurate measurements.
The results for the flow field visualisation are very similar to what was predicted. The really interesting things to
note with both these images is that to the left the smooth unbroken wave face can be seen, while the motion around
the rail, and departing the board has bubbles through it and is quite unsteady. The way in which the water is moving
around the rail is considerably different to what is seen in the testing of Hornung et al. In figure 39 we see a plan
view of a model board riding the standing wave. The first notable difference that we can observe is the presence of
capillary waves along the leading edge of the boards wetted area (horning et al, 1976). This is considerably different
to the crest that we can see from the tests in figure 38, which shows a gravity wave. This difference is due to the
dissimilarity in Weber number, the balance between surface tension and gravitational forces. The next difference
which can be observed is how deep the board is sitting in the water. In the real life case the board is sitting
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Final Thesis Report 2009, UNSW@ADFA
considerably deeper in the water, as can be seen by the higher degree of water wrapping around the rail. This is
because on a real wave we expect to see the board operating at a lower Froude number. The consequence of this is
that the board is deriving more of its lift by buoyancy than in the testing of the scale board.
The final dissimilarity that can be seen between the testing is that the flow around the model board is completely
laminar and undisturbed. This can be compared with the testing on real waves where we see the flow is separating
and moving unsteadily, hence quite a turbulent flow pattern. This difference can be seen from the difference in the
Reynolds number between the model and real life case.
C. Fin Angle Analysis
1.
Results
In this section the results from the fin angle tests are presented. As was seen in the experimental methodology
section the design to record the data went through several iterations. Before looking at the graphs showing the fin
angles a short visual comparison is presented between the footage obtained using each design.
The initial design used, with only the foam mount glued to the board was unable to
obtain any results due to the mount failing before any waves were ridden. The second
design, using the aluminium brackets which were fibre glassed to the surfboard recorded
some footage as can be seen in figure 40. As can be seen the tufts are barely visible
against the background. There were several factors contributing to this, most importantly
that the cavity between the camera and the Perspex lens was not water tight. The tufts
used were also pure white, which under poor light did not show up as well.
In figure 41 the final mount design is shown with short red tufts and longer white
tufts taped to the underside. The blue line provides the reference for the fin 0o angle of
attack. As can be seen the imaged is considerably clearer with the red tufts particularly
visible in the murky light and water conditions. Figures 42 and 43 show the same
Figure 40: Unsealed
system in operation however using brighter red tufts that were longer.
cavity makes image
impossible to process
Figure 41: First test using final
camera mount. Tufts clearly
visible. Note dashed line is fin
centreline
Figure 42: Final mount using
longer red tufts to increase
effectiveness. Note dashed line is
fin centreline, showing slight
negative angle of attack
Figure 43: Longer tufts
showing a high angle of attack,
and really good contrast . Note
dashed line is fin centreline
In the following section of results graphs are presented showing the angle of attack measured as a function of time.
The numbers on the graph itself relate to the figures at the top of the page showing what the board and rider were
doing at that particular time. The images are as a guide only, and are not of the test rides themselves.
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Final Thesis Report 2009, UNSW@ADFA
(1)
(2)
Figure 38: Different positions on wave (Neville, 2005)
(3)
Figure 39: Graph 01, first wave ridden. The spiked profile is likely due to the unsteady flow which
rapidly fluctuates as the rider moves along the wave face. Sampling frequency here is 5 hz Note:
numbers correspond to condition shown in figure 38, “I” represents uncertainty
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Final Thesis Report 2009, UNSW@ADFA
(1)
(2)
Figure 40: Different positions on wave (Neville, 2005)
Figure 41: Graph 02, “I” represents uncertainty
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Final Thesis Report 2009, UNSW@ADFA
(3)
(1)
(2)
Figure 42: Different positions on wave (Neville, 2005)
Figure 43: Graph 03, “I” represents uncertainty
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Final Thesis Report 2009, UNSW@ADFA
(3)
(1)
(4)
(2)
(3)
(5)
Figure 44: Different positions on wave (Neville, 2005)
(6)
Figure 45: Graph 04, “I” represents uncertainty
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Final Thesis Report 2009, UNSW@ADFA
The following is a brief description of the waves which the test results were obtained from and the conditions under
which they were obtained. Each wave represented in the graphs above were ridden on different days, with wave 1
ridden on day 1 and wave 2 ridden on day 2 etc.
Wave
1
2
Approx Size (m)
1
1.5
Break type
Sand Bar
Reef
3
4
1.5
2.5
Reef
Point
2.
Comments
Relatively small day with onshore sloppy waves
Good day but relatively short rides. Offshore and quite
clean waves
Good day again shorter rides. Clean waves
Really good day, solid swell with powerful offshore
winds. Good long rides with nice open face
Discussion
The first thing that can be noticed from these results are
the very sudden changes in angle, creating the jagged graphs
seen. One reason why this is the case is that a real wave face
is not smooth, as can be seen in figure 45. This means that
the board constantly changes its angle relative to the flow of
water as it moves over the changing surface and bumps, and
when moving at around 10 m.s-1 this occurs very rapidly. At
some points when manoeuvring on the wave the board went
through the broken part of the wave which is a very turbulent
flow, as can be seen in figure 44(6). The author does believe
after watching the video obtained in testing that this rapid
movement is indeed representative of the flow.
In future for this section a camera with a higher frame
rate of 100 to 300 frames per second would be ideal as this
Figure 45: Chop on water surface can be
would allow the progression of the tufts to be more
clearly
seen on the unbroken section of wave
accurately measured.
An uncertainty analysis was carried out for these results,
at left of photograph (Muirhead, 2009)
by running the same clip through the program multiple
times, and selecting slightly different sized areas and tufts to be analysed. The outcome was that at most the results
for each time step varied by 0 to 0.9 degrees. Hence all results have been rounded to two significant figures and the
error bar on each graph is for one degree either side. A full table of results can be found at Appendix D.
What is particularly interesting to note with the results that have been obtained is the range of angles that can be
encountered when riding along what are a fairly standard range of waves. As was outlined briefly the waves
represented a range of sizes, from 1m to 2.5 m. From the first test day the conditions were quite small which meant
that the board was moving at lower speeds. This means that to generate the same amount of lift a relatively higher
angle is required for the fins. For this short wave alone a range of more than 36o was measured. The largest and
longest wave, obtained on the final day of testing was really interesting. The wave which is presented here was ideal
for the purposes of this testing, as it had enough size to give the speed and space to throw the board around and push
the limits. This allowed some of the best results to be obtained, with a range from 12o down to a remarkable -43o.
Because of the symmetry of the board this meant that the left hand fin, the fin providing the lift into the turn was
seeing a flow at 43o, well beyond the effective limit of a conventional hydrofoil, which would be expected to stall at
around 15 – 20 degrees.
Unfortunately due to time restrictions the number of tests conducted was considerably less than intended. This
was a result of the development of an effective test rig for the experiment took considerable time. Each iteration had
to be tested under the real conditions which involved selecting a day where the surf would be good, and each test
would take a day. Then the results had to be analysed and a new design developed, and this process in itself took
around 6 weeks. In addition once the test equipment was developed to a usable level an unusually long flat spell was
encountered with practically no rideable surf for 3 weeks. This left a testing window of around 4 weeks in which the
results above were obtained, which gave a good spread of conditions. More tests would have been ideal, but the data
obtained has shown the fins going through angles far in excess of those predicted.
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Final Thesis Report 2009, UNSW@ADFA
These results are particularly interesting when they are examined in comparison to the predictions of Brown et al in
their 2004 thesis on surfboard fin performance. “However, it is believed that in reality the forces on a fin when
surfing would only correspond to maximum angles of attack up to 10º to 15º” (Brown et al, 2004). It appears from
the results of the testing that in fact fins can see angles up to three times this, meaning that current fin design which
is aimed at being effective over the narrow band of angles in fact are going to be working inefficiently at the angles
encountered on a real wave.
V. Conclusions
In conclusion while the initial aims of this project proved too vast, the adjusted aims have been successfully
achieved. First a system was successfully developed that would provide the footage of a surfboard working on a real
wave, and in doing so allowed the flow properties of the board to be examined and compared to the work of Killen
et al. In doing so the work showed that there were several important differences in the flow field that would lead to a
considerably different interaction of forces acting on the board.
Through the second stage of the project a mount and camera system was successfully developed which allowed
the angles of the right hand fin to be measured whilst riding actual waves with minimal disruption to the rider‟s use
of the board. In doing so the results have consistently shown that the range of flow angles that the fins encounter are
considerably broader than predicted by Brown et al in their analysis of surfboard fin performance in 2004. The
project has been a great opportunity for the author to conduct a research project and in doing so broaden his
knowledge of a subject that is fascinating and contribute a small piece to the overall understanding of surfboard
hydrodynamics.
VI. Recommendations
With the results which are presented here there is considerable scope for
further research into the performance of surfboard fins. The findings that the
fins are moving through such extreme angles while surfers are riding waves
would suggest one of two approaches could be employed to improve their
effectiveness. The fin area could be increased, which would allow the same lift
generation at a lower angle of attack, however the downside of this is that a
board would more than likely become stiffer and therefore more difficult to
manoeuvre. The other solution would be to borrow some of the design features
employed by high speed and high manoeuvring aircraft. The author believes
that the next step in developing high performance surfboard fins lies in the use
of vortex generation through leading edge extensions and highly swept fins to
allow effective operation at the higher angles that have been found through the
course of this research (Patent pending on this at present).
Another region which would be very interesting to study for a future project
would be the performance of the rails in generating lift on a wave. Testing
could quite easily be conducted using pressure sensors along the rail. By doing
this it would move the knowledge of surfboard performance along another step.
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Final Thesis Report 2009, UNSW@ADFA
Figure 45: An F/A-18
employing its leading edge
extensions to their full
extent in this high angle
manoeuvre (Wikimedia,
2008)
Acknowledgements
This report and project have been a really great learning experience for me, and a great chance to learn more
about a topic that I am passionate about. Understandably this would not have been possible without the support that
I have received throughout. First of all my thanks go to Dr Michael Harrap. Your help and guidance with this
subject has been absolutely invaluable throughout. Next I would like to thank the University workshop staff, in
particular Doug Collier, Andrew Roberts, Geno Ewyk, Mike Jones, and Marcos De Almeida, for your help and
advice in getting my designs working. To Andrew Kiss my thanks for providing the essential background on
Oceanography, and to Peter Killen your consultation on this work was greatly appreciated. Finally many thanks to
my mum and Amy for putting up with me throughout the year for providing support for me to achieve this. To dad I
dedicate this work, my many thanks, you taught me well.
References
1.
Brown, S., Carswell, D., Foster, G., Lavery, N., “Optimization of Surfboard Fin Design for Minimum Drag by
Computational Fluid Dynamics” 4th International Surfing Reef Symposium, University of Swansea, 2005
2.
Butt, T., Grigg, R., Russell, P., Surf Science: An Introduction to waves for surfing, University of Hawaii Press,
Honolulu, 2008, Chapters 4 – 5
3.
Corona, H., Photographs from Victoria, taken on 02 July 2009
4.
Hendrix, T., “Surfboard Hydrodynamics: Part 1 Drag” Surfer Magazine, Vol 9, No 6, 1969
5.
Hornung, H. G, Killen, P, “A stationary oblique breaking wave for laboratory testing of surfboards” Journal of Fluid
Mechanics, Vol 78, Part 3, pp 459 – 480, 1976
6.
Hyatt, A., New Zealand Adventures, taken on 13 July 2009
7.
Kiss, A, “Marine Science 1A Field School Notes Jervis Bay 2008” School of PEMS, UNSW @ ADFA, 2008
8.
“MATHWORKS Online Support”, Mathworks Inc, www.mathworks.com, 2009
9.
Muirhead, S., Northern Points, Swell Net sessions, www.swellnet.com.au, 2009
10. Munson, B., Okiishi, T., Young, D., Fundamentals of Fluid Mechanics, 5th Ed, John Wiley & Sons, USA, 2006
11. Neville, K., ASL Hot 100: Amigos, ASL Publications, Australia, 2005
12. Paine, M. “Surfboard Hydrodynamics”, BE(MECH) Thesis, Mechanical Engineering Department, Sydney University,
1974
13. Pattriachi C, “Design Studies for an Artificial Surfing Reef: Cable Station, Western Australia.” Proceedings of the 1 st
International Surfing Reef Symposium, Centre for Water Research, University of WA, 1997
14. Peachey, D. R, “Modelling Waves and Surf” ACM Siggraph Computer Graphics, Vol 20, No 4, pp 65 – 78, 1986
15. Robertson, M., Puerto Escondido, Swell Net sessions, www.swellnet.com.au, 2008
16. Savitsky, D., Prowser, E. & Lueders, D. H. “High speed Hydrodynamic Characteristics of a flat plate and 20o dead rise
surface in Unsymetrical Planing Conditions” NACA TN 4187, NASA, 1958
17. Sedov, L.I, Two Dimensional Problems in Hydrodynamics and Aerodynamics, Interscience, New York, 1965
18. Sheffield, N., NSW, Swell Net sessions, www.swellnet.com.au, 2009
19. Stoker J.J, Water Waves: The mathematical theory and applications, Interscience, New York, 1957, Chap 10
20. Wagner, H. “Phenomena Associated with Impacts and Sliding on liquid surfaces” NACA TN 1139, NASA, 1932
APPENDICES
Appendix A. Definition of angles
26
Final Thesis Report 2009, UNSW@ADFA
A1
Appendix B. Force Balance
Appendix C. MATLAB code for tests
Appendix D. Full numerical results from fin angle testing
27
Final Thesis Report 2009, UNSW@ADFA
A2
A3
A4