Final Report - CFD Analysis on Aerodynamic

CFD ANALYSIS ON
AERODYNAMIC
PROPERTIES OF
SURFACE ROUGHNESS
OF AN OBJECT
Rugby balls have poses complex aerodynamic structures. Unlike other
sports with a spherical shape, rugby balls n ellipsoid shape. There are
only a few documentations which look into the aerodynamics of a rugby
ball as opposed to the numerous studies on different sports ball. To
further knowledge surrounding the Aerodynamic characteristics of a
Rugby ball a Computational study of different Wind speeds and Yaw
angles have been performed. A resulting Airflow around the Rugby ball
was determined.
Keywords:
Aerodynamics, Rugby
ball, Drag Coefficient,
Lift Coefficient, CFD

CONTENTS
1. INTRODUCTION ..................................................................................................................2
1.1. Background Research..................................................................................................2
1.2. Literature Review ........................................................................................................8
1.3. Aims and Objectives..................................................................................................11
2. METHODOLOGY................................................................................................................12
2.1. Design (Model)..........................................................................................................13
Design Process..................................................................................................................14
Yaw Angles........................................................................................................................16
2.2. Flow Simulation (Test)...............................................................................................16
3. RESULTS AND DISCUSSION...............................................................................................22
Limitations/Challenges.........................................................................................................26
6. CONCLUSIONS ..................................................................................................................27
7. RECOMMENDATIONS FOR FURTHER WORK ....................................................................28
8. REFRENCES........................................................................................................................29

CFD Analysis Jermaine Ako 2014
Page 1
Table of Figures
Figure 1: Rugby match in action........................................................................................2
Figure 2: A Prolate spheroid formed by rotating an ellipse about its major axis. ................2
Figure 3: Gilbert ball used in Rugby Union. (BBC.Sport) .....................................................3
Figure 4: Pebble grain surface stamped on a leather American football.............................3
Figure 5: Different Rugby ball surfaces..............................................................................4
Figure 6: Aerodynamic forces acting on objects.................................................................5
Figure 7: Flowchart of fluid analysis using Solidworks Flow Simulation..............................7
Figure 8: External dimension of Rugby ball...................................................................... 13
Figure 9: A Rugby ball ..................................................................................................... 13
Figure 10 ........................................................................................................................ 14
Figure 11 ........................................................................................................................ 14
Figure 12: CAD model and Wind tunnel Meshing............................................................. 15
Figure 13: Final Rugby ball Design 1 ................................................................................ 15
Figure 15: Settings for analysis type................................................................................ 17
Figure 16: Initial and ambient conditions wizard ............................................................. 17
Figure 18: Wall conditions wizard ................................................................................... 17
Figure 19: Initial and Ambient Conditions ....................................................................... 18
Figure 20: Result resolution ........................................................................................... 18
Figure 20: Computational Domain parameters................................................................ 19
Figure 23: Global goal set to X-Component of Force ........................................................ 20
Figure 22: Expression for equation goal .......................................................................... 20
Figure 23: Solidworks Frontal Area of Ellipsoid Calculation.............................................. 21
Figure 24: Solver window for simulation of flow around Rugby ball................................. 21
Figure 25: Cut plot window............................................................................................. 21
Figure 27: Velocity vectors around the rugby simplified ball at 90° yaw angle.................. 24
Figure 28: Static distribution around ball at 90° yaw angle .............................................. 24
Figure 29: Drag Coefficients (CD) as function of yaw angles and wind speeds ................... 25
Figure 30: Error of computational geometry ................................................................... 26

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Figure 2: A Prolate spheroid formed by
rotating an ellipse about its major axis.
Figure 1: Rugby match in action
1. INTRODUCTION
Some sports are commonly known for their use of a ball specified for the type of play
in adherence to rules and regulations. Balls are commonly rounded and spherical, but for
some balls they possess an oval shape. The aerodynamic characteristics around a ball plays a
huge part in the speed, trajectory of the ball when in flight as well as where and how the
ball lands. Regardless of the importance of understanding the flow around a ball there
doesn’t seem to be a large catalogue of information surrounding this area. [Alam],
performed studies on the flow around sports balls. The 2012 Olympics showed that the
distance at which the ball is kicked can make a difference to the outcome of the game
whether it is a small kick or a set kick between the goal posts. Open literature doesn’t
contain This section looks into the sport of Rugby and its roots, along with a look at the ball
used in the sport. The effects and measurement of surface roughness as well as
Aerodynamic forces acting on objects travelling through fluid are detailed in addition to
different flow types. The Importance of CFD in fluid study. Finally the aims and objectives of
this paper are outlined. Since there aren’t facilities to perform a replicated experiment, the
next available option is the use of a model tested in CFD software. Only the drag Coefficient
was calculated in this paper and plotted against the yaw angles.
1.1.Background Research
Rugby is an intense physical sport which was founded in the UK and slowly spread to
other countries. It is similar to American Football, with less defence armour. It uses an oval
shaped ball to play the game. It is believed that the gaming sport was started in 1823 when
‘William Webb Ellis’ picked up a Football during a
match and ran towards the opposing goal (History,
2007). The ball in the game plays a vital role besides
the ability and form of the player. It helps improve
handling and kicking skills. (BBC.Sport)
The Sport is played using a prolate spheroid
(oval) shaped ball shown in [Figure 2]. A prolate
spheroid can be described as a spheroid where the
polar radius is greater than the equatorial radius. It
is also seen as a surface of revolution about an ellipse’ major axis (Wikipedia, 2013). The ball
is made of four panels sewn together. This is
identical shape is also used in other sports i.e.
American football. American balls have more
pointed ends while rugby balls have more rounded
ends (Wikipedia, 2013).
The first Rugby balls were made of pigs
bladder covered in tightly knitted leather, likely
made from deer (BBC, 2006). When the bladder was

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Figure 4: Pebble grain surface stamped on a
leather American football.
inflated it represented a plum like shape, hence the Oval shape which is still continuously
used today (Sport.Academy). “They’re stitched inside out and begin Five or six stitches are
left loose to enable the ball to be turned the right way and finished with a new thread”.
The ball must be oval and made of four panels. Length in line: 280-300mm,
Circumference (end to end): 740-770mm. Circumference (in width): 580-620mm.
Weight: 410-460 grams. Air pressure of 65.71–68.75 kilopascals, or 0.67–0.70 kilograms per
square centimetre, or 9.5–10.0 lbs per square inch” (Board, 2013).
The original ball design would get heavy when weather conditions were rainy making
it slippery and harder to grip under wet circumstances (BBC.Sport). Technology has seen
new hi-tech waterproof materials which make the ball easier to handle in wet and muddy
conditions, whilst keeping their shape and withstand the weather - which can alter between
kick-off and the final whistle (BBC.Sport).
[Figure 4] shows a macro/zoom of the surface of a Rugby ball. The surface of each
panel is stamped with a pebble-grain texture in
order to assist players grip.
Figure 3: Gilbert ball used in Rugby Union. (BBC.Sport)

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A look at [Figure 5] reveals the measurements of four different balls which each have
a different pimple orientation. These measurements will be used as a pimple sizing and
orientation guide. Pimple height: 0.5mm, Diameter 1 mm, spaces ranging from 0.2 to 2.6.
Surface Roughness has been found to have effects on the efficiency of an object
when in use. The conditions under which certain items are faced with mean their surface
roughness properties change after certain time of use. “Indicates the state of a machined
surface” (OLYMPUS, 2013).
Roughness impacts quality and function of a surface. It can either be visible or can be
felt. A few reasons why a surface face may experience abnormalities are; accidental or
intentional and can be gained by; tool wobbling or the nature of the machined material,
these may be measured in two ways; contact type or non-contact type. Contact type: Form
and size of irregularities vary. There are two ways to measure roughness. The first way is a
linear roughness measurement normally used; it is measured along a random long line
allowing long dimensions to be measured. The second way is a real roughness measurement
using an area, starting to arise, measured in a random rectangular range, this method is
more accurate.
For the contact type method a stylus makes direct contact with the surface. As the
roughness changes, the stylus moves up and down along with it. Non - contact type is
different, light is reflected and read with no contact made to the object.
Figure 5: Different Rugby ball surfaces

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Figure 6: Aerodynamic forces acting on
objects
Tests have been performed in order to improve accuracy and grip of a ball such as
the Gilbert's Xact match ball, used during the Rugby World Cup 2003, however there aren’t
any sources of these literatures for the open public. This could most likely be due to other
competing brands potentially abducting results.
Rugby is a worldwide known sport, even
though this shows the popularity of the sport, there is
minimal research imposed within this area. The recent
2012 London Olympics showed the values towards the
distance at which the ball was kicked, and the result of
the match.
Objects which move through air are subjected
to aerodynamic forces acting on the object. There are
four forces which act on an object moving through air; Lift, Weight, Thrust and Drag. The
intensity of each individual force determines the objects behaviour through the air either;
slower, faster up or down.
Weight exists with everything on earth due to gravity. The more weight something
possess the more upward push force is required. A paper plane would need less lift than an
aeroplane. Lift is the direction of this force is upward and opposite to opposite to weight. It
moves objects upwards while. The object will only go upwards when this force exceeds that
of the weight force. All flying objects are a result of this force, such as helicopter propellers
and aeroplane wing. Drag force is the cause of slowing down objects. The more drag
experienced by an object the slower it is to travel, for example moving through water is
harder than moving through the air due to water having more drag properties. Round
surfaces have less drag than flat surface. Narrow surfaces have less drag than wide ones.
Thrust flows against an object in the opposing direction to drag. This force moves results in
the motion of an object heading in a forward direction. A forward direction is only
achievable if the thrust force is more than the drag force. Items which move through fluids
experience drag. The drag can be calculated using the following equation: 𝐷 = 𝐶 𝐷
1
2
𝜌𝑉2
𝐴
where; D = drag force (N), cd = drag coefficient, ρ = density of fluid (1.2 kg/m3 for air), V =
flow velocity, A = characteristic frontal area of the body 𝐴 =
𝜋𝐷2
4
=
𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑓𝑟𝑜𝑛𝑡𝑎𝑙 𝑎𝑟𝑒𝑎 (Toolbox). 𝐶 𝐷 =
𝐷
1
2⁄ 𝜌𝑉2 𝐴
= 𝐷𝑟𝑎𝑔 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, this is the non-
dimensional coefficient of drag (Alam, et al., 2010).
CFD has had a major effect on the way we look at fluid Dynamics today. It is
important to understand its evolution and how it helps the Engineering world today. In fluid
dynamics, there are three ways to conduct study’s; Theoretical, experimental,
computational. CFD gives a third perspective in the philosophical study and development of
fluid dynamics.

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CFD is a great research tool. The results obtained can be compared with results from
a laboratory wind tunnel experiment. Benefits of CFD are that a Wind tunnel is heavy while
CFD can be carried by hand with the use of a USB, essentially being a transportable wind
tunnel with the ability to be accessed on terminals across the globe. Computer experiments
are considered numerical experiments. CFD has the ability to study the differences between
laminar and turbulent, at a specified unchangeable value by means of flicking a switch, or
changing a few settings for the computer.
CFD is now seen as an equal partner with theoretical and experimental to figure fluid
dynamic issues. CFD is only a third approach which compliments other methods but doesn’t
replace them. The future requires all three to be equally balanced.
The study of Subsonic compressible flow over the Wortmann airfoil is example of
CFD being required. This study Trying to see the difference in laminar and turbulent flow at
Re = 100,000. CFD showed laminar flow unsteady. Numerical time-marching technique used
time-accurate finite-difference of the unsteady Navier-stokes equations. This CFD analysis
allowed for Clarification of the flow which wouldn’t have been able in a laboratory. CFD
allows an in depth study of the difference between the laminar and turbulent flow, with
other parameters being equal which would be a difficult procedure in a laboratory
experiment. When used in parallel with physical experiments CFD helps to interpret these
laboratory results and its phenomenological aspects. This was a test of lift coefficient versus
the angle of attack and drag coefficient versus angle of attack. Uncertainty in wind tunnel
experiments whether flow was laminar or turbulent. Comparing experiment against
computation, the flow was found to be turbulent after comparing the CFD data with the
experimental data. Laminar flow data was far off by but turbulent flow matched up. There
are three fundamental principles which outline the flow of fluid:
o Mass [conserved]
o Newton’s second law [force = mass x acceleration]
o Energy [conserved].
CFD requires the need of up to millions of numbers to be operated; this would take a
normal human an extremely long time to complete. It is possible to represent these
principles as basic math equations, with their general form being either integral or partial
differential equations. CFD replaces the need of an equation, with discrete algebraic forms.
Once a description of the problem has been provided, the results are a collection of
numbers with a “closed-form analytical solution.” An image of a flow field around the object
at discrete points in time, are also resultant.

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CFD is a third dimension approach to looking at
objects and their characteristics as the move through
fluid. It is a process which is ever expanding and will
continue to be used side by side with theory and
experiment. CFD has aided the link between
aerodynamicist and fluid dynamists. It has impacted the
design of airplanes and is suggested to be used more
often for the next decade. “CFD is a growth industry
with an unlimited number of new applications and new
ideas just waiting in the future.” p g 532
The cost of conducting multiple wind tunnel
experiments is a factor that CFD avoids due to its
computational based approach. This in turn saves
money for companies and cuts down on the amount of
time and resources which would be required for the
physical experiments. (John D.Annderson, 1995). CFD
will be shown to be a productive and sensible method to
use in Engineering. Solidworks Flow simulation follows a
pattern shown in [
Figure 7]. Solid works will be used to conduct the project. This section takes a look
into the Solid works software and how the object will be tested.
To perform the fluid analysis, the flow simulation in Solidworks needs to be set up by
selecting; a fluid, a solid, settings of the wall condition and the initial ambient conditions.
Flow simulation has to be categorised as either internal or external. The internal setting is
relative to flows bounded by walls such as pipes. In the case of this study the setting shall be
Figure 7: Flowchart of fluid analysis
using Solidworks Flow Simulation

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external because the flow of the fluid occurs externally around the outside of the ball. The
fluids possible to select are: gas, liquid, incompressible flow, non-Newtonian liquid, real gas
or steam. In the case of this study the fluid, Air shall be used. Physical Features to be taken
into account when conducting a flow simulation are: heat conduction in solids, radiation,
and time varying flows, gravity and rotation. Though it is possible to look at the temperature
and humidity of the air surrounding the ball, in this study the characteristics of the air plus
the physical features of the rugby ball are to be treated as negligible though possibilities into
future work in that area is recommended. Roughness of the surface can also be selected.
After the solid has been exported into the Flow simulation study and the Settings
have been set up, a mesh is created. Meshing of Solidworks flow consists of cells in the form
of rectangular parallelepipeds seen in the mesh in [Figure 12]. After that, results can be
visualized by cut plots, surface plots, flow trajectories +more. Limitations exist with
Solidworks. It can’t conduct flow over a moving part.
A look at previous works relating to the aerodynamic characteristics of a rugby ball
will be conducted in the next section. A lot of he studies carried out were by Alam.

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1.2.Literature Review
Ball Length Diameter Speeds Angles Ref Journal
SUMMIT 280mm 184mm
[60-80 inc 20]
60, 80, 100,
120 140
+100° to -
80°
Inc - 10
(Djamovski, et
al., 2012)
DRAG
MEASUREMENTS
OF A RUGBY
BALL USING EFD
AND CFD
Summit
Australia
280 184
40 km/h to 120
km/h inc 20
40, 60, 80, 100,
120
±90º
Inc-10
(ALAM, et al.,
2008)
An Experimental
and
Computational
Study of
Aerodynamic
Properties of
Rugby Balls
Summit
Australia
0.28m 0.184m
60, 70, 80, 90,
100, 110, 120,
130
-90º to
+90º with
an
increment
of 15º.
(Alam, et al.,
2005)
A comparative
study of rugby
ball
aerodynamics
STEEDAN 5 and 15 ms� 1 0° to 60°
(Vance, et al.,
2012)
Aerodynamics of
a Rugby Ball
SUMMIT 280 184
60, 80, 100,
120 140
±90º
Inc-10
(Alam, et al.,
2010)
A comparative
study of rugby
ball
aerodynamics
From the available journals and articles out there, a few open literature studies in
regards to Rugby balls or oval shaped objects exist. There are few journals which take a look
at Aerodynamics through the use of CFD such as the look at Surface Roughness of air foils by
(Hooker, 1933). There are many articles on Sports ball Aerodynamics (especially Footballs)
but these are typically spherical balls such Tennis balls and golf balls tested by (Alam, et al.,
2011) (Djamovsk, et al., 2012). The only available journals for rugby aerodynamic testing
were (KINS, et al.) (Alam, et al., 2010), a similar type of CFD experiment was conducted with
an American football by (Vance, et al., 2012) (Alam, et al., 2012) this was performed in a
wind tunnel.
Looking through other similar journals, only a few were relative to this study. Those
that were performed on a Rugby ball were a CFD analysis but, these were performed in a
Wind Tunnel with an actual ball. (Alam, et al., 2012) Looks at an American football, similar to
that of a rugby ball, tested on NFL and NCAA ball. Inflated to 13 psi (89.6 kPa) American
footballs have a rough surface but experiences drag coefficient similar to other oval that of a

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10
rugby ball or an Australian football. The study measures aerodynamic forces at different
wind speeds and yaw angles simulating crosswinds.
Wind tunnel
The studies conducted have been within a wind tunnel with the ball in a stationary
position. They were tested at different yaw at different angles. RMIT Wind tunnel was used,
Closed return circuit, approx. 150 km/h max speed. The tunnels dimension are; 3m (wide)
2m (high) 9m (long), and is equipped with a turntable for obtaining different yaw angle.
These specifications of the tunnel are identical to that used by (Alam, et al., 2012).
Drag lift and side force plus opposing forces were measured. For crosswinds effects
+-90degree yaw angles were used. Measured at a range of wind speeds 40 km/h to 130
km/h with increments of 20 km/h. Yaw angles were at increments of 15 degrees up until +-
90 degrees. Non dimensional parameter, drag coefficient was measured.
In order to measure the air speeds an ellipsoidal head Pitot-static tube was connected to a
MKS Baratron pressure sensor (type JR-3), and computer software was used to digitize and
record all 3 forces (drag, side and lift forces) and 3 moments (yaw, pitch and roll moments)
unison. Tested at speeds ranging from 20 km/h to 130 km/h at wind speeds under +90º to -
90º yaw angles with an increment of 15º. (ALAM, et al., 2008)
Balls
The balls used for this experiment were a ‘Summit’ rugby ball (4 Synthetic rubber
segments and an ‘AFL Sherrin ball’ (4 leather segments). Dimensions: ‘Summit’ Diameter =
184mm length = 280 mm. ‘AFL’ Diameter= 172 mm, length = 276 m. Both balls were
pumped up to a pressure of between 62 – 76 kPa. Bottom edge of ball and tunnel floor was
420mm and considered negligible along with the effects of the sting mount. Study was
performed in a RMIT wind tunnel with a max speed of 150 km h-1 in a closed return circuit.
Re
Not much was change in Re was found when the ball was at 0° Yaw angle. When the
ball was facing yaw angles between 75° and 85°, the Re was more significant (this was
experimentally) for the CFD study on the other hand there was no noticeable change
between both the balls for the Re.
Tunnel
The experimentally determined drag coefficient (0.18 at 0º yaw angle and 0.60 at
90º yaw angles) is higher compared to computationally estimated drag coefficient for the
smooth Rugby ball (0.14 at 0º yaw angle and 0.50 at 90º yaw angles), but the experimental
value is lower at 0º yaw angle compared to the value of pimpled Rugby ball (0.22).

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11
However, it is higher at 90º yaw angles compared to the pimpled Rugby ball (0.55). The
Reynolds number dependency was noted at 90º yaw angle in experimental analysis.
However, a small variation at lower Reynolds numbers was noted in computational
analysis.
Results
R-drag coefficient can be almost four times higher under crosswinds. Ball has rough
surface and pointed edges. NCAA balls have semi-circle stitching on each pointed edge
which could, make airflow complex. NFL balls don’t have seams at edges. With no
knowledge of the drag coefficient it is difficult to create a model of the flight trajectory
Both CFD and experimental results have shown similar trends. However, in reality, the
experimental approach is more realistic as it incorporates the real flow. The study was
conducted in same wind tunnel as (Peters, 2009) (Alam, et al., 2012). At 0 yaw angles
Average cd was 0.18 experimentally, CFD: 0.14 smooth, 0.22 pimpled.
The Results were plotted in a graph: Drag coefficient was plotted against yaw angles. Results
at 0 degree yaw angle was NFL= 0.19 to NCAA=0.2. NCAA being higher may be due to
surface profile. Average drag between 0.18 – 0.20 [major axis pointed to wind direction].
0.75 - 0.78 [minor axis to wind direction]. NCAA has slightly higher drag coefficient than NFL
ball. There is a Reynolds number dependency at yaw angles over +-50°. Crosswinds make a
difference as the drag coefficient can be 4 times higher under +-90° yaw angles
Symmetry
A close inspection has revealed that the rugby ball is not fully symmetrical along the
longitudinal axis. The ball surface was rough and was not fully oval shape as it was made of
four segments. On the other hand, the rugby ball in CFD analysis was fully symmetrical along
the longitudinal and lateral axes. The surfaces were smooth and pimpled, and the flow was
uniform. The cross sectional area was approximately circular compared to the real Rugby
ball and the cross sectional geometry was slightly larger compared to a Circular geometry
that modelled in CFD.
My work
Due to the lack of aerodynamic information available to the public there is a need for
continuous study. The focus behind this work is to study the aerodynamic property of drag
around a rugby ball

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12
1.3.Aims and Objectives
Aims
The aim of this paper is to computationally study the flow around a Rugby ball at
different wind speeds and yaw angles, along with flow visualisations of the flow at different
angles.
Objectives
1. Research the necessary fields associated to project.
2. Understand the current design of a rugby ball and the way it is designed.
3. Use SolidWorks to design a model a Rugby ball comparative to the rules and
regulations produced by IRB (Board, 2013).
4. Test the 3D Model in SolidWorks flow simulation and compare against existing Rugby
Ball Simulations.

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13
2. METHODOLOGY
Since it is important to complete the set objectives as best as possible, this section
explains and shows the resources which will be needed in order to achieve them. This study
will be taking a computational approach and an organised view from start to finish as to
how the objectives will be tackled is needed. In order to make sure the methodology is
going to plan, a Gantt chart shall be presented in the Appendix outline when and how long
necessary takes are going to take.
1. The research needed will be of the Ruby ball and its parameters along with the
way it’s manufactured and the materials involved.
2. Books, Journals and Internet will be the necessary resources in this field.
Including relative literature will be required. The relative obtained information
shall be laid out in a report form for view of the results.
3. The Rules and Regulations should be known at this point and will be a guideline
to the parameters that he Rugby ball cannot exceed. With research done into
other Rugby balls studies, there shall be knowledge of previous parameters used.
4. The Rugby ball will be designed and require testing by means of CFD, to achieve
this, it shall be put through the Flow Simulation extension of SolidWorks. Further
research will be needed to understand the functionality of the flow simulation of
solid works, such as video tutorials. The size settings of the wind tunnel that the
rugby will be tested in will be firstly necessary. The Drag equation will have to be
set in order for Solidworks to return back the required results.
SolidWorks is Computational software used for the purposes of design and testing.
There are other software’s out there that can perform similar tasks as SolidWorks. GAMBIT
is an example of 3D modelling software which was used by (KINS, et al.). SolidWorks is the
main software to be used in this study due to it being only software readily available.
An exact replica of the ball being used was difficult has there was no physical
representation to analyse, neither were there minor dimensions such as seam size and
surface texture roughness. A 3D model will be designed with the use of solid works and a
CFD Analysis will be used on the object of different wind speeds to resemble the object
moving through the air.

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14
2.1.Design (Model)
Measurements of the Drag Coefficient were made using the Flow simulation add-in
of Solidworks. In order to conduct the flow measurements a simple model of an official
Rugby ball was created using SolidWorks. The dimensions given were 280 mm (Length) and
184 mm (Diameter) external
dimensions of the rugby ball can be
viewed in [Figure 9
Figure 8]. Balls are made of four segments of synthetic rubber stitched together to
achieve the oval shape. A semi-circle was sketched and revolved around the Z axis.
In [Figure 9] you can see an image of an official rugby ball. From the IRB Rugby Law 2
(Board, 2013), the specific dimensions for the rugby ball were outlined earlier. The rule
states that the ball Length should be between 280 mm to 300 mm length. Previous journals
such as [ref] have experimentally tested balls manufactured by: Gilbert, SUMMIT and
SEEDAN
a) Longitudinal view b) Lateral view
Figure 9: A Rugby ball
Table 1: Table 1: Ball Parameters
Diameter 184 mm
Length 280 mm
Figure 8: External dimension of Rugby ball

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15
Design Process
Figure 10
The “ellipse sketch” tool was used to sketch an ellipsoid. A centreline was created in order
to achieve a semi-circle sketch by trimming the bottom half of the divided ellipse.
Figure 11
Using the “Revolved boss/base” tool the sketch was revolved 360 degrees to achieve an
ellipsoid. A surface cut was created to replicate the seams of a real ball at 2mm depth [REF].
The ball was smooth for the first set of angles. To test for surface roughness a pimpled
texture was added to the surface seen in [Error! Reference source not found.].

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16
a) CAD model b) Meshing of wind tunnel and
Rugby ball
Figure 12: CAD model and Wind tunnel Meshing
Following the completion of the design of the Rugby ball in SolidWorks, the ball will
tested using the Flow simulations in SolidWorks.
From the aid of the IRB Rules and the study by (Djamovski, et al., 2012) the ball was
designed using a similar method of creating one semicircle panel and rotating it to create an
oval shape for the ball. The dimensions were kept to that of the ball used within that same
experiment. The difference with the balls used by them and the ball tested for this study is,
the surface roughness of the ball has been altered. None of the Journals have a look at the
different orientations of the pimples of the ball.
In my design the given surface textures were computationally accurate. When a
physical ball is to go into production, there will be different and unequal roughness imprints.
The design of the ball has achieved the necessary ellipsoid shape for the flow tests to be
tested on but it terms of its reliability in reflecting a real life rugby ball is questionable.
Figure 13: Final Rugby ball Design 1

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17
Yaw Angles
To create the effect of the turntables used in the studies of [ref] to achieve different
yaw angles, the model part was brought into an assembly. An axis going through the balls y
axis was mate coincident with the assembly axis also in the y direction. The planes were
mated at the angle the ball was being tested at the time. The first being 0° followed by a
mate of a 30° angle.
2.2.Flow Simulation (Test)
The Study the flow will be conducted in this section here with visuals of the flow
simulation surrounding the ball. These results shall be compared against those obtained
experimentally such as (Djamovski, et al., 2012).
The RMIT wind tunnel used to analyse the flow around a rugby ball in the works of
(Djamovski, et al., 2012) measured 3m wide, 2m high and 9m long. The parameters would
be scaled down to suit the size of the rugby ball as well as avoid being too large for the
computer to process the analysis. [Table 2] shows the parameters used for the
computational wind tunnel in this paper. The dimensions are taken from the works of (REF),
where a scaled down version of the RMIT Wind Tunnel was used in order to compensate for
computer speed and to reduce the required CPU time and computer memory.
Table 2: Parameters of (Djamovski, et al., 2012) CFD of a Rugby Ball (mm)
Length Width Height
2500 2000 2000
The Analysis needs to be set up using the required conditions; the following is the
step through process to achieving the first test and repeating at the different angles.

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18
The unit system was kept at default, the Analysis Type was set to External and remains at
that setting throughout the remainder of the analysis, with the reference axis being the x-
axis.
Figure 15: Initial and ambient conditions wizard
The project fluid selected was Air (gases).
Figure 16: Wall conditions wizard
Figure 14: Settings for analysis type

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19
The Wall conditions for the first ball were set to default, to firstly to gain similar results to
those performed by others.
Figure 17: Initial and Ambient Conditions
The Velocity was set in the x direction and was firstly set to 6.67 m/s. following the
completion of this study, the velocity would be adjusted o the selected speeds for this
paper. From [ref ] the RMIT tunnel is said to have a 1.8% turbulence. For that reason the
conditions were changed to reflect that.
Figure 18: Result resolution

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20
The resolution is kept to 3 so the computer to can perform the test as quickly and effectively
as possible.
Figure 19: Computational Domain parameters
The scaled down dimensions were outlined earlier. The dimensions were set so the ball was
near the entry of the tunnel. The box is shown in [Figure 12(b)].

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21
Goals
Setting up the study to calculate Drag force and Coefficient of drag
Figure 20: Global goal set to X-Component of Force
Once the wizard has been set up to replicate the conditions of the full size wind tunnel, the
next step is to set up goals. This force in the (x) direction is selected for the direction of the
wind through the tunnel.
Figure 21: Expression for equation goal
Inserting an equation goal in order to calculate the coefficient of drag on the ball using
Equation: ({GG Force (X) 1}*2)/(1.204*16.67^2*0.027). This equation uses the coefficient
drag equation: 𝐶 𝐷 =
2𝐷
𝜌𝑉2 𝐴
where; ρ = 1.204 (Air density), (Velocity) V = 16.67, (Drag Force) D
= GG Force (X) 1, (Area) A = 0.027
The hand calculations for the Frontal area: 𝐴 =
𝜋0.182
4
= 0.02659044𝑚 = 0.027 𝑚

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22
Using the evaluate feature in Solidworks for the cross section of the ball and the
surface area was calculated and divide by two. This resulted in the validation of the hand
calculations of the equation outlined earlier. (Surface area) 53758.93/2 = 26879.46 mm2.
(Converting from mm2 to m) 26879.465/106 = 0.026879465m = 0.027m
Running the test
Figure 23: Solver window for simulation of flow around Rugby ball
When everything is set up then the test is run and the results are presented, these results
are then plotted on a graph for analysis.
Figure 24: Cut plot window
Cut plots are inserted to get a flow visualisation of the pressure distribution and velocity.
This process is repeated for the smooth and the pimpled ball.
Figure 22: Solidworks Frontal Area of Ellipsoid Calculation

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23
3. RESULTS AND DISCUSSION
From the beginning of this paper, the intention was to test a Rugby ball at different
speeds and angles with the use of SolidWorks Software 2013. The ball was tested at speeds;
60, 80, 100, 120km/h at angles of 0° - 90° with increments of 30° in respect to the direction
of the wind from the inlet of the x-axis. A look at the flow was made for the speeds from 60
km/h to 120 km/h. Cut Plots were made for the velocity and pressure, however only the
flow visualisation of the velocity vectors and pressure distributions at 0° and 90° yaw angles
at 120 km/h are presented here. The pressure distribution is seen in [Figure 25Error!
Reference source not found.] and [Figure 26]. At 90°, the highest negative pressure is seen
for the side facing the wind. The ball was he force measured was converted into non-
dimensional measurements. The flow around the rugby ball seen in [Error! Reference source
not found.] at 90° is seen to be quite complex, this flow is a result of the increase in drag
coefficient when increasing the yaw angle. A similar flow pattern is visible for 0° yaw angle
in [Error! Reference source not found.]. As expected the results indicate symmetry in the
results, this being due to the model being generated by accurate dimensions. Drag
Coefficients (CD) for the speeds of 60 – 120 km/h are plotted against the yaw angles in [
Figure 27]. A variation in the vector velocity around the ball at 0° can be seen to be
slightly different to that of 90° yaw angles. Aerodynamic forces were converted to non-
dimensional values and plotted. The computational analysis resulted in an average drag
coefficient of […] for the smooth ball, the […] ball and the[ …] ball (respectively) at zero yaw
angles. Flow separations are seen to occur at 75% from the front edge of the ball, with the
major axis in the x-direction. The flow is seen to be more streamlined and attached.
However at 90 degrees the separation is seen to be complicated. The pressure distribution
is not symmetrical around the ball.
Table 3: Speed conversion from km/h to m/s
km/h m/s
1 60 16.67
2 80 22.22
3 100 27.78
4 120 33.33
Table 4: Tested yaw angles
1 2 3 4
0° 30° 60° 90°

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24
Surface parameters for the velocity of 16.67 ms:
Table 5: Local surface parameters
Local parameters
Parameter Minimum Maximum Average
Bulk
Average
Surface Area
[m^2]
Pressure [Pa] 101057.116 101543.354 101272.343 0.144511955
Density (Fluid) [kg/m^3] 1.20021383 1.20587628 1.20292117 0.144511955
Velocity [m/s] 0 0 0 0.144511955
Velocity (X) [m/s] 0 0 0 0.144511955
Velocity (Y) [m/s] 0 0 0 0.144511955
Velocity (Z) [m/s] 0 0 0 0.144511955
Mach Number [ ] 0 0 0 0.144511955
Heat Transfer Coefficient
[W/m^2/K] 0 0 0 0.144511955
Shear Stress [Pa] 0 4.93791467 0.613789679 0.144511955
Surface Heat Flux [W/m^2] 0 0 0 0.144511955
Temperature (Fluid) [K] 293.075232 293.337228 293.231751 0.144511955
Relative Pressure [Pa]
-
267.883922 218.353561 -52.6566186 0.144511955
Table 6: Integral surface parameters
Integral parameters
Parameter Value
X-
component
Y-
component
Z-
component
Surface Area
[m^2]
Heat Transfer Rate [W] 0 0.144511955
Normal Force [N] 2.14040784 2.13870002
-
0.025262154
-
0.08166846 0.144511955
Friction Force [N] 0.067098851 0.06709838
-8.02882E-
05
-
0.00023811 0.144511955
Force [N] 2.20746405 2.2057984
-
0.025342442
-
0.08190657 0.144511955
Torque [N*m] 0.001274768 0.001190859
-
0.000452501
4.61651E-
05 0.144511955
Surface Area [m^2] 0.144511955
-1.87201E-
18 7.29846E-18 -8.5714E-18 0.144511955
Torque of Normal Force
[N*m] 0.00125864 0.001183309
-
0.000427326
3.66796E-
05 0.144511955
Torque of Friction Force
[N*m] 2.79419E-05 7.55023E-06
-2.51747E-
05
9.48546E-
06 0.144511955
Uniformity Index [ ] 1 0.144511955
CAD Fluid Area [m^2] 0.146488738 0.146488738
Theory
The forces related to the Integral Parameters, shows the drag force (D) as 2.20746405
for 16.67 m/s wind speed at 90° yaw angle shown in [Table 6] found from the List of goals
selected. Drag Coefficient is calculated using the equation:
𝐶 𝐷 =
𝐷
1
2⁄ ∗ 𝜌 ∗ 𝑉2 ∗ 𝐴
=
2.17814
1
2⁄ ∗ 1.204 ∗ 16.672 ∗ 0.027
= 0.482230123
Where 𝜌 is the fluid density, V is the fluid Velocity and A is the frontal area of the ball.

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25
Figure 25: Velocity vectors around the rugby simplified ball at 90° yaw angle
Figure 26: Static distribution around ball at 90° yaw angle

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26
Figure 27: Drag Coefficients (CD) as function of yaw angles and wind speeds

Page
27
Due to the ball being a digital model the flow simulation was symmetrical along both
lateral and longitudinal axes. The cross section of the Model is more circular than a real
rugby ball. The Drag coefficient and the yaw angles are presented in [Figure 27]. At 0° angle,
the CD value for the Rugby ball is (…). The drag coefficient is seen to increase when the yaw
angles increase.
Limitations/Challenges
Figure 28: Error of computational geometry
Each time the ball was being edited or the angle was being changed, an error
message would come up prompting to allow a change to the computational Domain though
for this study the work required the parameters to remain the constant [see Figure 28]. This
made the process longer than intended.
Difficulties when trying to create the model of the ball was trying to achieve a ball
with more rounded edges which is more relative to the rugby union type balls rather than
the pointed edge spheroid type balls used in American football. A first attempt was made at
using the “3 point arc tool” to achieve the semi-circle 2d sketch before revolving it around a
centre axis. Getting the surface of the rugby ball to set a certain texture pattern was a
problem as well. Different sketches on different planes had to be generated.
The Limitations behind SolidWorks is that it can’t detect the effects of aerodynamics
while the ball is travelling through the air. The test was conducted with the ball being in a
static position. To have a better look at the trajectory path of the ball through the air, it
would be suggestive that the ball were to have a trajectory path set for it while wind speed
is direct in one way and a set of results returned.

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28
5. CONCLUSIONS
The aerodynamics of a modelled rugby ball was studied with the use of CFD using
Solidworks software, up to 90 °. There is a complexity fixed with the analysis of a non-
spherical sports ball, even when the analysis was undertaken with the ball in a stationary
position. In this paper an analysis of the aerodynamics of a rugby ball was measured for drag
coefficient of speeds from60km/h to 120km/h for yaw angles 0° - 90°. Based on the findings
and work disclosed the following conclusions can be made:
For the Smooth Rugby ball when the major axis is facing the wind at zero Yaw angles
the average drag coefficient was found to be … and … at a 90° yaw angle. For the ball with a
surface roughness off … the average drag coefficient. The Average drag coefficient for the
smooth ball study was found to be lower than the experimental result. The … surface
possesses slightly higher value of drag coefficient compared to the Rugby ball with …
surface.
These findings can be used for comparison. An Experimental Study is more reliable
than the CFD Analysis due to there being a difference in each individual Rugby ball after
manufacturing. The effect of a surface roughness is important because the drag coefficient
can be […] times higher with a rougher surface. At 90° the drag coefficient is […] times
higher showing that crosswinds will create further drag to a straight flying rugby ball
The CFD findings are indicative only. The experimental study is more reliable due to
the complexity of 3D oval shapes of Rugby ball and the inherent limitations of CFD
incorporating two equation turbulence models. Although rough surface due to pimples gives
better grip to the players, it comes at a cost as it generates more aerodynamic drag.

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29
6. RECOMMENDATIONS FOR FURTHER WORK
There are possibilities of further work to be conducted, to better understand the flow of
a Rugby ball, these recommendations are:
 Effects of spin on aerodynamic; drag, lift and side force are necessary.
 A Study of drag, lift and side force on other Major Rugby ball Brand used in official
games i.e Adidas.
 With modern technology advancing, future work would see a different approach to
gaining accurate results, an idea would be to use a 3D scanner to gauge a true
likeness of the object and its properties and put it under CFD analysis.

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30
7. REFRENCES
Alam Firoz [et al.] A Comparative Study of Rugby Ball Aerodynamics [Journal]. - Dhaka :
[s.n.], 2010. - Vol. 13.
Alam Firoz [et al.] A study of golf ball aerodynamic drag [Journal] // Procedia Engineering. -
2011. - 13. - pp. 226-231.
Alam Firoz [et al.] Aerodynamic drag measurement of American footballs [Journal] //
Procedia Engineering. - 2012. - 34. - pp. 98-103.
ALAM FIROZ [et al.] An Experimental and Computational Study of Aerodynamic Properties
of Rugby balls [Journal]. - London, New York : WSEAS Transactions on Fluid Mechanics,
2008. - Vol. 3.
Alam Firoz [et al.] DRAG MEASUREMENTS OF A RUGBY BALL USING EFD AND CFD
[Journal]. - Dhaka : [s.n.], 2005.
Bardal Lars Morten Aerodynamic properties of textiles [Online]. - January 2014. -
http://www.ntnu.no/documents/11601816/59a31853-ee0e-4f65-ab8a-d16a44ffd033.
BBC Oldest football to take cup trip [Online]. - 25 April 2006. - December 2013. -
http://news.bbc.co.uk/1/hi/scotland/tayside_and_central/4943664.stm.
BBC.Sport Rugby Union equipment: ball [Online] // BBC Sport. - December 2014. -
http://news.bbc.co.uk/sport1/hi/rugby_union/rules_and_equipment/4204838.stm.
Board International Rugby LAWS OF THE GAME. - Dublin : International Rugby Board, 2013.
Djamovsk Victor [et al.] Effects of seam and surface texture on tennis balls [Journal] //
Djamovski Victor [et al.] A comparative study of rugby ball aerodynamics [Journal] //
History Rugby Football Origins of Rugby [Online]. - 2007. - December 2014. -
http://www.rugbyfootballhistory.com/originsofrugby.htm.
Hooker Ray V. THE AERODYNAMIC CHARACTERISTICS OF AIRFOILS [Journal] // NATIONAL
ADVISORY COMMITTEE FOR AERONAUTICS [NACA]. - 1933. - 457.
John D.Annderson JR. Computational Fluid Dynamics (The Basics with applications) [Book]. -
Singapore : McGraw-Hill, Inc, 1995.
KINS SIMON, NASER JAMAL and RASUL M.G. An Experimental and Compuy Balls [Journal]. -
3 : Vol. 3.

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31
OLYMPUS Surface Roughness [Online]. - 2013. - 2014. - http://www.olympus-
ims.com/en/knowledge/metrology/roughness/.
Peters Martin Computational Fluid Dynamics for Sport Simulation [Journal]. - London, New
York : Springer, 2009.
Redding Rogers and Haplin Ty 2008 NCAA Football Rules and Interpretations [Journal] //
NATIONAL COLLEGIATE ATHLETIC ASSOCIATION. - 2008. - pp. 1-93.
Sport.Academy Why are rugby balls egg-shaped? [Online] // BBC Sports News. - December
2014. -
http://news.bbc.co.uk/sportacademy/hi/sa/rugby_union/features/newsid_3733000/37333
04.stm.
Toolbox Engineering Drag Coefficient [Online] // Engineering ToolBox. - Janurary 2014. -
http://www.engineeringtoolbox.com/drag-coefficient-d_627.html.
Vance A. J., Buick J. M. and Livesey J. Aerodynamics of a Rugby Ball [Journal]. - 2012.
Weisstein Eric W. Prolate Spheriod [Online]. - 8 November 2013. -
http://mathworld.wolfram.com/ProlateSpheroid.html.
Wikipedia List of Ball games [Online]. - 2013. - November 2013. -
http://en.wikipedia.org/wiki/List_of_ball_games.
Wikipedia Prolate Spheriod [Online]. - 2013. - 8 November 2014. -
http://en.wikipedia.org/wiki/Prolate_spheroid.
Wikipedia Rugby Union [Online]. - 2013. - November 2013. -
http://en.wikipedia.org/wiki/Rugby_union.

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32
Nomenclature:
Fd – Drag Force
cd = drag coefficient
v = flow velocity
A = characteristic frontal area of the body
Re = Reynolds number
d = Diameter of the ball measured at midpoint

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Final Report - CFD Analysis on Aerodynamic

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