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

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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)

http://en.wikipedia.org/wiki/Pascal_(unit)


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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 = 𝐶𝐷1

2𝜌𝑉2𝐴

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). 𝐶𝐷 =𝐷

12⁄ 𝜌𝑉2𝐴

= 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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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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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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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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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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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


Page 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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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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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.


Page 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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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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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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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: 𝐶𝐷 =2𝐷

𝜌𝑉2𝐴 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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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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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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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:

𝐶𝐷 =𝐷

12⁄ ∗ 𝜌 ∗ 𝑉2 ∗ 𝐴

=2.17814

12⁄ ∗ 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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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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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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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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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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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.

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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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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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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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