Analysis of Cristiano Ronaldo’s Free Kick using Computational Fluid

Dynamics (CFD)

Prashanth S. Shankara

Siemens PLM Software, 5800 Granite Parkway, Suite 600, Plano, Tx 75024, U.S.A.

1 OBJECTIVES

The aerodynamics of footballs has come into

prominence in the last decade with the advent of

new ball designs, particularly for the world cup. In

this study, the free kick goal from Cristiano Ronaldo

against Spain in the group stages of the 2018 world

cup is studied (FIFATV, 2018). Detached Eddy

Simulation (DES) method in the CFD code,

Simcenter

™

STAR-CCM+

™

is used. Simulations of

a spinning football are performed on the Telstar 18

ball from 2018 and the Jabulani ball from 2010. This

study aims to uncover the influence of football

design and the resulting aerodynamics on curving

free kicks in match situations, in addition to detailed

flow features. Full, transient CFD simulations of ball

behaviour will help ball designers and players in

understanding curving free kicks. The amount of

curvature resulting from Magnus force (side force)

for different balls calculated from simulations will

also impact the choice and success of free kicks in

match situations.

2 METHODS

2.1 CFD Setup

To perform CFD simulations, a 3-dimensional (3D)

model of the Telstar 18 (geometrically constructed)

and Jabulani (laser-scanned) balls are used (Figure

1). Ball diameter (d) is 0.22 m and weight (m) is

0.436 kg (Goff et al., 2018). Ronaldo kicked the ball

22 meters away from the goal traveling at 60 mph

(26.8 m/s) and spinning at approximately 5

revolutions per second. The speed corresponds to a

Reynolds Number (Re) of 3.828 x 10

. The ball took

0.82 seconds to hit the goal. Surface roughness is

unknown and assumed to be 5 microns from

literature.

Boundary conditions are based on the kick

characteristics detailed earlier. Flow turbulence is

modelled using the DES principle, a combination of

Reynolds Averaged Navier Stokes (RANS) method

closer to surfaces and Large Eddy Simulations

(LES) in regions of high vorticity.

The balls are meshed in Simcenter STAR-CCM+

with trimmed hexahedral cells (between 20 and 30

million cells). Proper wake refinement is added in

the wake of the ball to capture the oscillating wake

region due to spin. 15 prismatic cells are used near

the surface to capture the boundary layer flow

accurately.

Figure 1: Telstar 18 (left) and Jabulani (right).

The DES runs have a time step of 5e-4 seconds

running for a total of 0.82 seconds, the time of flight

of Ronaldo’s kick. This ensures a 1 degree rotation

of the ball per time step to accurately capture flow

fluctuations in time and space. Ball is rotated using

Rigid Body Motion (RBM) method in Simcenter

STAR-CCM+. Simulations are run on 96 cores. Lift

(Fl), drag (Fd) and side (Magnus) force (Fs) and the

force coefficients are computed with time, using

ground conditions on match day.

2.2 Validation of Methodology

To confirm the validity of the Telstar geometry and

simulation methodology, comparisons are made with

wind tunnel data (Goff et al., 2018) at 69 mph and

76 mph on a non-spinning Telstar. Re at these

speeds corresponds to 4.426 x 10

and 4.858 x 10

respectively. In these conditions, lift and side forces

are negligible and hence only drag coefficient (CD)

is compared (Table 1).

Shankara, P.

Analysis of Cristiano Ronaldo’s Free Kick using Computational Fluid Dynamics (CFD).

In Extended Abstracts (icSPORTS 2018), pages 40-43

Table 1: Comparison with wind tunnel data.

Speed (mph) CD (test) CD (CFD)

69 0.201 0.220

76 0.196 0.222

Wind tunnel blockage effects are unaccounted

for and the laser scanned geometry from test is

different from the simulation model. With these

assumptions and investigation of flow physics, the

result is deemed satisfactory for the purpose of the

study. Flow features around the seams, wake behind

the ball and flow separation are investigated and

confirmed.

2.3 Calculating Ball Deviation

As a soccer ball rotates, the boundary layer closer to

surface is ‘pulled’ in the rotation direction leading to

late flow separation compared to the other side. This

force imbalance generates a side force, called the

Magnus force (Kiratidis et al., 2017). This force

causes the ‘deviation’ or ‘curve’, a phenomenon

referred to as the Magnus effect.

Total deviation (curve) of a spinning ball from a

straight line path over 0.82 seconds is calculated

from the aerodynamic side force (Fs) data using

“bending” calculations from NASA (Hall N., 2015).

Radius of curvature (V

/a) is calculated from kick

speed (V) and acceleration due to gravity, a (Fs/m).

Ball deviation (Yd) is then derived from the

formula:

Yd = R – sqrt(R

– D

) (1)

where D is the distance from the goal (22 m).

The deviation of the ball for Ronaldo’s kick

executed with the Telstar and Jabulani are

compared. A knuckle ball simulation is also

performed on the Telstar at 60 mph with no spin to

compare Ronaldo’s trademark kick with the free

kick studied here.

Deviation of the actual kick is calculated using

match footage (FIFATV, 2018) from various angles.

Standard goal post measurements (7.32 m wide) are

used. The ball curves away from the goal initially

before curving back towards the goal. From final

ball location, diameter and goal width, actual ball

deflection is calculated to be approximately 3.5 m.

3 RESULTS

The Telstar 18 curves less compared to the Jabulani

while the knuckleball has minimal curvature (Table

2). Transient animations of the velocity and vorticity

fluctuations behind the ball at center plane are

compared with video footage. These show larger

vortices behind the Jabulani in comparison to the

Telstar 18 (Figure 2) leading to a larger deviation.

Table 2: Comparison of side force and deviation.

Scenario

(N)

Fl (N) Yd (m)

Telstar 18 4.9 0.277 3.95

Jabulani 5.65 0.366 4.57

Telstar 18 knuckleball 0.41 0.58 0.59

The net side force is a result of the vortex pairs

in the wake and the size of the vortices, measured by

vorticity. Skewing of the wake to one side and the

side force direction from Simcenter STAR-CCM+

confirm deviation in the correct direction.

Figure 2: Vorticity behind Telstar 18 (left) and Jabulani

(right) with video footage at 0.62 s (Footage courtesy:

FIFATV).

Figure 3: Velocity behind Telstar 18 (left) and Jabulani

(right) compared with video footage at 0.6 s (Footage

courtesy: FIFATV).

Analysis of Cristiano Ronaldo’s Free Kick using Computational Fluid Dynamics (CFD)

Knuckleball simulations show a deviation of just

0.59 N but the side force changes direction

throughout the time of flight. This causes the

knuckling effect, causing the ball to oscillate

unpredictably. In this scenario, animations show that

counter rotating vortex pairs behind the ball are

unstable. This coupled with vortex breakdown

causes the unstable knuckling behaviour.

Figure 4: Line Integral Convolution (LIC) and vorticity in

knuckleball scenario at 0.63 s.

4 DISCUSSION

Spanish goalkeeper, David De Gea is 6 ft 3 in (1.9

m) tall with an overall reach of 2.2 m when diving.

Before the kick,

he is around 2.75 m from the left

post (Figure 5) and the ball hits the net around 5.9 m

from the left post. The gap of 3.15 m is too far

considering his diving range, hence he doesn’t even

attempt to stop the kick. Simulations show that the

Jabulani would deviate a further 0.7 m towards De

Gea compared to the Telstar, leaving a gap of only

2.45 m between De Gea and the ball. Goalkeepers

rely on instinct and with the ball just 0.25 m outside

his range and accounting for trigger motion, De Gea

could have stopped the Jabulani kick.

The seam depth of the Jabulani is 0.5 mm while

that of Telstar 18 is 1.1 m. The balls have different

panel shapes and numbers as well. Flow

visualizations with skin friction coefficient suggest

that flow separation occurs at different points for

both balls, precisely due to the depth and geometry

of the seams. This leads to differences in wake size

and vorticity behaviour, contributing to different

aerodynamics of the balls.

Even though Ronaldo’s signature kick is the

knuckleball, simulations show that lift force changes

direction during flight and the side force is small.

The small distance to the goal means that getting the

elevation and dip to go over the defenders wall with

precision is risky considering there was no curve to

the ball. The longer the ball is in flight, the more

fluctuations occur in the wake causing more

knuckling and making the kick harder to stop.

Assumptions in the study due to lack of

information included initial seam orientation,

surface roughness and spin rate. The arc of the ball

from the ground to its position above the defenders

wall and the dip is not accounted for.

Figure 5: Initial position of David De Gea (FOX Soccer,

2018).

5 CONCLUSION

The simulations show detailed deviation differences

between the Telstar 18 and Jabulani due to seam

depth and panel shapes, meaning that ball trajectory

is reliant on ball design. Predictable ball behaviour,

a smoother curve during free kicks and deviation

distance all factor into game results and success of a

ball design. DES analysis of spinning soccer balls

will provide additional information on ball

behaviour to ball designers, players and teams,

influencing ball design, style of play and game

outcome.

An important subject for future analysis is

repeating the simulations with more game and ball

information. Dynamic Fluid-Body Interaction

(DFBI) technique in conjunction with RBM and

overset meshing will allow for modelling the exact

position and path of the ball at each time step by

moving the ball based on instantaneous deviation.

ACKNOWLEDGEMENTS

Telstar 18 and Jabulani are registered trademarks of

Adidas AG. FIFA, World Cup and 2018 World Cup

are trademarks of FIFA. Siemens PLM Software and

its subsidiaries and products are not affiliated with,

endorsed by, sponsored by, or supported by Adidas

AG or FIFA.

icSPORTS 2018 - 6th International Congress on Sport Sciences Research and Technology Support

REFERENCES

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surface comparisons between Telstar 18 and Brazuca,

Proc IMechE Part P: J Sports Engineering and

Technology 1–7 IMechE 2018. DOI: 10.1177/

1754337118773214

Hall, N., 2015. “Bending” a soccer ball. Available at:

https://www.grc.nasa.gov/www/k-12/airplane/straj.

html

[FIFA TV]. (2018, Jun 15). Portugal v Spain - 2018 FIFA

World Cup Russia™ - MATCH 3 [Video File].

Retrieved from https://youtu.be/4rp2aLQl7vg

[FOX Soccer]. (2018, Jun 15). Watch Cristiano Ronaldo

score his 3rd goal vs. Spain | 2018 FIFA World Cup™

Highlights [Video File]. Retrieved from

https://youtu.be/y-5dQdaj1kQ

Kiratidis, Adrian & B. Leinweber, Derek. (2017). An

Aerodynamic Analysis of Recent FIFA World Cup

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Analysis of Cristiano Ronaldo’s Free Kick using Computational Fluid Dynamics (CFD)