Aerodynamic Differences Between New and Used Soccer Balls

applied sciences

Article Aerodynamic Differences between New and Used Soccer Balls

Sungchan Hong 1,2,* and Takeshi Asai 1,2

1 Faculty of Health and Sport Sciences, University of Tsukuba, Tsukuba 305-8574, Japan; [email protected] 2 Advanced Research Initiative for Human High Performance (ARIHHP), University of Tsukuba, Tsukuba 305-8574, Japan * Correspondence: [email protected]; Tel.: +81-29-853-2650

Abstract: The surface structure of soccer balls, such as the number and shapes of the ball panels, has recently changed, and research on the aerodynamics and ﬂight trajectories of new soccer balls is actively proceeding. However, these studies are focused on new soccer balls, whereas the used soccer balls were never studied. In this study, the aerodynamic characteristics of soccer balls kicked 1000 times by a robot were investigated through wind tunnel tests. The results were compared with those obtained using new soccer balls. Regarding the aerodynamic characteristics of the soccer balls,

it was found that the critical Reynold number, Recrit, changes with usage. This is related to the transition from laminar to turbulent ﬂow of airﬂow around the ball. The comparison of the drag

coefficients of the balls at Recrit showed that the drag coefficients of the new and used Telstar18 balls were 0.15 (Re = 2.5 × 105) and 0.14 (Re = 2.2 × 105), respectively; those of the new and used Merlin were 0.13 (Re = 2.8 × 105) and 0.13 (Re = 2.2 × 105), respectively; and finally, those of the new and used Derbystar were 0.14 (Re = 2.1 × 105) and 0.14 (Re = 2.1 × 105), respectively. The surface conditions of a soccer ball, such as the surface roughness and surface damages, are essential factors

to determine the aerodynamics of the soccer balls. Keywords: soccer; soccer ball; used ball; critical Reynolds number; worn and torn Citation: Hong, S.; Asai, T. Aerodynamic Differences between New and Used Soccer Balls. Appl. Sci. 2021, 11, 7204. https://doi.org/ 10.3390/app11167204 1. Introduction In the last few years, the design of the official soccer balls has changed in each FIFA Academic Editor: Mark King World Cup. In particular, between the 2006 World Cup in Germany (Teamgeist, 14-panels, Adidas) and the 2018 World Cup in Russia (Telstar 18, 6-panels, Adidas), the shape of the Received: 26 June 2021 official soccer balls changed significantly. The number of ball panels was considerably Accepted: 3 August 2021 reduced from 32 (used from the 1970 World Cup in Mexico until the 2002 World Cup in Published: 4 August 2021 South Korea and Japan), to 14 (2006 World Cup), 8 (2010 World Cup), and 6 (2014 and 2018 World Cup). Furthermore, from the 2008 EURO Cup event, the surface roughness of Publisher’s Note: MDPI stays neutral the soccer balls changed from being very smooth to having small protrusion patterns with with regard to jurisdictional claims in different shapes, such as square, triangular, and hexagonal [1]. The players, the coaches, published maps and institutional affil- and the spectators are very interested in the aerodynamics and flight trajectories of the new iations. type of soccer balls. Many studies on the effects of the soccer balls’ shapes on aerodynamics and flight trajectories have been conducted [2–13]. Studies on the effects of the panel orientation variations, owing to the number of panels reduction, on the aerodynamics and flight trajectories of the soccer balls have also been published [14–18]. In modern soccer Copyright: © 2021 by the authors. balls, not only the number of panels but also the surface roughness (bumps and dimples) Licensee MDPI, Basel, Switzerland. significantly change, substantially affecting the ball aerodynamics [1,19–22]. Additionally, This article is an open access article depending on the type of soccer ball and its producer, the material used for the ball distributed under the terms and surface varies considerably. Specifically, the aerodynamic properties change significantly conditions of the Creative Commons depending on whether the seam structure between the soccer ball panels is made using Attribution (CC BY) license (https:// stitching threads or adhesive bonds. This increases or decreases the distance of the soccer creativecommons.org/licenses/by/ ball, and also affects the stability of the ball during flight [8,19]. It is considered extremely 4.0/).

Appl. Sci. 2021, 11, 7204. https://doi.org/10.3390/app11167204 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7204 2 of 11

extremely difficult to directly compare such soccer balls as is. A review on these soccer balls was also published [23]. However, in all previous studies, only new soccer balls were tested to study their aerodynamics. While in international events such as the FIFA World Cup, it is possible to use a new ball for each game, in games not involving the professional teams, such as amateurs, schools, and club teams, used balls are utilized. However, no fluid dynamics studies were ever conducted on used soccer balls. For this reason, in this study, we analyzed the flight trajectories and aerodynamics of soccer balls kicked 1000 times (used balls) by a robot for a certain period. In this study, we used three new and three used soccer balls (① Telstar 18 (Adidas), ② Merlin (Nike), ③ Derbystar (Select Sports)) designed by three different manufacturers. We compared the aerodynamics of these soccer balls through wind tunnel tests. Additionally, we studied the effects of the soccer ball conditions (used vs. Appl. Sci. 2021, 11, 7204 2 of 10 new) on the aerodynamic forces acting on the ball by analyzing the flight trajectories of

difficulteach to directlyball. compare Based such socceron ballsthe as is.results A review on obtained these soccer balls wasfrom also these experiments, we aim to elucidate the published [23]. aerodynamicHowever, in all previous characteristics studies, only new soccer ballsand were flight tested to studytrajectory their characteristics of the used soccer balls. aerodynamics. While in international events such as the FIFA World Cup, it is possible to use a new ball for each game, in games not involving the professional teams, such as amateurs, schools, and club teams, used balls are utilized. However, no fluid dynamics studies2. Tests were ever and conducted Methods on used soccer balls. of For Analysis this reason, in this study, we analyzed the flight trajectories and aerodynamics of soccer balls kicked 1000 times (used balls) by a2.1. robot forWearing a certain period. Out In this Balls study, we Using used three newa Kicking and three used Robot soccer balls ( 1 Telstar 18 (Adidas), 2 Merlin (Nike), 3 Derbystar (Select Sports)) designed by three different manufacturers. We compared the aerodynamics of these soccer balls through wind tunnelThe tests. Additionally,balls used we studied in thethe effects tests of the soccer were ball conditions all kicked (used 1000 times by a robot to generate the same vs. new) on the aerodynamic forces acting on the ball by analyzing the flight trajectories of eachsurface ball. Based conditions on the results obtained (Figure from these experiments, 1). The we aimspeed to elucidate of the the ball, when kicked by the robot, was set to aerodynamic30 m/s, characteristics and the and flightkicks trajectory were characteristics repeated of the used soccer1000 balls. times. Since there is no previous research on 2. Tests and Methods of Analysis 2.1.used Wearing balls, out Balls Using we a Kicking set Robotthe standard as 1000 strong kicks (30 m/s), which can cause the ball to The balls used in the tests were all kicked 1000 times by a robot to generate the same surfacewear conditions out. (Figure A large1). The speed net of thewas ball, when placed kicked by at the robot,approximately was set to 1 m in front of the robot to limit exter- 30 m/s, and the kicks were repeated 1000 times. Since there is no previous research on usednal balls, interferences. we set the standard as 1000Since strong kicksthe (30 three m/s), which “used can cause soccer the ball balls” used in the tests had been all kicked to wear out. A large net was placed at approximately 1 m in front of the robot to limit external1000 interferences. times, Sincethey the threewere “used in soccer the balls” same used in the condition. tests had been all kicked 1000 times, they were in the same condition.

Figure 1. Kicking robot used to wear out soccer balls. Figure 1. Kicking robot used to wear out soccer balls. The soccer balls used in this study were official balls used in the 2018–2019 season: 1 Telstar 18 (6-panel, Adidas) EPL (English Premier League) official soccer ball, 2 Merlin (4-panel, Nike) Seria A (Italian Football League) official soccer ball, 3 Derbystar (32-panel, Select Sports)The Bundesliga soccer (German balls Football used League) officialin this soccer ball.study Three used were and official balls used in the 2018–2019 season: three new balls (Figure2) were utilized in the wind tunnel tests. ① Telstar 18 (6-panel, Adidas) EPL (English Premier League) official soccer ball, ② Mer- lin (4-panel, Nike) Seria A (Italian Football League) official soccer ball, ③ Derbystar (32- panel, Select Sports) Bundesliga (German Football League) official soccer ball. Three used and three new balls (Figure 2) were utilized in the wind tunnel tests. Appl. Sci. 2021, 11, 7204 3 of 11

Appl. Sci. 2021, 11, 7204 3 of 10

Figure 2. Soccer balls used in the tests. (A–C) are the Telstar 18, Merlin, and Derbystar used balls, Figurerespectively. 2. Soccer (D–F) are the balls Telstar 18,used Merlin, in and the Derbystar tests. new balls,(A respectively.–C) are the Telstar 18, Merlin, and Derbystar used balls, respectively.2.2. Wind Tunnel ( TestsD–F) are the Telstar 18, Merlin, and Derbystar new balls, respectively. The tests were conducted using the closed-circuit, low-speed, and low-turbulence wind tunnel (San Technologies Co., Ltd., Tochigi, Japan) at the University of Tsukuba (Figure3). The maximum flow speed of this wind tunnel is 55 m/s, the blower outlet 2.2.surface Wind is 1.5 Tunnel m × 1.5 m, theTests flow speed distribution is within ±0.5%, and the turbulence is 0.1% or less. Furthermore, the blockage of the measured soccer ball was within 5% of the nozzleThe size.tests For example, were when conducted the wind speed wasusing set to 25 m/s,the the closed-circuit, measured mean low-speed, and low-turbulence wind speed was 25.28 m/s, with the measurement position in the range of −0.46 to 0.45 and winda wind tunnel speed distribution (San within Technologies±0.5%. Similarly, the Co., degree LTD., of turbulence Toch downstreamigi, Japan) at the University of Tsukuba of the nozzle at a wind speed of 25 m/s was 0.05 to 0.06, within approximately 0.1%, so the (Figureerror from 3). the ballThe position maximum was believed to fl haveow a negligible speed effect of on this the wind wind speed [17tunnel]. is 55 m/s, the blower outlet sur- Furthermore, in this study, the dynamic pressure can be measured automatically with face0.1 Paisintervals 1.5 m using × the1.5 Pitot-static m, the tube placedflow above speed the measuring distribution portion of the soccer is within ±0.5%, and the turbulence is ball. In addition, because the position of the ball during the measurement procedure is set 0.1%almost or at less. the center Furthermore, of the nozzle cross-section the to adjustblockage the distance of between the themeasured nozzle soccer ball was within 5% of the nozzleand the ballsize. to zero, For the flowexample, generated from when the Pitot the tube maywind not have sp aeed direct effectwas set to 25 m/s, the measured mean on the flow around the ball. Furthermore, the sting used in this study was 0.6 m long and wind0.02 mspeed wide. Moreover, was because 25.28 the effectm/s, of stingwith vibrations the isme reducedasurement to a small value position in the range of −0.46 to 0.45 by placing the six-component force detector behind the soccer ball, the magnitude of the andsting a forceswind was ignoredspeed in thisdistribution study. The tests were within conducted ±0.5%. by placing threeSimilarly, used the degree of turbulence down- and three new balls in the wind tunnel. In this study, aerodynamic measurements for each streamsoccer ball of were the performed nozzle for wind at speeds a wind (Reynolds speed number) from of 7 m/s25 (approximately m/s was 0.05 to 0.06, within approximately Re = 1.0 × 105) to 35 m/s (approximately Re = 5.5 × 105) at intervals of 1 m/s [17]. The 0.1%,relationship so the between error the Reynolds from number the and ball wind speedposition is as follows: was believed to have a negligible effect on the

wind speed [17]. Furthermore,Re = UD/v in this study, the dynamic(1) pressure can be measured auto-

maticallywhere Reynolds with number 0.1 (Re Pa) is aintervals dimensionless numberusing deﬁned the asPitot-static the ratio of inertial tube placed above the measuring por- force to viscous force, U is the wind speed (m/s), D is the ball diameter (m), and v is the tionkinematic of the viscosity soccer (m2/s). ball. In addition, because the position of the ball during the measurement procedure is set almost at the center of the nozzle cross-section to adjust the distance between the nozzle and the ball to zero, the flow generated from the Pitot tube may not have a direct effect on the flow around the ball. Furthermore, the sting used in this study was 0.6 m long and 0.02 m wide. Moreover, because the effect of sting vibrations is reduced to a small value by placing the six-component force detector behind the soccer ball, the magnitude of the sting forces was ignored in this study. The tests were conducted by placing three used and three new balls in the wind tunnel. In this study, aerodynamic measurements for each soccer ball were performed for wind speeds (Reynolds number) from 7 m/s (approximately Re = 1.0 × 105) to 35 m/s (approximately Re = 5.5 × 105) at intervals of 1 m/s [17]. The relationship between the Reynolds number and wind speed is as follows: Re = UD/v (1) where Reynolds number (Re) is a dimensionless number defined as the ratio of inertial force to viscous force, U is the wind speed (m/s), D is the ball diameter (m), and v is the kinematic viscosity (m2/s). These forces were measured using a sting-type six-component force detector (LMC- 61256, Nissho Electric Works). In addition, through the aerodynamic forces measured in the tests [1,5–8], the drag coefficient (CD), lift coefficient (CL), and side force coefficient (CS) were calculated using Equations (2)–(4): 𝐶 = (2) 2𝐿 𝐶 = (3) 𝜌𝑈𝐴 Appl. Sci. 2021, 11, 7204 4 of 10

Appl. Sci. 2021, 11, 7204 These forces were measured using a sting-type six-component force detector (LMC-61256, 4 of 11 Nissho Electric Works). In addition, through the aerodynamic forces measured in the tests [1,5–8], the drag coefficient (CD), lift coefficient (CL), and side force coefficient (CS) were calculated using Equations (2)–(4):

2D C = (2) D ρU2 A 2𝑆 2L 𝐶 = (4) C = (3) L ρU2 A 𝜌𝑈 𝐴 2S C = (4) 3 where ρ is the air density,S ρU2 Aexpressed as ρ = 1.2 kg/m ; U is the flow velocity, and A is the whereprojectedρ is the air density,area expressed of the as soccerρ = 1.2 kg/m ball,3; U is theexpressed ﬂow velocity, and asA isA the = π × 0.112 = 0.038 m2. projected area of the soccer ball, expressed as A = π × 0.112 = 0.038 m2.

FigureFigure 3. Wind 3. tunnel Wind test setup. tunnel test setup. 2.3. Simulation of the Flight Trajectory The ﬂight trajectory simulation was performed using the drag force measured in the wind2.3. tunnel Simulation tests. A 2D ﬂight of simulation the Flight [24] was Trajectory used for the computations. Furthermore, the knuckling effect occurring in non-spinning soccer balls [25,26] and the lift and side forces acting on the ball were not considered in this study. The followingThe flight equations trajectory were used for the simulation simulation: was performed using the drag force measured in the wind tunnel tests. A 2D flight simulation [24] was used for the computations. Further- mah = −D cos γ (5) more, the knuckling effect occurring in non-spinning soccer balls [25,26] and the lift and mav = −D sin γ − mg (6)

wheresidem isforces the mass ofacting the football, onah theis the horizontalball were acceleration not ofconsidered the ball, av is the in this study. vertical acceleration of the ball, g is the gravitational acceleration, and γ is the initial attack angle of theThe ball ﬂightfollowing trajectory. equations were used for the simulation:

𝑚𝑎 = 𝐷 cos 𝛾 (5)

𝑚𝑎 = 𝐷sin𝛾𝑚𝑔 (6)

where m is the mass of the football, 𝑎 is the horizontal acceleration of the ball, 𝑎 is the vertical acceleration of the ball, 𝑔 is the gravitational acceleration, and 𝛾 is the initial attack angle of the ball flight trajectory.

3. Results 3.1. Drag Coefficient Obtained from the Wind Tunnel Tests Figure 4 shows the drag coefficient curves of the soccer balls. The drag characteristic curves represent the mean values over three trials for each soccer ball. Additionally, the error of the CD value in each soccer ball is denoted by the dotted line (Figure 4). The comparison of the drag coefficients of the balls at the critical Reynolds number (Recrit) showed that the drag coefficients of the new and used Telstar18 balls were 0.15 (Re = 2.5 × 105) and 0.14 (Re = 2.2 × 105), respectively, those of the new and used Merlin were 0.13 (Re = 2.8 × 105) and 0.13 (Re = 2.2 × 105), respectively. Finally, those of the new and used Derbystar were 0.14 (Re = 2.1 × 105) and 0.14 (Re = 2.1 × 105), respectively. Appl. Sci. 2021, 11, 7204 5 of 10

3. Results 3.1. Drag Coefficient Obtained from the Wind Tunnel Tests Figure4 shows the drag coefficient curves of the soccer balls. The drag characteristic curves represent the mean values over three trials for each soccer ball. Addi- tionally, the error of the CD value in each soccer ball is denoted by the dotted line (Figure4). The comparison of the drag coefficients of the balls at the critical Reynolds number (Recrit) showed that the drag coefficients of the new and used Telstar18 balls were Appl. Sci. 2021, 11, 7204 × 5 × 5 5 of 11 0.15 (Re = 2.5 10 ) and 0.14 (Re = 2.2 10 ), respectively, those of the new and used Mer- lin were 0.13 (Re = 2.8 × 105) and 0.13 (Re = 2.2 × 105), respectively. Finally, those of the new and used Derbystar were 0.14 (Re = 2.1 × 105) and 0.14 (Re = 2.1 × 105), respectively.

Figure 4. (A–C) show the drag coefﬁcients obtained for the Telstar18, Merlin, and Derbystar soccer balls, respectively. Figure 4. (A–C) show the drag coefficients obtained for the Telstar18, Merlin, and Derbystar soccer balls, respectively. 3.2. Changes in the Lift and Side Forces 3.2. Changes in the Lift and Side Forces Figure5 shows the variations in lift and side forces acting on each ball. To illustrate the irregularFigure movement 5 shows the of variations the soccer ballin lift accurately, and side weforces used acting scatter on plotseach forball. the To lift illustrate and side theforces irregular instead movement of the lift of and the side soccer coefﬁcients. ball accura Thetely, graphs we used show scatter the variations plots for the of the lift forcesand sideacting forces on theinstead balls of in the lift vertical and (up–bottom)side coefficients. and lateralThe graphs (left–right) show directionsthe variations measured of the in forcesa 10 sacting interval on with the anballs airspeed in the ofvertical 20 m/s. (u Ap–bottom) comparison and between lateral the(left–right) standard directions deviations measured(SD) of the in a variations 10 s interval of thewith forces an airsp actingeed of on 20 the m/s. soccer A comparison balls showed between that forthe thestand- new ardTelstar18 deviations the SD(SD) of of the the side vari andations lift of forces the forces were 0.37acting and on 0.46, the respectively,soccer balls showed while for that the forused the Telstar18,new Telstar18 the SD the of SD the of side theand side lift and forces lift forces were 0.42were and 0.37 0.53, and respectively. 0.46, respectively, For the whilenew for Merlin, the used the SD Telstar18, of the side the and SD liftof the forces side were and 0.49lift forces and 0.55, were respectively, 0.42 and 0.53, while respec- for the tively.used Merlin,For the thenew SD Merlin, of the sidethe SD and of lift the forces sidewere and 0.42lift forces and 0.56, were respectively. 0.49 and 0.55, Similarly, respec- for tively,the new while Derbystar, for the theused SD Merlin, of the sidethe andSD of lift th forcese side were and 0.57lift forces and 0.58, were respectively, 0.42 and 0.56, while respectively.for the used Similarly, Derbystar, for the the SD new of theDerbystar, side and th lifte SD forces of the were side 0.76 and and lift forces 0.68, respectively. were 0.57 andThus, 0.58, among respectively, the tested while soccer for the balls, used the Derbys used Derbystartar, the SD showed of the side the and most lift irregular forces were force 0.76changes. and 0.68, respectively. Thus, among the tested soccer balls, the used Derbystar showed the most irregular force changes. Appl.Appl. Sci. Sci. 20212021, 11, 11, 7204, 7204 6 of6 of11 10

FigureFigure 5. 5.Changes Changes in in the the lift lift and and side side forces forces of eachof each soccer soccer ball ball (airspeed (airspeed 20 m/s,20 m/s, 10 s10 interval). s interval). (A ,C(A,E,C), areE) are the the Telstar Telstar 18, 18, Merlin,Merlin, and and Derbystar Derbystar used used balls, balls, respectively. respectively. (B ,(DB,DF),F are) are the the Telstar Telstar 18, 18, Merlin, Merlin, and and Derbystar Derbystar new new balls, balls, respectively. respectively.

3.3.3.3. Results Results on on the the Soccer Soccer Balls Balls Flight Flight Trajectories Trajectories FigureFigure 66 shows shows the the flight ﬂight trajectories trajectories of of the the soccer soccer balls. balls. In In these these graphs, graphs, the the soccer soccer ballball flight ﬂight trajectories trajectories were were estimated estimated using using an an initial initial speed speed of of 30 30 m/s m/s and and a arelease release angle angle ofof 20°, 20◦ which, which are are representative representative values values of of a ast strongrong kick kick [14]. [14]. For For Telstar18, Telstar18, the the horizontal horizontal trajectorytrajectory lengths lengths of of the the new new and and used used balls balls were were 43 43 m m and and 41.7 41.7 m, m, respectively, respectively, while while for for thethe new new and and used used Merlin, Merlin, the the corresponding corresponding lengths lengths were were 45.5 45.5 m m and and 43.7 43.7 m, m, respectively. respectively. Finally,Finally, for for the the new new and and used used De Derbystar,rbystar, the correspondingcorresponding lengthslengths were were 44.7 44.7 m m and and 45.6 45.6 m, m,respectively. respectively. Figure7 shows the trajectories of the soccer balls when kicked from the starting point (0 m) to the impact point (height) with the net at 20 m. The trajectories were estimated using an initial speed of 20 m/s and a release angle of 15◦. For Telstar18, the heights of the trajectories at the impact point of the new and used balls were 1.48 m and 1.42 m, respectively. For the new and used Merlin, the corresponding values were 1.63 m and Appl. Sci. 2021, 11, 7204 7 of 10

Appl. Sci. 2021, 11, 7204 7 of 11 1.54 m, respectively. For the new and used Derbystar, the corresponding values were 1.61 m and 1.64 m, respectively.

◦ Figure 6. ComparisonFigure 6. Comparison of the ﬂight of the trajectoriesflight trajectories of the of the soccer soccer balls balls (initial (initial speed 30 30 m/s, m/s, release release angle angle 20°) ( 20A–C)() showA–C )the show the Appl. Sci. 2021, 11, 7204 8 of 11 results forresults Telstar18, for Telstar18, Merlin, Merlin, and Derbystar, and Derbystar, respectively. respectively.

Figure 7 shows the trajectories of the soccer balls when kicked from the starting point (0 m) to the impact point (height) with the net at 20 m. The trajectories were estimated using an initial speed of 20 m/s and a release angle of 15°. For Telstar18, the heights of the trajectories at the impact point of the new and used balls were 1.48 m and 1.42 m, respectively. For the new and used Merlin, the corresponding values were 1.63 m and 1.54 m, respectively. For the new and used Derbystar, the corresponding values were 1.61 m and 1.64 m, respectively.

Figure 7. ComparisonFigure 7. Comparison of the of height the height of the of impactthe impact point point of of the the soccersoccer ball ball from from the the front front (initial (initial speed speed 20 m/s, 20 release m/s, angle release angle 15◦). 15°).

4. Discussion In this study, we investigated the aerodynamics and flight trajectories of used soccer balls for the first time. The balls were prepared by kicking them repeatedly 1000 times for a certain period of time using a kicking robot.

4.1. Usage Effects on the Ball Aerodynamics The wind tunnel test results showed that the aerodynamic forces (drag coefficient) acting on the ball slightly differ between a new and used ball. Furthermore, it was observed that at Recrit, where the transitions from laminar to turbulent flows occur, the results differ depending on whether the ball is used or new. In fact, these transitions occur when the ball is used owing to the variations in the surface roughness produced by kicking the ball. As observed in Figure 4, the CD values of the new and used balls differ in the power- kicks speed range. A previous study on the aerodynamics of cricket balls has reported that when the air boundary becomes turbulent and unstable (at approximately Re = 3.5 × 105), the CD of a used ball is 0.65, which is much larger than the CD of a new ball, which is 0.45. This result was attributed to the increase in the drag force owing to a worn surface [27]. Similar results were observed in our tests for speeds beyond the medium speed range (Re ≥ 3.5 × 105) for the Telstar18 and Merlin soccer balls. However, for the Derbystar, although the CD value of the used ball increased in the medium speed range (3.0 × 105 ≥ Re ≥ 4.0 × 105), it decreased in the high-speed range (Re ≥ 4.0 × 105), as shown in Table 1.

Table 1. CD values of the new and used balls used in this experiment.

Airflow Velocity Type Telstar18 Merlin Derbystar Re = 3.5 × 105 Used ball 0.22 (about 10% up) 0.15 (about 7% up) 0.18 (about 20% up) (about 23 m/s) New ball 0.20 0.14 0.15 Re = 5.0 × 105 Used ball 0.21 (about 15% up) 0.17 (about 15% up) 0.15 (about 7% down) (about 33 m/s) New ball 0.18 0.15 0.16

Furthermore, in previous studies on tennis ball aerodynamics, it was reported that as the fuzz of tennis balls has longer fibers, the drag force increases by about 10% [28–30]. Appl. Sci. 2021, 11, 7204 8 of 10

4. Discussion In this study, we investigated the aerodynamics and ﬂight trajectories of used soccer balls for the ﬁrst time. The balls were prepared by kicking them repeatedly 1000 times for a certain period of time using a kicking robot.

4.1. Usage Effects on the Ball Aerodynamics The wind tunnel test results showed that the aerodynamic forces (drag coefﬁcient) acting on the ball slightly differ between a new and used ball. Furthermore, it was observed that at Recrit, where the transitions from laminar to turbulent ﬂows occur, the results differ depending on whether the ball is used or new. In fact, these transitions occur when the ball is used owing to the variations in the surface roughness produced by kicking the ball. As observed in Figure4, the CD values of the new and used balls differ in the power-kicks speed range. A previous study on the aerodynamics of cricket balls has reported that when the air boundary becomes turbulent and unstable (at approximately 5 Re = 3.5 × 10 ), the CD of a used ball is 0.65, which is much larger than the CD of a new ball, which is 0.45. This result was attributed to the increase in the drag force owing to a worn surface [27]. Similar results were observed in our tests for speeds beyond the medium speed range (Re ≥ 3.5 × 105) for the Telstar18 and Merlin soccer balls. However, for the Derbystar, although the CD value of the used ball increased in the medium speed range (3.0 × 105 ≥ Re ≥ 4.0 × 105), it decreased in the high-speed range (Re ≥ 4.0 × 105), as shown in Table1.

Table 1. CD values of the new and used balls used in this experiment.

Airﬂow Velocity Type Telstar18 Merlin Derbystar Re = 3.5 × 105 Used ball 0.22 (about 10% up) 0.15 (about 7% up) 0.18 (about 20% up) (about 23 m/s) New ball 0.20 0.14 0.15 Re = 5.0 × 105 Used ball 0.21 (about 15% up) 0.17 (about 15% up) 0.15 (about 7% down) (about 33 m/s) New ball 0.18 0.15 0.16

Furthermore, in previous studies on tennis ball aerodynamics, it was reported that as the fuzz of tennis balls has longer fibers, the drag force increases by about 10% [28–30]. In this study, the CD of used balls showed a tendency to increase by approximately 7–20%. The significant variations in the surface structures (number of panels and patterns) of the soccer balls used in this study caused a considerable variation in the CD values. The effects of a worn and damaged surface are similar to those of the fuzz of a tennis ball. They induce a faster transition from laminar to turbulent flows around the ball, shifting the airflow separation line towards the back of the ball. Detailed studies on the airflow around used and new soccer balls are considered necessary for future visualization tests such as the PIV (Particle Image Velocimetry) and CFD (Computational Fluid Dynamics). These studies have never been conducted before, and many concepts have not yet been understood. In this work, a comparative study was conducted using new balls, and balls kicked 1000 times. However, a study on the difference with unused balls based on a finer definition of used balls (for example, the state after 100, 1000, and 5000 kicks) is necessary to better quantify the data.

4.2. Usage Effects on the Flight Trajectories of the Balls The simulations of the flight trajectories of the soccer balls show that in powerful long kicks (initial speed 30 m/s, release angle 20◦), the flight distance (horizontal) differs depending on the ball type. In particular, the new Telstar18 and Merlin reach farther distances compared to the used ones. However, the flight distance of the new Derbystar was approximately 1 m shorter than the used one. Furthermore, the simulations of free kicks (initial speed 20 m/s, release angle 15◦) show that the vertical positions (height) Appl. Sci. 2021, 11, 7204 9 of 11

In this study, the CD of used balls showed a tendency to increase by approximately 7–20%. The significant variations in the surface structures (number of panels and patterns) of the soccer balls used in this study caused a considerable variation in the CD values. The effects of a worn and damaged surface are similar to those of the fuzz of a tennis ball. They induce a faster transition from laminar to turbulent flows around the ball, shifting the airflow separation line towards the back of the ball. Detailed studies on the airflow around used and new soccer balls are considered necessary for future visualization tests such as the PIV (Particle Image Velocimetry) and CFD (Computational Fluid Dynamics). These studies have never been conducted before, and many concepts have not yet been understood. In this work, a comparative study was conducted using new balls, and balls kicked 1000 times. However, a study on the difference with unused balls based on a finer definition of used balls (for example, the state after 100, 1000, and 5000 kicks) is necessary to better quantify the data.

4.2. Usage Effects on the Flight Trajectories of the Balls The simulations of the flight trajectories of the soccer balls show that in powerful long Appl. Sci. 2021, 11, 7204 kicks (initial speed 30 m/s, release angle 20°), the flight distance (horizontal) differs9 ofde- 10 pending on the ball type. In particular, the new Telstar18 and Merlin reach farther distances compared to the used ones. However, the flight distance of the new Derbystar was approximately 1 m shorter than the used one. Furthermore, the simulations of free kicks (initialof the speed ball impact 20 m/s, point release at angle the net 15°) placed show atthat 20 the m vertical from the positions kick position (height) differed of the ball by impactapproximately point at 0.2the mnet depending placed at 20 on m the from ball the type. kick These position differences differed areby approximately 0.2comparable m depending to the on size the of ball a soccer type. These ball and diff areerences therefore are approximately significant from comparable the goalkeeper’s to the sizeposition. of a soccer Furthermore, ball and dependingare therefore on signif the ballicant type, from the the difference goalkeeper’s in height position. between Further- the more,used and depending new balls on varied the ball significantly type, the difference from 0.03 in m height (Derbystar) between to the 0.09 used m (Merlin). and new These balls variedresults significantly are similar to from the 0.03 variations m (Derbystar) in the flight to 0.09 trajectories m (Merlin). depending These results on the are ball similar type toreported the variations in previous in the studies flight [trajectories9,19]. However, depending in these on tests, the ball the type computation reported resultsin previous were studiesobtained [9,19]. using However, the CD values in these from tests, the the wind computation tunnel tests. results Further were studies obtained are necessaryusing the to determine the flight trajectories of used balls through a launching device such as a CD values from the wind tunnel tests. Further studies are necessary to determine the flight trajectorieskicking robot. of used balls through a launching device such as a kicking robot. The differences in the flight flight distances may be attributed to the worn surface of the kicked ball, the ball type, and the properties of the leather used for the balls (Figure8). kicked ball, the ball type, and the properties of the leather used for the balls (Figure 8). The Telstar18 and Merlin balls are manufactured using rubber-based synthetic leather and The Telstar18 and Merlin balls are manufactured using rubber-based synthetic leather and adhesive bonds, while the Derbystar balls are manufactured using artificial leather-based adhesive bonds, while the Derbystar balls are manufactured using artificial leather-based synthetic leather and hand-stitching. However, a detailed study on this topic using a synthetic leather and hand-stitching. However, a detailed study on this topic using a su- super-microscope is necessary for the future. per-microscope is necessary for the future.

Figure 8. The surface of used soccer balls.

InIn summary, thethe surface surface conditions conditions (roughness, (roughness, worn worn and and torn torn leather leather materials) materials) of the of themodern modern soccer soccer balls balls change change with with usage, usage, causing causing variations variations in the in airﬂow the airflow around around the balls, the balls,which which affect theaffect aerodynamics the aerodynamics and ﬂight and trajectories flight trajectories of the balls. of the Based balls. on Based thevariations on the vari- of ationsthe aerodynamic of the aerodynamic forces acting forces on acting the ball on depending the ball depending on the surface on the structure, surface structure, we assumed we assumedthat the surface that the conditions surface conditions of the ball of are the essential ball are to essential study their to study aerodynamics their aerodynamics in addition to the number and shape of panels, ball orientation, and surface structure reported in previous studies [6,8,18].

5. Conclusions In this study, we employed soccer balls by kicking them for a certain period of time, compared the aerodynamics of these balls with the new soccer balls, and investigated their differences in aerodynamics. The results indicate that the surface conditions with materials such as leather and vinyl-based synthetic leather covering the soccer ball surface significantly affect the aerodynamic forces acting on the soccer ball. In other words, it is determined that with the increased use of the soccer ball, the flying distance of the ball becomes shorter or longer. It is necessary to understand these advantages and adjust the strength of the pass or kick according to the condition of the ball used during practice and play. This study, for the first time, shows that the surface conditions of the soccer balls could affect the aerodynamics of modern soccer balls. Hence, it is suggested that the aerodynamic characteristics and flight trajectory of a soccer ball change with use.

Author Contributions: S.H. and T.A. designed the study and experiments. Both authors conducted the experiments and analyzed the collected data. Both authors participated in the discussion of the experimental results and made contributions throughout the project and the writing of the manuscript. All authors have read and agreed to the published version of the manuscript. Appl. Sci. 2021, 11, 7204 10 of 10

Funding: This research was funded by the Ministry of Education, Culture, Sports, Science and Technology of the Japanese government, JSPS KAKENHI grant number 15K16442, 20K11413 and 20H04066. Data Availability Statement: Data sharing not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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