Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology http://pip.sagepub.com/
Effect of temperature on the dynamic properties of soccer balls N Wiart, J Kelley, D James and T Allen Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology 2011 225: 189 originally published online 22 August 2011 DOI: 10.1177/1754337111411644 The online version of this article can be found at: http://pip.sagepub.com/content/225/4/189
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Effect of temperature on the dynamic properties of soccer balls N Wiart, J Kelley, D James, and T Allen* Sheffiled Hallam University, Sheffield, UK
The manuscript was received on 14 December 2010 and was accepted after revision for publication on 6 May 2011. DOI: 10.1177/1754337111411644
Abstract: Soccer is played over a wide range of temperatures. Previous research has shown that the dynamic properties of sports balls, such as squash balls, tennis balls, and baseballs are dependent on temperature. The aim of this research was to determine whether the dynamic properties of soccer balls are temperature dependent. Quasi-static tensile testing was conducted on samples of soccer ball material, at nominal temperatures of 0, 20, and 40 °C. Normal impact testing at speeds up to 22 m/s was undertaken at nominal ball temperatures of 0, 20, and 40 °C. The stiffness of the material decreased as the temperature increased. The coefficient of restitution, contact time, and maximum deformation of the ball all increased with temperature. The mean coefficient of restitution was 0.82 6 0.03 at 40 °C in comparison to 0.73 6 0.02 at 0 °C. A foot-to-ball impact model combined with a trajectory model was used to simulate a penalty kick directed at the top corner of the goal. The results showed that the time available to the goalkeeper was 7 per cent shorter at 40 °C in comparison to that at 0 °C. Therefore, the time available for a goalkeeper to prevent a goal decreases as temperature increases. Keywords: penalty, high-speed video, impact, sport, material, kick
1
INTRODUCTION
Soccer is one of the most popular ball sports in the world and it is played over a wide range of temperatures. For example, the range in temperature for matches played at the 2010 World Cup in South Africa alone was 22 °C (3–25 °C). Temperatures in the preliminary rounds of the 1982 World Cup in Spain were as high as 36 °C. The host nation for the 2022 World Cup will be Qatar where the highest temperature on record is 50 °C (14 July 2010). Alternative measures are being considered to ensure games at this tournament are not played at extremely high temperatures. The Fe´de´ration de Internationale Football Association (FIFA) are responsible for ensuring that the soccer balls used around the world are of the highest quality and consistency. A soccer ball must pass a series of laboratory tests, such as mass, circumference, and rebound, to become FIFA Approved [1]. *Corresponding author: Sheffiled Hallam University email:
[email protected]
The rebound test, which is considered to be the most relevant to play, involves dropping the ball onto a rigid surface from a height of 2 m and measuring the rebound height. To gain approval, the ball must have a coefficient of restitution of 0.82–0.88 at 20 °C and 0.79–0.88 at 5 °C. In this instance, the coefficient of restitution is defined as the square root of the ratio of the rebound height to the inbound height [2]. An equivalent definition of coefficient of restitution is the ratio of the normal rebound velocity to the normal inbound velocity. The criterion of the rebound test indicates that the coefficient of restitution decreases with temperature in the range 5–20 °C, for low-speed impacts (~6 m/s). However, relatively little is known about how temperature may influence the dynamic properties of soccer balls at higher impact speeds, which are more relevant to play. The maximum deformation of a soccer ball has been found to increase with inbound speed for normal impacts, while the coefficient of restitution and contact time decreases [3–5]. Similar trends have been found for tennis balls impacting normal to a Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
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rigid surface [6, 7]. A lower coefficient of restitution equates to higher energy losses, while a lower contact time indicates increased structural stiffness. The effect of temperature on the dynamic properties of various sports balls has been investigated for normal impacts [8–12]. The coefficient of restitution has been shown to increase with temperature for tennis balls [9, 10], squash balls [8, 12], and baseballs [11]. Contact time has also been found to increase with temperature for tennis balls [9] and squash balls [8]. In addition, Bridge [8] reported that the contact area of squash balls increased with temperature, which indicates an increase in deformation. None of the above authors conducted materials testing on samples taken from the balls at different temperatures. Material testing could explain why the dynamic properties of these sports balls were dependent on temperature. The aim of this research was to determine the effect of temperature, in the range 0–40 °C, on the dynamic characteristics of a soccer ball. 2
METHODS
A soccer ball approved by FIFA in 2009 was selected for investigation because it was considered to utilize the most recent advances in materials and construction techniques. Two different experimental procedures were conducted to explore the effect of temperature on soccer balls; these were, first, material analysis and second, impact testing. The three nominal temperatures of 0, 20, and 40 °C were used in both protocols. The range 0–40 °C was assumed to encompass the majority of playing temperatures and was comparable to the range used by previous authors when investigating the effect of temperature on other sports balls [9–12]. For the material analysis, quasi-static tensile testing was undertaken on dogbone-shaped samples punched from a new ball. For the impact analysis, balls were projected normal to a rigid surface at speeds up to 22 m/s. The maximum impact speed corresponded with the ranges 15–20 m/s [13] and 22–25 m/s [14] for pre-impact foot speeds reported for instep kicks to a stationary ball. Results were obtained for coefficient of restitution, contact time, and the maximum deformation of the ball. 2.1 Material analysis Quasi-static tensile testing was performed using an Instron 3367 test machine (Instron, High Wycombe, UK), fitted with a 5 kN load cell. Dogbone-shaped tensile samples were punched from a new soccer ball. The tensile samples were layered composites Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
consisting of a thermally bonded outer panel, foam backing, and an internal balanced plain-weaved carcass. It has been shown previously that balanced plain-weaved fabrics from soccer balls are anisotropic [4, 15]. The maximum Young’s modulus of the woven fabrics occurred at the warp (0°) and weft directions (90°), with minimums at the bias (45° to the warp/weft). In this investigation the long axis of each dogbone-shaped sample was aligned with either the warp or weft of the internal carcass to eliminate anisotropic effects during testing. The dogboneshaped samples had a width, parallel to the clamp direction, of 4 mm and a thickness, perpendicular to the clamp direction, of 4.5 mm. The foam backing represented approximately 75 per cent of the samples’ thickness. The clamped test section was 32 mm long. The displacement rate was 8.3 mm/s and the preload was 1 N. Failure strain was ascertained and a maximum extension limit was set to ensure that no rupture occurred during testing. Soccer balls are constructed of viscoelastic materials [5]. The stress–strain curve of the first deformation of a viscoelastic material is unique and of little significance [16]. Repeated deformation to the same strain results in a constant or equilibrium stress–strain curve. This phenomenon is known as the Mullins effect and as a result the viscoelastic materials found in sports balls should be stretched a few times before measuring their properties to get meaningful results, as per Allen et al. [6]. Therefore, the dogbone-shaped samples were each cyclically loaded five times and the results were obtained for a sixth and final load. The 20 °C dogbone-shaped test sample was acclimatized at room temperature, an oven was used to acclimatize the 40 °C dogbone-shaped test sample for 1 h, and the 0 °C dogbone-shaped test sample was placed in ice in a metal can filled with silica beads for 3 h. The actual temperatures following acclimatization were 5, 21, and 39 °C. The temperature of each dogbone-shaped test sample was recorded immediately after testing to ensure that no change larger than 2 °C occurred. The mass of each test sample was measured before temperature treatment and directly after testing to ensure that it had not changed by more than 1 per cent due to moisture absorption. The variation between material samples was established by testing four of them at room temperature. At maximum displacement the standard deviation was 7 N. Table 1 provides an overview of the materials analysis. 2.2 Impact testing A bespoke two-wheel launch device was used to project soccer balls normal to a rigid wall, as shown
Effect of temperature on the dynamic properties of soccer balls
Table 1 Summary of materials testing Testing Test temperature (°C) section length (mm)
Number of Displacement Maximum pre-test rate extension loading (mm/s) (mm) cycles
5, 21, 39
5
32
8.3
4.5
in Fig. 1. Both wheels were rotated at the same angular velocity to ensure the ball was projected without spin. The experimental set-up is comparable to those used in investigations previously reported in the literature [3–5, 15]. The impacts were filmed using a Phantom V4.3 high-speed video camera operating at 6006 Hz, an exposure time of 0.15 ms, and a resolution of 256 3 256 pixels. A climate chamber (Watford Refrigeration, Watford, UK) was used to acclimatize the balls to temperatures of 0 and 40 °C. It was not possible to conduct the impact tests within the climate chamber, due to size constraints. Therefore, all the impact testing was conducted at room temperature (20 6 2 °C) in a laboratory located within the same building as the climate chamber. An insulated container was used to transport the balls from the climate chamber to the laboratory. 2.2.1 Acclimatization and static testing of the soccer balls Three new soccer balls were used for the impact tests. Prior to acclimatization and testing, each ball was projected five times against the rigid wall at approximately 28 m/s, to account for the Mullins effect. The balls were acclimatized for a minimum of 16 h at the required temperature, in preparation for impact testing. For 0 and 40 °C this was done in the climate chamber and for 20 °C this was done in the testing laboratory. The internal pressure of the balls
Fig. 1 Experimental set-up for soccer ball impact testing
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was set to 80 kPa before acclimatization, following FIFA specifications [1]. After acclimatization the internal pressure of the ball was reset to 80 kPa. The mass of the ball was then measured three times using a digital scale. The diameter of the ball was then measured at 16 marked locations. Finally, the temperature of the ball was measured using a thermocouple attached to a digital thermometer. 2.2.2 Impact testing For the temperature of 20 °C acclimatization and testing were undertaken in the laboratory. For the temperatures of 0 and 40 °C, one ball at a time was removed from the climate chamber in an insulated container and transported to the testing laboratory. In the first instance the ball was projected at nominal speeds of 14, 18, and 22 m/s. The temperature of the ball was then measured in the laboratory using the thermometer before it was returned to the climate chamber for a minimum of 1 h. The impact tests were then repeated in reverse order. The projection order was reversed to reduce any errors as a result of slight changes in the temperature of the ball during testing. The largest change in temperature following impacting testing was 4 °C. There were a total of six impacts for each of the three balls at each temperature. This resulted in a total of 18 impacts at each temperature. 2.2.3 Image processing and error analysis The high-speed video footage was manually analysed in two-dimensions using the Richimas v3.4 image analysis software, which is explained in detail by Goodwill and Haake [17]. The coefficient of restitution was measured as the ratio of the normal rebound velocity to the normal inbound velocity. The contact time was measured by visual inspection of the start and end of each impact. An operating error of one frame corresponded to 0.2 ms. The measure of the maximum deformation of the ball is defined in Fig. 2. The methods for measuring the coefficient of restitution, contact time, and maximum deformation were comparable to those of other authors [3–5, 15]. A step-wise linear multiple regression analysis was performed on the experimental data to determine if the normal impact velocity and temperature caused any observed changes in the coefficient of restitution, contact time, or maximum deformation. A significance level of 0.05 was used throughout. The balls were found to impact the rigid surface at a slight angle above the horizontal, as a result of acceleration due to gravity. The angles were all less than 12°. Goodwill et al. [18] found the coefficient of Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
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restitution, contact time, or maximum deformation. The location of the drop test did not have a significant effect on the coefficient of restitution, contact time, or maximum deformation (p . 0.05 in all cases).
restitution to be marginally higher for oblique impacts in comparison to normal impacts for tennis balls. However, the inbound angles (˜ 50°) investigated by those authors were considerably larger than those measured in this investigation, and no such effect is likely to be apparent. A repeatability study was undertaken to assess the uncertainty in the manual analysis of highspeed video footage. An impact from each of the three nominal inbound speeds was analysed ten times. The standard deviation was taken as a measure of the uncertainty for each impact. Taking the highest standard deviation from the three impacts, the uncertainty in the normal inbound velocity, coefficient of restitution, contact time, and deformation were found to be 0.2 m/s, 0.02, 0.2 ms, and 0.4 mm, respectively. The uncertainty in the ball’s velocity was similar to those reported by other authors [17, 19]. An investigation was undertaken to determine if conducting the impact tests outside the climate chamber introduced noticeable error. Drop tests were performed in the climate chamber and in the laboratory for the nominal temperatures of 0 and 40 °C. The three balls were each dropped once from a height of 2 m onto a concrete slab, inside the climate chamber and in the laboratory. The balls were dropped with the air valve up to reduce the effects of material anisotropy. The largest change in temperature following the drop tests in the laboratory was 2 °C. A one-way analysis of variance (ANOVA) test with the location as the between factor was performed on the drop test data to determine if location had a significant effect on the coefficient of
The mass and diameter of the ball did not change with temperature. The internal pressure of the balls was the same before and after impact testing at 20 °C. The internal pressure of the balls was 7 per cent lower after impact testing at 40 °C and 3 per
Fig. 2 Diagram to show the definition of maximum soccer ball deformation
Fig. 3 Force–displacement curves obtained for tensile testing of layered composite soccer ball materials at 5, 21, and 39 °C. The displacement rate was 8.3 mm/s. The confidence intervals displayed at 21 °C correspond to the standard error
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3
RESULTS
The results are separated into two sections corresponding to the material analysis and impact testing. 3.1 Materials analysis Figure 3 shows the results for the quasi-static tensile testing of dogbone-shaped samples punched from a new soccer ball. The dogbone-shaped samples were constituted by a layered composite material that consisted of an outer panel, foam backing, and carcass. The results were expressed as force against displacement plots. There were three sets of data corresponding to test sample temperatures of 5, 21, and 39 °C. The results showed that the force decreased as the temperature increased, which corresponds to a decrease in stiffness. 3.2 Impact tests
Effect of temperature on the dynamic properties of soccer balls
cent higher after impact testing at 0 °C. The marginal changes in the internal pressure of the ball were due to changes in temperature, in accord with the combined gas law, as a result of testing outside the climate chamber. Figure 4 shows the results for the impact tests. The coefficient of restitution, contact time, and the maximum deformation of the ball are each plotted against normal inbound velocity. There are three sets of data corresponding to ball temperatures of 0, 20, and 40 °C. The maximum deformation of the ball increased with inbound velocity, whereas the coefficient of restitution and contact time decreased. These finding are in agreement with other studies of high-velocity soccer ball impacts [3–5, 15]. The results also show that the coefficient of restitution, contact time, and maximum deformation increased with temperature. Figure 5 shows ball deformation during the impact, for a nominal inbound velocity of 22 m/s. There are two sets of data corresponding to temperatures of 0 and 40 °C. The difference in ball deformation between the two temperatures can be observed in maximum deformation and deformation during the restitution phase of the impact. Step-wise multiple linear regression analyses indicated that both normal inbound velocity and temperature together significantly predict changes in the coefficient of restitution, contact time, and maximum deformation (p\0.001 in all cases). The regression equations were COR = 0:844 0:008VIN + 0:003T
(2)
stiffness was defined at a nominal displacement of 2 mm. There are three sets of data corresponding to the nominal impact velocities. The error bars correspond to the maximum standard error across all nine groups of impacts (same temperature and inbound velocity). The coefficient of restitution, contact time, and maximum deformation of the ball all decreased as stiffness increased. The relationships were all nonlinear. A reduction in stiffness from 6.7 kN/m (at 20 °C) to 2.5 kN/m (at 40 °C) resulted in a 9, 5, and 8 per cent increase in the mean coefficient of restitution, contact time, and maximum deformation averaged across three impact speeds, respectively. While the increase from 6.7 kN/m (at 20 °C) to 37.5 kN/m (at 0 °C) only resulted in a 5, 9, and 4 per cent reduction in the mean coefficient of restitution, contact time, and maximum deformation, respectively. A one-way ANOVA test with material stiffness as the between factor was performed on the experimental data to determine if material stiffness had a significant effect on the coefficient of restitution, contact time, or maximum deformation, for each of the three nominal inbound velocities. A significance level of 0.05 was used throughout. There was a significant effect of material stiffness on the coefficient of restitution, contact time, and maximum deformation (p\0.001 in all cases). Tukey HSD post hoc analysis was undertaken to determine which stiffness values were significantly different. The results were all significantly different (p\0.05 in all cases) with the following exceptions. First, there was no significant difference for contact time between 6.6 and 2.4 kN/m (20 and 40 °C) at 18 m/s (p = 0.086). Second, there was no significant difference for the coefficient of restitution between 37.5 and 6.6 kN/m (0 and 20 °C), at 21 m/s (p = 0.101).
(3)
4
(1)
(adjusted R2 = 0:88) CT = 11:596 0:225VIN + 0:031T
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(adjusted R2 = 0:929) DM = 25:957 + 0:746VIN + 0:117T (adjusted R2 = 0:925)
where COR is the coefficient of restitution, VIN is the normal inbound velocity, T is the temperature, CT is the contact time, and DM is the maximum deformation. Equation (1) indicates that the ball would meet the criteria of the FIFA rebound test at both of the specified temperatures (5 and 20 °C). 3.3 Relationship between material properties and ball dynamics Figure 6 shows the variation in the coefficient of restitution, contact time, and maximum deformation of the ball as a function of material stiffness. The
KICK SIMULATION AT DIFFERENT TEMPERATURES
The impact testing indicated that the dynamics of a soccer ball are temperature dependent. Therefore, temperature is likely to affect the rebound velocity of the ball from the range of pitch, foot, or head impacts which occur during a typical game. In this research the results from the impact tests were used to simulate a penalty kick at the different temperatures. The process involved analysing the penalty kick in two stages: (a) the impact between the foot and ball; (b) the trajectory of the ball.
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Fig. 4 (a) Coefficient of restitution; (b) contact time; and (c) maximum deformation for normal soccer ball impacts at temperatures of 0, 20, and 40 °C. The error bars correspond to the highest standard deviation from the uncertainty analysis
Fig. 5 Displacement–time plots for soccer balls at 0 and 40 °C impacting normal to a rigid surface at a nominal velocity of 22 m/s. The error bars correspond to the highest standard deviation from the uncertainty analysis
4.1 Foot-to-ball impact The mechanics of the soccer kick and the resulting ball velocity was formulated by Lees and Nolan [20], using the effective striking mass method of Plagenhoef [21], as being vb =
½Mf Vf ð1 + e Þ Mf + m b
(4)
where vb is the launch velocity of the ball, Mf is the effective mass of the foot and leg, Vf is the velocity of the foot, e is the coefficient of restitution between the ball and foot, and mb is the mass of the ball. A mass of 0.44 kg was used for the ball as this was the Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
mean value measured. Lees and Nolan [20] state that the effective mass of the foot and leg is approximately four times that of the ball. Furthermore, the coefficient of restitution e is typically 0.5. The velocity of the foot was taken as 22 m/s as this value corresponds to the maximum impact speed tested and it is also comparable to reported values for instep kicks [13, 14]. Linear trend lines fitted to the experimental data (Fig. 4(a)) were used to obtain a value for the coefficient of restitution, between the ball and rigid surface, at the three different temperatures, for an impact velocity of 22 m/s (Table 2). The coefficient of restitution between the ball and rigid surface at room temperature (20 °C) was scaled to account for the different nature of the foot-to-ball impact. The additional energy losses in the foot-to-ball impact, in comparison to the ball-to-rigid surface impact, were accounted for using the constant c as follows c = eR0 0:5
(5)
e = eR c
(6)
where eR is the coefficient of restitution between the ball and rigid surface and eR0 is the coefficient of restitution between the ball and rigid surface at 20 °C. For an impact velocity of 22 m/s eR0 was equal to 0.71, which equates to a value of 0.21 for c. Substituting (6) into equation (4) gives the following vb =
½Mf Vf ð1 + eR 0:21Þ Mf + m b
(7)
Equation (7) was used to obtain the launch velocity of the ball for each of the three temperatures. The
Effect of temperature on the dynamic properties of soccer balls
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Fig. 6 Material stiffness value obtained from quasi-static tensile testing compared to: (a) coefficient of restitution; (b) contact time; and (c) maximum deformation from impact testing. There are three nominal impact velocites of 14, 18, and 21 m/s
Table 2 Results of foot-to-ball impact model. eR was calculated from linear trend lines fitted to the experimental data Temperature (°C)
0 20 40
Coefficient of restitution between ball and rigid surface eR
Ball velocity (m/s)
0.69 0.71 0.79
26.0 26.4 27.7
dynamic properties of the foot/leg were assumed to remain constant with temperature. The post-impact velocity of the ball for the three temperatures is listed in Table 2. The initial velocity of the ball at 20 °C was within the ranges reported by previous authors for instep soccer kicks [13, 14, 22]. 4.2 Ball trajectory To represent the results in the context of how the player might perceive the effects of temperature, a step by step trajectory model was developed. The initial velocity of the ball at each temperature was taken from the foot-to-ball impact model (Table 2). The ball was assumed to have a launch angle of 15° relative to the horizontal and no spin. As the ball had no spin the lift force was zero. The mean measured diameter of the ball was 220 mm. Asai et al. [23] found the drag coefficient of non-spinning soccer balls to be approximately 0.15 for Reynolds numbers which correspond to the launch speeds in Table 2. In this trajectory model the drag coefficient was assumed to remain constant. Two scenarios were simulated as follows:
(a) the density of the air remained constant (20 °C value used) with temperature; (b) the density of the air was modified to simulate the different temperatures. A time step size of 0.001 s was used in the trajectory model. The simulated penalty kick was directed towards the inside edge of the vertical goalpost. The clearance between the edge of the ball and the goalpost was 50 mm when the centre of the ball intercepted the goal line. The results of the penalty kick simulation are listed in Table 3. There are two sets of results: one corresponding to constant air density, and the other to a changing air density. There was very little difference in the two sets of results. Therefore, only the results for changing air density with temperature will be discussed. The trajectory of the ball is shown Fig. 7. The results indicate that the height of the ball at the goal line and the time it reached the goal line are both dependent on temperature. The height of the ball at the goal line was approximately 7 per cent higher at 40 °C in comparison to 0 °C. The time to the goal line was approximately 7 per cent shorter at 40 °C in comparison to that obtained at 0 °C. In a penalty kick scenario, the goalkeeper cannot leave the goal line until the ball has been struck. The goalkeeper has two options: either anticipate or ‘guess’ where the ball will be directed or react to how the penalty taker strikes the ball. Assuming the goalkeeper chooses the second strategy, the time it takes the ball to reach the goal line is the amount of time the goalkeeper has to react and then move to intercept the ball. Subtracting the Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
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Fig. 7 Simulated penalty kick at temperatures of 0, 20, and 40 °C. The graph shows the trajectories at 0.475 s
Table 3 Results of penalty kick analysis Temperature (°C)
0 20 40
Constant density
Change in density
Vertical clearance below cross bar (mm)
Time to goal line (s)
Vertical clearance below cross bar (mm)
Time to goal line (s)
226 194 95
0.481 0.475 0.452
231 194 90
0.483 0.475 0.451
human reaction time from the total time gives the amount of time the goalkeeper has in which to move. Assuming the limit of human reaction time is 0.11 s [24]; the amount of time the goalkeeper has for movement is 9 per cent shorter at 40 °C in comparison to 0 °C.
5
DISCUSSION
The impact properties of soccer balls are temperature dependent. The results obtained for the impacting testing at room temperature (20 °C) were comparable with other studies. In comparison to Price et al. [3–5], the maximum deformation of the ball in the current investigation was slightly lower at the higher impact speeds (.15 m/s) and the contact Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
time was slightly longer at the lower impact speeds (\18 m/s). The discrepancies between the current research and previous investigations are likely to be due to either differences in the balls, i.e. materials and construction techniques and/or internal pressure of the balls, which were not reported in references [3–5]. Therefore, the results of this investigation are limited to a single design of ball pressurized to 80 kPa. Further research should investigate the influence of temperature on the dynamic properties of a range of soccer ball designs. A relatively large scatter was observed in the experimental data, for all three testing temperatures. The observed scatter at 20 °C was comparable with that reported in [3–5] and was likely due to variations in the orientation of the ball at impact [15]. Any additional scatter at 0 and 40 °C was likely due
Effect of temperature on the dynamic properties of soccer balls
to marginal variations in the temperature of the ball during testing. The quasi-static tensile properties of the soccer ball materials were found to be temperature dependent. Stiffness increased as temperature decreased. The dynamic properties of the soccer balls were also found to be temperature dependent. The initial internal pressure of the ball was constant across all temperatures. Therefore, any observed changes in dynamic properties were caused by a change in material properties. The change in dynamic properties with temperature was relatively linear, despite a nonlinear change in material stiffness. During an impact the internal pressure of a ball increases with its deformation. Therefore, it is likely that when material stiffness is low the internal pressure of the ball has a greater influence on the dynamics of the impact. The finite element technique could be applied to determine the relationship between material properties and the internal pressure during impact. The increase in the coefficient of restitution with temperature was in agreement with other studies of sports balls [8–12]. The increase in contact time with temperature was in agreement with Downing [9] for tennis balls and Bridge [8] for squash balls. In addition, the increase in the maximum deformation of the soccer ball with temperature was in agreement with Bridge [8] for squash balls. The increase in contact time and maximum deformation of the ball with temperature was due to the reduction in the structural stiffness, as confirmed in material testing (Figs 3 and 6). Soccer ball manufacturers could aim to use construction materials with minimum temperature dependence to limit the variation in impact properties with temperature. It may be possible to reduce the dependence of the dynamic properties of current soccer balls on temperature by adjusting the internal pressure. Previous authors have shown that the coefficient of restitution increases with internal pressure, while contact time decreases, for a tennis ball [25] and a play ball [8]. Reducing the internal pressure of a soccer ball as temperature increases could potentially lead to a constant coefficient of restitution. Foot-to-ball impact analysis in combination with a trajectory model was used to simulate a penalty kick. The time for the ball to reach the goal line decreased as the temperature increased. Therefore, the goalkeeper has less time to prevent a goal at elevated temperatures. The goalkeeper is unlikely to defend a penalty targeted at the top corner of the goal [26]. However, the ability of the attacking player to kick the ball into the top corner is also likely to be affected by temperature. The results
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showed the height of the ball at the goal line to increase with temperature. This indicates that the accuracy of a shot may also be dependent on temperature, i.e. the ball is more likely to pass over the crossbar at higher temperatures. These findings were limited to a model where the launch angle and spin of the ball were assumed to remain constant with temperature. However, it is likely that both of these factors would be dependent on contact time and deformation, which are, in turn, dependent on temperature. Further research should confirm the predictions of the model experimentally and explore the potential relationships between the launch angle and spin of the ball for a typical kick at different temperatures. The finite element technique could be applied to simulate the impact between the ball and foot at different temperatures. The effect of temperature on the temporal dynamics of the soccer ball impact could then be analysed in depth. 6
CONCLUSIONS
Quasi-static tensile testing showed the stiffness of a layered composite material taken from a soccer ball increases as temperature decreased. The results obtained in the impact tests showed that the coefficient of restitution, contact time, and maximum deformation of the soccer ball all increase with temperature. A foot-to-ball impact model, combined with a trajectory model, was used to simulate a penalty kick, aimed at the top corner of the goal. The results showed that the time available to the goal keeper would be approximately 7 per cent shorter at 40 °C in comparison to that at 0 °C. These findings indicate that the time available for the goalkeeper to prevent a goal decreases as temperature increases. Variations in playing temperatures within and between soccer tournaments are inevitable. Therefore, manufacturers could consider reducing the effect of temperature on soccer ball dynamics. FUNDING This research received no specific grant from any funding agency in the public, commercial, or not for profit sectors
ACKNOWLEDGEMENTS The authors would like to thank adidas for providing the soccer balls, Dr Martin Strangwood and David Binney for their advice, Terry Senior for technical support, Stephen Adams for assistance with experimental testing, and Heather Driscoll and Dr Jon Wheat for proofreading the manuscript. Proc. IMechE Vol. 225 Part P: J. Sports Engineering and Technology
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