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White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/90806/

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Article: Ura, D., Carré, M. and Dominguez-Caballero, J.A. (2015) Tennis shoe–court interactions: examining relationships between contact area, pressure and available friction. Footwear Science, 7. S87 - S89. ISSN 1942-4280 https://doi.org/10.1080/19424280.2015.1038624

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[email protected] https://eprints.whiterose.ac.uk/ Tennis shoe-court interactions: Examining relationships between contact area, pressure and available friction

Daniel Uraa*, Javier A. Dominguez-Caballeroa and Matt J. Carréa aDepartment of Mechanical Engineering, The University of Sheffield, Sheffield, UK

Introduction previous biomechanics tennis studies and In tennis, complex dynamic movements (side measure the available dynamic friction force. jumping, cutting and braking) affect the loading conditions experienced by players Methods (Orendurff et al., 2008). The magnitude of Tennis shoes were pressed against a surface these forces in combination with other using a bespoke lab-based traction testing variables, e.g. surface roughness (Clarke et device (Clarke et al., 2013). The vertical al. 2012) and shoe orientation (Ura et al., loads ranged from 600 to 1600 N in intervals 2013) affects the friction generated between of 200 N. Three commercially available hard the shoe and surface. Previous tennis studies court tennis shoes of the same design but have reported peak vertical forces of 1243.9 ranging in size (EU sizes 31, 39 and 49) were ± 99.1 and 1680.5 ± 483.7 N on hard court tested. The shoe-surface contact area of the for a side jump and running forehand forefoot segments was calculated using an movements respectively (Damm et al., ink print protocol developed previously 2013). Despite the high loading conditions, (Clarke et al., 2012). Blank paper was rigidly repeatable mechanical lab-based test devices attached onto a smooth acrylic sheet under have been developed to reliably measure the shoes before they were loaded. The ink shoe-surface friction (Clarke et al. 2013). prints were digitised and analysed with a However, the challenge remains to replicate bespoke Matlab threshold programme to these for portable friction test devices. calculate the ink area. This procedure was Pressure insole data collected in previous repeated 4 times for each condition. The tennis studies (Girard et al., 2010; Damm et paper surface was then replaced with a al., 2014) could be a key source to develop commercial hard court sample (mean reliable portable test devices more roughness value of Ra= 14) and friction representative of loading conditions during testing was carried out over the same range realistic movements. Variables such as shoe- of vertical loads. The average dynamic surface contact area, pressure and available coefficient of friction (DCOF) was friction need to be assessed in order to calculated using the mean dynamic friction examine this further. force in the direction of movement between 10 mm and 30 mm horizontal displacement Purpose of the study (detailed in Clarke et al., 2013). The purpose of this study was to investigate shoe-surface contact area at different vertical Results loads, relate them to pressures measured in For this study the results indicated an increase of contact area as the vertical load increases, showing strong and significant linear shoe before the onset of sliding. As the regressions (R2 > 0.81, p < 0.05, where n = applied pressure increases, there is a tendency 72) with varying gradients, showing for the DCOF to decrease. Based on the differences between each shoe size. Figure 1 calculated pressure and despite the size of the exhibits the pressure values calculated from shoe and the contact area with the surface, the vertical load and contact area for each similar friction measurements were obtained. shoe. 800 600 N 1600 N Discussion and conclusion 700 Significant linear relationships exist between

600 contact area, pressures and normal force

R² = 0.9231 investigated in this study. Similar trends are 500 then observed with friction data. By using R² = 0.9381 400 relatively smaller shoes and scaling down the

Pressure(kPa) 300 vertical load applied, it is possible to generate R² = 0.9442 pressures that are comparable to previous 200 Small shoe Med shoe Large shoe biomechanical studies. Damm et al. (2014) 100 reported peak pressure values ranging from 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 Vertical load applied (N) 340.4 – 596.6 kPa. It is therefore possible to Figure 1. Plot of the pressure against vertical consider small shoes under small loads that load for each shoe tested. Examples of ink are still capable of maintaining levels of prints are shown for the size EU 31 shoe, at applied pressure that are representative to real-match conditions when considering 600 and 1600 N of vertical load. measuring friction with portable devices.

1.00 Small shoe Acknowledgments 0.95 Medium shoe Large shoe The authors would like to thank the 0.90 International Tennis Federation and EPSRC 0.85 for their continued support of this research.

0.80

0.75 References

Average Dynamic COF Dynamic Average Clarke, J. et al. (2012). Proc. Inst. Mech. Eng. 0.70 J J. Eng. Tribol., 226(7), 636-647. 0.65 Clarke, J. et al. (2013). Proc. Inst. Mech. Eng. P J. Sports Eng. Technol. 227(3). 149-160. 0.60 150 250 350 450 550 650 Damm, L. et al. (2013). Sports Biomech. Average Applied Pressure (kPa) 12(4), 389-402. Figure 2. Plot of the pressure against average Damm, L. et al. (2014). Footwear Sci. 6(3), DCOF for each shoe. Best fit 2nd order 155-164. polynomial shown to illustrate trend (black Girard, O. et al. (2010). J. Sport Sci. 28, 873- 880 . line). Orendurff, M.S., et al. (2008). Am. J. Sports Med. 36, 566-571. Figure 2 shows the results for DCOF against Ura, D. et al. (2013). Footwear Sci. 5:sup1, average applied pressure (as predicted from S86-S87 the linear fits in Figure 1). This is assumed to be the average pressure experienced by the