Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 72 ( 2014 ) 563 568 The 2014 conference of the International Sports Engineering Association Field Measurements of Ice Hockey Stick Performance and Player Motion Brendan Kays a, Lloyd Smith a * a Washington State University, 201 Sloan, Spokane St., Pullman, WA 99164, USA Abstract Hockey sticks have undergone a dramatic transformation from wood to aluminum to composite in just over 10 years. Other than reduced weight, it is not clear what advantage composite materials provide. This study examined the effects of stick stiffness and swing motion on puck speed. Stick evaluation involved a six player field study, quasi-static stiffness measurement, and video motion analysis. The difference in average puck speed between players was greater (32%) than the difference between sticks (14%). No effect of inertia or swing speed was observed on slap shot puck speeds. Prior to puck impact, the stick-ice contact had a large effect on generating puck speed. Swings where the blade bounced on the ice, released energy stored in the stick, resulting in lower puck speeds. Puck speed was sensitive to stick stiffness and depended on the shot motion. Shots employing large player force, such has a slap shot, tended to follow a constant player force model. Shots employing a small player force, such as a wrist shot, tended to follow a constant player motion model. 2014 2014 The Published Authors. by Published Elsevier Ltd. Open access under CC BY-NC-ND license. by Elsevier Ltd. Selection Selection and and peer-review peer-review under under responsibility responsibility of of the the Centre Centre for for Sports Sports Engineering Engineering Research, Research, Sheffield Sheffield Hallam Hallam University. University Keywords: Type your keywords here, separated by semicolons ; 1. Introduction Due to the introduction of new materials and manufacturing techniques, there have been significant changes in stick construction over the last several decades (Hache, (2002)). This work seeks to understand how stick responses, made possible by new materials and designs, contribute to stick performance. The stick is used for * Lloyd Smith. Tel.: +001 509 335 3221; fax: +001 509 335 4662. E-mail address: lvsmith@wsu.edu 1877-7058 2014 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Centre for Sports Engineering Research, Sheffield Hallam University doi: 10.1016/j.proeng.2014.06.071
564 Brendan Kays and Lloyd Smith / Procedia Engineering 72 ( 2014 ) 563 568 handling, passing, and shooting the puck. The two most common shooting techniques are the slap shot and the wrist shot. The slap shot involves six distinct phases: the backswing, downswing, preloading, loading, release, and follow through (Pearsall, et al., (1999)). Preloading involves contacting the ice several inches behind the puck to initiate bending in the stick. The puck is then impacted by the stick which increases shaft deflection during the loading phase. The strain energy created in the stick is transferred to the puck during the release. The slap shot is the fastest method for propelling the puck with recorded speeds up to 200 km/h (Hoerner, (1989)). The wrist shot is executed more quickly and propels the puck more accurately, but results in lower puck speeds. For these reasons, it is often used close to the net when the speed of the shot is more important than the speed of the puck. During a wrist shot, the player starts with the puck near the middle or heel of the blade (toward the shaft) then makes a forward sweeping motion while applying downward pressure to create shaft deflection. The stick then recoils as the puck rolls off of the end of the blade. Several studies have looked at the effects of shaft stiffness on puck speeds and deflection for both the slap shot and the wrist shot but results have varied. Pearsall, et al. (1999) found significant differences in puck speeds when comparing a medium and extra stiff stick. Others have found little correlation of shaft stiffness on slap shot puck speeds even with significant differences in stick deflection (Lomond & Pearsall, (2007)) (Wu, et al., (2003)) (Worobets, et al., (2006)) (Hannon, et al., (2011)). Lomond concluded the impact location along the blade had little effect on shot speed, yet Bigford and Smith (2009) found an optimum blade impact location 50 100 mm from the heel of the blade. Bigford and Smith also found that stick moment of inertia (MOI) had little effect on stick performance and wood sticks outperformed composite sticks by 10%. Many factors affect puck speeds, including player skill, blade-puck contact time, and stick loading and unloading (Pearsall, et al., (1999)) (Lomond & Pearsall, (2007)) (Wu, et al., (2003)) (Worobets, et al., (2006)) (Hannon, et al, (2011)). This investigation examined the effect of stick stiffness on slap and wrist shot speeds using high-speed video. Differences in player motion were explored in relation to slap shot puck speeds. 2. Methods The stiffness and MOI of the sticks were representative of sticks available commercially. The MOI was found using ASTM F2398 (2011), where the pivot location was taken to be 0.91 m (36 inches) from the tip of the blade. Stick stiffness was measured by clamping each stick to a table at locations 0.03 m and 0.79 m from the butt end of the stick, analogous to a player s hand locations, as shown in Fig. 1. A 4.54 kg mass was hung from the blade at 0.03 m intervals starting at the toe. The stiffness at each location was found from the displacement of the weight, which decreased linearly away from the heel of the blade. The stiffness at the toe was typically half the stiffness at the heel. The stiffness of the stick at the 0.23 m location (close to the heel) is given in Table 1 since it is representative of the stiffness along the blade and is similar to stiffness reported elsewhere (Pearsall, et al., (1999)) (Lomond & Pearsall, (2007)) (Wu, et al., (2003)) (Worobets, et al., (2006)). As depicted in Fig. 2, a field study was conducted in which six players, ages 18 44 and of varying skill, took slap shots and wrist shots on real and artificial ice. Three right handed players and three left handed players were used. High-speed video was recorded by two cameras (Vision Research V711, Wayne, NJ) at 1000 fps for slap shots and 400 fps for wrist shots using 1280 x 800 resolution. The cameras were calibrated using two 1.1 m by 1.1 m panels with 98 equally spaced dots. The mean error of the calibration was 1.27 mm. Each player took 10 slap shots and 10 wrist shots with each stick, corresponding to their shooting hand. Approximately 40 frames before and after puck contact were recorded. A radar gun was used to measure pucks speeds (JUGS Sports, Tualatin, OR).
Brendan Kays and Lloyd Smith / Procedia Engineering 72 ( 2014 ) 563 568 565 Table 1: Stiffness and weight measures of the hockey sticks used in the field study. Stick Number Stiffness Rating Material Shooting Hand Weight (g) MOI (g m 2 ) Stiffness (kn/m) 1 100 Composite Right 467 133 1.18 2 85 Composite Right 439 125 1.05 3 100 Composite Left 450 127 1.06 4 100 Composite Right 543 158 1.18 5 100 Composite Left 593 166 1.12 6 90 Wood Right 723 202 1.07 7 85 Composite Left 537 155 1.00 Tracking dots were placed 0.28 m, 0.58 m, 1.04 m, and 1.35 m from the butt end of each stick and on each glove (Fig. 1). The stick and hand markers were tracked using commercial software (ProAnalyst 3D Professional, Cambridge, MA). Each swing was divided into a downswing, preloading, and loading phase. The coordinates for each marker were fit to third order polynomials for each phase of the swing. Shots where the error in the average distance between marker pairs was greater than 1.6 cm were not used. A total of 177 out of 211 slap shots and 136 out of 201 wrist shots were analyzed. The majority of the unusable data was due to the player s gloves blocking a stick marker from the view of the camera. Stick and hand velocities were obtained by differentiating the polynomial fits with respect to time. The velocity of the blade was extrapolated from the four stick markers. Stick deflection was found from the angle between the line through SM4 and SM3 and the line through SM2 and SM1. The coefficient of restitution (COR) of the stick-puck collision was found from =, (1) where v p and v s are the final speeds of the puck and stick, respectively, and V s is the initial speed of the stick (Nathan, (2000)). 3. Player Performance and Swing Characteristics There were four instances throughout the slap shot where the blade speed was of interest: just prior to ice contact, just prior to puck contact, 1 ms after puck contact, and after puck release. The blade speeds show the three shot phase changes with speeds decreasing at the preloading phase, decreasing more significantly at the start of the loading phase, and increasing during the release phase as energy is transferred to the puck. Fig. 3 presents the blade speed during a slap shot showing the four distinct phases and speed changes. Figure 1: Stick marker locations, constraints and deflected shape when loaded for stiffness testing.
566 Brendan Kays and Lloyd Smith / Procedia Engineering 72 ( 2014 ) 563 568 4 Author name / Procedia Engineering 00 (2013) 000 000 95 a b c d Blade Linear Velocity (km/h) 85 75 65 55 45 35-0.04-0.02 0 0.02 0.04 0.06 Time (seconds) Fig. 4 shows the average COR for each player. Player 1 had an average COR close to zero indicating a relatively low energy transfer where the puck and stick speeds were nearly equal. Player 6, achieved an average COR of 0.38, describing a much greater difference between players than was observed between sticks. In comparison to other sports, the COR in ice hockey is relatively small, dissipating 85% of the stored energy. Fig. 5 compares stick deflection of the fastest shot by player 1 (77.2 km/h) and player 6 (104.6 km/h) Note that for player 1 deflection increases sharply at ice contact, then decreases before reaching a peak. This is characteristic of the blade bouncing on the ice where the stick unloads and releases energy that otherwise would be applied to the puck. The blade for player 6, on the other hand, approaches the ice more gently, avoiding the bounce and storing more energy to be applied to the puck. Interestingly, nearly half of the shots from player one have a coefficient of restitution less than zero. This occurs when the final stick speed is greater than the puck speed. The stick undergoes large vibrations during contact with the ice and puck. At the end of the stick-puck contact, poorly timed shots have a blade speed less than the average stick speed. This results in a puck speed less than the stick speed and, consequently, a negative coefficient of restitution. COR 0.6 0.5 0.4 0.3 0.2 0.1 0-0.1-0.2 Figure 2: Schematic of field study setup. 1 2 3 4 5 6 Player Figure 4: Average COR of each player Figure 3: Blade speed during slap shot. (a) Downswing, (b) pre-loading, (c) loading, (d) release. Deflection (deg) 16 12 8 4 a b c d 0 Player 1 Player 6-4 -0.02 0 0.02 0.04 Time (s) Figure 5: Deflections during a slap shot for players 1 and 6. (a) blade contacts ice, (b) blade contacts puck, (c) puck leaves blade for player 1, (d) puck leaves blade for player 6.
Brendan Kays and Lloyd Smith / Procedia Engineering 72 ( 2014 ) 563 568 567 4. Stick Stiffness As illustrated in Table 1, stiffness is often viewed as an important parameter in stick selection. Given the relatively large amount of stick deflection in ice hockey shots, stiffness may affect puck speed. Since the stick is nearly elastic, its stored energy, e, may be expressed as =, (2) where k and x represent the stick stiffness and deflection, respectively. Equation (2) may be used to describe a shot where player motion is independent of stick stiffness (i.e. x is constant). In this scenario the stick is sufficiently compliant that its response does not impede the player motion and puck speed, v d, would increase with stiffness according to. (3) A hockey shot could also be described where player force is constant. In this scenario a stiffer stick would lead to lower deflection and decreased puck speed, v f, according to. (4) The average puck speed from all players for each stick is shown in Fig. 6. With increasing stiffness puck speed tended to increase for wrist shots and decrease for slap shots. Equations (3) and (4) are included in Fig. 6, suggesting that the motion of wrist shots is nearly constant displacement and the motion of slap shots is nearly constant force. The different effect of stiffness on the slap and wrist shot is likely related to the characteristic stick deflection for each shot. Wrist shots and slap shots had a maximum average deflection of 9.8 and 13.7, respectively. Shots with lower stick deflection (wrist shots) impart lower force to the player s hands, which would lead to a more constant deflection of the stick. The stiffness between sticks varies by less than 20%, while the stiffness measured along the blade of any stick varied by over a factor of two. This would suggest that puck speed should have a strong dependence on the blade impact location. Fig. 7 compares the field study results as a function of blade impact location with Eqs. (3) and (4). The agreement is favorable, but the field study puck speeds appear to have a weaker dependence on impact location (i.e. stiffness) than the idealized relations in Fig. 6. The puck-stick impact duration is relatively long, involves multiple collisions, and locations along the blade. These complex interactions likely also contribute to puck speed. Summary The forgoing has described performance characteristics of hockey sticks measured under play conditions. The difference in shot speeds between players was twice that observed between sticks. Slap shot speeds and efficiency were influenced by the blade impact location and the ability of the player to load the shaft. Shaft loading was largely due to player motion leading to greater blade-puck contact time. Puck speed was shown to correlate with stick stiffness, but the dependence depended on the shot type. The puck speed from shots involving large stick loading, such as a slap shot, was observed to follow a constant force model. Puck speed from shots involving small loading, such as a wrist shot, was observed to follow a constant displacement model.
568 Brendan Kays and Lloyd Smith / Procedia Engineering 72 ( 2014 ) 563 568 29 27 Slap Shot Wrist Shot 35 30 Slap Shot Wrist Shot Puck Speed (m/s) 25 23 21 19 Puck Speed (m/s) 25 20 15 17 15 0.95 1 1.05 1.1 1.15 1.2 1.25 Stick Stiffness (kn/m) Fig. 6. Average puck speed for each stick as a function of stick stiffness. Lines are approximations for ideal player motion: eq. (3) (dashed line) for the wrist shot and eq. (4) (solid line) for the slap shot. 10 50 150 250 350 Blade Impact Location (mm) Fig. 7. Average puck speed for all players a function of blade location (distance from toe, averaged every 12 mm). Lines are approximations for ideal player motion: eq. (3) (dashed line) for the wrist shot and eq. (4) (solid line) for the slap shot. (Stiffness at each blade location is the average of all sticks.) References ASTM International. (2011). F2398 Standard Test Method for Measuring Moment of Inertia and Center of Percussion of a Baseball or Softball Bat. In Book of Standards (p. 3). West Conshohocken, PA: ASTM International. doi:10.1520/f2398-11 Bahill, A. T. (2004). The Ideal Moment of Inertia for a Baseball or Softball Bat. IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 34(2), 197-204. Bigford, R. L., & Smith, L. V. (2009). Experimental Characterization of Ice Hockey Pucks and Sticks. Journal of ASTM International, 6(7). Cross, R., & Bower, R. (2006). Effects of swing-weight on swing speed and racket power. Journal of Sports Sciences, 24(1), 23-30. Fleisig, G., Zheng, N., Stodden, D., & Andrews, J. (2002). Relationship between bat mass properties and bat velocity. Sports Engineering, 5, 1-8. Hache, A. (2002). The Physics of Hockey. Baltimore, MD: John Hopkins University. Hannon, A., Michaud-Paquette, D. J., & Turcotte, R. (2011). Dynamic strain profile of the ice hockey stick: comparisons of player calibre and stick shaft stiffness. Sports Engineering, 14, 57-65. Hoerner, E. F. (1989). The Dynamic Role Played by the Ice Hockey Stick. Safety in Ice Hockey, 154-163. Lomond, K. T., & R.A. Pearsall, D. (2007). Three-dimensional analysis of blade contact in an ice. Sports Engineering, 10, 87-100. Nathan, A. (2003). Characterizing the performance of baseball bats. American Jounal of Physics, 71, 134-143. Nathan, A. M. (2000). Dynamics of the baseball-bat collision. American Journal of Physics, 979-990. Pearsall, D., Montgomery, D., Rothsching, N., & Turcotte, R. (1999). Pearsall, D., Montgomery, D., Rothsching, N., & TuThe Influence of Stick Stiffness on the Performance of Ice Hockey Slap Shots. Sports Egineering, 2, 3-11. Smith, L., Burbank, S., Kensrud, J., & Martin, J. (2012). Field Measurements of Softball Player Swing Speed. Procedia Engineering, 34, 538-543. Worobets, J., Fairbairn, J., & Stefanyshyn, D. (2006). The influence of shaft stiffness on potential energy and puck speed during wrist and slap shots in ice hockey. Sports Engineering, 9, 191-200. Wu, T.-C., Pearsall, D., Hodges, A., Turcotte, R., Lefebvre, R., Montgomery, D., & Bateni, H. (2003). The performance of the ice hockey slap and wrist shots: the effects of stick construction and player skill. Sports Engineering, 6, 31-40.