The Role of Effective Mass and Hand Speed in the Performance of Kung Fu Athletes Compared with Nonpractitioners

The Role of Effective Mass and Hand Speed in the Performance of Kung Fu Athletes Compared With Nonpractitioners

Osmar Pinto Neto,1 Marcio Magini,1 and Marcelo M. F. Saba2 1Universidade do Vale do Paraiba and 2Instituto Nacional de Pesquisas Espaciais

The main goal of this article is to quantify the Chinese martial arts (wushu) have a history

contribution of effective mass (me) and hand- of thousands of years. They were developed out speed (shi) on the palm strike performance of of the necessity of the Chinese people to defend kung fu athletes (kung fu group) compared with themselves from the harms of nature and attacks of nonpractitioners (control group). All subjects other humans (Chow & Spangler, 1982). Through were asked to strike a basketball. Hand and history, various warriors developed different tech- ball speed (s ) were determined by high-speed bf niques (styles) of self-defense with particular sets video analysis. The value for me was determined by an equation that does not depend upon post- of movements and ideas (Despeux, 1981). The impact measurement of the hand speed. The yau-man style of kung fu was developed during the results show that kung fu athletes had greater Ch’ing Dynasty (1644–1911) with the purpose to help Chinese revolutionaries in the war against the shi (6.67 [SD 1.42] m/s), p = 0.042), higher me (2.62 [SD 0.33] kg, p = 0.004), and greater Manchu invaders, and, for this reason, its main focus

sbf (9.00 [SD 1.89] m/s), p = 0.004) than the is efficiency (New Martial Hero Magazine, 1972). nonpractitioners (5.04 [SD 0.57] m/s, 1.33 [SD A strike performed in the yau-man kung fu differs 0.19] kg, and 5.72 [SD 0.44] m/s, respectively). from other fighting styles, such as karate or boxing Comparing the average values obtained for m e punches, among other factors because the striking and hand and forearm mass (m), it was found hand begins closer to the target (30 cm on average), that for the control group m is statistically equal e the striking arm is slightly adducted throughout to m (p = 0.917), whereas for the kung fu group motion, and the the motion is terminated before full me is significant greater than m (p = 0.003). It is suggested that for impacts against heavier extension of the arm (Pinto Neto et al., 2006a). objects, the effective mass would be the main Over the last decades, several studies have factor to distinguish a martial arts–trained from been conducted to further the understanding of the an untrained subject. biomechanical aspects of karate and boxing (e.g., Wilk et al., 1983; Smith & Hamill, 1986; Walilko Key Words: biomechanics, motion analysis, et al., 2005). However, only a very few articles in kinematics, exercise performance the literature discuss the biomechanics of kung fu (e.g., Pinto Neto et al., 2006a, 2006b). In general, Pinto Neto and Magini are with the Instituto de Pesquisa e these studies were concerned with the enhancement Desenvolvimento, Universidade do Vale do Paraiba, São José of performance and extending the understanding of dos Campos, Brazil, and Saba is with the Departamento de Geofísica Espacial, Instituto Nacional de Pesquisas Espaciais, injury risk. São José dos Campos, Brazil.

139 140 Pinto Neto, Magini, and Saba

Wilk et al. (1983) suggested that the hand Although boxing is not considered a martial speed right before the impact was the primary art, it also deals with punching efficiency. In the factor contributing for the greater impact force of study done by Walilko et al. (2005), seven Olympic a karate martial artist strike compared with that of boxers from five weight classes delivered 18 straight a nonpractitioner. However, they did not verify this punches to the face of a Hybrid III dummy. Their suggestion in their study. Walker (1975) suggested reported average hand speed before impact was 9.14 that another important variable, the effective mass (SD 2.06) m/s and effective punch mass was 2.9 (SD of impact (me), could vary in different forms of 2.0) kg; they also reported a slight linear association karate strikes and affect the impact force; how- of the effective mass with the weight of the boxer ever, he did not report values of this variable. The (r = 0.484, p = 0.042). Walilko et al. (2005) were effective mass of impact is a measure of a body’s the first to suggest that the effective mass could be inertial contribution to the transfer of momentum linearly related to the body mass. during a collision. In the case of a martial art strike, One limitation of the methodologies used in the the effective mass can be seen as the mass of an past to determine values of effective mass (Smith imaginary rigid body that could replace the striker & Hamill, 1986; Voigt 1989; Walilko et al., 2005), and with the same speed as the hand speed before in view of using untrained subjects, was that the the impact produce the same effect on the collision striking surfaces used in the experiments were either as the striker would. Blum (1977) suggested that too heavy (punching bag) or too hard (dynamometer an adept karate practitioner achieves a “high mass” and Hybrid III dummy) for a untrained subject be by tightening all the appropriate arm and upper able to hit it with maximum hand speed without body muscles at the moment of impact, but further having a serious risk of getting injured. Addition- insight into this theory was not provided. Smith and ally, if a untrained subject were asked to do so, he Hamill (1986) were the first authors to investigate or she would probably do it with fear and this fear this suggestion. They measured the fist velocities could interfere in the results. This idea is supported from karate athletes of different skill levels and the by a study conducted by Vos and Binkhorst (1966). relative momentum of a 33-kg punching bag. The They reported that beginner karate students did bag momentum was greatest for the highest skilled not have the courage enough to strike bricks with subjects compared with the lowest skilled punch- their maximum force. Currently, there is a need ers even though their respective fist velocities were to further understand the varying contributions approximately the same, 11.03 (SD 1.96) m/s for all of effective mass and hand speed to trained and subjects. Smith and Hamill (1986) suggested that untrained subjects, which subsequently requires the the increase in bag momentum was due to the skilled development of methodologies that employ lighter boxer’s ability to generate a greater effective mass and softer surfaces. This paper presents the applica- during the impact than the lower skilled boxers. The tion of biomechanics to a novel situation in order estimated average effective mass for the highest to quantify the effective mass of yau-man “palm” skilled boxers was approximately 4.1 kg. Because strikes performed by subjects trained and untrained this value is greater than the mass of the hand, the in martial arts. The investigation’s primary goal is authors believed it reflected the ability of the athletes to quantify the contribution of effective mass and to link the mass of the arm into the punch. They hand speed on the performance of kung fu athletes did not report implications of a greater effective compared with nonpractitioners. mass with respect to injury risk and concentrated their analyses on only the performance aspect of Methods the matter. Voigt (1989) analyzed punches from 10 well-trained karate students and found values of Experimental Setup effective mass significantly smaller than did Smith Seven adept practitioners of kung fu yau-man (the and Hamill (1986). He reported average hand speed kung fu group) and five individuals with no martial before impact of 9.5 m/s and average effective mass, arts experience (the control group) were selected to obtained using data from a punching dynamometer, participate in the experiment. All 12 subjects were of 1.4 kg. Effective Mass of Kung Fu 141

Caucasian physically active males. The subjects and in the elbow (100 degrees), drawn toward the from the kung fu group had on average 12 years body with the wrist semiextended (Figure 1). Both of martial arts training time. The subjects’ average forearms are pronated. The movement consists of a height, mass, and age were 1.72 (SD = 0.07) m, fast rotation of the upper body that sends the striking 68.59 (SD = 9.4) kg, and 25.1 (SD = 6.6) years for hand forward and inverts the position of the arms. the kung fu group, and 1.69 (SD = 0.09) m, 68.62 The upper body ends in a position symmetrically (SD = 21.2) kg, and 22.2 (SD = 6.0) years for the opposite of where it started (Figure 2). During this control group. The subjects in the control group all strike, the lower body remains static in a standing had previous athletic experience. The body mass position called yau-man ma-bu. Target contact is of the subjects was obtained using a digital scale made with the heel of the hand. (Model UL-PH; Digi-Tron, Brazil). During the experiment, the striking hands of the Each subject was asked to strike a basketball at subjects were placed approximately 30 cm from the rest on a table five times with maximum force using basketball. The mass of the basketball (mb = 0.594 the yau-man palm strike (Pinto Neto et al., 2006 a, kg) was obtained using an electronic precision scale 2006b). The number of trials performed by each (Model AC10K; Marte, Brazil). Each impact was subject was limited to five owing to the potentially recorded by a high-speed digital imaging system injurious nature of performing multiple strikes, espe- (Model 8000s; Red Lake, Tucson, AZ) adjusted in cially for the control group. The yau-man palm strike this experiment to 1,000 Hz. At this acquisition rate, begins with the upper body slightly rotated and the the system can record digital images with 240 × 210 nonstriking (or defense) hand in front. The nonstrik- pixels of resolution (the CCD sensor total resolution ing arm is flexed at the shoulder (80 degrees) and is 656 × 496 pixels), where each pixel has dimen- at the elbow (160 degrees), slightly drawn toward sions of 7.4 µm × 7.4 µm; the total recording time is the body, with the wrist fully extended. The strik- 2.0 s, and each created file has 2,000 frames (Saba ing arm is also flexed in the shoulder (50 degrees) et. al, 2006). High-contrast markers were placed on

Figure 1 — Starting position of the yau-man palm strike. Figure 2 — Final position of the yau-man palm strike. 142 Pinto Neto, Magini, and Saba the lateral surface of the subjects’ forearms from the subject’s hand has a certain momentum defined as elbow to the junction between the hand and wrist me times its velocity. During the collision, the hand and vertically and horizontally across the basketball transfers part of its momentum to the basketball. to facilitate motion analyses (Figure 3). The data To solve the problem, the principle of conservation analysis was done using the ProAnalyst software of momentum was applied; this principle states (Xcitex Inc., Cambridge, MA), which is a profes- that the total momentum of an isolated system is sional analytical software for extracting motion constant (Halliday et al., 1997). It was considered from video and data. ProAnalyst is a full-featured that the coefficient of restitution of the hand–ball auto-tracking software that can measure position and interface for the collisions (e) was the same for all velocity of a moving part and analyze the motion strikes and subjects. components with no need for special tracking mark- The value of e was approximated by the coef- ers. Figure 3 shows an example of a digital image of ficient of restitution hand–ball interface obtained one of the strikes recorded by the high-speed camera by Equation (1) (Enoka, 2002), where the heights with several additional annotations done during the were found through the following method. It was video analysis using the ProAnalyst software. measured by the height up to where the ball bounced

This methodology was approved by the Univer- (h2) after it was dropped from a known height (h1) sity of Vale do Paraiba Ethics in Research Commit- into the bottom of the palm of one subject from each tee (Protocol #: L008/2005/CEP), and all subjects group with average height and weight among both provided their informed written consent. groups. Both heights were measured from the palm of the subjects. The subjects were asked to lie down Physical Approach and place their elbow rested on the floor, positioning their palm facing upward; arms were flexed 90° at To obtain the values of the effective mass, each strike the shoulder joint. was analyzed as a collision problem between two h bodies of masses m and m ; only interaction forces e = 2 (1) e b h between the two bodies were considered to influence 1 h was arbitrarily chosen to be 1.7 m; the value of their motions during the collision. The term me rep- 1 resents the effective mass of impact of the subject; h2 was found using a high-speed camera to record the basketball falling and bouncing in front of a tape mb represents the effective mass of the basketball, which was considered to be the same as the mass measure. This procedure was repeated several times of the basketball. An instant before a collision, the so that the camera lens could be placed at a height approximately the same as h2 and could record three sequences in which the ball bounced straight up for each subject. To determine another important physical characteristic of the basketball used in this experiment, the coefficient of restitution of the basketball was calculated similarly to the manner in which the hand-ball interface coefficient of restitution was calculated, but by dropping the ball onto the floor (coefficient of restitution approximately equal to 1) instead of the hand. The measured coefficient of restitution of basketball was 0.764 (SD = 0.014). The effective mass was obtained by combin- ing Equations (2) and (3). Equation (2) represents another formula for the coefficient of restitution (McInnis and Webb, 1971; Meriam, 1966) and Equation (3) expresses the conservation of linear Figure 3 — Example of a digital image of one of the yau- man palm strikes recorded by the high-speed camera showing momentum (Halliday et al., 1997). several annotations made during the video analysis using the sbf − shf (2) ProAnalyst software and markers on the subject’s forearm and e = on the basketball. sbi − shi Effective Mass of Kung Fu 143

men were analyzed and their average height, weight, me s hi+m b sbi = me s hf+ m b sbf (3) and age were 1.74 (SD 0.06) m, 74.5 (SD 9.3) kg, where s is the hand speed immediately before the hi and 23.8 (SD 6.2) years, respectively. Student t test collision, s is the initial ball speed (in this case, bi comparisons between these characteristics and those zero), s is the ball speed after the collision, and s bf hf from the subjects of this study show no significant is the hand speed after the collision. The vaules for differences (p = 0.692 for height, p = 0.380 for s and s were obtained through video analyses. To hi bf weight, and p = 0.933 for age). Regression equations find s , first hand displacements in 1-ms intervals hi specific for populations according to age, gender, during the last 20 ms before the instant of the impact race, and morphology provide accurate estimations were measured and a displacement-vs.-time graph of body segment parameters for use in kinetic equa- was plotted. The displacement of the hand was mea- tions of motion (Durkin & Dowling, 2003). Average sured using the contrast marker placed at the lateral values for me were compared with average values of surface of the forearm near the junction between the m for both the kung fu and control groups. Addition- hand and wrist. In these 20 ms, it was considered ally, the values of me for each subject were normal- that the hand describes a straight-line trajectory. ized by their respective value of m. The values of the Second, a high-degree polynomial was fitted to the normalized effective mass (me/m) were compared displacement-vs.-time data. Finally, we calculated between the groups so that individual characteristics the derivative of the fitted polynomial in the instant were taken into consideration. immediately before the impact. The value for s bf In this experiment, the performance (P) of the was found as the average speed of the basketball in athletes was defined by the ball speed after collision, the 5-ms period after the end of the collision. The Equation (5), which is derived from Equation (4). displacement of the basketball was measured using m()1+ e the center marker on it (Figure 3) considering a P = e s (5) m+ m hi straight-line trajectory during the 5-ms period. e b It follows that Equation (5) shows that the performance is directly

mb s bf proportional to the hand speed and not to the effec- me = (4) shi ()1+ e − sbf tive mass. Equation (5) also shows that the graph of

P vs. shi is a straight line with slope (S) that increases The use of Equation (4) to findm e has the advantage with the increase of me, Equation (6). that it is not necessary to have the value of shf. This fact is important because there are muscle forces m()1+ e S = e (6) acting on the motion during and especially immedi- me+ m b ately after the collision. These forces are responsible In order to compare the contribution of an to terminate arm motion before its full extension, increase in the effective mass alone in the per- which is a characteristic of yau-man strikes. The formance of the kung fu group, the values of the values of hand speed after collision that could have ball speed from individuals of both groups were been found through video analyses would not neces- normalized, dividing them by their respective hand sarily represent the variable s in Equations (3) and hf speeds. It is important to note that a martial artist (4), because these equations were used considering performance on a strike is usually related to values that only interaction forces between the two bodies of impact force (Atha et al., 1985; Walilko et al., influenced their motion. The approach of not con- 2005; Wilk et al., 1983). According to Newton’s sidering these forces on the physical analysis did laws, and considering that the durations of the not influence the results because these forces have impact do not vary much for all collisions with the no significant effect on any other variable besides basketball, 0.015 (SD = 0.001) s for all strikes, the shf itself. value of sbf is directly proportional to the average Regression equations developed by Zatsiorsky impact force. and Seluyanov (1983) were used to estimate each subject’s hand and forearm mass (m). They were Statistics used based on the similarity between the individuals studied by Zatsiorsky and Seluyanov (1983) and Anderson–Darling and Kolmogorov–Smirnov tests the subjects of this study. In their work, 100 white were done to verify the normality of the data. For 144 Pinto Neto, Magini, and Saba the variables that demonstrated normality, the mean were considered as valid data. Only the strikes values were compared using the Student t test for where the ball did not touch the table during its equal or different variances. F tests were used to trajectory and it did not spin were considered. verify the possibility of same variances. Student’s From the validated strikes, two strikes were chosen paired t test was used to compare variables within from each subject for the statistical analyses. The the groups. The correlation between variables was choices were done based on the trajectory of the investigated by Pearson’s correlation. Because the basketball; trajectories closer to the horizontal line validation of normality tests is questionable when were preferred. The choice of using only the two applied to samples of low size (Hoel, 1984; Ryan strikes for each person was made considering that Jr. & Joiner, 1976), nonparametric statistical proce- most subjects had only two strikes validated. The dures were also conducted. The comparison between average of the two values from each individual was the means was done using the Mann–Whitney test. used in the statistical analysis. The comparison between variables within the groups To obtain the value of the coefficient of res- was done using the Wilcoxon matched-pairs test. titution of the hand–ball interface, the ball had to

The correlation between variables was determined be dropped 17 times. The average value of h2 was by Spearman’s correlation (R). Because in all 0.757 (SD = 0.039) m, and the average value of e cases, the p values of the nonparametric tests are was 0.667 (SD 0.017). There was no significant greater than those of the parametric tests, only the difference between the values of e obtained for the nonparametric p values are reported in the Results two subjects (p = 0.184). Table 1 shows the average section, and they are considered significant when data obtained for both groups. less than 0.05. More details on the statistical analysis Kung fu athletes presented significantly higher described above can be found in Hoel (1984) and averages of effective mass (p = 0.004), normalized Ryan Jr. and Joiner (1976). effective mass (p = 0.004), hand speed (p = 0.042), and performance (ball speed after collision) (p = Results 0.004) than did the control group. The average effective mass for the kung fu group was 2.62 (SD Considering the physical approach, not all strikes 0.33) kg and for the control group it was 1.33 (SD

Table 1 Data from the Kung Fu and Control Groups

mc (kg) m/mc m (kg) d (cm) shi (m/s) sbf (m/s) me (kg) me/m (kg) Control group 1 56.45 0.023 1.30 30.0 5.4 6.2 1.32 1.02 2 52.25 0.024 1.25 38.9 5.7 6.0 1.02 0.81 3 51.4 0.024 1.23 29.4 5.0 5.65 1.37 1.11 4 96 0.021 2.02 21.7 4.2 5.05 1.54 0.76 5 87 0.022 1.91 26.0 4.9 5.7 1.42 0.74 M 68.62 0.0228 1.54 29.18 5.04 5.72 1.33 0.89 SD 21.21 0.0013 0.39 6.36 0.57 0.44 0.19 0.16 Kung fu group 1 54.8 0.023 1.26 34.9 7.6 9.95 2.2 1.75 2 69.05 0.022 1.52 37.7 8.35 11.3 2.6 1.71 3 80.8 0.022 1.78 42.5 8.35 11.35 2.74 1.54 4 72.5 0.022 1.60 19.0 5.3 7.4 3.14 1.97 5 78 0.022 1.72 26.1 4.95 6.6 2.37 1.38 6 65 0.023 1.47 21.7 5.9 8.05 2.9 1.97 7 60 0.023 1.38 26.4 6.25 8.35 2.4 1.73 M 68.59 0.0225 1.53 29.74 6.67 9.00 2.62 1.72 SD 9.40 0.0006 0.18 8.73 1.42 1.89 0.33 0.21

Note. mc = corporeal mass; m/mc = results of Zatsiorsky and Seluyanov regression equations; m = hand and forearm mass; d = hand initial distance to target; shi = hand speed before impact; sbf = ball’s speed after impact; me = effective mass; me/m = normalized effective mass. Effective Mass of Kung Fu 145

0.19) kg. The average hand speed was 6.67 (SD For both groups and all subjects, no significant 1.42) m/s for the kung fu group and 5.04 (SD 0.57) correlation was found between the values of m/s for the control group. The average ball speed effective mass and body mass (R = 0.7 and p = 0.188 was 9.00 (SD 1.89) m/s and 5.72 (SD 0.44) m/s for for the control group; R = 0.393 and p = 0.383 for the kung fu group and control group, respectively. the kung fu group; R = 0.392 and p = 0.208 for all The kung fu group’s average effective mass was subjects). approximately 97% greater than the control group’s, Figure 4 shows a plot of the values of ball speed the hand speed was 32% greater, and the ball speed vs. hand speed for both groups. It also shows the was 57% greater. linear fit equation for both groups. Kung fu group Although for all strikes, the hands were placed values presented a significant correlation between approximately 30 cm from the basketball surface, the two variables (R = 0.991 and p < 0.001). The most of the subjects moved their hand before start- control group correlation was not significant (R ing, which caused slight differences among the = 0.8 and p = 0.104). The slope of the regression distances. The average distance was 29.74 (SD 8.73) line for the kung fu group is 1.33, whereas for the cm for the kung fu group and 29.18 (SD 6.36) cm for control group is 0.72. From Equation (6), it can be the control group; there is no significant difference seen that the theoretical slope (S) increases as the between these averages (p = 1). It was observed that effective mass increases. hand speed increased with distance for the kung fu Figure 5 shows a plot of the values of the group (R = 0.883 and p = 0.008) and for the control normalized performance parameter vs. the effec- group (R = 1 and p = 0.008). tive mass for both groups. These variables were Comparing the values obtained for the average significantly correlated for both groups (R = 1 and effective mass and hand and forearm mass, it was p < 0.001 for the kung fu group; R = 0.9 and p = found that for the control group, me is statistically 0.037 for the control group). Figure 5 also shows a equivalent to m (p = 0.917), whereas for the kung fu clear separation between the data points of the two group, me is significantly greater thanm (p = 0.002). groups; the values of both variables are larger for the kung fu group.

Figure 4 — Plot of the values of the ball speed after the strike vs. hand speed before strike for both kung fu and control groups. 146 Pinto Neto, Magini, and Saba

Figure 5 — Plot of the values of the normalized performance parameter vs. the effective mass for both kung fu and control groups.

Discussion A comparison of our results on effective mass with those reported by Voigt (1989) (average effec- The study of kung fu strikes using a soft strike sur- tive mass of 1.4 kg) shows that the kung fu group’s face made it possible to investigate for the first time effective mass is higher than their reported effective the main differences related to effective mass and mass. The average value of effective mass for the hand speed between trained and untrained martial kung fu group is approximately the same as the arts athletes. The fact that the subjects in this study value (2.9 kg) reported by Walilko et al. (2005). were asked to hit something light and soft made The 4.1-kg value of average effective mass reported possible for all of them to hit it with maximum by Smith and Hamill (1986) is much larger than intensity. all others. Nevertheless, the difference between all Our study presents two main limitations: the these values of effective mass might be attributed low number of subjects within each group and the to the different methods of obtaining these values low number of valid trials per subject. The low (basketball, dynamometer, dummy, and punching number of subjects within each group was due to bag). This suggests that the effective mass may the low number of yau-man kung fu athletes and vary depending on the object being hit. In order to the difficulty in having yau-man kung fu athletes compare different forms of strikes, the same meth- with available time to participate in the experiment. odology must be applied to all strikes. The low number of valid trials per subject was The results show that two subjects of the kung consequence of the methodology and the physical fu group had average hand speeds in the range of approach. Other less significant limitations are as the values measured for the control group. For one follows: assuming the preservation of momentum, of the subjects, that probably happened because he neglecting the error in the speed measurements, and had the smaller average distance to target within using linear regression equations for comparison of all twelve subjects. The low values obtained by the groups. Nevertheless, the study was successful in other subject might have happened for different providing some insightful findings and it serves as reasons; the most probable is individual genetics, a foundation for future research. but other possibilities are daily performance Effective Mass of Kung Fu 147 variation, psychological aspects such as motivation, speculation is in agreement with Pain and Challis low number of trials, or other reasons beyond (2002), who found that muscle tension reduced the our speculations. It is important to note that even intrasegmental motion by 50% during high-energy though both of them presented low hand speeds, impacts, contributing to a decrease in the energy lost they differentiated themselves from the subjects from the forearm during these impacts. Other fac- of the control group by their values of effective tors that might contribute to higher effective masses mass and performance. This is in agreement with are the positioning of the hand, wrist, elbow, and Smith and Hamill (1986), who suggested that better shoulder joints into a very firm position, and better trained individuals who had obtained approximately muscle coordination for synchronizing the motion the same hand speeds as lesser trained individuals from different segments of the body as much as pos- displayed better performance because of higher sible. Future electromyographic studies should be effective masses. done to confirm some of these speculations. The values of hand speed measured in this study Comparing the values of the ball speed after the are smaller than the values reported in the literature strike with the hand speed before the strike for both (Walilko et al., 2005; Smith and Hamill, 1986). That kung fu and control groups, the role of the effective probably happened because of the difference in the mass becomes clear. Because of the higher effective starting distances between hand and target for the masses of the kung fu athletes, the kung fu group’s kung fu yau-man movements and the boxing and performance increased approximately twice as much karate movements (Atha et al., 1985; Walker, 1975). with the increase of hand speed than did the control The average distance of approximately 30 cm for group’s performance. This suggests that the subjects the palm strike is much smaller than the 50–80 cm from the kung fu group transferred their kinetic average distance of the boxing and Karate punches energy into the ball more effectively at all speeds (Atha et al., 1985; Walker, 1975). The results show desired, and particularly for faster strikes. that in this study the hand speed increased as the Equation 5 shows that, for objects much heavier starting distance to target increased. It is reason- than the basketball, the values of P become approxi- able to expect that this relation would be true for mately directly proportional to both the effective other types of strikes and larger distance variability mass and the hand speed. This fact—in addition to because a greater distance to target provides more the results found in this article showing that the dif- time for accelerating the hand and more space for ference between the average values of effective mass the performance of wider movements. The 30-cm for trained and untrained subjects is much larger distance used in this experiment is the standard than the difference in the average values of hand distance for the strike studied. speed—suggests that for impacts against heavier The results of effective mass and the estimations objects, the effective mass would be the main factor calculated based on the Zatsiorsky and Seluyanov to distinguish a trained from a untrained subject. (1983) regression equations verify that all subjects That would be the case of a board- or block-break- presented higher effective masses than their esti- ing demonstration, a strike during a competition, or mated hand masses, confirming what was suggested an actual self-defense situation, considering that the by Smith and Hamill (1986). Additionally, these mass of a stack of bricks, patio block, or a person results show that the kung fu group subjects could is much greater than the basketball mass and all link more than their hands and forearm masses into these possible targets present a much larger resis- the strikes, whereas the subjects from the control tance to movement than the basketball itself. This group could not. Contrary to what happened in the fact might be one of the reasons why martial arts study done by Walilko et al. (2005), no significant masters pay more attention to proper striking tech- linear correlation between the effective mass and niques, bone alignment, coordination, and proper the weight of the subjects from both groups was timing of muscle contractions, than to hand speed. found. This result suggests that the effective mass is Interestingly, these same factors that contribute to highly dependent on factors other than body mass. higher effective masses and performances are also The well-trained martial artists may achieve higher responsible for preparing the body to sustain a high effective masses by tightening appropriate muscles reaction force from the target being hit. The correct immediately before the impact (Blum, 1977). This bone alignment and muscle contraction timing are 148 Pinto Neto, Magini, and Saba responsible to turn the hand, forearm, and arm into a Hoel, P.G. (1984). Introduction to mathematical statistics. New very firm unit. Perhaps the role of the posturing and York: John Wiley and Sons. muscle contractions is to distribute the reaction force Meriam, J.L. (1966). Dynamics. New York: John Wiley and Sons. among a sufficient number of structural members, McInnis, B.C., & Webb, G.R. (1971). Mechanics dynamics: and doing so avoids causing harm to the body. In The motion of solids. Englewood Cliffs, NJ: Prentice turn, the lack of technique of untrained subjects, Hall Inc. demonstrated in numbers by their lower values of New Martial Hero Magazine. (1972). New Martial Hero Maga- effective mass, would probably be responsible for zine, 76, 56-59. Pain, M.T.G., & Challis, J.H. (2002). Soft tissue motion during injuries if they were to hit much heavier or harder impacts: Their potential contributions to energy dissipa- objects. tion. Journal of Applied Biomechanics 18, 213-242. The importance of studying effective mass goes Pinto Neto, O., Magini, M., & Saba, M.M.F. (2006a). Power beyond its application to kung fu. Effective mass is analyses of a yau-man kung fu strike. FIEP Bulletin, 76, important in many other sporting activities in which 15-17. the striking of a mass is performed, such as baseball, Pinto Neto, O., Magini, M., & Saba, M.M.F. (2006b). 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