INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1988.4. 260-281 Techniques Used in Performing Handspring and Salto Forward Tucked in Gymnastic Vaulting Yoshiaki Takei The purpose of this study was to determine the mechanical factors that govern success in the performance of the handspring and salto forward tucked vault. The subjects were the 41 all-around gymnasts participating in the 1986 USA Gymnastics Championships. A motion-picture camera placed with its optical axis at right angles to the runway was used to record the performances of the subjects. Significant correlations indicated that the horizontal velocity at takeoff from the board was an important determinant for successful results, and also that the more the gymnast's focus was on horse contact or blocking and the more vertical the direction of his effort at takeoff into the postflight, the better the final result. Quite unexpectedly, significant correlations revealed that the greater the relative height of takeoff from the horse and the less the height of CG at landing on the mat, the greater the points awarded by the judges. These relationships were almost entirely a consequence of the landing angle. Rationale for these findings were based on close observations of the filmed performances and the correlational analyses. Gymnastic vaul'.s may be classified into two categories (Kaneko, 1974, 1977): (a) the continuous rotation vaults, in which the rotation of the body about the gymnast's transverse (or somersault) axis is in the same forward direction throughout, and (b) the counter-rotation vaults, in which the direction of rotation of the body about the transverse axis is reversed during the contact with the horse. The handspring, Yamashita, handspring salto forward, Tsukahara, and their variations are examples of the continuous rotation vaults, whereas the hecht vault and its variations are examples of the counter-rotation vaults. Counter-rotation vaults are generally less spectacular and less popular than continuous rotation vaults, in part because the technique involved in initiating counter rotation during contact with the horse is difficult and requires a great deal of timing and control, and in part because the introduction of the springy takeoff (or Reuther) board, at the time of the 1956 Olympic Games in Melbourne, Yoshiaki Takei is with the Biomechanics Laboratory, Department of Physical Education, Northern Illinois University, DeKalb, IL 601 15-2854.
GYMNASTIC VAULTING 261 Australia, markedly increased the difficulty the gymnast experiences in reversing the direction of rotation during contact with the horse. The vaults most commonly performed in national and international competitions today are variations of the round-off, flic flac entry vault for women and the front handspring for men-the vaults of the continuous rotation category. Among these variations is the handspring and salto (somersault) forward tucked vault (Figure 1). In women's gymnastics this vault is regarded as a C-vault with a base score of 9.80 points. In view of training progression and safety, the handspring and salto forward vault is the foundation for learning more advanced vaults seen frequently today. Once this vault is mastered, more complex vaults can be learned more safely and efficiently. This is one of the reasons that the vault was chosen as men's compulsory vault in major competitions for the 1985-88 Olympic period. Now it is crucial to master this vault in order to do well in compulsory competition and simultaneously to develop a sound foundation for learning more complex optional vaults. Thus, there is an urgent need to identify factors that govern successful performance of the handspring and salto forward vault to help coaches understand the mechanics involved. Figure 1 - Selected positions and the trajectory of the CG of a subject performing a handspring and salto forward tucked. Several investigations have been made of the handspring and salto forward tucked vault (Bajin, 1979; Cheetham, 1982; Dillman, Cheetham, & Smith, 1985). Bajin studied the pushoff phase of the vault performed by four top world-class gymnasts. The four vaults studied were two near-end vaults (hand contact at the near end of the horse) and two far-end vaults (hand contact at the far end of the horse). He found that the duration of the pushoff and the extension of the active joints (arm and trunk) in repulsion were quite different, depending upon the end of the horse at which hand contact was made. Although duration of the pushoff was longer in the near-end vaults, none of the four vaulters achieved a full extension of the active joints during the pushoff, indicating there was room for improvement in their performances.
Cheetham (1982) investigated selected characteristics of the preflight phase that might affect the postflight when seven collegiate gymnasts and a former Australian Olympian performed the handspring and salto forward tucked vault. The postflight variables considered were (a) the judged distance, the horizontal distance from the far end of the horse to the point of landing on the mat; (b) the judged height, the vertical distance from the top of the horse to the highest point attained by the hip; and (c) the angular velocity of the shoulder joint about the body center of gravity (CG) at takeoff from the horse. Significant positive correlations @<.05) were found between the judged distance of the postflight and (a) the time of preflight (r=0.68), (b) the distance of preflight (r=0.80), and (c) the horizontal velocity of takeoff from the board (r =0.78). In addition, significant negative correlations were found between the judged distance and (a) the angle of takeoff from the board (r= -0.74), (b) the change in horizontal velocity on the board (r= -0.71), and (c) the vertical velocity at touchdown on the horse (r= -0.73). All vaulters were found to have positive, or upward, vertical velocity of the CG on horse contact. During the 1984 Olympic Games in Los Angeles the eight gymnasts in the men's vaulting finals were filmed, each performing two vaults for a total of 16 performances. Dillman et al. (1985) categorized the 16 vaults into Tsukahara and handspring families for the purpose of analysis. Comprehensive kinematic descriptions including the temporal, displacement, and velocity measurements were presented for the two types of vaults in the continuous rotation category. The present study was not only conducted in a competitive situation involving a large number of subjects but was also the first attempt to systematically identify and analyze the factors that are causally related to the performance of this vault by developing the mechanical model. The purpose of this study was to determine the mechanical factors that govern success in the performance of the handspring and salto forward tucked vault. Model Methods The ultimate measur: of a gymnast's performance of a vault is the number of points awarded for the performance (see Figure 2). This number is determined by the average of the two middle scores awarded by the four judges. According to the Code of Points of the Federation of International Gymnastics (1985), the evaluation of a horse vault is categorized into five general areas: (a) a base score designated for the vault, (b) preflight, (c) postflight, (d) the execution during the vault, and (e) possible bonus points for display of originality and/or virtuosity. The factors to consider in analyzing a vault are, first, linear motion of the gymnast in phases (b), (c), and (d) above, reflected in the path followed by the gymnast's CG, and second, angular motion of the gymnast in phases (b), (c), and (d) above, reflected in the angular distances through which the gymnast rotates about the transverse (or somersault) axis. The trajectory of a gymnast's CG in preflight is governed by the gymnast's velocity at takeoff from the board, by the gymnast's relative height at takeoff (i.e., the height of the CG at takeoff from the board relative to its height at the instant of contact with the horse), and by the air resistance encountered. Sirnilarly, the trajectory of the CG in postflight is governed by the velocity at takeoff
AWARDED BY JUNES ANGULAR DISTANCE (PRE.FLIGHT) ANGULAR MOMENTUM AT TOUCHDOWN (BOARD) CHANGE IN ANGULAR MOMENTUU (BOARD) HORIZONTAL \ VERTICAL VELOCITY AT TAKEOFF GYMNAST VERTICAL IMPULSE (BOARD) Figure 2 - Model showing preflight factors that determine the official score. (The postflight factors that determine the official score are almost identical to those shown above. For the sake of brevity, they have not been included in the model.),., m W
from the horse, by the gymnast's relative height at takeoff (i.e., the height of the CG at takeoff from the horse relative to its height at the instant of contact with the mat), and by the air resistance encountered in flight. The velocity at takeoff of a vault may be considered as the vector sum of the horizontal and vertical velocities at takeoff. The horizontal and vertical velocities at takeoff in turn are equal to the sum of the corresponding velocity at touchdown and the change in that velocity that occurs during takeoff. The velocity with which the gymnast lands on the board at the conclusion of the hurdle step is governed by the velocity at takeoff from the floor, the relative height at takeoff (i.e., the height of the CG at takeoff from the floor relative to its height at touchdown on the board), and the air resistance. Similarly, the velocity with which the gymnast lands on the horse at the conclusion of the preflight is governed by the velocity at takeoff into the preflight, the relative height at takeoff (i.e., the height of the CG at takeoff from the board relative to its height at touchdown onto the horse), and the air resistance. The changes in horizontal and vertical velocities that occur during the takeoff are determined by the horizontal and vertical impulses that the board or the horse exerts on the gymnast (in reaction to the impulses the gymnast exerts on the board or the horse), and by the mass of the gymnast (impulse-momentum relationship). The horizontal and vertical impulses exerted on the gymnast are, by definition, determined by the corresponding average forces exerted and the time for which these forces act (i.e., the time of support). The angular distance through which a gymnast's body rotates while he or she is in the air depends on the gymnast's angular momentum at takeoff, on his or her average moment of inertia during flight, and on the time of flight. The time of flight is determined by the velocity at takeoff, the relative height of takeoff, the air resistance encountered in flight, and acceleration due to gravity. The aesthetic characteristics, or form, of a gymnast's performance such as elegance, sharpness, smoothness, finess, and harmony depend on a number of factors. These include the positions of the various body parts during the vault and the manner in which they move from one position to another. The effort required to identify all of them and to define them precisely in mechanical terms is nearly impossible, or is much greater than any benefit that might be gained from doing so. In fact, Kaneko (1974) goes as far as to say that the form in gymnastics lies outside the realm of mechanics and should be studied as art and aesthetics. For this reason the model was not developed further in the direction of aesthetics or form. With all of these identified factors included, the complete deterministic model for the handspring and salto forward tucked vault is as shown in Figure 2. (The postflight factors that determine the official score are nearly identical to those in the preflight, and thus have not been included in the model for the sake of brevity.) Data Collection Subjects. The subjects were 41 all-around gymnasts (including members of the USA team at the 1984 Olympic Games and the 1986 World Championships) who performed the handspring and salto forward tucked vault during the 1986 USA Gymnastics Championships in Indianapolis. The means, standard deviations, and
GYMNASTIC VAULTING 265 Table 1 Means, Standard Deviations, Maxima, and Minima for Height, Mass, and Judges' Scores of the Subjects Variables M SD Min Max Height (m) 1.69 0.06 1.55 1.80 Mass (kg) 64.72 5.66 53.64 79.55 Score (pts) 8.76 0.35 7.90 9.50 ranges for score, height, and mass of the gymnasts filmed in the present study are presented in Table 1. Filming Protocol. A 16-rnm motion-picture camera, filming at a nominal rate of lollfps, was used to record the performance of the subjects in each trial. This camera was placed at a distance of 2@ m from the midline of the horse and runway, with its optical axis at a right angle to this line. The camera was aligned with the front (or near) end of the horse and was used to record the vaulters' performances during the hurdle onto the takeoff board, preflight, support, postflight, and landing. Before the start of the competition a 2-m linear scale was Nmed in the primary plane of motion. This scale enabled the film measures to be converted to actual values. Internal timing lights and a timing light generator pulsing at a frequency of 10 Hz were used to mark the sides of the films and thus provide a basis for determining appropriate temporal scales. Data Reduction Each of the 41 vaulting performances was analyzed with the aid of a computerized digitizing system consisting of a Vanguard projection head (Vanguard Instrument Corp., Melville, NY) and Complot digitizer (Houston Instruments Division, Bausch & Lomb, Austin, TX) linked on-line to a laboratory microcomputer. Approximately 50 frames of the film for each trial were digitized. These included the frames showing the gymnast's position as early in the hurdle phase as possible, the touchdown on the takeoff board, the takeoff from the board, the touchdown on the horse, the takeoff from the horse, and the touchdown on the mat. In addition to the frames showing the instants of takeoff and touchdown, every other frame was digitized for the on-board, the on-horse, and the on-mat phases. For the preflight and postflight phases, every third and fifth frame, respectively, was digitized for subsequent analysis. The x- and y-coordinates of 21 points defining the configuration of a 14- segment model of the human body described by Clauser, McConville, and Young (1969) were recorded for each frame analyzed. Takeoff was defined as the instant depicted in the frame in which the gymnast was first seen to have broken contact with the board or the horse, and touchdown as the instant depicted in the frame in which he was first seen to have regained contact with the board,
horse, or mat. The time of support (contact) was considered as the time that elapsed between the exposure of the first frame showing the gymnast in contact with the board or the horse and the first frame in which he was seen to have broken contact with the horse or the board. The time of flight was considered as the time that elapsed between the exposure of the first frame in which the gymnast was seen to have broken contact with the board or the horse and the first frame showing he was in contact with the horse or the mat. A specially developed software program was used to identify and correct outliers in digitizing data points for each frame analyzed. The data were then smoothed using a second-order polynomial least-squares approximation to five data points as described by Wood (1982). Subsequently, the location of the CG in each analyzed frame was computed using Clauser et al.'s (1969) segmental mass proportions and segmental CG locations. CG coordinate data for the first frame showing that the gymnast had broken contact with the board or the horse and the frame in which he was last seen to have remained in the air before contact with the board, horse, or mat were used to calculate velocities using the appropriate equations of uniformly accelerated motion. Air resistance was assumed to be negligible. This procedure was chosen instead of other commonly used methods in the belief that it was less sensitive to small errors in the location of the CG used in the computation. The average impulses and forces exerted during the support phases imrnediately preceding the takeoff into preflight and postflight were determined using the impulse-momentum relationship, which states that the change in the linear momentum of a body is equal to the linear impulse that produced the change. In algebraic terms, where F=average force; t=time of support; m=the mass of the athlete, and Vf and Vi=the velocities of takeoff and touch&own, respectively. This equation, when rearranged, yields an expression for F: The angular momentum about a transverse axis through the CG of the gymnast during the preflight and postflight was calculated as described using the method of Hay, Wilson, Dapena, and Woodworth (1977), and the segmental moment of inertia data of Whitsett (1963). The angular distance (6) through which the gymnast rotated about a transverse axis through his CG during pre- and postflights was defined as, where H=the angular momentum andl=the average moment of inertia of the gymnast about the same axis, and t=time. Although direct measurement of angular distance is easily made on a single rigid body, the same is not possible on interconnected body systems that experience relative motion. The method described above was therefore chosen to characterize the angular distance through which the multisegmented body of the gymnast rotated.
GYMNASTIC VAULTING 267 Data Analysis The data analysis procedures used in this study consisted of (a) computation of the means and standard deviations of all factors identified in the deterministic model and for which data could be collected, (b) computation of the Pearson product moment correlations between each of the factors in the second level of the model and the judges' score, and (c) when a significant relationship was found between one of these factors and the judges' score, the computation of the zero order correlation between the factors linked to it at the third level, and the judges' score. The basic procedure of step (c) was then repeated to advance the analysis to progressively lower levels in the model. A value of P<.05 was taken to indicate statistical significance. Descriptive Data Results and Discussion The means and standard deviations for the horizontal and vertical velocities at takeoff and touchdown, the angles of takeoff and touchdown, and the heights of CG at takeoff and touchdown are presented in Tables 2 and 3. For comparison of times and velocities of interest, selected data from the present study are included in Table 4 together with data from the studies of Cheetham (1982) and Dillman et al. (1985). Because the average competitive standards of the subjects involved in these studies increased from the national-level athletes of the present study, through the college athletes of the Cheetham study, to the Olympic finalists of the Dillman et al. study, these data are presented in the corresponding order. Velocity Changes During Horse Support. As shown in Table 4, the Olympic finalists contacted the board with the least downward vertical velocity and Table 2 Means, Standard Deviations, Maxima, and Minima for Horizontal and Vertical Velocities and Angles of Resultant Velocity to Horizontal at Selected Instants Horizontal velocity Vertical velocity Angle (mls) (mls) (deg) Instant M SD Min Max M SD Min Max M SD Min Max Board touchdown 7.33 0.46 6.57 8.54-1.17 0.38-2.02-0.25-9.1 3.2-16.5-2.0 Board takeoff 5.020.304.435.71 3.690.24 3.40 4.36 36.42.8 32.3 43.7 Horse touchdown 5.02 0.30 4.43 5.71 2.23 0.42 1.65 3.46 23.9 4.3 17.9 37.3 Horse takeoff 3.590.243.064.12 2.790.27 2.15 3.24 37.83.4 29.3 46.1
Table 3 Means and Standard Deviations for Heights of CG at Takeoff and Touchdown Height of Height of Relative height of takeoff touchdown takeoff (m) (m) (m) Preflight 1.40 (.05) Postflight 2.39 (.05) Note. Standard deviations shown in parentheses. Table 4 Comparison of Mean Values for Times of Flight and Support, Velocities, and Angles Present study (1988) Cheetham (1982) Dillman et al. (1985) (USA Champion- (college gymnasts, (Olympic finals, ships, handspring handspring salto salto forward salto forward) forward) variations) Time (sec) Time on board 0.13 Time of preflight 0.17 Time on horse 0.20 Time of postflight 0.83 Horizontal velocity (mls) Board touchdown 7.33 Board takeoff 5.02 Horse takeoff 3.59 Vertical velocity (mls) Board touchdown - 1.17 Board takeoff 3.69 Horse touchdown 2.23 Horse takeoff 2.78 Angle of takeoff & touchdown (deg) Board touchdown - 9.13 Board takeoff 36.36 Horse touchdown 23.88 Horse takeoff 37.76
GYMNASTIC VAULTING 269 departed from it with the greatest upward vertical velocity. They also contacted the horse with the greatest upward velocity and departed from it with the greatest upward vertical velocity. With all else equal, this latter ensures that on average the Olympic finalists had more time in the air, traveled a greater horizontal distance due to a longer time of postflight, and attained a greater maximal height of postflight than did the subjects of the other two studies. However, the increase in vertical velocity during the horse support for the Olympic finalists was only 8%, compared to 14% and 25 % for the college gymnasts and the subjects in the present study, respectively. This does not necessarily indicate that the Olympic finalists did not apply as much blocking or impulses as did the gymnasts in the other two groups, but rather that the vertical velocity at touchdown on the horse for the Olympic finalists was already high. Therefore it was unlikely that the Olympic finalists could achieve a similar percent change in vertical velocity by exerting the vertical impulse of the same magnitude employed by the gymnasts in the other two groups. In fact, the Olympic finalists were executing complex vaults for which twisting or additional somersault had to be initiated either during or immediately after the horse contact to the takeoff into the postflight. Apparently the Olympic finalists recognized the difficulty in devoting all of their efforts to maximize the change of vertical velocity during the horse support (as they might have done in performing a plain handspring salto forward vault) while they are simultaneously preparing to twist. They thus attempted to optimize the phases of the vault prior to takeoff from the horse, as indicated by much higher vertical velocity of takeoff from the board than that of the other groups. Impulses and Average Forces. Information on the impulses and average forces exerted during the board and horse contact phases of the handspring and salto forward vault was unavailable in the previous literature. It was thus of interest to determine the magnitude of the impulses and average forces exerted on the gymnast during these critical phases of the vault. The means and standard deviations for the horizontal and vertical impulses and the average horizontal and vertical forces during periods of support are presented in Table 5. The largest value of the average forces found was 3312 N, which translated into 5.2 times the mean body weight of the subjects. Angular Momentum and Times of Flight and Support. As in the case of the impulses and the forces exerted during the support phases of the handspring and salto forward vault, the magnitude of the angular momentum for the vault was not available in the previous literature. It was therefore of interest to determine the magnitude of the angular momentum of the vault. The mean angular momenta of pre- and postflight were 11 1 Kg m2/s and 64 Kg m2/s, respectively, for the subjects in this study. The means and standard deviations for the average angular momentum and average moment of inertia and angular distance of pre- and postflight are presented in Table 6. The means and standard deviations for the times of board and horse support and pre- and postflight are presented in Table 7. Causal Relationships Preflight Technique and Official Score. Of the three variables identified in the second level of the deterministic model for the preflight (Figure 2), trajectory
Table 5 Means, Standard Deviations, Maxima, and Minima for Mean Impulses and Forces During Support Phases Horizontal impulses (Ns) Vertical impulses (Ns) Phase M SD Min Max M SD Min Max Board Support - 149 32-232 -96 314 37 256 393 Horse Support -93 26-157 -46 36 29-47 92 Avg horizontal force (N) Avg vertical force (N) Phase M SD Min Max M SD Min Max Board Support - 1272 296-2130 -809 3312 395 2709 4274 (- 2.0) (5.2) Horse Support -501 143-830 -274 838 178 412 1174 (- 0.8) (1.3) Note. Values for the mean forces divided by the mean weight of the gymnasts are included in parentheses. Table 6 Means, Standard Deviations, Maxima, and Minima for Angular Momentum, Moment of Inertia, and Angular Distance of Preflight and Postflight Average angular Average moment of Angular momentum (Kg m21s) inertia (kgm2) distance (deg) Phase M SD Min Max M SD Min Max M SD Min Max Preflight -111 16-160 -84 15.8 2.2 11.5 22.1-60.2 10.8-83.2-37.1 Postflight -64 7-79 -48 6.9 0.9 5.3 9.0-481.4 12.9-514.5-456.9
GYMNASTIC VAULTING Table 7 Means, Standard Deviations, Maxima, and Minima for Times of Flight and Support (sec) Variables M SD Min Max Time on board 0.128 0.007 0.12 0.14 Time of preflight 0.170 0.028 0.1 1 0.22 Time on horse 0.198 0.021 0.15 0.25 Time of postflight 0.835 0.040 0.75 0.91 of body CG and form were not quantified and only the angular distance was determined in this study. Correlation of the angular distance with the judges' scores yielded a nonsignificant correlation coefficient (r=-.20). Subsequent correlation of the variables that determine the angular distance with the points awarded was thus not indicated. Velocity of takeoff from board-of the three remaining variables in the third level of the model, two-the velocity of takeoff from the board and the relative height of takeoff-were quantified in this study. Correlation of these variables with the judges' scores yielded a significant correlation coefficient in the case of the velocity of takeoff from the board (Figure 3). This correlation (r=0.32, p<.05) indicated that, within the range of values recorded in this study, the greater the magnitude of the velocity of takeoff, the greater the number of points awarded by the judges. Horizontal and vertical velocities at takeoff from board-subsequent correlations of the horizontal and vertical components of the velocity of takeoff with the points awarded yielded a significant correlation only in the case of the horizontal component (r=0.46, p<.01) (Figure 3). The correlation found here indicated that the greater the horizontal velocity of takeoff from the board, the higher the points awarded. Finally, correlation of two variables that determine the horizontal velocity of takeoff with the judges' score yielded a nonsignificant correlation in both cases. It thus appears that while the horizontal velocity at takeoff is an important determinant of the points awarded by the judges, there is little to indicate that the horizontal velocity at touchdown was either more or less important than the change in horizontal velocity during board contact. This is rather surprising, given that the horizontal velocity generated during the period required to run some 12 or more strides over the run-up distance of as much as 25 m might have been thought more decisive than the change (reduction) in horizontal velocity that occurs during the much shorter period (approximately 0.13 sec) of board contact. All subjects lost horizontal velocity during contact with the board. Significant negative correlation (r=-0.78, p<.001) between the horizontal velocity at
- TRAJECTORY OF BODY CG POINTS AWARDED BY JUDGES ANGULAR DISTANCE FORM (PRE-FLIGHT) (PRE-FLIGHT) (PRE.FLIGHT) VELOCITY OF TAKEOFF RELATIVE HEIGHT OF AIR (BOARD) TAKEOFF RESISTANCE HORIZONTAL VELOCITY AT TAKEOFF (BOARD) VERTICAL VELOCITY AT TAKEOFF (BOARD) HORIZONTAL AT TOUCHDOWN HORIZONTAL Figure 3 - Zero order correlations of the preflight factors with the points awarded by judges. The asterisks indicate significant correlations. The lines linking factors show the magnitude of their relationships. Five lines indicate a coefficient of 0.5, four lines a correlation of 0.4, etc. The correlation coefficients represent relationships between the factors in the lower of the two linked boxes, in each case, and the points awarded by judges. 2
GYMNASTIC VAULTING 273 touchdown on the board and the change in horizontal velocity during board contact, therefore, indicated that subjects with large horizontal velocity 2 touchdown had large losses in horizontal velocity during board contact. Conversely, subjects with small horizontal velocity at touchdown on the board had small losses in horizontal velocity during board contact. This suggests that the lack of significant correlations of these variables with the points awarded probably means that a large horizontal velocity at takeoff from the board is more important than the manner in which that velocity is generated. Postflight Technique and Official Score. Of the three variables identified in the second level of the model (Figure 2), trajectory of body CG and form were not quantified and only the angular distance of the postflight was determined in the present study. Correlation of the angular distance with the judges' score once again yielded a nonsignificant correlation coefficient (r = - 0.10). Subsequent correlation of the variables that determine the angular distance with the points awarded thus was not indicated. Of the three remaining variables in the third level of the model, two-the velocity of takeoff from the horse and the relative height of takeoff-were quantified in the study. Correlation of these variables with the points awarded yielded a significant correlation coefficient in both cases (Figure 4). Velocity of takeoff from horse-the positive correlation (r= 0.40, p =.01) obtained here between the velocity of takeoff from the horse and the points awarded indicated that the greater the velocity of takeoff from the horse, the higher the points awarded. Vertical velocity of takeoff from horse-subsequent correlations of the horizontal and vertical components of the velocity of takeoff, identified in the next level of the model, yielded a significant correlation coefficient with the points awarded only in the case of the vertical component (Figure 4). This correlation (r = 0.45, p<.01) indicated that the greater the vertical velocity at takeoff from the horse, the higher the points awarded. Because the horizontal velocity at takeoff was not significantly correlated with the points awarded (r = 0.1 l), subsequent correlation of the variables that determine the horizontal velocity at takeoff with the judges' score was not indicated. Change in vertical velocity during horse contact-of the two variables in the fifth level of the model that determine the vertical velocity of horse takeoff with the judges' score-the vertical velocity of horse touchdown and the change in vertical velocity during horse contact-the latter was significantly correlated with the points awarded (Figure 4). This correlation (r= 0.52, p<.01) indicated that the greater the change in vertical velocity during the horse contact, the higher the points awarded. Vertical impulse during horse contact-of the two variables identified in the sixth level of the model that determine the change of vertical velocity during horse contact-the mass of the gymnast and the vertical impulse exerted during horse contact-the latter was found to be significantly related to the points awarded (Figure 4). The correlation (r =0.52, p <.01) obtained in this instance indicated that the greater the vertical impulse exerted on the gymnast during the horse contact, thi higher the points awarded. Time of horse contact and average vertical force during horse contact- Finally, two variables were identified in the last level of the model that deter-
Figure 4 - Zero order correlations of the postflight variables with the points awarded by judges. (Both the numerical and graphical representations of correlation coefficients are as described in Figure 3.)
GYMNASTIC VAULTING 2 75 mine the vertical impulse during horse contact-the time of horse contact and the average vertical force exerted-for which a significant relationship with the points awarded (r= -0.37, p<.02, and r=0.52, p<.01, respectively) was obtained (Figure 4). These correlations indicated that (a) the less the time of horse contact and (b) the greater the average vertical force exerted on the gymnast during horse contact, the higher the points awarded. Interestingly, significant negative correlations were found for the time of horse contact versus the vertical force exerted on the horse (r= -0.37, p<.02), the vertical impulse on the horse (r= -0.39, p<.02), and the change in vertical velocity on the horse (r=-0.44, p<.01). These findings indicated that the less the time of horse contact, the greater the vertical force exerted, the greater the vertical impulse exerted, and the greater the resulting change in vertical velocity on the horse. This indicates that a sharp, quick blocking is more effective than a slow one in generating a change in vertical velocity during horse contact. Thus, in summarizing the significant causeleffect relationships identified, it can be seen that (a) the shorter the time of horse contact, the greater the average vertical force exerted on the gymnast; @) the greater the average vertical force exerted, the greater the vertical impulse; (c) the greater the vertical impulse exerted on the gymnast, the greater the change of vertical velocity; (d) the greater the change in vertical velocity during horse contact, the greater the vertical velocity at takeoff from the horse; and (e) assuming that the heights of release and landing are reasonably constant, the greater the vertical velocity of takeoff into the postflight, the greater the time and the maximal height of the postflight. Of the two variables that determine the vertical velocity at takeoff from the horse, the change in vertical velocity during horse contact was more important than the vertical velocity at horse touchdown in its relationship to the points awarded. A strong negative correlation (r= -0.80, p<.001) between the vertical velocity at horse touchdown and the change in vertical velocity during horse contact indicated that the subject who contacted the horse with a low vertical velocity generated a greater increase in his vertical velocity during horse contact, and vice versa. As in the case of horizontal velocity at takeoff into the preflight, this suggests the possibility of compensating for an insufficient vertical velocity at touchdown by generating a greater increase during takeoff. Relative height of takeoff-the relative height of takeoff from the horse, that is, the height of CG at takeoff from the horse relative to its height at the instant of contact with the mat, was found to be significantly related to the points awarded (r=0.53, p<.01) (Figure 4). This meant that the greater the difference between the height of CG at takeoff from the horse and its height at touchdown on the mat, the more points awarded by the judges. According to the Code of Points (Federation of International Gymnastics, 1985), the CG at the instant of takeoff from the horse and at the instant of touchdown on the mat should be as high as possible. An increase in the height of CG at the instant of takeoff from the horse may be brought about by improving the alignment of body segments during horse support and by properly timing the instant of takeoff from the horse. In this regard it is of some interest to note that five of the six typical faults listed in the Table of Deductions and Judging Format for the 1988 Olympic Compulsory Exercises (Federation of International Gymnastics, 1984) are (a) bent arms during the horse support, @) insufficient length or height in the postflight, (c) body or legs insufficiently tucked during the for-
ward somersault, (d) lack of body extension or "kick out" in midair prior to landing, and (e) landing position too low. On the other hand, the height of the body CG at the instant of touchdown on the mat can be maximized by assuming a tightly tucked position, thereby minimizing the moment of inertia about a transverse axis through CG, and completing the required front somersault near the peak of flight. Increasing the moment of inertia by extending the body in a controlled manner during the descending phase after the somersault reduces the speed of rotation, allows adjustment for the desired landing angle, and simultaneously maximizes the CG height at landing. However, an insufficient time of flight and/or angular momentum at takeoff can cause a reduced rotation (Hay & Reid, 1982). Consequently, the gymnast is unable to complete the required somersault efficiently in midair, continues struggling to complete the somersault till landing, and thus leaves himself or herself very little time and vertical distance to effect a safe landing. The semisquat landing position, typically seen in such cases, not only decreases the landing height but simultaneously increases the relative height of takeoff. Thus it is evident that relative height of takeoff can be maximized by either maximizing the height of CG at takeoff from the horse, minimizing the height of CG at touchdown on the mat, or a combination of both. Height of CG at touchdown on mat-subsequent correlation of the height of the CG at takeoff from the horse and at touchdown on the mat with the points awarded yielded a significant correlation coefficient only in the latter case (Figure 4). Because the height of the gymnast may have been a confounding factor in the relationship between the height of CG at touchdown on the mat and the points awarded, the correlation initially found between these two variables (r= -0.35, p<.03) was recomputed with the standing height of the subject partialled out. The negative correlation (r= -0.43, p<.01) obtained here indicated once again that the less the landing height, the higher the points awarded. This finding seemed to suggest that those who landed in a semisquat position scored higher, on the average, than those who landed in a well-extended position. There appears to be some reason to doubt this. The possible advantage in landing in a semisquat position is that it allows a greater angular displacement before the line of gravity has moved forward beyond the base of support and thus increases the gymnast's chance of "sticking" the dismount. In other words, it minimizes the possibility of losing balance. However, this semisquat landing position may well be due to insufficient height of postflight, angular momentum, flexibility, or control to complete the somersault in midair and thus may be regarded as a technical fault. Furthermore, when an athlete lands in a semisquat position, (a) considerable joint reaction force and muscle force may develop in the knee joint and (b) the range over which the gymnast can dissipate the impact force of landing by eccentric contraction of the leg extensor muscles is reduced. Reilly and Martens (1972) found that during level walking, when the amount of knee flexion was small, the peak value for the patellofemoral joint reaction force was one-half body weight. During stair climbing and descending, when knee flexion approached 90, this peak force was almost seven times the value obtained during level walking. An even higher joint reaction force occurred during knee bends to 90". This joint reaction force remained higher than the quadriceps muscle force throughout the knee bend. Thus the impact force on the tibiofemoral joint, the patellofemoral
GYMNASTIC VAULTING 277 joint reaction force, and the quadriceps muscle force that develops upon landing can all increase the possibility of a joint injury as the vaulter lands with smaller knee angle. Common belief by coaches and gymnasts regarding the landing height of vaulting is that the higher the CG at the instant of touchdown on the mat, the better the performance. However, the present finding indicated that the reverse was the case in performing the handspring and salto forward vault. The fdms of the individual vaulting performances were carefully reviewed to further investigate the relative height of takeoff and the height of CG at touchdown on the mat. The vaulters of lesser caliber, after having completed the somersault, did not show appreciable efforts to actively kick out or extend the body in the air. Instead the poorer vaulters came out of the tucked position slowly by extending the hip and knee joints downward with their arms extended over the head (Figure 5) and landed in a more upright body orientation than the better vaulters. This style of landing employed by the poorer vaulters caused the height of CG at the instant of landing to be higher than that of the better vaulters. Better vaulters, on the other hand, achieved a greater height of postflight, tighter tuck position, and faster rotation of the front somersault. In addition, they completed the somersault early in midair, extended the body more rapidly and completely well above the horse, maintained a fully extended body position throughout the last third of postflight, and landed on the mat showing a distinct backward body inclination with the arms extended downward and backward (Figure 5). Therefore, the above style of landing used by better vaulters caused Figure 5 - The upright landing (a) versus inclined landing (b) and their respective height of body CG at touchdown on the mat. Landing angle 8 ranged from 110" to 135".
the CG at the instant of touchdown on the mat to be lower than that of the poorer vaulters. Consequently, the relative height of horse takeoff for the better vaulters increased. To quantify the above observations, the angle formed by the two linesthe line connecting the body CG and the point of contact with the mat at the instant of touchdown and the horizontal to which the front of the body faces the same instant-was calculated to represent the body orientation angle for landing on the mat. This angle ranged from 110" to 135O, with a mean of 124", indicating a consistent backward body inclination at the instant of touchdown on the mat. A series of correlational analyses were made to investigate if the significant negative correlation between the height of CG at touchdown on the mat and the judges' score is due to the landing angle. Initially, a correlation between the landing angle and the judges' score was computed. The significant correlation coefficient (r=0.47, p<.01) between the two variables indicated that the greater the landing angle or the angle of backward body inclination, the higher the judges' score. Second, a correlation coefficient was computed between the landing angle and the height of CG at touchdown on the mat. The significant negative correlation (r= -0.84, p<.001) found here indicated that the greater the landing angle or the angle of backward body inclination, the lower the height of CG at touchdown on the mat. Finally, a partial correlation between the height of CG at touchdown on the mat and the judges' score was computed with the effect of the landing angle partialled out. The nonsignificant correlation (r =0.08, p =.64) found in this case indicated no relationship between the two variables when the influence of the angle was eliminated. Thus the apparent negative relationship between the height of CG at touchdown on the mat and the judges' score is almost entirely a consequence of the landing angle. The height of CG at the instant of touchdown on the mat ranged from 1.15 to 1.51 m. Apparently this distinct backward body inclination at touchdown was a crucial and necessary adjustment that had to be made in order to increase the chances of sticking the dismount, and simultaneously to provide a greater range over which the impact force of landing is dissipated by eccentric contraction of hip, knee, and ankle extensor muscles. On the other hand, the gymnasts who landed more in an upright body orientation tended to take several steps or a long hop forward immediately after landing. These extra steps are caused by errors in making due allowances for the body's inertia and forward motion in landing. Other Factors of Significance To determine whether important factors could be overlooked if a higher level factor did not correlate significantly with judges' scores, all the variables in the lower levels of the model were studied. It is possible for zero order correlations down in the causal tree to show significance even when the higher branches fail. When dealing with many correlations, isolated effects of this type appear reasonably likely by virtue of the number of tests performed (more than 40 correlations performed in the present study). Another possibility is that of confounding. If the item of concern is correlated to some other factor (perhaps from a separate part of the causal tree) that itself is correlated to the judges' score, then an apparent correlation of the confounded item may arise, even without any causal basis. There were no signifi-
GYMNASTIC VAULTING 2 79 cant variables in the lower levels of the preflight. However, five postflight variables were found to be significantly related to the judges' scores: time of postflight, horizontal velocity at touchdown on the horse, change in horizontal velocity on the horse, horizontal impulse on the horse, and average horizontal force on the horse. Of the above five variables, the horizontal velocity at touchdown on the horse will not be discussed here because it has already been mentioned in preflight as horizontal velocity at takeoff from the board. Of all the variables analyzed, the time of postflight in the third level of the model was found to be the most closely related to the judges' score. The study's highest correlation coefficient (r = 0.65, p<.001) obtained here indicated that the longer the time of postflight, the higher the judges' score. This finding was no surprise, given that the longer the time of postflight the easier the execution of the required somersault and landing, and thus the better the performance. The change of horizontal velocity on the horse in the fifth level of the model was found to be negatively related to the judges' score. Because all subjects lost horizontal velocity during contact with the horse, negative correlation (r= -0.33, p<.04) here indicated that the subjects who lost more horizontal velocity on the horse scored higher. The change of horizontal velocity on the horse is determined by the horizontal forces that act on the gymnast and by the times during which these forces act, that is, horizontal impulse. The negative correlation (r= -0.33, p<.04) found between this variable in the sixth level of the model and the judges' score indicated that the less the horizontal impulse, that is, the more negative or braking the impulse (i.e., directed backward against the gymnast's forward motion), the higher the official score. The average backward horizontal force exerted on the gymnast, in reaction to the forward horizontal force the gymnast exerts against the horse, ranged from - 830 N to -274 N. The negative correlation (r= -0.46, p<.01) found between this variable in the last level of the model and the judges' score indicated that the less the force, that is, the more negative or braking the force, the higher the official score. In addition, the negative correlation consistently found between the horizontal and the vertical forces (r= -0.76, p<.001), the horizontal and the vertical impulses (r= - 0.58, p<.001), and the change in horizontal and vertical velocities (r= -0.55, p<.001) during the horse support indicated that a gain of vertical velocity during the horse support to takeoff into postflight almost inevitably accompanies a loss in the gymnast's horizontal velocity. Therefore there are both positive and negative effects: maximizing the gain of vertical velocity positively influences the time and maximal height of postflight, and causing a loss in horizontal velocity negatively affects the horizontal distance of the postflight. This fundamental conflict, coupled with the current requirements for the postflight distance (2 m) and maximal height (1 m), offers one of the greatest challenges for successful performance of this vault. In this regard, the results of the present study suggest that training should focus on learning effective blocking technique to achieve optimal combination of the distance, height, time, and angular distance of postflight. By the application of vertical force and horizontal braking force against the horse in a properly timed and coordinated manner, the desired increase of vertical velocity and reduction of horizontal velocity can be accomplished without too much gain or loss of the other variable.
Summary The development of the model and the factors identified in this study enabled a systematic and more complete analysis than the previous studies found in the literature. The model also helped to evaluate which of the identified mechanical factors are causally related to successful performance of the vault as represented by the official score. The highest r value found in the present study was 0.65 (i.e., explained variance of 42.3%) between the time of postflight and the judges' score. The overall low correlations indicate that the judges' scores reflect many variables, each accounting for a small variance and interacting in a very complex manner. An analysis of the techniques employed by the gymnasts in performing the handspring and salto forward vault during the compulsory session at the 1986 USA Gymnastics Championships resulted in the following conclusions: 1. Mean values for the average horizontal and vertical forces exerted on the subjects during the board contact were 2.0 and 5.2 times body weight, respectively. Mean values for the average horizontal and vertical forces exerted during the horse contact were 0.8 and 1.3 times body weight, respectively. 2. Mean values for the average angular momentum of pre- and postflight were 11 1 Kg m2/s and 64 Kg m2/s, respectively. 3. The horizontal velocity at takeoff from the board is an important determinant for successful performance. This large horizontal velocity at takeoff can be achieved either by maximizing the horizontal velocity at touchdown or minimizing the change (or reduction) in horizontal velocity during board contact. 4. The vertical velocity at takeoff from the horse is an important determinant for successful results. Of the two variables that determine the vertical velocity at takeoff, the change in vertical velocity during horse contact is of greater importance than the vertical velocity at horse touchdown. 5. Five on-horse factors that were related to each other in a logical sequence were also significantly correlated with the points awarded by judges. These variables were (a) the time of horse contact and the vertical force exerted on the horse, (b) the vertical impulse exerted on the horse, (c) the change of vertical velocity during horse contact, and (d) the vertical velocity at takeoff from the horse. These correlations, and the ones among these on-horse factors, indicate that the more the gymnast focuses on horse contact or the blocking and the more vertical the direction of his or her effort at takeoff into the postflight, the better the final result. 6. A sharp, quick blocking is more effective than a slow one in generating an increase in vertical velocity during the horse support. 7. A gain of vertical velocity during horse contact almost inevitably accompanies a loss in the gymnast's horizontal velocity. This fundamental conflict positively influences the time and height of postflight and negatively influences the distance of postflight. 8. Quite contrary to common belief by coaches, (a) the greater the relative height of takeoff from the horse and (b) the less the height of CG at touchdown on the mat, the higher the points awarded by the judges. These relationships were found to be almost entirely a consequence of the landing angle. The better vaulters had a landing position of distinct backward body inclination of stretched body with their arms pointing down toward the mat, while the poorer vaulters landed in a more upright orientation with their arms held above their head. This caused the CG to be lower in the better vaulters, which was apparent-