Takeoff Mechanics of the Double Backward Somersault

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1 INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1990, 6, Takeoff Mechanics of the Double Backward Somersault lnseong Hwang, Gukung Seo, and Zhi Cheng Liu This study examined the biomechanical profdes of the takwff phase of double backward somersaults in three flight positions: seven layout double backward somersaults (L), seven twisting double backward somersaults 0, and seven tucked double backward somersaults (TDB). Selected kinematic variables and angular momenta were calculated in order to compare the differences resulting from different aerial maneuvers. The amount of total body angular momentum about the transverse axis through the gymnasts' center of mass progressively increased from TDB to TW to L. The gymnasts performing the skill in the layout position tried to minimize the angle of block in a direction opposite the intended motion by maximizing the angle of touchdown and takeoff. In so doing, the horizontal velocity center-of-mass curve of the L showed a slowly decreasing curve compared with those of the other two somersaults while the vertical velocity curve of the L increased more slowly than the other curves during the takeoff phase. In all cases the legs played the dominant role in contributing to total angular momentum during takeoff. Since the gymnast is subject to no external forces or moments apart from gravity, the gymnast cannot alter his or her total body angular momentum in the air. Angular velocity can only be changed by altering the moment of inertia about a transverse wis through the center of mass. Thus the technique used during the takeoff phase is important. The gymnast must achieve sufficient linear and angular momentum during this phase to perform an airborne somersault. To gain sufficient height and angular momentum, the gymnasts perform the roundoff back handspring and takeoff movements. The linear and angular momentum developed during the roundoff back handspring movement changes due to vertical and horizontal reaction impulses during the takeoff phase. The final remaining linear and angular momentum are used for the airborne somersaults. It is crucial that the gymnast and coach understand the sensitive balance between linear and angular momentum at takeoff in order to perform a successful airborne movement. Inswng Hwang is with the Dept. of Physical Education at Yonsei University, Seoul, Korea. Gukung Seo is with the Dept. of Physical Education at Pusan University, Pusan, Korea. Zhi Cheng Liu is with Beijing Institute of Physical Education, Beijing, PRC.

2 178 Hwang, Seo, and Liu Very little quantitative data regarding the takeoff mechanics of the backward somersault are available. Payne and Barker (1976) analyzed the kinematics and kinetics with four club level gymnasts performing the flic-flacs and back somersaults. Nicol and Watkins (1987) also analyzed the kinematics and kinetics of the back somersault and a flic-flac using six subjects. More thorough studies regarding kinematics, kinetics, and their relationships to the somersault takeoff on the floor were reported by Briiggemann (1983, 1987), using highly skilled gymnasts. However, there is a lack of data concerning high skill athletes during competition. This study was undertaken to examine biomechanical features of somersault performances of male gymnasts during the Olympic Games in Seoul. The purpose of this study was to investigate the differences in biomechanical profiles during takeoff between three different double backward somersaults from the floor. Methods The somersaults of the floor exercise final individual all-around at the 1988 Seoul Olympic Games were filmed with two 16-mm cameras (Locarn). Both cameras were secured on tripods and placed behind the audience above the floor. The cameras were positioned with about a 50" separation angle between them so that the photographic field covered half of the floor. Six reference frames, which had seven calibration points in each frame, were placed on two comers in the photographic field and photographed before and after the main event (Figure 1). Each REFERENCE FRAME CAMERA1 A - DIRECTION Figure 1 - Reference frame and camera locations.

3 The Double Backward Somersault 179 camera operated at 70 frames per second with a three-factor shutter resulting in an exposure time of 1/210 s. This investigation was limited to a total of 21 successful double backward somersaults including seven layout double backward somersaults (L), seven twisting double somersaults (TW), and seven tucked double backward somersaults (TDB) (Table 1). Three touchdown events were used to synchronize the two cameras. This was verified by comparing the timing light exposure patterns on both films. Segmental endpoints were digitized and three-dimensional coordinates were obtained using the DLT technique (Abdel-Aziz & Karara, 1971). After the data were viewed and gross digitizing errors were eliminated, a digital filtering technique with a cutoff frequency of 8 Hz was applied to all of the data as described by Winter, Sidwall, and Hobson (1974). Once the three-dimensional coordinates were obtained, only the sagittal plane coordinates were used for quantitative analysis in this study. Segment masses, center of mass (CM) location, and moments of inertia were predicted from the data of Dempster (1955), Dempster and Gaughran (1967), and Chandler, Clauser, Table 1 Descriptive Data of Gymnasts Description Gymnast Age (yr) Height (m) Weight (kg) Score Layout double backward somersault Csaba Valeri Christian Charles Daiauke 19 ' GYO~~Y Alfonso Twisting double backward scmers~ult Yukio Koich Marius Paolo Nicolae Kevin Claude Tucked double backward somersault Jonghoon Sven Yun Csaba Curtis Ralf Vladimir Mean

4 180 Hwang, Seo, and Liu McConville, Reynolds, and Young (1974). All necessary kinematic data were calculated by differentiating the displacement data with respect to time. Total body angular momentum about a principal axis (Z) normal to the body's plane of motion (the XY-plane) was determined by the following equation: N Hz = C [ (Iz)~ (uz)~ + m, (r~z)'~ (USZ)~ 1 (1) i= 1 where Hz = total body angular momentum about a principal axis (Z) normal to the body's plane of motion; ( 1~)~ = moment of inertia of segment i relative to its principal axis parallel to the Z axis; (uz)~ = angular velocity of the body relative to its principal axis parallel to the Z axis; m, = mass of segment i; (r~z)~ = distance from s, the center of gravity of segment i, to axis z; and (USZ)~ = angular velocity of s about z. The segment's moment of inertia and the moment arm of the segment's linear momentum for computing local and transfer terms were adjusted to estimate the z-component of the angular momentum of a human body undergoing three-dimensional motion using the method of Hay, Wilson, Dapena, and Woodworth (1977). The ANOVA and Duncan's post hoc statistical procedures were used to compare variables of the three different double back somersaults. Touchdown and Takeoff Angles Results The absolute angles of the direction vector from the CM to the toe were measured at touchdown and takeoff and referred to touchdown angle and takeoff angle, respectively. The mean angles of touchdown and takeoff are presented in Figure 2. Both touchdown and takeoff angles of the L showed the largest value. The smallest angles of the touchdown and takeoff were observed in the TDB. However, LAYOUT DOUBLE TWISTING DOUBLE TUCKED DOUBLE BACKWARD BACKWARD BACKWARD SOMERSAULT SOMERSAULT SOMERSAULT (L) W) fldb) Figure 2 - Takeoff and touchdown angles of L, TW, and TDB. The mean angles and standard deviations of takeoff and touchdown are 51.4f 3.7 and 85.2f2.9" for L; 49.0f 3.2 and 82.1f 2.4" for TW; and 48.1f 2.7 and 82.6*2.9" for TDB, respectively.

5 The Double Backward Somersault 181 results of the ANOVA indicated that the angle differences between the types (L, TW, TDB) were statistically not Takeoff Duration There was no appreciable difference in takeoff duration between the three backward somersaults. The mean durations of takeoff were , , and seconds for L, TW, and TDB, respectively. The duration of TDB was longer than that of the others, but differences were not statistically significant QK.05). Velocity of CM During Takeoff The velocity time histories of the CM during the takeoff phase of the L, TW, and TDB are presented in Figure 3. The horizontal velocity (X) of the CM at touchdown averaged 4.30&0.39,4.10& 0.29, and 4.20*0.51 m-s-' for L, TW, and TDB, respectively. The vertical velocities (Y) of the CM at touchdown were , , and m-s-i for L, TW, and TDB, respectively. The horizontal and vertical velocities at touchdown of the CM did not show any statistically significant differences between L, TW, and TDB positions. The horizontal velocity curves of the L, TW, and TDB decreased by 27.9,30.2, and 48.1 %, respectively; the vertical velocity curves of the L, TW, and TDB increased A TUCK ( TDB) 1 TWIST (TW) LAYOUT( L ) Figure 3 - Velocity time histories of the CM during the takeoff phase of the L, TW, and TDB.

6 182 Hwang, Seo, and Liu by 11.1, 14.3, and 16.8 times, respectively, until takeoff. Vertical velocities (Y) at takeoff were , , and 4.46+_0.29 m-s-' for L, TW, and TDB, respectively. Horizontal velocities (X) at takeoff were , 2.90+_0.45, and m-s-' for L, TW, and TDB, respectively. Results of the ANOVA indicated significant main effects for somersault styles when analyzing the takeoff horizontal velocities, F(2,18) =20.43,60.05, and in terms of vertical velocities, F(2,18) =21.53, Post hoc analysis of the data indicated that the horizontal velocities of the L and TW were significantly higher than the velocity of the TDB, and the vertical velocity of the L was lower than the velocities of TW and TDB. Angular Momentum Since the body is free of external torques while in the air, the total angular momentum during the airborne phase should be constant. When angular momentum was computed during the flight phase, however, variations of about 510% were found. Hay et al. (1977) reported similar variations and explained that they are presumably due to measurement errors and choice of inappropriate body segment parameters. Thus the mean (n = 7 subjects) of the means of the angular momenta during the airborne phase for each style was reported in this study and referred to as the mean angular momentum. The mean angular momentum (Hg) time curves during takeoff and flight representing L, TW, and TDB are presented in Figure 4. The largest magnitude of Hg during flight was observed in the L with a mean valueof kg-m2*s-'. ThemeanHgvalueoftheTWandTDBwere kg em2 s-i and kg-m2* s-l, respectively. Results of the ANOVA indicated significant differences among the somersault styles in terms of mean Hg during the airborne phase, F(2,18) =25.11, p<0.05. Post hoc analysis of the data indicated that the absolute mean Hg values of the TW and TDB were significantly lower than the mean Hg of the L. The Hg decreased rapidly during the takeoff phase in all three somersault positions. The major change occurred at touchdown. The Hg profiles of the L showed a different pattern from that of the other two Hg histories. The decreased Hg of the L position at touchdown remained relatively constant or slightly increased during the final takeoff phase. The largest magnitude of Hg at touchdown and takeoff were observed in the L, and the smallest values were the Hg for the TDB. Local and Transfer Term Contributions The number of frames from touchdown to takeoff varied between 10 and 12 frames in all subjects. The mean (n = 7 subjects) of means (n = 10 frames from touchdown) of total Hg, local Hg, and transfer Hg during takeoff are presented in Table 2. In all cases the magnitude of the local term of Hg was considerably less than the transfer term of Hg (Table 2). The local term of Hg in the L, TW, and TDB accounted for a mean of 26.93,29.92, and 28.50%, respectively, of the total Hg. Segmental Contributions The contributions of the arms, trunk, and legs to the total Hg for L, TW, and TDB are presented in Figures 5,6, and 7, respectively. The arms, legs, and trunk in the three somersaults have similar time histories. The contribution of the legs to the total Hg played a dominant role in the three somersaults, since the total

7 The Double Backward Somersault - TAKEOFF A l RBORNE - - -=" I 3 7 I-Z W s i' 0 TOUCH DOW a - 4 -I z TDB ) ( T W ) T( L ) TIME (NORM) Figure 4 - Mean Hg time curves of L, TW, and TDB during takeoff and flight. Table 2 Mean Angular Momentum Values During Takeoff for 7 Subjects Total Hg Local Hg Transfer Hg M SO M SD 010 of total M SD % of total Layout double backward somersault Twisting double backward somersault Tucked double backward somersault

8 Hwang, Seo, and Liu," ARMS I TRUNK LEGS A TOTAL Figure 5 - Contributions to total Hg of the arms, trunk, and legs for L. I I I I I I I 1 I [ TIME( NORM) 1 Figure 6 - Contributions to total Hg of the arms, trunk, and legs for TW.

9 The Double Backward Somersault ARMS I TRUNK LEGS m, A TOTAL '" TI ME (NORM) Figure 7 - Contributions to total Hg of the arms, trunk, and legs for TDB. Hg was simply the mathematical addition of segmental Hg. Results of an ANOVA and Duncan's post hoc analysis indicated that the Hg of the arms in TDB was significantly smaller than that in the L and TW, F(2,18) = 8.13, p< The trunk Hg of the L was significantly larger than that during the TW and TDB, F(2,18) = 8.67, Hg of the legs during the L was significantly larger than during the TW and TDB, and Hg of the legs during the TW was significantly larger than during the TDB, F(2,18) = 12.43, JK Discussion The most important mechanical factors at takeoff for successful somersault are jumping height and Hg. If the required number of rotations is increased or if required airborne movement limits full control of the moment of inertia, the jumping height, Hg, or both must be increased for completion of the given somersault. The jumping height is determined by the vertical velocity at takeoff. Generation of the necessary Hg is accomplished by the angular impulse during takeoff and segmental angular momenta at takeoff. The angular impulse varies with the reaction force, moment, and duration of the takeoff phase. The selected somersault types in this study (L, TW, and TDB) impose different constraints on the control of moment of inertia during the airborne phase. The vertical velocity of L, which determines the jumping height, was lower than the velocities of TW and TDB. However, horizontal velocities of L and TW were higher than for TDB. The touchdown and takeoff angles of the L were found

10 186 Hwang, Seo, and Liu to be the largest among the three somersaults, although the differences were not statistically significant w.05). The takeoff duration was not appreciably different among the three backward somersaults. The amount of Hg generated at takeoff progressively increased from TDB to TW to L. The gymnasts performing L tried to minimize the angle of block in a direction opposite the intended motion, using the opportunity to emphasize maximum rotation at the expense of some lift. Analysis of the segmental contributions to Hg revealed that the transfer terms accounted for about 70% of the total Hg, and in all cases the legs played the dominant role in contributing to total Hg during takeoff. Briiggemann (1987) reported similar results. The segmental Hg of L was larger than the segmental Hg of TDB. The trunk and legs Hg of L was larger than the trunk and legs Hg of TW. The arms and trunk Hg of TW was larger than the arms and trunk Hg of TDB. The gymnasts performing L tried to maintain the decreasing total Hg at touchdown by developing more segmental Hg at takeoff than other gymnasts. References Abdel-Aziz, Y.I., & Karara, M.M. (1971). Direct linear transformation from computer coordinates into object space coordinates in close-range photogrammetry. In Proceedings of the Symposium on Close-Range Photogrammetry (pp. 1-18). Falls Church, VA: American Society of Photogrammetry. Briiggemam, P. (1983). Kinematics and kinetics of the backward somersault take-off from the floor. In H. Matsui & K. Kobayashi (Eds.), Biomechanics VZZ-B (pp ). Champaign, IL: Human Kinetics. Briiggema~, P. (1987). Biomechanics in gymnastics. In B. Van Gheli~we & J. Atha (Eds.), Medicine and Sports Science (Vol. 25) (pp ). Basel: Karger. Chandler, R.F., Clauser, C.E., McConville, J.T., Reynolds, H.M., & Young, J. W. (1974). Investigation of inertialproperties of the human body (AMRL Tech. Rep ). Dayton, OH: Wright-Patterson Air Force Base. (NTIS No. AD-A ) Dempster, W.T. (1955). Space requirements of the seated operator (WADC TR ). Dayton, OH: Wright-Patterson Air Force Base. Dempster, W.T., & Gaughran, G.R.L. (1967). Properties of the segments based on size and weight. American Journal of Anatomy, 120, Hay, J.G., Wilson, B.D., Dapena, J., & Woodworth, G.O. (1977). A computational technique to determine the angular momentum of a human body. Journal of Biomechanics, 10, Nicol, A.C., & Watkins, J. (1987). Biomechanical analysis of somersault activities. In B. Jonsson (I%.), Biomechanics '7). Champaign, IL: Human Kinetics. Payne, A.H., & Barker, P. (1976). Comparison of the take-off forces in the flic-flac and the back somersault in gymnastics. In P. Komi (Ed.), Biomechanics ). Baltimore: University Park Press. Winter, D.A., Sidwell, H.G., & Hobson, D.A. (1974). Measurement and reduction of noise in kinematics of locomotion. Journal of Biomechanics, 7,

TAKE-OFF CHARACTERISTICS OF DOUBLE BACK SOMERSAULTS ON THE FLOOR

TAKE-OFF CHARACTERISTICS OF DOUBLE BACK SOMERSAULTS ON THE FLOOR H. Geiblinger, W. E. Morrison & P. A. McLaughlin Biomechanics Unit, Dep't of Physical Education and Recreation and Centre for Rehabilitation,