INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1988,4, 231-259 Factors Contributing to Maximum Height of Dives After Takeoff From the 3M Springboard Ross H. Sanders and Barry D. Wilson This study investigated factors contributing to the maximum height achieved by divers after takeoff from the 3m springboard. Twelve elite male divers and 12 elite female divers competing in the 1986 Australian National Championships were filmed using high-speed cinematography. Kinematic and kinetic data for the takeoff phase were derived from the digitized film. Variables analyzed included center of gravity (CG) displacement and velocity, the acceleration of the CG relative to the springboard, and the components of mechanical energy contributing to height achieved by the diver's CG. Body orientation was described in terms of the angles at the hip, knee, and ankle, and whole body angle of lean. Comparison of timing differences among dive groups and divers was aided by normalizing the data with respect to time. It was found that the height achieved was highly dependent on the rotational requirements of the dive, with males achieving greater heights than females. Divers who achieve good height compared to other divers performing the same dive are characterized by a large vertical velocity at touchdown from the hurdle and a minimization of hip flexion (forward dives) and knee flextion (reverse dives) at takeoff. Height achieved during the flight phase of springboard dives is known to be an important contributing factor to points awarded for a dive (McCormick, Subbaiah, & Arnold, 1982). Apart from this direct contribution to the dive score, increased height in flight allows the diver more time to perform the necessary movements and rotations leading to an aesthetically pleasing and controlled dive. Greg Louganis, the acknowledged world springboard champion, is distinguished by superior height attained in his dives (Miller & Munro, 1985a, 1985b). The height attained in a dive is dependent upon the diver's vertical velocity at the instant of takeoff from the springboard and, to a much smaller extent, the height of the center of gravity (CG) at takeoff. Miller and Munro (1984) identified the determinants of final vertical velocity: (a) vertical velocity of the diver Ross H. Sanders and Barry D. Wilson are with the Faculty of Physical Education, University of Otago, Box 56, Dunedin, New Zealand.
232 SANDERS AND WILSON at the commencement of the final bounce on the board, (b) the upward acceleration of the diver's CG relative to the board during the downward deflection of the board, and (c) the negative (downward) acceleration of the diver's CG relative to the board. The role of each of these is related to storing and utilizing strain energy. Vertical velocity at touchdown from the hurdle and the upward acceleration of the CG with respect to the board serve to depress the board, thereby storing energy in it. Much of this energy can then be used by the diver during the recoil of the board to increase vertical velocity at takeoff. Downward acceleration of the diver's CG with respect to the board dissipates energy, reducing the height achieved. Few studies have analyzed the factors affecting this storage and utilization of springboard strain energy for the purpose of gaining height. Golden (1981) closely examined the body orientations of three male divers performing somersault dives from the forward and inward groups. Variables examined included CG position, displacement and velocity, angle of takeoff, takeoff lean, whole body angular velocity about the CG at the peak of flight, and angular position of body segments. The loss of vertical velocity with increasing rotational demands was recognized. In a series of studies, Miller (1984) and Miller and Munro (1984; 1985a, 1985b) have examined in detail the characteristics of forward and reverse dives and have identified factors that affect the height achieved. The purpose of the present study was to quantify factors that affect the height achieved in forward and reverse dives and to describe the influence of these factors in terms of the storage and utilization of springboard strain energy. Data Collection Procedures Forward and reverse dives of 12 male and 12 female divers competing in the finals of the Australian National Diving Championships held in Brisbane, February 1986, were filmed and subsequently analyzed. The divers were all elite at national level. All but 2 of the males and 2 of the females had competed at international competitions such as Junior World Cup, World Cup, Commonwealth Games, and Olympic Games. Four of the females and 4 of the males had won medals in international competition. One Photosonics high-speed camera set to operate at 100 fps was positioned level with the end of the springboard with the optical axis at 90' to the plane of motion. The filming distance was approximately 22m and an Angenieux zoom lens was adjusted so that the image size was maximized while still capturing all of each diver's hurdle and takeoff phase (defined as the period from the instant of touchdown from the hurdle to the instant of last contact with the springboard). An internal light-emitting diode operating at 100Hz during filming was used to calculate the actual film framing rate for each dive prior to digitizing. The dives filmed and analyzed were the following: 1. The forward dive straight (101a) (4 females); 2. The forward dive in a pike position (101b) (2 females, 5 males); 3. The forward 1 112 somersault in a pike position (103b) (1 female, 7 males); 4. The forward 2 112 somersault in a pike position () (1 1 females, 4 males);
DIVES FROM 3M SPRINGBOARD 5. The forward 3 112 somersault in a tuck position (107c) (6 males); 6. The reverse dive in a pike position (301b) (1 female, 5 males); 7. The reverse dive straight (301a) (9 females, 7 males); 8. The reverse 2 112 dive in a tuck position (30%) (5 females, 10 males); 9. The reverse 1 112 dive straight (303a) (1 female). Mean data was obtained only from those forward and reverse dives that were performed by at least four competitors. The film was digitized according to the landmarks of Dempster and Gaughran (1967) utilizing a 14-segment body model: head and neck, right arm, left arm, right forearm, left forearm, right hand, left hand, trunk, right thigh, left thigh, right shank, left shank, right foot, and left foot. The metatarsal phalangeal joint (MP) was also digitized to act as a landmark for the calculation of maximal springboard depression, whole body angle of lean, relative acceleration, and torques. During the last frames of contact, as the MP began to lift from the surface of the springboard, this landmark was taken as the upper surface of the springboard in the center of the area of contact. Every second frame from the commencement of the hurdle to the eighth frame beyond the instant of last contact (takeoff) was digitized. The first frame to be digitized was selected so that the fifth last sample coincided as closely as possible to the actual instant of last contact. A second-order Butterworth digital filter was used to smooth the positiontime data of each segment endpoint and employed the procedure of Jackson (1979) to determine the frequency cutoffs. These were commonly 6 or 7Hz. After the various parameters for each film frame were calculated, the values were time-normalized using a quintic spline to 101 equispaced values (0 to 100) from the frame corresponding to touchdown to the frame corresponding to takeoff. Therefore particular values (e.g., maxima and minima) could be found and expressed as a percentage of the takeoff phase. Variables Analyzed The selection of variables for analysis and discussion was based on the factors identified by Miller and Munro (1984) which were thought to affect the height achieved through their iduence on the storage and utilization of springboard strain energy by the diver. Thus the diver's CG displacement, velocity, and vertical acceleration relative to the springboard were determined as functions of time. Segmental contributions to relative acceleration were also calculated. The change during the takeoff phase in the potential energy possessed by virtue of the height of the CG and the kinetic energy possessed by virtue of the vertical velocity were quantified as an indication of the effectiveness of the diver's efforts to "work" the board to gain height. To provide a temporal description of the diver's orientation and segmental movements, hip, knee, and ankle angles and whole body angles of lean were determined as functions of time. Methods of Calculation Mean score-the average score for each dive was calculated as the average of the judges' scores after rejecting the highest and lowest scores and prior to consideration of degree of difficulty. Mean scores for each dive type were then the mean of the average scores of the divers performing that dive type.
234 SANDERS AND WILSON Displacements-All displacements were expressed with respect to the tip of the springboard in its normal resting position. Center of gravity (CG)-The coordinate location of individual segment centers of gravity were determined using the digitized coordinates of segment endpoints in conjunction with Dempster's (1955) data for segment masses, and segment mass centers. The fractional masses for median subjects were used. Maximum jzight height-this was calculated by applying the formula, where H, is the maximum flight height, hf is the height of the CG at the instant of takeoff, Vf is the vertical velocity at the instant of takeoff, g is the acceleration due to gravity (-9.8 1 m. s+). Flight height difference-difference between the maximum flight height and the height of the CG at takeoff was determined by Velocities-Vertical and horizontal velocities were calculated by applying central difference formulae to the CG position data. Work on the board contributing to height-the fraction of work performed on the board relevant to acquiring height was calculated by where Wh is the fraction of work performed that contributes to height. PEf and PEi are the potential energies due to the position of the CG with respect to the resting level of the springboard at the instants of takeoff and touchdown, respectively. ICEd and KEvi are the fractions of kinetic energy due to the vertical translation of the diver. In order to compare divers, the energies were normalized by dividing the mass of the diver. Thus the formula applied was (P.E. component) (K.E. component) where Wh is the work performed to gain height normalized with respect to diver mass and expressed in joules per kilogram of body mass (J.kgl); g is the acceleration due to gravity, hf and hi are the vertical displacements of the CG of the diver with respect to the resting level of the springboard at the instants of takeoff and touchdown, respectively; vf and vi are the vertical velocities of the CG of the diver at the instants of takeoff and touchdown, respectively. Relative acceleration-the methods of Miller and Munro (1984) were used to calculate the segmental contributions to the acceleration of the CG relative to the metatarsal-phalangeal joint (MP). Because the MP was digitized as the undersurface of the joint, acceleration of the CG relative to the MP for the period of contact may be regarded as being equivalent to acceleration of the CG relative to the springboard at the point of contact of the diver. The body was regarded as comprising three sections: (a) upper extremities-arms, forearms, and hands; (b) head and trunk; (c) lower extremities-thighs, legs, and feet. The three active and three passive components of vertical acceleration of the CG with respect to the MP were calculated using the relationship presented by Miller and Munro (1984):
DIVES FROM 3M SPRINGBOARD 235 where 1, t, and u refer to centers of gravity of the lower extremities, head-trunk, and upper extremities, respectively; s and h represent the shoulder and hip, respectively; m is mass. Accelerations (a) are vertical accelerations with respect to the metatarsals. These were calculated using central difference formulae to obtain the second derivative of the vertical position data expressed with respect to the MP. The first three terms (i, ii, iii) are the active components of the lower extremities, trunk-head, and upper extremities, respectively. The last three (iv, v, vi) represent the passive components-the relative acceleration of the trunk due to the lower extremities (iv), the relative acceleration of the upper extremities through the trunk due to the lower extremities (v), and the acceleration of the upper extremities due to the action of the trunk alone (vi). Hip, knee, and ankle angles and whole body angle of lean-the angles made by the lines joining the shoulder-hip and hip-knee (hip angle), hip-knee and kneeankle (knee angle), knee-ankle and heel-toe (ankle angle), and the whole body angle of lean are shown in Figure 1. These were obtained by applying the arctangent function to the endpoint position data. Statistical Analysis Descriptive statistics are provided for variables for males and females and the different types of dives. Due to the small sample numbers, no statistical comparisons between males and females or among dive types was attempted. However, to further investigate the relationships between variables, simple and multiple regression analysis was performed on the pooled data of the forward dives (n = 37: 101a=4; 101b=7; 103b=8; =14; 107c=4) performed by males and females, and the reverse dives (n=37: 301a=15; 301b=6; 305c=15; 303a=1) performed by males and females. Pooling of the data was deemed justified since the differences in heights achieved among dive types and between males and fe- Figure 1 - Angles used to describe the body orientation of divers: 0, =hip angle; 0, =knee angle; 0, =ankle angle; 0, = whole body angle of lean.
236 SANDERS AND WILSON males can be explained in terms of the variables studied rather than being a function of dive type or gender per se. For the development of a regression model to explain the variance in height achieved, the difference between the diver's CG height at takeoff and the maximum height during the flight was selected as the dependent variable. This variable has a direct linear relationship with the fraction of kinetic energy the diver has at takeoff by virtue of vertical translation. Using height difference (HD) rather than actual height has the advantage of normalizing the takeoff height to exclude the direct and obvious contributions of the diver's physique and orientation at takeoff. After the initial analysis of the data, the kinetic energy at touchdown due to the vertical component of translation (KETD), change in potential energy due to the change in CG height from touchdown to takeoff (APE), change in the vertical component of kinetic energy from touchdown to takeoff (AKE), maximum and minimum relative acceleration, and the hip and knee angles at touchdown and takeoff were selected as the independent variables for the multiple regression analysis. Results and Discussion Mean scores-these are presented in Table 1 to indicate the overall standard of the performance of the dive. Center of gravity displacement-this data is presented in Table 1. It is apparent that the mean CG height at takeoff becomes lower as the rotational demands (in terms of the number of rotations and body position) are increased. Thus the mean height at takeoff for the males performing of 1.07m is approxi- Table 1 Mean CG Height at Takeoff and Peak of Flight* CG height (m) Dive n Mean score Takeoff Max. flight HD Males lolb 103b 107c 301 b 301 a 305c Females 101a 301a 305c "SD in parenthesis.
DIVES FROM 3M SPRINGBOARD 237 mately 0.14m less than the mean height at takeoff for a lolb of 1.21m. The trend toward lower CGs at takeoff for dives of higher rotational requirements is also evident in the reverse dives (30%: males = 1.1 lm, females = 1.Olm, compared to 301a: males= 1.26m, females = 1.19m). Some of these differences may be due to the physiques of the divers comprising the samples, but most are clearly attributable to the body orientations adopted at takeoff. All divers decreased HD with increasing rotational requirements. This trend is clearly shown by the mean HDs for the males in the forward dives (101b = 1.55m; 103b = 1.39m; = 1.22m). The same trend is observable for the reverse dives. Consequently, the divers achieve greater HDs in 301b (males= 1.61m) than a 301a (males= 1.38m, females =.97m), or 30% (males= 1.32m, females=.95m). Comparison of the heights for males and females performing equivalent dives shows that the males gain considerably more height than the females by about 0.5m. Vertical velocity-the vertical velocity at takeoff directly determines HD. The mean vertical takeoff velocities (Table 2) of the males performing forward dives display a decrement of approximately 0.3m.s-I with each pike somersault increment (101b=5.51m.s-I, 103b=5.23m.s-', =4.90m.s-I). With each somersault increment, an increasing quantity of strain energy is converted to kinetic energy of rotation and less is available for kinetic energy of translation. This leads to a reduced vertical velocity at takeoff. Similar findings have been reported by Golden (1981) and Miller and Munro (1984). Decreasing vertical velocity at takeoff with increasing rotational requirements is also apparent in the reverse dives (301b=5.62m.s-I, 301a=5.21m.s-I, 305c=5.09m.s-I). Table 2 Mean Vertical Velocity at Critical Points During the Takeoff Phase* Velocity (m.s-l) Dive n Touchdown Max. depression Takeoff Males 101b 103b 107c 301 b 301 a 305c Females lola 301 a 305c *SD in parenthesis.
238 SANDERS AND WILSON Since the springboard tends to convert the kinetic energy of the diver into strain energy during depression, the vertical velocity at takeoff (and therefore HD) is strongly influenced by the vertical velocity at touchdown. This is readily apparent in the regression plots displayed in Figures 2a and 2b. These show a close relationship between KETD and HD (forward dives, R=.71; reverse dives, R=.75). Since KETD is proportional to the square of the vertical velocity at touchdown, it may be stated that vertical velocity at touchdown accounts for approximately 50% of the variance in HD. o! I I I I I 6 7 8 9 10 11 a) KE at Touchdown (~.k~-l) 180- rn m 160-. V 120-- A 60 I I I I I 5 6 7 8 9 10 11 b) KE at Touchdown (~.kgl) Figure 2 - Relationship between kinetic energy due to vertical translation at touchdown (KETD) and height difference (HD). (a) forward dives, (b) reverse dives.
DIVES FROM 3M SPRINGBOARD 239 There are no apparent differences in the vertical velocity at touchdown among dive types. However, the standard deviations (SDs) ranging from 0.lOm.s-' to 0.40m.s-' indicate considerable differences among divers and point to a major area in which improvement can be made. The mean vertical velocities at touchdown were considerably higher for the male divers than for the females. In the case of, in which direct comparison is possible, the absolute mean vertical velocity at touchdown for the males (4.12m.s-') was.32m.s-' greater than that of the females (3.80m.s-'). By takeoff, this difference increased to 0.99m.s-' (males =4.90m.s-', females = 3.91m.s-'), indicating more work on the board by the male divers than the female divers. This result corresponds closely to the findings of Miller (1984), who found that for any particular dive the males had higher vertical velocities at takeoff than the females by approximately 1m.s-'. With regard to reverse dives, differences in the vertical takeoff velocity between males and females performing equivalent dives were found to be approximately 0.8m.s-'. At maximal springboard depression there is a substantial vertical velocity of the CG in the positive (upward) direction. This indicates that the body is moving away from the springboard (which has zero vertical velocity) as a result of the diver working the board by extending during its depression. It is worth noting that the mean vertical velocities at maximal springboard depression for the males performing forward dives (0.60m.s-' to 0.77m.s-') are substantially higher than those tabled for the females (0.33m. s-',o. 39m. s-i). This data may provide another indication that the female divers do not work the board as vigorously as the males during depression. However, it may not be implied that the higher the vertical velocity at maximal springboard depression the better. Presumably there is an optimum above which early unweighting of the board and energy wastage occurs. Miller and Munro (1985b) reported the vertical velocity of Greg Louganis at maximal depression of one trial of lola to be 0.71m.s-' and 0.78m.s-' in a trial of 107b. In the reverse dives the velocities at maximal depression were slightly higher for the males than in the forward dives (301b=0.92m.s-'; 301a=0.79m.s-'; 30% =0.93m.s-') and substantially higher for the females (301a=0.76m.s-', 30% =0.81m.s-I). It would appear that these differences may be linked to the necessity to extend fully in reverse dives before hyperextending the hips to assume the takeoff posture. Horizontal velocity-although the mean horizontal velocities at touchdown in the forward dives displayed in Table 3 are similar for each dive ranging from 0.62m.s-' to 0.69m.s-', the variation among divers as indicated by the range in SDs of 0.08m. s-' to 0.20m. s-' is considerable. There is a tendency toward larger horizontal takeoff velocity with each pike somersault increment (101b males = 1.00m. s-', 103b males = 1.30m.s-', males = 1.53m. s-i). A greater horizontal velocity at takeoff is expected for dives of higher rotational requirements due to the increased forward lean necessary in these dives. However, a high degree of variability among divers is indicated by the SDs (0.13m.s-' to 0.3 1m. s-i). The extent to which horizontal velocity is gained through the use of strain energy is not known. However, in forward dives it should be noted that some strain energy may be used for this purpose. In forward dives, high horizontal velocities are probably detrimental to flight height, particularly in view of their association with forward lean. The horizontal springboard reaction forces responsible for the development of horizontal velocity also produce torques that are counter to the desired direc-
SANDERS AND WILSON Table 3 Mean Horizontal Velocity at Touchdown and Takeoff* Dive Touchdown Velocity (m.s-') Takeoff Males lolb 103b 107c 301 b 301 a 305c Females 101a 301 a 305c *SD in parenthesis. tion of rotation. Thus from a coaching point of view, if a diver has a pronounced forward lean at takeoff and also enters the water well away from the springboard, it is likely that helshe can achieve the same rotation and greater height with a reduced forward lean. In reverse dives, it is likely that an increase in horizontal velocity during the takeoff phase is achieved primarily without the use of the energy stored in the board. Because the desired rotation is produced primarily through horizontal springboard reaction forces acting late in the takeoff phase rather than by vertical reaction forces (as in forward dives), the rotation is not highly dependent upon strain energy. As a result of these horizontal reaction forces there is a tendency for horizontal velocity to increase with increasing rotational demands (males: 301b=0.94m.s-l, 301a= 1.08m.s-', 305c=1.30m.s-'; females: 301a=l.OOm.~-~, 305~=0.91m.s-~). Work on the board contributing to height-the work on the board by the diver is equal to the sum of AKE and APE. The effect of the rotational demands of a dive on the energy available for producing height is easily seen from Table 4. For example, the mean work performed by the males during lolb was 8.7J.kg-' while that during 103b was 7.3J.kg-' and only 3.3J.kg-' during. Most of this difference among dives of varying rotational requirements was due to the lower vertical takeoff velocities which reduced the AKE component of work performed on the board. However, it is evident from Table l that the position of the CG at takeoff for the high rotation dive (1.07m) was considerably lower than for 103b (1.18m) or lolb (1.21m) so that there was a substantial reduction in APE from lolb and 103b
DIVES FROM 3M SPRINGBOARD Table 4 Mean Work on the Board Contributing to Height* Work (J.kg-') Dive n APE AKE Total work Males 101 b 103b 107c 301 b 301 a 305c Females 101a 301 a 305c 'SD in parenthesis. (2.3J.kg-') to (0.9J.kg-I). The trend toward less work to gain height with increasing rotational requirements is also observable for the reverse dives of the male divers (301b=8.9J.kg-'; 305c=5.5J.kg-') and for the dives of the female divers (301a=4.6J.kg-'; 305c=2.OJ.kg-'). Females tend to perform less work to gain height than do males for dives of equivalent rotational requirements. Most of this difference is in the AKE component rather than the APE component. For example, for the mean of the total work by the females was 1.OJ.kg-' compared to 3.3J.kg-I for the males. Of the 2.3J.kg-' difference, only O.4J.kg-' was due to the difference in the APE component. Similarly, the mean work by the females performing 30% (2.0J.kg-') was considerably less than the work performed by the males (5.5J.kg-I). Although the total work performed to gain height may be regarded as the sum of AKE and APE from touchdown to takeoff, the fraction that affects HD is AKE. Thus, a strong relationship between AKE and HD is expected. This relationship is shown in Figures 3a and 3b (forward dives, R=0.93; reverse dives, R=0.86) and emphasizes the importance of work on the board to gain height. Timing patterns of relative acceleration-some similarities in the pattern of relative accelerations are evident in the plots of all divers. Regardless of dive type, there tended to be a period of positive relative acceleration of substantial magnitude during the first half of the depression. This is instrumental is storing additional energy in the springboard. There is also a period of slight unweighting of the springboard in the latter half of the depression phase. This minimum in the acceleration curve is primarily due to the negative relative acceleration of
SANDERS AND WILSON 200 '2 U w B 100 0 a) - 2 0 2 4 6 8 10 AKE (~.kg-l) Figure 3 - Relationship between change in kinetic energy due to vertical translation at touchdown (AKE) and height difference (HD). (a) forward dives, (b) reverse dives. the lower segments which are unable to maintain the rate of extension attained during the active push. Theoretically it is desirable to maximize the magnitude and duration of the positive relative acceleration during the depression of the board. The magnitude of the maximum relative acceleration was found to be moderately related to HD (forward dives, R=0.33; reverse dives, R=0.42). These relationships are shown in Figures 4a and 4b.
DIVES FROM 3M SPRINGBOARD 200. l To v /. - o l... vv. a"%. a m / v V v vd rn v. v/. 0 I I I I I I I I I 20 22 24 26 28 30 32 34 36 38 40 Maxirnuln Relative Acceleration (n~,s-~) 60! I I I I 10 2 0 3 0 4 0 5 0 Maxilnuln Relative Acceleration (ln.~-~) Figure 4 - Relationship between maximum relative acceleration and height difference (HD). (a) forward dives, (b) reverse dives. The duration of the period of positive acceleration as a percentage of the depression phase was not quantified in this study. However, Miller and Munro (1985a) estimated that the duration of Louganis' active push was approximately 58% of the depression phase. This was reported to be a longer period than for eight Canadian females (52% f 2) previously studied by Miller and Munro. A second period of partial unweighting occurs around 80 to 85% of the takeoff phase and is associated with flexion of the trunk in preparation for takeoff
244 SANDERS AND WILSON in the case of forward dives and with flexion of the knees in the case of reverse dives. Consequently, this unweighting is greater with increasing rotational requirements. This is clearly evident in the mean relative acceleration plots for dives of varying rotational requirements displayed in Figure 5. It appears as though the magnitude of these periods of negative relative acceleration has a considerable bearing upon the amount of energy available to the diver to gain height. The first reduces the depth to which the springboard is depressed and therefore the quantity of stored energy. The second is primarily associated with the actions of the diver to achieve the desired rotation. Because the vertical reaction forces are reduced by the unweighting, less work is performed to change the vertical fraction of kinetic energy of the diver. Much of the strain that is not used by the diver to gain height may be used for rotation of the diver. Some may remain in the springboard (observed as continued oscillation of the board after takeoff) and some may be dissipated through various forms of damping. The magnitude of the minimum relative acceleration showed a strong relationship with HD in the forward dives (R=0.55) but a very low relationship in the reverse dives (R=0.17) displayed in Figures 6a and 6b. Observation of individual plots reveals that, in general, divers who attain good height are characterized by a strong "push" that continues well into the depression phase and a minimization of the magnitude and duration of negative relative acceleration. Figure 7 displays the segmental contributions to relative acceleration of the reverse dive for which the greatest work to produce height (10.3J.kg-') was performed. Of this, the potential energy fraction was 3.0J.kg-' and the kinetic energy fraction was 7.3J.kg-'. The height of the CG above the resting springboard level achieved in this dive was 3.02m. It is worth noting that the absolute TIME (% takeoff phase) Figure 5 - Mean acceleration of the center of gravity relative to the metatarsal phalangeal joint during the takeoff phase of selected dives from the forward and reverse groups.
DIVES FROM 3M SPRINGBOARD n V V a) 0 1 I I I I -25-2 0-1 5-1 0-5 0 Minilnulll Relative Acceleration (n~.s-~) 1 8 0 rn 0 160- m 140-. 120-100- 80-60 A A4 A A A 4s. A A A A A *. A A A 0 8 - I I I I -50-40 - 3 0-2 0-1 0 0 Minilnuln Relative Acceleration (n~.s-~) Figure 6 - Relationship between minimum relative acceleration and height difference (HD). (a) forward dives, (b) reverse dives. vertical velocity at touchdown in this dive of 4.46m. s-' (KETD = 9.95J.kg-') was also very high. Thus the great heights achieved by this diver are clearly the result of a combination of high touchdown velocities and a high degree of work on the board. The vigorous push during the depression of the springboard is a feature of this dive. The large area above the zero line during board depression is indicative of the applied impulse used to store energy in the board. There is a very small area below the zero line during recoil. Thus the degree of unweighting of
246 SANDERS AND WILSON TOTAL UPPER EXTREMITIES ------- LOWER EXTREMITIES ----- TRUNK AND HEAD......_.I..._ Depression Recoil 0 10 20 30 40 50 60 70 80 90 100 TIME (% takeoff phase) Figure 7 - Segmental contributions to acceleration of the center of gravity relative to the metatarsal phalangeal joint of the best diver during the takeoff phase of 301b. the board during recoil is kept comparatively small while the applied impulse during the depression phase is substantial. It should be noted, however, that this diver has the advantage of being tall (178cm). Therefore he has the range of extension available for a sustained positive relative acceleration and minimal negative relative acceleration. While short stature would appear to be a disadvantage, divers with large areas of negative relative acceleration tended to have insufficient scope for extension due to an inadequate crouch at touchdown rather than a lack of height. Another common cause of unweighting was failure to extend as much as other divers. However, even with a deep crouch it is possible to work too hard on the board during the depression phase, extending too quickly, and leaving insufficient range of extension to prevent a large degree of unweighting during the remainder of the takeoff phase. Percentage contributions of the segments to the maximum relative acceleration-in view of the fact that the diver seeks to exert an additional force on the springboard by accelerating vertically upward with respect to it, the magnitude of this acceleration is linked to the work performed on the board. There are no obvious differences in maximal relative acceleration among dive types (Table 5). However, there is considerable variation among divers (SD = 2.8 to 9.3m. s-~). The segment contributions to maximal relative acceleration display considerable similarity to the findings of Miller and Munro (1984). Clearly, the lower extremities are predominant in producing vertical acceleration of the CG with respect to the MP (65 to 84 % of the maximum relative acceleration). Of this, the relative acceleration of the trunk and head due to the extension of the lower extremities is the major component because the trunk is comparatively massive. The next largest contribution (forward dives= 13 to 25%, reverse dives= 15 to 26%) is due to the combined effect of the active component of the trunk-head relative acceleration and the relative acceleration of the upper extremities due to the ac-
DIVES FROM 3M SPRINGBOARD 247 Table 5 Mean Oh Contributions of Body Segments to the Maximum Upward Acceleration of the Diver With Respect to the Metatarsals" Lower extremities Trun Whead UE Total ACT TH UP TOT ACT UP TOT ACT ACC. Dive n % % 010 010 010 Oh 010 010 (m.s-i) Males 101b 4 19 37 8 64 17 5 22 14 31 (2.1) (6.6) (1.5) (10.0) (6.4) (3.5) (9.6) (7.3) (2.9) 103b 7 17 40 9 66 17 7 24 10 31 (1.9) (7.0) (1.6) (10.4) (8.4) (3.1) (11.6) (1.8) (3.9) 4 18 37 9 64 18 8 25 11 30 (1.8) (5.3) (1.2) (8.1) (6.3) (1.9) (8.1) (1.5) (3.2) 107c 6 18 40 9 68 14 6 20 13 34 (3.7) (2.3) (.5) (4.5) (2.1) (1.3) (3.1) (1.8) (9.3) 301 b 5 1 8 38 9 65 18 6 24 11 32 (1.2) (4.1) (.9) (5.6) (5.2) (2.8) (7.2) (6.0) (3.2) 301 a 7 20 43 10 72 16 7 23 5 29 (1.2) (4.3) (1.0) (6.4) (5.1) (2.2) (7.1) (4.7) (3.0) 305c 10 18 41 9 68 18 8 26 5 29 (3.6) (4.0) (.9) (7.9) (4.3) (1.9) (6.0) (8.3) (4.5) Females 101a 4 18 44 10 72 13 5 19 9 28 (3.8) (7.7) (1.7) (8.2) (6.2) (2.7) (8.6) (7.1) (6.8) 11 21 41 9 72 11 5 16 12 31 (4.3) (8.5) (1.9) (12.2) (9.3) (3.0) (11.9) (3.8) (3.7) 301a 10 23 47 11 81 10 5 15 4 27 (2.1) (9.3) (2.1) (13.0) (11.8) (3.3) (13.4) (6.7) (3.9) 305c 5 20 45 10 76 11 5 16 8 32 (2.5) (4.6) (1.O) (8.0) (4.1) (1.8) (5.8) (2.4) (2.8) *SD in parenthesis. UE = Upper extremities. ACT= Active component of the relative acceleration for (a) lower extremities, (b) trunk and head, (c) upper extremities. TH =Relative acceleration of the trunk and head due to the relative acceleration of the lower extremities. UP = Relative acceleration of the upper extremities due to the relative acceleration of (a) lower extremities, (b) trunk and head. TOT=Total contribution to relative acceleration of (a) lower extremities, (b) trunk and head. tion of the trunk. Significantly, the action of the upper extremities contributes relatively little to the total maximal relative acceleration (forward dives=9 to 14 %, reverse dives =4 to 11 %). These findings suggest that emphasis should be placed on developing a strong leg drive and trunk extension from a relatively deep crouch, rather than on the development of a vigorous arm action. Hip angles during the takeoff phase-although the mean hip flexion at touchdown presented in Table 6 for the males shows little variation among dives
248 SANDERS AND WILSON Table 6 Mean Hip Angles at Critical Points During the Takeoff Phase* Angle (O) Dive n Touchdown Max. depression Takeoff Males lolb 103b 107c 301 b 301a 305c Females lola 301 a 305c *SD in parenthesis. (1 14 to 1 18 "), the SDs are large (6.5 to 15.4) and indicate a high degree of variation among divers. The association between hip flexion at touchdown and HD is evident from Figures 8a and 8b. Although the correlation of R=0.37 for forward dives and R=0.48 for reverse dives is low, the regression is significant at p<0.05 for forward dives and p<0.01 for reverse dives. At touchdown in the dive for which the greatest height was achieved (3.14m in 103B), the diver's hip flexion was 95". Hip flexion at touchdown, together with knee flexion, provides the diver with the range of extension required to do work on the board. A secondary benefit is the postponement of contact due to the raising of the feet with respect to the CG. Thus, vertical velocity at touchdown and therefore KETD is increased by adopting a crouch prior to landing from the hurdle. This is evident in the plots of hip flexion at touchdown against KETD displayed in Figures 9a and 9b. The correlation between hip angle and KETD was 0.71 for both the forward and reverse dives. It may be concluded that, within the range of this data, the greater the hip flexion at touchdown the better. The limit to a diver's hip flexion may depend on the diver's strength and various timing considerations. Hip flexion at takeoff in the forward dives is strongly influenced by the rotational requirements (101b= 165", 103b= 152", = 130"). This displays considerable consistency with values found by Golden (1981) (101b=168.6", 103b= 147.7", = 129"). It is observable from Figure 10 that the divers perform most of the hip extension during the depression of the springboard, and the required flexion prior to takeoff is performed during the last 30% of the takeoff phase. Hip flexion at takeoff is associated with HD (R=0.52) and is evident from Figure 1 la.
DIVES FROM 3M SPRINGBOARD a) 0! I I I I I 90 100 110 120 130 140 1 Hip Angle at Touchdown (degrees) 180- m 160-80- b) 60 I I I I 90 100 110 120 130 140 Hip Angle at Touchdown (degrees) Figure 8 - Relationship between hip angle at touchdown and height difference (HD). (a) forward dives, (b) reverse dives. In the reverse dives the hips continue to extend throughout the recoil, reaching a peak close to takeoff. At this time the hips are actually hyperextended through the action of arching the back. This hyperextension is greater for dives performed in a layout position (301a females=207", 301a males = 199") compared to tuck (30% females= 182", 30% males=190 ) and pike (301b males=186"). There is only a low correlation of R=0.34 with HD, although the regression shown in Figure llb is significant w0.05). Knee angles during the takeoffphase-the knee angles presented in Table 7 show that the bulk of the knee extension in forward dives occurs in the latter
SANDERS AND WILSON lola r lolb R = 0.71 v 103B P < 0.001 1053 B = -0.067 + 0.011 107C a) 90 100 110 120 130 140 150 Hip Angle at Touchdown (degrees) 5 1 I I I I 1 90 100 11 0 120 130 140 b) Hip Angle at Touchdown (degrees) Figure 9 - Relationship between hip angle at touchdown and kinetic energy due to vertical translation at touchdown (KETD). (a) forward dives, (b) reverse dives. half of the takeoff phase. Nearly all divers displayed full extension or close to full extension by the end of the takeoff phase. Figure 12 shows that, in general, the knee joints were still extending up until the instant of takeoff. As with hip flexion, greater variability among divers occurs at the commencement of the takeoff phase (SD=6.0 to 11.4") than at takeoff (1.4 to 6.0'). The deep crouch of divers who achieve good height is reflected in the large amount of knee flexion at touchdown. Thus, knee flexion at touchdown in forward dives is correlated with HD (R=0.51) and is evident in Figure 13a. This permits a
DIVES FROM 3M SPRINGBOARD 251 I MEAN HIP ANGLE TIME (% takeoff phase) Figure 10 - Mean hip angles during the takeoff phase of dives from the forward and reverse groups. large range of knee extension to work on the board. Greg Louganis is distinguished by his range of knee extension during takeoff (Miller & Munro, 1985a). Knee flexion also increases the KETD by delaying contact with the springboard, as indicated by the correlation between knee angle and KETD of R=0.75. A similar situation exists in the case of reverse dives. The correlation between knee angle at touchdown and KETD and HD was R=0.68 and R=0.53 (Figure 13b), respectively. Unlike the forward dives, the knees tend to flex toward the end of the takeoff phase in the reverse dives. The greater the rotational requirement, the greater the knee flexion at takeoff tends to be (301b males=174", 301a males = 172", 301a females = 172", 30% males = 128", 30% females= 119"). Due to the fact that the high degree of knee flexion in the high rotation dives was common to all divers, it may be concluded that the flexion was not associated with premature adoption of the tuck position. Rather it was a necessary process associated with the development of angular momentum. In 30% this knee flexion begins around 70% of the takeoff phase and coincides with the period of rapid development of angular momentum. Force data reveal that this action coincides with large horizontal reaction forces that produce the torques necessary to build up the required angular momentum to perform the dive. It appears as though the diver deliberately pulls back with hislher feet, and that flexion of the knees is a natural consequence of this action. Flexion of the knees at takeoff in reverse dives was found to be weakly associated with HD (R=0.25). Ankle angles during the takeoflphase-the divers tend to land on the springboard with the ankles somewhat dorsiflexed. From Table 8 it is evident that there is very little variation in ankle angle at touchdown among dives (for-
SANDERS AND WILSON a) Hip Angle at Takeoff (degrees) b) 60! I I I I I I -1 150 160 170 180 190 200 210 220 Hip Angle at Takeoff (degrees) Figure 11 - Relationship between hip angle and takeoff and height difference 0). (a) forward dives, (b) reverse dives. ward dives =77 to 8 1 O, reverse dives = 8 1 to 83 O) or among divers (SD =2.2 to 5.1"). However, the individual variation at takeoff is quite substantial, particularly in the forward dives (SD = 3.8 to 14.0 O). There are no apparent differences between males and females. Plantar flexion of the feet begins shortly after touchdown, increasing the footlknee angle. The bulk of this flexion occurs after maximal springboard depression and roughly coincides with the flexion of the hips. Thus the diver is able
DIVES FROM 3M SPRINGBOARD 253 Table 7 Mean Knee Angles at Critical Points During the Takeoff Phase' Angle (O) Dive n Touchdown Max. depression Takeoff Males 101b 4 120 (11.4) 137 (5.0) 177 (1.4) 103b 7 119 (10.6) 133 (6.9) 181 (2.9) 4 122 (7.6) 133 (10.3) 181 (5.0) 107~ 6 118 (6.1) 130 (8.4) 176 (6.0) 301 b 5 118 (6.8) 137 (4.6) 174 (3.8) 301 a 7 121 (9.5) 133 (10.5) 172 (7.1) 305~ 10 124 (10.5) 137 (11.0) 128 (7.0) Females 101a 4 126 (6.0) 150 (5.0) 186 (2.2) 11 123 (6.8) 139 (8.2) 184 (4.7) 301 a 10 127 (6.4) 143 (8.8) 172 (4.4) 305c 5 122 (9.3) 149 (7.0) 119 (11.0) *SD in parenthesis. MEAN KNEE ANGLE al u Y W --- 101 B 103 B -------- 105 B 301 A *---- 305C 0 10 20 30 40 50 60 70 80 90 100 TIME (% takeoff phase) Figure 12 - Mean knee angles during the takeoff phase of selected dives from the forward and reverse groups.
SANDERS AND WILSON a) 0 1 I I 1 I I 100 110 120 130 140 150 Knee Angle at Touchdown (degrees) 60! I I I I I 100 110 120 130 140 150 Knee Angle at Touchdown (degrees) Figure 13 - Relationship between knee angle at touchdown and height difference (HD). (a) forward dives, (b) reverse dives. to plantar flex rapidly during the period in which the vertical springboard reaction forces diminish through the combined effects of hip flexion and the return of the springboard to its neutral position. It would seem that plantar flexion toward the last 30% of the takeoff phase serves to reduce, to a certain extent, the negative acceleration of the CG relative to the board during this time. Whole body angle during the takeoffphse-the whole body angle of lean is strongly influenced by the rotational requirements of the dive. In the forward dives, a decrement of approximately 2 to 3" in the angle of lean at touchdown for each additional pike somersault is evident from the means of the male divers presented in Table 9 (101b=98", 103b=96", =93"). Although the diver's
DIVES FROM 3M SPRINGBOARD 255 Table 8 Mean Ankle Angles at Critical Points During the Takeoff Phase* Angle (O) Dive n Touchdown Max. depression Takeoff Males 101b 103b 107c ' 301b 301 a 305c Females 101a 301 a 305c 'SD in parenthesis. Table 9 Mean Whole Body Angle of Lean at Critical Points During the Takeoff Phase* Angle (O) Dive n Touchdown Max. depression Takeoff Males 101b 103b 107c 301 b 301 a 305c Females lola 301 a 30% *SD in parenthesis.
SANDERS AND WILSON Table 11 Correlation Matrix for Reverse Dives (n = 37) HD KETD HATD HAT0 KATD KATO APE AKE RAMAX RAMIN HD = Difference in height of the CG at takeoff and flight maximum. KETD = Kinetic energy at touchdown from the hurdle due to vertical velocity. HATD = Hip angle at touchdown from the hurdle. HAT0 = Hip angle at takeoff from the springboard. KATD = Knee angle at touchdown from the hurdle. KATO = Knee angle at takeoff from the springboard. APE = Change in gravitational potential energy from touchdown to takeoff. AKE = Change in kinetic energy due to vertical velocity from touchdown to takeoff. RAMAX = Maximum relative acceleration. RAMIN =Minimum relative acceleration. AKE were included (see Table 11). Similar to the forward dive model, hip and knee angles at touchdown were unnecessary due to their strong association with KETD (R =0.7 1 and R =0.68, respectively). The uncorrelated variables KETD (R=0.75) and knee angle at takeoff (R=0.25) were able to explain 63 % (adjusted R2 =0.61) of the variance in HD. Maximum and minimum relative acceleration accounted for a further 6%. It appears that the explanation of height achieved is more complicated for reverse dives than for forward dives. A substantial percentage of the unexplained variance for both groups is likely to be linked to timing aspects. These include the phase of oscillation of the springboard at touchdown and the temporal pattern of forces applied to the springboard as a result of the diver's acceleration of the CG with respect to the board. Other variables affecting the height achieved would be the physiques of the divers and the characteristics of the springboard including fulcrum setting. Conclusion The rotational requirement of a dive is a major factor affecting the height achieved by divers. This is because the energy stored in the board must be used to produce both translation and rotation. With increasing rotational demands, less energy is available for translation and height is reduced. The quantity of energy stored in the board is dependent on the vertical velocity of the diver at touchdown from the hurdle and on the work performed on the board during its depression. Thus, better divers were characterized by high vertical velocities at the completion of the hurdle. A deep crouch at this time increased the vertical velocity by delaying contact with the board. This body orientation at touchdown also provided the range
DIVES FROM 3M SPRINGBOARD 259 of extension required to perform work on the board by accelerating the CG away from the MP in a vertical direction. Regression analysis revealed that in view of the strong association between hip and knee flexion at touchdown and KETD, 77% of the variance in HD for forward dives could be explained by two uncorrelated variables-ketd (51 %) and hip flexion at takeoff (26 %). The increased hip flexion associated with dives of greater rotational requirements partially unweights the board during recoil, reducing the height achieved. Maximum and minimum relative acceleration explained a further 8 % of the variance in HD. Similarly, 63 % of the variance in height difference achieved in reverse dives could be accounted for by KETD (57%) and knee angle at takeoff (6%). The action of flexing the knees prior to takeoff for the higher rotation reverse dives reduces the height achieved by partially unweighting the board during recoil. In the reverse dives, maximum and minimum relative acceleration increased the explained variance by a further 6%. Further research is required to investigate the relationship between segmental timing patterns and the storage and utilization of strain energy to gain height and rotation. The substantial differences in the height achieved between males and females and the need for a high hurdle, deep crouch, and vigorous extension during the depression phase suggest that strength may be a limiting factor for many divers. References Dempster, W.T. (1955). Space requirements of the seated operator (WADC TR 55-159). Dayton, OH: Wright-Patterson Air Force Base. Dempster, W.T., & Gaughran, G.R.L. (1967). Properties of body segments based on size and weight. American Journal of Anatomy, 120, 33-54. Golden, D. (1981). Kinematics of increasing rotation in springboard diving. In D. Golden (Ed.), Proceedings of the 1981 United States Diving Sports Science Seminar (pp. 55-81). Snowbird, UT: United States Diving. Jackson, K.M. (1979). Fitting of mathematical functions to biomechanical data. IEEE Transactions in Biomedical Engineering, 26, 122-124. McCormick, J.H., Subbaiah, P., & Arnold, H.J. (1982). A method for identification of some components of judging springboard diving. Research Quarterly for Exercise and Sport, 53, 313-322. Miller, D.I. (1984). Biomechanical characteristics of the final approach, step, hurdle and takeoff of elite American springboard divers. Journal of Human Movement Studies, 10, 189-212. Miller, D.I., & Munro, C.F. (1984). Body contributions to height achieved during the flight of a springboard dive. Medicine and Science in Sports and Exercise, 16(3), 234-242. Miller, D.I., & Munro, C.F. (1985a). Greg Louganis' springboard takeoff: I. Temporal and joint position analysis. International Journal of Sport Biomechanics, 1, 209-220. Miller, D.I., & Munro, C.F. (1985b). Greg Louganis' springboard takeoff: II. Linear and angular momentum considerations. International Journal of Sport Biomechanics, 1, 288-307. Sanders, R.H., & Wilson, B.D. (1987). Angular momentum requirements of the twisting and nontwisting forward 1 112 somersault dive. International Journal of Sport Biomechanics, 3, 47-62.