INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1985, 1, 185-196 Techniques Used in the Triple Jump James G. Hay and John A. Miller, Jr. University of Iowa The purposes of this study were (a) to describe the techniques used by elite triple jumpers and @) to determine which characteristics were significantly related to the officially recorded distance of the jump. The subjects were the 12 finalists in the Triple Jump at the 1984 Olympic Games. Two motion-picture cameras placed with their optical axes at right angles to the runway were used to record the performances of the subjects. Means and standard deviations of the variables identified in a theoretical model and correlations between these variables and the distance of the jump were computed. Correlation of the distances achieved in each of the phases with the official distance of the jump suggested that, although the hop and jump phases made greater percentage contributions to the official distance than did the step phase, they accounted for only small amounts of the variance in that distance. Significant correlations of other independent variables with the distance of the jump suggested that the more the athlete's resources are expended prior to the jump phase and the more vertical his effort at takeoff into the jump, the better is the final result. The techniques employed in the men's long jump have been the subject of many biomechanical analyses. In sharp contrast, the techniques employed in the triple jumpthe second of the so-called horizontal jumps in athletics-have received very little attention from researchers in biomechanics. This is somewhat surprising, given that with three times as many takeoffs and landings the event makes much greater technical demands on those who compete in it than does the long jump. The purposes of this study were (a) to describe selected kinematic characteristics of the techniques used by elite triple jumpers, and (b) to determine which of these characteristics are significantly related to the officially recorded distance of the jump. The authors wish to express their appreciation to Lisa Smith for digitizing the films, to The Athletics Congress of the USA, for fmancial support, and to the International Amateur Athletic Federation, the Los Angeles Olympic Committee, and the Medical Commission of the International Olympic Committee for making it possible to gather data at the 1984 Olympic Games. Direct all correspondence to James G. Hay, Biomechanics Laboratory, Dept. of Exercise Science and Physical Education, University of Iowa, Iowa City, IA 52242.
HAY AND MILLER Methods Model Assuming that the triple jump is a legal one, the distance with which an athlete is credited in a triple jump is obtained by measuring the length of an imaginaxy perpendicular line from the front edge of the takeoff board to the nearest mark that the athlete makes in the sand. For the purposes of analysis, this distance may be considered equal to the sum of three lesser distances-the horizontal distance from the toe of the athlete's takeoff foot at the instant of takeoff into the hop phase to the toe of the takeoff foot at the instant of takeoff into the step phase (the distance of the hop); the corresponding distance for the step phase (the distance of the step); and the horizontal distance from the toe of the athlete's takeoff foot at the instant of takeoff into the jump phase and the mark in the sand from which the distance of the triple jump is ultimately measured (the distance of the jump)- minus whatever distance is lost at takeoff because the athlete has the toe of his takeoff foot behind the front edge of the board. For the two-dimensional analysis of the present study, the projections of the distances of the hop, step, and jump on a plane perpendicular to the takeoff board and along the midline of the runway were taken to represent the distances themselves. This was equivalent to assuming that the subjects planted their feet in a straight line along the midline of the runway. The use of this assumption was supported by previous work that showed lateral deviations from a straight line path have little effect on the measured distance of each phase of a triple jump (Hay, 1975). The distances of the hop, step, and jump may themselves be considered to be the sum of three lesser distances: the horizontal distance from the toe of the takeoff foot to the center of gravity of the athlete (the takeoff distance); the horizontal distance that the center of gravity travels during the flight phase (the flight distance); and the horizontal distance from the center of gravity to the toe of the touchdown foot at the instant of touchdown in the case of the hop and step phases, and from the center of gravity at touchdown to the mark in the sand from which the official measurement will eventually be made in the case of the jump phase (the landing distance). These various distances, and the biomechanical factors that determine them, are shown in the block diagram (or model) of Figure 1. Data Collection Subjects. The subjects were the 12 finalists in the triple jump at the 1984 Olympic Games in Los Angeles (see Table I). Filming Protocol. Two motion-picture cameras, filming at nominal rates of 100 frames per second, were used to record the performance of the subjects on each trial. These cameras were placed at distances of 19.4 m and 22.1 m from the midline of the triple jump runway, with their optical axes at right angles to this line. The first camera was placed 0.9 m forward (or on the pit side) of the front edge of the board and was used to record the subjects' performances during the last stride and the hop phase of the triple jump. The second camera was placed 13.0 m forward of the front edge of the board and was used to record performances during the step and jump phases. A series of markers was placed in carefully measured locations along the inside curb of the track between the runway and each camera. These markers served later as
THE TRIPLE JUMP I I 13 Fl DISTANCE DISTANCE DISTANCE DISTANCE OF STEP DISTANCE OF JUMP Figure 1 - Theoretical model showing biomechanical factors that determine the distance of a triple jump. Each factor is completely determined by the factors below it and to which it is linked. The factors that determine the distance of the step and the distance of the jump are as shown for the distance of the hop. For the sake of clarity, they have not been included in the model. (a) a basis for determining appropriate linear scales, and (b) a fixed origin for the coordinate system used in the analysis. Internal timing lights and timing light generators 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 Serious difficulties were encountered with people passing along the track between the cameras and the triple jump runway during the course of the competition. As a result, the best efforts of several of the subjects could not be recorded completely. From those for which a complete record was obtained, the best trial by each subject was selected for analysis. The distances of the trials analyzed are indicated in Table 1. Each of the selected trials was digitized with the aid of a Complot digitizer (Houston Instruments Division, Bausch & Lomb, Austin, TX) linked on-line to a laboratory microcomputer. Ten frames of the films for each trial were digitized: those showing the touchdown for the second-last stride, the takeoff and touchdown for the last stride, the
HAY AND MILLER Table 1 Subjects and Performances Best jump** Athlete Height* Weight* in final (Country) Birthdate (m) (N) (m) Place Comments Joyner (USA) Conley (USA) Connor (Great Britain) zou (China) Bouschen (FRG) Banks (USA) Agbebaku (Nigeria) McCalla (Great Britain) Taiwo (Nigeria) Herbert (Great Britain) Badra (Egypt) Diallo (Senegal) 17.26 (1 7.04) 17.18 (Foul, 16.78) 16.87 (1 6.67) 16.83 (16.71) 16.77 16.75 16.67 16.66 (15.89) 16.64 16.40 16.07 15.99 4th in World Championships, 1983. Ranked No. 1 in world, 1982. Ranked No. 1 in world, 1981. 2nd in World Championships, 1983. 3rd in World Championships, 1983. *Official Men's Athletics Entries, Games of the XXlllrd Olympiad, Los Angeles, 1984. **In those cases where the best trial could not be analyzed, the distance of the jump analyzed is shown in parentheses. takeoff and touchdown for the hop, and the takeoff for the step (first camera) and those showing the takeoff and touchdown for the step, and the takeoff and touchdown for the jump (second camera). Takeoff was defined as the instant depicted in the frame in which the subject was first seen to have broken contact with the ground, and touchdown as the instant depicted in the frame in which he was first seen to have regained contact with the ground. Indicator boards placed along the near side of the pit obscured parts of the subject's body during the landing. Thus it was necessary to estimate the instant at which the heels made contact with the sand and the positions of the obscured body parts at this in-
THE TRIPLE JUMP 189 stant. The values obtained for the flight time and the landing distance for the jump phase should therefore be regarded as the best available estimates rather than as precise measures. The x- and y-coordinates of 21 points defining a 14-segment model of the human body were recorded for each frame analyzed. These data were then used as input to a computer program designed to compute the variables included in the model shown in Figure 1. Data Analysis The data analysis procedures used in this study consisted of the computation of the means and standard deviations of all the variables identified in the theoretical model and for which data could be collected, and the computation of the Pearson product-moment correlations between each of these variables and the official distance of the triple jump. To identify important associations among the independent variables, correlations were also computed between those variables found to be significantly related to the official distance of the jump and the other variables identified in Figure 1. A value of P =.10 was taken to indicate statistical significance. Results and Discussion Descriptive Data Distance Lost at Takeoff. The mean distance lost at takeoff in the 11 legal trials analyzed was 10.0 cm. This distance was obtained from the last frame in which the subject was shown to be in contact with the board prior to takeoff. Phase Distances and Ratios. The lengths of the last stride of the approach and the individual phases of the triple jump for each of the subjects are in Table 2. The contribution that each phase makes (or sh~uld make) to the total distance of a triple jump has been the subject of extended debate over the years. Much of this debate has been concerned with the relative merits of the two most common techniques: the Russian technique (which emphasizes the hop phase) and the Polish technique (which emphasizes the jump phase). The lengths of the three phases are typically about 39 %: 30% : 31 % of the total length of the jump for the Russian technique, and 35 %: 29 %: 36% of the total length for the Polish technique (McNab, 1968). Seven of the 12 subjects of the present study used techniques that produced longer hop distances than jump distances. They might thus be said to have been exponents of the Russian technique. None of the seven, however, recorded ratios in which the hop phase was as overwhelmingly dominant as suggested by McNab for the Russian technique. The nearest that any came to the 39%: 30%: 31 % ratio of McNab were the 36.6%: 30.7%: 32.7 % and the 36.4%: 30.9%: 32.6% recorded by Agbebaku and Connor, respectively. The mean ratio of the phase distances for the seven subjects was 36.4%: 29.5 %: 34.2 %. The remaining five subjects recorded shorter hop distances than jump distances and, with two exceptions (Bouschen & Banks), ratios that were close to the 35 %: 29% : 36% of the typical Polish technique (McNab, 1968). Bouschen and Banks-with ratios of 32.7%: 30.5%: 36.7% and 35.6%: 26.8%: 37.8%, respectively-used techniques in
HAY AND MILLER Table 2 Length of the Last Stride and Phases of Triple Jump (m) Athlete Last stride HOP Step Jump Joyner Conley Connor zou Bouschen Banks Agbebaku McCalla Taiwo Herbert Badra Diallo M SD which the jump phase was even more strongly emphasized. The mean ratio of the phase distances for the five subjects who used the Polish technique (34.4%: 29.3%: 36.3%) was virtually a mirror image of the mean ratio for those who used the Russian technique. Heights of Takeoff and Touchdown. The mean values for the height of the center of gravity at the instant of takeoff into each phase of the triple jump were, in order, 1.20 m, 0.95 m, and 1.03 m. This high-low-medium pattern was characteristic of all but two of the trials analyzed. In the remaining two (Banks & McCalla), the height of the subject's takeoff into the jump was 1-2 cm lower than for the hop. The substantial change in the height of the center of gravity from the hop to the step takeoff (a mean decrease of 0.25 m), together with an accompanying mean increase in the takeoff distance of 0.05 m, suggests a marked lowering and a forward movement of the trunk and free limbs from one takeoff to the next. Under such circumstances one might have expected such changes to be accompanied by a lowering of the angle of takeoff, but the mean value for this variable was actually slightly greater for the step than for the hop (Table 3). The mean values for the height of the center of gravity at the instant of touchdown at the end of the last stride of the approach and each of the three phases of the triple jump were, respectively, 1.00 m, 1.03 m, 0.82 m, and 0.38 m. All of the analyzed trials exhibited a high-medium-low pattern for the touchdowns at the end of the hop, step, and jump phases-a pattern exemplified by the last three of these mean values. A comparison was made of the mean values for the height of the center of gravity at the instants of touchdown and takeoff associated with each support phase. This revealed a low-high trend for the support phases preceding both the hop and jump takeoffs, and a high-low trend for the support phase preceding the step takeoff. Velocities at Takeoff and Touchdown. The mean velocities of the center of gravity at the instants of takeoff and touchdown for the last stride of the approach and for each
THE TRIPLE JUMP Table 3 Mean Velocities at Takeoff and Touchdown (standard deviations are included in parentheses) Horizontal Vertical Angle of velocity * velocity takeoff & touchdown (mls) (mls) (deg.) TO TO TD TO TD Last stride 10.02 (0.68) HOP 9.42 (0.33) Step 8.06 (0.39) Jump 6.96 (0.34) *The effects of air resistance were assumed to be negligible for the purpose of computing horizontal velocities. For this reason, the horizontal velocities at touchdown were equal to the corresponding horizontal velocities at takeoff and are not included here. of the three phases of the triple jump are shown in Table 3. The mean values for the horizontal velocities at takeoff indicate that the subjects' forward velocity decreased by 6% during the support phase preceding the hop takeoff and by more than twice that much during each of the succeeding support phases. The absolute (and relative) changes in the horizontal velocities during the period of support preceding each phase were: Hap -0.60 mls (-6.0%) Step - 1.36 rn/s (- 14.4%) Jump -1.10 mls (-13.6%) The mean values for the vertical velocity of takeoff into the three phases were 2.09 rnls, 1.82 m/s, and 2.37 rnls, respectively. These vertical velocities at takeoff would cause the center of gravity of an athlete to rise to heights of 0.22 m, 0.17 m, and 0.29 m above its height at the instant of takeoff. These values, combined with the corresponding mean heights of the center of gravity at takeoff, indicate that the peak heights attained by the subjects' centers of gravity were, on average, 1.42 m, 1.12 m, and 1.32 m, respectively. Air Resistance. The air resistance encountered by a triple jumper is equal to the the summed effect of the resistance due to his motion through still air and the resistance due to the motion of the air itself. Although no measure of the first of these two influences is available, the official wind reading provides a crude indication of the influence of the second. The wind appears to have had an important influence on the distances recorded in the Olympic final. Seven of the 12 subjects recorded their best distances in those trials for which they had the most favorable wind conditions-either the greatest tail wind or
192 HAY AND MILLER the least head wind-and another two recorded their best distances with the second most favorable conditions. Only those trials in which the subjects recorded a legal jump are included in this analysis. No wind readings were reported for those trials in which they fouled. Average Forces. The average forces exerted during the support phases immediately preceding the takeoff into the hop, the step, and the jump were determined using the impulse-momentum relationship: - Where F = average force; t = time of support; m = the mass of the athlete, and vf and vi = the velocities of takeoff and touchdown, respectively. The mean values for the average horizontal and vertical forces were: HOP Step Jump Average horizontal force (N) -360 (-0.5) Average vertical force (N) 2419 (3.2) 2860 (3.8) 2776 (3.7) The values given in parentheses are the mean values for the average forces divided by the mean weight of the subjects. The largest value presented in this table is thus equal to 3.8 times the mean body weight of the subjects. The values reported here for the average vertical forces during the support phases preceding the step and the jump are similar to those reported by Dyson (1977), who stated that "the average pressure of the foot on the ground after the hop would be 4 times that of the body weight; after the step, 3.8 times" (p. 194). The corresponding values obtained by Fukashiro, Iimoto, Kobayashi, and Miyashita (1981) were also reported to be similar to those of Dyson. It should be pointed out here that the value obtained in the computation of an average force depends, among other things, on the accuracy with which the time of support is determined. This in turn depends on the way in which the instants of touchdown and takeoff are defined. In the present study, touchdown was defined as the instant depicted in the frame in which the athlete was first seen to be in contact with the ground; takeoff was defined as the instant depicted in the frame in which he was first seen to have broken contact with the ground. The instants of touchdown and takeoff were thus taken to be a little later on average than they were in reality. The time of support, however, should have been little affected in this process. In contrast, Fukashiro et al. (1981) defined the time of support as "the time of the whole contact phase on the ground" which presumably means the time that elapsed between the exposure of the first and last frames showing the athlete in contact with the ground. On average, such a definition leads to an underestimation of the actual time of support by an amount equal to the time between consecutive frames of the film-nominally 0.01s in the Fukashiro et al. study.
THE TRIPLE JUMP Table 4 Mean Times of Flight and Support (s) Last stride HOP Step Jump Support Flight Support Flight Support Flight Support Flight Present study 0.127 0.093 0.132 0.497 0.169 0.436 0.188 0.682 Dyson (1977) - - 0.132 0.562 0.164 0.421 0.171 0.640 Fukashiro et al. (1 98 1) 0.12-0.15-0.16 - Times of Flight and Support. The mean times of flight and support for the last stride of the approach and the three phases of the triple jump are presented in Table 4. Also presented in the same table are the corresponding results reported by Dyson (1977) following "an analysis of slow-motion film showing twelve good triple-jumpers in action (some Olympic and world record-holders)" and the times of support reported by Fukashiro et al. (1981). Although the times of flight recorded for the first two samples differ by up to 13.1 %-possibly as a result of differences in the distances jumped and/or the techniques used-the medium-low-high pattern is the same in both cases. With the exception of the time of support for the jump phase, where the mean value for the present sample was 0.017 s (or 10.4%) greater than that for the Dyson sample, the times of support for these two studies were remarkably similar. The times of support reported by Fukashiro et al. were consistently 0.01-0.03 s less than those reported in the other two studies (see earlier comment). Relationships with Official Distance None of the four variables in the second level of the model of Figure 1, the distance lost at takeoff and the distances of the three phases, was significantly related to the official distance of the jump. However, the correlation coefficients obtained for the distance lost at the board (r = 0.51) and the distance of the step phase (r = 0.50) closely approached the level (r = 0.52) required for significance. The coefficients obtained for the distances of the hop and jump phases (r = 0.39 and r = 0.34, respectively) were much lower. The negative correlation between the distance lost at the board and the official distance of the jump is exactly as might have been expected. The less the distance lost at the board due to a less-than-optimum placement of the takeoff foot, the greater the distance of the jump. The other correlations suggest that, although the hop and jump phases made greater contributions to the official distance of the triple jump than did the step phase (35.8% and 35.3% compared to 29.6%), they accounted for only small amounts (15.2% and 11.6%, respectively) of the variance in that distance. There is some similarity between these findings and those obtained by Fukashiro et al. (1981) in a study of 15 Japanese triple jumpers
194 HAY AND MILLER whose analyzed performances ranged from 13.78 m to 15.33 m. They found (a) significant correlations between the distances of the hop and step phases and the official distance of the jump and (b) a nonsignificant correlation between the distance of the jump phase and the official distance of the jump. The differences in the two studies with respect to the significance of the results obtained may well be due to corresponding differences in the number of subjects and in the homogeneity of their performances. Seven of the other variables identified in the model of Figure 1 were found to be significantly correlated with the official distance of the jump. These were the heights of the center of gravity at touchdown at the end of the hop and step phases (r = 0.56 and 0.53, respectively), the flight distance for the step phase (r = 0.52), the takeoff and landing distances for the jump phase (r = -0.60 and -0.62, respectively), and the average horizontal and vertical forces exerted during the support phase preceding the jump takeoff (r = -0.56 and.0.54, respectively). Center of Gravity at Touchdown. The significant correlations between the heights of the center of gravity at the instants of touchdown at the end of the hop and step phases are difficult to rationalize. It is widely believed that the best results are obtained in the triple jump if the athlete sweeps his forward leg downward and backward just prior to the touchdowns at the end of the hop and step phases. This action-this active landing-is believed to reduce the braking impulse that the athlete experiences at the end of each phase and thus to contribute to the overall distance that he records. The use of an active landing could also be expected to result in the foot making first contact with the ground close to the athlete's line of gravity. This in turn could be expected to produce a higher height of the center of gravity at touchdown than might otherwise be the case. In short, one might argue that an active landing should produce both a high center of gravity at touchdown and a large overall distance. This line of argument falters, however, when the correlations between the landing distance and the height of the center of gravity at touchdown at the end of the hop and step phases are examined. These correlations were r = 0.02 and r = 0.30, respectively. The possibility that the athlete's height is an important determinant of the distance he can achieve, and that the heights of the center of gravity at touchdown are also a function of the athlete's standing height, falters in a similar fashion. The correlation between the height of the subject and the official distance of the jump was a nonsignificant r = 0.24. Flight Distance for Step. The significant correlation between the flight distance for the step phase and the official distance of the jump indicated that the greater the flight distance, the greater the official distance. The other variables with which the flight distance was significantly correlated provided some indication of the factors that accounted for the observed variation in the flight distance. These included the average horizontal and vertical forces exerted on the athlete during the support phase immediately preceding the step (r = -0.66 and r = 0.55, respectively), and the vertical velocity and angle of takeoff into the step (r = 0.79 and r = 0.71, respectively). These correlations suggest that the greater the average braking force and the greater the average vertical force to which the athlete is subjected, and the greater the vertical velocity and angle of takeoff into the step, the greater is the flight distance for the step. The average horizontal forces exerted on the athlete during the support phase preceding the step ranged from -984 N to -436 N. The negative correlation between the average horizontal force and the official distance of the jump thus meant that the less the force, that is, the more negative or braking the force, the greater the official distance of the jump.
THE TRIPLE JUMP 195 Takeoff Distance for Jump. The significant correlation obtained in this case indicated that the less the takeoff distance for the jump, the greater the official distance of the jump. An examination of the variables that were significantly related to the takeoff distance for the jump suggests a sequence of closely related events culminating in the takeoff to the jump. These significant relationships suggested that (a) the larger the vertical velocity at takeoff into the step, (b) the larger the flight distance for the step, (c) the larger the downward vertical velocity at touchdown at the end of the step, (d) the larger the average vertical force during the support phase preceding the jump, (e) the shorter the time of, the support phase preceding the jump, (f) the larger the change in vertical velocity during the support phase preceding the jump, (g) the larger the vertical velocity at takeoff into the jump, and (h) the smaller the takeoff distance for the jump, the greater the official distance of the jump. In short, the more emphasis the athlete puts on the step phase and the more vertical the effort at takeoff into the jump, the better is the final result. Landing Distance for Jump. The significant correlation between the landing distance for the jump and the official distance of the jump indicated that the less the landing distance, the better the official distance. Given that long and triple jumpers usually strive to maximize the contribution the landing distance makes to the final result by having their legs extended as far forward as possible at touchdown in the sand, this finding is a little difficult to explain. One possible explanation is that the more completely the athlete has used the forward momentum generated in the approach-and thus the less he can afford to have his legs extended well in front of him as his heels hit the sand-the better the overall result. This notion is supported to some extent by the significant correlations found between the landing distance for the jump and four variables that characterize the athlete's performance during the hop phase. These were the vertical velocity at takeoff, the angle of takeoff, the flight distance, and the distance of the hop-four variables that are related in a cause-effect sequence indicated by the order in which they have been stated. The correlations between these variables and the landing distance for the jump were all negative and indicated, therefore, that the greater the variables that determine the hop distance (and thus the greater the hop distance), the less the landing distance for the jump. Average Horizontal and Vertical Forces at Takeoff to Jump. The significant correlations obtained in this case indicated that the greater the braking horizontal force and the greater the vertical force, the greater the official distance. These results are entirely consistent with those described earlier with respect to the takeoff and landing distances for the jump. Summary In summary, an analysis of the techniques used by the finalists in the triple jump at the 1984 Olympic Games revealed that: 1. Seven of the 12 subjects used techniques that produced longer hop distances than jump distances (Russian technique). The other five used techniques that produced shorter hop distances than jump distances (Polish technique). The mean ratios for these two groups of subjects-36.4%: 29.5%: 34.2% and 34.4%: 29.3%: 36.3%, respectivelywere virtually mirror images of each other. 2. Consistent patterns were observed in the heights of takeoff and touchdown for the three phases of the triple jump. These patterns were high-low-medium (for the height of takeoff) and high-medium-low (for the height of touchdown).
196 HAY AND MILLER 3. There was a mean loss in horizontal velocity of 6% during the support phase preceding the hop takeoff and losses of more than twice that much during each of the succeeding phases. 4. Seven of the 12 subjects recorded their best distances in those trials for which they had the most favorable wind conditions. 5. Mean values for the average forces exerted on the subjects ranged from 0.5 to 0.8 times body weight (in the horizontal direction) and 3.2 to 3.8 times body weight (in the vertical direction). 6. Correlation of the distances achieved in each of the phases with the official distance of the jump suggested that, although the hop and jump phases made greater percentage contributions to the official distance than did the step phase, they accounted for only small amounts of the variance in that distance. 7. Five variables that were related with each other in a logical, sequential fashion were found to be significantly correlated with the official distance of the jump. These variables were the flight distance for the step phase, the average horizontal and vertical forces exerted during the support phase preceding the jump takeoff, and the takeoff and landing distances for the jump phase. These correlations, and the correlations among these independent variables, suggested that the more the athlete's resources are expended prior to the jump phase and the more vertical his effort at takeoff into the jump, the better is the final result. 8. Two other variables-the height of touchdown at the end of the hop and step phases-were also significantly correlated with the official distance of the jump. No obvious rationale could be found for these relationships. References Dyson, G.H.G. (1977). lhe mechanics of athletics. London: University of London Press Ltd. @. 194) Fukashiro, S., Iimoto, Y., Kobayashi, H., & Miyashita, M. (1981). A biomechanical study of the triple jump, Medicine and Science in Sports and Exercise, 13(4):233-237. Hay, J.G. (1975). Lateral deviations in the triple, Athletic Journal, 55(5):32, 87-88. McNab, T. (1968). Triple Jump. London: Amateur Athletic Association. (p. 14)