How does buoyancy influence front-crawl performance? Exploring the assumptions

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1 DOI: /jst.23 Review How does buoyancy influence front-crawl performance? Exploring the assumptions Toshimasa Yanai 1, and Barry D. Wilson 2 1 School of Life System Science and Technology, Chukyo University, Toyota, Japan 2 National Sports Institute of Malaysia, Kuala Lumpur, Malaysia A new theoretical framework for understanding the influence of buoyancy on swimming performance is proposed in this paper. During front-crawl swimming, the hydrodynamic force acting on the hands generates the leg-sinking moment around the center of mass, which is counteracted by the leg-raising moment generated by the buoyant force. & 2008 John Wiley and Sons Asia Pte Ltd Keywords:. horizontal alignment. fluid forces. stability. moment. rotation 1. INTRODUCTION In front crawl, the swimmer uses alternate overhead arm strokes and executes near-vertical kicks. These limb movements generate time- and position-dependent fluid forces, which in turn, control linear and angular motions of the swimmer s body. These fluid forces acting on a swimmer s body can be categorized into two components: hydrodynamic forces and hydrostatic, or buoyant, forces. Since Houssay studied hydrodynamic forces in 1912 [1], many researchers have devoted their energy to understanding the propulsive and resistive characteristics of swimming. Researchers generally agree that swimming performance is improved by maximizing the propulsion, minimizing the resistive drag forces, and optimizing the swimming efficiency. The influence of buoyancy on swimming performance has not received comparable attention, and as a result, there is a limited amount of knowledge on the topic. In this paper, how buoyancy of the human body the floatability and the stability in fluid has been examined and is reviewed first, and then the influence of buoyancy on swimming performance is discussed. In the second part of this paper, a widely-accepted mechanism that explains how the swimmer s buoyancy influences swimming performance is demonstrated to be invalid. A new theoretical framework is presented so as to fully understand the mechanism of how buoyancy influences swimming performance. *School of Life System Science and Technology, Chukyo University, 101 Tokodachi, Kaizu, Toyota , Japan tyanai@life.chukyo-u.ac.jp 1.1 Does Our Body Float Motionless in Fresh Water? A key principle for approaching the problem Does our body float in water? is derived by the ancient Greek mathematician and physicist, Archimedes. Archimedes presumably arrived at the famous principle while taking a bath, noting the partial loss of weight after submerging his arms and legs in the water. The partial loss of weight is due to the buoyant force, and its magnitude is determined as the product of the specific weight of the fluid and the volume of the body under the water surface. Whether a motionless body could float or not is determined by the balance between the magnitudes of buoyant force and the weight acting on the body. If the buoyant force acting on the body completely submerged in fluid is greater than the weight, in other words, if the specific weight of the fluid is greater than that of the body, the body accelerates upwards and floats on the water surface. If the buoyant force equals the weight, the body at rest stays at the same depth. If the weight is greater than the buoyant force, the body accelerates downwards and sinks towards the bottom of the water. An early scientific reference on our floating ability was found in the mid 18th century. Robertson [2] was motivated to answer the question: What quantity of timber would be sufficient for a man to afloat in river or seawater? He asked 10 men to completely sink in a water tank and measured the displacement of the water surface, which enabled him to compute the body volume and the buoyant force acting on the body. The buoyant force (mean: 729 N) was found to be greater than the body weight (mean: 649 N) for nine participants, and he concluded that: (i) excepting some, every man was lighter than his equal bulk of fresh water and thus, many might be preserved from drowning ; and (ii) a piece of wood, Sports Technol. 2008, 1, No. 2 3, & 2008 John Wiley and Sons Asia Pte Ltd 89

2 Review not larger than an oar, would buoy a man partly above the water. After one century, this finding was supported by Pettigrew [3] who investigated the floating positions of motionless humans. On the basis of the data, he claimed that everyone could float in water if breathing was held naturally and the body was relaxed. In the 20th century, the primary question on the buoyancy of the human body continued to be whether or not a motionless human could float in water. More methodologicallysound approaches were used in the research conducted in this period so as to overcome some of the obvious limitations associated with the earlier investigations. Several researchers measured the so-called underwater weight (Figure 1) [4 6] to evaluate one s buoyancy, which was later used to determine the specific weight of the body [5 7] so as to examine the body s floatability. On the basis of these anthropometric measurements, the answer for the question Does our body float in water? was obtained as follows: (i) not all human can T. Yanai and B. D. Wilson float motionless in fresh water; (ii) women are generally more buoyant than men; and (iii) the volume of air in the lungs affects one s buoyancy. The buoyancy of a human body not only determines sink or float, but it also determines the body s stability in the fluid. Depending on the locations of the center of mass (CM) and the center of buoyancy (CB), the body could either be stable, neutral, or unstable (Figure 2). The stability of a human body in a horizontal, motionless floating position is determined by how the body is configured to form a certain posture and by the composition of the parts of the body. As many of us may know from our own experiences, our body is not generally stable in a horizontal, motionless floating position: the legs tend to sink to a lower position than the initial horizontal position. Studies confirm that the legs in fact tend to sink. This is due to the buoyant force acting more cranial to the CM of the body (Figure 3), generating the moment around the CM that causes the legs to sink [7,8 12]. Some of these studies examined the sex differences in the body s stability and found that women tend to float more horizontally than men [10,11,13], due primarily to women having a greater amount of body adipose tissue stored around the hips and thighs, causing the CB to be located closer to the CM [11]. The state of breathing was found to affect the stability in a horizontal, motionless floating position [10,12]. When air is inhaled, the lung volume increases and the CB shifts cranially to increase the leg-sinking moment. As far as a motionless human body floating in water is concerned, the floatability and stability of the human body were measured successfully and reliably with anthropometric measurements. It could therefore be said that the analysis of the morphology of the human body has led to the answer for the question Does our body afloat in water? Most humans can float, but not every one can float motionless in fresh water. Buoyant force Figure 1. The underwater weighing method for measuring the specific gravity of the human body. Reprinted with permission from [7]. Copyright (1937) by the American Alliance for Health, Physical Education, Research and Dance, 1900 Association Drive, Beston, VA, r 2008 Taylor and Francis. Reproduced by kind permission. Weight Figure 3. Positions of the center of mass and the center of buoyancy of a typical human body in a horizontal, motionless floating position. Buoyant force acts more cranial to the center of mass, generating a leg-sinking moment around the center of mass of the body. Stable Neutral Unstable Figure 2. Stability of a floating body. Position of the center of buoyancy relative to the center of mass of the body determines the stability of the floating body & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 2 3, 89 99

3 1.2 Does Buoyancy Influence Swimming Performance? A widely-accepted mechanism In swimming, the human body is not motionless, but is in motion. How does buoyancy change with the motion of the body? Does buoyancy play a role in determining swimming performance? In the literature, the buoyancy of a given swimmer was measured either as the surplus of the buoyancy over the weight of the swimmer [14 16] or as the leg-sinking tendency of the swimmer s body in a horizontal, motionless floating position [10,11,13,16,17] to examine whether or not the buoyancy of a swimmer influences swimming performances. These quantities of buoyancy were investigated to examine their relationship with the energy cost of swimming and the drag encountered by the swimmers. The results of these studies demonstrated that: (i) the buoyant force acted more cranial to the CM for a horizontal, motionless floating human body in both anatomical and streamlined positions [10]; (ii) a reduced energy cost of swimming was recorded among the swimmers whose surplus buoyancy was large compared to those whose surplus buoyancy was small [15]; (iii) a reduced energy cost of swimming was recorded among the swimmers whose leg sinking tendency was small compared to those whose leg sinking tendency was large (Figure 4) [13,17,19]; (iv) for a given swimmer, a reduced energy cost of swimming was recorded when the leg-sinking tendency was decreased by attaching an air-filled tube around the waist than when the leg-sinking tendency was increased by attaching a lead-filled tube around the same position (Figure 5(a)) [16,18]; and (v) for a given swimmer, the resistive force acting on a swimmer during the performance was smaller when the leg-sinking tendency was decreased by attaching an airfilled tube than when the leg-sinking tendency was increased by attaching a lead-filled tube (Figure 5(b)) [18]. It seems that the answer to the question Does buoyancy influence swimming performance? is yes. Both the most buoyant swimmers and those swimmers whose legs float high in the water swim with reduced energy cost. These experimental findings are interpreted to hypothesize mechanisms that explain how the swimmer s buoyancy influences the swimming performance. The first mechanism is that a swimmer with less buoyancy will float lower in the water and have more drag than a swimmer who floats higher in the water, requiring a greater effort to overcome the drag [14,15,20]. This mechanism appears self-evident and will not be debated. The second mechanism [11,16,19,21] is that a swimmer whose Figure 4. Energy cost of swimming (VO 2 fs /d) plotted as a function of the extent of the leg-sinking effect of buoyancy measured in a horizontal, motionless floating position. The plot contains the values measured from males (J) and females (). Reprinted from [13]; used with permission. r 2008 Taylor and Francis. Reproduced by kind permission. Figure 5. Normalized values of energy cost of swimming plotted as a function of the normalized values of the leg-sinking effect of buoyancy (a) and normalized values of resistive force acting on the swimmer plotted as a function of the normalized values of the leg-sinking effect of buoyancy (b). Reproduced with kind permission of Springer Science and Business Media from [18]. Sports Technol. 2008, 1, No. 2 3, & 2008 John Wiley and Sons Asia Pte Ltd 91

4 Review buoyancy generates the greater leg-sinking moment in a horizontal, motionless floating position will have a lower leg position during swimming, which increases drag and/or requires a greater effort to execute kicks so as to maintain a streamlined horizontal alignment. Consequently, a greater amount of energy is required to overcome the increased drag and/or to maintain strong kicks. The second mechanism was postulated on the basis of two unverified assumptions: (i) the turning effect of buoyancy on a swimmer during the front crawl is the same as that in a horizontal, motionless floating position; and (ii) the flutter kick generates moments that counterbalance the leg-sinking effect of buoyancy. The key to validating these assumptions, and consequently, for validating the postulated mechanism is to examine the turning effect of the buoyant force acting on human body during the performance of swimming. 1.3 Validating the First Assumption One study [22] in the literature determined the buoyancy of a swimmer during front-crawl swimming. There was and still is no method to directly measure such an effect of buoyancy, and thus an indirect method was developed for the measurement. In this study, the performances of competitive swimmers captured with a videography technique and the body dimensions estimated from the literature values of body segment parameters were used to compute the volume of the submerged parts of the swimmer s body and its centroid for every field of captured images, so that the buoyant force and the CB were determined throughout the stroke cycle as discrete time variables. The CB and CM positions and the distance between them were computed for the model in two horizontal, motionless floating positions (the anatomical position and a streamlined position) and two breathing states (full exhalation and full inhalation [residual volume and total lung capacity of competitive swimmers [23]]). The values computed using the model closely matched the corresponding values reported in the previously mentioned experimental studies [10 12], suggesting that the human body model represents well the distributions of mass and volume across body segments. The study demonstrated that: (i) the CM fluctuated in the mean range of 23 mm, shifting toward the head as the recovery arm was swung forward during the recovery phase; and (ii) the CB fluctuated in the mean range of 105 mm, shifting toward the legs as the recovery arm was lifted out of the water (Figure 6). These different directions of a shifting pattern caused the CB to be located closer to the feet than the CM during the recovery phase and the overall turning effect of the buoyancy was to raise the legs (mean value of 22 Nm), rather than to sink the legs. This observation was consistent across all 11 participants of the study. The results indicated clearly that the turning effect of buoyancy in a horizontal, motionless floating position obtained from the competitive swimmers was to sink the legs, whereas in swimming conditions, it was to raise the legs. Yanai [22] reported that the turning effect of buoyancy obtained for horizontal, motionless floating were significantly different from that obtained for the front-crawl swimming, indicating that the first assumption associated with the widely-accepted mechanism is invalid. Why did the directions of the turning effect of buoyancy differ between horizontal, motionless floating and front-crawl swimming? The difference occurred because the volumes of the head, arm, and shoulder, all of which were located cranial to the CM, exited out of the water during the recovery phase and were no longer subject to the buoyant force. The CB shifted caudally and passed beyond the CM, and the leg-raising moment around the CM was generated. A simple simulation illustrates the influences that this phenomenon would have on the extent of the caudal shift on the CB (Figure 7). For a streamlined body completely submerged in water, the CM and CB are located respectively at 60.4% and 61.4% of stature cranial from the feet [10]. When the hand and the forearm of one arm are assumed to be out of the water, the buoyant force would no longer act on the entire body, but acts only on the volume of the submerged parts of the body (which is approximately 98% of the total body volume as the volumes of one hand and one forearm are 0.57% and 1.7% of the entire body volume, respectively [Drillis and Contini, 1966]). The CB should thus be located at a position caudal to the centroid of the entire body. A simulation estimated that the CB would shift caudally by 1.1% of stature to locate at 60.3% of the stature cranial to the feet. The caudally-shifted CB position nearly coincides with the CM, resulting in the leg-sinking moment of the buoyant force to disappear. When one entire arm (accounts for 5.7% of the entire volume of the body [Drillis and Contini., 1966]) is not subject to the buoyancy, the CB shifts caudally by 2.4% of stature in total to locate at 59% of stature cranial from the feet. During the recovery phase of front-crawl swimming, not only is an entire arm of the swimmer s recovery arm moved out of the water, but also a substantial part of the head and the recovery shoulder. The CB is displaced even more caudally and estimated to be located at approximately 57% of the stature from the feet. For a swimmer of 1.8 m stature and 75 kg body mass, this magnitude of caudal shift of the CB (approximately 80 mm) results in the leg-raising moment of the buoyancy to attain 40 Nm. The results of Yanai s experimental study and the present simulation indicate that the buoyancy during the performance of swimming is heavily affected by the extent of the body that is out of the water, and hence the moment due to buoyancy could not be determined solely by the anthropometric quantities. The finding that swimmers receive a substantial amount of legraising moment during the performance of front-crawl swimming raises a serious question as to the validity of the second assumption that the flutter kick generates moments that counterbalance the leg-sinking effect of buoyancy for maintaining the horizontal alignment. 1.4 Validating the Second Assumption T. Yanai and B. D. Wilson The contribution of the flutter kick to swimming propulsion has been studied to some extent [20,24 28], but its contribution to maintaining the horizontal alignment of the 92 & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 2 3, 89 99

5 (a) 0.10 CB CM Positions of CB and CM relative to the torso center (m) 0.15 closer to head closer to feet (b) Recovery phase Recovery Phase Recovery Phase Recovery Phase Rotational effect of buoyancy (Nm ) Legsinking effect Frame number Leg-raising effect Figure 6. Typical positions of the center of mass (CM) and center of buoyancy (CB) observed during two stroke cycles of front-crawl swimming (a) and the moment of buoyant force about the CM (b) for a member of a collegiate men s swim team. Reprinted from [22] with permission from Elsevier. CM=0.603 h V =0% out CB=0.614 h V =4.2% out CB=0.599 h V =7.85% out CB=0.589 h V =10% out CB=0.584 h Figure 7. Caudal shift in the center of buoyancy (CB) position due to some body parts exited out of the water. 8 out indicates the percent volume of the body parts that were assumed to be out of the water. CM, center of mass. Sports Technol. 2008, 1, No. 2 3, & 2008 John Wiley and Sons Asia Pte Ltd 93

6 Review swimmer s body has not been examined. The function of the flutter kick, in particular, the contribution of the flutter kick to maintain the horizontal alignment of front-crawl swimmers was therefore examined on a theoretical basis. First, the mechanism is examined by which the horizontal alignment is achieved by a swimmer undergoing kicking drills with no arm strokes. In a typical kicking drill, the swimmer holds a floatable board by the outstretched arms, maintains the arms and the torso in a streamlined position, and executes the flutter kick to propel the body forward. If the swimmer stops kicking, the advancing speed of the swimmer decreases and the legs tend to sink lower. On the horizontally-streamlined swimmer, the buoyant force acts cranial to the CM, generating the leg-sinking moment. The force exerted by the floatable board on the hands should act upwards and slightly backwards, also generating a leg-sinking moment around the CM. The drag also acts on the arms, head, and torso, the result of which may or may not act through the CM. The moment of the drag force around the CM is however expected to be small because the magnitude of the drag acting on a streamlined swimmer (up to 100 N) is much smaller than the magnitude of the buoyant force and the moment arm is limited to the vertical breadth of the horizontally-streamlined swimmer s body. The phenomenon that the swimmer s legs tend to sink when they stop executing the flutter kick suggests that the resultant moment due to the buoyant force, the force exerted by the floatable board on the hands and the drag, acts in the direction that lowers the legs and raises the head. Apparently, the hydrodynamic forces generated by the flutter kick is the only source for counterbalancing the leg-sinking moment generated by other forces, suggesting that the flutter kick generates an upward-directed resultant hydrodynamic force and leg-raising moment around the CM. Second, the mechanism is examined by which horizontal alignment is achieved by a swimmer using a pull-buoy for practicing arm stroke techniques. The swimmers practice various stroking drills without executing the flutter kick so that they can concentrate on the arm stroke techniques and improve the strength of the arm muscles. The pull-buoy is used presumably to prevent their legs from sinking without executing the flutter kick. Observations and experiences generally suggest that the swimmer s legs tend to sink if swimmers do not execute the flutter kick and do not use the pull-buoy. It has been thought that this leg-sinking tendency was for the same reason that the legs of a swimmer in a horizontal, motionless floating position tended to sink. However, we now know that the reasoning is incorrect and the tendency is not due to the turning effect of buoyant force, but due to something else. Figure 8 shows the hydrodynamic forces acting on the hand reported by Schleihauf et al. [29]. The resultant fluid force acts eccentric to the CM of the swimmer s body in both positions, generating a leg-sinking moment around the CM. Its magnitude is estimated to be approximately Nm for this participant. This magnitude is greater than the mean leg-raising moment of buoyancy presented by Yanai [22]. The reason that the swimmers legs tend to sink during the drills of arm stroke techniques should be that the hydrodynamic forces acting on the hands generate a leg-sinking moment around the CM that overcome the leg-raising moment of the buoyant force acting during the drills. The swimmers use the pull-buoy during the drills so as to generate an additional amount of leg-raising moment from the pool buoy and to counterbalance the leg-sinking moment of the hydrodynamic forces acting on the hands. The function of the flutter kick now seems apparent: It is not to counterbalance the leg-sinking effect of buoyancy, but to counteract the moment of the hydrodynamic forces generated by the hands which have a leg-sinking effect (Figure 9). Thus the second assumption associated with the widely-accepted mechanism is invalid. 1.5 Validity of the Widely-Accepted Mechanism T. Yanai and B. D. Wilson The two invalid assumptions jeopardize the validity of the widely-accepted mechanism that has previously been advanced to explain how buoyancy influences swimming performance. The research findings on the mechanism of horizontal alignment of front-crawl swimmers and their theoretical implications are as follows: 1. During front-crawl swimming, buoyancy generates moment around the CM that raises the legs and lowers the head. 2. This moment counteracts against the leg-sinking moment generated by the hand forces. P = 38N P = 114N Figure 8. Hydrodynamic forces (P) acting on the right hand of a swimmer during front crawl. The resultant forces acting on the hand at all three instants generate the leg-sinking moment about the center of mass of the swimmer. Reproduced with permission from [29] & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 2 3, 89 99

7 Figure 9. A postulated mechanism for maintaining the horizontal alignment during the performance of front-crawl swimming. The leg-sinking moment around the CM generated by the hydrodynamic forces acting on the hands is counter-balanced by the leg-raising moment generated by the buoyant force and, presumably, the hydrodynamic forces acting on the legs. r 2008 Taylor and Francis. Reproduced by kind permission. 3. The flutter kick functions to counteract against the legsinking moment generated by the hand forces. Using the above list as premises of the argument, we evaluate the widely-accepted mechanism of how the swimmer s buoyancy influences the swimming performance, that is, a swimmer whose buoyancy generates a greater leg-sinking moment in a horizontal, motionless floating position naturally will have a lower leg position during swimming, which increases drag and/or requires greater effort to execute kicks so as to maintain a streamlined horizontal alignment. Consequently, a greater amount of energy is required to overcome the increased drag and/or to maintain strong kicks. First of all, buoyancy does not generate a leg-sinking moment during front-crawl swimming, and thus it does not cause lowering of the legs during swimming. The legs are not naturally lowered during swimming, which causes no increase of drag and no deviation from the horizontal alignment to require additional effort for stronger kicks. As a result of this evaluation, the widely-accepted mechanism is suggested to be invalid, and therefore, the answer to the question How does buoyancy influence swimming performance? needs to be restated. 1.6 How Does Buoyancy Influence Swimming Performance? New framework and new interpretations Since the buoyant force does not generate a leg-sinking moment during the performance of front-crawl swimming, how do we explain the results of the experimental studies that found the leg-sinking tendency of the swimmer s body in a horizontal, motionless floating position was related to the resistive force and the energy cost of swimming? Replacing the former assumption the turning effect of buoyancy on a swimmer during the front crawl is to sink the legs with the new finding, the turning effect of buoyancy is to raise the legs and lowers the head during front-crawl swimming, we will attempt to build a new theoretical framework for understanding the mechanism of how buoyancy influences swimming performance. 1.7 New Framework As argued and suggested in the previous section, one function of the flutter kick is to counteract the leg-sinking moment generated by the arm strokes. In other words, the flutter kick supposedly generates upward-directed resultant hydrodynamic forces and leg-raising moments around the CM during the performance of front-crawl swimming. This moment, together with the moment of the buoyant force, counterbalances the leg-sinking moment generated by the arm strokes. Evidently, the horizontal alignment of front-crawl swimmers is controlled primarily by the moments due to the three forces (Figure 9): the hydrodynamic forces generated by the arm strokes, the hydrodynamic forces generated by the flutter kick, and the buoyant force. Using this as the fundamental framework, how the balance among the three moments might influence the drag and the energy cost of swimming is discussed. The drag should be reduced by streamlining the swimmer s body during the stroke. One approach by which the swimmer might gain this benefit is to reduce the leg-sinking effect of hydrodynamic forces generated by the arm strokes. Reduction of this leg-sinking effect disturbs the balance among the three moments, causing the leg-raising moment to overcome the legsinking moment. As a result, the swimmer s legs should raise and/or the swimmer s upper body should sink until the balance among the three moments reaches equilibrium. Consequently, the swimmer s body should align in a better streamlined position to reduce the drag. The leg-sinking moment generated by the arm strokes may be minimized by moderating the hydrodynamic force generated by the arm strokes and its moment arm around the CM. The moderation of the hydrodynamic forces, however, requires caution. The swimmers ought to maintain the maximum propulsive force, but modify the effect of the hydrodynamic forces to reduce the leg-sinking effects. The modifications should thus be made only on the moment arm of the propulsive forces of the arm strokes or on the non-propulsive component of the hydrodynamic forces generated by the arm strokes. Such modifications (Figure 10) could be enabled by making a smooth arm entry into the water (which reduces the vertical component of the hydrodynamic forces) and/or by executing the backward stroke close to the body (which decreases the moment arm of the propulsive Sports Technol. 2008, 1, No. 2 3, & 2008 John Wiley and Sons Asia Pte Ltd 95

8 Review T. Yanai and B. D. Wilson (a) (b) Figure 10. Possible technical moderation for reducing the leg-sinking moment of the hydrodynamic force acting on the hand. Smooth arm entry into the water reduces the vertical component of the hydrodynamic force acting on the hand (a), and the execution of the backward pull close to the body decreases the moment arm of the propulsive forces generated by the hands (b). forces generated by the hands). If the swimmer reduces the legsinking moment of the hand forces substantially, the kicking effort necessary for horizontally aligning the body may be minimized, which should result in the swimmer further reducing the energy cost of swimming. Another approach by which the swimmer might improve performance is to increase the leg-raising effect of buoyancy during the performance of swimming. An increase in the legraising effect of buoyancy disturbs the balance among the three moments and overcomes the leg-sinking moment. Consequently, the swimmer s body aligns in a better streamlined position to reduce the drag and/or to reduce the effort necessary for executing the flutter kick. The buoyant force generates the leg-raising moment around the CM as the CB shifts caudally by the mean range of 105 mm during the recovery phases and passed beyond the CM [22]. For a given range of caudal shifting of the CB during the recovery phase, those swimmers whose CB is located close to the CM in a horizontal, motionless floating position (which results in a decreased legsinking tendency in the horizontal, motionless floating position) should attain an increased moment arm of the buoyant force around the CM during the recovery phase of swimming, resulting in these swimmers attaining a greater leg-raising effect of buoyancy. The swimmers whose leg-sinking tendency in a horizontal, motionless floating position is smaller seem to be advantaged in attaining a large leg-raising moment of buoyant force during the stroke. This explanation sounds adequate, provided that the extent of the CB s caudal shifts in the recovery phase is similar among all swimmers. However, the additional analysis of the data presented by Yanai [22] fails to support this possibility (Figure 11(a)). The supportive evidence was not obtained, even after the moments due to buoyancy were normalized by the swimmer s height and body weight. This evidence suggests that the between-subject variance in the leg-raising moment due to buoyancy during the stroke is not significantly affected by the swimmer s anthropometric characteristics, but by the movement pattern of the swimmer s body to perform the front-crawl stroke. Theoretically, the extent to which the CB shifts caudally during the stroke is determined predominantly by the volume of the body out of the water during the recovery phase and its moment arm around the CM. The greater the volume of the upper body out of the water during the recovery phase, the greater the legraising moment of buoyancy the swimmer generates. The data obtained in Yanai s study were further analyzed to examine the relation between the moment due to buoyancy and the volume of the body exiting out of the water. The results showed a significant positive correlation between them, indicating that those swimmers who had a greater portion of the body out of the water during the stroke generated a greater leg-raising moment due to buoyancy (Figure 11(b)). The results clearly suggest that the between-subject variance in the leg-raising moment due to buoyancy is explained for the most part by the between-subject variance in the extent to which the volume of the body is out of the water during the stroke. This provides further evidence to support that the between-subject variance in the leg-raising moment due to buoyancy during the stroke is affected primarily by the movement pattern of the swimmer s body to perform the front-crawl stroke, rather than by the swimmer s anthropometric characteristics. As the legraising effect of buoyancy was found to be determined by the extent to which the volume of the body was out of the water during the stroke, the swimmers should theoretically be able to reduce the drag and/or the energy cost of swimming by modifying the out of water aspects of their stroke techniques to generate an increased leg-raising moment of the buoyant force. Further studies are indicated to obtain experimental evidence for examining the described mechanical link among the magnitudes of the drag, the energy cost of swimming and the legraising moment due to buoyancy, and the stroking techniques. Despite the obvious lack of experimental evidence, a new theoretical framework for understanding the mechanism of how buoyancy influences swimming performances seems possible. The balance between the leg-sinking moment due to the arm strokes and the resultant leg-raising moment due to the buoyant force and the flutter kick determines the horizontal alignment of front-crawl swimmers, and thus an increase in the leg-raising moment due to the buoyant force or a reduction in 96 & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 2 3, 89 99

9 Figure 11. Relation between the leg-sinking moment of the buoyant force in a horizontal, motionless floating position and the average legraising moment of the buoyant force during front-crawl swimming for 11 members of a collegiate men s swim team (a), and the relation between the average ratio of the body volume exiting out of the water and the average leg-raising moment of the buoyant force during frontcrawl swimming (b). A swimmer with a lesser leg-sinking moment in a horizontal, motionless floating position does not attain a greater legraising moment during front-crawl swimming, whereas a swimmer who exits s greater proportion of their body out of the water during the recovery phase attains a greater leg-raising moment during front-crawl swimming. This provides evidence to support that the between-subject variance in the leg-raising moment due to the fact that buoyancy during the stroke is affected primarily by the movement pattern of the swimmer s body to perform the front-crawl stroke, rather than by the swimmer s anthropometric characteristics. the leg-sinking moment due to the arm strokes should result in the swimmer attaining a better streamlined position during the performance of front-crawl swimming and/or to reduce the effort necessary for executing the flutter kick. 1.8 New Interpretations of the Mechanical Link This theoretical framework, however, does not explain the mechanical link between the leg-sinking effect of buoyancy in horizontal, motionless floating and the swimming performance that was reported in the literature [13,16 18]. It might be possible that the observations reported in the literature are not appropriately interpreted due to the invalid assumption that prevailed for a long time: buoyancy causes the legs to sink both in horizontal floating and in swimming. For instance, the between-subject variance observed in the energy cost of swimming [13,16 18] might not result directly from the extent of the leg-sinking tendency in horizontal, motionless floating, but from other factors that affected both variables simultaneously. In these studies, the energy cost of swimming was expressed as the amount of oxygen consumed by the swimmer to swim a given distance. The energy required to swim a given distance is generally greater for a taller and heavier individual than for a shorter and lighter individual [15] if the skill levels of the two are equivalent. One possible factor that might have affected the results of the previous studies would be the swimmer s body size. The effect of buoyancy determined in the studies of Pendergast et al. [13] and Rennie et al. [17] was the net value of leg-sinking torque in a horizontal, motionless floating position. For two individuals of a given density distribution, the net value of the leg-sinking torque in horizontal, motionless floating is expected to be greater for a taller and heavier individual than a shorter and lighter individual, because the magnitude of the buoyant force and its moment arm should be greater for the taller and heavier individual. The additional analysis of the data presented by Yanai [22] also supported this expectation (Figure 12). It is therefore possible that the observations that the swimmers of less leg-sinking torque in horizontal, motionless floating were found to consume lesser volumes of oxygen to swim a given distance might be the result of different body size among the participants, which determines the extent of leg-sinking torque due to buoyancy. In fact, Kjendlie et al. [21] showed that the significant correlation that they found between the energy cost of swimming and the leg-sinking torque in a horizontal, motionless floating position for 23 swimmers (r ; Po0.001) disappeared when the values were normalized by the swimmer s stature (r ). Further studies are needed to confirm whether or not the reported interrelations among the leg-sinking effect of buoyancy in horizontal, motionless floating and the energy cost of swimming are free from the influence of the body size. Another possible factor that might have affected the results of the previous studies would be the magnitude of buoyancy, rather than its moment around the CM. In the studies of Capelli et al. [16] and Zamparo et al. [18], the leg-sinking effect of buoyancy for each swimmer was altered by attaching a tube filled either with air, water, 1 kg lead, or 2 kg lead around the waist, and the net values of the leg-sinking torque were normalized by the individual average value across the four filling materials. The leg-sinking torque decreased when the tube was filled with air, and it increased when the tube was filled with the lead. In the two studies, the authors mutually observed that the swimmers consumed the greatest amount of oxygen when the tube was filled with 2 kg lead and consumed the least amount of oxygen when the tube was filled with air. On the basis of the observations, they concluded that the leg-sinking torque affected the swimming economy. Filling the tube with different materials does not only alter the leg-sinking torque in a horizontal, motionless floating position, but it also affects the floatability of the swimmers. The swimmer becomes less floatable when the tube is filled with lead because the total Sports Technol. 2008, 1, No. 2 3, & 2008 John Wiley and Sons Asia Pte Ltd 97

10 Review T. Yanai and B. D. Wilson effects of the altered floatability when interpreting the observations with tubes. Additional experiments should be conducted in which the leg-sinking torque is altered by attaching the tube around the upper part of the chest or around the neck, so that an increased leg-sinking torque by filling the tube with air results in an increase in the oxygen consumption and a reduction of the leg-sinking torque by filling the tube with 2 kg lead reduces the oxygen consumption. Further studies are required to demonstrate that their conclusion is not contaminated by the altered floatability. 2. CONCLUSION Figure 12. Relation between the average leg-sinking moment of buoyant force in a horizontal, motionless floating position and the body size for 11 members of a collegiate men s swim team. (a) Stature; (b) body mass. Significant positive correlations indicate that the leg-sinking moment of buoyancy is greater for tall and heavy swimmers than short and light swimmers. weight of the swimmer with the tube-filled lead should increase more than the buoyant force. The swimmers with reduced floatability struggle hard to maintain floating at the water surface for performing the swimming techniques, and consequently, increase their oxygen consumption. In addition, the diminished floatability should reduce the volume of body segments that could exit out of the water during the recovery phase of the stroke because the swimmer needs an increased volume of the body submerged in the water to gain the buoyant force sufficient for counterbalancing the increased weight. The magnitude of the leg-raising moment due to buoyancy should be reduced (Figure 12), which consequently causes the swimmer s body to be less streamlined and/or the kicking effort necessary for maintaining the horizontal alignment to be increased. Either consequence would increase the energy cost of swimming. This theoretical relation between the swimmer s floatability and the energy cost of swimming was partially supported by Chatard et al. [15] who demonstrated that the energy cost of swimming is highly related to the floatability of the swimmer s body. Capelli et al. [16] and Zamparo et al. [18] seemed to have overlooked the adverse In this paper, the buoyancy of human body the floatability and the stability in fluid was reviewed, and its influence on swimming performance was discussed. In the discussion, a widely-accepted mechanism that had explained how the swimmer s buoyancy would influence the swimming performance was demonstrated to be invalid. A new theoretical framework was built to understand how buoyancy could influence swimming performance and the possible reasons for the leg-sinking tendency of the swimmer s body in a horizontal, motionless floating position being related to the drag and the energy cost of swimming were discussed on the basis of the new framework. Explanations of the mechanical link between the leg-sinking tendency in a horizontal, motionless floating and the swimming performance have also been presented. The experimental findings of previous studies should be re-examined carefully so that they can be interpreted in light of our new understanding of the influence of buoyancy on swimming performance. Additional experimental studies are necessary for fully understanding the influence of buoyancy on swimming performance. When we obtain experimental support for the new theoretical framework, a paradigm shift might occur to advance the current understanding of the swimming biomechanics. REFERENCES 1. Houssay F. Forme, Puissance et Stabilite des Poissons (form, force and stability of fish). Hermann et Fils: Paris, Robertson J. An essay towards ascertaining the specific gravity of living men. Philosophical Transactions 1757; 50: Pettigrew JB. Animal Locomotion. Appleton and Co.: New York, Cotton CE, Newman JA. Buoyancy characteristics of children. Journal of Human Movement Studies 1978; 4: Packard JC. Specific gravity of the human body. Scientific American Supplement 1900; No.1271, (May 12) Sandon F. A preliminary inquiry into the density of the living male human body. Biometrika 1924; 16: Rork R, Hellebrandt FA. The floating ability of women. Research Quarterly for Exercise and Sport 1937; 8: Carmody JF. Factors influencing the horizontal motionless floating position of the human body. New Zealand Journal of Physical Education 1965; 37: Carter JEL. Buoyancy and floatation. New Zealand Journal of Physical Education 1955; 6: & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 2 3, 89 99

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