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Relationships between glide efficiency and swimmers’ sizeand shape characteristics

Journal: Journal of Applied Biomechanics

Manuscript ID: Draft

Manuscript Type: Article

Keywords:Glide factor, glide coefficient, glide constant, anthropometry,morphological indices

Human Kinetics, 1607 N Market St, Champaign, IL 61825

Journal of Applied Biomechanics



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TITLE PAGE1

Article Type: Original research2

Title: Relationships between glide efficiency and swimmers’ size and shape characteristics3

Authors: Roozbeh Naemi1, Stelios G Psycharakis2,3, Carla McCabe2,3 , Chris Connaboy2,3 and4

Ross H Sanders3 5

6

Affiliations:7

1Faculty of Health, Staffordshire University, Stoke-on-Trent, UK8

2School of Life Sciences, Edinburgh Napier University, Edinburgh, UK9

3Centre for Aquatics Research & Education, University of Edinburgh, Edinburgh, UK10

11E-mail addresses of authors:12

[email protected] 13


[email protected]



18

Corresponding Author: Stelios G Psycharakis19

Address for correspondence:20

School of Life Sciences, Edinburgh Napier University21

10 Colinton Road22

Edinburgh, EH10 5DT23

Scotland, UK.24

E-mail: [email protected] 25

Telephone: +44 (0) 131 455221526

Fax: +44 (0) 131 455229127

28

Key words: Glide factor, glide coefficient, glide constant, anthropometry, morphological indices.29

Word count (main text): 392830

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mailto:[email protected]

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ABSTRACT 31

Glide efficiency, the ability of a body to minimise deceleration over the glide, can vary with32

variations in the body’s size and shape. The purpose of this study was to investigate the33

relationships between glide efficiency and the size and shape characteristics of swimmers. Eight34

male and eight female swimmers performed a series of horizontal glides at a depth of 70cm35

below the surface. Glide efficiency parameters were calculated for velocities ranging from 1.4 to36

1.8 m/s, and at the Reynolds numbers of 3.5 and 4.5 million. Several morphological indices were37

calculated to account for the shape characteristics, with the use of a photogrammetric method.38

Relationships between the variables of interest were explored with correlations, while repeated39

measures ANOVA was used to assess differences between different velocities for each group.40

Glide efficiency of swimmers increased when velocity decreased. The glide factor had a positive41

significant correlation with the glide coefficient for all velocities and for both groups. Some42

morphological indices and postural angles showed a significant correlation with the glide43

efficiency. The findings suggested that gliding efficiency was more dependent on shape44

characteristics and appropriate postural angles rather than on size characteristics.45

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Nomenclature46

X: The longitudinal axis perpendicular to the transverse plane47

Y: The frontal axis perpendicular to the frontal plane48

Z: The sagittal axis perpendicular to the sagittal plane49

hc: The vertical distance between each level and the superior level for each zone (m)50

hz: The height of each zone or the total height of body in the streamlined position(m)51

Ps: The relative position of cross-section (dimensionless).52

dnom: Nominal diameter (m)53

FR: Fineness ratio (dimensionless)54

CR: Cross-sectional ratio (dimensionless)55

TI: Taper index (m2 /m)56

m: Body mass (kg)57

Ac: Cross sectional Area. (m2)58

ρ: Water density (kg/lit)59

θh: Segmental angle of attack for a horizontal rectilinear glide (degrees)60

θi: Segmental angle of attack for an inclined rectilinear glide (degrees)61

φ: Joint angle (degrees)62

63

INTRODUCTION64

In swimming, improving the glide performance in starts, turns and the stroking cycle of 65

breaststroke has been shown to positively affect the overall performance (e.g. Hay and66

Guimaraes, 1983; D’Acquisto, et al., 1988). The glide performance is highly affected by the glide67

efficiency, which is defined as the ability of a body to minimise deceleration through the course68

of a glide. Naemi and Sanders (2008) showed that glide efficiency, which is influenced by the69

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inertial and the resistive characteristics, is affected by the body’s size and shape. These authors70

established that the glide factor, which is a product of a glide constant and a glide coefficient, is71

an indicator of glide efficiency. The glide constant incorporates the size-related parameters of the72

body, such as the body mass and the maximum cross-sectional area. The glide coefficient is73

related to the shape characteristics of the body while in a streamlined gliding position. Although74

in theory glide efficiency can be improved by increasing either or both of these two parameters75

(the glide constant and the glide coefficient), in practice the relationship between these two76

parameters and the glide factor is unknown. Figure 1, based on the findings of Naemi and77

Sanders (2008), presents a deterministic model that illustrates the relationship between the glide78

factor and the glide constant and coefficient. For the purposes of the present study, this model has79

been expanded to include the parameters that determine the size and shape characteristics80

affecting glide efficiency, as described in the following sections.81

82

Insert Figure 1 around here83

84

Several authors have examined the effect of size and shape parameters on the resistive85

characteristics. Size-related parameters such as head and thorax circumference, depth and86

breadth, chest girth and maximum cross-sectional area, body surface area, mass and height, have87

been found to be correlated positively to the drag values (Clarys et al., 1974; Chatard et al., 1990;88

Lyttle et al., 1998; Benjanuvatra et al., 2001). Some shape-related parameters, such as the ratio of 89

height to the maximum cross-sectional area, have been found to be correlated negatively to the90

resistive characteristics of the human body (Clarys et al. 1974; Clarys, 1978; Clarys, 1979). As91

the glide coefficient depends on the shape of the body in a streamlined position, morphological92

indices from naval architecture and from the hydrodynamic studies of aquatic animals can be93

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adapted to quantify the shape characteristics of the body (Clarys, et al., 1974). It should be noted94

that the shape of the body changes with variations in the body posture. For example head position95

has been found to play an important role in the amount of the resistance encountered by a96

swimmer (Miyashita & Tsunoda, 1978). Also, the correlation between joint laxity and drag force97

indicates the ability of subjects with higher flexibilities to adopt a superior streamlining position98

that creates less resistance (Chatard et al., 1990). This suggests that the joint angles need to be99

considered as a determining factor for the drag forces.100

101

Since the glide efficiency is influenced by both the resistive force and virtual mass, the latter102

being the sum of body mass and the added mass of water entrained with body (Naemi & Sanders,103

2008), the relationship between these parameters and the size and shape characteristics is of great104

interest. Moreover, due to the difference between the shape of the body in a streamlined position105

and that of the other objects, there is a need to more specifically adapt the existing parameters106

and define new morphological indices which are better able to identify the merits of the shape107

characteristics of the human body in a streamlined position.108

109

For a body gliding underwater at a depth adequate to avoid wave drag, the glide efficiency110

(Figure 1) is affected by the same phenomena as the boundary layer and the flow separation, and111

may be determined by the boundary layer thickness and the size of the wake (Naemi & Sanders,112

2008; Naemi et al., 2009). The body contours affect how the water flows over the body; it113

influences the thickness of the boundary layer at different parts of the body. Further, the areas of 114

flow separation that determine the size of the wake are influenced by the body contours. In115

determining the body contours the amount of change in the cross-sectional areas as well as the116

position of these changes are important. These can be quantified as the morphological indices117

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while the orientation of each cross-section relative to the flow can be quantified as the postural118

angles (Figure 1). The positions of each cross-section are important as they determine the119

potential places where the flow would be separated from the body (Aleyev, 1977). These can be120

referred to the position of the chest and buttocks, which have not been previously investigated.121

122

An optimal ratio of body length to maximum diameter known as fineness ratio of 4.5 has been123

assumed to decrease the drag forces (Hertel, 1966). As this is based on the investigation of the124

aquatic animals with almost circular cross-sectional areas (Fish & Hui, 1991), it would be125

interesting to calculate the fineness ration during a glide for the human body that has elliptical126

rather than circular cross-sections (Wicke & Lopers, 2003).127

128

In addition to the above, there is a need for defining the parameters that quantify the changes in129

the cross-sectional ratios, in order to determine how the flow changes as moving from one cross-130

section to another.131

132

The purpose of the present study was to investigate the relationships between size and shape133

characteristics and glide efficiency of male and female swimmers and for a range of gliding134

velocities.135

136

METHODS137

Participants138

Sixteen swimmers (eight male and eight female) competing and national and international level139

participated in this study. Ethical approval was granted by the University Ethics Committee and140

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all swimmers signed informed consents. The descriptive data for the swimmers are shown in141

Table 1.142

143

Insert Table 1 around here144

145

Data collection146

The procedure and protocol for glide efficiency measurements was adopted from Naemi and147

Sanders (2008). In brief, swimmers pushed off from the wall at a depth of 70cm below the148

surface and adopted a streamlined position (arms extended forward towards the direction of 149

travel; hands pronated and overlapping; feet together and plantar flexed). A JVC KY-F32 camera150

(50 Hz) was positioned underwater, 10m away from the swimmers, with its axis perpendicular to151

the glide path. A second camera was mounted at a 5m height directly above the swimmers with152

its axis perpendicular to the intended glide path. Swimmers were requested to sustain a153

horizontally aligned position and to maintain the depth during the glide. The glide intervals were154

selected from the acceptable glide sequences of each trial that complied with the condition of no155

deviation from the pool T line or horizontal alignment. A minimum of 20 acceptable glide156

intervals for each individual were used for the analysis.157

158

Selection and calculation of anthropometric variables159

Anthropometric variables were measured for the swimmers on land in an upright position,160

simulating as closely as possible the streamlined position adopted during the underwater glide. A161

photogrammetric method was used to determine the anthropometric measurements. The162

procedure and anatomical landmarks used have been described by Naemi and Sanders (2008).163

164

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The body was divided in the upper zone (from the waist level to dactylion) and the lower zone165

(from the akropodion level to the waist level), and five measurement levels were defined (Table166

2), based on combing the fluid dynamic principles reviewed extensively in Naemi et al. (2009)167

with the results of previous CFD studies of the flow around the swimmer like Bixler et al. (2007)168

that allowed flow visualisation. Also a pilot study was conducted to qualitatively assess the169

potential areas of flow separation using tufted full-body suit. Thicknesses and breadths of the170

areas of interest at each measurement level were calculated from the digitised outline (Figure 2).171

The cross sectional areas were calculated based on the assumption that the segmental cross-172

sectional area of a human body could be well modelled by an appropriate ellipse with the same173

thickness and breadth (Jensen, 1978; Wicke & Lopers, 2003). Ten heights or vertical distances of 174

interest were calculated as described in Table 3.175

176


178


180


182

Calculation of cross-sectional areas183

The area of each cross-section was calculated at each level:184

185

T B Ac ××=

4

π 186

187

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Selection and calculation of morphological indices188

The body was considered as two zones attached at the waist, so that each part has a gradual189

increase in the cross-sectional area followed by a gradual decrease. In the case of the upper zone,190

the cross-sectional area increases from the dactylion to the chest area and from there decreases to191

the waist. For the lower zone the cross-sectional area increases from the waist to the hip level and192

then decreases down to the akropodion. By dividing the body into these two different zones it193

became possible to define a more specific hydrodynamic characteristic for each zone. This194

allowed the fineness ratio to be defined for each zone as well as for the whole body. To quantify195

the body contour the ‘relative position of maximum cross-sectional area’ and the ‘fineness ratio’196

the ‘taper index’ and the ‘cross-sectional ratio’. These were based on the fluid dynamics197

principles and on how the flow moves around the swimmer, as discussed by Naemi et al. (2009).198

199

Calculation of the relative position of cross-section200

The relative position of each cross-section with regards to each zone’s length or the whole body201

length was defined as:202

203

z

cs

h

hP = 204

205

Calculation of the fineness ratio206

A nominal diameter was defined for each cross-section as the diameter of the circle that has the207

same area as the cross sectional area as the ellipse that approximates the cross-section of body:208

209

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π

cnom

Ad

.4= 210

211

The nominal diameter of cross-sectional areas at chest and hip were calculated as represented the212

maximum cross-sectional areas of the upper and lower zones. The fineness ratio was defined as:213

214

nom

z

d

hFR = 215

216

Calculation of the taper index217

A ‘taper index’ can be defined to account for the magnitude of the direction changes as the218

particles in the flow pass from one cross-sectional area to another. Since the areas behind the219

buttocks and back are vulnerable to flow separation, the taper indices from the chest to waist,220

waist to hip and hip to thigh are useful in quantifying the potential for flow separation in these221

areas. A taper index was defined as the ratio of changes in the cross-sectional area to the distance222

between the two consequent cross-sections:223

224

21

21

cc

cc

x x

A ATI

−

−

= 225

226

Cross-sectional ratio227

The ratio of two cross sectional areas was calculated as:228

229

2

1

c

c

A

ACR = 230

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231

Selection and calculation of postural angles232

Segmental angles were calculated based on the joint centre’s coordinates during glide intervals as233

follows:234

235

is

ish

x x

y y Arc

−

−

×= tan180

π θ 236

237

Seven segments were considered: hand, arm (forearm and upper arm together), trunk, thigh,238

shank, foot and head. As the elbow’s axis of rotation was not parallel to the optical axis of the239

camera, the forearm and upper arm were considered together. The segmental angles of the240

adjacent segments were used to calculate the joint angles as shown below. Six joint angles241

including wrist, shoulder, neck, hip, knee and ankle were calculated (Figure 3).242

243

1−−= nn θ θ ϕ 244

245


247

Calculation of glide efficiency parameters248

The glide factor was calculated based on the curve fitting technique (Naemi & Sanders, 2008).249

Glide constant was calculated according to the following formula:250

251

ρ λ

..2

1 A

m= 252

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253

The glide coefficient was calculated as:254

255

d

m

gC

C C = 256

257

Because of the differences in the attainable glide velocities between the gender groups, the glide258

efficiency parameters were calculated at the velocities of 1.4, 1.5 and 1.6 m/s for the female and259

at the velocities of 1.6, 1.7 and 1.8 m/s for the male group. Moreover, as the glide efficiency260

parameters change with the Reynolds number, these parameters were calculated for identical261

Reynolds numbers across swimmers. Because of the differences in the streamlined length262

between the gender groups, the glide coefficients were calculated at a Reynolds number of 3.5263

million for the female group and at a Reynolds number of 4.5 million for the male group.264

265

Statistical Analysis266

The SPSS software (version 14, SPSS Inc, USA) was used for statistical analysis. The Pearson267

product moment correlation coefficients were calculated between the glide factor and: a) the glide268

coefficient, b) the glide constant at all velocities. Given that differences in the glide coefficient269

and the glide factor have not been assessed for the velocities tested in the present study, a270

repeated measures ANOVA was performed for each gender group. Mauchly’s test was used to271

assess sphericity and the Greenhouse-Geisser adjustment was applied when sphericity was272

violated. When significant differences were found, post hoc comparisons were conducted for all273

pairs of different velocities and a Bonferroni adjustment was applied to reduce the alpha level and274

eliminate the possibility of type I errors. Correlations were also performed between the glide275

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coefficient and all morphological indices at the Reynolds number of 4.5 million for the male and276

3.5 million for the female group, respectively. For all statistical analyses significance was277

accepted at p<0.05.278

279

RESULTS280

The glide constant was 1.80±0.14m for the female group and 1.88±0.08m for the male group.281

The glide factor and glide coefficient at each velocity are presented in Table 4. The glide factor282

and glide coefficient decreased significantly when velocity increased in both groups. All pairwise283

comparisons for the glide factor and glide coefficient were statistically significant (p<0.001) for284

the female group. For the male group, all pairwise comparisons for the glide coefficient were285

statistically significant (0.014≤p≤0.015). The glide factor for the male group was significantly286

lower at 1.8m/s than at 1.6m/s (p=0.033), but not significantly different for any other pairwise287

comparisons. When calculated according to the Reynolds numbers, the glide coefficient was288

2.59±0.54 for the female group (at Reynolds number of 3.5 million) and 2.47±0.61 for the male289

group (at Reynolds number of 4.5 million).290

291

Insert Table 4 around here 292

293

The glide factor had a positive significant correlation with the glide coefficient for all velocities294

and for both groups (0.919≤r≤0.986, p≤0.002). No significant correlation was found between the295

glide factor and the glide constant (-0.344≤r≤-0.041, 0.403≤p≤0.974).296

297

The correlations between the glide coefficient and the shape characteristics are shown in Table 5.298

The glide coefficient had a positive significant correlation with the chest to waist taper index for299

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both groups. There were also positive significant correlations between the glide coefficient and300

ratio of chest to hip cross sectional areas (for the male group only), and the waist to hip taper301

index (for the female group only). Finally, the glide coefficient for the male group had a negative302

significant correlation with the fineness ratio of the upper body, the hip angle and the knee angle.303

304


306

DISCUSSION307

The results of this study indicated that both the glide factor and glide coefficient decreased308

significantly when velocity increased. This finding emphasises the importance of the separate309

calculation of the glide efficiency parameters for different swimming velocities.310

311

The relationship between the size and the shape characteristics of a body in a streamlined position312

and its glide efficiency and hydrodynamic parameters had not been determined previously. The313

main aim of this study was to investigate the relationship between the glide efficiency parameters314

and the size and the shape characteristics quantified by the anthropometric measures,315

morphological indices and postural angles of a body in a streamlined position. Although the316

existence of a significant correlation does not necessarily imply a cause and effect between two317

parameters, it enables us to identify the size and shape characteristics of bodies with superior318

gliding efficiency and hydrodynamic parameters.319

320

Size versus shape321

The results indicated that the shape-related glide efficiency parameters were associated more with322

the glide efficiency than the size-related parameters. It can be stated that swimmers with superior323

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shape (determined by a higher glide coefficient) tend to glide more efficiently than swimmers324

with a superior size (determined by a higher glide constant). These findings emphasise the325

relative importance of the shape-related parameters compared to the size-related parameters when326

considering the efficiency of the glide.327

328

While mathematically increasing the glide constant or the glide coefficient would increase the329

glide factor, the findings suggested that the disadvantage of having a non-optimum size may be330

compensated by an appropriate shape. This was supported by the strong correlation found331

between the glide factor and the glide coefficient while no significant correlation was found332

between the glide factor and the glide constant. This may explain how some of the best333

swimmers in the present study with large chest cross-sectional areas -that would be expected to334

create a high resistive force- performed better than swimmers with smaller cross sectional areas.335

It is also likely that the intense training may contribute to a better streamlining shape. A336

correlation between the glide coefficient and the weekly training volume supported this notion, as337

these variables were positively correlated for both groups (r=0.810 and r=0.779 for the female338

and male groups respectively, p<0.001). The findings of this study are in line with the findings of 339

Chatard et al. (1990) who reported that swimmers with lower drag force had better swimming340

performance, which was assumed to be related to their higher gliding ability.341

342

The importance of morphological characteristics343

Relative position of cross-sections344

As the relative position of each cross-section to the whole length of a body for aquatic animals345

determines the point where the boundary layer separation is expected to occur, an increase in the346

relative position is associated with a decrease in passive drag (Mordvinov, 1972). The fact that no347

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correlation was found between the relative position of the maximum cross-sectional area and the348

glide coefficient in the present study indicated that this assumption might not be applicable to349

human bodies. This could be because of differences between shape characteristics of a human350

and the more streamlined shapes, and due to the irregularities of the human body that make the351

possible flow separation not to happen in the positions of the maximum cross-sectional areas, as352

indicated previously by Clarys (1979).353

354

Fineness ratio355

Fineness ratio of the upper body in this study was negatively correlated with the glide coefficient356

for the male group. The upper-body fineness ratio for the male group (4.99±0.96) was higher than357

the optimal fineness ratio of 4.5 (Hertel, 1966). In this range, the drag coefficient was expected to358

increase with increasing fineness ratio. This could perhaps explain the negative correlation359

between the upper body fineness ratio and the glide coefficient.360

361

Contrary to the results of Clarys (1978), who found a negative correlation between passive drag362

and fineness ratio, no correlation was found between the fineness ratio of the whole body and the363

glide coefficient in the present study. This discrepancy could be due to the fact that Clarys (1978)364

tested the swimmers on the water surface and used the values of body height instead of 365

streamlined height to calculate the fineness ratios. In such conditions wave drag may cause other366

parameters to become important and the results may differ to those of submerged bodies.367

368

Taper index369

The chest to waist taper indices for both groups were positively correlated with the glide370

coefficient. This can perhaps be explained by the fact that the taper indices were negatively371

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correlated with the drag coefficient. As these indices determine the gradient of changes in two372

consecutive cross-sectional areas of the body, it seems that bodies with faster changes of cross-373

sectional areas from chest to waist have a lower drag coefficient that would help them to glide374

more efficiently. In the female group, a faster change in cross-sectional area between the waist375

and hip was correlated significantly with glide efficiency, indicating that the faster change in the376

cross-section between the waist and hip probably prevents flow being separated from the body.377

However, it should be emphasised that a very abrupt change in the cross-sectional area could378

result in sudden changes in the flow travelling over the body contours and in creating areas of 379

flow separation (e.g. see Naemi et al., 2009).380

381

Cross-sectional ratio382

Male swimmers with a higher ratio of chest to hip cross-sectional area showed a better383

streamlining characteristic by having a significantly higher glide coefficient. This could be384

explained by assuming that during glides the lower zone ‘drafts’ the upper zone. As the chest and385

hip cross-sectional areas represent the maximum cross-sectional areas of the upper and the lower386

zones of the body, the lower the ratio of the maximum cross-sectional area of the drafting zone to387

the maximum cross-sectional area of the leading zone, the more the drafting zone would be able388

to take advantage of drafting and reduce resistive force. This may decrease the drag coefficient389

and consequently increase the glide coefficient, which could explain the positive correlation390

between the ratio of chest to hip cross-sectional area and the glide coefficient.391

392

Postural angles393

Male subjects with hyperextension in their hips and knees had lower glide coefficients, and hence394

glide efficiency, than male subjects with no hyperextension in these joints. It can be argued that395

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the hyperextension of the hips causes the thigh and trunk to not be aligned along each other, so396

that the water flows around the body with more disturbances than when the hips are extended.397

Hyperextension of knee and hip together may have resulted in separation of flow and an increase398

in the drag coefficient and, therefore, a decrease in the glide coefficient.399

400

Implications401

Talent identification402

The results of this study have practical applications in talent identification with the aim of 403

selecting novice swimmers with a potential of performing at high level. The findings indicate that404

in talent identification the evaluation could prioritise the shape characteristics of the body. For405

example, swimmers who possess a higher chest to waist taper index are more likely to be able to406

glide more efficiently compared to the swimmers with a lower chest to waist taper index.407

Although the relative importance of different morphological indices might vary among408

swimmers, the results of the present study suggest that the emphasis should remain on the body409

shape characteristics.410

411

Posture optimisation412

The results of the correlation of certain joint angles with the hydrodynamic and glide efficiency413

parameters are helpful in developing an optimised streamlined posture with the aim of enhancing414

glide efficiency and, hence, swimming performance. In developing such a streamlined posture,415

specific attention needs to be paid to avoid hyperextension at the hip and knee joint angles, as this416

seems to decrease glide efficiency for male swimmers. Further studies must be conducted to417

explore in more details the effects of these angles and their optimal values for swimmers.418

419

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Swimming suit design420

The findings of the present study could have important applications in designing swimming suits421

for improving performance. Based on the positive correlation between gliding efficiency and the422

hip to waist taper index, it is possible that designing a swimming suit that compresses the waist423

area to further decrease its cross-sectional area (with a consequent increase in the taper index)424

may help to improve performance. Further studies are required to determine the optimal range of 425

taper index for each individual, and to determine the tension characteristics of the suit for426

designing swimmer-specific suits.427

428

Conclusion429

The glide efficiency of swimmers seems to increase when velocity decreases. Swimmers with430

superior shape characteristics were able to glide more efficiently than subjects who had large431

body mass with low cross-sectional area. Moreover, swimmers with superior shapes encountered432

lower resistance and were able to entrain more added mass of water than those with higher433

maximum cross-sectional area or higher body volume respectively. Thus, the difference of glide434

efficiency parameters between two bodies depends predominantly on the differences in shape435

characteristics, such as morphological indices and postural angles. Some of the morphological436

indices and joint angles investigated in this study were shown to affect glide efficiency. To437

further improve glide efficiency and swimming performance, future research should focus on438

identifying the optimal values of such indices and angles for different swimmers.439

440

REFERENCES441

Aleyev, Y.G. (1977). Nekton. The Hague: Dr W. Junk b. v. publishers.442

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Benjanuvatra, N., Blanksby, B.A., & Elliott, B.C. (2001). Morphology and hydrodynamic443

resistance in young swimmers. Paediatric Exercise Science, 13(3), 246-255.444

Bixler, B., Pease, D., & Fairhurst, F. (2007). The accuracy of computational fluid dynamics445

analysis of the passive drag of a male swimmer. Sports Biomechanics, 6 (1):81–98.446

Chatard, J.C., Lavoie, J.M., Bourgoin, B., & Lacour, J.R. (1990). The contribution of passive447

drag as a determinant of swimming performance. International Journal of Sports448

Medicine, 11(5), 367-372.449

Clarys, J.P. (1978). Relationship of human body form to passive and active hydrodynamic drag.450

In E. Asmussen & K. Jorgenson (Eds.), Biomechanics VI-B (pp. 120-125). Baltimore:451

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Clarys, J.P. (1979). Human morphology and hydrodynamics. In J. Terauds & E.W. Bedingfield453

(Eds.), Swimming III (pp. 3-41). Baltimore: University Park Press.454

Clarys, J.P., Jiskoot, J., Rijken, H., & Brouwer, P.J. (1974). Total resistance in water and its455

relation to body form. In R.C. Nelson & C.A. Morehouse (Eds.), Biomechanics IV (pp.456

187-196). Baltimore: University Park Press.457

D’Acquisto, L.J., Costill, D.L., Gehlsen, G.M., Young, W.T., & Lee G. (1988). Breaststroke458

economy skill and performance: study of breaststroke mechanics using a computer based459

“velocity video”. Journal of Swimming Research. 4, 9–14460

Fish, F.E., & Hui, C.A. (1991). Dolphin swimming – a review. Mammal Review, B (21), 181-461

195.462

Hay, J.G., & Guimaraes, A.C.S. (1983). A quantitative look at the swimming biomechanics.463

Swimming Technique, 20(2), 11-17.464

Hertel, H. (1966). Structure-Form-Movement . New York: Reinhold Publishing Corporation.465

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Jensen, R.K. (1978). Estimation of the biomechanical properties of three body types using a466

photogrammetric method. Journal of Biomechanics, 11(8-9), 349-358.467

Lyttle, A.D., Blanksby, B.A., Elliott, B.C., & Lloyd, D.G. (1998). The effect of depth and468

velocity on drag during the streamlined glide. Journal of Swimming Research, 13, 15-22.469

Miyashita, M., & Tsunoda, R. (1978). Water resistance in relation to body size. In B. Eriksson &470

B. Furberg (Eds.), Swimming Medicine IV (pp. 395-401). Baltimore: University Park 471

Press.472

Mordvinov, Y.E. (1972). Some hydrodynamic parameters of body shape in pinnipeds.473

Hydrobiologia, 8, 81-84.474

Naemi, R., & Sanders, R.H. (2008). A ‘hydro-kinematic’ method of measuring glide efficiency of 475

a human swimmer. Journal of Biomedical Engineering, 130, 061016.476

Naemi, R., Easson, W.J., & Sanders, R.H. (2009). Hydrodynamic glide efficiency in swimming.477

Journal of Science & Medicine in Sport , (In press; doi:10.1016/j.jsams.2009.04.009).478

Wicke, J., & Lopers, B. (2003). Validation of the Volume Function within Jensen’s (1978)479

Elliptical Cylinder Model. Journal of Applied Biomechanics, 19(1). 3-12.480

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FIGURE CAPTIONS481

482

Figure 1. The deterministic model of the glide factor and its contributing shape-related and size-483

related parameters.484

485

Figure 2. Sample photographs of a swimmer, taken from front and side views. The five486

measurement levels (I to IV; see also Table 2) and nine heights (1-9; see also Table 3) calculated487

in this study are also shown.488

489

Figure 3. The joint angles of a swimmer while gliding in a horizontal position.490

491

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TABLES492

Table 1. The mean ± standard deviation (SD) for age, height, mass and training volume, for the493

swimmers in the present study.494

Group Age (years) Height (cm) Mass (kg) Distance /week (km)

Female(N=8) 22.3±2.2 173.5±7.7 66.8±5.2 24.3±7.4

Male (N=8) 19.4±3.0 186.2±5.9 77.5±4.9 44.5±6.2

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Table 2: The five measurement levels defined for this study (see also Figure 2).495

Measurement Levels Locations

I-:Forehead level Horizontal level immediately superior to glabella (portions of

the frontal bone between the supraorbital ridges)

II-Chest level At the level of mesosternale

III-Waist level: At the level of minimum girth around the waist

IV-Hip level: At the level of the greatest posterior protuberance of the buttocks

V-Thigh level: At a level 2 cm below the gluteal fold

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Table 3: The ten heights or distances of interest measured in this study (see also Figure 2).496

Height/Distance Vertical Distance used for the Calculation

1) Streamlined height Between the akropodion (the most superior point of the foot

that may be the first or second digit) and dactylion (the most

distal point of the third digit of the hand)

2) Head height Between the akropodion (ground level) and vertex (the most

superior point on the skull) of the head

3) Chest height Between the akropodion (ground level) and the chest level

4) Waist height Between the akropodion (ground level) and the waist level

5) Hip height Between the akropodion (ground level) and the hip level

6) Chest to dactylion

distance

Between the chest level and dactylion (top level)

7) Waist to dactylion

distance

between the waist level and dactylion (top level)

8) Waist to chest distance Between the waist level and the chest level

9) Head to dactylion

distance

Between the head level and dactylion (top level)

10) Hip to waist distance Between the hip level and the waist level

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Table 4. The mean ± SD values for the glide factor calculated for the male and female groups at497

corresponding velocities.498

Females

Velocity (m/s) 1.4 1.5 1.6 Repeated Measures ANOVA

Glide Factor (m) 4.93±0.70 4.59±0.70 4.25±0.69 F=346.3 (p<0.001)*

Glide Coefficient 2.77±0.53 2.58±0.51 2.39±0.50 F=224.8 (p<0.001)*

Males

Velocity (m/s) 1.6 1.7 1.8 Repeated Measures ANOVA

Glide Factor (m) 4.98±1.30 4.73±1.12 4.49±0.95 F=8.8 (p=0.003)*

Glide Coefficient 2.66±0.73 2.53±0.62 2.40±0.52 F=14.7 (p=0.005)*

* Significant at p<0.05499

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Table 5. The correlations between the glide coefficient and the shape characteristics.500

Female

(at Reynolds 3.5 million)

Male

(at Reynolds 4.5 million)

Correlation of glide coefficient

with

r p r p

Position of head to the whole body -0.516 0.191 -0.273 0.513

Position of chest to the whole body -0.112 0.792 0.346 0.401

Position of waist to the whole body -0.247 0.555 -0.550 0.158

Position of chest to the upper-body 0.025 0.953 0.542 0.165

Position of hip to the lower-body 0.399 0.168 0.117 0.391

Fineness ratio of the whole body -0.480 0.229 -0.527 0.180

Fineness ratio of upper-body -0.492 0.216 -0.788* 0.020*

Fineness Ratio of lower-body -0.577 0.134 -0.390 0.340

Hip to thigh taper index (m) 0.220 0.601 0.432 0.285

Chest to waist taper index (m) 0.732* 0.039* 0.808 * 0.015*

Waist to hip taper index (m) 0.718 * 0.045* -0.515 0.192

Chest to hip cross section 0.550 0.158 0.759* 0.029*

Hip to waist cross section 0.364 0.375 -0.234 0.577

Chest to waist cross section 0.680 0.064 0.577 0.134

Hand segment 0.254 0.544 -0.179 0.672

Wrist angle 0.671 0.069 0.064 0.880

Arm segment -0.359 0.383 -0.203 0.630

Shoulder angle 0.396 0.332 0.353 0.391

Head segment -0.228 0.587 -0.225 0.592

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Neck angle 0.263 0.529 0.363 0.377

Trunk segment 0.323 0.435 0.578 0.133

Hip angle -0.086 0.840 -0.88 * 0.040*

Thigh segment 0.415 0.307 -0.704 0.051

Knee angle 0.600 0.116 -0.709 * 0.049*

Shank segment -0.339 0.411 0.611 0.108

Ankle angle -0.273 0.513 -0.09 0.832

Foot segment -0.667 0.071 0.626 0.097

* Significant at p<0.05501

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FIGURES502

Figure 1503

504

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Figure 2 505

506

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Figure 3507

508

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