Differences in kinematics and energy cost between front crawl and backstroke below the anaerobic

threshold

Tomohiro Gonjo1,2, Carla McCabe3, Ana Sousa4,5,6, João Ribeiro4,5,6, Ricardo J. Fernandes6, João Paulo

Vilas-Boas6, and Ross Sanders7

1: Faculty of Health and Sport Sciences, University of Tsukuba, Tsukuba, Ibaraki, Japan

2: Institute for Sport, Physical Education & Health Sciences, The University of Edinburgh, Edinburgh,

Scotland, UK

3: Faculty of Life and Health Sciences, Ulster University, Antrim, Northern Ireland, UK

4: Research Centre for Sports, Exercise & Human Development, CIDESD,Portugal

5: University Institute of Maia, ISMAI, Maia, Portugal

6: Faculty of Sports, CIFI2D, and LABIOMEP, University of Porto, Porto, Portugal

7: Exercise and Sport Science, Faculty of Health Sciences, The University of Sydney, Sydney, New South

Wales, Australia.

Corresponding author

Tomohiro Gonjo, Ph.D

Faculty of Health and Sport Sciences University of Tsukuba

5C217, 1-1-1, Tennodai, Tsukuba, Ibaraki, Japan

Phone: +81-29-853-5733

Fax: +81-29-853-5737

e-mail: gonjo.tomohiro.ga@u.tsukuba.ac.jp

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Differences in kinematics and energy cost between front crawl and backstroke below the anaerobic

threshold

Purpose The purpose of this study was to determine kinematic and energetic

differences between front crawl and backstroke performed at the same aerobic speeds.

Methods Ten male competitive swimmers performed front crawl and backstroke

at a pre-determined sub-anaerobic threshold speed to assess energy cost (through oxygen

uptake measurement) and kinematics (using three-dimensional videography to determine

stroke frequency and length, intra-cycle velocity fluctuation, three-dimensional wrist and

ankle speeds, and vertical and lateral ankle range of motion). For detailed kinematic

analysis, resultant displacement, the duration, and three-dimensional speed of the wrist

during the entry, pull, push, and release phases were also investigated.

Results There were no differences in stroke frequency/length and intra-cycle

velocity fluctuation between the swimming techniques, however, swimmers had lower

energy cost in front crawl than in backstroke (0.77 ± 0.08 vs 0.91 ± 0.12 kJ·m-1, p < 0.01).

Slower three-dimensional wrist and ankle speeds under the water (1.29 ± 0.10 vs 1.55 ±

0.10 and 0.80 ± 0.16 vs 0.97 ± 0.13 m·s-1, both p < 0.01) and smaller ankle vertical range

of motion (0.36 ± 0.06 vs 0.47 ± 0.07 m, p < 0.01) in front crawl than in backstroke were

also observed, which indirectly suggested higher propulsive efficiency in front crawl.

Conclusion Front crawl is less costly than backstroke, and limbs motion in front

crawl is more effective than in backstroke.

Keywords: swimming, freestyle, backstroke, kinematics, energy, efficiency

Abbreviations

3Duankle Three-dimensional ankle speed in relation to the speed of centre of mass3Duwrist Three-dimensional wrist speed in relation to the speed of centre of massAnT Anaerobic thresholdC Energy costCOM Centre of massCV Coefficient of variationIVfluc Intracycle velocity fluctuationROM Range of motionSF Stroke frequencySL Stroke lengthvAnT Swimming speed at anaerobic threshold intensityvCOM Mean speed of the centre of mass during the upper limb cyclevinst Instructed speedvS Mean swimming speed during the whole testingV O2 Oxygen uptakeWint Internal workηF Froude efficiencyηH Hydraulic efficiencyηO Overall efficiencyηP Propelling efficiency

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Introduction

Front crawl and backstroke have similar mechanical characteristics, such as the alternating upper

and lower limbs motion and the body roll around the longitudinal axis (Seifert and Chollet 2009;

Psycharakis and Sanders 2010). However, swimmers usually achieve shorter competition times and faster

mid-pool swimming speeds in front crawl than in backstroke (Craig et al. 1985; Chollet et al. 2000;

Chollet et al. 2008). Mathematically, the rate of energy expenditure in a given time (metabolic power: E)

is the product of the speed of the locomotion (v) by the energy cost (C: the energy required to move a

given distance). In other words, v in human locomotion is determined by E and C, as shown in the

following equation (di Prampero 1986):

v=E ∙C−1 (1)

Given that v and C are inversely related, and swimmers usually achieve faster swimming speeds in front

crawl than in backstroke, it is possible that swimmers have a lower C in front crawl than in backstroke

when swimming at the same speed. In fact, it has been shown that front crawl is less costly than

backstroke at both sub-maximal and maximal speeds (Smith et al. 1988; Capelli et al. 1998; Barbosa et al.

2006a). However, these evidences were based on C values in front crawl and backstroke reported in

different studies and/or for different individuals. Therefore, it is unclear whether the difference is due to

the specificities of the two swimming techniques or caused by the use of distinct sample groups with

different anthropometric and physiological characteristics. In fact, there have been no studies which

directly compare front crawl and backstroke C using the same individuals.

In swimming, C at a given speed and for a specific overall efficiency (ηO: the efficiency that

indicates the transformable E ratio into mechanical power W tot) is determined by the following equation

(Zamparo et al. 2011):

C=W d ∙(ηP ∙ ηo)−1 　(2)

Where Wd is the work done to overcome hydrodynamic drag per unit distance, and ηp is the propelling

efficiency (the rate of useful mechanical work/power in relation to the overall mechanical work/power

produced by the swimmer). This equation suggests that, for the same speed, the potentially low C in front

crawl compared with backstroke is due to its lower Wd and/or higher ηp. There is currently no method for

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direct Wd measurement in swimming. However, Gatta et al. (2015) estimated form drag coefficient by

obtaining frontal area of the swimmer during both front crawl and backstroke and reported no difference

in the drag coefficient (based on the frontal area) between the techniques. Even though the effects of

wave drag and friction drag were not considered in the study, it is possible that Wd is not different

between the techniques at speeds where the primary drag component is form drag, e.g., v = 1.0 m·s-1 at

which the contribution of form drag is 74% of the total drag (Pendergast et al. 2005). This implies that the

main difference in C between front crawl and backstroke is attributable to ηp (at least at low v).

Results from existing studies on simple parameters such as the frequency of upper limb cycle

(stroke frequency: SF) and the distance the swimmer travels in one upper limb cycle (stroke length: SL)

also indirectly suggest higher ηp in front crawl than in backstroke. For example, it has been suggested that

C and SF/SL are positively/negatively correlated in both front crawl and backstroke swimmers (Barbosa

et al. 2008), while data of the same study also indicated that C tended to be lower in front crawl at similar

SL or SF. These results indicate that swimmers probably expend greater energy in backstroke to achieve

similar propulsion to front crawl with comparable SF and SL. However, these variables are affected by

anthropometric characteristics such as axilla cross-sectional area and arm span (Grimston and Hay 1986),

and therefore, it is useful to compare SF and SL in front crawl and backstroke using the same individuals

to investigate the difference in ηp between the techniques.

**Fig. 1**

It is currently difficult to obtain ηP using direct investigations, however, it is possible to assess ηP

using indirect methods. Fig.1 shows the flow diagram of the energy conversion in swimming. As the

diagram suggest, ηP can be expressed as Equation 3 (Zamparo et al. 2005b).

ηP=ηH ∙ηF (3)

Where ηF is Froude efficiency (the ratio of the mechanical work/power to overcome the hydrodynamic

drag opposing the locomotion to that required to overcome total external forces) and ηH is Hydraulic

efficiency (the required external work/power in relation to the overall mechanical work/power). In

swimming, ηF has been estimated using simplified mathematical models. The mathematical models are

based on the theory that ηF of the rowing or swimming with oar-motion with constant speed of the boat

(U) and the oar (u) is proportional to the ratio U/u (Alexander 1983; Alexander 2003). Zamparo et al.

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(2005b) adapted this theory in swimming and suggested the equation below for ηF calculation for arm

stroke in front crawl, under the assumption of the contribution of kicking to v being 10%.

ηF=(( v ∙ 0.9 ) ∙ (2 π ∙ SF ∙L )−1)(2 ∙ π−1) (4)

Where L is average shoulder to hand distance during the upper limb cycle. Figueiredo et al. (2011; 2013a;

2013c) developed this equation to calculate ηF in front crawl with three-dimensional motion of the limbs

being taken into account (Equation 5).

ηF=vCOM ∙3 Duhand−1 　(5)

Where vCOM and 3Duhand are the mean velocity of the centre of mass (COM) and sum of the mean

underwater three-dimensional (3D) speed of left and right hands during the upper limb cycle,

respectively. These equations have assumptions such as: (i) the upper limb is considered as a rigid

segment; (ii) the COM speed of the swimmer throughout an upper limb cycle is stable; and (iii) the effect

of lower limb motion is negligible (assumption in the latter model). It is therefore obvious that this

equation is very simplified, and further investigation is necessary to establish the accuracy of the ηF

estimation in swimming. Nevertheless, as the mathematical model suggests, ratio of vCOM to 3Duhand

(vCOM/3Duhand ratio) can be an indirect indicator of ηF.

As Fig. 1 suggests, ηH depends on work required to accelerate the limbs (Wint) at given Wd,

wasted work (Wk), and work related to elastic/viscous. It has been suggested that kick frequency and

vertical range of motion (ROM) of the foot in the water are determinants of Wint in flutter kicking

(Zamparo et al. 2002). This suggestion is based on the investigation using a two-dimensional motion

analysis. To explore kick kinematics in whole body swimming, further considerations are required. Both

kick frequency and foot ROM have usually been obtained based only on vertical speed and displacement

of the foot (Zamparo et al. 2006; Figueiredo et al. 2013b). However, in both front crawl and backstroke,

swimmers roll their shoulders and hips around their longitudinal axis (Psycharakis and Sanders 2010),

which means that they move their lower limbs in three-dimension. Therefore, 3D foot speed relative to

COM (3Dufoot) and the foot ROM in both vertical and lateral directions during whole body swimming

should be investigated to provide more accurate information on lower limb kinematics.

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Even though direct investigation for ηp is difficult in swimming, the aforementioned evidences

suggest that obtaining the kinematic variables (3Duhand, 3Dufoot, and foot ROM) is useful to investigate the

difference in ηp between front crawl and backstroke – which is important to assess the difference in C

between the techniques in detail. Another kinematic factor that has often been associated with C is the

fluctuation of vCOM during the upper limb cycle (IVfluc) (Vilas-Boas et al. 2011; Figueiredo et al. 2013a). It

has been suggested that 10% of IVfluc result in an ~3% additional work demand (Nigg 1983). It has also

been reported that front crawl and backstroke C values are related with IVfluc when the effect of mean vCOM

is controlled (Barbosa et al. 2006b). Although not all studies support that suggestion (Kjendlie et al. 2004;

Figueiredo et al. 2012), this idea is logical since extra energy is required when the swimmer accelerates

his/her body and added mass (Vilas-Boas et al. 2011). Therefore, when comparing front crawl and

backstroke, it is useful to investigate IVfluc as well as C.

To date, distinct results in IVfluc difference between the techniques have been reported. For

example, a similar pattern of IVfluc during one stroke cycle between front crawl and backstroke has been

displayed (Barbosa et al. 2011), while Craig and Pendergast (1979) showed larger IVfluc in relation to v in

front crawl than in backstroke. On the other hand, Alves et al. (1996) reported smaller IVfluc in front crawl

(even though the author did not specify if the comparison was within or between participants as well as

the numerical results). Considering the relationship between C and IVfluc in both techniques and possible

difference in C between the techniques, it is reasonable to hypothesise that IVfluc is smaller in front crawl

than in backstroke when comparing within-participants.

According to Equation 1 and given that race times are shorter in front crawl than in backstroke,

it is probable that front crawl is physiologically less costly. However, there have been paucity of

information on the difference in C between front crawl and backstroke performed by the same swimmers.

Differences in kinematic variables that are related to C and ηF between the swimming techniques are also

unclear. Therefore, the purpose of this study was to determine kinematic and energetic differences

between front crawl and backstroke performed at the same aerobic speeds. Since the frontal area of

swimmers during swimming does not differ among the two techniques (Gatta et al. 2015), i.e., the form

drag (which is the primary drag in low swimming speed) is similar among the techniques, it was

hypothesised that front crawl would be less costly and have more efficient kinematic features (such as

lower 3Duhand and 3Dufoot, smaller foot ROM, and lower IVfluc) than backstroke.

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Methods

Ten male well-trained swimmers - front crawl (n=4), backstroke (n=3), and medley (n=3)

specialists (17.47 ± 1.00 years, 179.14 ± 5.43 cm and 69.94 ± 6.54 kg), volunteered to participate in the

current study. The participants were chosen based on annual national ranking of the year prior to the

testing session (within top 200 for both front crawl and backstroke in either 50, 100, or 200 m events).

Their mean best records were 54.50 ± 1.23 and 60.56 ± 1.29 s in short course 100 m front crawl and

backstroke, corresponding to 82.49 ± 1.91 and 80.85 ± 1.72% of the respective world records.

Participants were informed about the procedures, benefits and potential risks of the study (which were

reviewed and approved by the ethics committee of the university based on the British Association of

Sport and Exercise Sciences guidelines), and a written informed consent was obtained from each

participant.

Testing speed

Researchers have estimated anaerobic energy expenditure using both oxygen uptake (V O2) and

blood lactate values in swimming (Zamparo et al. 2000; Barbosa et al. 2005; Figueiredo et al. 2011). It

has been reported that within-individual differences in the energy equivalent of the lactate accumulation

are small during front crawl swimming (Thevelein et al. 1984), and therefore, this method is reliable

when front crawl is investigated. However, it is still unclear if this is the case when comparing different

types of exercise (i.e. different swimming techniques). Thus, in this study, the testing speed was set to be

below the anaerobic threshold (AnT) to investigate C using only direct V O2 measurement. The same

testing speed was set for both front crawl and backstroke to minimise the effect of the drag on C.

To determine testing speeds for each participant, AnT of each swimmer was obtained using 7 ×

200 m incremental tests for both swimming techniques (Fernandes et al. 2011). The initial speed of the

test was set at 0.3 m·s-1 less than the average speed of 400 m maximum effort performances, and there

was a rest of approximately 30 s between each stage. Since 400 m race is not an official event for

backstroke, the 400 m performance times were determined based on the daily training performance

through the interview and questionnaire for coaches of the swimmers for both techniques, rather than

obtaining the official race results. The speed was increased by 0.05 m·s-1 each stage and the speed of the

swimmer was controlled by a visual light pacer (Pacer2, GBK-Electronics, Aveiro, Portugal). The pacer

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was positioned at the bottom of the pool for front crawl trials and located approximately 2 m above the

pool with a stainless wire for backstroke trials.

The swimmers were instructed to conduct an individual warm-up session prior to the incremental

test, and the tests for front crawl and backstroke were separated by at least 24 h rest to ensure recovery

between the two sets of incremental tests. The order of the front crawl and backstroke testing was

randomised. Swimmers were supposed to achieve their exhaustive intensity at the end of the incremental

test (i.e. seventh 200m trial), therefore, additional stage was included when the swimmer could follow the

instructed speed throughout the seventh stage. All swimmers completed the incremental test with seven or

eight trials, which was sufficient to obtain their individual AnT.

To determine the speed at AnT (vAnT), a blood sample was taken from a fingertip of the

swimmer before the protocol and after each stage of the protocol to measure the blood lactate value using

Lactate Pro (Arkay, Inc, Kyoto, Japan). The blood lactate value was plotted on the graph as a function of

the speed, and AnT was defined as the intersection of two regression lines (one regression line and one

exponential line), which were fitted to the lactate curve in accordance with the procedure established by

Fernandes et al. (2011). To set the same testing speed for front crawl and backstroke that would not

exceed vAnT for both swimming techniques, it was necessary to determine the speed based on slower

vAnT among front crawl and backstroke. In this study, all participants achieved slower vAnT in

backstroke than in front crawl, and thus, the testing speed was determined as 95% of vAnT of backstroke

in both swimming techniques. The select of 95% of vAnT (rather than 100% of vAnT) was based on an

extent literature in which all participants showed lactate steady state at 95% of AnT intensity, while four

out of 30 participants had slight elevation of lactate value at 100% of AnT in cycle ergometer exercise

(Urhausen et al. 1993).

Testing protocol

Prior to the testing, participants were marked on a total of 19 anatomical landmarks (the vertex

of the head, the right and left of the: tip of the third distal phalanx of the finger, wrist axis, elbow axis,

shoulder axis, hip axis, knee axis, ankle axis, fifth metatarsophalangeal joint, and the tip of first phalanx)

using black oil and wax based cream (Grimas Créme Make Up). To obtain personalised body segment

parameter data of the participants, each participant was captured by digital cameras from front and side

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view simultaneously to apply the elliptical zone method (Jensen 1978; Deffeyes and Sanders 2005;

Sanders et al. 2015). Then, each participant performed their individual warm-up.

The testing lane was calibrated prior to the testing sessions using a calibration frame with

dimensions of 6 m length, 2.5 m height, and 2 m width (total volume of 30 m3 with 236 control points)

which was designed for the 3D direct linear transformation (3D-DLT) method. The reconstruction error

of the calibration frame was less than 0.1, 0.3, and 0.4% of the calibrated volume for the X, Y, and Z

direction, respectively (De Jesus et al. 2015). These dimensions ensured that one upper limb cycle, which

was defined as the cycle from entry to re-entry of the same wrist, could be completed with all body

landmarks within the calibrated space. In this study, the motion of wrist and ankle joints were assumed to

represent the hand and foot motion to minimise the error due to the difficulty of digitising fingertips and

toes because of the turbulence. A total of 64 control points (32 underwater and 32 above the water control

points) were chosen for the 3D coordinates reconstruction in later analysis. The definition of the 3D

coordinates was X direction (swimming direction), Y direction (vertical direction) and Z-direction (the

direction perpendicular to X and Y directions)

Testing sessions to investigate the differences between front crawl and backstroke at the aerobic

exercise intensity consisted of 1 × 300 m tests for both techniques separated by at least 24 h in

randomised order. Although 300 m front crawl and backstroke are not official race events in

competitions, the distance for the testing was chosen to ensure V O2 reaching steady-state. The testing

speed for both front crawl and backstroke was maintained at the speed determined by the incremental test

described earlier. The testing speeds were controlled by the aforementioned visual light pacer and the

final time of each 300 m test was manually recorded by a stopwatch (SVAS003, SEIKO, Tokyo, Japan).

Data collection

To quantify C during front crawl and backstroke, V O2 (mLO2∙min-1) during each 300 m test was

collected using a low hydrodynamic resistance snorkel: AquaTrainer® (Ribeiro et al. 2016). It has been

reported that the error in V O2 value when using the snorkel is less than 1.0%, which is based on a

comparison between V O2 values obtained by the snorkel and a standard face mask (Baldari et al. 2013).

The snorkel was connected to a telemetric gas exchange breath-by-breath system (K4b2, Cosmed, Rome,

Italy). During the testing, swimmers were instructed to avoid using a tumble turn and underwater kicking

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after the start and turn since the snorkel device restricted the tumble motion and the submersion of the

swimmers (this was also the case in the 7 × 200 m incremental tests).

To obtain kinematics in front crawl and backstroke using the 3D-DLT method, each 300 m trial

was captured by six high definition cameras (four underwater and two above the water, Sony, HDR-

CX160E, Tokyo, Japan, sampling rate: 50 fps, shutter speed: 1/120 s, movie resolution: 1920×1080/50p)

with waterproof camera cases for the underwater ones (Sony, SPK-CXB, Tokyo, Japan). The six cameras

were synchronised using a LED system which was visible from all the six cameras. To maximise

accuracy of the DLT calculations, the cameras were fixed at different heights and angles to the line of

motion of the swimmer to avoid the camera axes being in the same plane (Psycharakis et al. 2005). The

distance between the cameras and the centre of the calibrated space was approximately 12.5 m, and the

field of view of each camera was set to ensure that the whole calibration frame was in view. Swimmers

were instructed to swim directly above the lane-line through the centre of the calibrated space in front

crawl and directly under a stainless wire that was suspended in line with the midline of the calibrated

space at a height of 2 m from the water surface in backstroke. The visual light pacer was on the pool floor

directly below the swimmer for front crawl and attached to the stainless wire in backstroke.

Data processing and analysis

After the testing, V O2 of the participants was averaged every five seconds over each testing

session (Sousa et al. 2010; Figueiredo et al. 2011) using the K4b2 software. The averaged V O2 value that

was achieved at steady state was assumed to be Eof each swimmer at the testing speeds. Net Ewas

calculated by subtracting the resting V O2, which was assumed to be 5 mLO2∙kg-1∙m-1 (Figueiredo et al.

2011), from E. The net Edata were normalised by the mean speed of the 300 m trials (calculated from

the final time recorded by a stopwatch) of each swimmer to obtain net C (Cnet: mLO2∙m-1). Assuming that

1 LO2 was equivalent to 20.9 kJ, Cnet was then converted from mLO2∙m-1 to kJ∙m-1 (Zamparo et al. 2005a).

The video files of calibration and the testing sessions were transferred into a computer, then all

six camera views were checked to ensure that the whole body of the swimmer was visible throughout the

selected upper limb cycle. The video files were then trimmed in Ariel Performance Analysis System

software (Ariel Dynamics, Inc, CA), and the same software was used to digitise and calculate 3D

coordinates. The manual digitising process was conducted by an operator who had five years of

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experience in digitising tasks at the time of data analysis. The digitised data were smoothed with a 2nd

order Butterworth dual pass recursive filter at 4 Hz. This frequency was selected since the cut-off

frequencies of 2-4 Hz were enough to ensure 95% of the power of original signal retaining in the filtered

signal in swimming (Yanai 2003; Yanai 2004). To obtain one complete upper limb cycle, the start and the

end points of the cycle were defined as the entry of the wrist point into the water and the next entry of the

same wrist, respectively.

An upper limb cycle from the last 25 m of the 300 m test was chosen for the analysis because the

calculation of Cnet was based on the last 30 – 60 s of the 300 m testing. Five extra points before and after

the upper limb cycle were included in the trimmed video files to minimise errors at the end of the data

sets associated with filtering and derivation of velocity data. The digitising process was conducted at a

frequency of 25 Hz. To ensure the digitising reliability at 25 Hz, one front crawl and backstroke trials

were digitised five times each to assess the digitising error.

This digitising frequency was chosen based on the following rationale. The appropriate sampling

frequency in motion analysis is 8 -10 times higher than the highest frequency present in the activity

(Challis et al. 1997). In front crawl, the highest frequency is likely produced by the kick motion – which

is a roll motion with three maxima and three minima (Sanders and Psycharakis 2009). It has also been

reported that SF in sprint front crawl is approximately 55 cycles·min-1 (McCabe et al. 2011), which means

the time taken for one upper limb cycle is 1.09 s. Therefore, the highest frequency present in front crawl

is 2.75 Hz, and the appropriate sampling frequency in front crawl would be 22.0 – 27.5 Hz. Given that the

SF in backstroke is lower than that in front crawl (Craig et al. 1985), digitising at 25 Hz should be enough

for both front crawl and backstroke.

Calculation of variables

COM location was determined by summing the moments of the segment COM mass about the X,

Y, and Z reference axes. vCOM (m·s-1) was obtained by differentiating the X displacement of COM values

with respect to time. SF (cycles·min-1) was obtained as the inverse of the time that the swimmer took to

complete one upper limb cycle, which was calculated from the number of the samples for one upper limb

cycle. SL (m·cycle-1) was obtained from the X displacement of COM during the upper limb cycle

(McCabe et al. 2011; McCabe and Sanders 2012).

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Underwater phase of the upper limb cycle (from the entry to the exit of the wrist into/from the

water) was divided into four phases based on extant definitions (Lerda and Cardelli 2003; Gourgoulis et

al. 2006; McCabe et al. 2015) – namely the entry, pull, push, and, release phases. The entry phase

commenced at the instant the wrist enters the water and concluded at the instant of first backward

movement of the wrist relative to the external reference frame. The pull phase was defined as the interval

between the instant of the end of the entry phase and the instant that the X coordinate of the wrist is the

closest to that of the X coordinate of the ipsilateral shoulder (i.e. wrist and shoulder are vertically

aligned). The push phase was from the end of the pull phase to the wrist having the first positive velocity

in X direction relative to the external reference frame following the negative (backward) wrist movement

with respect to the X direction. The release phase was defined as the interval between the end of the push

phase and the wrist exiting from the water. The recovery phase was defined as the interval between the

end of the release phase and the instant of the next entry of the wrist.

The duration of each phase (s) was determined from the normalised time record (101 samples

per upper limb cycle, defining 100 time percentiles of the upper limb cycle) which yielded greater

temporal resolution than using times corresponding to video frames. The mean values of left and right

phase durations were assumed to represent the duration of each phase of the swimmer in each swimming

technique. 3D wrist speed during the underwater phase (3Duwrist: m·s-1) was calculated by Equation 6:

3 Duwrist=(∑k=1

n−1 √( dxk +1−dxk )2+( dyk+1−dyk )2+ (dzk+1−dzk )2

time ) ∙100−1

(6)

Where n is the last number of the sample in the underwater phase of the limbs, dx, dy, and dz are X, Y,

and Z displacements of the wrist relative to COM, respectively, and time is the duration between each

sample. vCOM/3Duwrist ratio was also calculated by dividing vCOM by sum of left and right 3Duwris (i.e. mean

3Duwrist ×2) since this parameter is an indirect indicator of ηFin swimming (Figueiredo et al. 2011)

To investigate which phases are responsible for the difference in 3Duwrist, 3Duwrist during each

phase was also calculated since 3Duwrist during the upper limb cycle could be divided into 3Duwrist during

each phase using Equation 7:

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3 Duwrist=3 DuEntry ∙ tEntry

tUW+

3 DuPull ∙tPull

tUW+

3 DuPush ∙tPush

tUW+

3 DuRelease ∙ tRelease

t UW

(7)

Where 3DuEntry, 3DuPull, 3DuPush, and 3DuRelease are 3Duwrist during each phase (m·s-1), tEntry, tPull, tPush, and

tRelease are the duration of each phase (s), and tUW is the duration of the whole underwater phase (s). This

equation suggests that 3Duwrist during the underwater phase is determined by 3Duwrist in each phase and the

relative duration of the phase (the duration of each phase in relation to underwater phase duration). In this

study, this value (3 DuPhase ∙ tPhase

tUW) multiplied by 100 relative to 3Duwrist during the whole underwater

phase was defined as the contribution of each phase to determine 3Duwrist (Phase contribution: %) and

compared between front crawl and backstroke. Since 3Duwrist during each phase is determined by the

phase duration during each phase and the distance of wrist travelled during the phase (resultant

displacement of the wrist: m), this value was also calculated by summing the instantaneous resultant

displacement of the wrist during the phase.

Ranges of motion of the ankle in vertical (Y-ROMkick: m) and lateral direction (Z-ROMkick: m)

were quantified as the difference between the maximum and minimum displacements of the ankle in both

vertical and lateral directions, respectively. The mean values of the left and right ROM values are

reported. 3D ankle speed during the whole upper limb cycle (3Duankle) was also calculated by Equation 8:

3 Duankle=(∑k=1

n−1 √( dxk+1−dxk )2+( dyk+1−dyk )2+(dzk +1−dzk )2

time ) ∙(n−1)−1

(8)

Where n is the last number of the sample in the upper limb cycle, dx, dy, and dz are X, Y, and Z

displacements of the ankle relative to COM, respectively, and time is the duration between each sample.

Since it was reported that IVfluc was associated with Cnet (Barbosa et al. 2006b; Vilas-Boas et al. 2011),

IVfluc was also obtained by calculating the coefficient of variation (CV) of vCOM during the upper limb cycle

(Vilas-Boas et al. 2011).

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Statistical analysis

The digitising error in this study was assessed by CV of each kinematic variable among each

repeated digitising trial. To assess the differences in Cnet and other kinematic variables between front

crawl and backstroke at the same swimming speed, a paired t-test was used. Statistical significance was

set at p < 0.05. Cohen’s d (d) was also calculated to estimate the effect size associated with each

difference. According to Cohen (1988), d values of 0.20, 0.50, and 0.80 were assumed to represent small,

medium, and large effects, respectively. Prior to the t-test, the normality of all data in front crawl and

backstroke was checked and confirmed using Kolmogorov–Smirnov test. The paired t-test was conducted

using IBM SPSS Statistics 19 (IBM Corporation, Somers, NY, USA).

Results

In the present study, the digitising error was assessed using CV among repeated digitising trials

(one trial each for front crawl and backstroke). The result suggested good reliability on kinematic analysis

in this study overall (less than 5% of digitising error in all kinematic variables). See Appendix 1 for

further details.

Fig. 2 shows vCOM during the analysed upper limb cycle, the mean swimming speed calculated

from the final time of 300 m trials (vS), and the speed instructed using the visual light pacer (vinst). There

were no differences in each variable between front crawl and backstroke. In front crawl, however, there

were differences between vCOM and vS (p<0.05, d=0.674) and between vCOM and vinst (p<0.05, d=0.691).

Table 1 shows physiological and kinematic variables obtained in front crawl and backstroke. There were

no differences in SF, SL, and IVfluc between the swimming techniques. However, swimmers showed

slower 3Duwrist (during the underwater phase only: p<0.01, d= 2.571) and 3Duankle (during the whole upper

limb cycle: p<0.01, d=1.173) as well as larger vCOM/3Duwrist ratio (p<0.01, d=3.445) during the upper limb

cycle, smaller Y-ROMkick (p<0.01, d=1.693), and lower Cnet (p<0.01, d=1.373) in front crawl than in

backstroke.

**Fig 2**

**Table 1**

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Detailed information during each stroke phase in front crawl and backstroke are shown in Table

2. Swimmers had smaller contribution of release phase to determine 3Duwrist in front crawl than in

backstroke (p<0.01, d=3.881), while 3DuRelease was faster in front crawl (p<0.01, d=3.724) than in

backstroke. On the other hand, swimmers showed shorter absolute and relative duration in front crawl

than in backstroke during the release (absolute duration: p<0.01, d=4.092; relative duration: p<0.01,

d=4.218) and recovery (absolute duration: p<0.01, d=3.031; relative duration: p<0.01, d=3.590) phases.

**Table 2**

Even though 3DuEntry was slower in front crawl than in backstroke (p<0.01, d=3.556), the

contribution of the entry phase to determine 3Duwrist was larger in front crawl (p<0.01, d=3.303). The

absolute and relative durations of the entry phase in front crawl was longer than those in backstroke

(absolute duration: p<0.01, d=6.771; relative duration: p<0.01, d=8.598). 3Duwrist of one participant

throughout the upper limb cycle in front crawl and backstroke are shown in Fig. 3 as examples.

**Fig. 3**

Discussion

Differences between front crawl and backstroke

At the same speed below AnT, Cnet was lower by 15% with large effect size (d=1.373) in front

crawl than in backstroke. However, there were no differences in SF and SL between the swimming

techniques, which suggested that greater energy was dissipated in backstroke. Lower Cnet in front crawl

than in backstroke at similar SF and SL with different groups of swimmers (i.e. groups with different

anthropometric features) was presented by Barbosa et al. (2008). The present study confirmed that this

was also the case even when minimising the effect of anthropometric characteristics of swimmers on the

variables. In this study, IVfluc during the upper limb cycle was quantified. It has been suggested that this

variable is a determinant of Cnet in swimming (Vilas-Boas et al. 2011). However, there was no difference

in IVfluc between front crawl and backstroke (with medium effect size; d= 0.447), and consequently, IVfluc

was not the cause of the difference in Cnet between the swimming techniques. These results indicate that,

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contrary to the suggestions which have been raised (Barbosa et al. 2010), IVfluc is not a sufficient indicator

of Cnet when different swimming techniques are compared at the same speed.

According to Equation 2, these results suggest lower Wd and/or higher ηP in front crawl than in

backstroke. In this study, Wd was not assessed, however, it has been reported that there is no difference in

frontal area between front crawl and backstroke during swimming (Gatta et al. 2015). Given that the

primary component of total drag in swimming at 1.0 m·s-1 (which is close to the testing speeds in present

study) is pressure drag (Pendergast et al. 2005), there is probably no major difference in Wd between the

two techniques. Therefore, the observed difference in Cnet between the techniques in the present study was

probably attributed to higher ηP in front crawl than in backstroke.

Even though ηPwas also not measured in the present study, the above argument was supported

by kinematic data. According to Equation 5, the larger vCOM/3Duwrist ratio (by 18%, with large effect size;

d=3.445) in front crawl than in backstroke indirectly suggested that ηF in front crawl was higher than that

in backstroke. Since there was no difference in vCOM, the difference was due to the slower 3Duwrist (by

17%, with large effect size; d=2.571) in front crawl than in backstroke. Although the direct relationship

between vCOM/3Duwrist ratio and ηF has not yet been established, the difference in 3Duwrist between front

crawl and backstroke was probably associated with the difference in ηF between the swimming

techniques, since larger kinetic energy must have been transferred from the hand to the water in

backstroke than in front crawl to achieve the same swimming speeds. Front crawl vCOM/3Duwrist ratio in the

current study was in accordance with the value during 200 m front crawl that was 0.41-0.43 (Figueiredo

et al. 2011), which supported the accuracy of the method for obtaining the variable in this study. In the

present study, swimmers also showed slower 3Duankle and smaller Y-ROMkick in front crawl than in

backstroke (by 18 and 23% with large effect sizes; d=1.173 and d=1.693, respectively), while Z-ROMkick

in the two swimming techniques were similar. Since these variables can be indirect indicators of Wint and

ηH (see Introduction), these results suggested that the swimmers produced less Wint in front crawl than in

backstroke, meaning that ηH is probably lower in backstroke than in front crawl. Since ηP equals to ηH

multiplied by ηF (Equation 3), the possible differences in ηF (suggested by the difference in 3Duwrist) and

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ηH (assumed based on the results in 3Duankle and Y-ROMkick) between the two swimming techniques

suggest that the front crawl is less costly than backstroke because front crawl has higher ηP.

It should be noted that vCOM (1.077 m·s-1) was faster than vS (1.043 m·s-1) and vinst (1.043 m·s-1) in

front crawl in this study. This result suggests that the analysed upper limb cycle might not have

represented overall upper limb cycles during the 300 m testing. However, given that both stroke and kick

frequency rise with the increase of the swimming speed (Zamparo et al. 2005b), mean 3Duwrist and

3Duankle values during the whole 300 m trial would probably be smaller than the analysed upper limb

cycle. Therefore, even though the analysed front crawl upper limb cycle might have differed from overall

kinematics during the 300 m testing, it is logical to conclude that front crawl probably has higher ηP than

backstroke.

Among the four underwater phases, the phase which had smaller contribution to determining

3Duwrist in front crawl than in backstroke was the release phase, which suggested that this phase was

responsible for the difference in 3Duwrist between the swimming techniques. In the present study, the

phase contribution was calculated using 3Duwrist in each phase multiplied by the relative phase duration ¿

in Equation 8), meaning that the difference in the phase contribution should be attributed to the difference

in 3Duwrist or the relative duration during the phase. In the release phase, the phase contribution was

smaller in front crawl than in backstroke because the absolute and relative durations of the phase were

shorter in front crawl, even though the 3DuRelease in front crawl was faster than that in backstroke. The

shorter absolute and relative durations of the release phase in front crawl than in backstroke were due to

smaller resultant displacement of the wrist during the phase. Even though 3DuEntry during in front crawl

was slower than that in backstroke, this did not contribute to the slower 3Duwrist during the whole

underwater phase in front crawl than in backstroke, which was supported by the larger entry phase

contribution to determining 3Duwrist in front crawl than in backstroke. This was due to the longer duration

of the entry phase in front crawl.

Fig. 4 shows examples of the displacement of the wrist in Y-direction (vertical direction). This

figure suggests that the swimmer had only up-sweep motion during the release phase in front crawl,

whereas the swimmer had both down-sweep and up-sweep motions during the phase in backstroke. This

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difference probably affected the difference in the resultant displacement of the wrist during the release

phase between the swimming techniques.

**Fig.4**

A limitation in this study is the exercise intensity of the testing. In this study, C measurement

was conducted under AnT to avoid indirect estimation of anaerobic energy contribution. However, races

in competitions are performed with much higher speed (consequently, with anaerobic energy source) in

both techniques. Therefore, C in the two techniques at anaerobic exercise intensities should be estimated

in the future. In the current study, swimmers had slower 3Duwrist (indirectly suggesting higherηP) in front

crawl than in backstroke, which was attributed to shorter duration of the release phase due to smaller

resultant displacement of the wrist during the phase in front crawl. This implies that swimmers might be

able to make backstroke technique more efficient by decreasing the release phase duration (for example,

by minimising the second down-sweep motion).

Conclusion

Although the relationship between the IVfluc and Cnet has been widely discussed in literature, there

was no difference in IVfluc between the swimming techniques, while Cnet in front crawl was lower than in

backstroke. Slower 3Duwrist, 3Duankle, and smaller Y-ROMkick (which indirectly suggest higher ηP) in front

crawl than in backstroke were also observed. The slower 3Duwrist in front crawl than in backstroke was

due to shorter duration of the release phase (which was caused by smaller resultant displacement of the

wrist during the phase) in front crawl than in backstroke.

Compliance with ethical standards

Funding

This work was supported by YAMAHA Motor Foundation for Sports (YMFS) International Sport

Scholarship.

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Conflict of interest

The authors declare no conflicts of interest.

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Table 1. Differences in kinematic variables between front crawl and backstroke.

Variables Front crawl Backstroke P-value Effect size

Cnet (kJ·m-1) 0.77 ± 0.08 0.91 ± 0.12 0.002 1.373

vCOM (m·s-1) 1.08 ± 0.06 1.06 ± 0.04 0.169 0.426

SF (cycles·min-1) 25.72 ± 1.30 24.90 ± 2.49 0.122 0.407

SL (m·cycle-1) 2.52 ± 0.14 2.55 ± 0.20 0.516 0.174

IVfluc 0.07 ± 0.01 0.08 ± 0.03 0.242 0.447

vCOM/3Duwrist ratio 0.40 ± 0.02 0.34 ± 0.02 < 0.001 3.445

3Duwrist (m·s-1) 1.29 ± 0.10 1.55 ± 0.10 < 0.001 2.571

3Duankle (m·s-1) 0.80 ± 0.16 0.97 ± 0.13 < 0.001 1.173

Y-ROMankle (m) 0.36 ± 0.06 0.47 ± 0.07 0.002 1.693

Z-ROMankle (m) 0.31 ± 0.04 0.35 ± 0.09 0.215 0.5743Duwrist (3D wrist speed during the underwater phase only); 3Duankle (3D ankle average speed during whole upper limb cycle);

vCOM/3Duwrist ratio (vCOM divided by sum of left and right 3Duwrist [i.e. 3Duwrist × 2])

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Table 2. 3D speed, absolute and relative duration, and resultant displacement of the wrist as well as the

phase contribution to determining 3Duwrist throughout the upper limb cycle during each stroke phase.

** shows differences from front crawl at p<0.01

VariablesPhase

Entry Pull Push Release

Phase contribution to determining 3Duwrist (%)

FC 28.25±2.15 27.52±1.52 31.29±2.14 12.94±2.14

BS 18.85±2.96** 26.27±3.00 30.02±3.63 24.86±3.75**

3Du during each phase(m·s-1)

FC 0.61±0.06 2.30±0.31 2.50±0.14 2.08±0.29

BS 1.05±0.15** 2.28±0.14 2.60±0.10 1.10±0.23**

Phase duration (s)FC 1.09±0.09 0.28±0.04 0.29±0.02 0.15±0.04

BS 0.45±0.10** 0.28±0.03 0.28±0.04 0.57±0.14**

Relative phase duration (%)

FC 46.59±3.16 12.18±1.68 12.57±0.92 6.41±1.58

BS 18.29±3.42** 11.60±1.23 11.65±1.96 23.51±5.51**

Resultant displacement of the wrist during each FC 0.66±0.07 0.65±0.05 0.73±0.05 0.30±0.05

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phase (m) BS 0.46±0.07** 0.64±0.07 0.73±0.10 0.61±0.11**FC (Front crawl); BS (Backstroke)

Fig. 1 A flow diagram of the energy conversion steps in swimming (adapted from Daniel, 1991). ηO:

Overall efficiency; ηP: Propelling efficiency; ηH: Hydraulic efficiency; ηF: Froude efficiency.

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Fig. 2 Differences between centre of mass velocity during the analysed upper limb cycle (vCOM), mean

speed during the 300m trial (vS), and the instructed testing speed (vinst) between front crawl and

backstroke. *significant differences at p<0.05

Fig. 3 Three-dimensional wrist speed of a swimmer in front crawl and backstroke throughout the

analysed upper limb cycle.

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Fig. 4 Vertical displacement of the wrist of a swimmer in front crawl and backstroke throughout the

analysed upper limb cycle.

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