ORIGINAL ARTICLE

Velocity profiling using inertial sensors for freestyle swimming

Andy Stamm • Daniel A. James • David V. Thiel

Published online: 23 December 2012

� International Sports Engineering Association 2012

Abstract The ability to unobtrusively measure velocity

in the aquatic environment is a fundamental challenge for

engineers and sports scientists and important in assessing

the skill level. The aim of this research was to develop a

method for velocity profiling in freestyle swimming uti-

lising a purpose-built inertial sensor. Seventeen swimmers

with different experience levels participated in this study

performing a total of 159 laps in the velocity range from

0.79 to 2.04 m s-1. Data were collected using a triaxial

accelerometer and a tethered velocity meter. The collected

acceleration data were filtered using a 0.5 Hz Hamming-

windowed FIR filter to remove the gravitational accelera-

tion before the lap velocity profiles were calculated. These

calculated lap velocity profiles were then compared with

the velocity profiles measured by the velocity meter using

Bland–Altman analysis. The scattering follows a normal

distribution with a mean skewness of 0.96 ± 0.47 and

kurtosis of 2.93 ± 1.12. The results show that an inertial

sensor alone can be used to determine a lap velocity profile

from single point acceleration records.

Keywords Swimming � Inertial sensors �Velocity profile � Acceleration � Velocity variation �Freestyle � Intra-stroke velocity

Abbreviation

SR stroke rate (cycles/min)

1 Introduction

Assessing the performance of elite swimmers is of signif-

icant interest to coaches and athletes. Equipment such as

video camera systems [1–5] or tethered velocity meters [1,

6–8] are complex to operate and time consuming in setup

and handling. It is obvious that such equipment cannot be

used during every training session of the athlete. Due to

these facts athlete assessment is not performed during all

training sessions which further reduces the amount of

useful information about an athlete. Additionally during

training sessions, the coach may not be able to see minor

improvements to the swimming style or detect time

improvements, which increases the need for help from

technical equipment in swimming assessment.

Video analysis is the most common technology used to

monitor swimmers and together with velocity meters, are

the only techniques which have been used to extract

velocity information [1, 6, 9]. Video camera systems are

very popular as they do not hinder the swimmer because

they are remote from the athletes. Performance analysis

using video systems has disadvantages such as (a) extensive

time to digitise the data, as every frame must be evaluated

(b) inaccuracy in measurements due to unrecognisable

reference points, mainly caused by water turbulences or

bubbles and (c) the parallax errors well known from the use

of video cameras. The time for post-processing is therefore

one of the major problems associated with the analysis of

swimmers and does not allow real-time processing or real-

time feedback to coaches. Tethered velocity meters [8] are

able to provide an accurate measure of velocity [1, 6, 10],

but are only capable of measuring one lap.

Inertial sensors [11–16] are small, light, easy to use and can

be operated by the athlete without any technical knowledge.

Small sensors do not encumber or restrict the athlete during

A. Stamm (&) � D. A. James � D. V. Thiel

Centre for Wireless Monitoring and Applications,

Griffith University, Brisbane, QLD 4111, Australia

e-mail: andy.stamm@gmail.com

Sports Eng (2013) 16:1–11

DOI 10.1007/s12283-012-0107-6

normal training and provide the opportunity to monitor all

training sessions. Thus the use of these sensors can increase

the number of monitored training sessions significantly.

Accelerometers used in inertial sensors are mainly micro-

mechanical systems (MEMS) accelerometers. Using this

technology introduces errors to the measurements such as (a) a

fixed bias, which represents a fixed offset between the mea-

sured acceleration and the acceleration experienced (i.e. at 0 g)

by the sensor (b) a varying scale factor, which represents the

inaccuracy between the input acceleration change as compared

to the measurement output change and (c) cross-coupling,

which represents a ratio of output error to input acceleration. It

is possible to measure the fixed bias by taking the mean over a

long time period of the acceleration of an accelerometer at rest.

This requires a calibration method, e.g. Lai et al. [17], so that

the accelerometer is perfectly aligned to gravity.

Integration of acceleration data to obtain velocity can

introduce further integrations errors, which can be mini-

mised by applying appropriate filtering techniques.

Parameters of interest to athletes and coaches are: the lap

count, stroke count, stroke rate (SR), mean velocity, and the

velocity variation during the swimming phase, which is

usually measured in percentage in relation to the mean

velocity. Lap and stroke counts are usually recorded manu-

ally by counting the laps and strokes by a coach on site or

using a video recording [1, 18] after the training session is

finished. The SR is usually determined by recording the time

for several strokes and dividing the mean time per stroke by

60 s. This can be either done by manually recording the time

taken for the strokes by a stop-watch or by post analysing a

video recording of the swimming session. Researchers have

used trial-axis accelerometers to find the lap count, stroke

count, SR or distance per stroke [3, 11, 12, 19, 20] and some

preliminary studies reported the use of triaxial acceleration to

derive velocity information [7, 10]. In [7] the match was not

strong and in [10] only a small portion of one lap for one

subject was reported. There is no validation study, to our

knowledge, which compared a velocity profile quantified

from an accelerometer with other measurement systems.

This research aimed to develop and validate a small,

wearable inertial sensor and the accompanying algorithms

required to quantify lap velocity profiles from recorded

sacrum acceleration. The developed system provides the

coach/athlete with timely information of mean velocity and

intra-stroke velocity variations.

2 Methods

2.1 Instrumentation

Data were collected using a purpose-built inertial sensor

(see Fig. 1) which offers a 3-axis accelerometer (±8 g,

LIS331DLH [21]), a 3-axis gyroscope (1,500�/s, LY5150

ALHTR & LPR5150ALTR [21]), a 2.4 GHz radio trans-

ceiver (nRF24L01 ? [22]), a 1 GB micro SD Card, dis-

play for interaction, keypad (for operating the device),

rechargeable battery, a USB port for downloading the

recorded data and a microprocessor (AT90USB1286 [23]).

This waterproof sensor has the dimensions 52 9 33 9

10 mm, a mass of 20 g and was set to record data at

100 Hz per channel [24].

A second set of data was captured simultaneously using

the Swift Sports Speed Probe 5,000 V (SP5000, Swift

Performance Equipment, Australia [8]), a tethered velocity

meter. This device is used to measure the velocity of

straight motion events such as running or swimming. The

tether cable passes by an optical sensor inside the device

which samples the time it takes for 1 cm of wire to pass by.

The time accuracy of the SP5000 is 10 ls with an accuracy

of the velocity of 1 mm/s. It was connected to a computer

which runs the measurement software (AMR Motion Stu-

dio 2008, Swift Performance Equipment, Australia) and

also provided the possibility of synchronising a video

camera to the velocity record. This system allows the

swimmer to swim only one lap as the tether needs to be

detached at the end of the lap. Therefore, this system is

unable to be used during normal training sessions which

involve turns.

2.2 Data collection

Seventeen swimmers (eight junior elite and nine retired

elite) gave their informed written consent to participate in

this study, which has been approved by the institution’s

ethics committee (Table 1). The data were collected at a

temperature-controlled (25 �C), 50 m Olympic-sized stan-

dard outdoor pool (eight junior elite swimmers) and 25 m

indoor pool (nine retired elite swimmers). The eight junior

elite swimmers swam 3 laps at low effort after a supervised

Fig. 1 Inertial sensor in its waterproof casing. The dimensions of the

sensor are 53 9 33 9 10 mm and the weight is 20 g

2 A. Stamm et al.

training session, while the nine retired elite swimmers swam

15 laps at three different efforts (5 laps comfortable, 5 laps

training and 5 laps race pace) after a self-defined warm-up

session. The inertial sensor was taped to the sacrum and a

tether attached to the swimmer’s costume as close as possible

to the sensor (see Fig. 2). The sensor was attached to the

swimmers before the warm-up session started to allow the

sensor to stabilise to the pool temperature to minimise drift

effects. As the normal operating temperature of the sensor is

25–28 �C, the water temperature was assumed to not influ-

ence the measurement accuracy.

2.3 Data processing

2.3.1 Data downloading

The data recorded on the inertial sensor were downloaded

using a MATLAB� (Version 7.7.0471, The MathWorks,

Massachusetts, USA) interface developed within this

research group using the sensor’s USB connection. The

SP5000 data were stored in a simple text file which was

imported into MATLAB� using the MATLAB� import

function.

Fig. 2 Taped inertial sensor at

the sacrum, with ax representing

the mediolateral direction

(body roll), ay representing the

swimming direction and

az representing the anterior–

posterior direction to the

swimmer’s body

Table 1 Overview of all swimmers and their experience, age, mass, height and preferred hand

Group Swimmer Height (cm) Mass (kg) Age (years) Experience Gender

Junior 1 182 73 18 National Male

2 186 86 18 National Male

3 184 75 17 National Male

4 184 78 17 National Male

5 186 83 18 National Male

6 171 71 17 National Male

7 194 85 17 National Male

8 178 67 17 National Male

Mean 183.13 77.25 17.38

SD 6.66 6.94 0.52

Retired 9 194 107 37 National Male

10 171 68 55 National Male

11 187 76 29 International Male

12 172 59 52 State Female

13 166 53 37 State Female

14 179 75 26 State Male

15 186 96 32 National Male

16 175 70 22 National Male

17 166 55 26 State Female

Mean 177.33 73.22 35.11

SD 9.87 18.21 11.58

Velocity profiling using inertial sensors for freestyle swimming 3

2.3.2 Data analysis

The recorded acceleration data were firstly calibrated by

aligning all three axes parallel to earth’s gravity (a = 0 g,

a = ?1 g and a = -1 g) to calculate the offset and sen-

sitivity of each axis. This calibration was used to convert

the raw acceleration data to gravity-related acceleration

data similar to the method used by Lai et al. [17]. The

mediolateral direction was represented by the x-axis, the

swimming direction by the y-axis and the anterior–poster-

ior direction by the z-axis as shown in Fig. 2.

The acceleration data in gravity-related units (g) were

low-pass filtered using a 0.5 Hz low-pass Hamming-win-

dowed finite impulse response (FIR) filter [25] to find the

sensor orientation during the swimming. The frequency

was chosen at 0.5 Hz as the lowest frequency in the signal

was the body roll with f [ 0.5 Hz. The output of the fil-

ter was then used to correct the acceleration data by sub-

tracting the filter output from the acceleration data. Thus

the output has been high-pass filtered.

The integration error for the velocity calculation was

quantified using a sensor sitting at rest (aligned to gravity)

recording acceleration for 40 s. These acceleration data were

processed in the same way the acceleration of a swimmer was

processed including the velocity calculation (described

below). The integration error was found to be 0.08 m s-1

after an assumed maximum lap time of 40 s, which equates to

an error of 0.002 m s-1 per integrated second. The noise level

of the acceleration data, which introduces a cumulative error

in the velocity, has therefore been considered as not signifi-

cant for the short duration of one lap (t \ 40 s).

The total acceleration atot was calculated using:

atot tð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X

3

i¼1

ai tð Þ2v

u

u

t ð1Þ

where i = x, y, z, t represented the time and atot the total

acceleration as time series data. The acceleration data

consisted of a three-column matrix; the x, y and z acceler-

ation time series data. The total acceleration was added to

the matrix forming a four-column matrix containing the

total acceleration as the fourth column.

The velocity at a particular time v(t) was calculated

using numerical integration (trapezoidal rule) of the

acceleration atot (discrete data) and was calculated using:

vðtÞ ¼ vðt � 1Þ þ DtaðtÞ þ aðt þ 1Þ

2ð2Þ

where v (0) = 0, a (t) and a (t ? 1) were adjacent accel-

eration values and Dt the time between two samples, which

was represented by 1/sampling rate of the sensor.

The lap velocity calculated using Eq. 2 was normalised

by the mean velocity of the lap. The mean velocity was

calculated from the lap distance divided by the lap split

time.

The corrected velocity vcorr(t) for one lap was therefore

calculated using:

vcorrðtÞ ¼ vðtÞ � �vðtÞ þ llap � loff

tel � tsl

ð3Þ

where tsl was the start time, tel the end time of the lap, llap

the length of the pool, loff the sensor offset, v(t) the cal-

culated velocity from Eq. 2 and �mðtÞ the mean of these

velocity between tsl and tel. The sensor offset describes the

difference between the lap length and the actual travelled

distance for the sensor and was determined by an offset at

the start and end of the lap.

The sensor offset at the start of the lap is described by

the difference in distance between the wall of the pool and

the sacrum and at the end of the lap by the distance

between the wall of the pool and the sacrum. This leads to a

total offset which is equal to the height of the swimmer.

Concluding that the swimmer pushes off the wall with bent

knees, we have an additional difference at the start which is

described by the difference in distance between bent and

extended knees. Considering that the swimmer finishes the

end of the lap with extended arms, we have an additional

difference at the end which is described by the difference in

distance between the head and fully extended arms.

Assuming that these two differences have the same mag-

nitude, the height of the swimmer can be used as lap offset

(loff). Even if there is a small difference between these two

offsets, a 0.2 m difference will result in a change in lap

velocity of less than 0.01 m s-1.

2.3.3 Data interpretation

There are five data points needed from the acceleration

record to calculate the velocity profile. These data points

are shown in Fig. 3, which represents the acceleration

profile of one low-effort lap, and are:

• tsl (start of the lap, atot [ 1 g, az is max)

• tep (end of push-off, atot = 1 g, az is max)

• tss (start of swimming phase, ax = 0)

• tes (end of swimming phase, ax = 0)

• tel (end of the lap, small spike in all channels)

The start of the lap (tsl) was determined from the time

where the total acceleration had a local minimum (after

atot [ 1 g) and az had a local maximum. The end of the lap

(tep) was chosen when the total acceleration returned to 1 g

and had a minimum at the same time as az had a local max-

imum. The start of the lap (tsl) and the end of the push-off (tep)

can be clearly seen on the acceleration plot as it contains

large acceleration changes due to the push-off power.

4 A. Stamm et al.

The swimming phase was detected by investigating the

mediolateral axis (x-axis) which shows the body roll of the

swimmer. The start of the swim phase tss was chosen where

the first zero crossing within the detected body roll

occurred. This was equivalent with the swimmer per-

forming his first stroke. The end of the swimming phase tes

was chosen at the end of the last stroke. In some cases the

end of the lap occurred during an arm stroke. In these rare

cases the end of the swimming phase was chosen at the

zero crossing of the last full detected body roll.

The body roll detection was carried out by manual

inspection of the calibrated mediolateral channel acceler-

ation data. The body roll can be identified by the medio-

lateral axis acceleration altering between ?1 g and -1 g.

Zero crossing detection algorithms are also used to detect

the body roll of a swimmer investigating the mediolateral

channels data or the low-pass filtered mediolateral channel

data. This kind of zero crossing detection algorithm is

usually applied to find stroke durations and SR as shown,

e.g. by Davey et al. [26], Le Sage et al. [12] and Daukantas

et al. [19]. As SR detection was not the main focus of this

research, inspection of the mediolateral channel accelera-

tion data for the start and end of the swimming phase was

sufficient to determine the start and the end of the lap.

The end of the lap coincides with a small spike in all

acceleration channels caused by the swimmer touching the

wall shortly before the ay channel returns to -1 g, which

represents the swimmer standing at the end of the pool.

2.3.4 Data statistics

The Bland–Altman [27] analysis was undertaken to mea-

sure the agreement between the two systems during the

swimming phase, by plotting the mean of both velocities

((vsensor ? vSP5000)/2) against the difference of both

velocities (vsensor - vSP5000). The velocity at each indi-

vidual time between the start of the swim tss and the end of

the swim tes was included in the analysis. The scattering

around the bias of the Bland–Altman analysis was inves-

tigated as compared to a normal distribution and the kur-

tosis and skewness recorded (see Table 2).

3 Results

Seventeen swimmers were investigated using the above-

described techniques. The results for all swimmers (mean per

swimmer) are presented in Table 2, with one swimmer pre-

sented in more detail in Tables 3 and 4. The results for the

presented swimmer (17) are representative for all swimmers.

The calculated sensor velocity profile during the swim

phase shows a good match (bias 0.02 m s-1, upper limit

5 10 15 20 25 30 35

−1

0

1

ax (

g)

5 10 15 20 25 30 35

−1−0.5

00.5

a y (g)

5 10 15 20 25 30 35

−1

−0.5

0

0.5

a z (g)

5 15 20 25 30 350.5

1

1.5

a tot (

g)

Time (s)tes

tel

tss

tep

tsl

strokespush off

glide

Fig. 3 Raw acceleration data converted to gravitational units (g) for a

low-effort freestyle swimming lap showing the push-off, glide and

strokes phases. ax represents the mediolateral, ay the swimming, az the

anterior–posterior direction and atot the total acceleration experienced

by the sensor. The start of the lap is described by ts, the end of the

push-off by tep, the start of the swim by tss, the end of the swim by tes

and the end of the lap by tel

Velocity profiling using inertial sensors for freestyle swimming 5

0.20 m s-1, lower limit -0.17 m s-1, see Fig. 6) with the

SP5000 velocity profile for the low-effort lap (see Fig. 4)

and a slightly diminished match (bias 0.01 m s-1, upper

limit 0.29 m s-1, lower limit -0.26 m s-1, see Fig. 7) for

the medium effort lap (see Fig. 5). This was caused by the

swimmer kicking too close to the tether during the swim,

which complicates the comparison of both velocity pro-

files. The Bland–Altman analysis was used to investigate

the agreement between the sensor-derived velocity and the

SP5000-measured velocity.

Figure 6 shows the results of the Bland–Altman anal-

ysis for the data presented in Fig. 4, with a slightly higher

bias of 0.02 m s-1, a lower limit of agreement of

-0.17 m s-1, and an upper limit of agreement of

0.20 m s-1. The scattering around the bias follows a

normal distribution with a measured skewness of 1.10 and

a kurtosis of 2.78 (note that MATLAB� was used to find

the kurtosis, which defines the kurtosis of 3 for a normal

distribution). Figure 7 shows the results for the presented

medium effort lap with a bias of 0.01 m s-1, a lower limit

of agreement of -0.26 m s-1, and an upper limit of

agreement of 0.29 m s-1. The scattering around the bias

follows as well as a normal distribution with a skewness

of 1.10 and a kurtosis of 2.62. The results for each lap of

the swimmer can be found in Table 3. It additionally

shows the number of data points used for the analysis ndata

and the percentage of data points lying inside the confi-

dence bounds nconfidence.

The mean bias for this swimmer is 0.02 m s-1 and the

upper and lower limits are 0.30 and -0.28 m s-1, respec-

tively. Table 2 presents the results of the statistical analysis

for all swimmers. The means across all swimmers show a

bias of 0.02 ± 0.04 m s-1 and the upper and lower limits

of 0.48 ± 0.12 and -0.44 ± 0.16 m s-1. Table 4 shows

the mean values of the Bland–Altman analysis for each

group and effort.

The mean velocity and error for the lap presented in Fig. 4

(lap 5) was 1.00 ± 0.01 m s-1 and 1.01 ± 0.01 m s-1 for

the SP5000 and the sensor-derived velocity, respectively. The

SR was found to be 33.88 ± 1.15 stroke cycles per minute.

Table 5 presents the SR with standard deviation and the mean

velocity derived by the sensor and the SP5000 system for all

individual laps of the presented swimmer.

Table 6 shows the mean values of the derived SR,

sensor and SP5000 velocity for each group and effort.

4 Discussion

The aim of this study was to show that a single inertial

sensor attached to the sacrum can be used to derive velocity

profiles for freestyle swimming. A tethered velocity meter

Table 2 Bland–Altman analysis results for all swimmers

Swimmer Mean Kicks

Bias (m s-1) Upper limit (m s-1) Lower limit (m s-1) Skewness distribution Kurtosis distribution

1 0.03 0.34 -0.28 0.52 1.79 No

2 0.04 0.49 -0.40 1.15 3.17 No

3 0.03 0.38 -0.33 0.77 2.15 No

4 0.02 0.42 -0.37 0.49 1.97 No

5 0.04 0.53 -0.45 0.81 2.86 Yes

6 0.02 0.42 -0.38 1.32 3.46 Yes

7 0.04 0.40 -0.33 0.61 2.21 Yes

8 0.01 0.36 -0.35 0.75 2.37 No

9 0.11 0.47 -0.25 0.61 2.22 No

10 -0.04 0.65 -0.72 1.86 5.22 Yes

11 0.10 0.50 -0.30 0.31 1.86 No

12 0.03 0.48 -0.43 1.19 3.41 Yes

13 -0.04 0.52 -0.60 1.72 4.77 Yes

14 -0.04 0.72 -0.80 1.68 5.01 Yes

15 0.02 0.65 -0.61 0.62 2.02 Yes

16 0.01 0.54 -0.53 0.86 2.37 Yes

17 0.02 0.30 -0.28 1.13 2.87 Yes

Mean 0.02 0.48 -0.44 0.96 2.93

SD 0.04 0.12 0.16 0.47 1.12

Data presents for each swimmer the mean bias (m s-1), upper and lower limit of agreement (m s-1), the results of the distribution analysis

(skewness and kurtosis) and the influence of kicks on the SP5000 velocity profile

6 A. Stamm et al.

Table 3 Overview results of Bland–Altman analysis for the representative swimmer

Lap Effort Bias

(m s-1)

Upper limit

(m s-1)

Lower limit

(m s-1)

ndata nconfidence

(%)

Skewness

distribution

Kurtosis

distribution

1 Low 0.03 0.28 -0.23 1,571 95.80 1.25 2.89

2 0.01 0.21 -0.19 1,514 95.64 1.78 4.72

3 0.03 0.25 -0.20 2,087 94.11 1.14 2.70

4 0.02 0.23 -0.20 1,401 95.93 0.89 2.23

5 0.02 0.20 -0.17 1,785 96.25 1.10 2.78

6 Full 0.03 0.34 -0.28 1,439 94.09 0.84 2.16

7 0.01 0.33 -0.31 1,442 95.15 0.76 1.94

8 -0.02 0.36 -0.40 1,381 94.79 0.97 2.33

9 -0.01 0.35 -0.38 1,544 94.49 0.75 2.11

10 -0.05 0.34 -0.44 1,752 94.06 1.30 3.36

11 Medium 0.03 0.37 -0.31 1,618 96.35 1.83 4.77

12 0.01 0.29 -0.26 1,427 94.74 1.09 2.62

13 0.01 0.34 -0.33 1,487 94.96 1.40 3.68

14 0.01 0.35 -0.34 1,711 94.45 0.90 2.21

15 0.00 0.24 -0.23 1,617 93.82 1.02 2.59

Data presents the lap number, swim effort, bias (m s-1), upper and lower limit of agreement (m s-1), number of data points used for analysis

(ndata), percentage of data points lying inside the confidence bounds (nconfidence) and the results of the distribution analysis (skewness and

kurtosis)

Table 4 Mean results of Bland–Altman analysis combined for each group and effort

Group Effort Bias

(m.s-1)

Upper limit

(m s-1)

Lower limit

(m s-1)

ndata nconfidence

(%)

Skewness

distribution

Kurtosis

distribution

Junior Low 0.03 0.42 -0.36 3,412.04 3,243.92 0.82 2.52

Retired Low 0.06 0.38 -0.26 1,503.47 1,428.98 1.01 3.22

Med 0.03 0.54 -0.48 1,464.40 1,386.80 1.14 3.44

Full -0.03 0.70 -0.76 1,435.53 1,327.78 1.17 3.26

Data presents the group, swim effort, bias (m s-1), upper and lower limit of agreement (m s-1), number of data points used for analysis (ndata),

percentage of data points lying inside the confidence bounds (nconfidence) and the results of the distribution analysis (skewness and kurtosis)

0 5 10 15 200

0.5

1

1.5

2

Time (s)

Vel

coity

(m

/s)

Fig. 4 Velocity profiles of a

low-effort (mean velocity

1.01 m s-1) swimming lap. The

solid line represents the sensor-

derived velocity profile and the

dashed line is the tethered

device velocity profile

Velocity profiling using inertial sensors for freestyle swimming 7

was attached to the swimmer’s costume to get a velocity profile

(criterion measure), which was compared to the accelerome-

ter-derived velocity profile using the Bland–Altman analysis.

The results of the Bland–Altman analysis (see Tables 2, 4)

demonstrated that there is a good agreement between the two

different velocity profiles during the swimming phase with a

mean bias of 0.02 m s-1, an mean upper limit of 0.30 m s-1,

and an mean lower limit of -0.28 m s-1 considering all 15

performed laps of the presented swimmer.

A comparison of the two different Bland–Altman plots

(Fig. 6 vs. 7) shows that more data points lie outside the

confidence bounds for the medium effort lap as compared

to the low-effort lap. This was due to the swimmer kicking

too close to the tether at some times during the swimming

phase. This leads to bigger differences at some data points

(at strokes where these artefacts occur), as the Bland–

Altman analysis includes the differences of the velocity at

every data point.

0 5 10 15 200

0.5

1

1.5

2

Time (s)

Vel

coity

(m

/s)

Fig. 5 Velocity profiles of a

medium effort (mean velocity

1.08 m s-1) swimming lap. The

solid line represents the sensor-

derived velocity profile and the

dashed line the tethered device

velocity profile

0.8 0.9 1 1.1 1.2 1.3

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

(vsensor

+ vSP5000

)/2 (m/s)

v sens

or −

vS

P50

00 (

m/s

)

data pointsbiasupper limitlower limit

Fig. 6 Results of the Bland–Altman analysis of the low-effort velocity lap during the swimming phase. It shows a bias of 0.02 m s-1, a lower

limit of agreement of -0.17 m s-1, and upper limit of agreement of 0.20 m s-1. 96.25 % of all data points lay inside the confidence bounds

8 A. Stamm et al.

Although the two velocity profiles (sensor vs. SP5000)

provide a good match, there are still some minor velocity

differences between the two profiles. Some of these dif-

ferences can be explained by the friction setting of the

SP5000 wheel which results in a delayed change of the

measured velocity. Other major difficulties were fluctua-

tions in velocity of the SP5000 caused by the swimmer’s

interference with the tether. Table 5 presented the mean

velocities for one subject and both systems. It can be

identified that there is an error of up to 4 % between the

accelerometer and the SP5000-quantified mean velocity.

The extracted mean SR for low-effort laps was measured

to be 34.36 ± 1.04; for a medium effort lap, 36.00 ± 1.31;

and for a full-effort lap, 41.32 ± 1.42 cycles/min. The SR

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

−0.4

−0.2

0

0.2

0.4

0.6

0.8

(v1 + v

2)/2 (m/s)

v 1 − v

2 (m

/s)

datapointsbiasupper limitlower limit

Fig. 7 Results of the Bland–Altman analysis of the medium effort

velocity lap during the swimming phase. It shows a bias of

0.01 m s-1, a lower limit of agreement of -0.26 m s-1, and upper

limit of agreement of 0.29 m s-1. 94.74 % of all data points lay

inside the confidence bounds

Table 5 Overview results for

the representative swimmer

from accelerometer-derived

stroke rate (SR) and the derived

mean velocity from the sensor

and tethered device (SP5000)

during the swim phase for each

trial

Lap Effort Sensor stroke rate ± standard deviation Mean velocity (m s-1) derived by

Sensor SP5000

1 Low 35.28 ± 0.94 1.12 1.11

2 34.34 ± 0.92 1.02 1.02

3 34.36 ± 0.92 1.01 0.99

4 33.93 ± 1.28 1.01 0.99

5 33.88 ± 1.15 1.01 1.00

6 Full 40.32 ± 1.45 1.24 1.21

7 39.88 ± 1.82 1.20 1.19

8 41.85 ± 1.54 1.18 1.20

9 42.05 ± 1.33 1.19 1.21

10 42.52 ± 0.95 1.22 1.26

11 Medium 37.14 ± 1.40 1.07 1.05

12 36.80 ± 1.14 1.08 1.07

13 36.35 ± 1.47 1.08 1.08

14 35.12 ± 1.15 1.05 1.05

15 34.59 ± 1.39 1.08 1.09

Velocity profiling using inertial sensors for freestyle swimming 9

values are similar to the findings of Le Sage et al. [12] who

found a mean SR of 33.5 cycles/min and the findings of

Daukantas et al. [19] who found a stroke rate between 43 and

49 cycles/min.

The recorded acceleration data (see Fig. 3) show a

repeatable acceleration pattern into the swimming direction

and a consistent body roll throughout the swimming phase.

The velocity profile gathered from acceleration data shows

a one-peak forward velocity pattern and can be used to

determine two stroke phases in freestyle swimming

according to Maglischo [28]. The maximum velocity rep-

resents the end of the upsweep and the minimum velocity

the start of the insweep stroke phase [28].

The use of the baseline corrected, filtered total accel-

eration was sufficient to eliminate the orientation of the

sensor from the acceleration data. It allowed an accurate

determination of the velocity profile in freestyle swimming.

5 Conclusion

This research showed that the direct comparison between

the accelerometer-quantified velocity profile and the

SP5000 velocity profile indicates a good match. Depending

on the swimming style of the swimmer, differences can

occur at some strokes (swimmer kicking the tether or close

to the tether) which influences the results of the Bland–

Altman analysis. This paper demonstrates that a single

inertial sensor attached to the lower back of a swimmer can

be used to derive a lap velocity profile in freestyle

swimming.

Conflict of interest The authors declare that they have no conflict

of interest.

References

1. Craig ABJ, Termin B, Pendergast DR (2006) Simultaneous

recordings of velocity and video during swimming. Port J Sport

Sci 6:32–36

2. Psycharakis SG, Naemi R, Connaboy C, McCabe C, Sanders RH

(2009) Three-dimensional analysis of intracycle velocity

fluctuations in frontcrawl swimming. Scand J Med Sci Sport

20(1):128–135. doi:10.1111/j.1600-0838.2009.00891

3. Le Sage T, Conway P, Justham L, Slawson S, Bindel A, West A

(2010) A component based integrated system for signal pro-

cessing of swimming performance. Paper presented at the SIG-

MAP, Athen, 28 June 2010

4. Rejman M, Borowska G (2007) Searching for criteria in evalu-

ating the monofin swimming turn from the perspective of

coaching and improving technique. J Sports Sci Med 7(1):11

5. Toshiaki G, Kaeko S, Hideki T, Teruo N, Atsunnori M, Osamu T,

Shigehiro T, Yumiko O (2003) Forces and image analysis of

gliding motion for beginners and competitive swimmers. In:

Chatard JC (ed) Biomechanics and medicine in swimming IX,

2003 l’Universite de Saint-Etienne, Saint-Etienne, pp 127–131

6. Craig ABJ, Pendergast DR (1979) Relationships of stroke rate,

distance per stroke, and velocity in competitive swimming. Med

Sci Sports Exerc 11(3):278–283

7. James D, Davey N (2007) Swimming stroke analysis using

multiple accelerometer devices and tethered systems. In: Fuss

FK, Subic A, Ujihashi S (eds) The impact of technology on sport

II, 2007 pp 577–582 doi:10.1201/9781439828427.ch83

8. Swift Performance Equipment (2006) Swift sports speed probe

5000 V. http://www.spe.com.au/. Accessed 24 Aug 2010

9. Stamm A, Thiel D, Burkett BJ, James DA (2009) Roadmapping

performance enhancement measures and technology in swim-

ming. Impact Technol Sport II:213–217

10. Stamm A, Thiel DV, Burkett B, James DA (2011) Towards

determining absolute velocity of freestyle swimming using 3-axis

accelerometers. Procedia Eng 13:120–125. doi:10.1016/j.proeng.

2011.05.061

11. Davey N, Anderson M, James DA (2008) Validation trial of an

accelerometer-based sensor platform for swimming. J Sports

Technol 1(4–5):202–207. doi:10.1002/jst.59

12. Le Sage T, Bindel A, Conway P, Justham L, Slawson S, West A

(2011) Embedded programming and real-time signal processing of

swimming strokes. Sports Eng 14(1):1–14. doi:10.1007/s12283-

011-0070-7

13. Ohgi Y (2002) Microcomputer-based acceleration sensor device

for sports biomechanics—stroke evaluation by using swimmer’s

wrist acceleration. In: Proceedings of IEEE Sensors 2002, 2002.

pp 699–704. doi:10.1109/icsens.2002.1037188

14. Ohgi Y, Yasumura M, Ichikawa H, Miyaji C (2002) Analysis of

stroke technique using acceleration sensor IC in freestyle swim-

ming. Eng Sport 7 2:503–511

15. Ohgi Y, Ichikawa H, Homma M, Miyaji C (2003) Stroke phase dis-

crimination in breaststroke swimming using a tri-axial acceleration

sensor device. Sports Eng 6(2):113–123. doi:10.1007/bf02903532

16. Pansiot J, Lo B, Guang-Zhong Y (2010) Swimming stroke

kinematic analysis with BSN. In: International Conference on

Body Sensor Networks (BSN), 2010 pp 153–158

17. Lai A, James DA, Hayes JP, Harvey EC (2004) Semi-automatic

calibration technique using six inertial frames of reference.

Table 6 Mean results of SR and velocity analysis combined for each group and effort

Group Effort Sensor stroke rate ± standard deviation Mean velocity (m s-1) ± standard deviation derived by

Sensor SP5000

Junior Low 30.40 ± 3.35 1.32 ± 0.10 1.30 ± 0.09

Retired Low 27.50 ± 1.00 1.11 ± 0.15 1.07 ± 0.12

Med 32.83 ± 1.31 1.25 ± 0.15 1.23 ± 0.12

Full 42.93 ± 2.02 1.45 ± 0.19 1.49 ± 0.20

Data presents the group, swim effort, SR (cycles/min), sensor mean velocity (m s-1) and SP5000 mean velocity (m s-1)

10 A. Stamm et al.

In: Microelectronics: Design, Technology, and Packaging, Perth,

2004 vol 1. SPIE, pp 531–542. doi: 10.1117/12.530199

18. Callaway A, Cobb J, Jones I (2009) A comparison of video and

accelerometer based approaches applied to performance moni-

toring in swimming. Int J Sports Sci Coach 4(1):139–153

19. Daukantas S, Marozas V, Lukosevicius A (2008) Inertial sensor

for objective evaluation of swimmer performance. In: 11th

International Biennial Baltic Electronics Conference 2008,

pp 321–324

20. Bachlin M, Troster G (2011) Swimming performance and tech-

nique evaluation with wearable acceleration sensors. Pervasive

Mob Comput 8(1):68–81. doi:10.1016/j.pmcj.2011.05.003

21. STMicroelectronics (2009) http://www.st.com. Accessed 02 Aug

2009

22. NordicSemiconducter (2008) http://www.nordicsemi.com/. Accessed

02 Aug 2009

23. Atmel (2009) http://www.atmel.com/. Accessed 02 Aug 2009

24. James DA, Leadbetter RI, Neeli MR, Burkett BJ, Thiel DV, Lee

JB (2011) An integrated swimming monitoring system for the

biomechanical analysis of swimming strokes. Sports Technol

4(3–4):141–150. doi: 10.1080/19346182.2012.725410

25. James DA, Wixted A (2011) ADAT: a Matlab toolbox for han-

dling time series athlete performance data. Procedia Eng

13:451–456. doi:10.1016/j.proeng.2011.05.113

26. Davey N, James D, Wixted A, Ohgi Y (2008) A low cost self con-

tained platform for human motion analysis. In: Fuss FK, Subic A,

Ujihashi S (eds) The Impact of technology on sport II. Taylor &

Francis, London, pp 101–111. doi:10.1201/9781439828427.ch14

27. Altman DG, Bland JM (1983) Measurement in medicine: the

analysis of method comparison studies. J R Stat Soc 32(3):

307–317

28. Maglischo EW (2003) Swimming Fastest, 3rd edn. Human

Kinetics, Champaign

Velocity profiling using inertial sensors for freestyle swimming 11