Acceleration-Based Method of Ice Quality Assessment in the Sport of Curling
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sensors
Communication
Acceleration-Based Method of Ice Quality Assessment in the
Sport of Curling
Bartosz Dzikowski 1, * , Jerzy Weremczuk 1 and Marek Pachwicewicz 2
1 Warsaw University of Technology, Faculty of Electronics and Information Technology, Institute of Electronic
Systems, Nowowiejska 15/19, 00-665 Warsaw, Poland; j.weremczuk@ise.pw.edu.pl
2 MKTronic Sp. z o.o., Puławska 14, 02-512 Warsaw, Poland; marek@mktronic.pl
* Correspondence: b.dzikowski@elka.pw.edu.pl
Abstract: Despite the significant influence of ice conditions on results in the sport of curling, players
and ice technicians lack a measurement device that would objectively measure ice quality during
a curling competition. This paper presents such a new measurement method by using a device
consisting an inertial measurement unit (IMU) attached to the handle of the curling stone and data
processing software. IMU is used to measure the vibration of curling stone during its movement
on the surface of the ice. The acceleration signal is recorded, and then the software calculates the
value of so-called R parameter in frequency domain. The value of R allows one to determine if an ice
sheet had been pebbled and if the shape of pebbles is suitable for the game of curling. The presented
system was tested in various ice conditions—on both freshly prepared and used ice. Ice technicians
and players may use the proposed system to decide whether the ice surface is suitable for play or if it
should be remade.
Keywords: curling; inertial measurements; sports measurements; curling ice; inertial measure-
ment unit
Citation: Dzikowski, B.; Weremczuk, 1. Introduction
J.; Pachwicewicz, M. Curling is a worldwide popular winter Olympic team sport, in which athletes slide
Acceleration-Based Method of Ice 20-kilogram granite stones over the flat surface of ice. The field of play (sheet) is 45-meters
Quality Assessment in the Sport of long and 5-meters wide. On both ends of the sheet, colored rings called the house are the
Curling. Sensors 2022, 22, 1074. targets for players. A game consists of 8 or 10 ends and features two four-person teams
https://doi.org/10.3390/s22031074 (or one male and one female per team in mixed doubles format). After each end (which
Received: 2 December 2021 features 16 stones and 8 per team), a point is awarded for each stone that is closer to the
Accepted: 27 January 2022 center of the house (called tee) than any stone of the opposition [1].
Published: 29 January 2022 During delivery, players set the stone in direct and rotational motion. Direct speed may
be up to 4–5 m/s, and imposed angular speed is usually between 50 and 150 ◦ /s. Rotation
Publisher’s Note: MDPI stays neutral
makes the stone follow a curved trajectory, and the lateral displacement in the stone’s path
with regard to jurisdictional claims in
is called the curl. Curl direction depends on the direction of rotation—clockwise rotation
published maps and institutional affil-
iations.
makes the stone turn right and vice versa. Kameda has shown that the amount of curl
mostly depends on the roughness of the curling stone’s running band [2]. This fact is widely
used by icemakers, who often scratch running surfaces of stones before major events.
The physics behind curling stone movement is still not fully described, and new mod-
Copyright: © 2022 by the authors. els are being proposed. Recently proposed models include front-back asymmetry models
Licensee MDPI, Basel, Switzerland. (assuming an asymmetry of friction forces at the front and the back of a running curling
This article is an open access article stone) [3–11] and pivot-slide models (taking that the curling stone pivots around specific
distributed under the terms and points in the ice during its movement) [12,13]. Currently, no model is widely accepted,
conditions of the Creative Commons and scientists’ discussions about various models are still ongoing [14–19]. Regardless of
Attribution (CC BY) license (https:// proposed models, it is evident for players that preparation of the field plays an essential
creativecommons.org/licenses/by/ role in the game of curling. Unprepared or badly prepared ice may strongly influence
4.0/).
Sensors 2022, 22, 1074. https://doi.org/10.3390/s22031074 https://www.mdpi.com/journal/sensors
Sensors 2022, 22, x FOR PEER REVIEW 2 of 13
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observe
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not only
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competition
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on gamemaintenance
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observed
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maintenance or
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andinfluence
pebbled
device
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conditions
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objectively
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objectively
objectively
observedresult,during
measure
measure
measure
curlers
and ice
the of
and
the
the
the
ice
qua
tech-
qua
qua
tech-
nicians lack
ensure
ensure a aameasurement
fair
fair game.
game. device
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This that
research
research wouldaims
aims objectively
to
to investigate
investigate measure whether
whether the quality
an
an accelerom
accelerom ice to
nicians
competition (B). Flat ensure
Despite
icealack
may thea
agame.
be fair
important
measurement
observedgame. This
influence
device
after research
aaimsof
that
very icelong aims
conditions
would to investigate
on
objectively
match game
without measure whether
result, curlers
maintenance an
the quality and accelerom
oriceof tech-
ice to
ensure to
tolack fair
the
the stone
stone This
handle
handle research
and
and data
data to
processing
processinginvestigate whether
software
software can an
can be be
beaccelerometer
used
used to attached
differentiate
to differentiate
differentiate
on a completely nicians
ensure to
unprepared
to thethreeathe
stone
stone
fairahandle
measurement
game.
field handle
of This
and play and
device
research
data (C). data
processing
that
aims processing
would
to investigate
software
software
objectively
can bewhether can
measure
used toan
used
accelerometer
differentiate
to
the quality of
between
ice to
attached the
ensure three
to thethree
stone abovementioned
abovementioned
a fairabovementioned
game. This
handle and data research structures
structures
aims tosoftware
structures
processing (A,
(A,
investigateB,
B,
(A, B, can and
and C).
C).
andwhether
beC). used to andifferentiate
accelerometer attached
between the
three abovementioned structures (A, B, and C).
tothree
the stone handle and data
abovementioned processing
structures B,software
(A,the andtoC). can be used to differentiate between the
Table 1. Types of observed curling ice (a coin is put in ice fix the photo scale; coin diameter is
three Table
Table 1.
1. Types
Types
abovementioned of
of observed
observed
structures curling
curling
(A, B, ice
ice
and (a
(a
C). coin
coin is put
isice
put in
in the
the ice
ice to fix
to fix
fix the photo
thecoin
photo scale;
scale; ccc
15.5 mm). TableTable
1. Types1. of
Types of observed
observed curling
curling ice (a coinice (a coin
is put in theis putto in
fixthe
the ice to
photo the
scale; photo scale;
diameter
Table is
1.
is 15.5
Types
15.5
is 15.5ismm).
mm).
of
mm).
15.5 mm). observed curling ice (a coin is put in the ice to fix the photo scale; coin diameter
is 15.51.mm).
Table Types of observed curling ice (a coin is put in the ice to fix the photo scale; coin diameter
Type
Type Type
of Ice
of Ice
Iceof Ice Photo
Photo
Photo Schematic Structure Structure
Schematic
Schematic Structure Comment Comm
Comm
Type of Ice
Type of is 15.5Photo
mm).Photo Schematic Structure Structure
Schematic Comment Comm
Type of Ice Photo Schematic Structure Comment
Type of Ice Photo Schematic Structure Comment
A—pebbled
A—pebbled ice ice observed during
observed during preparation
observed during
A—pebbled
A—pebbled ice ice
A—pebbled
A—pebbled ice ice observed
preparation
observed
observed
during during
during
preparation
(not for
(sharp pebbles)
(sharp (sharp pebbles)
pebbles) (not suitable (not play)
suitable
(sharp
A—pebbled
(sharp
(sharp pebbles)
ice
pebbles)
pebbles) observed
suitable during
(not for (not
play)(not
suitable suitable
preparation
suitable
for play)
(sharp pebbles) (not suitable for play)
B—pebbled and observed during the compe-
B—pebbled andand observed
observed duringthethe compe-
B—pebbled
B—pebbled
scraped ice andand and
B—pebbled
B—pebbled titionduring
observed
observed
(suitable during
during
for play)
observed during
B—pebbled
scraped and
ice observed
competition during the
(suitable
tition (suitable forcompe-
play)
scraped
scraped
scraped ice
scraped
ice
ice ice tition
tition
tition (suitabl
(suitabl
(suitabl
scraped ice for play)
tition (suitable for play)
observed after a very long
observed after a very long
competition without
observed mainte-
after
C—flat ice surface observed
competition
observed after observed
after
awithout
very
observed after
a verymainte-
long
after
C—flat ice surface nance or unprepared (not
competition
long competition
without
competition
competition
nance or unprepared
competition wit
mainte-
wit
(not
C—flat
C—flat ice surface
iceC—flat
ice surface
C—flat surfaceice suitable for play) with
C—flat ice surface without maintenance
nancesuitable
or unprepared
nance
for
nance or
play)
or(not
unpre
unpre
surface nance or unpre
or unprepared (notplay)
suitable for suitable fo
suitable fo
suitable for play) suitable fo
2. Measurements
2. Measurements
2.2.1. Method
Measurements
2.1. Method
A 2.
2. Measurements
2.MEMS
Measurements
Measurements
(microelectromechanical system) inertial measurement unit (IMU) with a
Despite the2.1. Method
important
A MEMS influence of ice conditions on game
(microelectromechanical result, curlersunit and(IMU)
ice with a
3-axis2.1. Method
accelerometer
2.1. Method was attached to thesystem) stone’s inertial
handle measurement
(Figure 1). The stone must have
technicians lack abeen
3-axisA2.1.
measurement
MEMS Method
accelerometerdevice was that would
(microelectromechanical
attached to objectively
system)
the stone’s measure
inertial
handle the
measurement
(Figure quality
1). The of
unit ice
(IMU)
stone to
mustwith
havea
cooled down before the experiment to avoid ice damage and produce reliable results.
3-axis
been
ensure a fair game. cooled
This A
A MEMS
accelerometerMEMS
down
research
A aMEMS (microelectromechanical
(microelectromechanical
was
before
aims attached
the
to to
experiment
investigate the stone’s
to avoid
whether system)
system)
handle
ice andamage inertial
inertial
(Figure
and
accelerometer1). measurement
measurement
The
produce stone must
reliable
attached unit
unit
have
results. (
That is why regular(microelectromechanical
stone handle was replacedsystem) inertialwith
with a handle measurement
IMU attached. unitA(
been
That
to the stone handle and 3-axis
cooled
3-axis
is why
data accelerometer
down
a before
accelerometer
regular
processing the
stone was
handle
software attached
experiment
was attached
was
can to to
avoid
to the
ice
the
replaced stone’s
damage
stone’s
with a handle
and
handle
handle produce
with(Figure
(Figure
IMU 1).
reliable
1). The
The
attached. ston
results.
ston
A
curler 3-axis
was accelerometer
asked to deliver wasstone
the bybe
attached used
to theto
playing differentiate
astone’s
draw handle
shot. Thebetween
(Figure the
1). Thewere
measurements ston
That
curler isbeenwhycooled
was a regular
asked down
to stone
deliverbefore
handle
the the
thewas
C).stone experiment
replaced to
awithavoid ice
a handle damage
with IMUand produce
andattached. Are
three abovementioned
saved been
been
in cooled
structures
cooled
IMU’s down
(A,
down
memory before
B, and
before
and the
copied tobyPC playing
experiment
experiment todraw
to
for analysis avoid
avoid shot.
uponice The
icemeasurement
damage
damage measurements
and produce
produce were
completion. re
re
curler
saved was
in
That
That is asked
IMU’s
is why
is why
why to
memory
adeliverand
regular the stone
copied
stone by
to playing
PC
handle for a draw
analysis
was shot.
upon
replaced The measurements
measurement
with a handle were
completion.
with IMU
The device
That was aa regular
attached regular stone handle
to the stone handle
horizontal, waspart
bottom
was replaced withhandle
of the stone
replaced with aa handle
handle with
usingwith IMU
wooden
IMU
saved
The devicein IMU’swas memory and copied to PCstone
for analysis upon measurement completion.
2. Measurements blocks curler
curler
(glued
curler toattached
was
was
was asked
asked
the to
handle)
asked tothe
to
to
horizontal,
deliver
deliver
and the
screws.
deliver
bottom
theAstone
the stone
similar by part
bymethod
by
of
playing
playing
playing
the
was stone
aaa used
draw
draw
draw
handle
shot.
shot.
inshot. using
The wooden
measur
Theresearch
previous
The measur
measur
The
blocksdevice
saved was
(glued in attached
to the
IMU’s to
handle) the
memory horizontal,
and screws.
and A bottom
copiedsimilar
to part of
method
PC forthe stone
was
analysisusedhandle
in
upon using
previous wooden
research
measurement
2.1. Method saved in IMU’s memory and copied to PC for analysis upon measuremen
blockssaved (gluedin to IMU’s
the handle)memory and copied
and screws. A similar to method
PC for was analysis
used in upon measurement
previous research
The device
The device was
device was
A MEMS (microelectromechanical
The attached
was attached
attached
system)to
to the horizontal,
to inertial
the horizontal,
the horizontal, bottom part
bottomunit
measurement
bottom of the
part(IMU)
part of the
of stone
the with handle
stoneahandle
stone u
handle u
u
blocks
blocks
3-axis accelerometer was (glued
attached
blocks (glued to
(glued to
to the
to the
the handle)
the stone’s
handle) and
handle)handle
and screws.
and screws.
screws. A similar
A similar
(Figure
A similar method
method
1). The method was used
washave
stone must
was in
used in
used prev
in prev
prev
been cooled down before the experiment to avoid ice damage and produce reliable results.
That is why a regular stone handle was replaced with a handle with IMU attached. A curler
was asked to deliver the stone by playing a draw shot. The measurements were saved in
IMU’s memory and copied to PC for analysis upon measurement completion. The device
was attached to the horizontal, bottom part of the stone handle using wooden blocks (glued
2). The character of vibration depends on the structure of the ice surface. Dur
bling,During
water droplets
its travelare
on sprayed on bottom
the ice, the the flat ice surface.
of the They
curling are touches
stone not uniform
the t
pebbles are formed taller and some are shorter. If a stone
and not the flat ice surface below pebbles (Figure 3). This fact makes thetravels on such pebb
and notthe
during onmotion,
nipped andice surfaces, it onlyiscomes
this vibration measuredin contact
in the with the tallest pe
experiment.
Sensors 2022, 22, 1074 3 of 13
nipping tops of pebbles, their height is much more uniform; thus, the stone r
The character of vibration depends on the structure of the ice surface. D
face hits much more pebbles. Hence, we propose a hypothesis that the spectr
bling, water droplets are sprayed on the flat ice surface. They are not unifor
tovibration
the handle)shifts towards
and screws. higher
A similar frequencies
method on nipped
was used in previous icebycompared
research authors [20].to fresh
pebbles are formed taller and some are shorter. If a stone travels on such pe
ice. weighs 80 g, which is omittable compared to the weight of a curling stone (20 kg).
IMU
and not on nipped ice surfaces, it only comes in contact with the tallest
nipping tops of pebbles, their height is much more uniform; thus, the ston
face hits much more pebbles. Hence, we propose a hypothesis that the spe
vibration shifts towards higher frequencies on nipped ice compared to fr
ice.
Figure
Figure 1. Curling
1. Curling stone stone with
with IMU. IMU.
In this experiment, the sampling frequency of IMU was set to 400 Hz. The sampling
frequency was chosen based on IMU bandwidth (550 Hz). Collected acceleration samples
were analyzed in the time and frequency domain (which is described in the next paragraph).
In this experiment, the X-axis was defined as parallel to the curling sheet length,
pointing from the start point to the target. The Z-axis was defined as pointing downward,
Figure
and 1. Curling
the Y-axis stoneaccordingly
was defined with IMU. to obtain a left-handed coordinate system (Figure 2).
Figure 2. Axes as defined in the experiment.
Figure
Figure 2. Axes
2. Axes as defined
as defined in the experiment.
in the experiment.
During its travel on the ice, the bottom of the curling stone touches the tops of pebbles
and not the flat ice surface below pebbles (Figure 3). This fact makes the stone vibrate
during the motion, and this vibration is measured in the experiment.
• Power system;
• Microcontroller;
• Data storage;
Sensors 2022, 22, 1074
•
Sensors 2022, 22, x FOR PEER REVIEW Sensors. 4 of 13
4 of 1
A block diagram of the device is presented in Figure 4. An Inert
produced by Analog Devices (ADIS 16467) was used in this experim
sensors: a triaxial accelerometer (range ±40 g) and a triaxial gyros
with temperature correction. These sensors have their own signal co
tocalibration procedures, and dynamic compensation formulas, en
sensor specifications [21]. The signal of both gyroscope and thermo
as well but were not considered in detailed research. A gyroscop
Figure3.3.Curling
Figure
choose Curling
the stone
stone
right traveling
traveling
part on pebbles
of on
the (not in
pebbles scale).
(not
accelerometer The local
in scale). The coordinate system rotates
local coordinate
signal for system
further withrotates wit
analysis
the
thestone.
stone.The
Theglobal
globalcoordinate
coordinate system is pictured
system above above
is pictured and is tied
andtoisthe
tiedsheet of ice.
to the sheet of ice.
A microSD card is used for data storage. Saved data are acce
The character of vibration depends on the structure of the ice surface. During ice
connection.
2.2. Hardware The data
pebbling, water droplets are saved
are sprayed on the flatin icebinary
surface. Theyformat;
are notthus,
uniform;an thus,additio
some The
decryption device
pebbles arewasuseddeveloped
formed intaller
the and
experiment
some was
byarethe developed
authors.
shorter. by
If a stoneIts authors
taskonis
travels and
such consists
topebbled
convert of th
fou
surfaces and not on
main functional nipped ice surfaces, it only comes in contact with the tallest pebbles.
blocks:
the
Aftermemory
nipping topscard intotheir
of pebbles, a human-readable
height is much more uniform; CSVthus, file.the stone running
• Power system;
surfaceThe primary
hits much more pebbles.energy Hence, source
we propose of athe device
hypothesis that is
the a lithium
spectrum polymer
of stone
• Microcontroller;
vibration shifts towards higher frequencies on nipped ice compared to freshly pebbled ice.
1300
• mAh
Data capacity. The device can be recharged using a standard
storage;
• Hardware
2.2. Sensors. is also used for data transfer from the PC. The micr
connector
The device
A block used in of
diagram thethe
experiment
device is was developed
presented by authors
in Figure 4. Anand consists
Inertial of four
Measurement Un
STM32F4
main functional family
blocks: is based on ARM architecture and is manufactured
produced by Analog Devices (ADIS 16467) was used in this experiment. IMU features tw
ics. It isa responsible
•sensors:
Power system;
triaxial accelerometer for the main
(range ±40loop g) andimplementation—sensors
a triaxial gyroscope (range ±500 re °/s
•
withMicrocontroller;
age. temperature correction. These sensors have their own signal conditioning paths, au
• Data storage;
•
tocalibration procedures,
Acceleration
Sensors.
and dynamic
signal has already compensation formulas, ensuring
been observed that datarese
in previous mee
sensor specifications [21]. The signal of both gyroscope and thermometer were recorde
AThe
block most
diagramcritical
of the devicemetrological
is presented in Figureparameters
4. An Inertial ofMeasurement
the developed Unit me
as well but were not considered in detailed research. A gyroscope signal was used t
produced by Analog Devices (ADIS 16467) was used in this experiment. IMU features two
presented
choose the
sensors: in accelerometer
right
a triaxial Table
part of the2.accelerometer
The
(rangechosen
±40 g)signal
and IMU for chip
further
a triaxial assures
analysis.
gyroscope (range a ±high
500 ◦ /s)level o
A microSD correction.
measurements
with temperature cardof istheused for sensors
stone
These data
forstorage.
a have
single Saved
their throw.
own data are accessible
It also
signal through
paths, a USa
has immunity
conditioning
connection. The
autocalibration data areand
procedures, saved
dynamicin binary format;formulas,
compensation thus, anensuring
additional program
that data meet for dat
load
sensor
caused
specifications
decryption
by a stone
[21]. The signal
was developed
hitting
by the
the
of authors.
ice
both gyroscope
or
Its task
other objects.
andisthermometer
to convert were
With
recorded
the binary
a resolut
fileassaved o
16,467
well accelerometer
but were
the memory not
card considered inhas typical
detailed
into a human-readable research.
CSVsensitivity
gyroscope of
Afile. 1.9was
signal × 10used g/LSB
−8 to choose (Leas
the right part of the accelerometer signal for further analysis.
The primary energy source of the device is a lithium polymer single-cell battery o
1300 mAh capacity. The device can be recharged using a standard micro USB port. Th
connector is also used for data transfer from the PC. The microcontroller from th
STM32F4 family is based on ARM architecture and is manufactured by STMicroelectron
ics. It is responsible for the main loop implementation—sensors readings and data sto
age.
Acceleration signal has already been observed in previous research [20].
The most critical metrological parameters of the developed measurement device ar
presented in Table 2. The chosen IMU chip assures a high level of accuracy for inertia
measurements of the stone for a single throw. It also has immunity against potential ove
load caused by a stone hitting the ice or other objects. With a resolution of 32-bit, the ADI
16,467 accelerometer has typical sensitivity of 1.9 × 10−8 g/LSB (Least Significant Bit).
Figure 4. Block diagram of the device used in the experiment.
Figure 4. Block diagram of the device used in the experiment.
A microSD card is used for data storage. Saved data are accessible through a USB
connection. The data are saved in binary format; thus, an additional program for data
decryption was developed by the authors. Its task is to convert the binary file saved on the
memory card into a human-readable CSV file.
The primary energy source of the device is a lithium polymer single-cell battery of
1300 mAh capacity. The device can be recharged using a standard micro USB port. This
Figure 4. Block diagram of the device used in the experiment.
Sensors 2022, 22, 1074 5 of 13
connector is also used for data transfer from the PC. The microcontroller from the STM32F4
family is based on ARM architecture and is manufactured by STMicroelectronics. It is
responsible for the main loop implementation—sensors readings and data storage.
Acceleration signal has already been observed in previous research [20].
The most critical metrological parameters of the developed measurement device are
presented in Table 2. The chosen IMU chip assures a high level of accuracy for inertial
measurements of the stone for a single throw. It also has immunity against potential
overload caused by a stone hitting the ice or other objects. With a resolution of 32-bit, the
ADIS 16,467 accelerometer has typical sensitivity of 1.9 × 10−8 g/LSB (Least Significant Bit).
Table 2. Selected metrological parameters of IMU ADIS16467 [21].
Parameter Value
ACCELEROMETER
Range 40 g
Sensitivity 52,428,800 LSB/g
In run bias stability 13 µg
√
Velocity random walk 0.037 m/s/ h
GYROSCOPE
Range 500 ◦ /s
Sensitivity 40 LSB/◦ /s
In run bias stability 2.5 ◦ /h
√
Angular random walk 0.15 ◦ / h
The firmware used in the microcontroller was developed by the authors in C pro-
gramming language. The main task of the firmware is to record the data. After interfaces
and modules initialization, the main loop of the program is started. Data from sensors are
read every 2.5 ms (to achieve 400 Hz sampling frequency) and buffered in RAM. Every
second, buffered data are written to a file on an SD card. The file can be read on a PC using
a standard socket. Data processing was performed on a PC using MATLAB software.
3. Results
Measurements were taken at Curling Łódź, a state-of-the-art four-sheet curling rink
located in Łódź, Poland. The stone used during the experiment came from one of the
Olympic sets that are used in all top-level competitions around the world. During a training
session, a competitive curler was asked to deliver the stone with IMU. No mechanical
device was used for stone delivery.
Results obtained with the accelerometer during the movement of a curling stone are
presented in Figure 5 (in the time domain). Actual stone movement is contained between
two vertical red lines. Before that period, the player delivered the stone, and afterward, the
stone stood still on the ice.
Three periods mentioned above are clearly visible in gyroscope data, presented in
Figure 6. Each shot had an initial angular velocity in the range of 50–100 ◦ /s. During most
of the curling shot, angular velocity decreases slightly, and most of the angular velocity is
lost in the last 0.25 s. Lozowski observed similar behavior [22].
Sensors 2022, 22, x FOR PEER REVIEW
Sensors 2022,
Sensors 22,22,
2022, x 1074
FOR PEER REVIEW 6 of 13 6
Figure
Figure
Figure 5.5.
5. Results
Results
Results obtained
obtained
obtained with
with
with the the accelerometer
the accelerometer
accelerometer in the
in the time
in the time domain (ftime domain
domain
s = 400 (f(fs s=is
Hz). X-axis =400
400Hz).
Hz).X-axis
horizontal X-axisis
zontal
zontal
and and parallel
andtoparallel
parallel the longerto the longer
to dimension dimension
the longerofdimension of the
of the
the curling sheet, curling
curling
and sheet,
sheet, and
Y is horizontal and
and YY is horizontal
is horizontal
perpendicular and
to and perp
X, perpe
ular
ularZto
and toX,
X,isand
axis and ZZ axis
axis is
vertical. is vertical.
vertical.
Figure 6. Results obtained with the gyroscope in the time domain (fs = 400 Hz).
Figure
Figure 6.6.Results
Results obtained
obtained withwith the gyroscope
the gyroscope in the
in the time time
domain (fsdomain
= 400 Hz).(fs = 400 Hz).
aX was analyzed in the frequency domain after Fourier transform (FFT algorith
aX was analyzed in the frequency domain after Fourier transform (FFT algorit
MATLAB) was performed on it. Figure 7 presents the spectrogram of aX. The obta
MATLAB) was performed on it. Figure 7 presents the spectrogram of aX. The ob
spectrum does not change rapidly during the middle part of curling stone movement.
spectrum does not change rapidly during the middle part of curling stone movemen
can observe fading of the signal during the last 5 s both in the frequency domain an
Sensors 2022, 22, 1074 7 of 13
The measuring device was rotating with the stone itself; thus, to obtain acceleration par-
allel to the length of a curling sheet, gyroscope data was used according to Equations (1)–(3):
aX = ax cos α + ay sin α, (1)
aY = −ax sin α + ay cos α, (2)
aZ = az , (3)
where x, y, z are defined in the measuring device coordinate system, and X, Y, and Z are
defined in the ice sheet coordinate system. α is the angle between X and x.
ensors 2022, 22, x FOR PEER REVIEW a was analyzed in the frequency domain after Fourier transform (FFT algorithm in
X
MATLAB) was performed on it. Figure 7 presents the spectrogram of aX . The obtained
spectrum does not change rapidly during the middle part of curling stone movement.
One can observe fading of the signal during the last 5 s both in the frequency domain
and in thespectrum.
signal time domain. It In further
is clear analysis,
that wethewill use a signal
signal portionon
obtained from the middleice has
pebbled
of a shot. Figures 8–10 present the spectrum of horizontal parallel acceleration obtained
frequency
during region
a 5-second periodof 80–100
(2000 samples)Hzand
than the signalfit.recorded
its polynomial on flat
The polynomial ice. Gene
degree
of 9,the
was andspectrum depends
it was fitted using the leaston icemethod
square quality. Three
to provide polynomial
a smoothed version fits
of theare pre
signal spectrum. It is clear that the signal obtained on pebbled ice has more power in the
Figure 11. The proposed physical explanation is that the stone hits on
frequency region of 80–100 Hz than the signal recorded on flat ice. Generally, the character
ofbles on freshly
the spectrum pebbled
depends ice. These
on ice quality. Three pebbles
polynomialare fits not as common.
are presented togetherAfter
in nip
Figure 11. The proposed
are struck by the physical
rock asexplanation
pebble isheight
that the is
stone
morehits only the highest
uniform, andpebbles
the accele
on freshly pebbled ice. These pebbles are not as common. After nipping, more pebbles
towards
are struck by higher
the rock asfrequencies.
pebble height isThe
moresignal
uniform,is much
and weakersignal
the acceleration on flat ice as h
shifts
not happen.
towards higher frequencies. The signal is much weaker on flat ice as hitting pebbles does
not happen.
Figure 7. Spectrogram of obtained accelerometer signal. The used window length is 1 s, and window
Figure 7. Spectrogram of obtained accelerometer signal. The used window leng
overlap is 75%.
overlap is 75%.
Sensors 2022, 22, 1074 Figure 7. Spectrogram of obtained accelerometer signal. The used window length is 1 s, and window
8 of 13
overlap is 75%.
Sensors 2022, 22, x FOR PEER REVIEW 8 of 13
Sensors 2022, 22, x FOR PEER REVIEW 8 of 13
Figure
Figure8.8.Results
Resultsobtained
obtainedwith
withthethe
accelerometer onon
accelerometer freshly pebbled
freshly iceice
pebbled (frequency domain).
(frequency domain).
Figure 9. Results obtained with the accelerometer on pebbled and scraped ice (frequency domain).
Figure 9. 9.
Figure Results obtained
Results with
obtained thethe
with accelerometer on on
accelerometer pebbled andand
pebbled scraped ice ice
scraped (frequency domain).
(frequency domain).
Figure
Figure10.
10.Results
Resultsobtained
obtainedwith
withthe
theaccelerometer
accelerometerononflat
flaticeice(frequency domain).
(frequency domain).
Figure 10. Results obtained with the accelerometer on flat ice (frequency domain).
Signal acquired during a curling shot must be compared to the sensor’s noise. Figure
Signalthat
12 shows acquired during aofcurling
the spectrum shot must
the sensor’s noisebe(acquired
compared to the
when sensor’s
the sensor noise.
was notFigure
mov-
12 shows that the spectrum of the sensor’s noise (acquired when the sensor was
ing) is about 40–50 dB lower than the spectrum of the signal obtained during a curling not mov-
ing)
shot.isItabout
shows40–50
that dB
the lower
naturethan the
of the spectrum
observed of the
signal signal obtained
is directly during
tied to the a curling
movement of a
shot. It shows
curling stone. that the nature of the observed signal is directly tied to the movement of a
calculations were performed on a linear scale and converted to decibels afterward. The
Sensors 2022, 22, x FOR PEER REVIEW
range 9 of 13
of parameter values for different types of ice do not overlap within one standard
Sensors 2022, 22, 1074 deviation. 9 of 13
calculations were performed on a linear scale and converted to decibels afterward. The
range of parameter values for different types of ice do not overlap within one standard
deviation.
11. Three
Figure 11.
Figure Threepolynomial
polynomialfitsfits
(from Figures
(from 8–10)8–10)
Figures presented on oneon
presented chart.
one chart.
Signal acquired during a curling shot must be compared to the sensor’s noise. Figure 12
shows that the spectrum of the sensor’s noise (acquired when the sensor was not moving)
is about 40–50 dB lower than the spectrum of the signal obtained during a curling shot.
Figure 11. that
It shows Three polynomial
the nature of fits
the(from Figures
observed 8–10)ispresented
signal on one
directly tied chart.
to the movement of a
curling stone.
Figure 12. Signal acquired during a curling shot compared to acceleration sensor’s noise (frequency
domain).
Table 3. The results of Lilliefors normality test for obtained data sets.
Figure 12.
Figure 12.
TypeSignal
Signalof acquired
acquired
Ice during during a curling
a curling
Freshly shot compared
shotPebbled
compared to to acceleration
acceleration
Ice Pebbled sensor’s
and noise sensor’s
(frequency
Scraped noise
Ice (frequency
domain).
Flat Ice
domain).
p-value
In order to compare spectra and types 0.36of ice objectively, parameter0.48 R was introduced.0.25
Critical
It is defined
Table 3. The as
value
follows.
results
0.16
of Lilliefors normality test for obtained data sets.
0.16 0.16
Test decision for the null
Type R of
[dB] not
− P80
Ice= P120 [dB]Freshly rejected
[dB] = P (120Ice
Pebbled [dB] − P
Hz) Pebbled not
(80rejected
andHz) [dB], Ice not
Scraped (4)rejected
Flat Ice
hypothesis
R wasp-value 0.36
calculated for 30 curling shots 0.48obtained sample set0.25
on each type of ice, and each
Critical value 0.16
was tested for normality using the Lilliefors test in MATLAB. In order0.16to perform the test,0.16
Test decision for the null
not rejected not rejected not rejected
hypothesisSensors 2022, 22, 1074 10 of 13
data were converted back to a linear scale (instead of using results expressed in dB). The
significance level was set to 0.05, and the null hypothesis stated that the dataset was normal.
The Lilliefors test proved that obtained datasets might be treated as normal distributions
(see Table 3). Thus, parametric measures will be used to describe the data. The obtained
results are presented in Table 4 and Figure 13. Mean and standard deviation calculations
were performed on a linear scale and converted to decibels afterward. The range of
parameter values for different types of ice do not overlap within one standard deviation.
Table 3. The results of Lilliefors normality test for obtained data sets.
Type of Ice Freshly Pebbled Ice Pebbled and Scraped Ice Flat Ice
Sensors 2022, 22, x FOR PEER REVIEW 10 of 13
p-value 0.36 0.48 0.25
Critical value 0.16 0.16 0.16
Test decision for the
Tablenull
4. Values notinrejected
of parameter R not rejected
various ice conditions. not rejected
hypothesis
Freshly Pebbled Pebbled And Scraped
Type of Ice
Table 4. Values of parameter R in various ice conditions.
Flat Ice
Ice Ice
R mean value—standard
Type of Ice Freshly Pebbled Ice Pebbled and Scraped Ice Flat Ice
−2.14 dB 1.59 dB 4.68 dB
deviation
R mean
−2.14 dB 1.59 dB 4.68 dB
R mean value
value—standard deviation −1.32 dB 2.84 dB 5.72 dB
R mean R value
mean+value
standard −1.32 dB 2.84 dB 5.72 dB
−0.57 dB 3.94 dB 6.65 dB
deviation
R mean value +
−0.57 dB 3.94 dB 6.65 dB
standard
Number of deviation
shots 30 30 30
Number of shots 30 30 30
Figure13.
Figure 13. Histogram ofRRparameter
Histogram of parameterforfor
different types
different of iceofand
types icevarious shots. shots.
and various
In order to compare three obtained distributions, a Welch t-test was performed in
In order to compare three obtained distributions, a Welch t-test was performed in
MATLAB with a null hypothesis that each pair of dataset came from distributions with
MATLAB with values.
different mean a null hypothesis that each
The significance pair set
level was of dataset cametest
to 0.05. The from distributions
proved that the with
different mean values. The significance level was set to 0.05.
datasets came from three distributions with different mean values. The test proved that the da-
tasets came from three distributions with different mean values.
Stability of Results within Curling Shot
The presented accelerometer results allow one to determine whether curling ice isSensors 2022, 22, 1074 11 of 13
Stability of Results within Curling Shot
The presented accelerometer results allow one to determine whether curling ice is
suitable for play. However, how parameter R changes with time during a curling shot must
also be analyzed. The values of R calculated for different parts of one curling shot per ice
type of ice are presented in Table 5. The parts are 5 s periods (2000 samples) starting at
different time points during the stone’s journey. The value of R does vary within each shot,
but it never leaves the region associated with the particular type of ice (Figure 14).
Table 5. Values of R parameter for different parts of one curling shot.
R on Freshly Pebbled Ice R on Pebbled and Scraped Ice R on Flat Ice
shot 1, part 1 −1.36 dB 2.01 dB 5.66 dB
shot 1, part 2 −2.07 dB 1.81 dB 5.12 dB
Sensors 2022, 22, x FOR PEER REVIEW shot 1, part 3 −1.56 dB 2.22 dB 6.27 dB
shot 1, part 4 −1.81 dB 1.03 dB 4.62 dB
shot 1, part 5 −2.18 dB 2.34 dB 4.47 dB
14. Histogram
Figure 14.
Figure Histogram of R
ofparameter for different
R parameter parts of one
for different curling
parts shot.
of one curling shot.
4. Discussion
4. Discussion
Several scientific papers in the field of curling try to explain the mechanism that
induces a curl scientific
Several (lateral motion) in the
papers instone
the [2,3,5–13,19,23,24];
field of curling moreover, the papers
try to explain the attempt
mechanism t
to analyze the effect of sweeping on the stone motion [25–27]. However, to
duces a curl (lateral motion) in the stone [2,3,5–13,19,23,24]; moreover, the papers a the authors’
best knowledge, no attempt has been made to develop a method to assess curling ice
toquality
analyze the effect of sweeping on the stone motion [25–27]. However, to the au
objectively.
best knowledge, no attempt
Inertial measurement units has beeninmade
are used sportsto develop a method
measurements to assess
[28–30]. IMU mounted curling ic
ity objectively.
to the handle of a curling stone was previously used by Lozowski [22]. However, in that
research study,
Inertial the IMU was used
measurement unitsto measure
are used theinmacroscopic movement of a[28–30].
sports measurements stone, andIMU mo
vibrations (resulting from the interaction of stone and ice) were filtered out and were not
to the handle of a curling stone was previously used by Lozowski [22]. However,
analyzed. Lozowski compared the obtained results with a numerical model of curling
research study,
ice friction the IMU
and dynamics was used
published to measure
in [23] the macroscopic
and demonstrated movement
that the “ordinary of a ston
friction”
vibrations (resulting from the interaction of stone and ice) were filtered out and we
analyzed. Lozowski compared the obtained results with a numerical model of curl
friction and dynamics published in [23] and demonstrated that the “ordinary fr
model is unable to predict any curl (lateral motion of the stone). Lozowski observeSensors 2022, 22, 1074 12 of 13
model is unable to predict any curl (lateral motion of the stone). Lozowski observed similar
behavior of stone’s angular velocity as presented in Figure 6 (slow deceleration for most of
the curling stone’s movement and rapid deceleration at the end). This manuscript presents
a different, novel approach of using an IMU to analyze the vibrations of a curling stone.
In this manuscript, a new, objective acceleration-based method was proposed to assess
curling field of play (ice) quality during the curling competition. The procedure is based on
signal analysis from the accelerometer attached to the handle of a moving curling stone.
In the studies, it was found that the sensor signal acquired during a curling shot is about
40–50 dB higher than the sensor’s noise. It confirms that IMU range and resolution was
correctly selected, and results of short-time analysis of signal frequency spectra could be
used to characterize curling stone vibration during movement. Parameter R was proposed
to characterize the ice state (freshly pebbled, pebbled and scraped, and flat). Changes in
R-value can be used to monitor the quality of ice during curling competitions continuously.
It was also confirmed that the value of R is stable for the all stone movements during a draw
shot and does not vary significantly between repeated attempts on the same ice conditions.
The experiments were conducted only on one rink. Further research is necessary to
determine whether the absolute value of R varies from one ice rink to another. If confirmed,
a correction formula on R-value should be elaborated (e.g., a new reference frequency set
for calculation of R value should be developed).
The method proposed in this manuscript may be easily applied by ice technicians and
players to evaluate the state of curing ice during competition and practice. It may indicate
whether the ice surface is suitable for the game and when it should be remade to assure
fair play. The method is fast, as curling stone delivery usually takes about 20–30 s and is
easy to apply. It could be used in between end breaks during a curling game (which lasts
for 1 to 5 min). The electronic recording device is small and light and does not change the
trajectory of a granite curling stone.
It is also worth considering extending the device functionality with wireless commu-
nication with PC (e.g., Bluetooth), improving sample transfer.
However, the proposed method also has some limitations. Most likely, it would not
be usable in an ice rink with high air humidity (e.g., without a dehumidifying system). In
such a case, water is condensed on the ceiling and then falls onto the ice as huge droplets,
changing the shape of the ice surface. It is also unknown how frost deposition on the ice
would influence results.
Author Contributions: Conceptualization, B.D. and J.W.; methodology, B.D. and J.W.; software, B.D.
and M.P.; validation, B.D.; investigation, B.D.; resources, M.P.; writing—original draft preparation,
B.D. and M.P.; writing—review and editing, B.D. and J.W.; visualization, B.D.; supervision, J.W. All
authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. World Curling Federation Rules of Curling. Available online: https://worldcurling.org/competitions/rules/ (accessed on 26
July 2021).
2. Kameda, T.; Shikano, D.; Harada, Y.; Yanagi, S.; Sado, K. The importance of the surface roughness and running band area on the
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