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CARDIFF SCHOOL OF SPORT
DEGREE OF BACHELOR OF SCIENCE
(HONOURS)
SPORT AND EXERCISE SCIENCE
TITLE: THE INFLUENCE OF LEG
DOMINANCE ON HEADING
PERFORMANCE IN ASSOCIATION
FOOTBALL
NAME: JAMIE WILLIAMS
UNIVERSITY NUMBER: ST09001847
NAME: JAMIE WILLIAMS
UNIVERSITY NUMBER: ST09001847
SCHOOL OF SPORT, SPORT & EXERCISE
SCIENCE
SPORT BIOMECHANICS
CARDIFF METROPOLITAN UNIVERSITY
THE INFLUENCE OF LEG DOMINANCE ON
HEADING PERFORMANCE IN
ASSOCIATION FOOTBALL
Cardiff Metropolitan University
Prifysgol Fetropolitan Caerdydd
Certificate of student
I certify that the whole of this work is the result of my individual effort, that all
quotations from books and journals have been acknowledged, and that the word
count given below is a true and accurate record of the words contained (omitting
contents pages, acknowledgements, indexes, figures, reference list and
appendices).
Word count:
Signed:
Date:
Certificate of Dissertation Tutor responsible
I am satisfied that this work is the result of the student’s own effort.
I have received a dissertation verification file from this student
Signed:
Date:
Notes:
The University owns the right to reprint all or part of this document.
TABLE OF CONTENTS
Page
LIST OF TABLES
LIST OF FIGURES
ACKNOWLEDGEMNETS
i
ABSTRACT
ii
CHAPTER ONE:
1.0 INTRODUCTION
1
1.1 Association Football
2
1.2 Success in Football
2
1.3 Coaching Heading
3
1.4 Biomechanics of Heading
4
CHAPTER TWO:
2.0 LITERATURE REVIEW
6
2.1 Heading Performance
7
2.2 Jumping with the Dominant and Non-Dominant Leg
8
2.3 Bilateral Differences within Football Players
9
2.4 Aims of the Study
10
2.5 Hypothesis
11
CHAPTER THREE:
3.0 METHODOLOGY
12
3.1 Participants
13
3.2 Protocol
13
3.3 Data Collection
13
3.4 Data Analysis
16
3.4.1 Kinetics
16
3.4.2 Kinematics
17
3.4.3 Quasi-Static Analysis
18
3.5 Statistical Analysis
20
CHAPTER FOUR:
4.0 RESULTS
22
4.1 Kinetics
23
4.1.1 Jump Height
23
4.1.2 Take-Off
23
4.1.3 Landing
25
4.1.4 Correlations
26
4.2 Kinematics
28
4.2.1 Angular Displacement
28
4.2.2 Angular Velocity
30
4.2.3 Joint Torque
32
4.2.4 Muscle Power
34
CHAPTER FIVE:
5.0 DISCUSSION
36
5.1 Ground Reaction Kinetics of Take-off
38
5.2 Ground reaction Kinetics of Landing
39
5.3 Kinematics
40
5.4 Summary
43
5.5 Delimitations
43
5.6 Limitations
43
5.7 Implications of the Study
44
5.8 Future Research
44
CHAPTER SIX:
6.0 CONCLUSION
6.1 Conclusion
REFERENCE LIST
APPENDICIES
Appendix A: Participant informed consent sheet
Appendix B: Raw data of participants
Appendix C: Filtering cut-off frequency
Appendix D: Anderson-darling test for normality result
46
47
48
LIST OF TABLES
Table
Title
Page
1.1
Coaching literature on how to head a football
4
3.1
Definitions of angles and segments
17
3.2
Correlation values and strength
20
4.1
Mean ± SD of performance variables for each trial for each
participant.
4.2
Mean ± SD of vertical (Fz) kinetic variables for each trial
for each participant
4.3
23
24
Mean ± SD of horizontal (Fy) kinetic variables for each
trial for each participant
25
4.4
Mean ± SD for vertical landing variables for each participant
25
4.5
Correlations of variables vs. jump height
26
4.6
Maximum values for flexion and extension of angular
28
displacement for the ankle, knee and hip between the DL
and NDL
4.7
Maximum values for flexion and extension of angular
30
velocity for the ankle, knee and hip between the DL and NDL
4.8
Maximum values for flexion and extension of joint torque for
32
the ankle, knee and hip between the DL and NDL
4.9
Maximum values for flexion and extension of muscle power
for the ankle, knee and hip between the DL and NDL
34
LIST OF FIGURES
Figure
Title
Page
1.1
The standing header and running jumping header
3
3.1
Protocol used in the study
13
3.2
Data collection set-up
14
3.3
Positions where CODA markers were placed on participants
15
3.4
Different phases of the running jump being analysed
16
3.5
Definition of angles
18
3.6
Quasi-static analysis and equations involved with calculations
19
4.1
Correlations of kinetic variables against jump height
27
4.2
Averaged time normalised graphs for angular displacement
29
of the ankle, knee and hip joints between the DL and NDL
4.3
4.4
Averaged time normalised graphs for angular velocity of the
ankle, knee and hip joints between the DL and NDL
31
Averaged time normalised graphs for joint torque of the ankle,
33
knee and hip joints between the DL and NDL
4.5
Averaged time normalised graphs for muscle power of the
ankle, knee and hip joints between the DL and NDL.
35
ACKNOWLEDGEMENTS
First of all I would like to thank my supervisor Dr.Gareth Irwin for his continued support
throughout this project and for putting up with my constant questioning and queries! Without
your advice and guidance completing this project would have been near impossible.
I would also like to thank the lads who participated in this study and the biomechanics staff
who helped out with collecting the data.
Finally, I want to thank my family and my housemates for keeping my spirits high when
things didn’t go so well and for helping to make this a fun dissertation to complete
Thanks everyone!
i
ABSTRACT
Leg dominance has been suggested to influence heading performance in association
football, knowledge of the affects of bilateral differences may be important to coaches and
the performer. The aim of the present study was to investigate leg dominance in footballers
and its influence on heading performance and the overall purpose was to examine the
biomechanics of jump strategy and how this affects jump height achieved. Six male national
league standard football players with a mean [±SD] age (20.3 ± 0.52 years), stature: (1.80 ±
0.39 m); and body mass: (73.33 ± 3.48kg) were chosen to participate in this study. Each
participant was instructed to perform six running jumping headers and take-off on one leg.
Three jumps were performed with their dominant leg and three with their non-dominant leg.
Eight active markers were placed on either side of the body to allow a full bilateral analysis
of the skill. This allowed for 3D joint centres to be calculated via the use of an automated
motion analysis (CODA) which was collected for a 5s period at 200Hz. Two Kistler force
plates allowed for kinetic variables and flight time to be calculated and kinetic data was
collected at 1000Hz, all of which were normalised to body weight. Kinematic and kinetic data
allowed for a quasi static approach to be utilised, estimating the muscle moments and
muscle power at the ankle, knee and hip joints. Parametric t-tests were used to test for
differences between the dominant and non-dominant leg, while a Pearson moment
correlation test was used to assess the relationships between jump height and the specific
kinetic variables. The use of an Anderson-darling test displayed that all data was normally
distributed and results displayed that participants were able to jump and header balls higher
by 0.062m (12.24%) when jumping off their non-dominant leg. The non-dominant leg also
displayed greater values for vertical and horizontal impulse during contact (22.7%, 15.2%),
peak vertical and horizontal force (8.6%, 14.9%), take-off velocity (16.1%) and flight time
(7.55%), all of which were significantly different (p ≤ 0.05). The ankle, knee and hip of the
non-dominant leg also displayed greater rates of extension for angular displacement (4.5%,
2.5%, 2.2%), angular velocity (48.9%, 2.3%, 7.1%), joint torque (20.2%, 7.9%, 1.7%) and
muscle power (57.1%, 22.8%, 18.7% respectively) at the latter stages of take-off (80-100%)
of take-off. Take-off velocity (r=0.80) and flight time (r=0.74) displayed the strongest
correlation with jump height. Performance increase for the non-dominant leg suggested that
the increased angular velocity and extensor power of the planter-flexors at the latter stages
of take-off had the greatest influence on the differences in jump height observed. The
increased horizontal impulse and take-off velocity of the non-dominant leg also contributed
to the performance increase and results suggest that footballers do exhibit bilateral
difference. Therefore coaches could focus on improving the strength of both legs equally so
players are not at a disadvantage when jumping for headers against other football players.
ii
CHAPTER ONE: INTRODUCTION
1
1.1 Association Football
Association football is the most popular sport worldwide and the sport was formalised by the
establishment of the Football Association in 1863 (Reilly, 1996). Association football is an
invasive game where eleven players from each team try to get a ball into the opposite’s goal.
The amount of goals scored in the game determines who the eventual winner is after 90
minutes in a game of football (Lago, 2009).
1.2 Success in Football
Due to the open nature of the game of football, success is determined by many factors.
Stolen et al. (2005) defined performance in football as the interaction of several factors, such
as the technical, tactical, physical and mental aspects of the game. Within the game of
football there are many individual game related skills which shape players level of technical
and skill ability which affects their overall performance (Bate, 1996). These skills include
passing, shooting, heading, dribbling, throwing and diving for goalkeepers. Decisions of
players of when and where to perform these game related skills accurately will determine
their level of skilled performance (Bate, 1996). Analysis of these game skills arise from
statistics that form throughout and after the game. Examples of these include: Number of
goals, shots on/off target, Total possession, amount of yellow/red cards etc. The majority of
these statistics form from the use of the lower extremities as the game itself primarily
involves using the legs to kick a football. However the use of the head in football cannot be
ignored.
Smodlaka (1984) stated that football players will head a football on average about six times
a game. Although six times may not seem a lot in a single game, it is reported that over a 15
year career the number of headers performed will rise to approximately 5250. Statistics
reported that Manchester United scored 78 goals in the 2010/2011 Barclaycard Premiership
season with 23% of these goals being headed goals. West Ham United also conceded the
most goals (70) with 21% of these being headed goals. Kenwynne Jones and Tim Cahill
were their clubs top scorers in the premier league with 9 goals each, 6 of them being headed
goals (Opta Stats, 2011). The statistics above highlight that heading is an important skill in
football. According to Sanchez (2002), once the fundamental importance of a skill has been
evaluated, classification of the skill is needed. Classification of the skill allows coaches to
inform players of the technical aspects of the skill and improve overall performance
(Sanchez, 2002).
2
1.3 Coaching Heading.
Heading a football was defined by Cappanna (2003) as a complex technical movement
which closely depends on physical-athletic abilities. Cappanna (2003) also stated that
technical mistakes in headers are quite common and result from movements which occur
before impact with the ball e.g. the run-up, take-off and flight phase. Therefore it would seem
logical that coaching players on how to header a ball correctly will improve overall football
performance, however within heading there are different types of headers as shown in
Figure 1.1 below
Figure 1.1. The standing header (a) and running jumping header (b). Reproduced from
Marcolin and Petrone (2006).
Table 1.1 below also displays the current coaching literature that is most commonly used
when coaching the standing and jumping header to football players:
3
Table 1.1 Coaching literatures on how to head a football.
Author
Type of header
Coaching points
Hargreaves &
Standing
Players heading the ball should:
Bate (2010).

Strike the ball rather than letting it hit them.

Form a good solid base with their feet and be
ready to anticipate any deviations of the ball.
Goldlbatt &
Standing

Acton (2009).
Use the eyes to direct the ball to the specific
target.

Extend the trunk prior to impact and flex post
impact with the ball to generate more force
Hargreaves &
Jumping with a run
Bate (2010).
up

Analyse the flight of the ball and time the jump
to head the ball at the highest possible

Use the arms to generate greater power in the
jump.
Bangsbo &
Jumping with a run
Pietersen
up
(2000).

Keep their neck and body muscles firm when
contacting the ball

Keep their eye on the ball and avoid closing
their eyes upon ball contact
The coaching literature above highlights the many points that are important for teaching
participants how to head a ball safely and correctly. However, to gain a greater
understanding of the technique of heading and more importantly improve the performance of
heading biomechanical analysis is needed.
1.4 Biomechanics of Heading
Lees and Nolan (1998) stated that to gain an understanding of the mechanical effectiveness
of skills in football we should identify factors that are essential for optimal performance. Lees
and Nolan (1998) also found that biomechanical modelling of soccer skills has helped inform
the underlying principles behind successful football performance.
According to Kirkendell et al. (2001) football is a unique sport due to the fact the head is
used to control an advancing ball, when the head is unprotected. Erkmen (2009) also stated
that heading is an integral part of football and is required for all levels of practice and
competition. To date the majority of research into heading has been concerned with the
consequences of heading and its effect on injury potential (Kirkendell et al., 2001; Matser et
al., 1998; Pickett et al., 2005; Smodlaka, 1984; Schneider & Zernicke, 1988; Thomas et al.,
4
1998) therefore there is a need to look at the performance aspect and the biomechanics of
heading.
Kirkendell et al. (2001) stated that to head the ball correctly, players should aim to hit the ball
with their forehead or near their hairline. Anything below may cause injuries to the face,
especially the nasal areas. Heading is an active motion and according to Ekblom (1994) the
movement itself is similar to a catapult e.g. there is a first movement, which is followed by a
countermovement. Figure 1.1 above displays that before ball contact the trunk is hyperextended and the chin is tucked in towards the chest e.g. the first movement. This is then
followed by flexion of the trunk after ball contact which represents the countermovement and
hence the catapult movement (Ekblom, 1994). Kirkendell et al. (2001) also stated that the
greater the trunk extension, the greater impact on the ball due to the forward increasing
velocity of the trunk. During the movement the arms are used to propel the player up by
swinging them back and forward to help raise the centre of mass and gain greater jump
height in the running jump header (Kristensen et al., 2004).
When jumping for a header the legs are generally slightly extended at the hip. In some cases
the knee is flexed in preparation for contact with another player (Kirkendell et al., 2001).
Ekblom (1994) stated that precise timing is needed for successful heading and movements
must happen in correct sequence. Firstly the hips are flexed in order to flex the trunk to bring
the whole upper body nearer the ball. The head and neck are then fixed by the neck
extensors and flexors, which produce a firm contact surface for the head. At the initial point
of contact with the ball, the neck muscles should contract isometrically to generate force on
the ball (Kirkendell et al., 2001). If the neck muscles are not contracted, it can lead to the
head being accelerated backwards and a strain on the neck flexors and extensors which
may cause injury (Kirkendell et al., 2001).
5
CHAPTER TWO: LITERATURE REVIEW
6
2.1 Heading Performance
From a performance perspective there is limited research into the skill of heading. Kirkendell
et al. (2001) highlighted that the lack of research into the skill may be due to the open nature
of football as there are many factors that can affect performance of the skill. The open nature
of football makes heading a difficult skill to perfect as most headers in a game situation are
performed under pressure and there is a variety of different positions a header can be
performed from in a game situation. These variations include heading a ball while running
backward or forward, diving, walking and jumping in all directions. Kirkendell et al. (2001)
defined the header as a coordinated series of mechanical events that result in the production
of one overall movement. These coordinated series of events may be the reason for the lack
of research into heading as quantifying performance parameters may be difficult.
A study by Thomas et al. (1998) used video based and kinematic analysis to quantify the
different types of headers evident in football. Kinematic analysis of the take-off, flight phase
and impact phase led to Thomas et al. (1998) classifying football heading into two
categories: a standing header or a jumping header and within both categories there are
three types of headers (shot, clear and pass). Another study by Kristensen (2002) also used
video based analysis and investigated the segmental characteristics of football heading and
found that skilled subjects were able to use their head as a free segment in the jumping
header and the angular momentum of the legs were high at impact. The study also found
that standardising the jumping header was difficult due to variations between each subject.
These individual variations included twisting of body parts during flight, velocity of the
football after impact and jump height. Following on from this study Kristensen et al. (2004)
looked at optimising the segmental movement in the jumping header and investigated the
effect of the body segments on the performance of the skill. Motion analysis and the use of a
biomechanical model revealed that arm movement during heading gave no advantages to
optimising ball speed after impact in the header. Another key finding of study was that the
use of legs was quantified as the most important factor of the skill. According to Kristensen
et al. (2004) strong contractions by the knee extensors and hip flexors facilitated angular
momentum of the upper body at impact and increased overall heading performance through
more powerful headers. Although the key finding of the studies by Kristensen (2002) and
Kristensen et al. (2004) the studies only looked at static jumping headers and failed to
evaluate the use of a running jump which Ekblom (1994) defined as the most common
format of heading.
7
The limited research into the running jump header led Marcolin & Petrone (2006) to evaluate
the performance of running jumping headers through a stereophotogrammetric system which
consisted of 6 infra-red cameras working at 60 Hz. Kinematic analysis of the jumping header
led to the skill being broke down into three key variables: jump height at take-off, incoming
ball velocity variation and initial ball angle after the impact with the forehead. Results of the
study found that jumping for a header with a run up generated most elevation and it was
possible to identify a maximum efficient heading elevation for each player due to the
elevation index created in the study. The elevation index created in the study may be useful
in comparing players ability to header high balls and evaluation of training methods.
However a limitation of the study was that ball angles of 15 degrees and above after contact
was deemed as an unsuccessful performance. In a real game situation a defensive header
may require lots of height e.g. a greater release angle than 15 degrees, therefore the study
might not be specific to real game situations.
Although all the above studies looked at different methods of evaluating heading
performance, all studies focused on the key aspect of heading that is ball impact during
heading. As stated by Kirkendell et al. (2001) heading is a series of co-ordinated events and
before impact comes the approach and take-off for running jump headers. The studies also
stated that the legs played an equally important role in heading as other body segments
during impact (Kristensen, 2002; Kristensen et al., 2004), however their effect on heading
performance before impact e.g. take-off has yet to be investigated. Ekblom (1994) also
stated that the most common format of a jumping header is when a run up is utilised and
players jump off one leg, most of the time their dominant leg. Therefore it seems logical to
look at the effect of jumping with the dominant and non-dominant leg e.g. the take-off phase
of heading.
2.2 Jumping with the Dominant and Non-Dominant Leg
Although there is limited research on jumping headers in football there is a lot of research
concerning jumping outside of football and more specifically jumping research with the
dominant leg (DL) and the non dominant leg (NDL). Within the research, findings have
generally tended to have mixed results. Stephens et al. (2007) conducted a study which
looked at the bilateral differences in double and single leg countermovement jumps. Results
from the study reported that there was a significant difference in jump height when
participants utilised their DL over their NDL (37.7cm ± 5.0 vs. 34.3cm ± 3.7 respectively).
The findings of the study by Stephens et al. (2007) agrees with the results of Newton et al.
(2006) and Yoshiokai et al. (2010) who also found that utilising the DL provided a significant
8
greater jump height. However this is in comparison to studies by Mcelueen et al. (2010),
Schutz et al. (2009) and Theoharpoulos et al. (2000) who found no significant differences in
jump height when participants used their DL and NDL to jump.
Although the studies above gained mixed results for jumping with the DL and NDL they all
share a common theme. All of the above studies did not use footballers as participants and
this may have affected the results of the studies as argued by Haaland and Hoff (2003)
below. According to Haaland and Hoff (2003) football players develop a DL and NDL which
represents their footedness due to the nature of the game e.g. kicking the ball. Menzel &
Simplico (2002) also stated that the unilateral demands of football e.g. kicking footballs with
one leg may cause bi-lateral differences as the majority of the time, kicking is done with the
player’s dominant or preferred leg. Although both studies don’t account for ambidextrous
football players there is the suggestion that footballers may have developed a DL due to the
unilateral demands of the game. Therefore the idea of footballers displaying a DL and
bilateral differences needs to be investigated.
2.3 Bilateral Differences within Football Players
In a football specific study by Sprattford et al. (2009) which examined the effect of using the
DL vs. NDL on diving in goalkeepers. Results reported a significant (p < 0.05) difference of a
27% quicker response to the ball when goalkeepers dived on their DL e.g. kicking leg.
Although a hanging ball was used for the study, which may have made the study less game
realistic and influenced the results the findings provide more insight into the suggestion that
footballers have developed a DL due to the nature of the game. Another study by Nunome et
al. (2004) investigated the effect of the DL and NDL on instep kicking in highly skilled
footballers and also found that the DL improved performance. The use of a threedimensional cinematographic and direct linear transformation (DLT) method found that the
DL produced greater angular velocity at the shank, higher ball velocities and a significantly
greater muscle moment. The study however only used right footed players and the effect of
instep kicking on left footed players was unaccounted for.
The results of the above studies are in comparison to a study by Silva et al. (2007) which
looked at the impulse production of DL and NDL in young soccer players. Results of the
study found no significant differences in impulse production between the DL and NDL ,
however a limitation of the study was that a young sample of football players was used
(mean age of 12.92 years). It could be argued that some of the sample may not have fully
developed limbs which may have compromised the results.
9
A study by Menzel et al. (2006) attempted to identify bilateral asymmetries of the lower limbs
in footballers through the use of force plates and isokinetic dynamometry. Results found that
there were no significant differences between the DL and the NDL for maximal ground
reaction forces (GRF). A limitation was the use of isokinetic evaluation used in the study.
Angular velocity was assumed as a constant for isokinetic dynamometry and this was a
major limitation as angular velocity during sporting movements varies constantly. (Menzel et
al., 2006). Another limitation of the study was the use of maximal ground reaction forces as
indicators of bilateral asymmetries. The authors later stated that the use of maximal power
output and impulse production, which were not used in the study are more reliable indicators
of bilateral asymmetries. A further study by Gstöttner et al. (2009) also found no significant
differences when investigating the effect of muscle response and balance function between
the DL and NDL.
All of the studies above have looked at limb dominance and bilateral differences in
footballers during a number of different skills and have reported contrasting results. However
the effect of limb dominance on the skill of heading and more specifically the take-off phase
of heading has yet to be investigated.
2.4 Aims of the Study
From the literature identified above, there is limited research on heading performance,
contrasting results on jumping and the idea that footballers may exhibit leg dominance due
to their kicking foot and the unilateral demands of the sport. Therefore the purpose of the
present study is to investigate leg dominance in footballers and its influence on heading
performance and more specifically to investigate the biomechanics of jump strategy and how
this affects the jump height achieved. The implications of the study could provide key
information to coaches as asymmetry in the lower limbs would be detrimental to football
performance and may cause injury. Coaches could change the focus of training on
improving player’s NDL or for players to jump for headers with their strongest limb. If leg
dominance is found, the findings of the study could be applied to other key skills in football
such as kicking, cutting and tackling to see investigate whether leg dominance exists in them
as well.
10
2.5 Hypothesis
The hypothesis of the present study is that participants jumping off their DL will achieve
greater jump height over jumping with their NDL and will display greater muscle moments at
the respective joints. Jumping off the DL will also display higher values for the kinetic
variables being analysed. The null hypothesis of this study is that participants jumping off
their NDL will achieve greater jump height over jumping with their DL and will display greater
muscle moments at the respective joints and kinetic variables values will be higher.
11
CHAPTER THREE: METHODOLOGY
12
3.1 Participants
Six Male first team University footballers all currently playing at national league level
participated in this study. The players had a mean [±SD] age (20.3 ± 0.52 years), stature:
(1.80 ± 0.39 m); and body mass: (73.33 ± 3.48kg). Participants had a reported playing
experience of (12.0 ± 1.41 years) and were all current members of the University first team.
Stature was measured using a Harpenden 602 Stadiometer (Holtain Ltd, Pembrokeshire,
UK) and body mass was measured using Seca 7701321004 digital scales (Seca, Hamburg,
Germany). Each participant completed an informed consent before the procedure (Appendix
A) which was approved by the Cardiff metropolitan university ethics committee. All
participants were given information sheets (Appendix B) with details of the procedure and all
had the right to withdraw from the study at any time. Full participation information can be
seen in appendix C.
3.2 Protocol
Participants warmed up for 5-10 minutes which consisted of light running and dynamic
stretches. This was done to increase body temperature and enhance free coordinated
movement of the participants. Participants performed three jumping headers off their DL and
three of their NDL and were instructed to attempt to head the hanging football (2.5m high)
from a 4.5 metre run-up. Before each trial participants indicated which foot they would be
using for the purpose of data analysis. Participants were instructed to jump off one leg on top
of one force plate and land on the other force plate as shown in Figure 3.1 below. This was
done so time flight time could be calculated by the force plates. If this was not done then the
jump was deemed invalid. Studies by Harrison & Mannering (2006) & Shinkai et al. (2006)
defined the dominant leg of their participants as their preferred kicking foot so this was also
used in the present study.
Figure 3.1. Protocol used in the study.
3.3 Data Collection
Data was collected at the National Indoor Athletics Center (NIAC). The NIAC Mondo
(Warwickshire, UK) track surface provided a solid, rigid flat surface in which to place the
13
CODA scanners. Anthropometric data was collected so that forces could be normalised to
body weight. Two Kistler 5233A (Kistler, Winterthur, Switzerland) force plates (sample rate:
1000 Hz) opposite each other were used to obtain ground reaction force profiles for each
jump. Both force plates were imbedded into the NIAC running track and measured 900mm
by 600mm. A Cartesian Optoelectronic Dynamic Anthropometer CODAmotion V6.78.2
(Charnwood Dynamics Ltd, Leicestershire, UK) motion analysis system was also used to
measure the kinematics of each jump, which consisted of four CODA marker scanners and
sixteen CODA markers. The full data collection set up can be viewed in Figure 3.2 below.
Although only the lower kinematics was being examined, sixteen markers (eight on each
side of the body) were placed to allow a bilateral analysis of the skill. The markers were
placed on the 5th metatarsal phalangeal joint (MTP) (distal), lateral malleolus of the ankle,
lateral epidcondyle of the knee, greater trocanter of the hip, acronium process (shoulder),
temporalis, lateral epicdondyle of the elbow and the lateral epicondyle of the wrist and is
displayed as Figure 3.3 below. A static net ball poll was also used to hang a football in and
was set at a standard height of 2.5m for each participant. Data was collected for a five
second period which allowed for the whole skill to be analysed. CODA analysis was
collected at 200Hz.
Figure 3.2. Data collection set-up.
14
Figure 3.3. Stick figure demonstrating marker locations placed on each participant.
15
3.4 Data Analysis
Figure 3.4. Different phases of the running jump being analysed.
The movement was split into the following phases: (a) approach, (b) touch-down, (c) takeoff, (d) flight phase and (e) landing. All analysis was focused on these phases as detailed
below. The rational for the phase separation was based on their functional role in the
successful performance of this skill.
3.4.1 Kinetics
In order for comparisons to be made between variables, key phases within the movement
were identified as shown in Figure 3.4 above. This was done to ensure that data obtained
from each phase originated from the same starting place for the movement. Once the skill
was broken down, comparisons were made from the three main phases of the skill;
touchdown - take off, flight phase and landing.
The vertical and horizontal force profiles (Fz) and (Fy) for each jump allowed for many
kinetic variables to be calculated. Peak Fz forces at take-off were identified as the highest
peak from the force time curves of each participant. Peak forces were split into two peaks;
active and passive. Novacheck (1998) defined the passive peak on a force trace as the first
visible peak during touchdown and is associated with the shock of contact with the ground.
The second peak was identified as the passive peak and is centred about phase absorption
and marks the end of deceleration and the begging of acceleration (Novcheck, 1998). Peak
Fz forces at landing were also calculated. Peak Fy forces of the braking force was calculated
by identifying the peak of the force trace during touchdown and take-off. From the peak
forces identified, loading rate was calculated by dividing the peak force by the time to peak
force for Fz and Fy forces (Hay, 1993). Impulse was also calculated by integrating the force
time curve, and more specifically the integral of the forces between touch-down to take-off
for each participant.
16
Flight time in the air was identified as the period between the instant of take-off and the
instant point of landing. The time for the point of take-off was identified as the point where
vertical forces dropped below 40N and the instant point of landing was identified when forces
surpassed 40N.
All kinetic variables were normalised to body mass and each data set was normalised to 100
points by linear interpolation. Each normalised data set was averaged over all participants
and all trials to provide a mean for each variable.
3.4.2 Kinematics
CODA motion analysis from the sixteen markers allowed for a seven segment model to be
analysed. Angles and segments are defined in Table 3.1 below
Table 3.1. Definitions of angles and segments
Variable
Angles
Ankle
Knee
Hip
Segments
Foot
Shank
Thigh
Trunk
Neck
Upper arm
Lower arm
Definition
The angle between the MTF CODA marker and the knee marker
The angle between the ankle CODA marker and the hip marker
The angle between the knee CODA marker and the shoulder marker
The segment between the MTF and the ankle
The segment between the ankle and knee
The segment between the knee and hip
The segment between the hip and shoulder
The segment between then shoulder and head
The segment between the shoulder and elbow
The segment between the elbow and wrist
For the purpose of the study the trunk was defined as a rigid segment and its origination
defined to the vertical. As no marker was placed on the hand, the wrist was assumed to be
at a fixed angle of 180º to the forearm. Angles of the ankle, knee and hip were defined as
the minor (i.e. flexion) angles at these joints. Flexion was defined as any joint angle closing
and extension was defined as any joint angle opening between 0º-200º and angles are
defined in Figure 3.5 below. All kinematic data was projected in the sagittal plane in order to
compute kinematic data.
17
Figure 3.5. Definition of angles
All kinematic data was filtered using a low pass filter (cut off frequency 11.5Hz, see Apendix
D). Cut off frequency was determined using residual analysis (Winter, 2005). Jump height for
each jump was quantified by calculating the hip marker displacement on the leg that was
used to jump with for each jump. Readings were taken at standing and at the peak of the
jump. The difference between standing and peak resulted in the height for each jump. Takeoff velocity was quantified as the velocity of the hip marker at the point of take-off for the leg
that was used to jump with. The hip marker was used for both these calculations as it
represented the closest approximation of the centre of mass (CM).
To determine angular displacement, angular velocity, muscle moment and muscle power,
data was collected for 0.4 seconds (400 points) before the instant point of take-off. Kinematic
data was extracted from CODA into Microsoft Excel to generate angular displacement,
angular velocity, joint torque and power graphs, all of which were time normalised. Angular
displacement was defined as a change in position (º) and was plotted against time to form
angular displacement graphs for the dominant and non dominant leg variables. Angular
velocities were also plotted against time and were defined as the rate of change of angular
displacement (rad.𝑠 −1 ) (Winter, 2005). Muscle moments and mechanical power graphs were
calculated via quasi-static analysis.
3.4.3 Quasi-static analysis
Based on the methods of Alexander & Vernon (1975) quasi-static analysis was used to
calculate approximate muscle moments at the ankle, knee and hip joints. According to
Winter (1990) providing muscle moment patterns gives valuable insight into the net effect of
all agonist and antagonist muscle activity. Figure 3.6 below briefly explains how muscle
moments were calculated.
18
The force plate was used to measure the centres of pressure, which was defined as Ay and
Ax. Robertson et al. (2004) defined the centre of pressure as the average location of for the
application of force and is expressed as coordinates (metres). The coordinates Ay and Ax
were measured along the y and x axis respectively.
Figure 3.6 Quasi-static analysis and equations involved with calculations. Adapted from
UWIC Blackboard.
To determine the muscle moment at each joint, ground reaction forces were multiplied with
the moment arm at each joint. The moment arm of the ankle was calculated by using the
following equations:

Fz moment arm (dyA) = (ay-Ay)

Fy moment arm (dzA) = (Az)

Moment of Fz about A = +(Fz*dyA)

Moment of Fy about A = +(Fy*dzA),
All four equations simplified left one final equation which represented the calculation for the
moment arm as shown below:
Ankle: MA= + (Fz* dyA) + (Fy* dzA)
19
The equations were also applied to the knee and hip and final calculations are represented
below respectively:
Knee: MK = + (Fz * dyK) + (Fy * dzK)
Hip: MH = + (Fz * dyH) + (Fy * dzH)
Extension muscle moments were presented as positive whereas flexion muscle moments
were negative. Muscle moments and muscle power were presented relative to the instant
point of take-off and data was collected for 0.4 seconds before the instant point of take-off.
Net mechanical power (MP) was calculated as the product of Muscle Moments (MM) and
angular velocity (ω) and is displayed as the equation:
MP = M x ω
According to Robertson et al. (2004) estimating mechanical power quantifies whether
muscles are being utilised to accomplish external work or used to absorb energy and
accelerate or brake the joint. Individual muscle moments and muscle power graphs were
plotted against time and the resulting graphs between the dominant and non dominant leg
were compared
3.5 Statistical Analysis.
All data was entered into a Microsoft excel spreadsheet for subsequent analysis and
interpretation. The SPSS 17.0 software package was used for statistical analysis. The mean
of all variables were calculated so that comparisons could be made between participants.
Vincent (1999) defined the mean as the statistical measure of central tendency that is the
average score of the group and is expressed by the equation below:
Mean- x=Σx/n
The standard deviation for each variable was also calculated and Vincent (1999) defined this
as an estimate of the variance within a set of data and is expressed by the equation below:
ndΣ=2σ
An Anderson-darling test was utilised to quantify whether all data was normally distributed. A
parametric dependant t-test was used to determine whether there was a statistical difference
between discrete variables in the DL vs. NDL and other key variables. A value of p< 0.05
was used to indicate statistical significance. Root mean square differences allowed for
comparisons to be made between wave forms of the angular displacement, angular velocity,
20
joint torque and power graphs. The root mean squared difference was expressed as a single
value and as a percentage of the range.
A Pearson correlation test was also used to examine the relationship between jump height
and discrete variables. Strength of correlation is denoted “r” and r values always lie between
1 and -1 (Fallowfield et al., 2005).
21
CHAPTER FOUR: RESULTS
22
4.1 Kinetics
Results of the Anderson darling test displayed that all concerning variables were normally
distributed (see Appendix E). This then allowed for parametric paired sample t-test to
examine the differences between variables for the DL and NDL. A Pearson moment product
correlation test was also used to assess the relationship between discrete variables and
jump height.
4.1.1 Jump Height
The mean ± standard deviation was calculated for three trials for each participant and results
displayed that jumping with the NDL yielded greater jump height in all six participants, all of
which were significantly different (p< 0.05) as illustrated in Table 4.1 below. Results
displayed an average increase in jump height of 0.062m (12.24%) for the NDL jump over the
DL. Accompanying the increase in jump height, jumping with the NDL also increased the
velocity of the CM at the instant of take –off and the flight time for each participant. Overall
velocity of the CM increased by 0.4m/s (16.10%) and all inter-participant differences were
significantly different with exemption to participant 5. Only participants 2 and 4 displayed
significant differences for flight time, however overall flight time was significantly different
and displayed an increased by 0.04s (7.55%).
Table 4.1. Mean ± SD of performance variables for each trial of all participants.
DL
NDL
Jump
TOVelocity
Flight time
Jump
TOVelocity
Height
CM
Height
CM
(m)
(m/s)
(s)
(m)
(m/s)
P1
0.53 ± .01*
2.43± .04*
0.51± .01
0.58 ± .01*
2.94± .12*
P2
0.51 ± .01*
2.67± .11*
0.55± .01*
0.57 ± .01*
3.00± .03*
P3
0.52 ± .02*
2.54± .31*
0.58± .02
0.59 ± .02*
3.03± .05*
P4
0.49 ± .02*
2.36± .16*
0.50± .01*
0.58 ± .02*
2.80± .17*
P5
0.47 ± .05*
2.48± .08
0.49± .02
0.52 ± .01*
2.63± .14
P6
0.51 ± .02*
2.49± .04*
0.56± .01
0.57 ± .02*
2.94± .07*
Flight time
(s)
0.56± .03
0.60± .01*
0.59± .01
0.56± .01*
0.51± .01
0.58± .01
Mean
0.505 ±. 23*
2.49± .11*
0.53± .03*
0.567 ± .23* 2.89± .15*
0.57± .03*
± SD
Note: *represents variables that were statistically significant p< 0.05. TO= Take-off. CM=
Centre of mass.
4.1.2 Take-off
Kinetic data and variables from the force plates were collected for three trials for each
participant and all data was normalised to body weight (BW). Table 4.2 below displays the
differences for vertical (Fz) kinetic variables between the DL and NDL during take-off. The
impulse created by the NDL at take-off was significantly greater than the DL and increased
by 0.05 BW.s (22.72%). Although the total mean difference was significantly different only
23
participant 1, 5 and 6 displayed individual significant differences. Peak force at take-off was
also greater for the NDL and was significantly different for participants 1 and 4. The mean
difference of all participants for peak Fz forces was significantly different and increased by
0.27BW (8.60%) for the NDL. The rate of force development (RFD) was also higher between
all participants for the NDL with exemption to participant 3 who elicited greater RFD for the
DL. Only participant 6 displayed a significant increase for the RFD on the NDL. Although no
average significant difference between the NDL and DL were observed, the RFD for the NDL
was 1.9 BW/s (7.76%) greater than the DL.
Table 4.2. Mean ± SD of vertical (Fz) kinetic variables for each trial of all participants.
DL
NDL
IFz
PeakFz
RFDFz
IFz
PeakFz
RFDFz
(BW.s)
(BW)
(BW/s)
(BW.s)
(BW)
(BW/s)
P1
0.18± .02*
3.32± .05*
24.6±5.6
0.27± .01*
3.77± .17*
27.8±3.5
P2
0.23 ± .03
2.62± .29
12.2±2.6
0.27± .01
3.00± .08
15.1±0.4
P3
0.26± .02
3.53± .04
38.9±6.3
0.29± .02
3.55± .03
29.5±0.5
P4
0.17± .02
2.81± .13*
22.2±6.3
0.24± .04
3.40± .08*
27.6±4.6
P5
0.22± .03*
3.11± .05
21.8±2.6
0.25± .01*
3.15± .96
21.9±8.2
P6
0.26± .01*
3.46± .13
27.0±2.8*
0.30± .01*
3.60± .01
36.3±2.0*
Mean
0.22± .04*
3.14± .37*
24.5±8.7
0.27± .02*
3.41± .29*
26.4±7.2
±SD
Note: *represents variables that were statistically significant p< 0.05. RFD= Rate of force
development. I= Impulse. Fz = vertical forces. BW=Body Weight.
Table 4.3 below illustrates the differences for horizontal (Fy) kinetic variables between the
DL and NDL observed in the study. The mean horizontal impulse (IFy) was significantly
greater in the NDL (0.06 BW.s, 15.23%) and all values for each participant were greater than
the values for the DL. Individual significant differences were found for participants 3, 5 and 6.
All peak horizontal forces were also greater in the NDL for all participants. The mean peak
horizontal force at take-off was also significantly greater in the NDL (0.14 BW.s, 14.89%)
and was significantly greater for participant 2. The horizontal rate of force development
(RFDFy) values was again greater for the NDL for each participant and the increases were
significant for participants 5 and 6. The mean horizontal rate of force of development was
also greater in the NDL (2.0 BW/s, 17.70%), however this difference was not significant.
24
Table 4.3. Mean ± SD of horizontal (Fy) kinetic variables for each trial
participants.
DL
NDL
IFy
PeakFy
RFDFy
IFy
PeakFy
(BW.s)
(BW)
(BW/s)
(BW.s)
(BW)
P1
-0.30 ± .03
-1.12± .04
-7.50±0.8
-0.38± .04
-1.20± .16
P2
-0.50 ± .04
-0.55±. 05*
-4.31±0.6
-0.57± .01
-0.75± .05*
P3
-0.40 ± .01*
-1.25± .16
-20.6±10.7
-0.50± .01*
-1.38± .13
P4
-0.42 ± .01
-1.11± .15
-21.1±2.0
-0.51± .07
-1.12± .05
P5
-0.35 ± .01*
-0.73± .15
-5.94±1.1*
-0.40± .01*
-0.91± .29
P6
-0.39 ± .01*
-0.94± .08*
-8.18±1.2*
-0.41± .01*
-1.11± .05*
of all
RFDFy
(BW/s)
-7.95± .6
-4.64± .6
-21.8±2.5
-21.2±5.9
-10.8±1.3*
-13.3±1.1*
Mean -0.40 ± .07*
-0.94 ± .26* -11.3 ±7.5
-0.46 ± .07* -1.08 ± .22*
-13.3 ± 7.0
±SD
Note: *represents variables that were statistically significant p< 0.05. RFD= Rate of force
development. I= Impulse. Fy = horizontal forces. BW=Body weight.
4.1.3 Landing
To quantify the end of flight time, the variables concerned with the landings of each
participant were examined and results are displayed in Table 4.4 below. The mean peak
vertical landing force (PeakFzL) displayed greater values for the NDL over the dominant leg
(7.46±1.16 > 7.12±1.90 respectively), however the difference was not significant. All
participants apart from participant 6 displayed greater Fz forces when landing after jumping
with their NDL. The greater peak landing forces observed for the NDL was in comparison to
the mean rate of loading as the DL exhibited greater rates over the NDL (216.6±152.7 >
203.7±61.9 respectively). Participants 2, 3, 4 and 5 displayed greater rates of loading for the
NDL and the difference for participant 5 was significant. However participants 1 and 6
displayed greater rates for the DL and the greater differences resulted in the mean rate of
loading being greater for the DL.
Table 4.4. Mean ± SD for vertical landing variables for each trial of all participants.
DL
NDL
PeakFzL
RFDL
PeakFzL
RFDL
(BW)
(BW/s)
(BW)
(BW/s)
P1
5.68±0.60
110.6±18.9
6.23±0.67
209.5±158.3
P2
8.91±0.44
421.4±147.2
8.73±1.51
234.0±57.5
P3
5.68±0.38
123.2±17.0
6.63±1.18
149.3±71.3
P4
6.03±1.53
139.1±67.2
7.23±1.22
161.8±32.8
P5
6.35±0.34
100.8±30.4*
6.91±0.41
157.4±16.0*
P6
10.1±0.63
404.6±118.1
9.05±1.04
310.5±51.1
Mean
7.12±1.90
216.6±152.7
7.46±1.16
203.7±61.9
± SD
Note: *represents variables that were statistically significant p≤ 0.05. RFD= Rate of force
development. L=Landing. Fz = vertical forces. BW=Body weight.
25
4.1.4 Correlation relationship between selected variables
To establish the relationship between the jump height and each variable a Pearson’s
moment product correlation test was conducted and results are displayed in Table 4.5
below. The vertical and horizontal rates of force development (RFD) variables at take-off
were not significant and displayed no correlation (0.208 and 0.201 respectively). This was
also the case for the landing rate of loading (0.043) and the peak forces at landing (0.088).
The velocity of the CM at take-off exhibited an r value 0.799 and was defined as having a
strong positive correlation with jump height. The flight time variable also displayed strong
positive correlation and exhibited an r value of 0.738. Peak vertical and horizontal take-off
forces displayed moderate positive correlation and exhibited r values of 0.461 and 0.432
respectively. Vertical and horizontal impulse also displayed moderate positive correlation
and exhibited values of 0.531 and 0.465 respectively. For variables that did exhibit
correlation, graphs were plotted for the each variable against jump height and are displayed
in Figure 4.1 (a, b, c, d, e & f) below.
Table 4.5. Correlation of kinetic variables vs. jump height and resulting correlation
strength.
Variable
r value
Correlation strength
TOVelocity CM
Flight time
Peak Fz
Peak Fy
RFD Fz
RFD Fy
Impulse Fz
Impulse Fy
Peak Fz landing
Landing RFD
Note: TO= Take-off
0.799
Strong positive correlation
0.738
Strong positive correlation
0.461
Moderate positive correlation
0.432
Moderate positive correlation
0.208
No correlation
0.201
No correlation
0.531
Moderate positive correlation
0.465
Moderate positive correlation
0.088
No correlation
0.043
No correlation
velocity. CM= Centre of mass. Fz = vertical forces. Fy = horizontal
forces. RFD= Rate of force development.
26
Figure 4.1. Correlation graphs of jump height against (a) Take-off velocity of the CM, (b)
flight time, (c) peak Fz, (d) peak Fy, (e) Fz Impulse and (f) Fy Impulse.
27
4.2 Kinematics
In order for comparisons to be made between the DL and the NDL at take-off the mean
curve for each trial of each participant for the ankle, knee and hip were plotted against each
other. Kinematic data were presented as a % of movement time so comparisons could be
made between variables.
4.2.1 Angular Displacement
Table 4.6 and Figure 4.2 below illustrate the difference in angular displacement for the ankle,
knee and hip between the DL and NDL. Maximum extension was higher for the NDL in all
three variables, however maximum flexion was lower for all three variables in the DL. The
hip displayed the least variance with a root mean squared difference (RMSD) value of 2.85º
and a percentage difference of 49.38%. Greatest variance was displayed in the knee with a
RMSD value of 10.07º and a percentage difference of 34.06%. Figure 4.2 d, e & f below
display the angular displacement difference between the DL and NDL. Positive values on the
graph represent the angular displacement of the DL being greater than the NDL.
Table 4.6. Maximum peak values for flexion and extension for the Angle vectors in the
dominant leg and non-dominant leg.
Variable
DL (max extension)
NDL (max extension)
DL (max flexion)
NDL (max flexion)
Ankle
Knee
Hip
139.64º
145.87º
88.59º
98.87º
165.88º
170.06º
104.61º
126.40º
172.24º
175.96º
133.38º
136.14º
10.07º
34.06%
2.85º
49.38%
RMSD
4.81º
%RMSD
31.43%
Note: RMSD = Root mean squared difference.
28
Figure 4.2. Averaged time-normalised graphs for the DL (blue line) and NDL (red line) for (a)
ankle angular displacement (b) knee angular displacement and (c) hip angular displacement.
The graphs on the right represent the differences between the DL and NDL for the (d) ankle,
(e) knee and (f) hip.
29
4.2.2 Angular Velocity
Angular velocity was greatest in the ankle joint and was highest for the NDL with a value of
16.04rad/s as shown in Table 4.7 below. Maximum extension was again greater in the ankle,
knee and hip for the NDL. Maximum flexion was higher in the ankle and knee for the NDL
and was greater in the DL for the hip (-5.23rad/s > -4.54rad/s). Figure 4.3 (a, b & c) below
illustrates the mean curves for the ankle, knee and hip and shows that the peak velocities for
each joint occurred at the latter stages of take off (90-100% of movement). The knee joint
had the lowest RMSD with a value of 1.36rad/s and a percentage difference of 35.05%. The
hip joint expressed the greatest variability with a RMSD value of 1.99rad/s and a percentage
difference of 36.47%. Figure 4.3 (d, e & f) display the differences between the DL and the
NDL and the figure indicates that the greatest differences were observed in the ankle joint.
Table 4.7 Maximum peak values for flexion and extension for the angular velocities in
the dominant leg and non dominant leg.
Variable
DL (max extension)
NDL (max extension)
DL (max flexion)
NDL (max flexion)
Ankle
Knee
Hip
10.77rad/s
16.04rad/s
-1.21rad/s
-3.17rad/s
9.28rad/s
9.49rad/s
-2.04rad/s
-5.29rad/s
7.83rad/s
8.38rad/s
-5.23rad/s
-4.54rad/s
1.36rad/s
35.05%
1.99rad/s
36.47%
RMSD
1.42rad/s
%RMSD
26.10%
Note: RMSD = Root mean squared difference.
30
Figure 4.3. Averaged time-normalised graphs for the DL (blue line) and NDL (red line) for (a)
ankle angular velocity (b) knee angular velocity and (c) hip angular velocity. The graphs on
the right represent the differences between the DL and NDL for the (d) ankle, (e) knee and
(f) hip.
31
4.2.3 Joint Torque
Figure 4.4 and Table 4.8 below display the differences in joint torque for the ankle, knee and
hip joints between the DL and NDL. Figure 4.4 (a, b & c) displays greater extension at the
ankle (4.05 BW.m), knee (5.34 BW.m) and hip joints (4.22 BW.m) for the NDL. This is in
comparison to flexion as the ankle (0.234 BW.m), knee (-0.0015 BW.m) and hip (0.0105
BW.m) joints were greater for the DL. Figure 4.4 displays the maximum values of the knee
and hip joint occurring at approximately 70% of the movement. Peak values for the ankle
joint occurred between 70-100% for the DL and NDL. The greatest differences between both
conditions are found in the ankle joint during 80-100% of the movement. The knee joint
exhibited the least differences between both conditions and had a RMSD value of 0.86
BW.m. The hip joint displayed the lowest RMSD value (0.38 BW.m) and had a percentage
difference of 37.26%.
Table 4.8. Maximum peak values for flexion and extension for the joint torque in the
DL and NDL.
Variable
Ankle
Knee
Hip
3.37 BW.m
4.05 BW.m
0.234 BW.m
1.59 BW.m
4.95 BW.m
5.34 BW.m
-0.00151 BW.m
-0.0086 BW.m
4.15 BW.m
4.22 BW.m
0.011 BW.m
0.234 BW.m
RMSD
0.63 BW.m
0.86 BW.m
%RMSD
31.52%
24.42%
Note: RMSD = Root mean squared difference. BW= Body weight.
0.38 BW.m
37.26%
DL (max extension)
NDL (max extension)
DL (max flexion)
NDL (max flexion)
32
Figure 4.4. Averaged time-normalised graphs for the DL (blue line) and NDL (red line) for (a)
ankle joint torque (b) knee joint torque and (c) hip joint torque. The graphs on the right
represent the differences between the DL and NDL for the (d) ankle, (e) knee and (f) hip.
33
4.2.4 Muscle Moment Power
Muscle moment power was also measured and greater values for extension were reported in
the ankle, knee and hip joint for the NDL as shown in Table 4.9 below. The knee joint
reported the greatest value of extension (19.84W/BW) between all three joints for the NDL.
Maximum values of flexion were higher in the ankle (-9.01W/BW) and hip joints (-8.89W/BW)
for the NDL. This is in comparison to the knee joint, as the higher values were observed for
the DL (-13.80W/BW). Figure 4.5 below displays the greatest difference between the DL and
NDL occurring at 40-60% of for the knee joint. Although the knee joint had the greatest value
for difference it displayed the lowest RMSD value (2.27W/BW) and had a percentage
difference of 20.25%. The greatest differences for the ankle and hip joints occurred between
50-60% of the movement and the ankle joint displayed the greatest RMSD value of
3.29W/BW with a percentage difference of 35.27%.
Table 4.9. Maximum peak values for flexion and extension for muscle power in the DL
and NDL.
Variable
DL (max extension)
NDL (max extension)
DL (max flexion)
NDL (max flexion)
Ankle
Knee
Hip
12.29W/BW
19.31W/BW
-1.83W/BW
-9.01W/BW
16.16W/BW
19.84W/BW
-13.80W/BW
-7.33W/BW
15.48W/BW
18.37W/BW
-3.94W/BW
-8.89W/BW
RMSD
3.29W/BW
2.27W/BW
%RMSD
35.27%
20.25%
Note: RMSD = Root mean squared difference. BW= Body weight.
34
2.33W/BW
21.06%
Figure 4.5. Averaged time-normalised graphs for the DL (blue line) and NDL (red line) for (a)
ankle muscle power (b) knee muscle power and (c) hip muscle power. The graphs on the
right represent the differences between the DL and NDL for the (d) ankle, (e) knee and (f)
hip.
35
CHAPTER FIVE: DISCUSSION
36
The aim of the present study was to examine the influence of leg dominance on heading
performance and the biomechanics of jump strategy and how this affects the jump height
achieved. Results of the study revealed that jumping with the NDL significantly increased
jump height by 6.18cm (12.24%) and therefore the null hypothesis of the study is accepted.
Results of the present study are in agreement with previous studies by Nunome et al. (2004)
and Sprattford et al. (2009) who also found bilateral differences between the DL and NDL.
This study, however found that the use of the NDL led to significant improvements in
performance rather than the DL.
The use of the NDL significantly increased take-off velocity (0.4m/s, 16.10%) and
significantly increased the duration of flight time (0.04s, 7.55%) for all participants. Studies
by Feltner et al. (1999) and Lees et al. (2004) looked at the influence of arms on vertical
jump performance and found that one of the main variables that increased jumping
performance was velocity of the CM at take-off. Although this study looked at running jumps,
there are clear links and agreements as take-off velocity was significantly greater for the
NDL. Take-off velocity also achieved a correlation r value of 0.799 which according to
Fallowfield et al. (2005) displays strong positive correlation when it was correlated against
jump height, which emphasises its contribution to the improved jump heights achieved. Flight
time also displayed strong positive correlation with jump height and produced a correlation r
value of 0.738 when correlated against jump height. Flight time has been shown to have a
strong relationship with jump height achieved as previous studies have used the flight time
method which calculates jump height achieved through the time of flight (Linthorne, 2001,
Park et al., 2008).
Like previous studies (Nunome et al., 2004; Sprattford et al., 2009) this study also found that
footballers exhibit differences between their DL and NDL. However this study found that
significant improvements resulted from the use of the NDL. The reason for this may be due
to the definition of the DL that was used for the study. Previous studies have defined the DL
of football players as their preferred playing foot (Harrison & Mannering, 2006; Shinkai et al.,
2006) and some studies have defined the DL through their strength characteristics (Haaland
& Hoff, 2003; Rahnama et al., 2005). The DL of this study was defined as the players
preferred kicking leg and according to Joesph et al. (2007) football players develop strength
favouring the non-favoured leg. This induced asymmetry is due to the opposite leg stabilising
the leg when the favoured leg performs the movement of kicking. Joseph et al. (2007) stated
that the preferred leg is used to control/manipulate objects and displays greater coordination. The non-preferred leg is then left to stabilise movements which leads to eccentric
and isokinetic strength adaptations to occur. The results of the present study would suggest
that this was also the case as all participants jumped higher off their NDL or non-preferred
37
leg. However, strength characteristics of each leg were not measured so this suggestion can
only remain an assumption to the reasoning behind the differences in jump height observed.
5.1 Ground Reaction Kinetics of Take-off
Results of the study displayed that the vertical impulse created by the NDL at take-off was
significantly greater than the DL and increased by 0.05 BW.s (22.72%) and all participants
produced greater impulse values with their NDL as shown in Table 4.2 above. Impulse was
also correlated against jump height and an r value of 0.531 was obtained which according to
Fallowfield et al. (2005) displays moderate positive correlation. The results are in a
agreement with a study by Feltner et al. (1999) who stated that improved jump height was
the results of larger net impulses created at take-off. The results are also in agreement with
a review conducted by Schieb (1986) who stated that to improve jumping success, greater
impulses must be produced as it is the time in which the force is acting. A later study by
Walsh (2004) also agreed with the results of this study as they found that increases in
vertical jump height were correspondent to greater vertical impulses exerted by athletes.
Closely linked to vertical impulse is the peak vertical forces created by participants during
take-off. Peak vertical force at take-off was also greater for the NDL (0.27 BW, 8.60%) and
was greater for all participants and significantly different for participants 1 and 4 as shown in
Table 4.2 above. Peak vertical forces at take-off achieved an r value of 0.461 which again
displayed moderate positive correlation with jump height. Although this study looked at
running jumps for heading, Khalid et al. (1987) found that increased ground reaction forces
and the influence of arms enhanced vertical jump performance and this theory is known as
the force transmission theory. However, later studies by Feltner et al. (1999) and Lees et al.
(2004) stated that this was a very simplistic view of quantifying the enhanced vertical jump
performance and other mechanisms were responsible for enhanced jump performance.
Although the difference in methods used, the results provide some support for the force
transmission theory as peak forces were higher in the NDL and participants were allowed to
use their arms to propel the CM vertically which overall increased jump height achieved.
According to Bruggemann (1994) during the take-off phase of a running jump, an athlete
exerts forces against the ground and it is these forces that determine the height and flight of
the centre of mass and the resultant jump height. For a jump which requires maximal vertical
displacement such as a high jump, higher horizontal peak forces and impulses are required
so that the body can propel vertically rather than horizontally (Bruggemann, 1994). Results
of the present study display that the mean horizontal impulse (IFy) of participants were
significantly greater in the NDL (0.06 BW.s, 15.23%) and all values for each participant were
38
greater than the values for the DL as shown in Table 4.3 above. Individual significant
differences were also found for participants 3, 5 and 6.
Peak horizontal forces were also greater in the NDL for all participants. The mean peak
horizontal force at take-off was also significantly greater in the NDL (0.14 BW, 14.89%) and
was significantly greater for participant 2. Correlations r values of 0.465 and 0.432 were
obtained for horizontal impulse and peak horizontal force respectively and display moderate
positive correlation with jump height. The results of this study emphasize the point made by
Bruggemann (1994) and suggest that the increased horizontal forces exerted by the NDL
may have influenced the take-off and the resultant increase in jump height observed.
Although peak vertical and horizontal forces and impulse have been shown to contribute to
the increase in jump height for the NDL, the rate of force development of each leg during
take-off and landing displayed no significant positive correlations with jump height. Although
no correlations were found between rate of force development and jump height the rate of
vertical force development for the NDL was 1.9 BW/s (7.76%) greater than the DL and the
differences were significant for participants 5 and 6. The horizontal rate of force development
was also greater in the NDL (2.0 BW/s, 17.70%). A significant difference was found for
participant 6, however the overall mean difference was not significant as shown in Table 4.3
above. The lack of significant correlation between rate of force developmennt and jump
height suggests that the rate of force development did not contribute to improvement in jump
height achieved.
5.2 Ground Reaction Kinetics of Landing
Results from a study by Yeow et al. (2009) displayed that Peak GRF followed an exponential
regression relationship; 𝑅 2 = 0.90 − 0.99 (𝑝 < 0.001) and peak GRF increased as landing
height increased. This would then suggest that the higher participants jumped the greater
the peak GRF at landing. This was not the case in the present study as peak forces (Fz) of
landings on were mixed between participants as shown in Table 4.4 above. Participant 1
displayed greater peak GRF for the NDL (9.68%), however participant 6 displayed greater
peak GRF for the DL (10.40%). Yeow et al. (2009) found that landings from 0.6m high, which
was approximately the jump height achieved for the NDL yielded peak GRF of approximately
3 BW. This is in comparison to the results of the current study as the average peak GRF for
the DL and NDL were 7.12 BW ±1.90 and 7.46 BW ±1.16 respectively. Although on average
the NDL exhibited greater GRF’s, no significant differences were found and no correlation
existed for its relationship with jump height which disagrees with the results of Yeow et al.
(2009). Only participant 6 displayed significant differences for the rate of force development
39
of landing and results were again mixed for which leg yielded the greatest rate of force
development. The reason for the lack of significance and difference may be due to the
landing strategies utilised by different participants. McNitt-Gray (1993) defined a selfselected landing strategy as a multi-joint coordination plan an individual executes to satisfy
the objectives of a landing task. Some participants may have landed on the balls of the feet
and then with the heels which according to Rojano et al. (2010) produces smaller peak
forces compared with the landings with the feet flat which produce larger forces and increase
the risk of injury. The landing strategies adopted by different participants may be the reason
for the mixed results of peak forces and the rate of force development of landing.
5.3 Kinematics of Take-off
Kinematic results of the study are also in favour of the NDL over the DL. In terms of angular
displacement, the NDL expressed greater values for extension at the point of take-off for the
ankle, knee and hip joints as shown in Table 4.6. Variation between both legs seemed to
increase from proximal to distal as the hip displayed the greatest percentage variance
(49.38%) and the ankle displayed the least (31.43%). According to Challis (1998) the actions
of the take-off during one-legged jumps are very similar to the actions of two-legged jumps.
These actions display initial flexion which is then followed by extension. Grimshaw & Burden
(2007) defined these actions as the braking and propulsive phases which occur after initial
heel strike of the foot. The results of this study would agree with the statement of Grimshaw
& Burden (2007) as all joints demonstrated initial flexion followed by extension towards the
end of take-off. The braking and propulsive phases are characterised in horizontal velocity
as there is an initial braking force followed by a propulsive force (Bruggemann, 1994).
For skills such as the one performed in this study higher braking forces followed by high
propulsive forces would result in greater vertical velocity of the centre of mass which would
increase overall jump height (Bruggemann, 1994). This would suggest that greater flexion
and greater extension would result in greater jump height. This was not the case in this
study as all joints achieved greater values of flexion when the DL was used for take-off.
However the using the NDL did produce greater extension for the ankle, knee and hip joints
as displayed in Table 4.6 and Figure 4.1 above. A study by Wilson (2004) investigated the
optimisation of performance in running jumps for height and found that the greatest jump
heights achieved were found when the ankle and knee joint hyper-flexed during take-off.
Although this was a planar eight-segment computer simulation model and hyper-flexion of
the ankle and knee would have resulted in injury for human performers, it suggests that the
greater the flexion of the ankle and knee at take-off, the greater the jump height a performer
40
can achieve. This may have been the case in this study as all participants displayed greater
extension in the ankle and knee joint when jumping off their NDL.
Although a two-legged jump was used a recent computer simulation study by Cheng et al.
(2008) which used a five segment model connected by frictionless joints found that greater
jump performance was linked to higher angular velocities in the ankle, knee and hip before
the point of take-off. The results of this study are in agreement with the results of Cheng et
al. (2008) as the ankle, knee and hip joints exhibited greater angular velocities in the NDL
during the latter stages of take-off (80-100%) as shown in figure 4.2 and table 4.7 above.
Although all joints had greater angular velocities in the NDL, the joint that displayed the
biggest difference between the NDL and DL was the ankle joint (16.04rad/s > 10.77rad/s,
respectively) which occurred at the latter stages of take-off (80-100%). The hip joint again
displayed the greatest percentage of variance (36.47%) and the ankle joint displayed the
least percentage variance (26.10%). A study by Mavromatis (1998) evaluated the effect of
performance dominance in the lower limbs and found that the highest jumps of each
participant corresponded with the angular velocity of the hips becoming positive earlier than
the velocity of the ankle and knee. This was not the case in this study as the hip angular
velocity in the NDL was the last joint to become positive during the take-off phase and
suggest that the angular velocity of the hips had little influence on improved jump height.
According to Huang et al. (2002) net joint torque can be used to determine whether a joint
displays extensor or flexor dominance at any given time during the joint contraction. Results
from the study display in that the extensors of the knee and hip displayed dominance up to
approximately 80% of the jump and the ankle displayed extensor dominance up until 90% of
the jump. After these points the flexors display dominance as all values began to drop as
shown in Figure 4.4. Table 4.8 also displays that the greatest difference between the joints
occurred again at the ankle (4.05 BW.m > 3.37 BW.m) and this difference was greatest at
80-100% of take off. Again, the hip joint displayed the least differences and exhibited the
least RMSD value of 0.38N. The knee joint displayed the greatest RMSD value, with a value
of 0.86 BW.m however the differences between peak muscle moment for the knee joint were
minimal between the NDL and DL (5.34 BW.m > 4.95 BW.m, respectively). The greatest
differences for the knee and hip were observed between 30-60% of take-off whereas the
greatest difference for the ankle occurred between 90-100% of take-off for the ankle. A
similar study by Hara et al. (2008) investigated the effect of arm swing on vertical jump
performance and found that an arm swing increased the torque produced by the hip joint
during the latter half of the propulsion phase. The increase observed was said to have a
direct effect on the improved vertical jump heights observed. The results of this study
disagree with the results of the results of Hara et al. (2006) as the hip joint expressed its
41
greater torque at approximately 70% of take-off. However this study looked at one-legged
jumps and direct comparisons cannot be made. The minimal differences observed for the hip
joint between the DL and NDL also suggest that this wasn’t the primary factor which caused
an increase in jump height for the NDL. Therefore the results suggest that that the greater
muscle moments of the ankle exhibited at take-off may be responsible for the increase in
jump height achieved by the NDL.
Bezodis et al. (2008) defined negative muscle power as power absorption and positive
muscle power as power generation. Results of the study show that the knee of the NDL
produced the greatest power (19.84W/BW) within all three joints. Power absorption was also
greatest in the knee (-13.80W/BW), however this was with the use of the DL as shown in
Table 4.9 and Figure 4.5. The most significant differences for power production was
observed in the ankle joint (19.31W/BW > 12.29W/BW) at the latter stages of take-off (80100%) and was higher in the NDL. The least differences were observed in the knee joint as it
displayed an RMSD value of 2.27W/BW and a percentage of variance of 20.25%. The
significant increase in power production for the NDL was expected due to the higher angular
velocities and torque exhibited by the ankle joint. The ankle of NDL seemed to reach peak
power later and at a greater rate than the DL which suggest that the planter-flexors of the
ankle were able to generate and more power and contribute to greater jump height. Although
power absorption was higher in the knee for the DL, power absorption was significantly
higher in the ankle (-9.01W/BW > -1.83W/BW) and the hip (-8.89W/BW > -3.94W/BW) in the
NDL. The greater values for power absorption in the ankle and hip correspond to the greater
values of horizontal impulse observed. The results suggest that the NDL was able to absorb
greater power and increase the braking forces e.g. horizontal impulse. This then may have
contributed to improved jump height observed in the NDL.
A study by Feltner et al., (1999) investigated the effect of arm swing on vertical jump
performance and stated that the arms cause extension rates of the ankle, knee and hip joints
to decrease, which allows muscles to produce greater force and improve jump height. This
theory was defined as the joint torque augmentation theory and agreed with previous results
by Dapena & Chung (1988) and Harman et al. (1990). Results of this study however
disagree with this theory proposed as increased jump height was associated with greater
rates of extension in the ankle, knee and hip for muscle power. A later study by Lees et al.
(2004) also rejected this theory as the results of their study did not agree with the statement
of previous authors in that an increased joint torque through an increase in angular velocity
leads to increased jump height. Therefore it seems that plantar-flexion power had the
greatest influence on jump height achieved.
42
5.4 Summary
Due to limited research on the performance of a one-legged take-off, which was analysed in
this study in the format of a header, the majority of research that has been discussed has
focused on two legged jumps. Although the mechanics of one-legged and two legged takeoffs have been shown to be very similar (Grimshaw & Burden, 2007), it would be
inappropriate to make direct comparisons between research that has been discussed.
However, a common theme identified from the kinematics results of the present study has
shown that the ankle joint displayed the greatest differences throughout all variables.
Significant increases in ankle velocity, torque and power suggest that this was the primary
joint which affected increases in jump height for the NDL. This statement is also
strengthened with the minimal differences between the NDL and DL that were observed for
the knee and hip joint. Therefore the results suggest that the ankle joint was the direct
influence on increased jump height achieved for the NDL.
5.5 Delimitations
The study was performed indoors due to equipment constraints. Although this allowed
constant conditions for each participant, it did not represent real game situations. The takeoff surface being used (running track) was significantly different to familiar surfaces such as
grass or astro-turf and therefore makes the study less realistic to football players. The
sample size is also relatively small due to the choice of footballers that were selected for the
study. Footballers chosen were first team university standard with majority of them playing in
the national leagues. Due to their busy training schedules only a small number out of this
sample were able to perform the study. Time available became problematic as data
collection had to be performed in one day so that players could return to their training normal
schedules. Fitness levels of each subject should be reasonably similar due to all of them
playing and training for the university first team. However players carrying or returning from
injury were not accounted for. Previous injury may have influenced the way players jumped
for headers and their jump height achieved.
5.6 Limitations
Many of the limitations of this study form from the research design. One of which was that
approach velocity was not quantified and according to Grimshaw & Burden (2007) approach
velocity can affect the impulse produced and take-off velocity which effects jump height
produced. Participants may have used different approach velocities for each leg and
therefore this may have affected their jump heights achieved. The study also used a hanging
football which made the study less game-realistic. If a ball cannon had been used to project
43
balls into the air at constant speeds like the one used in the Marcolin & Petrone (2006)
study, stride pattern or approach velocity may have altered and a true account for take-off in
heading would have been quantifiable.
Another error which was evident in this study was the estimation of joint centres. Since the
running jumping header is a dynamic movement, CODA markers placed on participants may
have moved during the trials and affected the data. Accuracy of the results may have
improved with the use of direct linear transformation to estimate joint centres. Finally the use
of quasi static analysis (QSA) over inverse dynamic analysis (IDA) was a limitation.
According to Dixon & Kerwin (1999) QSA is an approximation method which ignores
segmental inertial and weight forces. If IDA had been used the accuracy of the results may
have improved, however QSA can still provide valuable information on the net effect of all
muscle activity of the agonists and antagonists (Winter, 1990)
5.7 Implications of the study
The present study shows support for the theory that football players display bilateral
differences and exhibit a dominant/preferred and non-dominant/non-preferred leg due to the
unilateral demands of the game. Football players were able to jump higher off their NDL and
this could lead to detrimental performance when performing headers off their DL. Although
jump height is not directly linked to improvement in heading performance, Ekblom (1994)
highlighted the benefits of being able to out jump the opposition and winning headers in
certain positions such as defending. Coaches should therefore change the focus of training
to improving the strength of both legs. Players should try to use their NDL more in training so
eccentric and isokinetic improvements can be made in the DL. As football is an open game
the ability of being able to jump equally high off each leg would be beneficial to heading
performance.
5.8 Future research
Future research should investigate further into the function of the legs, throughout the whole
skill of heading and not just the take-off. Future studies should also look at heading with the
use of EMG (Electrographic-myography) to investigate the individual roles of the muscles at
take-off. Inverse-dynamics over a quasi-static analysis approach should also be used to
improve the overall accuracy of the results (Dixon & Kerwin, 1999). The legs have also been
shown to play an important role in the flight phase of heading (Kristensen et al., 2004) so this
also needs to be investigated further. This idea that footballers have a dominant limb should
also be applied to other footballing skills such as cutting, tackling and running etc to
investigate further into the idea. Therefore future studies should use inverse dynamics
44
analysis and EMG to investigate further into the full role of the legs during heading and
whether limb dominance exists in other footballing skills.
45
CHAPTER 6: CONCLUSION
46
6.1 Conclusion
The aim of this study was to examine leg dominance in footballers and its influence on
heading performance and more specifically to investigate the biomechanics of jump strategy
and how this affects the jump height achieved. The NDL was established as the players’
non-preferred foot and results displayed that footballers do exhibit leg dominance as they
were able to jump 0.062m (12.24%) higher and head balls when taking off with their NDL.
Results also revealed that jump strategy altered when footballers used the NDL as the
planter-flexors at the ankle were able to increase the velocity, torque and power production
of the planter flexors during take-off. The greater power production by the planer flexors in
the non-dominant leg contributed to significant differences in peak vertical and horizontal
forces and impulses exhibited at take-off. Take-off velocity for the NDL was also significantly
higher and contributed to the increase in jump height by greater vertical transfer of the centre
of mass at the point of take-off. Previous research also suggested that the bilateral
differences observed in this study may stem from the NDL possessing greater eccentric and
isokinetic strength. These strength increases arise from the frequent use of the nondominant leg/ non-preferred leg which stabilise movements as the DL is used for more cocoordinative movements such as the unilateral movement of kicking a football. In conclusion
football players are able to jump higher and head footballs when jumping off their nondominant/non-preferred leg, therefore coaches should focus on improving the strength of
both legs equally so players are not at a disadvantage when jumping for headers against
other football players.
47
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APPENDICIES
APPENDIX A
Participants Consent Form
Title of Project: The effect of using dominant leg vs. non dominant leg when
jumping for headers in footballers
.
Name of Researcher: Jamie Williams
Please fill this form by ticking the box by each question.
I understand the protocol of this project and I’m willing to participate
I have had a chance to ask questions and get them answered
I know I can stop at any time and that it will be OK
I am happy to be participating in this project
I agree to have images of me participating in the data collection taken for record
keeping and presentation purposes (refusal to do so does not affect my
participation in the study)
________________________________
Your Name
________
Date
________________________________
Your Signature
_______________________________
Name of person taking consent
Date
________________________________________
Signature of person taking consent
* When completed, one copy for participant and one copy for researcher’s files.
APPENDIX B
Participant Information Sheet
Title of Project: The effect of using dominant leg vs. non dominant leg when jumping for
headers in footballers
Background
This project is an attempt to understand the effectiveness of utilising different legs when
running and jumping for headers in football. The project is being undertaken by Jamie
Williams, a 3rd year Sport & Exercise Science student at The University of Wales Institute,
Cardiff.
In brief, this project is concerned with weather or not footballers exhibit a dominant limb due
to their footedness and the nature of the game. This is then applied to a skill such as
heading as footballers tend to jump with one leg when challenging for the ball.
Your participation in the research project
Why you have been asked
You have been invited to take part in this project because you have played for the UWIC
football team and will be a useful participant to the project.
What would happen if you agree to participate in the project
If you agree to join the study, there are two main things that will happen.
1. You will have some measurements taken (height and weight).
2. You will attend one session and be fitted with CODA markers and will be required to
perform 10 jumps, 5 with each leg. That is all that is needed on your behalf.
Are there any risks?
We do not think there are any significant risks to you from taking part in the study. If s/he is
feeling unwell, we’d advise that s/he doesn’t take part. And in any case, s/he should do
anything that s/he doesn’t want to – just tell us.
Your rights
You have the right to pull out of the project at any given time. In the very unlikely event of
something going wrong during the evaluation, UWIC fully indemnifies its staff, and
participants are covered by its insurance.
What happens to the results?
The measurements that are taken at the start will be stored securely in locked filing cabinets
at UWIC.
Are there any benefits from taking part?
Participating in a dissertation project, may offer insight for future projects. Also results of the
study may lead to information on how to improve performance.
What happens next?
If you are willing to participate in the study, you will be asked to sign consent forms so we
have conformation.
How we protect your privacy:
As you can see, everyone working on the study will respect your privacy. We have taken
very careful steps to make sure that you cannot be identified from any of the information that
we have about you. All the information about you will be stored securely away from the
consent forms. We will only keep the consent and assent forms with your name and
address. We keep these for ten years because we are required to do so by UWIC.
Further information
If you have any questions about the research or how we intend to conduct the study, please
contact us.
Dr.Gareth Irwin

02920 416 649

[email protected]
APPENDIX C
Raw subject data
Name
Height
Weight
Age (years)
Playing experience
Kicking foot
(cm)
(kg)
James
177.6
78.2
20.0
13.0
Left
Henry
175.3
69.9
21.0
13.0
Right
Gareth
177.5
78.4
20.0
9.0
Right
Adam
185
78.1
20.0
12.0
Right
Daniel
181.2
73.2
21.0
13.0
Right
Steffan
184.1
74.2
20.0
12.0
Right
Mean
180.1
75.3
20.3
12.0
±SD
3.93
3.48
0.5
1.41
(years)
APPENDIX D
Cut off frequency
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
3
2.5
2
Series1
1.5
Linear (Series1)
1
y = -0.1068x + 4.0292
0.5
0
0
10
20
30
40
APPENDIX E
Anderson-darling test for normality results