Examination of the Relationship between Speed, Agility & Measures of Strength & Power
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Transcript of Examination of the Relationship between Speed, Agility & Measures of Strength & Power
Examination of the Relationship between
Speed, Agility and Measures of Strength
and Power.
Student Name: Donal Doyle
This thesis is submitted in fulfilment of the requirements for a B. Sc.
Degree in Sport Science and Health at the Centre for Health and Human
Performance in Dublin City University
Abstract
Purpose:
The main purpose of this study was to examine the relationship between performance
in speed and agility and certain measures of strength and power.
Methods:
The study involved 16 males who participate in field games sports and had at least six
months resistance training experience. A number of strength and power measures
were carried out on the subjects. The subjects also had various split times of straight-
line 25 m speed test (5m, 10m, 15 to 25m and 25m) recorded and a total time for a 25
m agility test. The correlations between the strength and power measures and speed
and agility performance were then analysed.
Results:
Speed over 25 m was not correlated with 25 m agility. There was no significant
correlation found between the measures of maximum strength, rate of power
development and leg stiffness and speed or agility. Some measures of strength and
power revealed significant correlations including reactive strength index, which
correlated significantly with 5 m (r = -0.52, p<0.05) and 10 m (r = -0.52, p<0.05)
speed, but showed a non-significant correlation with 15-25 m speed and 25 m agility.
Absolute PP in the CMJ correlated significantly with 15-25 m (r = -0.57, p<0.05), 25
m speed (r = -0.53, p<0.05) and was the only measure of strength or power to
significantly correlate with 25 m (r = -0.57, p<0.05) agility. The most significant
correlation found was between vertical jump height and all split sections of speed, 10
m (r = -0.73, p<0.01) and 25 m (r = -0.665, p<0.01) speed. The CMJ also significantly
correlated with 10 m, 15-25 m and 25 m speed (r = -0.67 to -0.70, p<0.01), while
CMJ with 30% 1RM also correlated with 10 m and 25 m speed (r = -0.50 to -0.56,
p<0.05).
Conclusion:
The main findings from this study in general were that some strength and power
measures were correlated with different split sections in speed, but to a very minor
extent in agility. Some specific measures of strength and power did not correlate with
speed and this was not in line with previous research. Agility did not seem to relate to
Relationship between speed, agility and measures of strength and power.
the majority of strength and power measures used in the study. And speed was not
significantly correlated with agility.
Table of Contents
1.0 Introduction
9
2.0 Literature Review 10
2.1 Speed 10
2.1.1 - Stride length and Stride rate 10
2.2 Agility 11
2.3 Relationship between Strength/Power and Speed & Agility 12
2.4 Strength 16
2.4.1 - Reactive Strength 16
2.4.2 - Rate of Force Development 17
2.5 Power 20
2.5.1 Leg Stiffness 22
2.6 Relationship between Strength & Power 23
2.7 Conclusion 24
3.0 Methods 25
2
Relationship between speed, agility and measures of strength and power.
3.1 Subjects 25
3.2 Experimental Protocol 26
3.2.1 Day one 26
3.2.2 Day two 28
4.0 Statistical Analysis 33
5.0 Results 34
6.0 Discussion 41
7.0 Conclusion 50
8.0 Future Research 51
9.0 References 52
10.0 Appendices 58
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Relationship between speed, agility and measures of strength and power.
List of Tables
Table 1 Correlation studies between maximum strength and speed 15
Table 2 Correlation studies between RSI using depth jumps and performance in speed and agility 18
Table 3 Correlation between performance in split sections of the 25 m 32
speed test, and with the 25 m agility test.
Table 4 Correlation between relative and absolute 1RM parallel squat strength and performance times in split sections of the 25 m speed test and the 25 m agility test 32
Table 5 Correlation between rate of power development (RPD) in
counter movement jump (CMJ) and performance times in
split sections of the 25 m speed test and the 25 m agility test 35
Table 6 Correlation between rate of power development (RPD) in
counter movement jump (CMJ) with 30% of one repetition
maximum (1RM) and performance times in split sections
of the 25 m speed test and the 25 m agility test 35
Table 7 Correlation between Absolute Peak Power (PP) in
Countermovement Jumps and performance times in split
sections of 25 m speed and the 25 m agility test 36
Table 8 Correlation between Relative Peak Power in Countermovement
Jumps and performance times in split sections of 25 m speed
test and 25 m agility test 36
Table 9 Correlation between Vertical Jumps, Countermovement
Jumps and Countermovement Jumps with 30% 1RM and
performance times in split sections of the 25 m speed
test and 25 m agility test 37
4
Relationship between speed, agility and measures of strength and power.
Table 10 Correlation between reactive strength measures [depth
jump (DJ) height and reactive strength index (RSI)] and
leg stiffness and performance times in split sections of the
25 m speed test and 25 m agility test 39
Table 11 Mean and standard deviation for all measures of speed, agility, strength and power 40
5
Relationship between speed, agility and measures of strength and power.
List of Figures
Figure 1 Model indicating main factors determining Agility (adapted
from Young (11)) 12
Figure 2 Rate of force development curve over time 20
Figure 3 Format of the study 25
Figure 4 Agility course devised for study (25 m) 29
Figure 5 Force-velocity curve with change in muscular power 31
Figure 6 Correlation between Vertical Jump height and 10 m speed 37
Figure 7. Correlation between Countermovement Jump and 10 m speed 38
Figure 8. Correlation between Countermovement Jump and 25m speed 38
Figure 9. Correlation between Depth Jump Height and 10 m speed 39
6
Relationship between speed, agility and measures of strength and power.
1.0 Introduction
Speed and agility are vital components of fitness in many sports. These two
components generally will have a major influence on a player’s performance
during field games as they can be essential in both gaining and maintaining ball
possession in many team sports (9). Several studies have demonstrated the extent
to which forward sprinting and agility performance can be increased with specific
sprint and agility training (6,7) and that speed and agility are relatively
independent components (12). Sprinting requires high force production, in light
of this, the training of strength and power has been used extensively to improve
speed (3). Strength can be described as the maximal force that a muscle or muscle
group can produce at a certain velocity (1), and power being the product of
strength and speed (2).
There seems to be a lack of scientific understanding of what specific strength and
power qualities determine performance success in speed and agility. However,
there is some research investigating relationships that exist between strength and
power measures and speed, but minimal research involving similar relationships
with agility.
Research has revealed that some strength and power measures do correlate to various
extents with speed (3, 5, 10, 28), but with only minimal research into the relationships
with performance in agility (10, 11). In general there has been contrasting correlations
between studies when investigating these relationships. Certain factors still remain
unclear regarding the relationship between speed, agility and the specific qualities of
strength and power.
Therefore the aim of this study is to examine the relationship between performance in
speed, agility and various measures of strength and power using field game players
conditioned to various levels of speed, agility, strength and power training. The
information gained would certainly benefit strength and conditioning professionals,
researchers and coaches in understanding these relationships and allow them to plan
more effective and specific training programmes for field sport athletes. It is
7
Relationship between speed, agility and measures of strength and power.
hypothesized that there will be various levels of correlation between some of the
measures of strength and power and performance of speed and agility.
2. Literature Review
The content of this literature review will outline components that are purported to be
involved in determining speed and agility performance, and explore a range of various
components of strength and power ability. These strength and power factors are
reported to have a relationship in the contribution to improvement of performance in
speed and agility (2). The primary components to be explored in the review include
strength, power, rate of force development, reactive strength and leg stiffness. The
review will reveal various correlations that have been reported from previous studies
when the relationship between these factors and speed and agility was examined.
2.1 Speed
Speed can be defined as the time taken to cover a specific distance, with acceleration
being the rate of change of velocity in running speed and maximum speed the
maximum velocity an individual can achieve (16). Research seems to suggest that
initial acceleration and maximum speed are reasonably independent of each other.
Baker and Nance (3) revealed a 52% common variance in speed over 10 and 40
metres. It was also reported that acceleration over 10 metres and maximum speed
taken from a flying 20 metres showed a 39% common variance (16), with another
study reporting 60.84% common variance between 10 metre and 30 metre speed (5).
In outlining the determinants of speed it is necessary to reveal that sprint running
performance is reported as being the product of both stride length and stride rate (13).
2.1.1 Stride Length and Stride Rate
Stride length can be defined as the distance from foot contact to the next contact of
the same foot (13). The term stride rate can be defined as half a running cycle, which
is the time taken from one foot contact to the next foot contact of the opposite foot
(13). If there is an increase in one factor this will result in an improvement in speed,
however if the other factor was to undergo a large decrease in the process this may
therefore have a negative effect on speed (13, 18). There is general disagreement on
8
Relationship between speed, agility and measures of strength and power.
which factor has the most influence on speed with some researchers (14 cited in 13)
proposing that stride rate can be a speed limiting factor in sprint running, with other
research outlining that long stride length is more important for speed (19, cited in 13).
Stride rate can be trained by increasing strength, power and flexibility in the hips and
the legs enabling the athlete to powerfully push off the ground, which can be achieved
from improved power and strength by completing a strength program which ideally
should comprise of Olympic and power lifts (18). When looking at speed over short
distances such as five and ten metres research suggests that this is still only an
acceleration phase, it is reported however that by 20 metres about 80% of maximum
speed is developed (15). Therefore with research also suggesting that as running
speed increases from almost maximum to maximum, stride rate also increases,
whereas stride length may stay the same or slightly decrease, revealing that stride
length may be the most important factor in the acceleration phase when foot to ground
contact times are longer (13). In general however there seems to various opinions
regarding which one of stride length or stride rate are specific to either initial
acceleration or maximum speed (13).
2.2 Agility
Agility is the ability to change direction while moving at speed, involving
deceleration, stopping and then acceleration (1, 11, 12, 16). Forward sprinting and
agility can be improved with specific sprint and agility training (6, 7) and sprinting in
a straight line versus sprinting with changes of direction are specific tasks and
produce limited transfer to each other (12). Agility is an essential component in all
sports where instant reactions regarding changes of direction are required, however
there is a lack of research of this type of running technique in team sports (11).
The factors outlined in figure 1 give an overview of the components associated with
agility, which are considered by Young (11) to be the main factors responsible for
determining agility. Most of the factors listed are out of the scope of this present
study, as the focus will primarily be on the relationship the leg muscle qualities
(strength, power, reactive strength) have with change of direction speed.
9
Relationship between speed, agility and measures of strength and power.
Figure 1. Model indicating main factors determining Agility (adapted from
Young (11)).
Previous research has primarily investigated the relationship that exists between
straight-line speed and measures of strength and power (3, 5, 10, 23, 28). There has
been limited research into the relationship between measures of strength and power
and agility (10, 11). Therefore this is an area that does require more investigation as it
is an essential physical component for all field game players.
2.3 Relationship between Strength/Power and Speed & Agility
Acceleration and sprinting require high force production (1) and it is on this basis that
strength and power training are used to make improvements in speed (3). There is
only limited research investigating the relationship between strength, power and 5 m
sprint time particularly in team sport players. From this limited research, Young et al
(23 cited in 3) in a study using track athletes from a block start, found that the initial
10
Agility
Perceptual anddecision making
factors
Visualscanning
Anticipation
Patternrecognition
Change of direction
speed
Technique Straight sprintingspeed
Knowledge ofsituations
Legmuscle qualities
Footplacement
Adjustmentof strides
to accelerate& decelerate
Bodylean &posture
Strength Power ReactiveStrength
Relationship between speed, agility and measures of strength and power.
acceleration phase (2.5m) is highly correlated to the force applied in a concentric-only
jump squat, relative to body mass. They concluded that this result could be due to
similarities in knee angle, time for force production, and the concentric nature of both
activities. Also the fastest 10 m interval in that study was highly correlated (r = -0.77
to -0.79) to concentric, SSC and isometric measures of force and power, while some
measures of force, relative to body mass, measured during concentric and SSC barbell
jump squats were strongly related to maximum speed performance. This leaves
questions about whether absolute or relative measures of strength and power are better
predictors of maximum speed performance and about the relationship between
strength, power and speed over 10-20m and 40-50m. Some research (40 cited in 32)
into the relationship between 5m sprint time and strength and power, determined by
concentric jump squats in 30 male athletes, showed that both average and peak power
expressed relative to body mass were significantly related to 5m sprint time (r = -0.64
to –0.68) with force (r = 0.59) and bar velocity (r = 0.40) also significantly related to
5m sprint time.
Baker and Nance (3) found that for the 10 m and 40 m sprint, maximum strength as
assessed by the 3RM full squat, was not significantly related to performance either in
absolute or relative terms to body mass. Cronin and Hansen (5) also found a non-
significant relationship between absolute 3RM squat strength and speed over 5, 10
and 30m (r = -0.01 to –0.29). However Wisloff et al (10) did report a high correlation
(r = 0.94) between absolute 1RM squat strength and 10 m speed. They also revealed a
significant correlation (r = 0.71) between 1RM and 30 m speed. Vertical jump height
from a free counter movement jump performed on a force plate also correlated with
both 10m (r = 0.72, p<0.01) and 30m sprint time (r = 0.60, p<0.01), but it was not
revealed if the arm were used or not. The players used in the study were professional
soccer players and were familiar with performing half squats in training with
emphasis on maximal mobilisation of force in the concentric part of the half squat and
half of the subjects used had undertaken an advised strength programme before the
study which may mean that the correlations found are not a global finding.
Bret et al (28) assessed leg strength using concentric half-squats with loads ranging
from 20 to 160kgs. During each lift the average velocity and average force was
determined along with maximal force (Fmax, in N.Bw-1), defined as the leg strength
11
Relationship between speed, agility and measures of strength and power.
developed for the heaviest load lifted by the subject. The results showed that maximal
force was significantly correlated (r = 0.61) to the 0-30m phase and the greatest
correlation of maximal force was obtained with 100m (r = 0.75, p<0.01).
Baker and Nance (3) found jump squat power relative to body mass, to be related to
10 m sprint performance (r = -0.52 to -0.61). Some similar correlations have also been
reported between 20 m sprint performance and countermovement jump with no extra
load (r = -0.66) and a countermovement jump squat with a barbell load of 50% of
body mass (r = -0.47) (24, cited in 3). Baker and Nance (3) believe that a concentric
only jump squat test using high loading (e.g. 80-100kg) or a maximum concentric
squat might prove to be the best predictor of starting speed. Cronin and Hansen (5)
found that measures for countermovement and loaded jump squats resulted in
correlations (r = -0.43 to –0.64) with sprint performance, with significant
relationships found between jump squat (absolute load 30kg) relative power output
and 5m (r = -0.55, p = 0.01), 10m (r = -0.54, p = 0.01) and 30m times (r = -0.43, p =
0.04).
Kukolj et al (26) reported a significant correlation (r = -0.48) between height of an
unloaded countermovement jump with the velocity of maximal speed phase (15-30m),
but an insignificant correlation (r = 0.09) with the 0-15m speed phase and also an
insignificant correlation between 15 seconds of continuous hopping on the Ergojump
apparatus (Bosco system) and overall sprint running performance. Bret et al (28) used
an unloaded countermovement jump performed on a force plate to assess explosive
leg strength, by recording flight time during the jump and therefore determining the
height reached. Thus reported that countermovement jump height was a predictor of
the 0-30 m phase of 100 metres (r = 0.66, p<0.01). Berthoin et al (31) carried out a
study using male physical education students and performed free squat jumps, which
correlated to 20 m speed (r = -0.51, p<0.05) and 50 m speed (r = -0.61, p<0.01) and
counter movement jumps that correlated to 20 m speed (r = -0.58, p<0.01) and 50 m
speed (r = -0.66, p<0.01). Allowing for this research there remains a certain amount
of unexplained variance indicating there may be other or better measures that predict
sport speed, it being probable that a single strength measure cannot totally express the
factors involved in speed performance. Table 1 gives a general summary of research
investigating the relationship between maximum strength and speed.
12
Relationship between speed, agility and measures of strength and power.
Table 1. Correlation studies between maximum strength and speed.
Author Subjects Speed distance Details Results RCronin and Hansen (2005)
26 male part-time/full- time rugby league players.
5, 10 and 30 m Start 30 cm behind line.
3RM squat -thighs below parallel.
Absolute 3RM (kg) and 5 m -0.05
Olympic BarbellAbsolute 3RM (kg) and 10 m
-0.01
Absolute 3RM (kg) and 30 m
-0.29
Bret et al (2002) 19 male regional &
national sprinters
30, 60 and 100m
Concentric squat (90 degree knee angle)
Peak relative force (N/ kg) and 100 m (m/sec)
0.75*
Smith machine Peak relative force (N/ kg) and 0-30 m (m/sec)
0.61*
Peak relative force (N/ kg) and 30-60 m (m/sec)
0.68*
Peak relative force (N/ kg) and 60-100 m (m/sec)
0.68*
Young et al (1995)
11 male and 9 female sprinters, hurdlers, jumpers
2.5, 5, 10, 20, 30, 40 and 50m
Isometric squat (120 degree knee angle)
Absolute peak force (N) and 2.5 m
-0.72
and multi-event athletes
Smith machine Absolute peak force (N) and fastest 10 m
-0.79*
Wisloff et al (2004)
17 male international soccer players
10, 20 and 30m 1RM half-squat (90 degree knee angle)
Absolute 1RM (kg) and 10 m sprint
0.94*
30 cm behind line, stand start.
Olympic barbell Absolute 1RM (kg) and 30 m sprint
0.71*
Baker and Nance (1999)
20 male prof. rugby league players
10 and 40 m 3RM full-squat (thighs below parallel)
Absolute 3RM (kg) and 10 m
-0.06
Olympic BarbellRelative 3RM (kg/ kg BW) and 10m
-0.39
Absolute 3RM (kg) and 40m
-0.19
Relative 3RM and 40m -0.66*
Absolute 3RM (kg) and 30 m
-0.29
*Statistical significance
13
Relationship between speed, agility and measures of strength and power.
2.4 Strength
Strength is the ability to exert force, but there is considerable disagreement as to any
standard method of assessing strength (1). Maximum strength is generally measured
using the one repetition maximum (1RM) method by establishing the maximum load
the subject can lift. The maximum strength measure is expressed differently between
studies. Some studies express it as absolute strength (kgs), which does not take into
account the subject’s own bodyweight. Other studies refer to maximum strength as
relative strength, which does take into account the subject’s bodyweight (kg lifted / kg
bodyweight). Strength is largely proportional to the cross-sectional area of the muscle
and as a result larger muscles would have the potential to develop more strength than
smaller muscles (40). Other major structural and functional factors also affect strength
including the density of muscle fibres per unit cross-sectional area, the number of
muscle fibres contracting simultaneously, the rate of contraction of muscle fibres, the
conduction velocity in the nerve fibres and the efficiency in synchronisation of firing
of the muscle fibres (40).
2.4.1 Reactive Strength
The ability to quickly switch from an eccentric contraction to a concentric muscle
action has been described as reactive strength (25 cited in 15). Reactive strength has
also been referred to as the ability to optimise the stretch shortening cycle (SSC) (35).
The eccentric movement that takes place results in a more forceful concentric muscle
action (1, 35). Plyometric exercises have been used to train the SSC and are reported
to have resulted in improvements in power output, with some traditional exercises
comprising of bounds, jumps and hops. However the exercise needs to involve a rapid
eccentric movement of the muscle and then a maximal effort involved in the
concentric phase, therefore various types of depth jumps activate this mechanism
(35). Reactive strength is usually measured by recording the flight time and ground
contact time while performing depth jumps from various heights. The height jumped
divided by the ground contact time results in a figure known as the reactive strength
index (RSI).
14
Relationship between speed, agility and measures of strength and power.
Lower body reactive strength has been assessed in studies by using the depth jump.
Subjects are instructed to jump for maximum height while using minimum ground
contact time, the primary objective being to maximise jump height. (11). Young et al
(11) carried out a study investigating the relationship between strength, power and
agility. It was reported that there were moderate correlations (r = -0.65, p<0.05)
between the depth jump from 30cm and agility time with a right turn of 20 degrees
and also for 40 degrees (r = -0.53, p<0.05). They also reported that right leg (r =
-0.59) and left leg (r = -0.54) were significantly correlated to an agility course, which
was made up of four 60 degrees changes of direction. They suggest that the
correlations between leg reactive strength and agility performance were mainly due to
the similarity in the push-off mechanism used to change direction. They concluded
that relationships between leg muscle power and change of direction were not
consistent.
Cronin and Hansen (5) reported a non-significant correlation between RSI measured
by a depth jump (from a 40cm box) and 5, 10 or 30 m sprint performance (r = -0.35, r
= -0.38, r = -0.34). Because the stance phase associated with 5 and 10 m times is
reported to be longer, depth jump performance may be less relative, but as speed
increases it is expected that drop jump performance would become more relevant as
contact times are decreased (13). Other research supports this view showing a
significant relationship between depth jump performance (50cm, r = -0.72) and 30 m
maximal running velocity (14, as cited in 5). In a study by Young et al (23)
investigating the relationship between strength qualities and sprinting performance a
non-significant relationship was found between depth jumps from 30, 45, 60 and
75cms (using RSI) and the fastest 10 m of a 50 m sprint (r = -0.19 to –0.44). The
investigators did report that the subjects had no experience of plyometric training and
this may be a possible reason for the poor correlation. Table 2 gives a general
summary of research investigating the relationship between the reactive strength
index (RSI) using depth jumps and performance in speed and agility.
15
Relationship between speed, agility and measures of strength and power.
Table 2. Correlation studies between RSI using depth jumps and performance in speed and agility.
AuthorSubjects Speed distance Details Results R
Cronin and Hansen (2005)
26 male part-time/full-time rugby league players.
5, 10 and 30 m Depth jump (40cm)
DJ40 and 5m -0.35
Start 30 cm behind line
DJ40 and 10m
-0.38
DJ40 and 30m
-0.34
Young et al (1995)
11 male and 9 female sprinters, hurdlers jumpers& multi-event
2.5, 5, 10, 20, 30, 40 and 50m
Depth jump (30,45,60,75 cm)
DJ and fastest 10m
Athletes. Range -0.19 to -0.44
Young et al (2002)
15 male soccer, basketball, Aussie rules footballers and
8m straight sprint
Depth Jump (30cm)
DJ30 and straight 8m
-0.55*
tennis players. 7 agility tests Unilateral depth jump (15cm)
DJ30 and 20 deg L turn
-0.50
DJ30 and 20 deg R turn
-0.60*
DJ30 and 40 deg L turn
-0.40
DJ30 and 40 deg R turn
-0.53*
DJ30 and 60 deg L turn
-0.31
DJ30 and 60 deg R turn
-0.35
DJ30 and 4 turns (60 deg)
-0.54*
Left RightDJ15 - straight 8m
-0.43 -0.61*
DJ15 - 20 deg L turn
-0.29 -0.51
DJ15 - 20 deg R turn
-0.50 -0.71*
DJ15 - 40 deg L turn
-0.29 -0.51
DJ15 - 40 deg R turn
-0.28 -0.44
DJ15 - 60 deg L turn
-0.23 -0.46
DJ15 - 60 deg R turn
-0.39 -0.43
DJ15 - 4 turns (60 deg)
-0.54* -0.59*
16
Relationship between speed, agility and measures of strength and power.
*Statistical Significance2.4.2 Rate of force Development
Rate of force development is considered a very important factor in explosive actions
because the time allowed to exert force is usually of short duration (37) and is usually
determined in the early phase of a muscle contraction (38). No research was found
that investigates the relationship that exists between rate of force development and
performance in agility running. Only minimal research has been carried out between
rate of force development and speed. From this small amount of research some
significant correlations have been shown between force at 100 ms in a loaded (19kgs)
squat jump and sprint performance over 5 m (r = -0.73) and 10 m (r = -0.80) distances
in a group of 11 male and nine female athletes (23). Young et al (23) also found a
strong correlation between the force applied in the first 100 ms and 2.5 m speed (r =
-0.73).
Cronin and Slievert (32) suggest that rate of force development may be just as
predictive of performance as maximum power. In activities such as sprinting, the rate
of force development in a similar time frame to the ground contact time (100-300ms)
might result in a stronger relationship between a strength or power measure and
performance (32). Some research has reported that the concentric force at 30ms was
the measure most significantly correlated to sprint performance (r = -0.616, p<0.05),
with the authors emphasising the superiority of concentric RFD tests over isometric
and SSC RFD tests and also suggesting the inclusion of this test in a battery of sport
science tests (39 cited in 32).
17
Relationship between speed, agility and measures of strength and power.
Figure 2. Isometric force as a function of time, indicating maximum strength, rate of
force development, and force at 200 ms for untrained subjects (solid line), those who
did heavy resistance training (dashed line), and those who did explosive, ballistic
training (dashed-dotted line). Impulse is the product of force and time, represented
by the area under each curve. Adapted from Hakkinen and Komi 1985 (1).
2.5 Power
Power can be defined as the amount of work produced per unit time (32) or the
product of force (strength) and velocity (speed). It is considered to be a very
important component involved in achieving peak performance in a wide variety of
sports (33, cited in 34). In particular the ability to produce lower body explosive
power which is deemed an essential requirement for successful sprinting performance
(35). It has also been suggested that neural factors could contribute to high power
output such as motor-unit recruitment, rate coding and synchronisation, with the high
threshold motor units, mainly composed of type II muscle fibres, needing to be
recruited to produce high power outputs (37). Rate coding is the rate of motor unit
firing with a greater rate coding leading to a greater force output. When it reaches a
level to achieve maximum force a further increase in firing frequency can contribute
to an increase in rate of force development (37). As a result, increased rate coding
could be a possible adaptation for the production of power and strength.
As regards training for power, from current literature there are two different
approaches: 1) to use lighter loads (<50% of 1RM) and 2) to use heavier loads (50-
70% 1 RM) (32). Siegel et al (36) reported that peak power outputs during the lower-
18
Relationship between speed, agility and measures of strength and power.
extremity squat exercise occurred in the range of 50-70% of 1RM, but the actual
value may depend on the amount of time (distance) allowed to develop peak power. It
is important also to take into account the relationship between force and velocity, as
power is a product of both these factors. The force velocity mechanism takes place as
load increases the force output of the muscle in concentric contraction increases, with
a concomitant decrease in the velocity shortening. It is suggested that maximum
power output is the product of optimum force and optimum shortening velocity (32).
When calculating power using resistance training methods, such as jump squats, it is
advised to take body mass into account as well as any load attached to the barbell, as
the subject must propel themselves as well as the bar (32). However there does not
seem to be a standard method that has been agreed upon in this regard (32).
Research has been carried out to assess power by using various types of loaded and
unloaded jump squats. Young et al (23) found significant correlations between
relative mean power in a concentric loaded (19kgs) squat jump and 2.5 m speed (r =
-0.74) and the fastest 10 m speed time (0.79) in 50 metres as a measure of maximum
speed. Cronin and Hansen (5) reported significant correlations between relative mean
power and 5 m (r = -0.55), 10 m (r = -0.54) and 30 m (r = -0.43) speed. In this same
study significant correlations were also revealed between loaded (30kgs) squat jump
height and 5 m (r = -0.64), 10 m (r = -0.66) and 30 m (r = -0.56) speed. Young et al
(24) found a significant correlation between a loaded (50% of bodyweight) squat
jump and 20 m (r = -0.47) speed, but they did not find a correlation (r = 0.01) between
this measure and agility performance including three 90 degrees changes of direction.
Baker and Nance (3) reported that power output from loaded (40, 60, 80, 100kgs)
squat jumps, were significantly correlated to both 10 m and 40 m speed (r = -0.52 to
-0.72). They also found that relative peak power was correlated with 10 m (r = -0.56)
and 40 m (r = -0.76) speed.
The unloaded countermovement jump height is also used as a test for leg power.
Cronin and Hansen (5) found significant correlations with 5 m (r = -0.60), 10 m (r =
-0.62) and 30 m (r = -0.56) speed. In this study the subjects went to a 120 degrees
knee angle and placed their hands on their hips. Bret et al (28) reported significant
correlations with 0-30 m (r = -0.66), 30-60 m (r = -0.53), 60-100 m (r = -0.44) and
total 100 m (r = -0.67) speed. The subjects went to a 90 degrees knee angle during the
19
Relationship between speed, agility and measures of strength and power.
countermovement and also placed their hands on their hips. Wisloff et al (10) found
significant correlations with 10 m (r = -0.72) and 30 m (r = -0.66) speed and what
may have been a vertical jump with the use of the hands (was not revealed) and
Kukolj et al (26) revealed a significant correlation with 15-30 m (r = -0.48) speed and
countermovement jump. When investigating the relationship with speed and agility
Young et al (24) found a significant correlation with 20 m (r = -0.66) speed but non-
significant correlations with agility over 20 metres including 90 degrees (r = -0.10)
and 120 degrees changes of direction (r = -0.20). There would seem to be reasonable
evidence to suggest that unloaded countermovement jumps are correlated to running
speed over the various distances from 5 to 100 metres. However there is little research
investigating the relationship with agility performance.
2.5.1 Leg Stiffness
Cavagna et al (41 cited in 27) found that power generated by the contractile
components of the leg muscles increased in line with speed up to sub maximal values.
They also suggested that the elastic component of the leg muscles provide additional
power when running at high speeds. Cavagna et al (8 cited in 27) also recognised that
at high running speeds the runner bounces more stiffly with leg stiffness becoming
more important. Leg stiffness is described by Bret et al (28) as one of the elastic
components of the muscle-tendon complex behaviour. Leg stiffness reported as being
different to leg strength, as it influences the mechanics and kinematics of the body’s
interaction with the ground. They propose that a high value for leg stiffness being the
ability to absorb, store and release energy imposed by the mechanical strain of impact
and by the resulting abrupt stretching (28). This process would therefore allow the
storage and re-utilisation of stored elastic energy process to take place rapidly without
any major joint movement which would be of major importance during the maximal
velocity phase of sprinting when ground contact times are reported to be very short
(29 as cited in 28). Leg stiffness reported by Chelly and Denis (27) was an important
component for the high running speeds measured over 40 m by demonstrating a
significant correlation (r = 0.68, p<0.05) with maximal velocity, but not with initial
acceleration (r = 0.18). In this study a protocol was used where the subjects were
instructed to hop aiming to achieve maximum height for 10 seconds, keeping their
hands on their hips. Bret et al (28) used a similar hopping test on a force plate for 10
20
Relationship between speed, agility and measures of strength and power.
seconds (2 trials) to assess leg stiffness. They found that the value for leg stiffness,
calculated from the ground contact time and flight time, was not correlated to the 0-30
m phase (r = 0.35) or the final phase (r = 0.24). However their research did show that
leg stiffness was significantly correlated to 100 m performance (r = 0.66). They also
showed that the 30-60 m phase (r = 0.58) of the 100 metres was correlated to leg
stiffness.
Research in leg stiffness and stride frequency by Farley and Gonzalez (30) found that
when humans increase their stride frequency at a given running speed leg spring
stiffness increases. They also report that when humans hop in place, the stiffness of
the leg spring increases by about twofold when they increase their hopping frequency
by 65%. And when running forward at a given speed the stiffness of the leg spring
increases by about twofold when stride frequency is increased by 65%. Therefore they
propose that a similar relationship exists between hopping in place and forward
running (30).
2.6 Relationship between Strength & Power
It has been suggested that maximal strength is a vital factor in power output when the
movement duration is longer than 250 ms (20, cited in 2). This view is based on the
belief that strength and movement are in hierarchical relation to power, with increases
in strength that result from maximal strength training reflected in a change in power
and speed (2). From a biomechanical analysis carried out on certain resistance
training exercises used for maximal strength training, it was concluded that they
produce high levels of force but low levels of power compared with other Olympic-
style exercises, characterised by high levels of power and faster movement speeds
(21). The relationship between strength and power is believed to be complex and it is
thought that mechanical, neural and structural differences between exercises used can
be a determining factor in maximising both strength and power production (22 cited
in 2). But a large degree of variance still exists and to maximise power adaptations
specific power training may be necessary.
Baker and Nance (2) found that maximal strength, as measured by 3RM full squat and
maximal power output as measured by counter movement jump squats against
21
Relationship between speed, agility and measures of strength and power.
absolute loads of 40, 60, 80 and 100 kgs were highly correlated (r = 0.81, p<0.05).
They also found a significant correlation between the 3RM squat and the 3RM power
clean (r = 0.79). Baker and Nance (3) revealed that the 3RM relative power clean was
correlated to 10 m (r = -0.56) speed, but the 3RM relative squat was not significantly
correlated (r = -0.39) to 10 m speed. This may indicate that maximum strength as
measured by the squat may not be a predictor of 10 m speed. However it could also be
said that maximum strength measured by the squat may be indirectly related to 10 m
speed because of its significant correlation with the 3RM power clean. With the
power clean being significantly correlated to 10 m speed (3).
2.7 Conclusion
This review has outlined research investigating the relationship between speed, agility
and measures of strength and power. As a result it has become clear that a range of
strength and power measures do have an influence on speed performance over
different distances. However it is not as clear from the limited research available what
strength and power measures influence agility performance. The existing research
would seem to suggest that maximum strength and power are associated with the
early acceleration phase of speed, with reactive strength being associated more with
maximum speed and unloaded countermovement jump height revealing association
with both. Taking this research into account it still cannot be concluded with certainty
that a particular measure of strength or power is directly related to any particular
phase of speed. With the even greater lack of investigation into the relationships
between these strength and power measures and agility performance it is therefore
very important that research continue in this area to help identify the strength and
power measures that are correlated with speed and agility performance.
22
Relationship between speed, agility and measures of strength and power.
3.0 Methods
3.1 Subjects
The subjects involved in the study consisted of sixteen male field game players
(twelve Gaelic footballers, two hurlers and two soccer players) of various playing
standard and resistance training experience (from six months to five years). The
subjects mean body mass, height, age and years of resistance training experience (±
SD) were 79.6 ± 8.5 kg, 178.9 ± 5.6 cm, 22.6 ± 0.6 years, and 2 ± 1.4 years
respectively. Subjects visited the biomechanics laboratory on two occasions. During
the first visit (referred to as Day one in the experimental protocol) the nature and risks
of the study were explained to the subjects and a written informed consent form was
obtained. All subjects were provided with the plain language statement, completed a
PAR-Q and were excluded if they had a history of heart disease, lower extremity
injuries or any medical condition that may contraindicate exercise participation.
Subjects included in the study were between the ages of 18-30 years with at least six
months resistance training experience and were currently involved in a team sport
requiring speed and agility movements.
Also on the first visit the subjects performed depth jumps, hopping test and a one
repetition maximum (1RM) in the parallel squat. On the second visit (Day two in the
experimental protocol) 25 metre sprint and agility tests, vertical jump and various
countermovement jumps were performed by the subjects (Figure 3). All subjects were
regularly participating in training and matches with testing being carried out during
the playing season of the different sports. Prior to each visit, subjects were required to
abstain from alcohol and strenuous physical activity for a minimum of 24 hours.
Day 1 Day 2Depth Jump 30cm 25 m SpeedHopping Test 25 m Agility1RM Vertical Jump
Countermovement JumpCMJ with 30%1RM
Figure 3. Format of the study.
23
Relationship between speed, agility and measures of strength and power.
3.2 Experimental Protocol
Testing was carried out on two separate occasions separated by at least 48 hours. All
subjects were familiarised and comfortable with the tests to be performed in advance
of testing.
3.2.1 Day one:
Height was measured using a stationary stadiometer (Seca Model, 222) and weight
was measured on a balance scales (Seca Balance Scales) with the subjects wearing
light training clothing and no shoes.
The warm up on day one consisted of jogging continuously at moderate intensity for
five minutes prior to testing. They then performed the following tests in the following
particular order.
Depth Jump from 30 cm
Subjects performed three trials using the force plate (AMTI & Biosoft force plate
software, USA) recording at 1000 Hz. The depth jump from 30cm was used because
this was a commonly used test in other studies when reactive strength was assessed.
Subjects were instructed to place their hands on hips, step off the box and jump for
maximum height, spending as little time on the force plate as possible. The subjects
were given a two-minute recovery between trials. The jump height was calculated by
using the following formula:
Jump height = 9.81 * flight time²/ 8
The reactive strength index (RSI) was also used in the analysis of the depth jumps.
RSI is measured as jump height divided by ground contact time. The reactive strength
index has been used regularly in previous research as a standard method of assessing
reactive strength (5, 11, 23).
Hopping Test
In order to measure leg stiffness the hopping test was used because research has
shown that leg stiffness can play a role in running speed (30, 43), and this test has also
been used in previous research (27, 28, 43). The hopping test involved 10 seconds of
24
Relationship between speed, agility and measures of strength and power.
hopping for maximal height keeping the legs as stiff as possible, with the hands
placed on the hips. Two trials were performed on the force plate (AMTI & Biosoft
force plate software, USA), recorded at a frequency of 1000 Hz. A recovery time of
two minutes was allowed for each subject between trials.
The value for leg stiffness was calculated from the average flight time and contact
time by using the following formula:
KN = M * π (Tf + Tc) (in N/m)
Tc² [(Tf + Tc/π) – Tc/4]
KN = leg stiffness
M = the mass of the body
Tf = flight time
Tc = contact time.
This method was used and validated by Dalleau et al (43) for assessing leg stiffness.
The method is fully described in Appendix A.
One repetition maximum (1RM) squat
Subjects were assessed for lower body strength by performing a 1RM squat to a
parallel position with an Olympic barbell. International Power lifting Federation rules
were used when assessing the depth of the squat (44). The lift was deemed successful
when the subject descended until the top surface of the legs at the hip joint was lower
than the knee joint. The subjects had the assistance of two spotters if required at all
times and an experienced investigator involved in the study assessed the squat depth
subjectively. For the warm up involved the subjects lifted a sub maximal weight in the
squat exercise, which was approximately 50 % of what they perceived to be their
1RM in the squat exercise. The subjects all performed three to five repetitions at this
weight. The subjects then progressed to approximately 85 % of their estimated 1RM
and performed one repetition. Subjects continued to perform one repetition lifts with
the loads being increased in a range of five to fifteen kilograms, taking into account
the investigators experience of such testing and feedback from the subjects, until they
could not complete the lift to the required standard.
25
Relationship between speed, agility and measures of strength and power.
3.2.2 Day Two:
The warm up on day two consisted of jogging continuously at moderate intensity for
five minutes prior to testing. This was followed by three to five minutes of dynamic
stretching involving all the main muscle groups (hamstrings, quadriceps, adductors,
gluteals). The range of dynamic stretching movements included walking forward
lunges and free parallel bodyweight squats stepping from side to side. Each stretch
was held for two-three seconds and performed five times on each muscle group.
Subjects then performed three straight-line runs over the 25 m speed course. They
were instructed to perform these runs at what they perceived to be 70%, 80% and 90%
intensity, with 100% intensity being their maximum speed.
25 metres sprint
Subjects completed a 25 m sprint test and split times were recorded every 5 metres (0-
5m, 5-10m, 10-15m, 15-20m, 20-25m). Subjects began each trial from a standing
position 30 cm behind the starting line. The split times were recorded using the
Muscle Lab software system (Ergo Test, Norway) in an indoor facility. Subjects
performed three trials with the best performance time for 5 metres, 10 metres, 25
metres and 15-25 metres being used for the final analysis. All subjects were allowed
on average 90 seconds recovery time between the trials.
25 metres agility test
The agility course outlined in figure 4 was used in the study. The investigator devised
the agility course used for the study. Subjects started from a standing position 30 cm
behind the start line. The test consisted of a 25 m run including four changes of
direction. These changes of direction involved firstly a 101 degrees angle on the right
side, then a 66 degrees angle on the left side, then a 66 degrees angle on the right side
and finally a 101 degrees angle on the left side (figure 4). Subjects were required to
place the outside foot over a line marked with tape at each of these angles. If the
subjects failed to complete this protocol, which was supervised by the study
investigator, the result of that test was not used for analysis and the subject had to
repeat the trial. Taking this into account each subject performed three trials with a 90
second recovery time between each trial.
26
Relationship between speed, agility and measures of strength and power.
Foot over line. Actual run.
Start
Figure 4. Agility course devised for study (25 m).
27
660
660
1010
1010
7.61m
5.22m
5m
2m
5.38m
7.61m
5.22m
5m
2m
4.78m
4.78m
4.78m
5.38m
2m 2m
Finish
Relationship between speed, agility and measures of strength and power.
Vertical Jump
Subjects performed a vertical jump using the vertex system (USA) to assess jump
height by requiring each subject to jump for maximum height and touch as many
plastic markers (each 0.5 inches apart) with one hand as possible. At the start the
subjects stand and reach height was obtained by standing under the markers and
reaching as high as possible with one hand touch the markers while keeping both feet
firmly on the floor. Subjects were instructed to squat down to a self-selected depth
and immediately jump as fast and as high as possible to touch the maximum number
of plastic sticks with their inside hand. Subjects used their arms to assist with the
jump. Each subjects’ stand and reach height with the right hand was subtracted from
their jump and reach height with the same hand to obtain the maximum jump height.
Subjects performed three trials with a similar recovery period between each trial. The
best trial was used for the overall analysis.
Countermovement Jump (CMJ) on the force plate
Subjects were also asked to perform countermovement jumps on the force plate
(AMTI & Biosoft force plate software, USA) (1000 Hz). Subjects were instructed to
squat to a self-selected depth and immediately jump for maximum height. Each
subject was instructed to perform the trial with their hands on their hips. Each subject
performed three trials. Jump height was calculated by the same formula that was used
for calculation of depth jump height, which was described earlier. The trial with the
best jump height was used for the analysis in the Chart 5 analysis software package
(AdInstruments, UK). From this trial jump height was recorded and used in the
overall analysis, and also a number of other strength and power measures were used
for analysis from this test. These measures consisted of:
- Rate of power development (RPD) in the initial 30, 100 and 200
ms of the concentric phase
- Peak power (PP)
- Peak force (PF)
- Maximum rate of power development (RPDmax)
28
Relationship between speed, agility and measures of strength and power.
Figure 5. Power production and absorption (solid line) as a function of force and velocity (dashed line) in concentric and eccentric muscle actions. Maximum concentric power occurs at approximately 30% of maximum force (Fm) and velocity (Vm). Adapted from Faulkner, Claflin, and McCully 1986 (1).
The results were obtained from the force plots using the following biomechanical
principles:
ΣF = ma FLOAD
FGRF – FBWT – FLOAD = (MBODY + MLOAD) * a FBWT
=> a = [FGRF – FBWT – FLOAD]/ [MBODY + MLOAD]
Where,
FGRF is total vertical ground reaction force FGRF
FBWT is force due to body weight
FLOAD is force due to load
MBODY is the mass of the body
MLOAD is the mass of the load
a is the acceleration of the whole system (lifter and load)
V = ∫a dt
29
Relationship between speed, agility and measures of strength and power.
Where,
V = velocity of the whole system
P = FGRF * V
Where,
P is the power of the whole system
Countermovement Jump on force plate with 30 % 1 RM
Subjects performed countermovement jumps with 30 % of their 1RM squat load,
which was recorded on day one. An Olympic bar was again used
carrying the appropriate weight and placed across the shoulders of the
subject, with the movement taking place on the force plate (AMTI &
Biosoft force plate software, USA) (1000 Hz). Subjects were instructed
to squat to a self-selected depth and immediately jump as high and as
fast as possible while holding the Olympic bar tightly to the shoulders
and back of the neck. Subjects performed three trials with a one minute
recovery period between each trial. Jump height for each trial was
calculated by the same formula used for calculation of depth jump
height. The information from the trials was used for analysis in the Chart
5 analysis software package (AdInstruments, UK). The same strength
and power measures as those used for the unloaded countermovement
jump were used in the analysis.
In all the tests, the best result from the trials performed was used in the statistical
analysis.
30
Relationship between speed, agility and measures of strength and power.
4.0 Statistical Analysis
The data was analysed using the statistical analysis package, SPSS 12.0 for windows
(SPSS Inc., USA). A bivariate Pearson r correlation analysis was performed to relate
all independent variable measures of strength and power recorded, to the best
performance time in the speed and agility tests. In all analyses the level of statistical
significance, alpha level, was set at p < 0.05.
31
Relationship between speed, agility and measures of strength and power.
5.0 Results
5.1 Speed and Agility
All of the split sections of the 25 m speed test analysed were significantly correlated
with each other, p<0.01 (table 3). However, there was no significant correlation found
between any of the split sections over the 25 m speed test and the 25 m agility test (r =
0.25 to 0.49, p>0.05, table 3).
Table 3. Correlation between performance in split sections of the 25 m speed test, and
with the 25 m agility test.
5m 10m 25m 15-25m Agility 25m5m 110m 0.87** 125m 0.79** 0.93** 115-25m 0.66** 0.77** 0.91** 1Agility
25m 0.41 0.49 0.45 0.25 1**Correlation is significant at p<0.01
5.2 Relative and Absolute Strength
There was no significant correlation found between relative or absolute maximum
1RM parallel squat strength and any split section of the 25 m speed test or the 25 m
agility test (Table 4).
Table 4. Correlation between relative and absolute 1RM parallel squat strength and
performance times in split sections of the 25 m speed test and the 25 m
agility test.
5m 10m 25m 15-25m Agility 25mRe 1RM -0.12 -0.15 -0.16 -0.31 0.26Abs 1RM -0.21 -0.24 -0.25 -0.32 -0.18
5.3 Rate of Power Development
For rate of power development (RPD), from countermovement jumps, there was no
significant correlation with any performance times in the split sections of the 25 m
speed test or the 25 m agility test (Table 5).
32
Relationship between speed, agility and measures of strength and power.
Table 5. Correlation between rate of power development (RPD) in counter movement
jump (CMJ) and performance times in split sections of the 25 m speed test and the 25
m agility test.
5m 10m 25m 15-25m Agility 25m RPD30 CMJ -0.07 -0.22 -0.23 -0.23 -0.08RPD100 CMJ -0.01 -0.14 -0.17 -0.16 0.01RPD200 CMJ -0.16 -0.34 -0.35 -0.21 -0.36RPDmax CMJ -0.09 -0.05 -0.10 -0.22 -0.06RPD30, RPD100 and RPD200 are rate of power development in 30, 100 and 200 ms at the
start of the concentric phase.
There were also no significant correlations found between measures of rate of power
development from the countermovement jumps with 30% of 1RM and performance
times in the split sections of 25 m speed test or 25 m agility test (Table 6).
Table 6. Correlation between rate of power development (RPD) in counter movement
jump (CMJ) with 30% of one repetition maximum (1RM) and performance times in
split sections of the 25 m speed test and the 25 m agility test.
5m 10m 25m 15-25m Agility 25mRPD30 CMJ 30% 0.09 -0.14 -0.27 -0.26 -0.48RPD100 CMJ 30% 0.03 -0.22 -0.36 -0.37 -0.36RPD200 CMJ 30% 0.13 -0.16 -0.28 -0.33 -0.03RPDmax CMJ 30% 0.11 0.01 -0.00 -0.09 -0.20RPD30, RPD100 and RPD200 are rate of power development in 30, 100 and 200 ms at the
start of the concentric phase.
5.4 Relative and Absolute Peak Force and Power
Absolute peak power in the countermovement jump was significantly correlated with
the 25 m speed test time (r = -0.53, p<0.05) and with the split time from 15 to 25
metres (r = -0.57, p<0.05). This absolute peak power measure was also the only
measure analysed to reveal a significant correlation with the 25 m agility test (r =
-0.53, p<0.05). Absolute peak power in the 30% 1RM countermovement jump
showed no significant relationship with split sections of 25 m speed test and 25 m
agility test. Absolute peak force in both countermovement jumps showed no
significant correlation with any of the speed times or the 25 m agility test (Table 7).
33
Relationship between speed, agility and measures of strength and power.
Table 7. Correlation between Absolute Peak Power (PP) in Countermovement Jumps
and performance times in split sections of 25 m speed and the 25 m agility test.
5m 10m 25m 15-25m Agility 25mAbs PP in CMJ (W) -0.44 -0.47 -0.53* -0.57* -0.53*Abs PP in 30% 1RM CMJ (W) -0.31 -0.38 -0.41 -0.40 -0.40Abs PF in CMJ (N) 0.04 -0.06 -0.04 0.05 -0.14Abs PF in 30% 1RM CMJ (N) -0.01 -0.14 -0.18 -0.22 -0.25*Statistically significant, p <0.05
Relative peak power in the unloaded countermovement jump was significantly
correlated with the split time from 15 to 25metres (r = -0.52, p<0.05). Relative peak
power in the 30% 1RM countermovement jump was not related to the speed and
agility tests. Relative peak force in both countermovement jumps showed no
significant correlation with any of the speed test times or agility test time (Table 8).
Table 8. Correlation between Relative Peak Power in Countermovement Jumps and
performance times in split sections of 25 m speed test and 25 m agility test.
5m 10m 25m 15-25m Agility 25mRel PP CMJ (W/kg) -0.36 -0.40 -0.45 -0.52* -0.24Rel PP 30% 1RM CMJ (W/kg) -0.29 -0.39 -0.43 -0.46 -0.05Rel PF CMJ (N/kg) 0.16 0.04 0.07 0.10 0.40Rel PF 30% 1RM CMJ (N/kg) 0.12 -0.06 -0.11 -0.24 0.26*Statistically significant, p <0.05
5.5 Jump Heights
Vertical jump height using the vertex system had a very significant correlation (r =
-0.73, p<0.01) with 10 m speed time (figure 6). Vertical jump also showed good
correlations with the other speed test times (-0.50 to –0.73). All height measures of
the unloaded countermovement jump were significantly correlated with each split-
time section of speed analysed (r = -0.53 to –0.70), revealing a high correlation with
10 m speed (-0.70, figure 7) and total 25 m speed (r= -0.69**, figure 8). Jump height
in the countermovement jump with 30 % 1RM squat load was significantly correlated
with 10 m speed (r = -0.50, p<0.05) and 25 m speed (r = -0.56, p<0.05) test times.
However, none of the jump heights recorded were significantly correlated with the
agility test (Table 9).
34
Relationship between speed, agility and measures of strength and power.
Table 9. Correlation between Vertical Jumps, Countermovement Jumps and
Countermovement Jumps with 30% 1RM and performance times in split sections of
the 25 m speed test and 25 m agility test.
5m 10m 25m 15-25m Agility 25mVJ ht (m) -0.50* -0.73** -0.67** -0.51* -0.38CMJ ht (m) -0.53* -0.70** -0.69** -0.67** -0.14CMJ30 ht (m) -0.34 -0.50* -0.56* -0.39 -0.47**Statistically significant, p<0.01, *statistically significant, p <0.05
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
1.7 1.75 1.8 1.85 1.9 1.95 2
10metre (secs)
VJ
he
igh
t (m
)
Figure 6. Correlation between Vertical Jump height and 10 m speed.
0.2
0.25
0.3
0.35
0.4
0.45
1.7 1.75 1.8 1.85 1.9 1.95 2
10m e tre (s e c s )
35
r = -0.73, p<0.01
r = -0.70, p<0.01
Relationship between speed, agility and measures of strength and power.
Figure 7. Correlation between Countermovement Jump and 10 m speed.
0.2
0.25
0.3
0.35
0.4
0.45
3.5 3.6 3.7 3.8 3.9 4
25metre (secs)
CM
J h
eig
ht
(m)
Figure 8. Correlation between Countermovement Jump and 25m speed.
5.6 Reactive Strength and Leg Stiffness
The depth jump height recorded was most significantly correlated with 10 m speed (r
= -0.68, p<0.01, figure 9), the split time from 15 to 25 metres (r = -0.51, p <0.05) and
25 m speed (r = -0.58, p<0.05) test. The reactive strength index (RSI) was
significantly correlated with 5 m speed (r = -0.52, p<0.05) and 10 m speed (r = -0.52,
p<0.05). Depth jump height and RSI were not significantly correlated with agility
over 25 metres. Leg stiffness was not significantly correlated with any performance
times in split sections of the 25 m speed test or the agility test (Table 10).
Table 10. Correlation between reactive strength measures [depth jump (DJ) height
and reactive strength index (RSI)] and leg stiffness and performance times in split
sections of the 25 m speed test and 25 m agility test.
5m 10m 25m 15-25m Agility 25mDJ ht (m) -0.47 -0.68** -0.58* -0.51* -0.20RSI (m/s) -0.52* -0.52* -0.50 -0.44 0.25
36
r = -0.69, p<0.01
Relationship between speed, agility and measures of strength and power.
Leg stiffness (kN/m) -0.12 -0.10 -0.15 -0.09 0.01**Statistically significant, p<0.01, *statistically significant, p <0.05
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1.7 1.75 1.8 1.85 1.9 1.95 2
10metre (secs)
DJ
he
igh
t (m
)
Figure 9. Correlation between Depth Jump Height and 10 m speed.
5.6 Summary of Results
A summary of the mean and standard deviation figures for speed, agility, strength,
rate of power development, absolute and relative peak power and force, jump heights,
reactive strength and leg stiffness are contained in table 11.
Table 11. Mean and standard deviation for all measures of speed, agility, strength and power.
Mean SDSpeed and Agility5m (secs) 1.108 0.06410m (secs)25m (secs)
1.861 0.082 3.745 0.125
15-25m (secs) 1.205 0.042Agility 25m (secs)
StrengthAbsolute 1RM parallel squat (kg)
6.500
115.63
0.255
17.02Relative 1RM parallel squat (kg/ kg body mass)
Rate of Power Development
1.45 0.19
RPD30 CMJ (W/s)RPD100 CMJ (W/s)RPD200 CMJ (W/s)
22327.03 21074.34 17656.73
8933.598881.046079.40
37
r = -0.68, p<0.01
Relationship between speed, agility and measures of strength and power.
RPDmax in CMJ (W/s)
RPDmax in 30% 1RM CMJ (W/s)
27633.38 21921.75
6186.12
4560.29RPD30 in 30 % 1RM CMJ (W/s) 12449.25 4315.49RPD100 in 30 % 1RM CMJ (W/s) 12398.91 4582.01RPD200 in 30 % 1RM CMJ (W/s) 11856.38 5544.96
Absolute and Relative Peak Power and ForceAbsolute P power in CMJ (W)Absolute P power CMJ with 30% 1RM (W)Absolute P force in CMJ (N)Absolute P force CMJ with 30% 1RM (N)
Relative P power in CMJ (W/ kg)Relative P power CMJ with 30% 1RM (W/kg)Relative peak force in CMJ (N/kg)Relative peak force CMJ with 30% 1RM (N/kg)
Jump HeightsVertical Jump height (m)Countermovement Jump Ht (m)CMJ with 30% 1RM (m)
Reactive Strength and Leg StiffnessDepth Jump Ht (m)Reactive Strength Index (m/ s)Leg Stiffness (kN/m)
4391.75 4051.75 1887.81 2089.04 55.51 50.82 23.76 26.27 0.57 0.37 0.20 0.34 1.33 25.41
816.15777.56235.02265.30
11.538.042.402.50
0.070.070.03
0.050.200.03
6.0 Discussion
The aim of this study was to examine the relationship between the performance in
speed, agility and various measures of strength and power. The outcome of the study
was that certain strength and power measures correlated with the 25 m speed test and
to lesser extent with the 25 m agility test. It was hypothesized that there would be
various levels of correlation between some measures of strength and power and the 25
m speed and 25 m agility tests, and this was in line with the final outcome of the
study.
The 25 m speed time did not correlate significantly with the 25 m time for agility (r =
0.45, p<0.01). This is a similar finding to that of Young et al (24), who revealed an
even lower correlation between 20 m speed and a 20 m agility course (r = 0.14).
However the agility course used by Young et al (24) consisted of three 90 degree
changes of direction over 20 metres compared to this study which consisted of two 66
degree and two 101 degree changes of direction over 25 metres. Subsequently all the
38
Relationship between speed, agility and measures of strength and power.
split sections of speed analysed (5m, 10m and 15-25m) were not correlated to the 25
m agility test (0.25 to 0.49, p<0.01). These findings were in line with those from
previous research, which indicated that speed in a straight line and agility
performance, were not related (12, 16, 24).
When the mean speed times for the subjects used in this study are compared with
other studies it is revealed that they were not as fast. A mean 5 m time (secs) of 1.12 ±
0.06 and 10 m time (secs) of 1.86 ± 0.06 was reported in this study. Similar research
has reported 10 m times (secs) of 1.60 to 1.82 (3, 5, 10) with Cronin and Hansen (5)
reporting a mean 5 m time (secs) of 0.95 ± 0.05. These differences could be due to the
quality of athletes involved or the type of training they had performed compared to
subjects used in previous research studies Therefore this needs to be taken into
account when comparing measures with previous research.
There was no significant correlation found between relative or absolute strength and 5
m (r = -0.12, r = -0.21), 10 m (r = -0.15, r = -0.24), 25 m (r = -0.16, r = -0.25) and 15-
25 m (r = -0.31, r = -0.32) speed. These findings are similar to other research with
Cronin and Hansen (5) reporting non-significant correlations between absolute and
relative strength from a 3RM parallel squat and 5 m (r = -0.05), 10 (r = -0.01), and 30
m (r = -0.29) speed. Baker and Nance (3) also reported non-significant correlations
between absolute strength (3RM squat) and 10 m (r = -0.06) and 40 m (r = -0.19)
speed, but did find a correlation between relative strength and 40 m (r = -0.66) speed.
Wisloff et al (10) found significant correlations between absolute strength (1RM
squat, 90 degree knee angle) and 10 m (r = -0.94) and 30 m (r = -0.71) speed. It was
expected that there might have been some form of correlation between maximum
strength and speed because of the inverse of Newton’s law (i.e. acceleration =
force/mass) (3). As was acknowledged by Baker and Nance (3), it may be best to
measure strength by concentric methods rather than exercises such as the squat as the
sprint start is primarily reliant on concentric force production. Baker and Nance (3)
suggested that the power clean may be a better predictor of sprint performance as the
knee angles are closer to that of sprinting more so than the squat.
Wisloff et al (10) was the only study to report significant correlations, as the
correlation in Baker and Nance (3) was with 40 m speed and the total speed distance
39
Relationship between speed, agility and measures of strength and power.
in this study was only 25 m. The subjects used in the present study were not of a
similar training standard compared to the professional soccer players used by Wisloff
et al (10) who were reported to be involved in regular resistance training. The subjects
in the present study all had the required resistance training experience but were
recruited from different teams and therefore it is not known if they were involved in a
continuous, progressive, specific or supervised resistance training programs. They
also had varying levels of resistance training experience (6 months to 5 years) and all
these factors combined may have an important bearing on their overall performance.
At one point in the study by Wisloff et al (10) it was reported that the subjects started
the sprint test from a moving position at 30cm behind the start line and it was also
reported that the subjects started from a standing position. Therefore it was unclear
the actual starting position of the subjects and this may have had an effect on the
corresponding speed times in that study.
Wisloff et al (10) reported a mean 1RM squat of 171 ± 21.2 kgs compared to the
mean 1RM squat in this study of 115.63 ± 17.02 kgs. This showed a significant
strength difference between the subjects used in both studies. There was also a
difference in the protocol used in the squatting technique for both studies. This
present study instructed the subject to descend until the top surface of the legs at the
hip joint was lower than the knee joint. Wisloff et al (10) instructed the subjects to
descend to a position where the knee angle was approximately 90 degrees. It should
also be remembered that exercises such as the squat have different
velocity/acceleration profiles compared to the sprinting motion (5) and therefore may
have little to offer in explaining the relationship between strength and speed in the
subjects used in this study.
Also in this study relative and absolute strength did not correlate significantly with 25
m agility (r = 0.26, r = -0.18). Only minimal research has been conducted in this area
with Wisloff et al (10) reporting a significant correlation between maximum strength
and a 10 m shuttle run (-0.68). This 10 m shuttle run test would have been a very
different agility course compared to the reasonably field game specific agility course
used in the present study. The shuttle run used by Wisloff would not seem to be a
game specific agility course to use when testing field game players for agility and
may be a far easier course for players to get accustomed to during performance
40
Relationship between speed, agility and measures of strength and power.
testing. In comparison to the test used in this study which the players were not
familiar with as a total course, but would have performed similar type movements in
game situations. Young et al (11) recognised this when revealing that agility is a very
complex and difficult skill for players to learn and they may find it very difficult
when presented with a difficult course, which they have not experienced beforehand.
It may be that it is very difficult to accurately assess agility performance, but any test
of agility should include the essential elements such as acceleration, deceleration,
stopping and changes of direction.
There were no significant correlations found between any measures of rate of power
development (RPD) calculated from the countermovement jumps and
countermovement jumps with 30% of 1RM and the speed (r = 0.13 to -0.37) and
agility (r = 0.01 to -0.48) tests. The strongest correlation found was between RPD in
the first 30 ms of the CMJ with 30% 1RM and the agility test (r = -0.48) but was still
not significant. No previous research was found that had sought to correlate speed and
agility test times with measures of RPD in loaded and unloaded CMJs, or that had
reported RPD values to allow a comparison be made with this current study. So taking
this present study into account measures of RPD did not seem to be related to speed or
agility. A factor in this result may have been that the subjects in the study did not have
the ability to produce high levels of force or power, which may have been due to
individual characteristics or the consistency of their resistance training programs.
More research may be required between these measures of RPD and speed and agility.
Absolute peak power in the unloaded CMJ was significantly correlated with the 15-25
m (r = -0.57, p<0.05) and 25 m speed (r = -0.53, p<0.05) test, but this only explained
32.5% of the common variance in the 15-25 m speed time and 28.1% of the common
variance in the 25 m speed time. This was a new finding as no research was found that
sought to correlate peak power from a similar CMJ with these speed tests. Absolute
peak force in the unloaded CMJ or peak force/power in the CMJ with 30% 1RM did
not correlate with any other speed (r = 0.05 to –0.41) test times. Baker and Nance (3)
also revealed no significant correlation between absolute peak power in loaded CMJs
(40-100kgs) and 10 m (r = -0.07) and 40 m (r = -0.1) speed.
41
Relationship between speed, agility and measures of strength and power.
The value found in this study for absolute peak power of the unloaded CMJ was
4391.75 ± 816.15 W and 4051.27 ± 777.56 W for the CMJ with 30% 1RM. These
figures were lower than that reported by McBride et al (48) for an unloaded CMJ of
4906.2 ± 222.1 W and a loaded CMJ with 40 kgs 4747.4 ± 16736 W. The peak force
values reported in this study were 1887.81 ± 235.02 N for the unloaded CMJ and
2089.04 ± 265.3 N for the CMJ with 30% 1RM. These figures are lower than those
reported by McBride et al (48) 1924.9 ± 57.2 N (unloaded CMJ) and 2140.7 ± 39.3 N
(CMJ with 40 kgs).
Relative peak power in the unloaded CMJ was significantly correlated to 15-25 m (r =
-0.52, p<0.05) speed and reasonably but still not significantly correlated to 25 m (r =
-0.46) speed. The significant correlation explained only 27% common variance in the
15-25 m speed time. However no other significant correlation was found between
relative peak power/force in the unloaded CMJs or CMJs with 30% 1RM and any
other speed time (r = 0.16 to -0.46). Cronin and Hansen (5) found significant
correlations between relative mean power in loaded CMJ (30kgs) and 5 m (r = -0.55)
and 10 m (r = -0.54) speed. However in their study Cronin and Hansen were using
subjects that were either part-time or full-time professional rugby league players.
Baker and Nance (3) also found a significant correlation between relative peak power
in loaded CMJs (40-100 kgs) and 10 m (r = -0.56) and 40 m (r = -0.78) speed, in a
study using professional rugby league players, but they performed the CMJs in a
smith machine.
The present study used subjects that were lighter and smaller (79.7 ± 8.5 kgs / 178.9 ±
5.6 cm) than those used in both Cronin and Hansen (5) (97.8 ± 11.8 kgs / 183.1 ± 5.9
cm) and Baker and Nance (3) (93.4 ± 11.7 kgs / 181.9 ± 7.0 cm). The current subjects
may have had similar loads (30% of 1RM – 24 to 42kgs) to that of Cronin and Hansen
(5) 30kgs, but lighter than that of Baker and Nance (3) who used 40-100kgs. The
subjects in the present study were 15.9 kgs lighter than the average of the other
studies and 3.6 cms smaller. This has been reported to have an effect on the
corresponding power outputs (5). Baker and Nance (3) suggested that with the heavier
the load used in the loaded CMJs, there was a greater power output and that the
appropriate load for peak power output may depend entirely on the individual. They
estimated this load to be between 30% and 65% of their 1RM.
42
Relationship between speed, agility and measures of strength and power.
Even though some correlations were evident between measures of power and speed in
the present study, these were not as significant as those shown in previous research (3,
5). Another factor in this is that sports players have been reported to adapt to the area
of the force velocity curve (Appendix B) that the majority of their training takes place
(48). It could possibly be that the current subjects performed the majority of their
training at the low force high velocity end of the force velocity curve. This might
explain to some extent why the correlations that existed were between the unloaded
CMJs rather than the loaded CMJs as compared to the other studies where resistance
training had been more regular and programmed. Some other factors, which might
also be relevant here, were the stage of training cycle the subjects were at, their
resistance training history and the effectiveness of their technique during the loaded
CMJs.
Absolute peak power in the unloaded CMJ correlated significantly with the 25 m
agility (r = -0.53, p<0.05) test. This was also a new finding from the present study but
only explained 28.1% common variance in the 25 m agility test. A factor in this may
be that both actions are SSC type movements that involve acceleration/deceleration
profiles and both are dynamic movements in nature. There was no research found that
examined the relationship between peak power and agility. There were no other
significant correlations found between absolute peak power/force in the unloaded
CMJ or CMJ with 30% 1RM and the 25 m agility (r = 0.40 to –0.40) test.
The vertical jump (from the Vertec system) heights were significantly correlated to all
the speed test times (r = -0.50 to -0.73), the strongest correlation was with 10 m (r =
-0.73, p<0.01) speed, similar to Wisloff et al (10) for 10 m speed (r = -0.72). However
the vertical jump in this study only explained 53% of the common variance with 10 m
speed. The height jumped in the vertical jump of 57 ± 7 cm was similar to that of 56.4
± 4 cms reported by Wisloff et al (10), which was assumed included the use of the
arms when the height of the jump was considered, as the study did not reveal this
information.
The unloaded CMJ height was also significantly correlated to all the speed times (r =
-0.53 to -0.70). Research has also reported significant correlations between this
43
Relationship between speed, agility and measures of strength and power.
similar type of CMJ and 5 m (r = -0.60) and 10 m (r = -0.62) speed (5). The
significant correlation found between unloaded CMJ and 25 m (r = -0.69, p<0.05)
speed was very much in line with previous research over 30 m (r = -0.48 to -0.66)
speed (5, 26, 28) and 20 m (r = -0.66) speed (24). Berthoin et al (31) carried out a
study, which used male physical education students and also found a significant
correlation between countermovement jumps with the hands placed on the hips and 20
m speed (r = -0.58, p<0.01) and 50 m speed (r = -0.66, p<0.01).
The findings from the present study are therefore similar to that of previous research.
There does seem to be a relationship between unloaded jump height and speed and
this was not unexpected considering that both are dynamic movements requiring high
muscle power (26). As mentioned previously this may be due to training at the low
force high velocity end of the force velocity curve. These jumps are dynamic and
ballistic in nature where the projection of the body takes place in conjunction with
acceleration/deceleration profiles that have been reported to more closely simulate the
movement profiles of athletic activity (50 cited in 5) and this may be a factor central
to the significant correlations reported between unloaded jumps and speed
performance. However it would be necessary to carry out a specific training study
comprised of CMJs to see if a cause and effect relationship existed and identify if
improvements in speed had taken place. The jump height from the unloaded
countermovement jump was 37 ± 7 cms in this study compared to figures reported by
Cronin and Hansen (5) of 36.9 to 45.5 cms.
The CMJ height with 30% 1RM was significantly correlated with 10 m and 25 m
speed (r = -0.50 to -0.56, p<0.05). Other research also reported a correlation between
loaded CMJ (30kgs) and 5 m (r = -0.64), 10 m (r = -0.66) and 30 m (r= -0.56) speed
(5). The correlations for this CMJ in this study are not as high as that for Cronin and
Hansen (5). This may be due to the experience level of the subjects in performing
these loaded jumps. Even though they had practiced the jumps and become familiar
with them, it was obvious that they had little or no experience of performing such
techniques in training and found it much easier to perform the unloaded jumps.
Cronin and Hansen (5) reported a loaded CMJ (30kgs) height of 25.6 to 31.2 cms
compared to that in this study of 20 ± 3 cms. This may also be due to subject
44
Relationship between speed, agility and measures of strength and power.
experience level and/or subject characteristics (strength levels), and the subjects in
this study were smaller and lighter than those used in other research.
There was a reasonable correlation found between CMJ height with 30% 1RM and
agility but it was not significant (r = -0.47). None of the other jump heights showed
any correlation with the 25 m agility test. These findings are in line with previous
research conducted between CMJ height and agility (10, 24). The reasonable
correlation found between CMJ 30% and agility, even if not significant was still
surprising considering the lower correlation with 5 m speed (r = -0.34), keeping in
mind that acceleration is a key factor in the performance of both.
There was a significant correlation found between the 30 cm depth jump height and
10 m (r = -0.68, p<0.01), 25 m (r = -0.58, p<0.05) and 15-25 m (r = -0.58, p<0.05)
speed. The correlations with 10 m, 15-25 m and 25 m are relatively new findings
compared to the existing literature. There was also a significant correlation between
the RSI from the depth jump and 5 m and 10 m (r = -0.52, p<0.05) speed. Young et al
(11) also reported a correlation between the RSI from 30cm depth jump and 8 m (r =
-0.55) speed. The RSI did not correlate with 25 m or 15-25 m speed, as was similarly
found by Cronin and Hansen (5) between RSI from 40cm depth jumps and 30 m (r =
-0.34) speed, and Young et al (23) between RSI from 30 to 75cm depth jumps and the
fastest 10 m within 50 m (r = -0.19 to –0.44) speed. The mean ground contact time for
the 16 subjects while performing the depth jumps was 258ms ± 4 ms. This time for
the depth jump, which is thought to be a measure of fast stretch shortening cycle
performance, was outside the 250ms that generally is accepted as a range for ground
contact time in standard depth jumps (46, 47 cited in 5). This may have been a factor
in the resulting correlation with 5 m and 10 m speed rather than 15-25m or 25 m
speed times, when its considered that ground contact times during acceleration are of
a longer duration compared to maximum speed (13, 45). The subjects in this study
had been given opportunity to practice the depth jumps, but still when they performed
the depth jumps during testing it was evident that some of them had little experience
of regularly performing these jumps in their training. This may have been a factor in
the high ground contact times that resulted.
45
Relationship between speed, agility and measures of strength and power.
Leg stiffness did not correlate with any of the speed test times (r = -0.09 to -0.12).
Similarly Chelly and Denis (27) found no correlation between leg stiffness and initial
acceleration (r = 0.18), while Bret at al (28) also found no correlation with 30 m (r =
-0.35) speed. The finding in this study could be a result of muscle contraction velocity
being low during the acceleration phase corresponding to the longest contact phases,
which does not require great leg stiffness (28). And therefore the suggestion is that leg
stiffness is more related to maximal speed running from 40 to 100m (27, 28, 30)
rather than acceleration. The leg stiffness values in this study were 25.41 ± 4.82 kN/m
which were similar to that of 26.0 ± 7 kN/m reported by Chelly and Denis (27) but
lower than what was reported by Bret et al (28) 31.4 ± 4.5 kN/m.
There were no significant correlations found between depth jump height (r = -0.20),
RSI (r = 0.25) or leg stiffness (r = 0.01) and the 25 m agility test. Young et al (24)
also found no significant correlations between reactive strength (r = 0.30) measured
from a 30cm depth jump and agility over 20 m, which consisted of 3 * 90 degree
changes of direction. However Young et al (11) found significant correlations
between 30cm depth jump RSI and agility (r = -0.54) over eight metres. Young et al
(11) attributed this correlation to the similarity in the push-off mechanism used to
change direction and that used in assessing reactive strength through the depth jump.
The agility course used by Young et al (11) consisted of four 60 degree changes of
direction over eight metres compared to the agility course in this study which
consisted of two 66 degree and two 101 degree changes of direction over 25 m.
The same study also reported some significant correlations and some non-significant
correlations between single leg 15cm depth jump RSI and agility courses with varying
angles in the changes of direction used (Table 2). It may be more appropriate to assess
individual leg reactive strength and compare it to agility. Similarly leg stiffness
showed no correlation with agility, which suggested the movement of hopping
continuously for height with low ground contact time was not related to the agility
test. No research has been carried out investigating the relationship between leg
stiffness and agility. Power and strength qualities contributed little to agility
performance from the results of this study and other previous research (24, 49).
Agility may be more reliant on other factors such as flexibility, limb length, stride
46
Relationship between speed, agility and measures of strength and power.
length, concentric/eccentric leg strength and the capacity to change velocity quickly
while also quickly changing direction (49). The combination of all the perceptual and
technical factors involved in agility makes it difficult to specifically identify the actual
factors that influence agility performance.
7.0 Conclusion
The main findings from this study in general were that a number of strength and
power measures were correlated with different split sections of speed, but to a very
minor extent in agility and that speed and agility seem to be independent tasks. Some
specific measures of strength and power did not correlate with speed and this was not
in line with previous research. The vertical jump and the countermovement jump
showed the most significant correlations with the speed test. The countermovement
jump with 30% 1RM was significantly correlated with 10 and 25 m speed but these
correlations were not as strong as those in previous research. Depth jump height and
reactive strength index showed some significant correlations with speed times but no
relationship seemed evident between absolute/relative strength, leg stiffness or rate of
power development and speed. Both absolute and relative peak power in the CMJ
47
Relationship between speed, agility and measures of strength and power.
correlated significantly with 15-25 m speed time, however no other correlations were
found between peak power/force and speed.
The only measure in the study to correlate significantly with agility was absolute peak
power in the countermovement jump. The subjects used had low strength levels when
compared to similar studies and because they may be at the low force high velocity
area of the force velocity curve in correspondence to their training, this could have
had a significant effect on the correlations revealed in the study.
8.0 Future Research
Some correlations between strength and power measures and speed and agility did
become apparent in the results of the study. This does not mean however that a cause
and effect relationship exists between the variables but only that there is some
relationship between them. The next step to investigate if a cause and effect
relationships exists would be to carry out a controlled training intervention study.
Future research should focus on the relationship between concentric methods of
strength assessment and 5 m and 10 m speed to more fully determine the effect that a
simple test of concentric strength has on the acceleration capabilities. Careful choice
and reporting of measures as well as the different types of movements (parallel squat,
countermovement jumps, vertical jumps) used in studies are required if assessment
48
Relationship between speed, agility and measures of strength and power.
and training protocols are to be advanced through the use of correlation research. The
majority of research carried out in this area seems to use vertical type movements
(squat, vertical jumps) to predict sprinting, which is a horizontal activity in nature.
Future research may be advised to examine movements that require predominantly
horizontal force production.
It would be important to investigate whether the different phases of speed improves in
conjunction with improvements in strength and power. This would require subjects to
take part in a properly organised and programmed training study. A training study
may also be required for agility to examine the effect of strength and power
improvements. This could involve one group carrying out specialised agility training
and strength and power training with another group carrying out just strength and
power training. To find out what type of improvements are made in agility by both
groups.
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Relationship between speed, agility and measures of strength and power.
10.0 Appendix Appendix A
The following equations for the calculations of leg stiffness are adapted from Dalleau et al (2003).
F (t) = Fmax * sin (π/ Tc * t) (1)
Where Fmax is PF, Tc is contact time, and is the half period of the sine wave.
Determining FmaxThe momentum changes during contact
Tc [F(u) – Mg] * du = MΔv = MgTf 0
where v is vertical velocity, M is body mass, g is gravitational acceleration, Tc is contact time
and Tf is calculated by the mean of flight time before and after one contact.
Substituting (1) in this equation gives
Tc [Fmax * sin (π/ Tc * u)– Mg] * du = MΔv = MgTf
55
Tc
0
∫
∫
Tc
0
∫ ∫ ∫ t
0
Relationship between speed, agility and measures of strength and power.
0
[-Fmax Tc/ π * cos (π / Tc * u)] - MgTc = MgTf
2Fmax Tc/ π = Mg[Tf + Tc]
The PF is then obtained:
Fmax = Mg * π /2 * [Tf/Tc + 1] (2)
Calculation of velocity:
By integrating the vertical acceleration of the body, the velocity is:
tv(t) = [F(u)/M – g] * du + v (0) 0
where v(0) is the downward vertical velocity at the moment of contact.
tv(t) = [Fmax/M * sin (π/ Tc*u) -g] * du + v (0) 0
v(t) = [ -Fmax/M *Tc/ π * cos (π/Tc * u)] -gt + v(0)
v(t) = -Fmax/M *Tc/ π * cos(π/Tc * t) + Fmax/M* Tc/ π – gt + v(0)
Knowing that the vertical velocity is zero at the middle of the contact:
V(Tc/ 2) = 0 = Fmax/M *Tc/ π – gTc/2 + v(0)
Fmax/M *Tc/ π + v(0) = gTc/2
Thus the final expression of the velocity is:
V(t) = - Fmax/ M * Tc * cos (π/ Tc * t) –gt + gTc/2 (3)
Calculating vertical displacement:
By integrating the above expression:
t
z(t) = [ -Fmax/M *Tc/ π * cos (π/Tc * u)- g * u + gTc/2] *du
0
z(t) = [-Fmax/M *Tc²/ π² * sin (π/Tc * u) –½g * u²] + gTc/ 2*t
The equation for displacement is then:
56
Relationship between speed, agility and measures of strength and power.
Z(t) = -Fmax/M *Tc²/ π² * sin (π/Tc * t) –½g * t² + gTc/ 2*t (4)
In order to calculate the stiffness, the total displacement at the middle of the contact is
calculated:
Z(Tc/2) = -Fmax/M *Tc²/ π² - ½g * (Tc/2) ² + gTc/2 * (Tc/2)
Z(Tc/2) = -Fmax/M *Tc²/ π² + gTc² /8 (5)
The stiffness calculation:
The stiffness is the ratio of the PF to the total displacement:
K = Fmax/ z(0) – z (Tc/2) = Fmax/ - z (Tc/2)
Using the expression from (2) of Fmax and (5) of z (Tc/2), the final equation is:
K/M = π * (Tf + Tc)/ Tc² *(Tf + Tc/ π - Tc/4) (6)
As a result the stiffness can be calculated from flight and contact time.
Appendix B
FORCE FORCE
VELOCITY
VELOCITY
after
after
(a) (b)
The relationship between force and velocity, based on the work of Hill (1953). (a) The dark curve shows the change produced by heavy strength training (b) the dark curve shows the change produced by low load, high velocity training (after Zatsiorsky, 1995) (40).
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Relationship between speed, agility and measures of strength and power.
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Relationship between speed, agility and measures of strength and power.
59