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

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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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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

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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

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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

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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

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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

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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.

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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

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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


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

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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.

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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)


-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*


-0.29

*Statistical significance

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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).

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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.

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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*


-0.40


-0.53*


-0.31


-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*


-0.29 -0.51


-0.28 -0.44


-0.23 -0.46


-0.39 -0.43

DJ15 - 4 turns (60 deg)

-0.54* -0.59*

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*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).

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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-

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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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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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http://www.powerlifting-ipf.com/IPF_rulebook.pdf

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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

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Tc

0

∫

∫

Tc

0

∫ ∫ ∫ t

0


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:

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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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Examination of the Relationship between Speed, Agility & Measures of Strength & Power

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