Key Concepts: Sport Biomechanics by peter walder

Key Concept Series

Low velocity (high-pressure)

Shortly after foot contact

Mid Stance

Shortly before toe off

High velocity (low-pressure)

Magnus Force

B C F

B E D

Mr Peter Walder: Dr Andrew Barnes: Mr David Malpass M r R o b i n G i s s i n g : M r To m J o l l e y FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

ÂŠ P. WALDER 2012

Sport Biomechanics Introduction

Key Concepts Series

This book presents a series of posters created as part of a project to support students studying sport biomechanics modules at Sheffield Hallam University. Each poster addresses a key concept in Sport Biomechanics and, via Quick Response (QR) codes, provides access to a movie based explanation by a module tutor or student of the content on the poster. In their original format the posters were presented on a learning wall. Students were encouraged to interact with the posters, outside of the standard lecture and workshop sessions, using scanning software on their mobile phones. The content on the posters, including the movies accessed via the QR codes, reviewed content that was covered in the lectures and workshops. Project Leader Mr Peter Walder Project Team Dr Andy Barnes, Mr David Malpass (student), Mr Robin Gissing, Mr Tom Jolley.

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

ÂŠ P. WALDER 2012

Sport Biomechanics

Key Concepts Series

SPORT BIOMECHANICS ‘Sport Biomechanics is the study of internal and external forces, and their effects, when considered in the context of sport activities’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

S p a t i a l a n d Te m p o r a l Va r i a b l e s An athlete’s pattern or style of running may be analysed by considering the timing and position of body landmarks and segments at key event in a running cycle. A running cycle is defined as the period from the occurence of one key event, such as a foot strike, to the next occurence of the same event. For example right foot strike to right foot strike. Within a running cycle there are key events which provide a basis for comparing body positions under different conditions. Figure 1 show a number of body positions during a running cycle with key events identified.

Running velocity may be calculated by finding the product of stride length and stride frequency:

Within a running cycle there are a number of different phases based on the periods of time a foot is in contact with the ground and the period that it is recovering and preparing for the next contact phase. Figure 2 shows a representation of the sequence of these phases for the left and right legs during running.

Running Velocity = SL

Figure 3. Shows trends of stride length and stride frequency that researchers have observed for different running speeds. LEFT LEG RIGHT LEG

LEFT FOOT STRIKE

2.5

LEFT FOOT RIGHT FOOT RIGHT FOOT LEFT FOOT TOE OFF STRIKE TOE OFF STRIKE

1 2

SUPPORT (RIGHT)

2.0

ONE STRIDE SUPPORT (LEFT)

SWING (RIGHT)

FLIGHT

Stride Frequency 1.5 (Hz)

FLIGHT SWING (LEFT)

SF SWING (RIGHT)

Figure 2. Phases in the running cycle

Stride Length (m)

0.5

0 0

Running Speed (m/s)

The distance between the contact point of a foot strike to the next occurence of a foot strike of the same foot is known as a stride length (SL). This is measured in metres. The period of time that passes between two such consective events gives the stride time (s) (ST). By noting that one running cycle has occured in the recorded time (1/ST) the stride frequency (Hz) is derived.

SL = stride length SF = stride frequency

Figure 3. Stride Length and Stride Frequency in relation to running speed

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis Figure 1. Running cycle and key events FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

http://goo.gl/R4zNU

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

KINEMATICS ‘The study of motion without reference to its cause(s)’ KINETICS ‘The study of the cause(s) of motion’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Ve c t o r s

Measures of biomechanical variables are either scalar or vector quantities. Scalar quantities, such as distance and speed, only report on the magnitude of the variable being measured. In contrast, vector quantities, such as displacment, velocity, acceleration and force, report both the magnitude and direction of a measured variable. Vector quantities may be represented by arrows whose length equates to the magnitude of the variable and whose orientation (angle) and sense (direction of the arrow head) represents the direction of the variable (fig. 1). Note that, in Figure 1, vectors A and B are equivalent (as their magnitued and direction are shown to be the same) but vector C is not an equivalent vector. This is because, despite the fact that it has the same length and orientation as A and B, its direction (shown by the arrow head) differs.

in Figure 3. This involves constructing a parallelogram where two sides are formed by the original vectors and the diagonal bisecting the original vectors represents the resultant.

Vectors which are acting at right angles lend themselves to deriving resultants using simple numerical techniques. Figure 4 shows two ‘component’ vectors acting at right angles. The resultant (R) can be calculated by applying Pythagoras’ theorem. The formula for this is: R=

(A2 + B2)

Figure 2. Resultant (R) derived using ‘head to toe’ method.

A B

Figure 1. Arrow representation of vector quantities Vector quantities can be combined and the ‘resultant’ derived. This is shown graphically in Figure 2 where two vector arrows representing two different quantities have been placed head-to-toe and the resultant shown to be an arrow drawn from the ‘toe’ of the first vector to the ‘head’ of the second vector. The new vector, called the resultant, shows the outcome that would be realised by combining the original two vectors. Another method, which achieves the same outcome, is shown FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 4 Resultant (R) for two components at right angles.

Consideration of Figure 4 shows that a reverse process to that for derving a resultant may be used to calculate the value of the components if the magnitude and direction of the resultant is known. In such circumstances, where R and are known, the following formula may be used to derive values for the components. A = R.Cos B = R.Sin

Figure 3. Resultant (R) derived using the parallelogram method. Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/OCirj

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

TANGENT ‘The tangent to a curve at a given point is the straight line that touches the curve at that point.’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Interpreting Graphs

If the average speed over the duration of the race is desired this can be calculated by dividing 100m by the time taken to complete the distance. In Figure 2 the average speed is represented by the gradient of the line joining the start and finishing position. However, if a value for an instantaneous speed is required then a tangent must be constructed at the point of interest and its gradient calculated as shown in Figure 3.

Interpreting graphs, beyond directly reading off values, is an important skill. Figure 1 shows a graphical representation of the position values versus time for a typical 100m sprint trace. Values of the position from the start can, in principle, be read off for any desired time between the start and end of the race. Position v Time for 100m 100

P O S I T I O N (m)

The steepness of the slope of a tangent corresponds to the magnitude of the variable represented by the gradient; steep slopes equate to hgh magnitudes and shallow slopes to low magnitudes.

first tangent which has a positive slope represents positive acceleration and the second tangent with a negative slope a negative acceleration. Figure 5 shows a tangent with a zero slope and therefore represents an instantaneous acceleration of zero. 12

T T

S P E E D (m/s)

Figure 4 shows a velocity versus time graph for a typical 100m race and two tangents representing instantaneous acceleration. The direction of slope equates to the direction of the acceleration. So the Position v Time for 100m

0 10

0 TIME (s)

Figure 4. Tangents on a velocity versus time curve with gradients representing positive and negative accelerations.

100 0

Zero

TIME (s)

Figure 1. Position versus time for a 100m sprint race x

Position v Time for 100m

P O S I T I O N (m)

100

P O S I T I O N (m)

S P E E D (m/s)

50 0

0 0

5 TIME (s)

Figure 3. Tangent drawn at a specific time with a slope of y/x representing the instantaneous speed. 0 0

TIME (s)

Figure 2. Average speed represented by the gradient of a straight line joining the start and end positions FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

0 TIME (s)

Figure 5. Tangent on a velocity versus time curve representing a zero acceleration.

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

http://goo.gl/JmQqX

ÂŠ P. WALDER 2012

Sport Biomechanics

Key Concepts Series

FORCE ‘A vector quantity that describes the action of one body on another either directly (e.g. ground reaction force) or indirectly (e.g gravity)’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics Ground Reaction Forces During the foot contact phase of a running cycle (see Figure 1) a runner applies a force to the ground that has a magnitude and direction that directly corresponds to the sum of the accelerations of all of the segments of the runner’s body. According to Newton’s Third Law of motion, if the ground (planet) is experiencing a force then, the runner must also be experiencing a force of equal magnitude but of an opposite direction. The force the runner experiences is known as the Ground Reaction Force. Shortly after foot contact

Mid Stance

Shortly before toe off

Key Concepts Series

Shortly after foot contact

Mid Stance

Shortly before toe off

Figure 3. Ground Reaction Force Components The single resultant ground reaction force may be considered in terms of its vertical and horizontal components (See Figure 3).

Force (N)

Time (s)

Figure 4. Vertical Ground Reaction Force v time Shortly after foot contact

Mid Stance

Shortly before toe off

Figure 1. Sequence positions during a single footfall The magnitude and direction of the ground reaction force will vary (see Figure 2) according to the sum of the accelerations of the body segments at any particular instant.

By plotting the variations in the vertical and horizontal ground reaction force components over the duration of the foot contact, force v time traces can be constructed for the footfall (see Figures 4 and 5). Consideration of the characteristics of the traces can reveal insights into the acceleration experienced by the runner and also potential causes of injury. + Force (N) 0 Time (s) -

Shortly after foot contact

Mid Stance

Shortly before toe off

Figure 2. Superimposed ground reaction force vectors at three instances during a footfall FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 5. Horizontal Ground Reaction Force v time Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

http://goo.gl/wWaOP

Sport Biomechanics

Key Concepts Series

IMPULSE ‘The effect of a force acting over a period of time’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics Impulse

Impulse is the action of a force applied over a period of time on an object. To understand the consequences of an impulse the fundamental principles of Newton’s Second Law needs to be considered. Newton’ Second Law can be stated as: F = ma

Key Concepts Series

+ Force (N) 0 Time (s)

By expanding the acceleration term the expression becomes F = m(vf - vi) t By rearranging the formula Impulse may be represented by the term on the left side of the equation. Ft = m(vf - vi) Consideration of the equation shows that the impulse (Ft) of the force generates a change in velocity (vf - vi) which is proportional to the mass (m) of the object on which the forces is being applied.

+ Force (N) 0 Time (s) -

Figure 1. Anterior-Posterior Ground Reaction Force acting during a single footfall In Figure 1 the horizontal (anterior-posterior) ground reaction force acting over the period of a footfall is shown. Consideration of the impulse formulae shows that it is the area under the force v time curve that represents Impulse (Ft).

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 2. Area Under Anterior-Posterior Ground Reaction Force representing the net impulse generated during a single footfall. The area shown in Figure 2 represents the impulse generated during a single footfall. The negative area below the horizontal axis represents the resistive effect of the impulsive force and the positive area above the horizontal axis represents the propulsive effect of the impulsive force. The combined area therefore shows the ‘net’ impulse, in a horizontal direction, acting on the athlete during the footfall. A net postive value for the net impulse would show that during the footfall athlete gained velocity and a negative net impulse would be associated with a loss in velocity. To determine a value for the change in the velocity the impulse equation can be rearranged again to show that the value for impulse must be divided by the mass of the object which is experiencing the force. Ft = (vf - vi) m

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/uyCX3

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

NEWTON’S FIRST LAW ‘Every object will continue in a state of rest of uniform motion in a straight line unless acted upon by a net external force’

NEWTON’S SECOND LAW ‘The acceleration experienced by an object is directly proportional to, and parallel to, the net applied force’

NEWTON’S THIRD LAW ‘When one object exerts a force on a second object there is an equal (in magnitude) but opposite (in direction) force exerted by the second object on the first’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Impulse(vertical)

Impulse is the action of a force applied over a period of time on an object. To understand the consequences of applying an impulse the fundamental principles of Newton’s Second Law need to be considered. Newton’s Second Law can be stated as:

Force (N)

Figure 4. Vertical Ground Reaction Force and Weight acting at an instant.

F = ma By expanding the acceleration term the expression becomes: F = m(vf - vi) t By rearranging the formula Impulse may be seen to be represented by the term on the left side of the equation. Ft = m(vf - vi) Consideration of the equation shows that the Impulse (Ft) of the force generates a change in velocity (vf - vi) which is proportional to the mass (m) of the object on which the forces is being applied.

Force (N)

Time (s) Figure 2. Area under Vertical Ground Reaction Force trace representing the impulse generated during a single footfall. The area shown in Figure 2 represents the Impulse generated during a single footfall by the vertical ground reaction force. This Impulse needs to be considered in association with the impulse generated by the gravitational force (weight) which is also acting on the runner. Figure 3 illustrates the combined Impulse generated by vertical ground reaction force and the gravitational force (runner’s weight) during a running footfall. Figure 4 illustrates the associated vertical forces acting on the runner at an instant during the footfall.

Force (N)

In Figure 1 the vertical ground reaction force acting over the period of a footfall is shown. Consideration of the impulse formulae shows that it is the area under the force v time curve that represents Impulse (Ft).

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Ft = (vf - vi) m An alternative way of conceiving net Impulse is to consider the net vertical force (vertical GRF weight) acting on the runner over the footfall as a single trace. When the Impulse associated with the net force is represented on such a trace, the relevant area is displayed as shown in Figure 5.

Force (N) +

Time (s) Figure 1. Vertical Ground Reaction Force acting during a single footfall

To determine a value for the change in the vertical velocity, the impulse equation can be rearranged again to show that the value for net Impulse must be divided by the mass of the object which is experiencing the force.

Time (s)

Figure 5. Net vertical impulse acting during a single footfall

Figure 3. Vertical Ground Reaction force impulse and Gravitational (weight) impulse acting during a single footfall Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/Z43qv

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

CENTRE OF GRAVITY ‘The point at which the weight of the body may consider to act’ CENTRE OF MASS ‘The imaginary point, associated with a body, that moves in response to net external forces in exactly the same way as would a particle of the same mass as that of the associated body’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Gravity And Projectiles

Vertical Displacement (m)

An object projected into the air without any effect of gravity would follow a path as indicated by line A in Figure 1. In accordance with Newton’s first law, once projected, an object would continue on a straight path at a constant speed. However, when gravity is considered to act this path changes to one represented by curve B in Figure 1.

Speed of release is represented by the magnitude of the vector arrow representing velocity

Angle of release

15 m/s 20 m/s 25 m/s

Angles of release = 30o, 45o & 60o

Height of release

Horizontal Displacement (m)

Figure 1. Paths of object projected into the air without (A) and with (B) the effects of gravity. As gravity acts in a vertical direction only the vertical component of the object’s velocity is affected by the gravitational force and this causes the object to follow a particular path called a parobola. Figure 2 shows the path of a projectile that is released at a height higher than that of its landing. Consideration of the illustration shows the variation in vertical velocity while the horizontal velocity maintains a constant value.

Figure 2. A projectile path showing changes in component velocities FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 3. Paths of projectiles released at different angles and at different speeds. Figure 3 shows paths of projectiles released at a variety of speeds and a variety of angles. Inspection of the traces reveals that, if a projectile lands at the same height as it is released and the aim of the projection is to maximise horizontal range, the optimum angle of release will be 45 degrees. For many sports the release and landing heights will be different. In such cases the optimum angle to maximise range will be different. Where the landing height is lower than the release height then the optimum release angle will a values less than 45 degrees. Where the landing height is greater than the release height the optimum angle will be greater than 45 degrees. To calculate the precise horizontal distance that a projectile will travel its speed and angle of release must be known along with the relative height of release (See Figure 4).

Figure 4. Release parameters of a projectile It is important to note that projectile principles apply to all objects that are projected into the air. In the case of sports performers, who project their bodies into the air e.g. long jumpers, high jumpers, gymnasts, divers etc. To understand projectile principles the path of centre of gravity of the performer must be considered. As with all analyses of projectile principles, for parabolic flight to be considered during a projection, any effects of air resistance need to be ignored.

http://goo.gl/jGIJN

Sport Biomechanics

Key Concepts Series

WORK ‘Work is done when a force moves an object through a distance’ POWER ‘The rate of doing work’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Power and Work

Power, as a term, is often used quite casually when describing sport performance. However, in mechanics, Power has a quite specific meaning. Power is defined as ‘the rate of doing Work’ where Work is considered to have been done when an applied force causes the point of application* to move along the line of action of the applied force. (*N.B. The point of application is considered to be

Power v Time: Vertical Jump 3000 2000 Power (W)

Velocity v Time: Vertical Jump

1000

the centre of mass for whole body investigations).

3.0

0 0

2.0 Velocity (m/s)

Work can therefore expressed as: W = fd where W = work f = force d = displacement

0.4

Time (s)

0.6

0.8

1.0

-2000

0.0 -1.0

0.2

0.4

Time (s)

0.6

0.8

1.0

-2.0

Given that Power is the rate of doing work the formula for Power can be written as: P = fd = fv t where P = power f = force d = displacement t = time v= velocity

0.2

-1000 1.0

Figure 2. Vertical velocity during a vertical jump take of movement. Figure 1 shows the vertical ground reaction force generated during the take off phase of a vertical jump. Figure 2 shows the corresponding vertical velocity trace for the same movement. Using the forumula P=fv to find the product of corresponding force and velocity values generates a Power trace as shown in Figure 3. This clearly illustrates the timing and magnitude of maximum power output.

Figure 4. Area under a Power v time curve reprsenting Work. The units of measurement for Power are Watts or Joules/second. If the second of these unit expresions is considered the rate of change nature of Power related to Work is evident P = fd t it can be noted that a re-arangement of the forumula wil give: Pt = fd This shows that the area under the Power curve (Pt) represents Work and this is shown in Figure 4. A continuos integration of the Power v time trace gives a Work v time trace (Figure 5.)

As Power = Force x velocity, measurements may be taken from a vertical jump peformed on a force platform to get a value of power output. Power v Time: Vertical Jump

Work v Time: Vertical Jump 400

3000

300 200

1000

GRF v Time: Vertical Jump

0 0

-1000

Force (N)

-2000

2000 1500 1000 500

0.2

0.4

Time (s)

0.6

0.8

1.0

Figure 1. Vertical ground reaction force during a vertical jump take off movement. FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

0.2

0.4

Time (s)

0.6

0.8

1.0

Work (J)

Power (W)

2000

100 100 -100 0 -200

0.2

0.4

Time (s)

0.6

0.8

1.0

-300

Figure 3. Power generated during a vertical jump Figure 5. Work v time trace derived from the area take off movement. under the Power v time trace. Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/4FDZE

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

ANGULAR DISPLACEMENT ‘The smallest angle between a starting and finishing position with direction specificed’ ANGULAR VELOCITY ‘The rate of rotation calulated ast the first derivative of angular displacement’ ANGULAR ACCELERATION ‘The rate of change of angular velocity with respect to time’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Angle Measurement (2D) There are a number of ways that angles can be measured to record the postions of the body. These can broadly be categoised into three types. Firstly there are those measurement systems that are designed to record the position of segments with respect to some fixed reference. These are called absolute angles. The fixed reference is often a horizontal line (but can be vertical) and is positioned either at the proximal or distal end of the segment. The angle is measured from the fixed reference in an anti-clockwise direction. An example of this type of

convention has been used. For the knee a three point joint angle convention and for the ankle a four point joint angle convention has been applied. There are good reasons why such a blend of conventions are used. The most compelling reason relates to the anatomical structures of the joints and the principle of modelling segments as rigid objects. Other variations of angle convention exist to ensure that appropriate measurements are made.

THREE AND FOUR POINT JOINT DEFINITIONS

HYBRID ANGLE CONVENTION FOR REOCORDING THE FLEXION/EXTENSION MEASUREMENTS OF THE HIP, KNEE AND ANKLE

CONVENTIONS FOR SEGMENT ANGLES OF UPPER AND LOWER LEG

A Right Leg Right Leg Left Leg Left Leg

Knee joint angle = four point based on intersection of long axes of upper and lower leg

Hip, knee and ankle joint angles based on three point definitions

Ankle joint angle = four point based on shank and foot parallel to surface

Figure 2 Joint Angles B Right Leg

Left Leg

A= Upper leg segement measured from the distal end of the segment B = Lower leg segement measured from the distal end of the segment

Figure 1 Segment Angles measurement system is shown in Figure 1 where the position of upper and lower leg segments are being recorded. A second type of measurement records relative angles. These do not rely on any fixed reference but

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

record the angle between two adjacent segments and as such normally define joint angles. The definition of a joint angle can be established using either 3 points with the middle point at the apex of the angle or using 4 points where the apex is defined by the intersection of the extensions of the line defining the longitudinal axes of the segments. Figure 2 ilustrates relative joint angles using these definitions. A third type of angle convention, sometimes known and the clinical convention (Hamill, 2003) adopts a measurement system which draws on both the relative and absolute definitions. Figure 3 shows such a system where hip, knee, and ankle flexion/extension angles are defined. For the hip, a variation of the absolute segment angle

Right Leg (furthest from camera) C Left Leg (nearest camera)

A= hip angle relative to the vertical - forward of the vertical equates to hip flexion; backward of the vertical equates to hip extension B = knee flexion relative to the longtitudinal axis of the upper leg C = ankle angle (four point based on shank and foot parallel to surface)

NOTE C

The angle c represents the plantar/dorsi flexion angle for the anke. A neutral position is represented by a 90 degree angle

Figure 3 Hybrid ‘clinical’ convention

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis HAMILL, J. and KNUTZEN, K. (2003) Biomechanical Bases of Human Movement. Lippincott, Williams and Wilkins

http://goo.gl/gA9vQ

Sport Biomechanics

Key Concepts Series

DEGREES AND RADIANS ‘Angle measurement uses degrees or radians a its unit of measurement. A degree represents 1/360 of a full rotation. A radian is equal to 57.3 degrees and is the standard unit of angle measurement in the SI system of measurement.’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Angular Kinematics

A number of different ways exist for defining joints. Fig 2 shows a convention for recording joint angles using flexion - extension definitions. This particular convention uses slightly different approaches to indentifying hip, knee and ankle angles. Different approaches are used according to the particular question that is being investigated.

ANGLE CONVENTIONS FOR SEGMENT ANGLES OF UPPER AND LOWER LEG

HIP Flexion 40

ANKLE

Angle (deg)

Dorsiflexion

130

120 -20

110

B Right Leg (furthest from camera)

Extension

100

-40

Left Leg (nearest camera)

0.1

0.3

0.2

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Time (s)

B = Lower leg segement measured from the distal end of the segment

Left foot strike

Moderate running speed (approx 3.5 m/s)

Right foot strike

High running speed (approx 7.5 m/s)

Plantarflexion

Figure 3. Hip joint angle v time for a running stride

100 80 60 40 20 0

Right Leg (furthest from camera)

0.2

0.3

0.4 0.5 Time (s)

0.6

0.7

0.8

0.9

1.0

Moderate running speed (approx 3.5 m/s)

Right foot strike

High running speed (approx 7.5 m/s)

Body positions are recorded by using angle measurements at key events or over a time series ‘frames’ such as those presented in video recordings. Key events are selected as easily identifiable positions within sports events which aid comparisons. For example in a running cycle events at foot strike, mid stance and toe of are often used. Over a time series angles are recorded sequentially and presented as graphical traces. Figures 3 4 and 5 show angle v time graphical presentations for hip, knee and ankle angles as defined using convention identified in Figure 2.

120

Angle (deg)

0.1

Left foot strike

Figure 5. Ankle joint angle v time for a running stride

KNEE

ANGLE CONVENTIONS FOR FLEXION/EXTENSION MEASUREMENTS OF THE HIP, KNEE AND ANKLE

90 80

A= Upper leg segement measured from the distal end of the segment

Figure 1. Segment angle convention Recording the position of the body requires measurement of segments and/or joint angles. A variety of different conventions can be used to achieve this. Fig 1 shows a common convention for recording segment angles using a fixed horizontal reference positioned at the distal end of a segment and the angle recorded in an anti-clockwise direction to the main axis of the segment.

Angle (deg)

0.1

0.2

0.3

0.4 0.5 Time (s)

0.6

0.7

0.8

0.9

Left foot strike

Moderate running speed (approx 3.5 m/s)

Right foot strike

High running speed (approx 7.5 m/s)

1.0

Once angular position and associated time values have been recorded further description of motion can be derived in the form of angular velocities and angular accelerations.

C Left Leg (nearest camera)

The angle c represents the plantar/dorsi flexion angle for the anke. A neutral position is represented by a 90 degree angle

Figure 2. Joint angle convention FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 4. Knee joint angle v time for a running stride

http://goo.gl/rOc7f

Sport Biomechanics

Key Concepts Series

LINEAR AND ANGULAR MOTION ‘In many sport movements, body segment rotations are sequneced to generate linear motion at segmental end points. This is seen is such activities as throwing and kicking. Where the aim is to optimise the linear velocity the timing of the sequencing of the rotations is critical.’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Relationship between Linear and Angular Kinematics Virtually all sport and exercise activities involve some form of rotation. This may be rotation of a body segment about a joint, or of the whole body about some axis. The objective is often to create a linear motion using rotation – e.g. a bowler gives linear velocity to the ball by rotating the arm about the shoulder The relationship between linear and angular motion is therefore relevant in many activities. Consider a rod of length r, that has rotated through an angle (θ). The linear distance (d) travelled by the end of the rod can be calculated as follows:

As a consequence of rotation about an axis, points on the rod possess a linear velocity (vT) that acts tangentially to the arc in which it is moving. The relationship between angular velocity (ω) and linear velocity (vT) is given by the following equation where (r) is equal to the radius of rotation. The objective is

An understanding of this relationship is used in many sports to help maximise the linear velocity of objects, e.g. golf.

EExample

A golf club being swung with an angular velocity of 30 rad∙s-1 and a radius from the axis of rotation to club head of 1.6 m.

d=r×θ (note that θ is expressed in radians) e.g. r = 1.5 m θ = 0.2 rad d = 1.5 x 0.2 = 0.3 m Therefore, for a given angular displacement the linear distance travelled by the end of the rod will be twice that of a point halfway down.

vT = r × ω

axis

Club head (tangential) velocity (vT) is given by: vT = r × ω vT = 1.6 × 30 vT = 48 m∙s-1 (Note that ω must be expressed in rad∙s-1) http://goo.gl/v9Bfw

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis Source: Cricket image used wtth permission. (http://www.flickr.com/photos/tgigreeny/4937542203/)

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

TANGENTIAL ACCELERATION ‘The component of linear acceleration tangent to the path of a particle moving in a circular path.’ CENTRIPETAL ACCELERATION ‘The radial component of the acceleration of a particle or object moving around a circle, which can be shown to be directed toward the centrr of the circle.’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Centripetal and tangential acceleration Centripetal acceleration:

Ta n g e n t i a l a c c e l e r a t i o n :

• When an object rotates around an axis, the direction of the ball is constantly changing therefore the ball is also accelerating l i n e a r l y, e v e n t h o u g h t h e a n g u l a r v e l o c i t y i s constant. • This linear acceleration is called centripetal a c c e l e r a t i o n ( α c) . • Centripetal acceleration always acts towards the axis of rotation. • D u r i n g a h a m m e r t h r o w, the hammer is experiencing a constant a n g u l a r v e l o c i t y ( ω) o f 2 0 r a d ∙ s -1 i n a c i r c u l a r path with a radius (r) of 1.5m. • Centripetal acceleration αc αc is calculated as: α c = r x ω2

e.g α c = r x ω2 α c= 1 . 5 x 2 0 2 α c= 6 0 0 m / s 2

• When an object rotates around an axis with an i n c r e a s i n g a n g u l a r v e l o c i t y, t h e o b j e c t i s a l s o experiencing angular acceleration. • This angular acceleration also causes a linear acceleration that acts on a tangent to the objects movement arc. • This linear acceleration is called tangential a c c e l e r a t i o n ( α t) . • D u r i n g a h a m m e r t h r o w, t h e h a m m e r i s experiencing an angular acceleration (α) of 70 r a d ∙ s -2, i n a c i r c u l a r p a t h w i t h a r a d i u s ( r ) o f 1.5m.

αt

eg.

• Ta n g e n t i a l a c c e l e r a t i o n i s calculated as: α t= r x α

α t= r x α α t= 1 . 5 x 7 0 α t= 1 0 5 m / s 2

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/eT8mU

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

TORQUE ‘Torque is the twisting or turning effect generated by a force acting off centre to an axis or pivot’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

To r q u e

torque may be considered to be mainly generated by the gymnast’s weight acting through the centre of gravity. Consideration of Figure 2. shows that the moment arm associated with the torque being generated varies cosiderably during a complete circle. At positions A and D there no moment arm and therefore zero torque is being generated. At positions C and F the moment arm is at its longest and therefore maximum torque is being generated; at position C this is a positive torque (anti-clockwise) and at F it is a negative torque (clockwise). So torque created by the gymnast’s weight through positions A D generates rotation in an anticlockwise direction and through positions D-A in a clockwise direction. In principle, if the gymnast started the move from a stationary handstand in position A, the rotation generated on the way up would exactly cancel out the rotation generated on the way down. In practice things are more complex with torques also being generated by friction forces at the gymnasts hands and by air resistance. Gymnasts employ techniques, such as adjusting their body position, to maintain their rotation. A

Torque or ‘Moment of the force’ are the terms used to describe the twisting or turning effect that a force applied away from an axis or pivot has on an object. For sports where rotation is a key part of the desired outcome, producing torque in order to create rotation is a fundamental requirement. Torque (or ‘moment of the force’) is defined by the formula: L=Fd where: L = torque F = the magnitude of the force acting perpendicular to the pivot or axis d = perpendicular distance (moment arm) from the pivot to the line of action of the force.

Observation of the formula shows that Torque can be changed by varying the magnitude of the force and/or the length of the perpendicular distance (moment arm) from the pivot/axis. Figure 1 illustrates the fundamental relationship between Force and the moment arm.

}

Figure 1. Torque defined by the magnitude of force acting a perpendicular distance from the pivot/axis. The rotation seen in the limb movements comprising human motion is generated by muscle forces being applied away from joint centres. For rotations of the whole body the axis, or pivot, may be a fixed point external to the body as is the case for a gymnast rotating around a high bar (see Figure 2) In such cases FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

}

E E

D Figure 2. Gymnast rotating around high bar with force and moment arm identified for position C and E. Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/MGkWy

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

MOMENT OF INERTIA ‘Moment of inertia is the reluctance of an object to change its rotational state of motion’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Conservation of Angular Momentum The quantity of angular motion that is possessed by an object is called its Angular Momentum. In order to generate angular momentum an external Torque or Moment of the Force must be applied to the object. In the absence of an external torque the Law of Conservation of Angular Momentum can be observed. Examples of this in sport are evident when performers are in a flight phase and where any effects due to fluid forces (air) are considered negligble. Figure 1 shows a series of positions, during the flight phase, of a gymnast peforming a front somersault.

The notion that the quantity of angular motion is conserved during flight can be difficult to appreciate as observers will see performers varying the speed at which they rotate. Such observations have their explanation in the relationship between Angular Momentum, Moment of Inertia and Angular Velocity. This relationship is stated as: H = Iw H = Angular Momentum I = Moment of Inertia w = Angular Velocity This relationship shows that during a period when Angular Momentum is conserved a change in Moment of Inertia will result in a change in Angular Velocity. Figure 3 shows the change in Moment of Inertia that occurs during the front somersault flight period and Figure 4 shows the corresponding change in Angular Velocity.

Figure 1. Sequence of somersault positions According to the principles associated with the Law of Conservation of Angular Momentum the gymnast, whilst in the air, will not be able to generate any more angular motion as there is no means for an external torque to be created. Therefore, during the period of flight, the Angular Momentum will remain constant as shown in Figure 2.

Angular Momentum High

Figure 3. Changes in moment of inertia

Low Time

Figure 2. Conservation of angular momentum during flight FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 4. Changes in angular velocity

By adjusting the distribution of their body mass relative to the transverse axis passing through the Centre of Mass, gymnasts, during a front somersault, can change their Moment of Inertia and therefore their Angular Velocity (rotational speed). Such changes in rotational speed are observed without there being any violation of the Law of Conservation of Angular Momentum. Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press http://www.youtube.com/watch?v=WTOPbtRBGoc

ÂŠ P. WALDER 2012

Sport Biomechanics

Key Concepts Series

MAGNUS EFFECT ’The magnus effect occurs when air flowing on different sides of a rotating object generates a pressure gradient due to spin thus causing force to arise in the direction of high to low pressure’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Fluid Mechanics and Ball Flight Fluid forces are important when explaining the flight characteristics of sport balls. Figure 1 shows air flowing around a ball in a laminar pattern. This is an ideal which is not repeated in the real world as the layers of air lose energy as they interact with the other layers and the surface of the ball.

Laminar Flow

The Bernouille Principle links the speed of air flow with pressure; high air flow speed is associated with low pressure and, conversley, low air speeds are associated with high pressure. In figure 2 this means that the fast moving air at the back of the ball will generate a low pressure. This creates a difference in pressure between the front and back of the ball and a force is generated parallel to the directon of air flow which acts from the front to the back of the ball. This is known as a drag force.

Magnus Effect Low velocity (high-pressure)

Figure 1 Laminar Flow

As the layer next to the ball slows down in separates from flowing around the ball contour and enters a phase of turbulent flow where the layers intermingle and the speed of the air flow increases.

Turbulent Flow High velocity (low-pressure) Magnus Force

S Figure 3 The Magnus effect for top spin

S=Separation Points Figure 2 Turbulent Flow FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

The Bernouille Priniciple can assist in providing the underlying explanation for the observation that, sports balls do not always follow the flight path that would be expected if gravitational force and the drag force (see Figure 2) alone were acting. The deviation from a ‘normal’ flight path is seen in sports where spin is introduced. The phenomena called the Magnus Effect occurs when a spinning ball drags the boundary layer (the layer next to ball’s surface) around in the direction of the spin. In Figure 3, which shows a top spin situation, the boundary layer being dragged around at the top of the ball is moving in a direction opposing the general flow; therefore the air slows down. In contrast, the boundary layer at the bottom of the ball is moving in the same direction as the general flow and therefore moves faster relative to the air at the top. This difference in velocity is associated with a difference in pressure and results in a force acting downwards (for top spin). The effect is seen, for example, in a tennis ball that ‘dips’ in its flight. The effect is not restricted to a downward acting force. A tennis ball with back spin will experience an upwards force. Whilst this will not overcome the effects of gravity, it will counter it to prolong the flight of the ball. Spin produced about a vertical axis will also generate the effect. This is commonly seen in soccer where the ball is seen to ‘bend’; note that the direction of spin will determine the direction of the ‘bend’.

Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis http://goo.gl/GOXUT WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

BERNOUILLE PRINCIPLE ’The Bernouille principle indicates that fast moving air is associated with low pressure and slow moving air with high pressure’

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Sport Biomechanics

Key Concepts Series

Lift and Drag

Lift and drag are forces that arise due to the characteristics of air flow around an object. Figure 1a shows a standard aerfoil shape with air flowing around the top within compressed layers which cause the air to speed up. Air flowing along the bottom surface of the aerofoil maintains a standard layer pattern. The relative difference of the speed of the air on the top and bottom surfaces is associated with a pressure differential. Low pressure on the top surface and high pressure on the bottom surface. This differential cause a force to act in the direction of the pressure gradient. The force is termed a lift force. The force acting at right angles to the lift force and opposing the directon of travel is termed the drag force. The relationship between the lift and drag forces can be varied by changing the attitude angle of the object. This angle is the angle between the main axis of the object and the direction of flow of the surrounding air. Figure 1b shows that an increase in the attitude angle up to a certain value will change the magnitude of the lift force in relation to the drag force. This change in lift force Lift

a Drag

Lift

Drag

b Lift

Figure 2. Attitude angle in ski jumping due to change various sports The change in value whereby

in attitude angle is exploited in including ski jumping and javelin. attitude angle may reach a critical the drag force becomes dominant

F i g u r e 4 . Va r i a t i o n s i n a t t i t u d e a n g l e a n d l i f t causing the object to ‘stall’ and losing its lift force (fig. 4a). This is sometimes seen in javelin. The attidude angle can also be varied so that the so called lift force generates a force in a downwards direction (fig. 4b). An alternative approach to achieving a downwards acting lift force from an aerofoil shape is to flip the object so the curved surface is on the bottom and flat surface at the top; this approach can be seen in the wings used on racing cars.

b Drag

Figure 1. Lift and drag in aerofoils FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY

Figure 3. Attitude angle in javelin Support Reading GRIMSHAW, P., LEES, A., FOWLER, N. & BURDEN, A. (2006). BIOS Instant notes in Sport and Exercise Biomechanics. Taylor and Francis

http://goo.gl/6qtI7

WALDER, P.J. (1994) Mechanics and Sport Performance. Feltham Press

Sport Biomechanics

Key Concepts Series

Units of Measurement TIME

s (second)

LENGTH

m (metre)

ANGLE

rad (radian) or (degree)

VELOCITY

m . s -1 o r m / s

A C C E L E R AT I O N

m . s -2 o r m / s 2

ANGULAR VELOCITY

r a d . s -1 o r . s -1

A N G U L A R A C C E L E R AT I O N

r a d . s -2 o r . s -2

FREQUENCY

Hz (hertz)

MASS

FORCE

N (newton)

IMPULSE

N.s

MOMENTUM

k g . m . s -1

PRESSURE

Pa (pascal)

TORQUE

N.m

MOMENT OF INERTIA

kg.m2

ANGULAR MOMENTUM

k g . m 2. s -1

ENERGY

J (joule)

WORK

J (joule)

POWER

W ( w a t t ) o r J . s -1

FACULTY OF HEALTH AND WELLBEING SHEFFIELD HALLAM UNIVERSITY