Moment = I x α

Moment = mass moment of inertia x angular acceleration 

I = m x d²

I = mass x radius of gyration²

F = m x a

F = m x ax - for horizontal

F = m x ay - for vertical

ΔS

Δt

Velocity x Δt = ΔS

ΔV

Δt

Acceleration x Δt = ΔV

V²

r

or

ω²r

Impulse = Δmv

Impulse = linear momentum

work

Δt

P = Fxd/Δt

P = F x v - linear 

P = T x ω - angular

Work = F x d

Work = F x d x cos(θ)

Work done = 1/2mv² final - 1/2mv² initial

The change in kinetic energy of an object is equal to the net work done on the object

F x d = ½mv²

When forces are balanced there is no movment, or movement happens at a constant velocity in a straight line

 A body in the state of static equilibrium is motionless and does not rotate

Shortest distance between the line of application of force and the axis of roation 

Moment is a measure of the ability of a force to generate roational motion

Torque = moment

Larger motor unit size = larger potentials
 

Higher recruitment frequency = larger potentials 

Larger fibres = larger currents

Larger the distance between electrodes and muscle = smaller potentials

Electrode skin interface - higher resistance = smaller potentials

DC offset - signal processing in the time domain 

DEMEANING

DC offset - signal processing in the time domain 

FULL WAVE RECTIFICATION

All positive values are kept

All negative values are made positive

DC offset - signal processing in the time domain 

SMOOTHING 

Data points range across 1-10 11-20 21-30

Take the average from each of these blocks and use that as the data point

Fast Fourier transformation - analysis of the frequency components of the EMG signal

Power spectral density 

Fatigue =

Lower frequency contents (leftward shift of MDF)

Fast twitch fibres become fatigued

More slow twitch fibres are utilised

Motor unit innervates more fibre

Leads to an increase in ARV & RMS

Also why older people may have higher EMG values

     Minimise injury

• shock absorption
• motion control

     Improve performance

• Sufficient traction
• energy return

Innersole

Outersole

Midsole 

Upper

The inward role of the foot

Dorsiflextion, adbuction and eversion

Excessive pronation linked to injury

Provide traction and minimal cushioning

Usually made of a rubber compound

Should be selected for the movements and surface on which it is to be used

Provides cushioning and stability 

Constructed from a foam composite

Contains cushioning and stability devices

Separates the midsole from the inside of the shoe

Draws moisture and heat away from the foot

Provides minimal cushioning

The provide fit, flexibility and support

Constructed from a variety of materials

• Leather
• Synthetic

The solid form around which the shoe is moulded

Designed to provide either cushioning or stability 

Designed with more support on the medial side

Preferred shoe for over pronation or flat foot

Less support on the medial side

Preferred for excessive supination

what are the 2 main categories of shoe technologies?

Cushioning devises 

Support devices

Located in the midsole

Made from viscoelastic material

Designed to absorb the initial impact strike

Located in forefoot or heel

Having the device enclosed makes the shoe more stable than having it exposed

Various locations within the shoe

Designed to perform different tasks

Most important is the heel counter - this may help control over pronation

Firmer matrial placed on the medial side of the midsole

Controls over pronation

Wedge shape piece of material (think end located on the medial side) placed in the midsole

Controls over pronation

Firm piece of material placed under the arch of the shoe

Controls over pronation 

reduced frequency of running related injuries in the barefoot population

Running shoes decrease sensory feedback, limiting protective adaptions inherent in the barefoot condition

Shod foot becomes inactive causing weakening of the ankle and the foot muscles, increasing long term injury risk

 Reduced impact forces barefoot

Loading rate is significantly increased barefoot

In the barefoot condition step length decreases and srep frequency increases. This is caused by changes in touchdown geometry

More horizontal placement at landing due to Increased PF and vertical shank caused by increased knee flexion

Height difference at launch and landing 

Aerodynamics

Acceleration due to gravity (9.81 m/s²)

Aerodynamics - magnus force, drag, lift

What is the equation for the range of a projectile in free flight with no aerodyanmic forced acting upon it?

v²sin(2xθ)

g

V²sin(2xθ)/2g [1+√1+2gh/V²sin²(θ)

Gravity

Structure of the human body

Run-up

The resultant force of a couple is 0 i.e itdoes not produce translation. A force couple results in pure rotation

The moment of a couple is the same for any point on the body and its magnitude is equal to the product of the magnitude of the force and the shortest distnce between the force couple

M=fxd

By obtaining:

accurate kinematic data

accurate anthropometric measures

record external forces

1. Predict performance
   Can predict elements of performance and sport you are most suited for
    
2. Implement a training programme
   pre training values - training - reevaluate- training
   etc
    
3. Assessment of rehab
   Measure strength pre season - injury - use pre season as a guideline for rehab
   
   
4. Identify muscle imbalance
   imbalance may lead to injury (ham:quad 0.65-.75) 

1.65um - less than optimal - fewer cross bridge interactions = reduced tension

2.25um - optimal - max cross bridge interactions = max tension

3.65 - greater than optimal - no crossbridge interaction = no tension

CSA 

PCSA 

pennation angle

muscle thickness

muscle length

Large CSA optimal for force generation

Low movement amplitude leading to low velocity shortening

Small CSA leading to low force generation

High movement amplitude optimal for high velocity shotening

Higher angular velocity leads to better prediction. However torque moments are difficult at high angular velocities

Consideration of the multifactorial nature of sports performance

Muscle length considerations

Control and standardisation of adjacent joint positions

A qualitative advance, or biological advance in biological makeup

May refer to cell, organ or system advancement in biochemical composition rather than size alone

- segmental growth in childhood is non-linear

-age changes body proportions, relative COM locations and radii of gyration

From ages 1-4 

Normalised step length increases

Step frequency decreases

Increase stability, decrease mobility and efficiency

High arms - avoid uncontrolled movements

Plant feet wide - increase base of support

Toes out - increase base of support

increase step frequency

Decrease step length

Decrease in muscle onset latencies

Enhanced intermuscular coordination

increase in muscle activation (IEMG)

Aquisition of unimodal ankle torque profile 

Unimodal GRF (flat foot contact)

Increased joint flexion

High arms

Increased base of support

A) Bench press example. Mass of weight is 60kg, it is lifted 40cm. What is the work completed?

B) What is the power produced when this bench press is completed over 2 and 4 seconds repectively?

 A) Work = f x d x cos(θ)

θ = angle between the line of force application and direction of movement

The overall mechanical work completed = 0
Positive work is done when lifting from chest to locked position, and negative work is down on the way down. 

= (60 x 9.81) x 0.4 = 235.4J

B) 235.4/2 = 117.7W

    235.4/4 = 58.85W

P = W/t

W = F x d

W = (100x9.81) x 50 = 49050J

3 min 45 = 225 sec

P = 49050/225 = 218W

P = T x ω

ω = readians per second

11.5-7.5 = 4

4 degrees/57.3 = 0.07 rads

0.07/0.02 = 3.5 rad/s

3.5 x 100 = 350W

-350W because power is being absorbed in the quads, the movement taking place is flexion, not extension.

work done = Δenergy

work done = 2000 x 0.4

Δenergy = ½ x 70 x v²

2000 x 0.4= ½ x 70 x v²

800 = 35 x v²

√800/35 = v

v = 4.78m/s

Aerodynamic drag

rolling resistance

drive chain efficiency and bearing friction

Decrease weight = 0.23-0.34% increase in performance

Decrease aerodynamic drag = 0.2-0.5% increase in performance

Decrease drag and weight = 0.5-0.7% increase in performance

Decrease in weight and power = 0.2-0.5 decrease in performance

Knee extensors, hip extensors and plantar flexors

knees = 50%

Hip = 30% 

Ankle = 20%

Are less effective but more efficient

The more efficient the rider, the more effective the pedal force application 

Preferred, pulling up, circling and pushing.

Pulling up is more effective but less efficient than pedalling with own preferred technique

It is important to note that measures of force effectiveness are not good indicators of metabolic efficiency

Magnitude of EMG is minimal between 60 & 100 RPM

Most economical cadence between 55-65 RPM

Preferred however is 85-95 RPM 

Joint moments are minimal between 80 - 100 RPM

Selection of preferred cadence is determined by biomechanical rather physiological factors

Aerodynamic drag is the most significant resistive force in cycling

Little changes in aerodynamic position or bike/rider weight can have significant effects on cycling performance 

Muscular power is mainly produced by hip extensors, knee extensors and plantar flexors 

Pulling up on the pedal is mechanically more effective but metabolically less efficient

Selection of preferred cadence is determined by biomechanical rather than physiological factors 

ω = 123 deg/s

ω = 123/57.3 = 2.15 rad/s

v = r x ω = 0.32 x 2.15 = 0.69 m/s

A runner is running around a bend with a 12m radius at 5 m/s. What is the runners centripedal acceleration?

a_r = v²/r = ω²r

a_{r =} 5²/12 = 2.08 m/s²

If a runner has a centripedal acceleration of 2.08 m/s² and a tangential acceleration (a_t) of 0.3 m/s², what os the magnitude and direction of the overall (total) acceleration of the runner?

atotal = √at² + ar²

atotal = √0.3² + 2.08² = 2.1 m/s²

tg = 0.3/2.08 = 0.144 

tan-1(0.144) = 8.2°

Runner experiences a total acceleration of 2.1 m/s² at an angle of 8.2°

A runner accelerates at a uniform rate up to 10m/s in 7.5s, moving on a circular track of radius 30m. Assuming constant tangential velocity, find the tangential acceleration

And what is the centripedal acceleration when the speed is 6m/s

a_t = Δv/Δt = 10-0/7.5-0 = 1.33m/s²

a_r = v²/r = 1.2m/s²

a) at = r x a = 1.5 x 6.28 = 9.42 m/s²

b) ar = v²/r = ω²r = 14.7² x 1.5 = 324.14 m/s²

c) atotal = √at² + ar² = √9.42² + 324.14²

= 324.27 m/s²

cosine rule =

c² = a² + b² - 2abcos(θ)

the angle between two vectors when forming a parallelogram = 180 deg - 45 deg = 135 deg 

c² = 1200² + 1500² - 2(1200)(1500)cos(135)

displacement = 2497.1 m

Angular velocity equation (ω)

and linear velocity using (ω)

Angular

ω = Δangular displcement (ΔΘ)/Δtime

Linear

ω = V/r

V = r x ω

EMG - Calculating signal to noise ratio

CMMR (linear) = 10000:1

Gain = 2000

Amplitude of EMG on skin = 2mv

Presence of hum  = 500mv

What is the signal to noise ratio?

   EMG output = gain x amplitude of EMG

Hum output = gain x amplitude of hum

EMG output = 2000 x 2 = 4000 mv

Hum output = 2000 x 500 = 1000000 mv

For CMMR hum output = 1000000/10000 = 100 mv

Signal:Noise = 4000:100

            = 40:1

              = 40 mv

What do the following stand for:

ARV

MAV

RMS 

Average rectified value

Mean absolute value

Root mean square