# Shared Flashcard Set

## Details

Biomechanical Principles
Biomechanics
121
Sports
04/07/2014

Term
 Speed and Velocity Units   Acceleration Units   Angle Units
Definition
 m/s or ms-1   m/s2 or ms-2 rad
Term
 Significant figures rule 1
Definition
 When multiplying or dividing the final answer has the same number of sinificant figures as the number with the least significant figures
Term
 Significant figures rule 2
Definition
 When adding or subtracting the final answer has the same number of decimal places as the smallets number of decimal places in any term
Term
 How to increase power
Definition
 Power = Force x Velocity Peak power occurs at approx one third of maximum isometric force and an intermediate velocity of contraction
Term
 ACL injury risk factors - Gender
Definition
 Females - 6 to 8 times higher injury rate Landing with knees less flexed Poor Hamstrings Quadriceps balance Hamstrings protection of ACL reduced Hamstring co-activation defacit Slow activation of Hamstrings
Term
 ACL injury risk factors - Poor landing technique
Definition
 Reduced knee and hip flexion angles Increased knee valgues Internal rotation of the femur on tibia Landing/Pivoting with knee extended: Patella tendon shear load higher Hamstring co-activation less effecive in protecting ACL
Term
 Joint moment
Definition
 Joint moment (Nm) = Muscle Force (N) x Moment arm (m) M=Fxd F=M/d
Term
 Mobility Problems in Older People
Definition
 Falls Balance Acciedents OA and Chronic Conditions Osteoporosis/Fractures Ergonomic Problems
Term
 Biomechanics
Definition
 Application of mechanical principles in the study of living organisms
Term
 Centre of Mass
Definition
 The centre of Mass is the point around which the body's mass is equally distributed
Term
 Mass of the Human body
Definition
 Upper body (head and trunk) - 50% Arms - 5% each - 10% Legs - 20% each - 40%
Term
 Calculating centre of mass
Definition
 Laying down on board with scales: Measure and record the length of the board = Board length (D) Record the mass measured on both scales in kg = M1 & M2 Calculate ratio of the two masses (R) = M1/M2 Divide the length of the board into two segments: d1=D/R+1 d2=D-d1
Term
 Location of COM in human body
Definition
 Under static conditions, the vertical projection of the COM has to fall within the base of support   The COM can be outside the human body, which has important impliations for sporting performance (eg high jumping)
Term
 Distance
Definition
 Measured along a path of motion (sum of all movements)
Term
 Displacement
Definition
 Result of movement (straight line between start and finish)
Term
 Scalar
Definition
 Specified by magnitude (number) only. May be positive or negative   Examples: Temperature (T) Volume (V) Mass (m) Time (t) Energy (E)
Term
 Vector
Definition
 Specified by magnitude and direction   Examples: Displacement, Velocity, Acceleration, Force, Momentum   Can be graphically represented as an arrow
Term
 Example: 400m sprint
Definition
 Distance 400m Displacement 0m
Term
 Example: 200m Sprint
Definition
 Distance 200m Displacement: 100m along straight 62 metres vertically across track.  O = 62 A = 100m Pythagoras. Square root of 62squared plus 100squared =118 Calculate angle = O A = TOA = TAN = 62/100 = 0.62 Angle therefore = Inverse Tan (0.62) = 32 degrees
Term
 Speed
Definition
 Distance/Change in time
Term
 Velocity
Definition
 Displacement/Change in time
Term
 Acceleration
Definition
 Change in Velocity Change in Time   Therefore   V2-V1 Change in Time
Term
 A sprinter's velocity is 3m/s on leaving the blocks and 7m/s two seconds later What is the acceleration?
Definition
 7-3 2   =2m/s2
Term
Definition
 Multiply by Pi and divide by 180
Term
Definition
 Multiply by 180 and divide by Pi
Term
 Degrees into Revolutions
Definition
 Divide by 360
Term
 Revolutions to Degrees
Definition
 Multiply by 360
Term
 Absolute Angle
Definition
 Angle of a body segment in relation to a fixed reference line eg vertical or horizontal
Term
 Relative anlge
Definition
 Angle at a joint formed between two body segments eg knee, hip or elbow angle
Term
 Projectile
Definition
 A projectile is a body in free fall that is only subject only to the forces of gravity and air resistance
Term
 Factors influencing the trajectory of a projectile
Definition
 Projection height Projection Angle Projection Speed
Term
 Projection angle
Definition
 For a given projection speed and a given projection height, the optimal angle for max horizonal distance is 45 degrees and max vertical distance is 90 degrees   However in sporting movements the optimum angle is not always 45 degrees - The reasons lie in the anatomical structure of the human body, humans are not machines Eg optimum shot angle is around 32 degrees optimum long jump angle is around 22 degrees
Term
 Projection height
Definition
 Is the difference in height from which the body is initially projected and the height at which it lands    The greater the projection height, the greater the horizonal distance
Term
 Projection speed
Definition
 The greater the projection speed the greater the horizontal and vertical distances   The horizontal distance increases in proportion to the square of the increase in projection speed
Term
 Long Jump example   Take of speed v is 9.81m/s and take of angle is 22.1 calculate the horizontal components of v - vx and vy
Definition
 9.81 = h to find vx which is a - we have h and need to find a = COS ?/H=COS(0) ?/9.81=COS(22.1)  ?=COS(22.1)x9.81 = 9.09 m/s to find vy which is o - we have h and need to find o = SIN ?/H=SIN(0) ?/9.81=SIN(22.1) ?=SIN(22.1)x9.81 = 3.69 m/s
Term
 Linear Motion
Definition
 Position - m Distance - m Displacement - m Velocity - m/s Acceleration m/s2
Term
 Angular motion
Definition
Term
 Angular distance and displacement
Definition
 Angular distance - The sum of all angular changes that have occured   Angular displacement - The distance between the initial and the final position of the pendulum:   Final angle - Initial angle
Term
 Angular velocity
Definition
 Linear: change in displacement change in time   Angular (w): change in displacement (02-01) change in time (t2-t1)
Term
 Relationship between linear and angular velociy
Definition
 For any given anguar velocity, the linear velocity increases with an increase in the radius of rotation:   Linear velocity = radius of rotation x angular velocity v=rw The unit for angular velocity HAS to be rad/s
Term
 Example of relationship between linear and angular velocity Known: r1 = 0.2m r2 = 0.4m w = 30 rad/s
Definition
 0.4-0.2 = 0.2m    0.2 x 30 = 6 m/s
Term
 Angular Acceleration
Definition
 Linear: Change in velocity Change in time   Angular: Change in angular velocity (w2-w1)   Change in time (t2-t1)
Term
 Step and Stride
Definition
 Step: Right heel contact to Left heel contact Stride: Right heel contact to Right heel contact
Term
 Swing phase and Stance phase
Definition
 Swing Phase: toe off to heel contact Single support phase: one foot on the ground Double support phase: both feet on the ground   Stance phase approx 60% (20% contact 30% midstance 50% propulsion) Swing phase approx 40%   In running there is no double support phase, rather a flight phase: both feet off the ground
Term
 Gait calculation exmple: 1.57s Swing Stance (contact, midstance, propulsive) Double support
Definition
 Swing = 0.628   Stance = 0.942 Contact = 0.1884 Midstance = 0.2826 Propulsion = 0.471   Double support is 20% in stride therefore  = 0.314
Term
Definition
 Cadence: Quantifies the number of steps per minute steps.min-1 Number of steps x 60 Time (s)   Stride freequency: Quantifies the number of strides per second (steps.s-1) or Hz number of strides   time (s)
Term
 Stride and cadence example: Usain bolt 41 steps in 9.63s   Calculate: Average speed, Number of strides, Average stride length, Cadence, Stride frequency
Definition
 Average speed = 10.38m/s Number of strides = 20.5 Average stride length = 2.44m Cadence = 255.45 steps.min-1 Stride frequency = 2.13Hz
Term
 Normalise stride length by height (stature)
Definition
 Stride length height
Term
 A more accurate way to calculate joint angles
Definition
 Use anatomical landmarks:   Greater Trochanter of Femur Lateral Femoral Epicondyle Lateral Malleolus Head of fifth metatarsal   Use 2-D angles to calculate joint angles properly
Term
 Calculating angles eg hip   Opposite - 0.26cm Adjacent - 0.43cm
Definition
 O and A = TOA = TAN   = TAN (0.26/0.43)    = 31.16 degrees
Term
 Force
Definition
 Push or a pull   Tends to cause a body to accelerate or change shape   Vector (has magnitude and direction)
Term
 Examples of forces
Definition
 Kicking or throwing a projectile pushing feet against the floor Lifting a weight Friction Gravity   Force is a vector  Unit: Newtons (N)
Term
 Mass
Definition
 A meaaure of a bodys inertia Depends on quantity of matter of which a body is composed    Units: Kg Scalar: Magnitude, but no direction
Term
 Weight
Definition
 Gravitational force exerted on a body by the Earth Weight = mass x gravitational acceleration (W=mg)   g is the acceleration due to gravity (9.81m/s2 on Earth) On the moon it is only abut 1.62   Vector (magnitude and direction)   Mass is a measure of a bodys inertia whereas weight is a force due to gravity
Term
 Newtons First law
Definition
 The acceleration of a body is zero if the sum of all forces acting upon this body is zero
Term
 Newtons 2nd law
Definition
 Force = Mass x Acceleration   Units: N  1N = 1kg.m/s2   A force applied to a body causes an acceleration of that body which is proportional to the force and inversely proportional to the bodys mass
Term
 Example for F=ma Sprinter has horizontal velocity of 15m/s2 she has a mass of 58kg   How much force is the sprinter applying to the blocks?
Definition
 58Kg x 15 m/s2 = 870N
Term
 Ground reaction force
Definition
 Keeps us from falling down by working in opposition to gravity
Term
 Newtons 3rd Law
Definition
 For every action there is an equal and opposite reaction   When a body exerts a force on a second, the second body exerts a reaction force that is equal in magnitude and opposite in direction on the first body
Term
 Ground reaction force example   calculate the reaction force that the ground is exerting on a person of a mass of 80kg
Definition
 80 x 9.81 = + 784.8 N
Term
 peak vertical ground reaction forces
Definition
 walking 1.2 x BW jogging 2.1 x BW sprinting 4.8 x BW Landing after countermovement jump 10 x BW
Term
 Impulse
Definition
 If a force is applied over a period of time, an impulse is applied   An impulse is the product of force and time:   Implse = Force x Time   Vector (magnitude and direction)   Unit: Ns
Term
 Calculating impulse F = 100N t = 10s
Definition
 100 x 10 = 1000Ns   An impluse can be though of as the area under a force curve
Term
 Linear Momentum
Definition
 Momentum, M, is a measure of the 'quantity of motion' of a body:   M = mv   m = mass of the body (m) velocity of the body (v)   Vector Units: kg.m/s or N.s
Term
 Conservation of momentum
Definition
 If the resulatant external force acting on a system is zero, the total momentum of a system remains constant   M1=M2   Total momentum of system at time t1 (M1) Total momentum of system at time t2 (M2)
Term
 Example problem for momentum   Ice hockey players collide: A 90kg ice hockey player travelling at 6.0m/s A 80kg ice hockey player travelling at 7.0m/s   They entangle and continue to move, but at what velocity?
Definition
 90 x 6 = 540 kg.m/s 80 x 7 = 560 kg.m/s   540 - 560 = 170kg (combined mass) (v) -20 = 170 (v) -20/170 = (v) = 0.12 m/s is the velocity
Term
 Conservation of linear momentum
Definition
 The total momentum of an isolated system is conserved   If the resultant external force acting on the system is zero the total momentum of a system remains constant
Term
 How does momentum change
Definition
 The change in momentum is equal to the impulse applied to the body    Impulse = change in momentum Impulse = m2-m1 Ft=(Delta) M   We call this the impulse momentun relationship
Term
 Torque
Definition
 A torque is a force that causes rotation   Torque = Force x Distance (T=Fd)   Vector Counterclockwise is positive  Units: Nm
Term
 Torque and muscle strength
Definition
 Torque = Muscle force x Moment arm   Muscule strength depends on both muscular force and moment arm   The moment arm of a muscle with respect to a joint axis of rotation depends on the joint angle
Term
 Example: Biecps and tricps co-contraction   F biceps = 2000N MA biceps = 0.05m   F triceps = 2500N MA triceps = 0.04m   What movement will occur
Definition
 2000 x 0.05 = 100Nm -2500 x 0.04 = -100Nm   100-100 = 0Nm   Isomeric contraction
Term
 Why is it difficult for a cyclist to accelerate?
Definition
 The moment of inertia is the property of a body to resist rotation   It is the angular equivalent for mass   Mass is the property of a body to resist linear acceleration
Term
 Moment of inertia
Definition
 Depends on:  The mass of the body How the mass is distributed about the axis of rotation I=mk2 I = moment of inertia m = mass of the body k = radius of gyration Units: Kg.m2 Scalar (magnitude, no direction)
Term
 Application of newtons 2nd law
Definition
 Force = Mass x Acceleration   Torque = Moment of inertia x Angular acceleration
Term
 Torque and force example   knee extensors 3cm from axis of rotation at knee   How much force must the knee extensors exert to produce an angular acceleration at the knee of 1rad/s2 at a given moment of inertia of 0.24kg.m2
Definition
 Moment of inertia = 0.24 Acceleration = 1 rad/s2   Torque = 0.24 x 1 = 0.24 Nm   Required force therefore is: Force = Torque/Distance 0.24/0.3 = 8.0 N
Term
 Angular momentum
Definition
 Angular momentum is a measure of angular motion possesed by a body   Angular momentum = Moment of inertia x Angular velocity   H = Iw   Units: Kg.m2/s   Vector
Term
 Angular momentum example   Moment of inertia of diver = 6 kg.m2 Angular velocity of diver = -9.2 rad/s What is the angular momentum?
Definition
 H = Iw   H = 6 x -9.2   H = -55 Kg.m2/s (clockwise)
Term
 Conservation of linear and angular momentum
Definition
 The total (linear) momentum of an isoalted system is conserved   If the resultant external force acting on the system is zero the total momentum of a system remains constant    The total angular momentum of an isolated system is conserved   If the resultant external torque acting on the system the total angular momentum of a system reamains constant
Term
 Conservation of angular momentum in a dive example   Moment of inertia at take of is 14 kg.m2 Angular velocity at take of is -2.6 rad/s Moment of inertia in pike is 5.8 kg.m2 Angular velocity as take of is what?
Definition
 H = Iw   14.0 x -2.6 = -36.4   Angular momentum must be conserved therefore angular momentum must remain as -36.4   rearrange equation to H/I = w   -36.4/5.8 = -6.3 rad/s
Term
 Angular analogues/equivalents
Definition
 Linear --- Angular Force --- Torque Force = mass x acceleration --- Torque = Moment inertia x agular acceleration Linear momentum (M=mv) --- Angular momentum (H=Iw) Work = Fd --- Work = T0 Power = Fv --- Power = Tw Linear Impulse Ft --- Angular Impulse Tt
Term
 Models and types of models
Definition
 A model can be defined as an artificial representation of reality    Types of biomechanical models are as follows: Conceptual Statistial or regression  Mathmatical (computer) Models can be used to increase knowledge and insight about reality and estimate or predict variables of interest
Term
 Information used to construct a model
Definition
 1. Knowledge of the system being modelled 2. Experimental data that constitute system inputs and/or outputs   In general simple is better, need to decide what should be neglected and included
Term
 Use of models
Definition
 Direct or indirect   In direct use, the model proceeds from cause to effect, nd typically yields a unique solution   In inverse use, a model attempts to move from the effect to the cause and typically yields several possible solutions (not unique)
Term
 Types of mathmatical models for sports motions
Definition
 Point mass (Athlete or implament) Rigid body Musculoskeletal Simulation nvolves the performance of a series of controlled experiments using the model
Term
 Blocks to sprinting power
Definition
 First step: 54% hip 31% knee and 15% ankle   Stecond stance: knee only accounts for 9% total power and ankle up to 38%   Maximal velocity: 39% hip 17% knee and 44% ankle
Term
 Closed kinetic chain
Definition
 The end of the chain is not freely moveable    Characterised by: High force production Low or moderate movement velocity Push like movement pattern (all joint angles change simultaneously)
Term
 Open kinetic chain
Definition
 The end of the chain is freely moveable   Characterised by: Can operate push like High force or high accuracy  All joint angles move simultaneously  Can operate throw like  Joint angles occur in a sequential order This maximises movement velocity
Term
 How do we maximise throwing distance?
Definition
 By maximising projection speed By rotating segments sequentially   Kinetic chain is all about angular momentum being transerred through segments   Eg trunk moves and angular momentum is transferred to arm, moment of inertia of the arm is smaller and so angular velocity must increase to conserve angular momentum
Term
 Baseball pitcher example Trunk rotation of 0.43 rad/s moment inertia of trunk 2.4 kg.m2 Trunk stops rotating and momentum transferred to arm with a moment of inertia of 0.023 kg.m2
Definition
 Angular momentum generated = 0.43 x 2.4 = 1.032 kg.m2/s   Angular velocity of arm after momentum transerref = 1.032/0.023 = 45 rad/s
Term
 Mono and Bi-articular muscles
Definition
 The function of mono-articular muscles is predominantly the generation of momentum    The function of bi-articular muscles includes both the generation and transfer of momentum (also contribute to more than one motion)
Term
 Work
Definition
 If a force is applied over a distance mechanical work is performed    Work is the product of force and displacement   Work = Force x Displacement   Scalar    Units: J
Term
 Work example   How much work is performed?    Mass of bar bells = 250kg moved 0.75m
Definition
 First must convert mass into weight 250 x 9.81 = 2452.5 N   2452.5 x 0.75 = 1839.375 J
Term
 Power
Definition
 Power is the rate at which work is done   Power = work/change in time   Scalar    Units: Watts (W)
Term
 Alternative expression for power
Definition
 Power is the product of force and velocity   P = w/change in time = force x distance/time   = F x d/change in time = Force x Velocity   P = Force x Velocity
Term
 Power example    A power lifter lifts 236kg over a distance of 0.62m in a time of 0.42 seconds
Definition
 236 x 9.81 = 2315.16 N x 0.62 = 1435.3992 J   1435.3992/0.42 = 3417.6 W
Term
 Energy
Definition
 Energy is a body's capacity to do work, forms of energy incule: kinetic, gravitational potential, elastic potential, chemical, thermal (heat)   Kinetic energy is the energy of motion KE=1/2.m.v2 m = mass of body v = speed of body Scalar Units: J
Term
 Kentic energy of pole vaulter example   Mass of pole vaulter = 80kg Speed at end of run up = 9.5 m/s
Definition
 0.5 x 80 x 9.5 sqaured = 3610 J
Term
 Gravitational Potential energy
Definition
 Gravitational energy is the enrgy due to a body's height above a reference surface Graviational potential energy is the product of a body's weight and height   PEgrav = mgh   m = mass of body g = acceleration due to gravity (9.81m/s2) h = vertical height above reference level
Term
 Gravitational potential energy example mass of diver 78kg height of centre of mass above water 3.83m
Definition
 78 x 9.81 x 3.83 = 2930.6 J
Term
 Elastic potential energy
Definition
 Elastic potential energy is the energy stored in a spring PEelastic = 0.5 . k . x2 k = stiffness of the spring x = deformation of the spring Scalar Units: J The total amount of enery is always consered, no energy is lost, simply transformed from one form to another
Term
 Pole vault example   Mass of vaulter 80kg Height of vaulter = 5.50m   What is the vaulters velocity at touchdown?
Definition
 Use conervation of energy Grav potential energy = KE at touch down   80 x 9.81 x 5.50 = 0.5 x 80 x v2 4316 = 40 x v2 4316/40 = v2 107.9 = v2 sqaure root 107.9 = v -10.39 m/s -because he's falling
Term
 Coefficient of restitution
Definition
 Bounce height = Drop height x e2
Term
 Hockey problem advanced 90kg at 6m/s 80kg at 7m/s   Calculate energy loss as a result of the collision
Definition
 Before the impact = (0.5 x 90 x 6 squared) + (0.5 x 80 x 7 squared) = 3580 J   (90 x 6 = 540) - (80 x 7 = 560) = -20 = 170 (v) 0.12m/s After the impact = 0.5 x 170 x 0.12 squared = 1.224 J   3580 - 1.224 = 3578.776 J
Term
 Surface friction
Definition
 The resistance force that acts at the interface  between two surfaces in contact   Arises due to applied force that produces relative motion (kinetic friction), or tends to produce relative motion (static friction)   Force therefore, units are: Newtons
Term
 Causes of surface friction
Definition
 Mechanical interaction between two bodies or surfaces (studs, cleats, spikes) Molecular interaction between two surfaces eg: sole of a sports shoe and the court such as basketball and netball Hand and a sports ball or implament eg: netball pass, discus throw, high bar or weight lifting Due to surface roughness, contact is only made at a few points This causes electrostatic force between atoms or moecules Leading to 'breaking off' of surface protrusions
Term
 Surface friction
Definition
 Magnitude of the friction force, F, is given by   F = uR u = coefficient of friction R = normal reaction force   Vector: Direction of friction force is opposite to the direction of motion (or opposite to the direction of aplied force)  Units: Newton (N)
Term
 Kinetic Friction
Definition
 Two surfaces are in relative motion (slding);    Fk = ukR   Fk = Kinetic friction force  Uk = coefficient of kinetic friction  R = Normal reaction force
Term
 Static friction
Definition
 Two surfaces are stationary;   Fs (less than or equal to) usR Fm = usR   Fs = static friction force Fm = maximum static friction force us = coefficient of static friction R = normal reaction force
Term
 Coefficient of friction (u)
Definition
 A dimensionless number (no units) An indicator of the ease of sliding of two surfaces (low value of u means easy sliding) Coefficent of static friction is greater than coefficient of kinetic friction (it is more difficult to get a body sliding than it is to keep sliding
Term
 Example problem (friction)   The coefficient of static friction between a sled and  the snow is 0.18 with a coefficient of kinetic  friction of 0.15. A 250 N boy sits on the 200 N  sled. a. How much force directed parallel to the  horizontal surface is required to start the sled in  motion? b. How much force is required to keep the sled in  motion?
Definition
 To start the sled in motion, the applied force must exceed the force of maximum static friction: Fm =usR Fm = (0.18) (200+250) =81N  Therefore the applied force must be greater than 81 Newtons   To maintain motion the applied force must equal the force of kinetic friction:   Fk =ukR Fk = (0.15) (200+250) =67.5N  Therefore the applied force must be at least 67.5 newtons
Term
 Example problem 2 (friction)   A sled including its passenger weighs 1200 N. It  takes a horizontal force of 250 N to start the sled  in motion. Once the sled is moving a force of 220  N is required to keep the sled in motion.  a. What is the coefficient of static friction? b. What is the coefficient of kinetic friction?
Definition
 a. Fm = usR 250 = (us)(1200) 250/1200 = us = 0.21   b. Fk = ukR 220 = (uk)(1200) 220/1200 = uk =0.18
Term
 Factors that do not affect friction
Definition
 Contact area eg size of shoe sole   Relative speed of two surfaces (the coefficient of kinetic friction is almost independent of the speed of the two surfaces
Term
 Practical ways to increase or decrease friction
Definition
 Increase/decrease the weight of the body   (Increase/decrease the normal reaction force)   Pull up/push down on the body  (increase/decrease the normal reaction force)   Apply a lubricant to the surface(s) - Water, oil, graphite powder, chalk -this reduces the coefficent of friction between the two surfaces   Change one or both of the surfaces -eg a rougher or smoother surface (increases or decreases the coefficient of friction between the two surfaces)
Term
 Applications of friction in sport
Definition
 – tests for playing surfaces in field sports  (hockey, American football) – ice surface in winter sports (bobsled) – ball surface texture (basketball, rugby) – gloves (Football, American football) – chalk and glue (gymnastics, weightlifting,  throwing, pole vaulting) – body oil, sweat (wrestling)
Term
 Measuring the coefficient of friction
Definition
 Horizontal sliding of two surfaces -measure the applied force with a spring balance or load cell)   Inclined plane -applied force increases with increasing angle -measure the angle at which the body begins to slide
Term
 Aerodynamic and hydrodynamic drag force
Definition
 Form drag (also called pressure drag or profile drag) Skin friction   Mechanism of form drag fluid separates from the surface of the body crates a turbulent wake energy is lost from the body in creating the eddy currents This creates regions of higher and lower pressure
Term
 4 Factors affecting drag
Definition
 Fluid density - Air = low density, low drag - Water = high density, high drag (form drag is important in water sports)  The frontal area - size of the body, ball or implament  Speed - Drag increases with speed (Flow separates earlier; greater turbulant wake = more drag  Shape - more streamlined the body the later the flow separates leading to less turbulant wake = less drag
Term
 Drag equation
Definition
 Density of fluid (p) air: 1.20 kg/m3; Water: 1000 kg/m3   Cross sectional (frontal) area (Ap)   Drag coefficient (Cd); depends on shape of the body   relative speed of the body and fluid (v) The aerodynamic/hydrodynamic 'form drag' force FD, is given by   FD = ½ApCdv²   Vector: oppose the forward motion of the body in the fluid   Units: N
Term
 Example drag problem    Usain Bolt (JAM) reached a top speed of 12.2 m/s   Calculate the form drag force acting on Bolt at this speed. (Bolt has a frontal area of 0.50 m2 and a drag coefficient of 0.60).  What forward propulsive power was Bolt generating to overcome this drag force? Remember, the air density is 1.20 kg/m3
Definition
 ½ x 1.2 x 0.5 x 0.6 x 12.2² = 26.8N
Term
 To reduce drag value...
Definition
 • Use ‘streamlined’ equipment (with a lower CD) • use teardrop shapes • Use ‘streamlined’ body position (with a lower AD) – use teardrop shapes
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