Linear Motion - Minimum Movement Time Overground (Running, Walking, & Road Cycling)

2 Biomechanical Model: Linear Moon Minimum Movement Time (Overground)

Slide 1 of 3 Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More

Joint Linear Joint Linear Joint Linear Sum of Speeds 1 Speeds 2 Speeds 3 Joint Forces

External Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down

Drag Friction Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Force Force Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance

Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces

Friction Slide 3 of 3 Force

Vertical Ground Coefficient of Reaction Force Friction Slide 2 of 3 3 Biomechanical Model: Linear Moon Minimum Movement Time (Overground) (Slide 1 of 3)

Linear Speed Principle

Movement Time

Linear Conservation of Momentum Principle Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More 4 Biomechanical Model: Linear Moon Minimum Movement Time (Overground)

(Slide 2 of 3) Sum of Joint Linear Speeds Principle Factors that Speed the Body Up More

Angular Linear Speed – Angular Joint Linear Joint Linear Impulse – Momentum Joint Linear Speeds 1 Velocity Principle Speeds 2 Speeds 3 Principle

Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Velocity Rotation Velocity Rotation Velocity Rotation

Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Force Arm Resistance Force Arm Resistance Force Arm Resistance

Joint Torque External Action - Reaction Angular Inertia Principle Forces Principle Principle External Forces Friction Principle Force

Vertical Ground Coefficient of Reaction Force Friction Friction Force Principle 5 Biomechanical Model: Linear Moon Minimum Movement Time (Overground)

Linear Factors that Slow the Body Down Less (Slide 3 of 3) Impulse-Momentum Principle 2 Sum of Joint Forces External Forces External Application Time of Principle Mass Forces each External Force Slowing the Body Down Drag Force Principle Drag Friction Force Force

Friction Force Principle Fluid Coefficient Area Relative Vertical Ground Coefficient of Density of Drag of Drag Velocity Reaction Force Friction

Linear Application Time of Mass Linear Speed The Internal Forces Slowing the Body Down Impulse-Momentum Principle 1 6 Biomechanical Model: Linear Moon Minimum Movement Time

Movement — Linear Speed Principle Time l Linear t = Distance s Speed 7 Biomechanical Model: Linear Moon Minimum Movement Time

Linear — Linear Conservation of Speed Momentum Principle

Factors that Slow Factors that Speed the Body Down Less the Body Up More 8 Biomechanical Model: Linear Moon Minimum Movement Time

Factors that Speed — Sum of Joint the Body Up More Linear Speeds Principle Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3 9 Biomechanical Model: Linear Moon Minimum Movement Time

Joint — Linear Speed – Angular Linear Speeds Velocity Principle

Joint Angular Radius of Velocity Rotation s = ωrrt 10 Biomechanical Model: Linear Moon Minimum Movement Time

Joint Angular — Angular Impulse – Velocity Momentum Principle

Joint Application Time Angular Tt Torque of the Joint Torque Inertia ω = I 11 Biomechanical Model: Linear Moon Minimum Movement Time

Joint — Joint Torque Principle Torque

TJ = FMd ⊥ Muscle Moment Force Arm 12 Biomechanical Model: Linear Moon Minimum Movement Time

Angular — Angular Inertia Principle Inertia

2 Radius of I = mr Mass rs Resistance 13 Biomechanical Model: Linear Moon Minimum Movement Time

Muscle — Action – Reaction Principle Force

External Forces 14 Biomechanical Model: Linear Moon Minimum Movement Time

— External Forces Principle — Speeding up (a) and slowing down (b) sides of the model

External External Forces (a) Forces (b)

Vertical Ground Friction Drag Vertical Ground Friction Reaction Force Force Force Reaction Force Force

Back to Speed Up Side Back to Slow Down Side 15 Biomechanical Model: Linear Moon Minimum Movement Time

Friction — Friction Force Principle Force — Speeding up and slowing down sides of the model Vertical Ground Coefficient Reaction Force of Friction

FFR = µFVGR

Back to Speed Up Side Back to Slow Down Side 16 Biomechanical Model Lowest Sum of Joint Forces When Landing aer a Jump

Vertical Ground — Linear Impulse – Reaction Force Momentum Principle 1

Linear Application Time Mass ms Speed of the Internal Forces F = Slowing the Body Down VGR t 17 Biomechanical Model: Linear Moon Minimum Movement Time

— Linear Impulse – Factors that Slow Momentum Principle 2 the Body Down Less

Sum of ΣFt Joint Forces Δs = m External Application Time Mass Forces of each External Force Slowing the Body Down 18 Biomechanical Model: Linear Moon Minimum Movement Time

Drag — Drag Force Principle Force

1 2 Fluid Coefficient Area Relative FD = ρfluidCDAD (vrel ) 2 Density of Drag of Drag Velocity 19

Linear Motion - Minimum Movement Time

Running & Walking 20 Biomechanical Model: Linear Moon Minimum Movement Time (Running & Walking)

Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More

Joint Linear Speed Joint Linear Speed Joint Linear Speed Sum of of the Ankle & All Joints of the Knee & All Joints of the Hip & All Joints Joint Forces Superior to the Ankle Superior to the Knee Superior to the Hip

Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of External Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down

Drag Friction Ankle PF Application Time Angular Knee Ext Application Time Angular Hip Ext Application Time Angular Force Force Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance

Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces

Friction Force

Vertical Ground Coefficient of Reaction Force Friction 21

Linear Motion - Minimum Movement Time

Road Cycling 22 Biomechanical Model: Linear Moon Minimum Movement Time (Road Cycling)

Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More

Joint Linear Speed Joint Linear Speed Joint Linear Speed Sum of of the Ankle & All Joints of the Knee & All Joints of the Hip & All Joints Joint Forces Distal to the Ankle Distal to the Knee Distal to the Hip

Application Time Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of External Mass Forces of each External Force Velocity Rotation Velocity Rotation Velocity Rotation Slowing the Body Down

Drag Friction Ankle PF & Application Time Angular Knee Ext & Application Time Angular Hip Ext & Application Time Angular Force Force DF Torques of the Joint Torque Inertia Flex Torques of the Joint Torque Inertia Flex Torques of the Joint Torque Inertia

Fluid Coefficient Area Relative Vertical Ground Coefficient of Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Reaction Force Friction Force Arm Resistance Force Arm Resistance Force Arm Resistance

Linear Application Time of Mass Speed The Internal Forces External Slowing the Body Down Forces

Friction Force

Vertical Ground Coefficient of Reaction Force Friction Linear Motion - Minimum Movement Time Through Water (Front Crawl Swimming)

24 Biomechanical Model: Linear Moon Minimum Movement Time (through water)

Slide 1 of 3 Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More Slide 2 of 3

Sum of Joint Forces Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3

External Application Time of each External Force Mass Forces Joint Radius of Joint Radius of Joint Radius of Slowing the Body Down Velocity Rotation Velocity Rotation Velocity Rotation

Body Drag Force Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Fluid Coefficient Area Relative Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Force Arm Resistance Force Arm Resistance Force Arm Resistance

Kick Buoyant External Force Force Slide 3 of 3 Forces

Foot Drag Body Hand Drag Hand Lift Force Density Force Force

Fluid Coefficient Area Relative Fluid Coefficient Area Relative Fluid Coefficient Area Relative Density of Drag of Drag Velocity Density of Drag of Drag Velocity Density of Lift of Lift Velocity 25 Biomechanical Model: Linear Moon Minimum Movement Time (through water) (Slide 1 of 3)

Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More 26 Biomechanical Model: Linear Moon Minimum Movement Time (through water) (Slide 2 of 3)

Factors that Speed the Body Up More

Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3

Shoulder Radius of Elbow Angular Radius of Wrist Angular Radius of Velocity Rotation Velocity Rotation Velocity Rotation

Joint Application Time Angular Joint Application Time Angular Joint Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Force Arm Resistance Force Arm Resistance Force Arm Resistance

External Forces

Hand Drag Hand Lift Force Force Lift Force Principle

Fluid Coefficient Area Relative Fluid Coefficient Area Relative Density of Drag of Drag Velocity Density of Lift of Lift Velocity 27 Biomechanical Model: Linear Moon Minimum Movement Time (through water)

Factors that Slow (Slide 3 of 3) the Body Down Less

Sum of Joint Forces

External Application Time Mass Forces of each External Force Slowing the Body Down

Body Drag Force

Fluid Coefficient Area Relative Density of Drag of Drag Velocity

Kick Buoyant Force Force Buoyant Force Principle

Foot Drag Body Force Density

Fluid Coefficient Area Relative Density of Drag of Drag Velocity 28 Biomechanical Model: Linear Moon Minimum Movement Time

Lift — Lift Force Principle Force — Speeding up side of the model Fluid Coefficient Area Relative 1 2 Density of Lift of Lift Velocity FL = ρfluidCLAL (vrel ) 2 29 Biomechanical Model: Linear Moon Minimum Movement Time

Buoyant — Buoyant Force Principle Force — Slowing down side of the model Body Density 30

Linear Motion - Minimum Movement Time

Front Crawl Swimming

31 Biomechanical Model: Linear Moon Minimum Movement Time Front Crawl Swimming

Movement Time

Linear Distance Speed

Factors that Slow Factors that Speed the Body Down Less the Body Up More

Sum of Joint Forces Joint Linear Speed of Joint Linear Speed of Joint Linear Speed of the Shoulder & All Joints the Elbow & All Joints the Elbow & All Joints Proximal to the Shoulder Proximal to the Elbow Proximal to the Elbow

External Application Time of Mass Forces each External Force Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Slowing the Body Down Velocity Rotation Velocity Rotation Velocity Rotation

Body Drag Force SH Adduction Application Time Angular EB Flexion Application Time Angular EB Extension Application Time Angular Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia Torque of the Joint Torque Inertia

Fluid Coefficient Area Relative Muscle Moment Radius of Muscle Moment Radius of Muscle Moment Radius of Mass Mass Mass Density of Drag of Drag Velocity Force Arm Resistance Force Arm Resistance Force Arm Resistance

Kick Buoyant External Force Force Forces

Foot Drag Body Hand Drag Hand Lift Force Density Force Force

Fluid Coefficient Area Relative Fluid Coefficient Area Relative Fluid Coefficient Area Relative Density of Drag of Drag Velocity Density of Drag of Drag Velocity Density of Lift of Lift Velocity 32

Locomotion – Minimum Movement Time

Fundamental Biomechanical Principles 33 Linear Speed Principle — When we speak of how fast or slow something moves linearly, we are describing its linear speed. — Linear Speed: rate of motion — Linear distance traveled divided by the time it took to travel that linear distance l s = t — Unit of Measurement — meters per second (m/s) 34 Linear Speed Principle — Real-World Application — A decrease in movement time (t) of the body is caused an increase in the body’s linear speed (s) and/or a decrease in the distance to be travelled (l). l t = s

— Unit of Measurement — seconds (s) 35 Linear Conservaon of Momentum Principle — Newton’s First Law of Motion (Linear) — This law explains what happens to a body if “no net external force” acts on it — There is no change in motion — A body that is moving will continue to move in the same direction with the same speed — A body at rest will stay at rest — But, what does it mean when we say “no net force”? — It simply means that any force that slows the body down must be matched by an equal force that speed the body up 36 Linear Conservaon of Momentum Principle — Real-World Application — To maintain a constant state of motion, any factors that would slow the body down must be balanced by factors that speeds the body up. — If the factors that slow the body down exceed the factors that speed the body up, the body slows down (i.e., the state of motion changes). — If the factors that slow the body down are less than the factors that speed the body up, the body speeds up (i.e., the state of motion changes). 37 Sum of Joint Linear Speeds Principle — The optimal of sum of joint linear speeds that “speeds the body up” is the result of modifying one or more Biomechanical Factors in the Biomechanical Model — The identification of this optimal combination of joint linear speeds is a skill that all individuals interested in understanding human movement must develop 38 Linear Speed – Angular Velocity Principle

— Radius of Rotation (rrt) — The linear distance from the joint’s axis of rotation to the point on interest on the rotating body component — Unit of measurement — meters (m) — Linear Speed (s) — This is the straight-line speed of a point on a rotating body segment — Unit of measurement — meters per second (m/s) 39 Linear Speed – Angular Velocity Principle — Angle (θ) — An angle is formed by the intersection of two lines — Unit of Measurement — Radians (rad) — Angular Velocity (ω) — The rotational speed of the body component — How fast does an angle’s value (Δθ) change — The speed of joint/body rotation — Unit of measurement — Radians per second (rad/s) 40 Linear Speed – Angular Velocity Principle — The body component being moved is the combination of all body’s segments that are being moved. — For example, when hip extension is performed the body component being moved is composed of the head segment, the torso segment, and the two arm segments. — If knee extension is being performed, the body component being moved is the same as for hip extension plus the upper leg segment of each leg. 41 Linear Speed – Angular Velocity Principle — Real-World Application — An increase in linear speed (s) of a point on a rotating body segment is caused by an increase in the body segment’s angular velocity (ω) and/or an increase the

radius of rotation (rrt).

s = ωrrt 42

Time 2 location s21 Time 1 location

s22

s11

s21 Radius of rotation (r ) Δθ RT

Axis of rotation 43

90 degrees 135 degrees 180 degrees

π 3 π radians radians π radians 2 4

Conversion Factor

180 degrees = π radians

(π) π Example: 90degrees = (90) = radians 180 2 44 Angular Impulse-Momentum Principle — Newton’s 2nd Law of Motion (Angular) — If a net torque (ΣT) is exerted on an object, the object will angularly accelerate in the direction of the net torque, and its angular acceleration (α) will be proportional to the net torque and inversely proportional to its angular inertia (I) — The equation for Newton’s 2nd Law of Motion (Angular) is ΣT = Iα 45 Angular Impulse-Momentum Principle — The Angular Impulse-Momentum Principle is derived from Newton’s 2nd Law of Motion (Angular) ΣT = Iα

⎛ Δω⎞ ΣT = I⎜ ⎟ ⎝ t ⎠ ΣTt = I(Δω) 46 Angular Impulse-Momentum Principle — ΣTt is known as angular impulse — Unit of measurement — Newton-meter-sec (N-m-s)

— I(Δω) is known as the change in angular momentum — Unit of measurement — kilogram meter squared per second (kg-m2/s) 47 Angular Impulse-Momentum Principle — Real-World Application — An increase in angular velocity (Δω) of a body component being rotated is caused by an increase in

joint torque (TJ) applied to the body component, and/or an increase in the application time (t) of the joint torque and/or a decrease in the body component’s angular inertia (I). ΣTt Δω = I 48 Joint Torque Principle — What is a Torque? — It is the effect of a muscle force to cause a joint rotation — Muscle Force — Muscle forces are caused by muscle contractions — These contractions pull on bones — Muscle forces are known as eccentric forces — An eccentric force is a force that does not pass through the joint connecting two body segments 49 Joint Torque Principle — Torque is directly related to the size of the muscle force that creates it — The larger the muscle force, the larger the torque — Torque (T) is also influenced by — The linear distance from the line of pull of the muscle force to the axis of rotation of the joint

— This distance is called the moment arm (dma) — The line of pull of the muscle force is determined by connecting a line between the attachments (origin and insertion) of the muscle into bones held together at the joint. — See Figure 5.6

— The larger the moment arm (dma), the larger the torque 50 Joint Torque Principle — Real-World Application

— An increase in joint torque (TJ) is caused by an increase in a muscle force (FM) pulling on the bones that are held together at the joint and/or an increase in the

moment arm (dma).

TJ = FMd⊥ — Units of Measurement — Newton-meter (N-m) 51

muscle force

axis of rotation

moment d⊥ arm 52 Angular Inera Principle — The property of a body component to resist changes in its angular motion — The smaller the body segment’s angular inertia; the easier it is for the body component to rotate quickly — Factors Influencing Angular Inertia (I) — mass (m) — The quantity of matter that makes up the body component: how much bone, muscle, fat, skin, internal organs, and water are in the body component — Units of Measurement — Kilogram (kg)

— radius of resistance (rres) — The linear distance from the body component’s axis of rotation to the center of mass of the body component — Units of Measurement — meters (m) 53 Angular Inera Principle — Real-World Application — A decrease in a body segment’s angular inertia (I) is caused by a decrease in the body segment’s mass (m)

and/or a decrease in the radius of resistance (rres).

2 I = mrrs

— Unit of measurement — kilogram meter squared (kg-m2) 54 Angular Inera Principle — A body component may have more than one angular inertia (I) — A body component may rotate about more than one axis of rotation — Body component movements may change the distribution of mass (m) about a specific axis of rotation, thus changing the angular inertia (I) about that axis — Examples — Figure Skating — Diving 55 56 57 Acon – Reacon Principle — This principle is derived from Newton’s 3rd Law of Motion (Linear) — For every action there is an equal and opposite reaction — This principle may be interpreted in several different ways. — For “speeding up” side of this Biomechanical Model, the principle is interpreted as follows: — for any muscle to create its greatest amount of muscle force, an oppositely directed external force of equal magnitude must exist. 58 Acon – Reacon Principle — For the “slowing down” side of this Biomechanical Model, the principle is interpreted as follows: — the sum of joint forces (i.e., the optimal combination of individual joint forces to slow whole body motion) is equal in magnitude and oppositely directed to the external forces applied to slow the body down 59 External Forces Principle — This principle may be interpreted in several different ways. — For the “speeding up” side of this Biomechanical Model, the principle is interpreted as follows: — Whenever the body is in contact with the ground, there are two ground reaction forces (one vertical and one horizontal) that can oppose the muscle forces create inside the body. — For the “slowing down” side of this Biomechanical Model, the principle is interpreted as follows: — Whenever the body is propelling itself forward, there are two ground reaction forces (one vertical and one horizontal) and one fluid force that can slow the body down. — Units of measurement — Newtons (N) 60

FFR Vertical Ground Reaction Force

FVGR 61 Fricon Force Principle — Friction Force — The horizontal ground reaction force between your foot and the ground

FFR = µFVGR 62 Fricon Force Principle — Real-World Application (Speed up side of the model) — An increase in friction force is caused by — an increase in the coefficient of friction (µ) and/or — an increase in the vertical ground reaction force — The coefficient of friction is a number that represents the material properties of a surface that influence friction force: — hardness/softness — smoothness/roughness — Friction force does not increase if the contact area increases! 63 Fricon Force Principle — Real-World Application (slow down side of the model) — A decrease in friction force is caused by — a decrease in the coefficient of friction (µ) and/or — a decrease in the vertical ground reaction force — The coefficient of friction is a number that represents the material properties of a surface that influence friction force: — hardness/softness — smoothness/roughness — Friction force does not decrease if the contact area decreases! Linear Impulse-Momentum Principle 1 — Newton’s 2nd Law of Motion (Linear) — If a net force (ΣF) is exerted on an object, the object will linearly accelerate in the direction of the net force, and its linear acceleration (a) will be proportional to the net force and inversely proportional to its linear inertia (m) — The equation for Newton’s 2nd Law of Motion (Linear) is ΣF = ma Linear Impulse-Momentum Principle 1 — The Linear Impulse-Momentum Principle is derived from Newton’s 2nd Law of Motion (Linear) ΣF = ma

⎛ Δs ⎞ ΣF = m⎜ ⎟ ⎝ t ⎠ ΣFt = m(Δs) Linear Impulse-Momentum Principle 1 — ΣFt is known as linear impulse — Unit of measurement — Newton-sec (N-s)

— m(Δs) is known as the change in linear momentum — Unit of measurement — kilogram meter per second (kg-m/s) Linear Impulse-Momentum Principle 1 — Real-World Application — A decrease in the Vertical Ground Reaction Force is caused by a decrease in the mass (m) of the body and/ or a decrease in the linear speed (s) of landing, and/or an increase in the application time (t) of the internal forces slowing the body down. ms F = VGR t 68 Linear Impulse-Momentum Principle 2 — Newton’s 2nd Law of Motion (Linear) — If a net force is exerted on an object, the object will linearly accelerate in the direction of the net force, and its linear acceleration will be proportional to the net force and inversely proportional to its linear inertia (m) — The equation for Newton’s 2nd Law of Motion (Linear) is

ΣF = ma 69 Linear Impulse-Momentum Principle 2 — The Linear Impulse-Momentum Principle is derived from Newton’s 2nd Law of Motion (Linear) ΣF = ma

⎛ Δs ⎞ ΣF = m⎜ ⎟ ⎝ t ⎠ ΣFt = m(Δs) 70 Linear Impulse-Momentum Principle 2 — ΣFt is known as linear impulse — Unit of measurement — Newton-meter-sec (N-s)

— m(Δs) is known as the change in linear momentum — Unit of measurement — kilogram meter per second (kg-m/s) 71 Linear Impulse-Momentum Principle 2 — Real-World Application — A smaller decrease in linear speed of the body is caused by a smaller net force that slows you down, and/or a smaller application time of the net force that slows you down and/or an increase in the body segment’s linear inertia (i.e., mass). ΣFt Δs = m 72 Linear Impulse-Momentum Principle 2 — Since an additional desired outcome of this Biomechanical Model is reducing the likelihood of injury, this principle has been modified to incorporate the Biomechanical concept known as sum of joint forces. — The sum of joint forces represents the internal forces that must be absorbed when the body collides with the ground. — A decrease in the sum of joint forces would reduce the likelihood of injury and is achieved when there is — a decrease in the external forces slowing the body down and/or — a modification in the application time of each external force slowing the body down. 73 Dynamic Fluid Forces — Dynamic Fluid Forces — When an object moves within a fluid (or when a fluid moves past an object immersed in it), dynamic fluid forces are exerted on the object by the fluid — Two Types of Dynamic Fluid Force — Drag Force — Lift Force — Unit of Measurement — Newton (N) 74

Figure 8-5 75 Drag Force Principle — Drag Force — The dynamic fluid force that opposes motion of the body or body component through a fluid (e.g., air or water; different densities, ρ)

1 2 FD = ρC DAD (vrel ) 2

76 Drag Force Principle — Fluid Density (ρ) — Represents the thickness of the fluid — It is a measure of how many molecules are in a specific volume of space. — The ratio of mass to volume ρ = m/V — The unit of measurement is a kilogram per meter cubed (kg/ m3) — The density of water is about 1000 kg/m3 — The density of air is only about 1.2 kg/m3 77 Drag Force Principle

— Surface Drag (CD) — The friction force between the fluid and the surface of the body or body component — It is also called skin friction or viscous drag

— The coefficient of drag (CD) is the measure of surface drag — It is influenced by several factors associated with surface drag — The roughness of the surface — See Figure 8-6 — The density (i.e., thickness) of the fluid (air vs. water) 78

Figure 8-6 79 Drag Force Principle

— Form Drag (AD) — Form drag represents the impact forces of the fluid colliding with the body — It is also called shape drag, profile drag, or pressure drag — Form Drag is influenced the two types of fluid movement — Laminar Flow (higher pressure) — Turbulent Flow (lower pressure) — See Figure 8-7 80 Figure 8-7 81 Drag Force Principle

— Form Drag (AD) — More collisions occur if the size of the turbulent flow region behind the body is large; thus, there is more drag force and opposition to movement — Several factors influence the size of the turbulent flow region — The shape of the object (at any relative velocity) — Aerodynamic shapes — See Figure 8-8 — Surface texture (when relative velocity if greater than 20 mph) — At lower relative velocities (less than 20 mph), an object with a smoother surface will have a smaller region of turbulent flow — At higher relative velocities (greater than 20 mph), however, a rougher surface will actually result in a smaller region of turbulent flow — See Figure 8-9 82

The Shape of the Object 83 Figure 8-9 84 Drag Force Principle

— Relative Velocity (vrel) — It is used to represent the relationship between the velocity of the body or body component and the velocity of the fluid — It is the difference between the object's absolute velocity and the fluid's absolute velocity — See Figure 8-4 85

Figure 8-4 86 Drag Force Principle

— Relative Velocity (vrel) — If the body or body component and the fluid are moving in the same direction, then the relative velocity is smaller and the drag force is smaller — We often refer to this condition as running with the wind or swimming with the current. — If the body or body component and the fluid are moving in opposite directions, then the relative velocity is larger and the drag force is larger. — This condition is often referred to as running against the wind or swimming against the current 87 Drag Force Principle — Strategies for Reducing Drag Force — Reduce Fluid Density — High-altitude — Warm-weather — Low humidity — Reduce the Coefficient of Drag — Make body surfaces and clothing (or equipment) smoother — Wear tight-fitting clothes — Reduce Cross-sectional Area for Drag — Reduce the area being hit by the fluid — Streamline the shape of the body or equipment 88 Drag Force Principle — Strategies for Reducing Drag Force — Reduce the Relative Velocity — Because this term is squared, it has the greatest effect on drag force, so — It is the most important variable that the athlete can control — The method for reducing relative velocity is known as “drafting” 89 Drag Force Principle — Strategies for Reducing Drag Force — Additional Considerations — Form drag accounts for most of the drag force at faster velocities, whereas — Surface drag accounts for most of the drag force at slower velocities — If you are moving through the fluid at speeds greater than 20 mi/hr, go for the streamlined shape which reduces the form drag — Otherwise, try to reduce the surface drag. 90 Li Force Principle — The dynamic fluid force component that acts perpendicular to the relative motion of the object with respect to the fluid

1 2 FL = ρC LAL (vrel ) 2

where, FL = lift force CL = coefficient of lift ρ = fluid density AL = surface area for lift vrel = relative velocity

— Some common examples (See Figure 8-11) 91 Figure 8-11 92 Li Force Principle — Fluid Density (ρ) — Represents the thickness of the fluid — It is a measure of how many molecules are in a specific volume of space. — The ratio of mass to volume ρ = m/V — The unit of measurement is a kilogram per meter cubed (kg/ m3) — The density of water is about 1000 kg/m3 — The density of air is only about 1.2 kg/m3 — The magnitude of lift force is approximately 1000 times greater through water than through air. 93 Li Force Principle — Characteristics of the Body or Body Segment to

Create a Lift Force (CL) — Bernoulli’s Principle — Daniel Bernoulli (1700-1782); Swiss Mathematician — Faster-moving fluids exert less pressure laterally than do slower-moving fluids — The “airfoil” — The lateral pressure exerted by the faster-moving molecules is less than that exerted by the slower-moving molecules — See Figure 8-12 94

Figure 8-12 95 Li Force Principle — Characteristics of the Body or Body Segment to Create

a Lift Force (CL) — Round objects do not have an airfoil shape; any distance around the object is the same. — This means the speed of the molecules around the sides of the round object are the same and there is no pressure differential. — “Spin” — The Magnus Effect — Gustav Magnus, German Scientist — Lift forces are also generated by spinning balls — These lift forces are known as “Magnus Forces” — See Figure 8-13 96 Figure 8-13

— When molecules strike the lower surface of the ball, they don't slow down as much — When the molecules strike the top surface of the ball, they are slowed down more — According to Bernoulli's principle, then, less pressure will be exerted by the faster- moving molecules on the bottom surface of the ball 97 Li Force Principle — Characteristics of the Body or Body Segment to

Create a Lift Force (CL) — What if the projectile does not have an airfoil shape and is not round (e.g., a football, a ski jumper, or a javelin)? — Changing the “angle of attack” is the solution — An angle of attack is created when the longitudinal axis of the object is not parallel with the direction of motion. — The longitudinal axis is longest dimension of a non-round object. 98 Li Force Principle — When an angle of attack is created, the flowing air collides with the front side of the object, slows down, and a higher pressure region is created. — See Figure 8-10 — A speed and a pressure differential are created and Bernoulli’s Principal applies. — This results in a lateral (lift) force being applied to the non- airfoil, non-round object. — A horizontal (drag) force is also created. 99 Figure 8-10 100 Li Force Principle

— Area of Lift (AL)

— The area of lift (AL) represents the area of the body or body component that is perpendicular to the direction of motion. — A larger area of lift will create a larger magnitude for the lift force. 101 LiForce Principle

— Relative Velocity (vrel) — It is used to represent the relationship between the velocity of the body or body component and the velocity of the fluid — It is the difference between the object's absolute velocity and the fluid's absolute velocity — See Figure 8-4 102

Figure 8-4 103 Li Force Principle

— Relative Velocity (vrel) — If the body or body component and the fluid are moving in the same direction, then the relative velocity is smaller and the drag force is smaller — We often refer to this condition as running with the wind or swimming with the current. — If the body or body component and the fluid are moving in opposite directions, then the relative velocity is larger and the drag force is larger. — This condition is often referred to as running against the wind or swimming against the current 104 Buoyant Force Principle — Buoyant Force — A buoyant force exists when the magnitude of the upward fluid force exceeds the weight of the body or body component submerged in water — The unit of measurement is a Newton (N) — The weight (W) of the body or body part submerged is determined by the density of the body, the volume of water displaced by the object, and the acceleration due to gravity.

W = (ρbody V)a g 105 Buoyant Force Principle — The upward fluid force is determined by Archimedes’ Principal — An upward fluid force exists whenever a body or body component is submerged in water. — The magnitude of the upward force is determined by the density of the water, the volume of water displaced by the object, and the acceleration due to gravity.

FB = (ρfluid V)a g 106 Buoyant Force Principle — Whether or not a buoyant force exists depends on the density of the body

FB = Fup − W = (ρfluid V)a g − (ρbody V)a g

FB = (ρfluid − ρbody ) — The value in parenthesis “must” be positive for a buoyant force to exist — This only happens if the density of the body is less than the density of water 107 Sinking and Floang — Whether or not something sinks or floats to the surface is determined by buoyant force — If the buoyant force exists, the body will float to the surface — If the buoyant force does not exist, the body will sink to the bottom. — Thus, if an body or body component has a — density greater than water it will sink, or — density less than water it will float up to the surface, or — density equal to the density of water it will do neither 108 Buoyancy of the Human Body — Body Composition — Muscle and Bone — Densities greater than 1000 kg/m3 — Fat — Density less than 1000 kg/m3 — Thus, body composition is a major factor in determining the buoyant force. This will influence — your tendency to sink or float up to the surface, and — the area of drag