Jumping for Height or Distance Construcng a Biomechanical Model — The procedure for constructing the model is straight forward. — You place the fundamental principle that most directly influences the achievement of the desired outcome at the top of the model. — The second fundamental principle is the principle that most directly influences the first principle and overlays the first principle wherever similar boxes exist. — The remainder of the fundamental principles overlay the preceding principles in a similar manner. Projectile Motion Principle Biomechanical Model Jump Height/Distance

Jumping for Height or Distance Time in the Air

Sum of Joint Linear Speeds Principle Jumper’s Jumper’s Relative Linear Speed Projection Angle Projection Height

Joint Linear Speed of Linear Speed – Angular Joint Linear Speed of Joint Linear Speed of the Ankle and all Joints Velocity Principle the Knee and all Joints the Hip and all Joints Angular Superior to the Ankle Superior to the Knee Superior to the Hip Impulse-Momentum Principle Joint Angular Radius of Joint Angular Radius of Joint Angular Radius of Velocity Rotation Velocity Rotation Velocity Rotation

Ankle PF Application Time Angular Knee Ext Application Time Angular Hip Ext Application Time Angular Torque of Joint Torque Inertia Torque of Joint Torque Inertia Torque of 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 Angular Inertia Principle Principle Action - Reaction Principle External Forces

External Forces Friction Principle Force

Friction Force Vertical Ground Coefficient Principle Reaction Force of Friction Biomechanical Model Jumping for Height or Distance

Jump Height/Distance — Projectile Motion Principle Time in the Air

Jumper’s Jumper’s Relative Linear Speed Projection Angle Projection Height Biomechanical Model Jumping for Height or Distance

Jumper’s — Sum of Joint Linear Speed Linear Speeds Principle Joint Linear Joint Linear Joint Linear Speeds 1 Speeds 2 Speeds 3 Biomechanical Model Jumping for Height or Distance

Joint Linear — Linear Speed – Angular Speeds Velocity Principle

Joint Angular Radius of Velocity Rotation s = ωrrot Biomechanical Model Jumping for Height or Distance

Joint Angular — Angular Impulse – Velocity Momentum Principle

Joint Application Time Angular Tt Torque of the Joint Torque Inertia ω = I Biomechanical Model Jumping for Height or Distance

Joint — Joint Torque Principle Torque

TJ = FMd MA Muscle Moment Force Arm Biomechanical Model Jumping for Height or Distance

Angular — Angular Inertia Principle Inertia

2 Radius of I = mr Mass res Resistance Biomechanical Model Jumping for Height or Distance

Muscle — Action – Reaction Principle Force

External Forces Biomechanical Model Jumping for Height or Distance

External — External Forces Principle Forces

Vertical Ground Friction Reaction Force Force Biomechanical Model Jumping for Height or Distance

Friction — Friction Force Principle Force

FFR = µFVGR Vertical Ground Coefficient Reaction Force of Friction Interpreng the Biomechanical Jump Height/Distance

Model Time in the Air

Jumper’s Jumper’s Relative Linear Speed Projection Angle Projection Height

Joint Linear Speed of Joint Linear Speed of Joint Linear Speed of the Ankle and all Joints the Knee and all Joints the Hip and all Joints Superior to the Ankle Superior to the Knee Superior to the Hip

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

Ankle PF Application Time Angular Knee Ext Application Time Angular Hip Ext Application Time Angular Torque of Joint Torque Inertia Torque of Joint Torque Inertia Torque of 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

Friction Force

Vertical Ground Coefficient Reaction Force of Friction Jumping for Height or Distance

Fundamental Biomechanical Principles Projecle Moon Principle — Projectile — An object that has been projected (thrown, struck or kicked) or dropped into the air — Three forces influence the movement of a projectile when it is in the air — Weight (W)

— Drag Force (FD)

— Lift Force (FL) — Unit of measurement — Newton (N) Projecle Moon Principle — Projectiles in Sport & Physical Activity — Round Projectiles — a tennis ball, a golf ball, a baseball, a softball, a basketball, a volleyball, a soccer ball, etc. — Non-Round Projectiles — a football, a discus, a javelin, a Frisbee, etc. — The Human Body — when it is running, high jumping, pole vaulting, playing volleyball, playing basketball, etc. Projecle Moon Principle — What Determines a Projectile’s Maximum Horizontal Distance — Two Factors — Projectile Speed — Time in the Air — Projectile Speed — Relative Projection Height — Projection Angle — Optimum Projection Angle Projecle Moon Principle — What Determines a Projectile’s Maximum Vertical Height — Two Factors — Projectile Speed — Projection Angle — Optimum Projection Angle Projecle Speed Relave Projecon Height (RPH)

RPH is negative Maximum Height RPH = 0

Range (distance)

RPH is positive Projecon Angle Opmum Projecon Angle Sum of Joint Linear Speeds Principle — A body’s total linear speed is the result of an optimal combination of individual joint linear speeds. — The identification of this optimal combination of joint linear speeds is a skill that all individuals interested in understanding human movement must develop Linear Speed – Angular Velocity Principle

— Radius of Rotation (rrot) — The linear distance from the joint’s axis of rotation to the point of 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 component — Unit of measurement — meters per second (m/s) 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 rotation — Unit of measurement — Radians per second (rad/s) 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. Linear Speed – Angular Velocity Principle — Real-World Application — An increase in linear speed (s) of a point on a rotating body component is caused by an increase in the body component’s angular velocity (ω) and/or an increase

the radius of rotation (rrot).

s = ωrrot Time 2 location s21 Time 1 location

s22

s11

s21

Radius of rotation (rrot) Δθ

Axis of rotation 90 degrees 135 degrees 180 degrees

π 3 π radians radians π radians 2 4

Conversion Factor

180 degrees = π radians

(π ) π Example: 90 degrees = (90) = radians 180 2 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 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) 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) 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 Joint Torque Principle — What is a Torque (T)? — It is the effect of a muscle force to cause a joint rotation

— Muscle Force (FM)

— Muscle force (FM) is caused by muscle contractions — These contractions pull on bones

— Muscle force (FM) is known as an eccentric force — An eccentric force is a force that does not pass through the joint connecting two body segments Joint Torque Principle — Torque (T) is directly related to the size of the muscle force that creates it

— The larger the muscle force (FM), 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 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 = FMdma — Units of Measurement — Newton-meter (N-m) muscle force

axis of rotation

moment dma arm 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) Angular Inera Principle — Real-World Application — A decrease in a body component’s angular inertia (I) is caused by a decrease in the body component’s mass (m)

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

2 I = mrres

— Unit of measurement — kilogram meter squared (kg-m2) 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

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 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. External Forces Principle — This principle may be interpreted in several different ways. — For this Biomechanical Model, this 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. — Units of Measurement — Newtons (N) FFR Vertical Ground Reaction Force

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

FFR = µFVGR Fricon Force Principle — Real-World Application — 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!