Jumping for Height or Distance Construc)ng 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 Interpre)ng 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 Projec)le Mo)on 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) Projec)le Mo)on 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. Projec)le Mo)on 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 Projec)le Mo)on Principle What Determines a Projectile’s Maximum Vertical Height Two Factors Projectile Speed Projection Angle Optimum Projection Angle Projecle Speed Relave Projec)on 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