Biomechanical Model Jumping.txt

Projectile Motion Principle

"three forces influence the movement of a projectile when it is in air"

• weight (W)
• drag force()
• lift force()

• "maximum horizontal distance"
• projectile speed

time in air

"time in air"

• projectile speed
• relative projection height
• projection angle

"maximum vertical height"

• projectile speed
• projection 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"

Linear Speed - Angular Velocity Principle

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 in the radius of rotation ()

EQUATION: ()

Joint Torque Principle

an increase in joint torque () is caused by...

an increase in a muscle force () pulling on the bones that are held together at the joint

and/or

an increase in the moment arm ()

EQUATION: ()

Angular Inertia Principle

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()

EQUATION: ()

Angular Impulse - Momentum Principle

an increase in angular velocity (ω) of a body component being rotated is caused by...

an increase in joint torque () 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)

EQUATION: ()

Action - Reaction Principle

"for any muscle to create its greatest amount of muscle force, an oppositely directed external force of equal magnitude must exist"

External Forces Principle

"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 created inside the body"

Friction Force Principle

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 ()

EQUATION: ()

A larger coefficient of friction will create more friction force and greater total external force to push against. Greater external force to push against allows greater ankle plantar flexion muscle force, knee extension muscle force, and hip extension muscle force to be exerted.

Greater ankle plantar flexion muscle force creates greater ankle plantar flexion joint torque and greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

Greater knee extension muscle force creates greater knee extension joint torque and greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

Greater hip extension muscle force creates greater hip extension joint torque and greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The coordinated increase in joint linear speeds due to a larger coefficient of friction will result in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

A larger vertical ground reaction force creates greater friction force and greater total external force to push against. Greater external force to push against allows greater ankle plantar flexion muscle force, knee extension muscle force, and hip extension muscle force to be exerted.

Greater ankle plantar flexion muscle force creates greater ankle plantar flexion joint torque and greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

Greater knee extension muscle force creates greater knee extension joint torque and greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

Greater hip extension muscle force creates greater hip extension joint torque and greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The coordinated increase in joint linear speeds due to a larger coefficient of friction will result in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the ankle muscle force box:

Greater ankle plantar flexion muscle force creates greater ankle plantar flexion joint torque and greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to the ankle due to greater ankle plantar flexion muscle force results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee muscle force box:

Greater knee extension muscle force creates greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to greater knee extension muscle force results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the  hip muscle force box:

Greater hip extension muscle force creates greater hip extension joint torque and greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to greater hip extension muscle force results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

From the ankle moment arm box:

A longer plantar flexion moment arm at the ankle joint creates greater ankle plantar flexion joint torque and greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to a longer ankle plantar flexion moment arm results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee moment arm box:

A longer knee extension moment arm at the knee joint creates greater knee extension joint torque and greater knee extension angular velocity. Greater knee exntesion angular velocity creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to a longer knee extension moment arm results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the hip moment arm box:

A longer hip extension moment arm at the hip joint creates greater hip extension joint torque and greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to a longer hip extension moment arm results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the ankle mass box:

A smaller body component mass superior to the ankle results in less angular inertia (i.e, less resistance to angular motion) for the body component. This will create greater ankle planter flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to the ankle due to smaller body component mass superior to the ankle results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee mass box:

A small body component mass superior to the knee results in less angular inertia (i.e., less resistance to angular motion) for the body component. This will create greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to a smaller body component mass superior to the knee results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the hip mass box:

A smaller body component mass superior to the hip results in less angular inertia (i.e., less resistance to angular motion) for the body component. This will create greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to a smaller body component mass superior to the hip results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the ankle radius of resistance box:

A shorter radius of resistance for the body component mass superior to the ankle results in less angular inertia (i.e., less resistance to angular motion) for the body component. This will create greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to the ankle due to a shorter radius of resistance for the body component superior to the ankle results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee radius of resistance box:

A shorter radius of resistance for the body component mass superior to the knee results in less angular inertia (i.e., less resistance to angular motion) for the body component. This will create greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to a shorter radius of resistance for the body component superior to the knee results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the hip radius of resistance box:

A shorter radius of resistance for the body component superior to the hip results in less angular inertia (i.e., less resistance to angular motion) for the body component. This will create greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to a shorter radius of resistance for the body component superior to the hip results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the ankle application time of joint torque box:

A longer application time of the ankle plantar flexion joint torque will create greater ankle plantar flexion angular velocity. Greater ankle plantar flexion angular velocity creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to the ankle due to the longer application time of the ankle plantar flexion joint torque results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee application time of joint torque box:

A longer application time of the knee extension joint torque will create greater knee extension angular velocity. Greater knee extension angular velocity creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to the longer application time of the knee extension joint torque results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the hip application time of joint torque box:

A longer application time of the hip etension joint torque will create greater hip extension angular velocity. Greater hip extension angular velocity creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to the longer application time of the hip extension joint torque results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the ankle radius of rotation box:

A longer radius of rotation for the body component superior to the ankle joint creates greater linear speed of the ankle and all joints superior to the ankle.

The increase in joint linear speeds superior to the ankle due to the longer radius of rotation for the body component superior to the ankle results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the knee radius of resistance box:

A longer radius of rotation for the body component superior to the knee joint creates greater linear speed of the knee and all joints superior to the knee.

The increase in joint linear speeds superior to the knee due to the longer radius of rotation for the body component superior to the knee results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

For the hip radius of rotation box:

A longer radius of rotation for the body component superior to the hip joint creates greater linear speed of the hip and all joints superior to the hip.

The increase in joint linear speeds superior to the hip due to the longer radius of rotation for the body component superior to the hip results in greater linear speed for the jumper when leaving the ground. This will lead to greater time in the air and greater vertical jump height and/or greater horizontal jump distance.