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.

to create a larger coefficient of friction, the bottom surface of the shows that you are wearing must have two characteristics:

• (1) the material of the soles must be soft
• (2) the surface of the soles must be rough

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 vertical ground reaction force 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.

To create a larger vertical ground reaction force, you must perform the vertical or horizontal jump on the hardest surface possible

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.

To create a larger muscle force, three (3) important factors that influence the size of the muscle force must be considered.

The first factor is muscle size. A muscle with a larger physiological cross-sectional area will create more muscle force. The method to increase physiological cross-sectional area is resistance training.

The second factor is muscle length. All muscles have a natural resting length. This natural resting length is found when the muscle is relaxed. Muscles that are stretched to approximately 120% of their natural resting lengths generate the most muscle force.

The third factor is the speed of the muscle contraction. Muscles that are concentrically contracted at slower speeds generate greater muscle force than muscles that are concentrically contracted at faster speeds.

The 6 muscles that you would increase muscle force through strength training to achieve the desired outcome are...

• (1) Tensor Fasciae Latae
• (2) Gluteus Maximus
• (3) Rectus Femoris
• (4) Vastus Lateralis
• (5) Vastus Intermedius
• (6) Vastus Lateralis

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.

The moment arm is the distance from the joint's axis of rotation to the line of pull of the muscle force. If the moment arm distance is increased, the size of the joint torque will increase.

To increase the moment arm distance, would would need to move the line of pull of the muscle force further away from the joint's axis of rotation. The line of pull of a muscle force is determined by drawing a line connecting the muscle's origin to it's insertion.

One method for moving the line of pull of the muscle force would be to change the locations of the origin and insertion points for the muscle. This is not an option because it would be unethical to perform this type of surgery.

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.

To create a smaller body component mass, you must consider short-term and long-term techniques. In the short-term, two things can be done to reduce body component mass:

• (1) wear the lightest clothing possible
• (2) wear the lightest shoes possible
• (3) losing fat mass

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.

The radius of resistance is the distance from the joint's axis of rotation to the center of mass of the body component. If the radius of resistance is shortened, the angular inertia will decrease.

We can shorten the radius of resistance by changing the angles of the joints within the body component being rotated.

Any change in a joint angle that brings a portion of the body component closer to the axis of rotation will shorten the radius of resistance.

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.

ANKLE

During the preparation phase, the ankle must be dorsiflexed and eccentrically contracted.

At the ankle, a concentric ankle plantar flexion joint torque is applied until the ankle is maximally plantar flexed. 

KNEE

During the preparation phase, the knee must be flexed and eccentrically contracted.

During the execution phase, a concentric knee extension joint torque is applied until the knee is maximally extended.

• HIP
• During the preparation phase, the hip must be flexed and eccentrically contracted.

During the execution phase, a concentric hip extension joint torque is applied until the hip is maximally extended.

The amount of hip flexion, knee flexion, and ankle dorsiflexion during the preparation phase depends on the environment in which the activity is being performed and on the muscle properties of the individual performing the jump.

If the activity is performed in a closed environment (i.e., an environment where the relevant stimuli in the environment for making a decision to move are not moving), then the amount of hip flexion, knee flexion, and ankle dorsiflexion would be slightly longer than 120% of their resting lengths. A standing vertical jump would be an example of a jump performed in a closed environment.

If on the other hand, the activity is performed in an open environment (i.e., an environment where the relevant stimuli in the environment for making a decision to move are moving), then the amount of hip flexion, knee flexion, and ankle dorsiflexion would be determind by a cognitive evaluation of these relevant stimuli. Rebounding in basketball would be an example of a jump performed in an open environment. How much hip flexion, knee flexion, and ankle dorsiflexion you can perform is dependent on the actions of other players in the game and the flight of the ball after the shot is missed. 

The second muscle property that influences the amount of hip flexion, knee flexion, and ankle dorsiflexion during the preparation phase is muscle fiber type: slow-twitch fibers versus fast-twitch fibers.

Fast-twitch fibers generate maximum muscle force in a shorter amount of time than slow-twitch fibers. Therefore, an individual with a greater amount of fast-twitch fibers in the hip extensor muscles would need a smaller amounts of hip flexion, knee flexion, and ankle dorsiflexion during the preparation phase.

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.

We can change the radius of rotation by changing the angles of the joints within the body component being rotated.

Any change in a joint angle that rotates a portion of the body component farther from the axis of rotation will lengthen the radius of rotation.

A positive relative projection height will result in greater time in the air and greater horizontal jump distance. Relative projection height does not have an impact on vertical jump height

To achieve a positive relative projection height for a horizontal jump, you would have to leave the ground with your center of gravity as high as possible and then land with your center of gravity as low as possible.

An optimal jumper's projection angle will result in greater time in the air and greater vertical jump height and/or greater horizontal jump distance.

To achieve the optimal projection angle for maximum vertical jump height, you would leave the ground with a projection angle of 90 degrees.

For the maximizing horizontal distance, the optimal projection angle is dependent on the relative projection height (RPH).

If RPH equals zero, you would leave the ground with a projection angle of 45 degrees to achieve maximum horizontal jump distance.

If RPH is positive, the jumper's projection angle should be less than 45 degrees (the exact value depends on how large is the positive RPH; the larger the positive RPH, the smaller the projection angle).

If RPH is negative, the jumper's projection angle should be greater than 45 degrees (the exact value depends on how large is the negative RPH; the larger the negative RPH, the greater the projection angle).