Biomechanics

Learning Objectives• Define the primary goals of biomechanics• Define what biomechanics is• Describe what power is and how it coincides with biomechanics• Define Rigid-Body Mechanics• Differentiate between statics and dynamics as well as ki-

netics and kinematics (linear and angular)• Know the definition and the various categories of strength• Know the definition and the various types of energy

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Introduction: The Role of BiomechanicsMost biomechanics textbooks state two primary goals for biomechanics: performance enhancement and injury prevention/rehabilitation. Biomechanics enhance performance by using mechanical principles to improve an individual’s technique, the equipment they use, and to modify specific training protocols that the coach or trainer implements to help an individual achieve their goals. Similarly, for injury prevention and rehabilitation, biomechanics is used to develop techniques that reduce the chance of injury as well as changes in equipment design that may reduce injury.

What is the goal of a coach or personal fitness trainer? To help trainees reach their goals in the most efficient, effective and safest way possible. Compare this statement with the goals of biomechanics – to reach goals (performance enhancement) in the most efficient, effective, and safest (injury prevention) way possible.

One of the primary goals of this chapter is to empower the coach or personal trainer with a solid foundation in bio-mechanics. Another is to introduce everyone to a new way of looking at exercise in general. This new perspective is:

Exercise is simply a mechanical stress placed on the body to which the body will adapt.

In order to understand this new perspective and its importance, one must be willing to accept three premises.

Premise #1

The primary physiological effects of exercise (both good and bad) are in direct response to the mechanical stress placed on the body.

Exercise can be seen as a mechanical stress (Force/Area), placed on the body where the body must accept forces from external sources and respond by creating the appropriate internal forces (from the muscles and connective tissue) to create the appropriate movement. These stressors (both externally and internally) stimulate the physiological adaptations within the body. These physiological adap-tations may be structural (adaptations to connective

tissue such as muscle, bone, and fascia) or functional (neuromuscular adaptations such as motor learning).

Premise #2

In order to facilitate the proper adaptations for our trainees, we have to understand forces, how they are applied (how much, in what direction, over what range of motion, and at what speed), and how the tissues of the body will adapt to those forces.

Put simply, understanding forces and their effects are at the core of physical training ideologies. Coaches and trainers must remember that there are forces on us all the time (whether something is moving or not). If there is movement, there is a force that caused that movement.

Premise #3

Proper understanding and implementation of biomechanics is essential in all aspects of training (Assess – Design – Instruct – Reassess).

When you reach the assessment section, you will find that much of the assessment process consists of postural and movement assessments. These assessments look at how the client’s body has adapted to forces imposed upon it over time. These assessments may indicate certain kinetic chain imbalances (short/tight muscles on one side of a joint) that need to be addressed.

As previously stated, understanding how the body is going to adapt to the biomechanical stresses placed upon it is essential to program design. The exercises chosen (and how they will be implemented) are based on the client’s goals and needs and your knowledge of how to make them adapt safely and efficiently. Once the exercises are chosen, exercise instruction is the area most coaches and personal trainers associate with the importance of biomechanics. Put simply, understanding basic biome-chanics is the basis of instructing proper technique.

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How do we use Biomechanics to Maximize Performance and Minimize Chance of Injury?There is a systematic thought process that every coach and personal trainer must use to ensure any person under their care is receiving optimal/maximal attention for every movement suggested.

• Analyze: individual’s fundamental movement patterns• Optimize: technique of all movements

within the training program

in order to...

• Maximize: overall performance/effectiveness of the program

• Minimize: the risk of injury

What do we Analyze?

When we evaluate a trainee’s technique for a specific movement, we are doing a biomechanical analysis for every rep of every set as well, since each repetition is viewed as an assessment. You should be able to distinguish between what is important and what is unimportant, what is correct and what is incorrect, what is possible and what is impossible, what is effective and what is ineffective, what is safe and what is unsafe.

The first thing to evaluate and understand is the move-ment itself without regard to the forces that caused it. In physics, this is known as kinematics. This involves analyzing such details as the osteokinematics (planes of motion) learned in Chapter 1, the direction of motion, the path of motion, and the range of motion (range of motion is covered in detail in the assessment chapter). A kinematic analysis may include basic kinematic variables such as distance, speed, and acceleration.

Only after you analyze the kinematics does one look at the forces that cause the movement (as well as other forces on the body). In physics, this is known as kinetics.

Another way of looking at the analysis process is to look at joints first (both moving and non-moving, describing

them kinematically), then the external and internal forces on the body (kinetics). Muscles are engineered to move joints in a particular fashion (based on the structure of the joint). Therefore, a basic understanding of joint structure and function is essential for proper muscle activation (if a trainee is moving the joints properly, then the muscles must be working properly). Furthermore, one doesn’t truly know which internal forces are developed without first looking at the external forces that caused it.

Basic Definitions

• Kinematics – The study of motion without regard to its causes (forces)

• Kinetics – The study of forces acting on a system• Kinesiology – The scientific and ar-

tistic study of human movement• Force – A “push” or a “pull.” Based on Newton’s

Second Law of Motion, Force = Mass × Acceleration or F = MA. This equation leads to impulse

How do we Analyze?

DOE-I: The Practical Way to Analyze and Optimize

While it is unlikely coaches and trainers will be using advanced biomechanical analysis tools with their trainees, there is a step-by-step process to perform a qualitative biomechanical analysis recommended by McGinnis (2013).

DOE-I

Step 1 D Describe (the ideal technique)

Step 2 O Observe (the trainee perform the technique)

Step 3 E Evaluate (the performance)

Step 4 I Instruct (the client)

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Step 1: Describe the Ideal Technique

In order to train anyone in a particular movement, you must have a fundamental knowledge of the skill. This begs the question, how does one know the “ideal” technique? If it’s a performance movement, such as pitching a fastball, the coach will watch successful pitchers, read coaching journals and textbooks, and find any source that discusses how successful individuals apply their skill.

More likely, the coach will be describing some sort of exercise or drill. Once again, the coach will use the same strategy of researching what the “ideal” technique is. That said, whether one is describing a sports-specific skill or an exercise, one must think critically and be skeptical of “experts.” Just because one person is successful doing a bench press in a particular fashion doesn’t mean everyone should use the same technique. Please remember that the coach or personal trainer’s job is to individualize the technique. It should be customized to the trainee’s current abilities, genetics, and goals.

When the coach or personal trainer is researching sources to describe the ideal technique, they are attempting to find the common characteristics of the most efficient techniques so that they may appropriately modify these characteristics for any individual trainee.

Step 2: Observe the Client Performing the Technique

When observing a client perform a particular tech-nique, we have to ask ourselves several questions:

• Who are we observing? • What is their current skill level? • What are their current limitations?• Under what conditions?

• Where to observe?• What to look for?

The answers to these questions will determine your ability to successfully evaluate the client.

Step 3: Evaluate the Performance

When the coach or personal trainer is evaluating a perfor-mance, they are simply comparing the “ideal” to the actual performance of the client. They are identifying errors and evaluating those errors to determine the focus of their correction efforts. Is the error actually dangerous and is there risk of injury? Is it a new trainee learning a new skill that will take time to develop the proper motor patterns?

How do we Optimize?

Step 4: Instruct the Client

This is where proper communication skills are vital, so the coach or personal trainer can successfully communicate with the trainee and correct errors in their technique. This will be discussed in greater detail in Chapter 8: Exercise Instruction.

What do we Optimize?

Again, we focus on both the movement (kinematics) and the forces that cause the movement (kinetics). The coach or personal trainer must take into account the structure of the body (specifically, the anatomy of the joints and the body type), its intended function, and the goal of the exercise. The need to understand the ideal movement and instruct accordingly is imperative, with the goal being that the trainee perform every movement as close as possible to the ideal technique (which may be unique to them) in order to maximize performance and minimize injury.

The Basics of Biomechanics and PowerAs previously stated in both the introduction and chapter one, the overall ideology of Biomechanics is the study of forces on the human body and their effect on movement. This subject is broken down into two major divisions:

• Kinesiology: The Study of Human Movement.

• Physics: Rigid Body Mechanics.

Both chapters show the breakdown diagram identi-fying the various categories within Biomechanics:

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Motion independent of force

Force causing motion

Statics

(Linear & Angular) (Linear & Angular)

Dynamics

Anatomy And Physiology

Nervous System

Skeletal System

Muscular System

Kinetic Chain

Kinesiology

Biomechanics

Kinematics Kinetics

Rigid Body Mechanics

Physics

Chapter one covered the first step to understanding why and how biomechanics is so important in the field of physi-cal training by reviewing the foundational information/ba-sics of kinesiology (the study of human movement/ motion). The general definition of motion is the displacement (move-ment) of any object or system. There are four types of mo-tion: linear (rectilinear or straight line), curvilinear (objects that travel in a curved path), rotary (circular motion or movement of a link/system around an axis or rotation), and general (combination of both linear and rotary motion).

We learned that the backbone of kinesiology is the kinetic chain. The kinetic chain is the “chain” of systems that “link” together to create human movement and is comprised of the skeletal, muscular, and nervous systems. In order for movement to take place, the systems must coordinate or integrate together; the entire body must work together as an integrated unit. Remember, a “system” is a body or group of bodies to be studied or examined. A “link” can be a segment, linkage, connection, or a “sub-system of a primary system” (Kreighbaum & Barthels, 1996). In this case we are referring to the human link system made up of eleven individual systems, or links.

Kinesiology also studies and identifies the muscles that create the internal forces imposed on any point in a link system, against gravity or some form of applied external load to the body or systems creating the external force (please note here that force is anything that causes or tends to cause a change in motion – F = ma and all the associated formulas). How forces influence these systems falls under the category of Kinetics. Movement independent of forces causing linear and rotary movement

is under the heading of Kinematics. Both kinetics and kinematics fall under the term Rigid Body Mechanics. The human body is considered a “rigid link system,” therefore the term “rigid body” is appropriate.

We must also investigate the concept of Power. Most people in the training industry relate this term to very fast or explosive types of movement; however, the term has been recently reviewed for a more concise interpretation (Knudson, 2009). Power output has long been a highly debated issue in both the sport performance and exercise training communities. Increasing or improving power out-put (training to increase “power,” such as in power train-ing) has caused the development of numerous measurement protocols by coaches and exercise trainers/specialists, as well as by sport scientists (biomechanists and exercise phys-iologists) to estimate energy expenditure during work or ex-ercise as well as rate of energy expenditure (power output) (Garhammer, 1993). These estimation protocols have also created the development of numerous training programs to increase power output based on inexact data not supported by legitimate training science (research-based and applied science data). Power is the rate at which work is performed (along with estimating energy expenditure). Work is force times displacement. A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A “displacement vector” represents the length and direction of that imaginary straight path. Displacement is often correlated with distance. This term (displacement) means “movement,” with distance meaning the length between two objects. An object can therefore

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be “displaced,” but its distance could be in a winding path motion (such as a running course) and measured in terms of meters, centimeters, feet, inches, etc. This dis-placement of the object in question is from start to finish.

Real life example: performing a bench press and a snatch. For the bench press, the bar is displaced from the chest to arm’s length (straight line up from the position on the chest); however, the path of the bar may not move in a straight line, but moved in a particular curved or slightly backward path. Again, the displacement is measured straight up from the chest. For the snatch, the displace-ment is measured from the floor to the highest position overhead, though the path taken is in an “S” shape.

The RED line is the path of the bar

The distance covered is measured from the chest straight up

The white line is the actual path of the bar but is measured straight up from the floor to its highest position overhead

The amount of work done (W = fd) can be very fast, or instantaneous, or it can be done slowly over a long period of time with substantial differences in energy expenditure (this will be addressed in depth later in this chapter).

We are taking a different approach to teaching the subject of biomechanics, based on the concept that the human body is a machine designed to create motion, whether in activities of daily living, exercise, or sport performance, and perform work of various kinds and at various speeds – all of which are directly and intimately related to power

and energy output. Biomechanics and power go hand in hand, and must be coupled together to evaluate how the kinetic chain operates efficiently and effectively for optimal performance. We will first explain the overall breakdown of biomechanics, then discuss the concept of power (what it is in relation to work and time) and its relationship to biomechanics. After this, we will discuss what force is along with its various properties, and how force is the cen-tral aspect of the multiple categories of strength (strength is the ability to exert force on an object at a specified velocity and in a specified direction). Once we examine what force and strength are, the next subject is kinetics, which is the branch of classical mechanics concerned with the relationship between the motion of bodies and its causes (namely forces and torques or how force causes linear and angular motion). Finally, we will identify the various parts of kinematics, which is the branch of classical mechanics describing the motion of points, bodies (objects), and sys-tems of bodies (groups of objects) without consideration of the forces that cause motion (velocity, speed, acceleration, displacement, translation). This will also include a section on types of energy. All the above coincide with understand-ing the concepts and terminology related to mechanics of human movement, and applying these concepts and terminology appropriately to facilitate onces ablility to analyze human movement efficiently and effectively.

What is Biomechanics?As previous stated in the kinesiology chapter, the human body is a living machine. All movement related to this human machine involves muscular power flow, i.e., work being done over a designat-ed period of time (a person exerts a designated amount of muscular force on an object over a specified distance). This indicates there are low power outputs involving low force application on an object over some specified period of time, or a high-force application done very briefly. Again, both are power outputs designating different types of strength (the maximum force a muscle or group of muscles can generate at a specified ve-

locity [Knuttgen & Kraemer, 1987]) and work outputs. The training industry consistently uses peak/average power out-puts, and does not analyze/define what creates power, i.e., RFD (rate of force development), impulse, and the types of strength (e.g., starting, acceleration, and explosive strength, strength endurance, etc.) that coincide with iRFD (intial RFD) and mRFD (maximum RFD) (Knudson, 2009).

If power is equal to force times velocity, to include RFD (rate of force development) and impulse, where does the force originate to create or influence

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power production/output along with the numerous variables that affect power? It should be noted that the three primary units in mechanics are:

• Time• Distance• Mass

This is where the fields of biomechanics and kinesiology help to explain how power is determined. Numerous definitions from various sources have attempted to explain what biomechanics is. Biomechanics is a complex field involving various branches of science; however, for simplicity, the follow definitions are given in an attempt to give the reader a basic understanding of the topic.

• Biomechanics: is the study of forces and their effects on living systems (McGinnis, 2013).

This is a basic definition of what the field of biomechanics is about; however, when reviewing all the aspects of power output, a more in-depth definition of biomechanics is:

Biomechanics is concerned with the internal and external forces that act on the human body and the effects produced by these forces (Hay, 1993).

Here is a more detailed explana-tion of the definition of force:

• Internal: (muscle actions) and external (gravity or any outside load applied to a system or systems) forces that act upon the human body determine how the parts of the human body (structure) move during the performance of a particular motor skill or some type of functional human movement.

Human movements include:

• Sitting/standing• Squatting up and down• Bending/twisting• Lunging/stepping• Lifting/carrying• Running/walking• Jumping up and landing• Throwing/catching an object• Various combinations of these movements

Note: The term “functional” has been used here in conjunction with internal and external forces applied to systems within the human body. This is an overstated and overused vernacular within the physical/exercise/strength training communities. This

particular use of the word “functional” within these communities pertains to what is understood as:

• Useful• Practical• Handy• Purposeful• Efficient• Well-designed• Serviceable

A recently updated version of the book Advances in Functional Training: Training Techniques for Coaches, Personal Trainers and Athletes (Boyle, 2010) validates this definition, stating func-tion is essentially purpose. Functional training can there-fore be described as purposeful training. This can be further demonstrated by the numerous training tools used by those in the strength and conditioning communities, particularly pertaining to the last example of normal hu-man movement (variations of all these human movements).

The goal of the person performing a particular movement, as well as the level of the trainee per-forming said movement, will dictate the functionality of any movement performed. Siff (2002) stated

“There is no such entity as a truly functional exercise, except for the actual sporting or daily movement that we are trying to enhance by training. Functionality depends not only on the exercise itself but on many other factors, such as the pattern of execution, the characteristics of the athlete, reps and sets, the manner of execution, the phase of training, interaction with other training, the current physical and mental state of the athlete (or trainee), the overall training program, and several other variables.”

As stated at the introduction of this chapter, biomechanics is intimately related to kinesiology (the study of human movement). While biomechanics deals with the forces that cause movement, we have observed how kinesiology examines the structure and function of the human body, i.e., the kinetic chain, or the force-producing elements affecting the various types of motion performed by the human body. This is the starting point to determine all the aspects of force production that affect power.

How is Biomechanics Broken Down?

The following diagram of how biomechanics can be broken down (into two major sections: kinesiology and mechanical physics) will be constantly repeated throughout

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this manual for visualizing this intimate relationship. As shown previously, biomechanics has two major divisions:

Motion independent of force

Force causing motion

Statics

(Linear & Angular) (Linear & Angular)

Dynamics

Anatomy And Physiology

Nervous System

Skeletal System

Muscular System

Kinetic Chain

Kinesiology

Biomechanics

Kinematics Kinetics

Rigid Body Mechanics

Physics

(Adapted from NESTA’s (National Exercise and Sport Trainer Association) Personal Fitness Trainer’s manual and Biomechanic’s Specialist course manual, copyright 2007. Used by permission.)

Kinesiology examines the basics of the kinetic chain:

Kinetic Chain: kinetic relating to, caused by, or producing motion.

• Anatomy and Physiology (Structure and Function) - Nervous System - Skeletal System - Muscular System

Physics: in this case, is considered classical mechanics

Rigid Body Mechanics is best suited to describing and explaining the forces imposed on the human body during sport and exercise performance.

Statics Dynamics

Kinematics Kinetics

Rigid Body Mechanics

To further explain these forces on human movement, rigid body mechanics (or mechanics as it will be known as from

here on) is further subdivided into statics (non-moving) and dynamics (moving). Dynamics is divided into kinetics (forces that causes movement) and kinematics (movement independent of the forces that cause movement, e.g., velocity, acceleration, displacement, etc., or the study of time and space factors of motion of a system).

One may attempt to remain motionless, but doing so is almost impossible. Even while standing, holding a weight overhead, etc., the body sways side-to-side and forward and backward, with the person attempting to maintain this position (this is referred to as stabilization). Nevertheless, a static analysis may be made of the human body in near-static conditions, or activities such as standing, balancing on any surface, or performing resistance training exercises. However, dynamic analysis is also required, due to total body or segmental move-ments taking place (Kreighbaum & Barthels, 1996).

Please note, the previously shown graph is differentiating static (isometric) strength applied to motion from the dynamic strength applied to a moving system. Initial application of the force is iRFD, with overcoming inertia related to mRFD, or maximum rate of force development. Notice the horizontal line labeled “W” on the left diagram. This is the resistance that must be overcome. During the isometric phase, substantial force is rapidly applied to this resistance. This isometric phase is comprised of starting strength, followed by acceleration strength, and finally explosive strength. These three types of strength combined are referred to as the mRFD or max rate of force devel-opment to overcome the external resistance W. The faster the force is applied, the more these strength categories affect the rate of force developed, and the external load moves faster during the dynamic phase. The steeper this line, the greater the RFD (see diagram on the right), and the lesser the time required to overcome said resistance.

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An application of biomechanics to movement-related areas

Mechanical Physicst

BIOMECHANICS

Biological Material Properties Properties

Goal –Oriented Movements

Daily Living Tasks

Walk/Run

Lift/Carry/Place

Sit/Stand/Squat

Push/Pull/Reach

Stairs (Ascend and Descend)

Bend/Twist

Air Environments

Water Environments

Sports Environments

Work Environments

Ergonomics

Human Design Factors

Adapted Human Movements

Gerontological

Prosthetic

Orthopedic

Sport Injury

Basic Human Movements

Walk

Run

Jump

Throw

Lift

Push

Strike

Pull

Swim

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The diagram above is an additional pictorial representa-tion (visual breakdown) of how the field of biomechanics relates to the study/field of human movement (kinesiology) (adapted from Kreighbaum and Barthels’s Biomechanics: A Qualitative Approach for Studying Human Movement, 1996)

In addition to functional movement, movement analysis must adhere to the following:

• Every movement performed uses a basic (standard) technique (how one performs a specific movement). Depending on the variations of the structure (anthro-pometry), every technique for any skill will eventually be individualized and called style of technique.

• Any technique for any movement is founded on the principles of biomechanics and based on: - A knowledge of motor learning to enable teachers/

coaches to make sound judgments on how to use specific methodologies of instruction to include length, frequency, and nature of technical practice, etc., to identify the optimal style of technique for an athlete performing a specific movement.

- A knowledge of physiology to enable teachers/coaches to design/implement proper training regimens concerning the amount and type of training for optimal adaptations based on level of participant, learning ability, etc.

- A knowledge of biomechanics to enable teachers/coaches to optimize movement mechanics (techniques) and to detect the root causes of faults as they arise in their use.

Power Output BasicsPower output has long been a highly debated issue in both the sport performance and exercise training communities. As previously stated, increasing or improving power output has led to the development of numerous measurement pro-tocols by coaches, exercise trainers/specialists, and sport scientists to estimate energy expenditure during work or ex-ercise as well as rate of energy expenditure (power output) (Garhammer, 1993). These estimation protocols have also led to the development of numerous training programs to increase power output based on inexact data not supported by legitimate training science (research based and applied science data). Knudson (2009) stated that various nebulous terms still exist in an attempt to educate both the sport and exercise industry (as well as the general public) as to the scientific explanation of exactly what power is, irrespective of the 100-plus years of scientific research identifying the nuances of what this term means. The problem is further

compounded by various organizations continuing to use colloquial definitions to explain “power.” This vocabulary may be unsuited to explain what the real meaning of power is, particularly how power is actually identified and developed along with categorizing the various stages and types of power. The popular vocabulary, as well as the training protocols used to educate those training with the intention to increase “power” production, is based on misinterpretation or misunderstanding of the multiple variants of power (P max, mean/median values of power, average power output, instantaneous power, rate of force development or RFD, impulse-momentum principle, etc.). This confusion ensues, based on disagreements document-ed in the training science journals between research results stating how the various types of power are increased in conjunction with the associated training protocols (Cronin & Sleivert, 2005). Verkhoshansky and Siff (2009) also stated that “the full ramifications of the concept of power often tends to be lost in Western strength training because the term ‘speed-strength,’ directly translated from the Russian texts on strength training, is used as its colloquial equiva-lent.” Thus, programs are encountered on how to “increase power,” which is entirely nebulous in the context of human movement, because the concept of power may appear in several different forms in biomechanics, namely “mean power” (over a given interval), peak power (at some specific instant), and power at any given instant. Just as it is not very meaningful to develop maximum strength (force) or high mean force in every situation or stage of movement, so can it be equally inappropriate to train an athlete (or any person) to simply develop “power” irrespective of context. One of the central features of all motor skill is the ability to produce maximum power in the most efficient manner pos-sible. In fact, all effective strength utilization and training means “optimal timing of the magnitude of force, power, and rate of force development (RFD) throughout any movement” (Knudson, 2009; Verkhoshansky & Siff, 2009).

Further problems exist when the subject of “biomechanics” is referenced with power, compounding this confusion (please note this confusion may be based on how the subject of biomechanics is presented to and interpreted by various audiences). This chapter will attempt to identify the various parts and types of power then relate how biome-chanics (and the various components within this science to include the subject of Kinesiology) correspond with and explain power. Once these items have been clarified, examples will be given to identify and simplify how biomechanics (as well as kinesiology) relates to the different types of power development/output and how this data is used effectively to increase all variants of power output.

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Power and Biomechanics Defined

Every human movement performed, whether done slowly or extremely fast, involves a power output of some magnitude (Knudson, 2009; Zatsiorsky & Kraemer, 2006; Cronin & Sleivert, 2005; McGinnis, 2013; Garhammer, 1993; Komi, 1992). Harman (Essentials, 2008) stated that all sports (as well as all movements) involve acceleration (change in velocity per unit of time) of the body (individual segments or whole body – refer back to Chapter One pertaining to motion, types of motion, planes of motion involved with whole body movements and/or individual link/segment movements/motions) or a particular im-plement being manipulated. Because of the individual differences in the ability to exert force at different speeds (which ultimately affects power output) (Verkhoshansky & Siff, 2009; Zatisiorsky & Kraemer, 2006), the ability to measure this output (to include strength measurements), and scores from various testing or training protocols (isometric, isokinetic, and low-speed lifting tests) may have limited value in predicting power output performance, especially in activities that involve movements at high speeds. These limited means of measuring power have led to an interest in power as a measurement of the ability to exert force at high speeds. Colloquial terms used loosely to define power, such as “force, energy, strength, and might,” are indicative of the misunderstanding and limited knowledge of what power is and how it relates to the categories of strength, along with how these strength categories affect the types of power output. The recent rush of interest in vague estimates of peak power in many short, dynamic human movements has ignored the large body of research on the definition of mechanical power, the principle of specificity, and the domains of muscular strength/neuromuscular performance that challenge the importance of this colloquial meaning. This misplaced emphasis, incorrect use of terminology, and lack of attention to previous strength and conditioning research has contributed to inconsistent results and misrepresented findings (Knudson, 2009; Cronin & Sleivert, 2005).

To support the idea that power output is only the ability to exert force at high speeds, Knudson (2009) stated that because forces only do mechanical work when movement is present, mechanical power flow is present in most human movements. It is therefore nearly useless to refer to “power events” or “power athletes” because all movements (refer to Chapter One on Kinesiology), except for stabilized postures created by isometric muscle actions, involve mus-cular power flow. There is no one-to-one correspondence between maximizing mechanical power output of the body and certain sport movements, so the colloquial use of the term “power” as a unique neuromuscular performance characteristic is not consistent with the true definition

of power. This statement is contradictory to how power is interpreted, since the generalized definition involves a “power” movement done very fast or explosively, hence the field of “power training.” This misinterpretation has also been documented in the text Strength and Power in Sports (Komi, 1992), stating the term power is commonly misused to mean force: power = work done (f × d) per unit time. This misinterpretation pertains to maximum force produced by the muscle, either in a single effort or repeated contractions of the muscle. In this case, the reader needs to think in terms of power (presented by Goldspink, chapter 8A in Komi’s book), which combines the two parameters of force and velocity (f × v); the higher and more rapid force generation (i.e., the rate of force production), the greater the power output. McGinnis (2013) also stated that power can be thought of as how quickly or slowly work is done.

What is Power?

Simply stated, power is the rate of performing or doing work. Notice this definition considers rate of doing work in-dicating a time element when any work is being performed (rate meaning degree, amount, proportion, percentage, speed, or velocity). Power can be defined as the amount of work produced per unit time or the product of force and velocity (Zatsiorsky & Kraemer, 2006; Cronin & Sleivert, 2005; O’Shea, 1996). Accordingly, an additional definition of power is the rate of mechanical work performed or the time rate of doing (mechanical) work (Harman, 2008). Mechanical work is defined as the scalar product (how much work is performed independent of its direction) of the net force applied to an entity/object with the resulting displacement (sum of each applied force multiplied by the corresponding distance moved in the direction of that force) (Garhammer, 1993). Mechanical power, then, is simply the rate of doing mechanical work or work done per unit of time (Garhammer, 1993). Also included in this explanation is metabolic power, the rate of metabolic work done per unit of time. Metabolic work is how energy substrates (proteins, fats, and carbohydrates) are broken down (metabolism) to create energy for doing work (hence the definition of energy being the capacity to do or perform work). Knudson (2009) stated that numerous papers have been published addressing “power” in human movement. In a space of 10 years (1998-2008), SportDiscus and Google Scholar indexed over 500 and 21,000 citations, respectively, for a search on “muscular” and “power.” With such numerous sources for what power is (particularly muscular power as an independent subject by itself ), the concept of power must be simplified from 1) a basic scientific definition/explanation/interpretation and 2) how power is cate-gorized/defined/created/utilized/displayed in terms of

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human performance. Since the term “power” is considered the timed rate of doing mechanical work, one must know how the scientific community defines power and what work is. This information can then be used to increase knowledge and the ability to develop appropriate training programs based on the type of power needed.

In physics, power is the rate at which work is performed or energy converted.

If ΔW (∆ designates a change in) is the amount of work performed during a period of time of duration Δt, the Average Power (Pavg) over that period is given by the formula

It is the average amount of work done or energy converted per unit of time. The average power is often simply called “power” when the context makes it clear.

The Instantaneous Power is then the limiting value of the average power as the time interval Δt approaches zero (d designates the derivative of ).

It should be noted here that “instantaneous power” is asso-ciated with peak power, which does not strongly correlate with how power relates to all activities (numerous studies examined external power flow in continuous, steady-state conditions, which only examine the work done in these conditions). Peak powers measured in these conditions may not be indicative of true external peak power in other activities. Much of these data have additionally been used to explain power output in numerous activities, including short-term, dynamic, and impulsive movement unrelated to cyclic work measured in continuous activities (Knudson, 2009). Please note these studies examined the speed of external muscular force on the designated object being studied, but little data refers to or has been presented on the internal power flow created by muscular actions to produce force and how this internal muscular force is developed accordingly to affect the external power flow.

In the case of constant power P, the amount of work performed during a period of duration T is given by:

W = PT

In the context of energy conversion, it is more customary to use the symbol E than W.

Since power is the timed rate of doing work, the next step is to identify what work is (in this case work is considered mechanical work). In mechanics, the work done on an object is related to the forces acting on it by

W = F · Δd

Where:

F is force

Δd is the (change in) displacement of the object

This is often summarized by saying that work is equal to the force acting on an object multiplied by its displacement (how far the object moves while the force(s) act(s) on it).

The formula for Work (W) is Force (F) times the distance (d) an object is moved or displaced (W = F × d). The Behind the Neck Overhead Barbell Press will be shown as an example to illustrate the basics of work done in a specified human performance (a pushing movement). Also note the displacement of the barbell is in a straight line motion and this straight line is measured to denote its linear distance traveled.

Starting Position Ending Position

The Behind the Neck Overhead Barbell Press requires the user to push a specified resistance using a barbell (or any weighted bar) upward from shoulder level to a straight arms’ length over the head. The movement begins with the bar taken from shoulder-height supports inside a power rack (or set of supports).

Upon review of this movement, let us begin to calculate work done using the following:

W = F times the distance the object travels or

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W = Fd

Where:

F = Force (ma)

mass = 30 kg (we are using this number for our example)

a = acceleration, in this case the gravity or force on the barbell (which equals approximately 9.81 m/s2)

d (Distance bar travels in an vertical (upward) and straight line path) = 1.5 feet or .4572 meters (feet × .3048 to achieve SI units)

Force (F) = Mass × acceleration (ma) = 30kg × 9.81 m/s2 = 294 N

F = 294 N* (newtons)

*Newton is the unit of force in the SI system

Acceleration of gravity is in meters per second squared

In computing the work done by a force, no account has been taken of the length of time that is involved in performing this work. Thus, if a person does a certain amount of work raising a barbell overhead, the amount of work done is not dependent on how long he or she takes to complete this movement. Whether the lift took .5, 1, or 2 seconds to complete, the amount of work done is still the same. What changes is the power production (output), or the rate at which the work was performed.

By measuring the force (ma), distance the bar traveled, and the time taken to complete the movement, one can then calculate Pavg for this particular movement.

or

Time to complete the movement = 2 seconds

Power = work/time or Force (F = ma) multiplied by distance bar travels (d) in meters divided by the time it takes to achieve the final overhead position

Power = W/t (work done per unit of time)W = 134.4 NmTime (t) = 2 secondsPavg = 67.2 joules/sec = 67.2 Watts

The watt (symbol: W) is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit measures the rate of energy conversion. It is defined as one joule per second.

What happens when the time to completion is decreased (i.e., the speed is increased)? The power output changes drastically. If the time to completion is decreased from two seconds to one second, the power output doubles (the work performed is done in half the original time).

P = W/t

P = F (ma) × d/t

P = (30kg × 9.81m/s2) × .4572 m/1 s

P = 294 N × .4572 m/1 s

P = 134.4 Nm/1 s

P = 134.4 J/s = 134.4 Watts

This is a very basic estimation of a power output utilizing a simple human movement (pushing). Notice that this is the average power output during the course of only one repetition of this movement with two different time factors.

Power output can also be estimated with multiple repetitions with same weight and two time factors.

Using the previous examples:

1.1 30 kg moved .4572 meters in 2 seconds (F × d/t or W/t) = 67.2 J/s = 67.2 watts

1.2 30 kg moved .4572 meters in 1 second (F × d/t or W/t) = 134.4 J/s = 134.4 watts

If this movement is performed for ten (10) repetitions (the downward or eccentric phase is not factored into the equation, only concentric. While the eccentric phase is considered negative work, we are only using the concentric portion to illustrate positive work com-pleted), the Pavg (average power output) for this exercise and the number of repetitions for the exercise is:

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Work done Mechanical Work

10 repetitions × 67.2 J/rep = 672 joules (Watts)

10 repetitions × 134.4 J/rep = 1344 joules (Watts)

Total energy expenditure and rate of energy expenditure (power output) are important considerations for exercise programs and training programs (Garhammer, 1993). Work done and the time taken to complete this work is the essence of power output, i.e., power flow that is present in all human movement. However, in human movement as well as in sports, there is ample concern with changing the velocity of an object (remember that velocity is simply the distance an object travels in a specified time). When an object’s velocity changes, it subsequently changes the kinetic energy (KE), thus establishing the work-energy principle (KE can be changed by doing work). Increasing the work done will cause a greater increase in energy output (usage) if the average force exerted is of large enough quantity or the displacement in line with this force is long. This concept is known as the impulse-momentum relationship, which is:

An impulse may also be regarded as the change in momentum of an object to which a force is applied. The impulse may be expressed in a simpler form when both the force and the mass are constant:

Where:

F is the constant total net force applied,

Δt is the time interval over which the force is applied,

m is the constant mass of the object,

Δv is the change in velocity produced by the force in the considered time interval, and

m Δv = Δ(mv) is the change in linear momentum.

Δp is the change in momen-tum from time t1 to t2

Please note the ∆p (change in momentum) is easier to understand and identify if written as:

∆M

When simplified:

Impulse: change in momentum

The impulse-momentum relationship, if used for technique analysis, states that a large change in velocity requires a large force be applied over a long time. In conjunction with this, the work-energy principle indicates that production of a large change in kinetic energy (along with a large change in velocity) requires that a large force be applied over a long distance.

Power creation: Visualization of Force Development

What is Force?

As we have learned, power is the rate of performing work. Work is force multiplied by the distance traveled by an object (displacement from start to finish in a straight line or curved path), therefore one must understand what force is. The mathematical description of force is

F = ma (Force = mass times acceleration)

However, we need to review what the practi-cal ideology of force is first before we discuss the subject of biomechanics in depth.

The general definition of force is:

Force: Anything that causes or tends to cause a change in motion or shape of an object or body

Force can be:

• A push or a pull on an object• Friction or rubbing• Gravity• A blow or impact on an object

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Left picture: Squatting (pushing on ascent phase) with gravity pulling down

Right picture: Deadlifting (pulling up from floor) with gravity pulling down

Forces are linear (applied in a straight line or the object having force applied to it moves linearly) or rotational (called torque). Reviewing the previous examples:

• Squat movement – the bar moves in a linear path (descent and ascent) with the body segments rotating around an axis of rotation ( joint).

• Deadlift – the bar is lifted upward in a linear fashion (straight line) with the body segments moving in a rotary manner around an axis of rotation ( joint). - The muscles used in both movements pull on

the segments (bones), creating torque (rotational force) and causing the bar to move directly opposite of gravity (downward force on the bar).

- In both movements the feet appear to be pushing into the ground to create an opposite reaction to the external load. The muscles are “pulling” on the bones to cause a pushing action of the lower body as well as a pulling like action in the deadlift.

- The acceleration of gravity only goes downward (a = f/m).

Again, forces have been described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything else that might cause a mass to accelerate (including muscular actions).

Push / Pull

Magnetism

Gravity

Force, in terms of human performance, is created by muscular actions causing movement of a segment or segments of the human body during a particular motion or movement pattern. Work performed by humans the product of a force (in this case muscular force) exerted on any object (muscles attached to a segment or segments or a particular human segment attached to or touching some external object), the distance that object (segment or an object other than a human segment) travels in any direction (linear or rotary/circular), and how that force is exerted or applied (pulling, pushing, accelerating or decelerating some object, etc.).

Both linear and rotary forces have four distinct properties: These four properties are:

• Magnitude: how much force is ap-plied – pushing, pulling, turning)

• Direction: the way the force is applied (forward, south, vertically, perpendicular to a surface, at a specific angle, etc.)

• Point of Application: where the force is applied on a body, a system, or the whole body/object receiving this force.

• Line of action/line of force: visualizing the straight line extending through the point of application and extending indefinitely along the direction of the force.

Any force may be represented on paper by an arrow called a vector. Vectors have both magnitude and direction.

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Forces can be visualized by a type of drawing or picture called a free-body diagram. It is a mechanical repre-sentation, in this case, of a subject performing a bicep curl,

hang clean position, and holding an object statically. The free-body diagram is a valuable tool for doing mechanical analyses, so we’ll be using free-body diagrams frequently.

In a free-body diagram, only the object in question is drawn along with all of the external and internal forces that act on the system being stressed.

y

x

L5/S1 Joint

Figure a (far left above) is a full body drawing of a weight-lifter during the first pull in the Clean and Jerk. Figure b (to the right of figure a) is a stick figure representation of the lifter’s trunk segment. Figure c is the same trunk stick segment showing the various forces just on this segment which includes COM (center of mass of the segment) as well

as the joint reaction forces at the hip joint at this position of the first pull. The far left full body diagram shows the COM for each individual segment and all the joint reaction forces involved in just this position holding a box. The purpose of this is to educate the reader on the numerous forces (static and dynamic) involved in human movement.

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When analyzing movement, one must visualize where all the forces come from to affect mo-tion. Force can be any of the following:

• Internal (within the system in motion) - This is considered muscular force in human motion

• A system is a body or group of bodies having a force or forces applied to a system

• External (outside forces on a system) - External load applied - Gravity - Resistance training - Any object having mass

• Applied• Reactive• Motive (propulsive)• Resistive (commonly viewed as decelerating)• Friction• Elastic• Linear (force creating a straight line motion)• Rotary (rotational or torque force

causing rotational motion)• Power (work per unit of time or force time distance)• Energy (capacity to do work – 6 forms)

- Mechanical energy (3 forms)• Kinetic• Potential• Strain

There are also various applications of force, particu-larly simultaneous application of motive and resistive forces (two or more external forces applied to some system, which will be explained in the next section)

• Linear/collinear• Parallel• Concurrent• General• Couple

In physics, a force is any influence that causes a free body to undergo acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or anything that can cause a flexible object to deform. A force has both magnitude and direction, making it a vector quantity (refer to the properties of force). This is directly supported by Newton’s Second Law of Motion, F=ma (a = F/m, The Law of Acceleration), which Newton stated as “The change of motion is proportional to the motive force impressed and is made in the direction of the straight line in which that force is impressed” (Verhhoshansky, 2009). This means the rate of change of velocity (acceleration) is proportional to the resultant force acting on a body and is in the same direction as the force or, if suitable units are chosen, Force = Mass × Acceleration (F = ma). Another version is that an object with a constant mass will accelerate in proportion to the net force acting upon it and in inverse proportion to its mass. Newton’s original formulation is stated to be exact: this version states that the net force acting upon an object is equal to the rate at which its momentum changes.

To fully understand the concept of Force (mass × accel-eration or ma), one must further break down this formula to understand acceleration, velocity, and momentum.

F = ma (m is the mass of the object being studied; a is the acceleration of that object)

F = m(vf – vi)/t

(vf – vi)/t is the formula for acceleration.

v = velocity; velocity is a vector quantity having both magnitude and direction.

vf is the final velocity with vi the initial ve-locity; t = the time taken from vi to vf.

Velocity: d/t or displacement of an object divided by the time it takes for that object to be displaced. This is im-portant since W (work) is F (force) times d (displacement).

F(t) = mv (mass times velocity)

F(t) = Force multiplied by the time the force was applied = impulse (I); mv = mass time velocity = Momentum (M)

Linear Force System

Parallel Force System

Concurrent Force System

General Force System

Force Couple

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I = ∆M or impulse; (I) is equal to the change in Momentum (∆M or mass times velocity, mv)

Note: F(t) = ∆M (change in momentum or mv) is the equation for linear impulse (straight line impulse) and ∆M (or m × v) is the equation of linear momentum.

There is also the angular equivalent (rotational) designated first as angular momentum L = Iω, where L = angular momentum, I = rotational inertia (Inertia is the resistance of any physical object to a change in its state of motion and one of the fundamental principles of classical physics which are used to describe the motion of matter or mass and how it is affected by applied forces), and ω is the angular velocity. Angular impulse, then, is torque (rotational force or T) multiplied by the time the torque is applied, or T(t),

equal to the change in angular momentum (∆L), which is equal to I ω2 - I ω1. The formula for angular impulse is:

T(t) = ∆L = I ω2 - I ω1 (I ω)

I is rotational inertia; ωf is the final angular velocity with ωi representing the initial angular velocity

Future understanding of how power is developed requires the reader to be familiar with both linear and rotary (angular) formulas (equations) that identify how force is applied to any system and what type of motion is created (linear, rotary, or a combination of the two, which is General Motion). The following table identifies force, work, displacement, acceleration, velocity/speed, and impulse-momentum for both linear and rotary motion.

Formula/Equation Linear Rotary (Angular)

Power (w = work; t = time)

Work w = fd (f = force; d = displacement) w = Tθ (T = torque or rotational force: θ = angular displacement

Force F = ma (m = mass; a = acceleration) T = Iα (T = Torque I = inertia; α = acceleration)

Acceleration (vf = final velocity;

vi = initial velocity; t = time) (ωf = final velocity; ωi = initial velocity; t = time)

Velocity (d = displacement; t =time) (θ = angular displacement; t = time)

Momentum M = mv (m = mass; v = velocity) L = Iω (I = inertia; ω = velocity)

Impulse F(t) = ∆M = mv (F = force; M = momentum; m = mass; v = velocity; t = time; ∆ = the change in)

T(t) = ∆L = (I ω) (T = torque; L = angular momentum; I = inertia; ω = angular velocity; t = time; ∆ = the change in)

Displacement Measured in meters Measured in Rads (1 rad = 57.3 degrees)

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This is crucial for movement analysis, since human motion combines linear and rotary motion, which equals general motion. General motion can be slow or fast depending on the goal of the movement.

These explanations coincide with what was previously described as instantaneous power, which is considered to be the limiting factor to calculating power output in any movement as the time factor approaches zero (hence the symbol d that indicates the derivative of some variable). Most power variables reported in the exercise training industry focus on the gross, muscular external power flow to another object from the person. The lack of specificity and citations in many papers, however, often does not allow readers to know if mechanical power is being accurately measured. Another distinction that is important to specify is if the power reported is an instantaneous (often a peak value) or an average power flow over a specified time or event. Peak or average mechanical powers are not strongly and uniquely related to explosive or impulse-momentum types of performances, which take place in many sports or activities of daily living ( jumping, landing from a jump, changing direction, throwing, lifting an object fast, decelerating from a particular activity, etc.). The peak muscular power (Pmax) observed will also vary based on the movement and other conditions, so it is not the unique, limit-defining muscular performance characteristic that it is commonly assumed to be in the colloquial usage of the word. Without reporting all the specifics about what power is being measured, there can be widely disparate power values. Again, instantaneous power is associated with peak power. Impulse (Ft) and momentum (mass times velocity) are instrumental in affecting the RFD or Rate of Force Development. RFD is how fast force is developed in any movement and directly affected by both internal and external forces on any system or object.

From Supertraining: Expanded Version. 6th edition, 2009. Verkhoshansky and Siff. Used by permission.

Some of the types and systems of forces that cause or affect movement were previously men-tioned. The basics of force application are:

• Forces are applied to a system (whole body, individual segments/link, or a link system) - Whole body – gravity is the downward force

(external) *where is the force of gravity working? - Muscles produce upward force (from in-

ternal force production from muscles)

• Applied Force – weight of body against the ground or object

• Reaction Force – produced by the mus-cles to move segments against something in the environment (decelerate)

• Forces come in pairs – action/re-action (agonist/antagonist)

Forces are considered either internal or external:

• Internal – originating within a body or system• External – originating outside a body or system• Whole body – external vs internal?• Whole body – external forces affect

internal force production• Segment/Individual System – in-

ternal and external forces• Applied verses Reaction forces

When analyzing any movement, numerous ques-tions must be asked regarding where all the forces are that affect this particular movement:

• What is the system? What is/are the system(s) being affected?

• Where is the CG (center of gravity) for the whole body and/or each individual system?

• What and where are the internal and external forces?• What is/are the applied verses reaction force(s)?

Motive and Resistive Forces

Any movement of a system (whole body, body part, or group of parts) can be examined in terms of the external forces acting on that system. These forces include motive and resistive forces.

• Motive (propulsive) – force that causes an increase in speed or change in direction. - Forces that cause a change in body segment’s

position can originate from within. - Greatest motive force is gravity

(it is always working). - Motive force is also muscle contraction

and the recoil of elastic connective tissue.

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• This is extremely important in rap-id force production (RFD).

• Increased motor unit recruitment (intramuscular coordination), volitional increase in RFD (inter-muscular coordination), optimal technique (optimal efficiency to maximize effectiveness) along with motive force can increase high power outputs.

• Resistive – force that acts to resist the motion caused by some other force or de-creases the speed of a moving system. - Oppose or resist movement of a system - External to the system being analyzed - Must first define which system to exam-

ine then identify resistive forces - Whole body versus segmental systems

Resistive forces specific to body seg-ment are enhanced by: - Tension in the muscles (static and dynamic actions) - All connective tissues (tendons, ligaments, fascia) - Contact forces (body segments, bone on

bone, connective tissue tension) - Fluid within tissues/joint capsules - Specific to direction (out of position

movement – tissue over stressed)

It should be noted that resistive forces (also called restrictive forces) can increase joint stabilization. Additional examples include muscle and CT lengthening (this is as important as concentric actions – remember the stretch-short-ening cycle [SSC] and elastic properties of tissue).

When performing most movements, there are simultaneous applications of motive and resistive forces on the systems utilized for a specific move-ment. These simultaneous applications state:

• Two or more external forces are be-ing applied to a system.

• The dominant force will change di-rection of motion and “win.”

Below is previous example of simultaneous application of motive and resistive forces (force systems (see p 96)

1. Linear/Collinear Force System1.1 Forces that have the same line of action1.2 Same direction or opposite direction

Linear Force System

2. Parallel Force System2.1 Opposite forces2.2 One side of force includes two or more forces

Parallel Force System

3. Concurrent Force System3.1 External forces on a system not collinear3.2 Forces do not act along the same line

but through the same point

Concurrent Force System

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4. General Force Systems4.1 A system that is exposed to many forces4.2 If a system is in equilibrium, all forces must be

concurrent ( up/down, right/left, forward/backward)4.3 X, Y, and Z (three-dimensional forces

producing movement in a primary plane of motion but stabilizing in the other two)

4.3.1 Fw,b = force of gravity(barbell), Fj = reaction force at joint, Fm = muscle force, Fw,u = weight of the lifter’s upper body, Fi = force of interabdominal pressure (Fi is a reflexively controlled force and is protective in nature).

4.3.2 These five forces represent the major interactions between this system and its surroundings.

4.3.3 Note – this is just the torso and some of the forces affecting it

General Force System

y

x

L5/S1 Joint

Friction Force

• Force between two contacting surfaces that rub or slide past each other - Running, walking, pulling a object - Muscles sliding past each other - Bones rotating/gliding/sliding on each other

• Amount of friction depends on the textures of both surfaces

• Greater the force pressing surfaces together (perpendicular force), greater the resistance

Elastic Force

Elasticity (elastic force) is the ability of a body or material to reform (recoilability). Examples of this are: - Human connective tissue - Exercise Equipment (elastic bands, tubing) - Concept of the degree of deformation in

connective tissue is called Viscoelasticity

This type of force is extremely valuable in power produc-tion. Connective tissue, in conjunction with the nervous system, can be utilized very effectively if one learns how to use materials in the ligaments and tendons, as well as effective usage of intra/intermuscular coordination and ef-ficient techniques/mechanics of any movement performed (i.e., stretch-shortening cycle and storage of kinetic energy).

All force systems, principally general force systems, are analogous with general motion or normal human movement (i.e., functional). As previously stated, human motion is a combination of linear and rotary motion (general) performed on one’s feet, performed in multiple planes of motion, and is multi-joint in nature (few movements are single-joint). Analyzing the forces involved in general motion (static and dynamic) reveal that a general force system is present for all systems involved. This is why we use a free-body diagram to “see” all the forces that affect static and dynamic motion for an active system used to create a particular motion/movement.

A summary stating the necessity for using a free-body diagram:

• Used to visualize, determine, and when necessary, calculate those forces causing motion on a system

• Useful in determining which forces may need altering to change and/or enhance/improve motion of a system

• Used to determine stress/strain on indi-vidual structures and/or tissues

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Torque

In linear or straight line movement, an external force is applied to a system that causes that system to move in a linear direction (rectilinear, curvilinear, or both). Torque, on the other hand, is the ability of a force to cause rotation of an object around an axis. It depends not only on magnitude and direction, but also the distance from the axis of rotation. This means the greater the distance some force is from the axis of a system, the greater the change in rotational motion that will be produced by a given force. There are 3 elements that make up torque:

1. The amount of force applied to the lever (F)2. The distance of the application of force

is to the lever (r = lever arm)3. The angle the force is being applied

to the lever (sin θ or force angle)

If a system is attached to a fixed point, the system will move around the AoR (axis of rotation) when a force is applied to any point on the system that does not act directly through the AoR.

A simple example of a system attached to a fixed point is a door. Notice the door is attached to hinges. These hinges are the system’s joints (axis of rotation). When someone pushes on the door, it will rotate around the hinges and move in a circular path. Following any push on the door (the push is a force), the door will move accordingly as long as the force applied is not directed into the joint (hinge); however, how easy or hard (fast or slow) the door moves depends on where the force is applied.

TorqueForce is applied at the door handle - force is not through the fixed point (hinges).

Off-Axis Force and its turning effect is called torque

Hinge

ForceLever Arm

• The perpendicular distance from the axis of rotation to the line of force is call a moment arm - A moment arm is also referred to as a

force arm, lever arm, or torque arm

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Torque, or rotational force, has the same four properties of force as linear force:

Torque can be calculated using the magnitude of the force multiplied by the length of the moment arm. This can be utilized with both internal and external force systems. This is vital to power production, due the types of lever systems in the human body; and more importantly, how the muscle “pulls” on each bone. All muscles do not pull at the same angle. This is called angle of insertion. Maximum torque is created when the force is perpendicular to the lever arm (90 DEGREES). If the angle of insertion is less than 90 degrees, it decreases the torque (force production). A classic example of the angle of insertion pull through a range of motion up to and beyond 90 degrees is the bicep curl.

This is a third-class lever system. Recall that this class of system requires a very large effort force to overcome the resistance force due to the effort moment arm being small

and the resistance moment arm being very large (mechani-cal disadvantage). This is also indicative of a first-class lever system (mechanical disadvantage), but in this instance the muscle insertion never appears to pull at a 90 degree angle.

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This next example shows how changing the angle of in-sertion can alter torque on a system.

Line of Action of F1

F1 = 20N

Axis

a

d T for F1 = 0.75m

Line of Action of F2

F2 = 20N

Axis

b

d T for F2 = 0.5m

Torque1 = F1 d T

= 20N x 0.75m = 15Nm of Torque

Torque2 = F2 d T

= 20N x 0.5m = 10Nm of Torque

The force arm in torque production (d┴) is the distance from the axis of rotation to the line of action of the applied force. (a) When the force is ap-plied at a 90 degree angle, the force arm is maximized. (b) The force arm decreases when the line of action of the force is not applied at a right angle to the lever. Also note that the farther away the effort arm is from the axis of rotation, the more torque but less range of motion within this system.

A summary of those variables that contribute to a mus-cle’s effectiveness at different angles:

• Greatest force produced at 90 degrees – muscle force is at 100%• < 90 Degrees, lever has a stabilizing and rotary component• > 90 Degrees, rotary component decreases and dislocating component increases• Other factors for force production:

- Number of joints crossed (bi-articulate muscles) - Distance of muscle insertion from the AoR

All torques on any system must be considered to determine the net torque on a system. The net torque ideally determines the rotation direction of the system in question. Additional torque variables to consider concerning torques on a bone or any system are:

• Static vs dynamic• Motive vs resistive• Concentric vs eccentric actions• Applied vs reactive

This is why using a free-body diagram, and even more accurate, performing video analysis to determine if the technique utilized in a particular movement is efficient for creating the optimal net torque for maximal effectiveness and limiting/minimizing any force (stress) that could cause injury to the tissues involved in that movement. An example of the effect of net torques on a system

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is a power clean in weightlifting. (Pictures are taken from Dartfish video analysis performed by the author at the 2004 US Olympic Trials for Weightlifting.)

• Torque divided into applied and resistive torques• If segment moving cw, mt is considered cw and rt is

ccw (depending on your frame of reference)• If static, ∑t = 0• If concentric, ∑t > 0• If eccentric, ∑t < 0• Identification of additional forces/torques for this movement will help in future

alterations of technique to improve efficiency and maximize performance.

Lastly, general considerations pertaining to force pro-duction of the musculoskeletal system are:• Human body built for rom/speed production and not for force production.• In most analyses, muscle exerts more force to

move the resistance than the opposite.• Resistance, however, will move in a greater linear or rotary distance,

therefore generating greater speed than that of the applied, motive force.• Speed of movement (velocity) is based not only on the rate of force

application, but on the mass/inertia of the object being moved. - Increase in mass or inertia (a body’s resistance to change) the

greater the force required to accelerate that object. - Force – velocity curve

Putting the math aside, it is imperative to under-stand that power is influenced by the magnitude of force application, both internal and external, and the time that magnitude of force is applied (how much and how fast this force is applied). If a sustained amount of force (same force) is applied to an object over an extended period of time (pushing an object, cycling, running, etc., or any cyclic type of motion), then this is a sustained (constant) power output – constant work done i.e., force times distance over a period of time or sustained RFD (rate of force development). This continuous work is considered

Applied Concentric

ConcentricResistive

Dynamic actions are analyzed as static positions in frame by frame analysis

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to be a type of special strength, called endurance strength (low force over a long time period). The concept of special strength might be a relatively new term to many novice coaches, trainers, and trainees, therefore we must now define what strength is, the categories of strength, and finally how strength and power work hand in hand. Strength is the maximum amount of force a muscle of groups of muscles can generate at a specified velocity (Knuttgen & Kraemer, 1987).

The Relationship of Strength (display of force) and Power

The NSCA’s Essentials of Strength Training and Conditioning (3rd Edition, 2008) states that the terms strength and power are widely used to describe some important abilities that contribute to maximal human efforts in sport and other physical activities. Unfortunately, there is often little consistency in the way the terms are used. All coaches and trainers should possess a basic scientific foundation for understanding human strength and power to show how various factors contribute to their manifestation. Though it is widely accepted that strength is the ability to exert force, there is considerable disagree-ment for describing strength and how strength should be measured. The weight that a person can lift is probably the oldest quantitative measure of strength. Technological de-velopments have popularized the use of isometric strength testing, and more recently, isokinetic strength testing.

As previously noted, all activity involves acceleration (change in velocity per unit time) of the body, and for some sports, of an implement as well (e.g., baseball bat, javelin, tennis racket). Acceleration is associated with resistive force according to Isaac Newton’s second law:

Force = Mass times Acceleration

Because of individual differences in the ability to exert force at different speeds, strength scores obtained from isometric and low-speed resistance tests may have limited value in predicting performance in sports, such as tennis or handball, that involve acceleration at high speed. That is why Knuttgen and Kraemer (1987) have suggested a more inclusive definition of strength.

Stength: The maximal force that a muscle or muscle group can generate at a specified velocity and in a specified direction

Although controlling and monitoring velocity during strength testing requires sophisticated equipment, the

resulting strength scores are more meaningfully related to sport ability than are static strength measures or maximum loads lifted. The limited meaning of isometric and low-speed strength scores has led to a heightened interest in power as a measurement of the ability to exert force at higher speeds. Outside of the scientific realm, power is loosely defined as “strength, might, force.” However, as previous noted and described, physics tells us power is precisely defined as “the time rate of doing work,” where work is the product of the force exerted on an object and the distance the object moves in the direction in which the force is exerted. Quantitatively, work and power are defined as follows:

Work = Force × Distance (displacement)AndPower = Work / Time

Power can also be calculated as the product of force on an object and the object’s velocity in the direction in which the force is exerted, or the product of the object’s velocity and the force on the object in the direction in which the object is traveling.

The previous statements from the text of the NSCA’s Essentials (2008) attempt to clarify strength and power; nevertheless, the attempt here in this chapter is to simplify the terms and concepts of strength and power and how they are directly related.

Basics of Strength

Strength has always been synonymous with numerous as-pects of the so-called “Iron Game” (all forms of resistance training, competitive lifting, weightlifting or powerlifting, Strongman competitions, bodybuilding, etc.). While feats of strength have appeared throughout history, it has only been in very recent times that training to increase strength has become a scientific discipline. This science did not arise overnight: it is the cumulative effort of thousands of years of trial-and-effort methods (Verkhoshansky & Siff, 2009).

Strength is an essential component of all human perfor-mance (sports and activities of daily living), and its formal development can no longer be neglected; not only in ath-letic preparation, but for overall fitness as well. Successful strength and conditioning programs depend on a thorough understanding of all processes underlying the production of strength by the body (Verkhoshansky & Siff, 2009).

The attempt here is to simplify what strength is by first defining precursor concepts related to strength develop-ment (physical activity, exercise, fitness, and their various

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components). We will then define strength along its various categories and how it affects everything humans do.

Precursors to Strength

Defining the concept of Physical Fitness

Although many definitions of physical fitness have been proposed, there is still much debate as to what this term represents. Several organizations have attempted to redefine physical fitness and exercise in light of modern ev-idence and understanding (Neiman, 2003). These debates include various ways to organize and create strength train-ing programs that are all-encompassing for sport training as well as general fitness. The NSCA was formed in 1978 to “bridge the gap between science and application” for developing training programs to improve strength/fitness at any level and for any person. Nevertheless, it is imperative that coaches, trainers, and trainees review some basic terminology to guide all involved to develop an understanding of the correlation between the terms associated with physical fitness and strength training.

What is Physical Activity?

Physical Activity has been defined as any bodily movement produced by skeletal muscles which results in energy expenditure. Everyone performs physical activity in order to sustain life. The amount, however, will vary considerably from one person to another, based on personal lifestyles and other factors (Neiman, 2003). Please note the above statement that everyone “performs” physical activity to sustain life. Performing may also include any activity, be it an activity of daily living or a sporting activity. The word “perform” will be essential in subsequent sections.

What is Exercise?

Exercise is not synonymous with physical activity. It is a subcategory of physical activity. Exercise is defined as “physical activity that is planned, structured, repetitive, and purposive, in the sense that improvement or maintenance of physical fitness is an objective” (Neiman, 2003). Virtually all conditioning programs as well as various sporting activities are considered exercise because they are performed to improve or maintain physical fitness.

The Meaning of Physical Fitness

Many organizations have submitted theoretical definitions of the term physical fitness. However, in 1996, the surgeon general’s report Physical Activity and Health (U.S. Department of Health and Human Services, 1996) adopted the Centers for Disease Control and Prevention’s (1985) definition that states “physical fitness is a set of attri-butes that people have or achieve that relates to the ability to perform physical activity.” Most other organizations have adopted this definition as well (Neiman, 2003). The focus in today’s society is on a comprehensive approach to physical fitness in which three major com-ponents – cardiovascular fitness, body composition, and musculoskeletal fitness (comprising flexibility, muscular strength, and muscular endurance) – are given equal attention for obtaining optimal health (see diagram below).

Physical Fitness

Cardiorespitory Fitness

(Aerobic Fitness)

Body Composition

Musculoskeletal Fitness

(Muscular Fitness)

All of these definitions place an emphasis on having adequate vigor and energy to perform work and exercise! Please notice the terms “perform” and “work,” since there has been a substantial emphasis on both up to this point. Everyone, regardless of partici-pation in activities of daily living or participation in a sporting/physical activity, is performing work in some capacity (force output done fast or slow, instantaneously or sustained). Physical Fitness is directly related to sport performance as well. The most frequently cited components fall into two groups: Health-Related Fitness and Skill-Related Fitness. The following is a breakdown of these two categories of fitness:

Health-Related Fitness

Skill-Related Fitness

Normally associated with decreasing hypokinetic disease*

normally associated with athletics

formerly five categories Recently incorporate in to main-stream fitness programs

Nieman (2003) • agility

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Health-Related Fitness

Skill-Related Fitness

1. strength • balance

1.1 flexibility • coordination

1.2 maximum endurance • power (RFD)

2. Cardiovascular fitness (VO2 max)

- high

3. body composition - low

• sustained

• speed

• reactive ability

*Hypokinetic diseases are conditions that occur from a sedentary lifestyle, including cardiovascular disease, various forms of cancer, back problems, obesity, type 2 diabetes, osteoporosis, and mental health complications.

Types of Performance

Physical fitness is one’s ability to perform physical activity. Physical Activity has been defined as any bodily movement produced by skeletal muscles. Chapter one described normal human movement as:

• Sitting/standing• Squatting up and down• Bending/ twisting• Lunging/ stepping• Lifting/carrying• Running/walking• Jumping up and landing• Throwing/catching an object• Various combinations of these movements

These movements are essential to the fundamentals of exercise, with the definition of exercise being considered and planned physical activity.

Each of the categories of fitness is considered a perfor-mance, with the exception of body composition. Therefore, all the components of fitness listed above must be understood as to what each category is and then addressed accordingly (especially from a mechanical perspective to perform any exercise correctly) when overseeing a

properly designed strength program for im-proving general fitness or sport performance.

The Elements of Health-Related and Skill- Fitness (Neiman, 2003)

Health-Related Fitness

Cardiovascular Endurance/Fitness

Cardiovascular endurance or aerobic fitness can be defined as the ability of the circulatory and respiratory systems to supply oxygen during sustained physical activity. High levels of cardiorespiratory endurance indicate a high physical work capacity (one’s ability to release relatively high amounts of energy over an extended period of time) in activities such as running, cycling, and swimming.

Body Composition

Body composition refers to the body’s relative amount of fat and lean body tissue, or fat-free mass (muscle, bone, water). Body weight can be subdivided into two components: fat weight (the weight of fat tissue) and fat-free weight (the weight of remaining lean tissue). Percent body fat, the per-centage of total weight represented by fat weight, is the pre-ferred index used to evaluate a person’s body composition.

Musculoskeletal Fitness

Musculoskeletal fitness, or muscular fitness, has three components: flexibility, muscular strength, and muscular endurance

1. Flexibility is the functional capacity of the joints to move through a full range of movements. Flexibility is specific to each joint of the body. Muscles, ligaments, and tendons largely determine the amount of movement possible at each joint

2. Maximum muscular strength relates to the ability of the muscle to exert force. However, while it is widely accepted that strength is the ability to exert force, there is considerable disagreement as to how strength should be measured. The weight that a person can lift is probably the oldest quantitative measure of strength. Because of individual differ-ences in the ability to exert force at different speeds ( Jorgensen, 1976), strength scores obtained from isometric and low-speed resistance tests may have limited value in predicting performance in sports. As previously stated, Knuttgen and Kraemer (1987)

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and Fleck and Kraemer (2014) have suggested a more inclusive definition of strength (Essentials, 2008):

The maximal force that a muscle or muscle group can generate at a specified velocity and in a specified direction.

3. Strength endurance (formerly known as muscular endurance) relates to the muscle’s ability to continue to perform without fatigue. It is the ability of the muscles to apply a submaximal force repeatedly or to sustain a submaximal muscular contraction for a certain period of time. Performing exercises with submaximal weights or body weight for multiple repetitions and multiple sets are consid-ered common strength endurance exercises.

Skill-Related Fitness

Skill-related fitness is commonly associated with sporting activities. Nevertheless, the elements of skill-related fitness are now considered a valuable part of strength training programs for both athletes and the general population (Neiman, 2003). The skill-related components of physical fitness have been defined as follows:

• Agility – the ability to rapidly change the position of the entire body in space, with speed and accuracy.

• Balance – the maintenance of equilibrium while stationary or while in motion.

• Coordination – the ability to use the senses, such as sight and hearing, together with body parts, in performing motor tasks smoothly and accurately.

• Speed – the ability to perform a move-ment within a short period of time.

• Power – the rate at which a person can perform work (strength over time). Please note the term “rate,” which denotes a time element (e.g., average velocity, instantaneous velocity, or rate of force development).

• Reaction Time/Reactive ability – the time elapsed between a stimulus and the beginning of the reaction to it.

Sports-Related Fitness: The Continuum between Health and Skill-Related Fitness

One’s ability to perform any activity (sports related or activities of daily living) utilizes all the categories of fitness described. Most physical activities exist on a continuum between health and skill-related fitness. Coaches must be familiar with these differences in fitness categories to optimize training protocols for every athlete participating in a sport.

Factors Affecting Performance

SKILL-RELATED FITNESS

HEALTH – RELATED FITNESS

1. Agility 1. Cardiorespiratory Endurance

2. Balance 2. Body Composition

3. Coordination 3. Musculoskeletal Fitness

4. Speed a. Flexibility

5. Power b. Muscular Strength

6. Reaction Time c. Muscular Endurance

The Sports Continuum The Measurable Elements of Physical Fitness

Basketball Tennis Aerobics Classes

Stair Climbing

Football Volleyball Resistance Training

Rowing

Baseball Hockey Swimming Running

Track and Field

Lacrosse Cycling Walking

Golf Wrestling Calisthenics Hiking

Weightlifting

There are many factors affecting performance; however, we are concerned with physical training factors. Coaching requires knowledge of what fitness is along with the various categories of fitness, and most importantly, how to develop training protocols that addresses each type of fitness to improve one’s ability to perform. One must be physically prepared to perform at any level to withstand the rigors of an activity, to improve performance, and to decrease the risk of injury.

Both health-related and skill-related fitness make up the sports and activity continuum. Athletes must have a foundation of all categories of musculoskeletal strength as well as cardiovascular endurance to support the various skill-related fitness components related to a sport. Those engaging in general fitness programs must also train all categories of strength (please note that cardiovascular fitness is considered a category of strength). Prior to each season, coaches perform various performance tests to deter-mine each trainee’s level in all categories of fitness. These

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tests determine the areas of weakness so each trainee may augment training to eliminate any area of weakness/deficit to improve performance while decreasing the risk of injury. Many tests are specific to the sport or activity the athlete is involved in; however, there are various tests every trainee must be evaluated in to identify deficits in basic movements before embarking on a more specialized training regimen. This begs the question, “what if the trainee has no formal training in various fitness categories, but is expected to be tested nevertheless?” Testing various components of fitness, as well as the sport-specific tests, gives the coach an overall snapshot of the trainee’s level of physical preparedness.

The ability of anyone to perform efficiently, effectively, and safely in a given sport or activity may be described in terms of three related factors (Verkhoshansky & Siff, 2009):

Work Capacity, Fitness (various categories), and Preparedness

Work capacity refers to the general ability of the body as a machine to produce work of different intensities and duration using the appropriate energy systems of the body. Fitness refers to the specific ability to use this work capacity to execute a given task under particular conditions as well as perform physical activities with vigor and energy. In general terms, fitness may also be defined as the ability to cope with the demands of a specific task

efficiently and safely (see previous definitions of physical activity and physical fitness). Preparedness, unlike fitness, is not stable, but varies with time. It encompasses two components, one of which is slow-changing and the other of which is fast-changing (Zatsiorsky & Kraemer, 2006), where the slow-changing component is fitness and the fast-changing component is exercise-induced fatigue (fitness-fatigue model) (Verkhoshansky & Siff, 2009; Zatsiorsky & Kraemer, 2006).

It has been stated that the while the concept of fitness seems to be intuitively obvious and well accepted, coaches and trainers should distinguish between fitness and preparedness. The term “physical fitness” refers to the functional state of the slow-changing physiological components related to motor activity (learning functional human movements, as previously stated). One’s fitness state does not vary significantly over any period up to as much as several days in length, but one’s ability to express fitness at any instant may be substantially affected by mental state, sickness, fatigue, sleepiness, and other fairly transient factors. This ability, or instan-taneous preparedness, is defined at any given instant and varies from moment to moment. The following diagram from Stone, Stone, and Sands (2007) details an overview of the stressors that may contribute to overall performance in both fitness and performance training.

Training

Performance

HeredityWork

School

Social Life

Injury

Coach / Athlete Interaction

Environment

Restoration

Nutrition

Sleep

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Adapted from Stone, Stone, and Sands, Principles and Practice of Resistance Training, 2007. Human Kinetics. Used by permission.

Base preparation, or simply preparedness, is the resultant of the interaction of the body’s long-term fitness increase stimulated by training and the opposing short-term fatigue aftereffects of training, excluding the effects of any other modifying factors such as exaggerated mental state or illness.

Training or conditioning is the process whereby the body and mind are prepared to reach a certain level or work capacity and fitness. This involves five interdependent processes that determine The Sports Preparation Process (Sports-Related Fitness):

1. Physical Preparation2. Learning of motor skills3. Psychological preparation4. Physical and psychological restoration5. Appropriate nutrition

Classically, the first two processes (or levels of train-ing) comprise a general phase (General Physical Preparation: GPP) and a specific phase (Special Physical Preparation: SPP – also called Special Strength Training), with various or sub-phases (e.g., stabilization, intensification, recuperation, conversion, or competitive) within, between, or after each of these phases. This manual focuses on the general and some specific phases of preparation, with special references to the upcoming special types of strength within all previously described categories of fitness. This is imperative to both activities of daily living and sport performance. The diagram below (also see “Program Design: Pyramid vs Block Diagram” on page 8) is a pictorial representation of a model of physical preparation :

Peak

Key Motor AblilitiesSpecial Strength, Speed, Endurance

Special Physical PreparationIncrease phyiological specialization based on goal

General Physical Preparation* Assessments/ Structural Evaluation

* Technique Training* Increase Work Capacity

Goals for performance- Increase Work Capacity

Technique Training- Develop Categories of Fitness

Physical Preparedness**Preparedness is completely based on the first vaiables due to instability, i.e., it can only be a stable variable if trained properly

**Adapted from Periodization: Theory and Methodology of Training, Bompa & Haff, 5th ed., 2009. Supertraining, Y. Verkhoshansky & M. Siff, 6th ed. 2009

What binds all these fitness categories together to form the foundation of all physical fitness? The answer is strength. Strength, according to Fleck and Kraemer (2008), is considered:

“The foundation of everything we do”

and

“A universal requirement to performing any and all activities”

As previously stated, “strength is the maximal force that a muscle or muscle group can gen-erate at a specified velocity and in a specified direction.” Earlier in this chapter we described forces and the properties of force, indicating that force has direction and magnitude (how much force applied). This indicates that forces applied to an object have a specified amount (magnitude), speed (velocity), and direction. The application of various amounts of force at different speeds indicates that multiple categories of strength exist. Knowing these different categories of strength enables coaches to apply and train appropriately.

A Model of Physical Fitness

This next section identifies two models of physical fitness. The first model (along with the initial text) is from Verkhoshansky and Siff (Supertraining – Expanded Edition, 6th Edition, 2009). The second model is from Stone, Stone, and Sands (Principles and Practice of Resistance Training, 2008). Stone et al. (2008) is a further clarification of Verkhoshansky’s original model.

First Model of Physical Fitness

The definition of fitness given earlier can be expanded to incorporate a number of the essential elements that make up physical fitness. Describing these essential elements can identify other aspects of physical fitness for clarification. Fitness is composed of a series of interrelated structural and functional factors that may be conveniently referred to as the basic S-factors of fitness (Verkhoshansky & Siff, 2009):

• Strength• Speed• Stamina (local muscular endurance)• Suppleness (flexibility)• Skill (neuromuscular efficiency)

- Style – the individual manner of expressing a particular skill (more on this in subse-quent chapters on exercise techniques)

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• Structure (body type, i.e., somatotype, size, shape)• Spirit (psychological preparedness)

Unlike work capacity, fitness is described not simply by laboratory measurements of qualities such as car-diovascular function, muscle strength, and flexibility, but also by the specificity of fitness required for each activity or sport depending on neuromuscular skills.

This first model is constructed from the functional motor elements of fitness. This model is divided into two stages: first, as a triangular model, which interrelates strength, stamina (muscular endurance), speed, and flexibility; and secondly, as a more complete and multi-level pyramidal model, which interrelates all of these factors with the process that makes all movement possible, namely neuromuscular control or skill.

Skill (Motor Control)

StrengthStatic/Dynamic

Endurance(Static/Dynamic)

Speed

FlexibilityStatic/Dynamic

Multiple Categories of Strength

Skill - Speed

Skill-Flexibility

Strength - Skill Strength – Flexibility

Endurance - Strength

Speed - Endurance

Flexibility - Speed

Speed - Skill

Speed - Strength

Strength - EnduranceStrength-Speed

Endurance - Speed

Endurance - Skill

Speed - Flexibility

Skill - Endurance

Flexibility-Skill

Flexibility - StrengthSkill - Strength

The below diagram corroborates the pyramid model (the Key Motor Abilities), depicting the various strength/motor qualities on a continuum that also relates to the sports continuum previously listed.

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The Interdependence of the motor qualities of strength, speed, and endurance. Verkhoshansky and Siff (Supertraining – Extended Version, 6th edition, 2009, page 152). Used by permission

The pyramid diagram illustrates that strength, endurance, and flexibility may be produced statically or dynamically, unlike speed, which changes along a continuum from the static (speed = 0) to the dynamic state. For this and other reasons, this model should be viewed as one that is representational or descriptive rather than scientifically analytical. Again, this model allows coaches to identify an extended list of fitness factors, i.e., the various types/categories of strength as follows (the factors bearing an asterisk are the various types of special strength:

Static strength* Speed-strength*

Static strength-endurance* Speed-strength endurance*

Dynamic strength* Strength-speed endurance*

Dynamic strength-endurance*

Speed

Strength-speed* Endurance

It is sometimes convenient to identify var-ious flexibility qualities as well:

Flexibility (static and dynamic)

Flexibility endurance

Flexibility-strength* Flexibility-speed

A series of skill-related fitness factors may also be identified, although it should be noted that skill forms an integral part of the process of exhibiting all of the above strength /fitness or motor qualities:

• Skill• Strength-skill* (Diachkov, 1961; Kuznetsov, 1970)• Flexibility-skill• Speed-skill• Skill-endurance

Example of the various categories of Strength

Weightlifting is considered an excellent example of strength-speed. Lifters must possess maximum strength and the ability to display this strength very fast (explosively). A review of a hang clean is below:

Example of Rate of Force Development and various types of strength. A typical force-time curve describing the lifting of free weights from a given position and returning it to rest. Movement occurs only when the force exceeds the weight of the object, namely the shaded portion of the curve. From Supertraining –Expanded Version, 6th edition, page 109, 2009. Used by permission

Second Model of Fitness

The second model is the star diagram depict-ing the relationship between skill, strength, endurance, flexibility, and speed.

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This diagram gives another perspective on the various categories of strength and how maximum strength is varied depending on the type of strength necessary for a specific event. Every activity has a primary and secondary type of strength utilized to achieve success in that activity or sport. Knowing which types of strength are necessary in a particular activity will enable coaches to optimize strength training. Again, this diagram depicts categories of special strength that are trained after building a basic foundation of strength. This is analogous with building a house: a foundation must be built before the walls. This also coincides with the Preparation Pyramid previously shown.

What Does This Mean?

All of the primary and more complex fitness factors (types of strength) should be viewed as convenient descriptors of qualities that are involved in different proportions in a particular activity. Nevertheless, the pyramid and star models enable a coach to understand the sport-specific fitness and training far more effectively than a simplistic model based only on the primary functional fitness factors of strength, endurance, speed, and flexibility.

It is also important that coaches and trainers understand that, at all stages of training, there are differences between work capacity, fitness level (various types of strength, especially foundation strength development, which includes technique development to coincide with work capacity), and preparedness, since a high level of work capacity (strength-endurance or endurance strength) and sport-specific strength will not guarantee exceptional performance. Instead, the ability to exhibit a maximal level of preparedness is essential if such performance is to be expected. Following the Performance Preparedness pyramid by building a foundation of strength first, then training for the specifics of a particular sport, will help to ensure increasing basic strength levels to improve performance and decrease the risk of injury.

The Basics of Power

Forces are required in all movements to accelerate/decelerate an object or maintain a specific velocity. These variables are applicable to rotary forces (torque) applied to rotation of segments within a system that cause rotational or linear motion. Please note that changes in force (magnitude and direction), whether applied slowly or instantaneously during linear or rotary motion, i.e., the Rate of Force Development, directly affect velocity and acceleration of any movement or object in any direction.

Power is work performed over a period of time. Work done is explained as force multiplied by the

distance the object travels (displacement), or force times displacement. All movement performed in-volves a power output. Some movements are done explosively (rate of force development involving starting, acceleration, and explosive strength) while others are sustained movements (sustained force output over an extended period of time, e.g., strength-endurance or endurance strength). Therefore, power is simply strength with speed.

If a substantial force is applied extremely fast to an object, then it pertains to a high power output (high or maximum RFD). The higher and more rapid force is generated (the rate of force production and impulse-momentum), the greater the power output for the designated period of time. This more rapid force generation in a short time period also involves starting strength, acceleration strength, and explosive strength.

Schematic of some of the force-time measures used by

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The ability to move any object is also affected by the mass or inertia of the body or object a force is imposed on. Mass is the measure of a body’s inertia (the amount of mass in a body). Inertia is the resistance of a body to change its state of motion (static or dynamic). This is explained by Newton’s first law of motion:

Every object or body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force, meaning that in the absence of a non-zero net force, the center of mass of a body or an object either remains at rest, or moves at a constant speed in a straight line.

Based on this, how quickly a body or object moves is subject to slowing based on how heavy it is. This is the essence of the force-velocity curve.

By increasing the load on the muscle (which consists of concen-tric, eccentric, and static actions), the shortening velocity is zero for static actions; this occurs when the load is great enough that the muscle cannot shorten. As the resistance decreases, the muscle can shorten, and the velocity of muscle action increases accordingly. The shorten-ing velocity is highest (maximum) when the load approaches zero.

Notice that when the load is increased, muscles increase eccentric action ability (force production for resistive force) in an attempt to decelerate (slow down or resist) a moving object.

A simplified power-velocity curve illustrates how power increases with velocity, but only up to a point. After that, the “peak power” value, however, changes; and any increase in velocity causes a decrease in the maximum force muscles can generate.

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Force-Velocity Curve

The product of force times velocity increases on the left side of the curve leading up to a maximum value, and then the force times velocity product decreases on the right side of the curve. The pro-duction of maximum power clearly depends on the production of optimal force and optimum velocity.

Rate of force production, known as muscular power production in the training community, is present in all activities. Note that the power of muscular contractions, or RFD, varies considerably with different combinations of muscle force and speeds of contraction, and is highly influ-enced by the mass or inertia of the system being moved.

It is imperative the reader understand that all power output (what type of power and how power is developed) is created by force production; therefore, one must understand what force is, where it comes from, how it is developed, how it is applied, and how it truly affects power output.

Strength and speed are the key elements for the differences in mechanical power and how it is developed. We now will look at what biomechanics is in order to ascertain how force is developed or produced and its effect on power output. Please remember, biomechanics and kinesiology go hand in hand with the concept of power output.

Rigid-body Mechanics

Rigid-body mechanics describe:• Kinetics – How forces causes move-

ment (linear and rotary)• Kinematics – The quantity or quality of move-

ment (velocity, displacement, acceleration, etc.)

The remainder of this chapter pertains to linear and angular kinetics, then linear and angular kinematics.

The information presented was obtained from the textbook Biomechanics of Sport and Exercise, 3rd. edition, by Peter M. McGinnis (Human Kinetics).

Linear Kinetics

Principia (Philosophiae Naturalis Principia Mathematica [Mathematical Principles of Natural Philosophy]) is a book written by Sir Issac Newton. This is the book most famous for introducing the world to the laws of physics. In it, Newton presented his three laws of motion and his law of gravitation. These laws form the basis for modern me-chanics, as well as for the sub-branch of mechanics called kinetics. Dynamics is the branch of mechanics concerned with the mechanics of moving objects, and kinetics is the branch of dynamics concerned with the forces that cause motion. This section deals with linear kinetics, or the causes of linear motion. In this section, readers will learn about Newton’s laws of motion and how they can be used to analyze motion. What you learn in this chapter will give readers the basic tools to analyze and explain the techniques used in many sport and movement skills.

Newton’s Laws of Motion

Newton’s first law of motion: Law of inertia. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. (Newton 1686/1934, p. 644)

This is Newton’s first law of motion in Latin as originally presented in Principia. It is commonly referred to as the law of inertia. Translated directly, this law states, “Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it” (Newton 1686/1934, p. 13).

One must also take into consideration what the term “inertia” means. Inertia is nothing more than an object’s “resistance to change.”

This law explains what happens to an object if no external forces act on it, or if the net external force (the resultant of all the external forces acting on it) is zero. More simply stated, Newton’s first law says that if no net external force acts on an object, that object will not move (it will remain in its state of rest) if it wasn’t moving to begin with; or it will continue moving at constant speed in a straight line (it will remain in its state of uniform motion in a straight line) if it was already moving.

How does Newton’s first law of motion apply to human movement in sports or activities of daily living? Can you think of any situations in which no external

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forces act on an object? This is difficult. Gravity is an external force that acts on all objects close to the earth. Apparently, there are no situations in sports and human movement to which Newton’s first law of motion applies. Is this true? Perhaps we can find applications of Newton’s first law in sport if we consider only motions of an object or body in a specific direction.

Newton’s first law of motion also applies if external forces do act on an object, so long as the sum of those forces is zero. So, an object may continue its motion in a straight line or continue in its state of rest if the net external force acting on the object is zero. The sum of all the external forces acting on an object is zero if the object is in static equilibrium. Newton’s first law of motion is the basis for this state. This law also extends to moving objects, however. If an object is moving at constant velocity in a straight line, then the sum of all the external forces acting on the object is zero, and there will be no change in motion of the object. If it is already moving, it will continue to move (in a straight line at constant velocity). If it is at rest, it will stay at rest (not move). Newton’s first law can be expressed mathematically as follows:

v = constant or ΣF = 0

or

ΣF = 0 if v = constant

where

v = instantaneous velocity and ΣF = net force.

Since Newton’s first law also applies to components of motion, the previous equations can be represented by

equations for the three dimensions (vertical, horizontal – forward and backward; and horizontal – side to side):

vx = constant if ΣFx = 0ΣFx = 0 if vx = constant

vy = constant if ΣFy = 0ΣFy = 0 if vy = constant

vz = constant if ΣFz = 0ΣFz = 0 if vz = constant

This is covered since most ground-based human movement (movement performed while on the feet) is three-di-mensional (all three planes of motion). The primary movement may be in one plane, but that movement may be stabilizing in the other planes concurrently.

With Newton’s first law of motion covered, an example is necessary to solidify this law. If a lifter is barbell squatting with 40 kg, how large a force must you exert on the barbell at the bottom position of the squat to hold it still? What external forces act on the barbell? Vertically, gravity exerts a force downward equal to the weight of the barbell, 40 kg. The lifter’s body exerts a reaction force upward against the barbell. According to Newton’s first law, an object will stay at rest only if there are no external forces acting on the ob-ject or if the net external force acting on the object is zero. The barbell is at rest (not moving): therefore, the net ex-ternal force acting on it must be zero. The diagram below shows a free-body diagram of the lifter (frontal and lateral views). The two external forces acting on the barbell are both vertical forces: the force of gravity acting downward and the reaction force from your hand acting upward.

Bar push down on shoulders (external load/force)Lifter pushing up into bar (internal force)

Lifter’s lower extremity muscles contracting (internal forces) to oppose external force of barbell

Since the barbell is not moving (v = constant = 0), we can use the following equation to solve for the reaction force from your hand. ΣFy = 0 ΣFy = R + (−W) = 0 R = W = 40 kg, where R = the reaction force from your hand, and W = the weight of the barbell (40 kg). When a lifter is holding the 40 kg barbell still, the force the lifter must exert against it is 40 kg upward. The problem was solved with upward considered the

positive direction. Since the answer calculated was a positive number, it represents an upward force.

If the lifter begins lifting the barbell, and during the lift it moves at a constant velocity upward, how large a force must she exert against the barbell to keep it moving upward at constant velocity? What does it feel like compared to the force required to hold the barbell in a

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static position? Remember, the goal here is to find the force one exerts when the barbell is moving upward at constant velocity, not when it starts upward. What external forces act on the barbell? Vertically, gravity still exerts a force downward equal to the weight of the barbell (40 kg), and the lifter still exerts a reaction force upward against the barbell. According to Newton’s first law, an object will move at constant velocity in a straight line only if there are no external forces acting on the object or if the net external force acting on the object is zero. Since the barbell is moving at a constant velocity in a straight line, the net external force acting on it must be zero. The two external forces on the barbell are exactly the same as when the barbell was still: the force of gravity acting downward and the reaction force from the body acting upward. Since the numbers are the same, we have the same reaction force of 40 kg upward. The force the lifter must exert against the barbell to keep it moving upward at a constant velocity is a 40 kg upward force. When the lifter is holding the barbell still, the force exerted on it is a 40 kg upward force. If she moves the barbell downward at constant velocity, the force she exerts on it would still be a 40 kg upward force.

Newton’s first law of motion may be in-terpreted in several ways:

1. If an object is at rest and the net external force acting on it is zero, the object must remain at rest.

2. If an object is in motion and the net external force acting on it is zero, the object must continue moving at constant velocity in a straight line.

3. If an object is at rest, the net external force acting on it must be zero.

4. If an object is in motion at constant ve-locity in a straight line, the net external force acting on it must be zero.

Newton’s first law of motion applies to the resultant motion of an object and to the components of this resultant motion. Because forces and velocities are vectors, Newton’s first law can be applied to any direction of motion. If no external forces act, or if the components of the external forces acting in the specified direction sum to zero, there is no motion of the object in that direction or the velocity in that direction is constant.

Newton’s first law of motion applies to the resultant motion of an object and to the components of this resultant motion.

Newton’s second law of motion: Law of acceleration. Mutationem motis proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur. (Newton 1686/1934, p. 644)

This is Newton’s second law of motion in Latin as originally presented in Principia. It is commonly referred to as the law of acceleration. Translated directly, this law states: “The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed” (Newton 1686/1934, p. 13).

This law explains what happens if a net external force acts on an object. Newton’s second law says that if a net external force is exerted on an object, the object will accelerate in the direction of the net external force, and its acceleration will be directly proportional to the net external force and inversely proportional to its mass. This can be stated mathematically as

→ΣF = ma

Where

ΣF = net external force

m = mass of the object

a = instantaneous acceleration of the object

This is another vector equation, since force and acceleration are vectors. Newton’s second law thus applies to the components of force and acceleration. The above equation can be represented by equations for the three dimensions (vertical, horizontal – forward and backward, and horizontal – side to side).

ΣFx = max ΣFy = may ΣFz = maz

Newton’s second law expresses a cause and effect rela-tionship. Forces cause acceleration. Acceleration is the effect of forces. If a net external force acts on an object, the object accelerates. If an object accelerates, a net external force must be acting to cause the acceleration. Newton’s first law of motion is really just a special case of Newton’s second law of motion – when the net force acting on an object is zero, its acceleration is also zero.

Going back to the squat movement, the external forces acting on the barbell are the pull of gravity acting down-ward and the reaction force from the lifter’s body acting upward. The net force is thus the difference between these two forces. When does the lift feel most difficult? When does it feel easier? To start the lift, one must accelerate the barbell upward, so the net force acting on the barbell must be upward. The force you exert on the dumbbell must be larger than 40 kg. Once the lifter has accelerated the

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barbell upward, to continue moving it upward requires only that a net force of zero acts on the barbell, and the barbell will move at constant velocity. The force exerted on the barbell must equal 40 kg. As one completes the lift, the lifter needs to slow down the upward movement of the barbell, so the net force acting on the barbell is downward. The force exerted on the barbell must be less than 40 kg. When the barbell is at a complete stop (finish position of the squat movement), it is no longer moving, so the net force acting on the barbell is zero. The force exerted on the barbell must be equal to 40 kg.

Any time an object starts, stops, speeds up, slows down, or changes direction, it is accelerating; and a net external force is acting to cause this acceleration.

Impulse and Momentum

Mathematically, Newton’s second law is expressed by equation:

∑F = ma

This tells what happens only at an instant in time. The acceleration caused by the net force is an instantaneous acceleration. This is the acceleration experienced by the body or object at the instant the net force acts. This instan-taneous acceleration will change if the net force changes. Except for gravity, most external forces that contribute to a net external force change with time. So the acceleration of an object subjected to these forces also changes with time.

In sports and human movement, we are often more concerned with the final outcome resulting from external forces acting on an athlete or object over some duration of time than with the instantaneous acceleration of the athlete or object at some instant during the force application. We want to know how fast the ball was going after the pitcher exerted forces on it during the pitching actions. Newton’s second law can be used to determine this. Looking at equation ΣF = ma slightly differently, we can consider what average acceleration is caused by an average net force:

where = average net force and a = average acceleration

Because average acceleration is the change in velocity over time

 or 

The equation becomes

Multiply both sides by Δt

or

This is the impulse–momentum relationship. Impulse is the product of force and the time during which the force acts. If the force is not constant, impulse is the average force multiplied by the duration of the average force. The impulse produced by a net force acting over some duration of time causes a change in momentum of the object upon which the net force acts. To change the momentum of an object, either its mass or its velocity must change. In sports and human movement, most objects we deal with have a constant mass. A change in momentum thus implies a change in velocity. When Newton stated his second law of motion, he really meant “momentum” where he said “motion.” The change in momentum of an object is proportional to the force impressed. The impulse–mo-mentum relationship described mathematically is actually just another way of interpreting Newton’s second law. This interpretation may be more useful to us in studying human movement. The average net force acting over some interval of time will cause a change in momentum of an object. We can interpret change in momentum to mean change in velocity, because most objects have constant mass. If we want to change the velocity of an object, we can produce a larger change in velocity by having a larger average net force act on the object or by increasing the time during which the net force acts.

The average net force acting over some interval of time will cause a change in momentum of an object.

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Using Impulse to Increase Momentum

The task in many sport skills is to cause a large change in the velocity of something. In throwing events, the ball (or shot, discus, javelin, or Frisbee) has no velocity at the beginning of the throw, and the task is to give it a fast velocity by the end of the throw. We want to increase its momentum. Similarly, in striking events, the racket (or bat, fist, club, or stick) has no velocity at the beginning of the swing (or stroke or punch), and the task is to give the implement a fast velocity just before its impact. Our bodies may be the objects whose momentum we want to increase in jumping events and other activities. In all of these activities, the techniques used may be explained in part by the impulse–momentum relationship. A large change in velocity is produced by a large average net force acting over a long interval. Because there are limits on the forces

humans are capable of producing, many sport techniques involve increasing the duration of force application.

Two other examples of using impulse to accelerate an ob-ject and change its momentum are weightlifting and pow-erlifting. Those familiar with weightlifting (snatch, clean & jerk) know these two movements are fast in nature. The be-ginning motion in both weightlifting movements (called the first pull in both lifts) is performed at a moderate speed. At the end of the first pull, the lifter performs the transitional phase/movement, or “scoop,” putting them into the begin-ning of the second pull, much like the transition from down to up in a jumping action. The second pull begins with a very high impulse (high force production over a period of time) to accelerate the barbell. This acceleration increases the barbell’s momentum and its upward movement.

In powerlifting, the loads (weights) are substantially increased, but the lifter attempts to move the load as fast as possible after the downward phase, changing direction to the upward (ascent) phase of the lift. The

lifter uses the impulse-momentum principle to move the weight upward quickly to increase the barbell’s momentum. This principle is utilized extensively in the squat and bench press movements.

Using Impulse to Decrease Momentum

In certain other activities, an object may have a fast initial velocity that we want to decrease to a slow or zero final velocity. We want to decrease its momentum. Can you

think of any situations like this? Landing from a jump? Catching a ball? Being struck by a punch? Does the impulse–momentum relationship apply in an analysis of these situations? A good example is landing from a jump. Upon landing, one flexes the ankles, knees, and

Both lifters are beginning the upward phase of the bench and squat by applying a very high force as fast as possible to change the barbell direc-tion from down to up.

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hips. This increases the impact time – the time it took to slow down. This increased Δt in the impulse–momentum equation and thus decreased the average impact force, ΣF–, since the change in momentum, m(vf − vi), would be the same whether one flexed their legs or not.

Newton’s third law of motion: Law of action/reaction. Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi (Newton 1686/1934, p. 644).

This is Newton’s third law of motion in Latin as presented in Principia. It is commonly referred to as the law of action-reaction. Translated directly, this law states: “To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal and directed to contrary parts” (Newton 1686/1934, p. 13).

Newton used the words action and reaction to mean force. The term reaction force refers to the force that one object exerts on another. This law explains the origin of the exter-nal forces required to change motion. More simply stated, Newton’s third law says that if an object (A) exerts a force on another object (B), the other object (B) exerts the same force on the first object (A), but in the opposite direction. So forces exist in mirrored pairs. The effects of these forces are not canceled by each other, because they act on different objects. Another important point is that it is the forces that are equal but opposite, not the effects of the forces.

If an object exerts a force on another object, the other object exerts the same force on the first object but in the opposite direction.

Newton’s Law of Universal Gravitation

Newton’s law of universal gravitation gives readers a better explanation of weight. This law was purportedly inspired by the fall of an apple on his family’s farm in Lincolnshire while he was residing there during the plague years. He presented this law in two parts. First, he stated that all objects attract each other with a gravitational force that is inversely proportional to the square of the distance between the objects. Second, he stated the alleged inspiration for Newton’s law of universal gravitation. that this force of gravity was proportional to the mass of each of the two bodies being attracted to each other. The universal law of gravitation can be represented mathematically as

Where F is the force of gravity, G is the universal constant of gravitation, m1 and m2 are the masses of the

two objects involved, and r is the distance between the centers of mass of the two objects. Newton’s universal law of gravitation was momentous because it provided a description of the forces that act between each object in the universe and every other object in the universe. This law, when used with his laws of motion, predicted the motion of planets and stars. The gravitational forces between most of the objects in sport are very small – so small that we can ignore them. However, one object that we must be concerned with in sport is large enough that it does produce a substantial gravitational force on other objects. That object is the earth. The earth’s gravitational force acting on an object is the object’s weight. For an object close to the earth’s surface, several of the terms in the equation are constant. These terms are G, the universal constant of gravitation; m2, the mass of the earth; and r, the distance from the center of the earth to its surface. If we introduce a new constant

Then equation

becomes

or

where W is the force of the earth’s gravity acting on the object, or the weight of the object; m is the mass of the object; and g is the acceleration of the object caused by the earth’s gravitational force.

Linear Kinematics

Dynamics is the branch of rigid-body mechanics con-cerned with the mechanics of moving objects. Kinematics is the branch of dynamics concerned with the description of motion. The outcomes of many sporting events are kinematic measures, so an understanding of these mea-sures is important. Some of the kinematic terminology should be familiar (speed, velocity, acceleration, and so forth). While basic knowledge of these terms is useful, it will be necessary to use them in specific ways. The precise mechanical definitions may not agree with the meanings most associate with the terms, and there will be misunderstandings unless all definitions agree.

Kinematics is the branch of dynamics con-cerned with the description of motion.

What is motion? Movement is a change in position. Moving involves a change in position from one point to an-other. Two things are necessary for motion to occur: space

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and time – space to move in and time during which to move. To make the study of movement easier, we classify movements as linear, angular, or both (general).

Linear Motion

Linear motion is also referred to as translation. It occurs when all points on a body or object move the same distance, in the same direction, and at the same time. This can happen in two ways: rectilinear translation or curvilinear translation. Rectilinear translation is the motion you probably would think of as linear motion. Rectilinear translation is when all points on a body or object move in a straight line so that the direction of motion does not change, the orientation of the object does not change, and all points on the object move the same distance. Curvilinear translation is very similar to rectilinear translation. Curvilinear translation is when all points on a body or object move so that the orientation of the object does not change and all points on the object move the same distance. The difference between rectilinear and curvilinear translation is that the paths followed by the points on an object in curvilinear translation are curved, so the direction of motion of the object is constantly changing, even though the orientation of the object does not change. To determine whether a motion is linear, imagine two points on the object in question. Now imagine a straight line connecting these two points. As the object moves, does the line keep its same orientation; that is, does the line point in the same direction throughout the movement? Does the line stay the same length during the movement? If both of these conditions are true throughout the movement, the motion is linear. If both points on the imaginary line move in parallel straight lines during the motion, the motion is rectilinear. If both points on the imaginary line move in parallel lines that are not straight, the motion is curvilinear. Consider the picture below of a long jumper. The jumper travels in a curvilinear path, but the jump displacement is measured in linear units.

Angular Motion

Angular motion is also referred to as rotary motion or rotation. It occurs when all points on a body or object move in circles (or parts of circles) about the same fixed central line or axis. Angular motion can occur about an axis within the body or outside of the body. A child on a swing is an example of angular motion about an axis of rotation external to the body. Examples of angular motion in sports and human movement are more numerous than examples of linear motion. What about a giant swing on the horizontal bar? Are parts of this motion rotary? What about individual movements of our limbs? Almost all of our limb movements (if they are isolated) are examples of angular motion. Examples are:

• Arm bicep curl• Leg curl• Tricep extension• Chest fly

Let’s consider motion about more than one joint. Is the limb’s motion still angular? Extend your knee and hip at the same time. Was the movement of your foot angular? Did your foot move in a circular path? Was the motion of your foot linear?

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General Motion

Combining the angular motions of our limbs can produce linear motions of one or more body parts. When both the knee and hip joints extend, you can produce a linear motion of your foot. An example is a leg press.

Similarly, extension at the elbow and horizontal adduction at the shoulder can produce a linear motion of the hand.

General motion is a combination of linear and angular motions. General motion is the most common type of motion exhibited in sports and human movement. Running and walking are good examples of general motion. In these activities, the trunk often moves linearly as a result of the angular motions of the legs and arms. Bicycling is another example of general motion. Think of various human move-ments in sports and consider how you would classify them. Classifying motion as linear, angular, or general motion makes the mechanical analysis of movements easier. If a motion can be broken down into linear components and angular compo-nents, the linear components can be analyzed using the mechanical laws that govern linear motion. Similarly, the angular components can be analyzed using the mechanical laws that govern angular motion. The linear and angular analyses can then be combined to understand the general motion of the object.

Linear kinematics is concerned with the description of lin-ear motion. Questions about speed, distance, and direction are all inquiries about the linear kinematics of an object

Distance and displacement are quantities commonly used to describe the amount of a body’s motion. When a body travels from one location to another, the distance through which it moves is the length of the path it follows. The displacement the body or object undergoes in that motion is found by measuring the length of a straight line from the starting point to its ending point. Distance is measured in kilometers, meters, centimeters, etc.

Linear Speed and Velocity

To start a body in motion (normally from a resting or static position), a force is need-ed to begin motion (motive force); or if the body is already moving, one must ask how fast it is moving. Speed is how fast a body is moving (the distance covered by the time it takes to cover a distance). Velocity is how fast an object is moving plus the direction it is traveling. Velocity is a vector quantity, meaning it has magnitude and direction; therefore, one must describe a system’s state of linear motion in two ways:

• How far the object traveled (distance)• How fast and in what direction the object moved (velocity)

Velocity = distance divided by time, or

Variable velocity: Average and Instantaneous ValuesAverage Velocity: speed of movement averaged over a specific time

period. One example of average velocity is the 100 meter sprint.

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The subject accelerates out of the blocks and changes speed from zero to their top running speed. After the initial acceleration, the subject sprints at a steady speed for a specified time. This constant speed indicates zero accelera-tion, since there was no change in speed. While the goal is to maintain top speed, some deceleration occurs near the end of the race. The time for the race was 13 seconds (start to finish), which is 7.7 meters per second (100 meters/13 seconds). This is the average velocity due to the subject not running the entire race at the same speed. If one examines the graph, specific points give the reviewer valuable infor-mation to calculate instantaneous velocity/speed during specific time intervals. This type of data enables one to evaluate performance for optimizing training procedures to maximize performance. This information can be valu-able for optimizing when to increase force production to in-crease velocity or speed specifically instantaneous velocity.

Instantaneous Velocity: also called projection, release, rebound, or takeoff velocity, is important in activities that accelerate/decelerate objects.

One example of instantaneous velocity is squatting.

1 2 3 4 5

6 7 8 9 10

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Force and RFD at this point of the movement

Start of decent 2

Standing

Downward phase (decent) 3, 4, 5

Bottom Position 6

Amortization phase downward to upward RFD (steep slope) High Acceleration (7)

Sticking point –

transition phase 8

2nd Peak

-Acceleration and

Momentum 9

Deceleration 10

The above example is a graph looking at the Ground Reaction Forces (GRF) in a heavy squat movement. The red and green lines are the GRF for each leg (red = right; green = left). Each foot is on an individual force plate to measure GRF and determine 1) RFD and 2) strength deficits for each limb (bi-lateral strength deficits). The first phase of the squat is when the lifter is preparing for the initial descent (approximately the first .8 seconds of the moment). Notice the left foot elicits a GRF of 1200 newtons (about 270 lbs of force), but the right foot is approximately 100 newtons (approximately 247 lbs) when standing upright in the beginning position of the squat. This difference is called a bi-lateral strength deficit (between two limbs), and if greater than 8-10%, a compensation effect may take place leading to a substitution movement pattern, and injury may ensue (in this case the deficit is almost 10%). Upon the initial descent, the GRF begins to decrease (eccentric action), representing the resistive force (decelera-tion) of the lifter coinciding with the motive force of gravity (motive force here is the mass of the barbell times the force of gravity) to slow down gravity’s effect (the GRF is decreasing because both forces are traveling in the same direction). Also notice that the GRF is equal through a portion of the downward (eccentric) phase, but the lifter “shifts” his weight, and thereby his force production or

resistive force, to the right side (considered the strong side in this case). As the lifter starts to slow down more, there is an eventual static action and a reversal of force production to reverse the direction of the external load (from down to up). This reversal point is called the amortization phase and starts the beginning of the second phase of the movement. The theory behind this action is taken from plyometrics ( jump or shock training), and is utilized to elicit a strong stretch-shortening cycle (SSC), also called a myotatic reflex. This action simply describes a reversal of the downward movement to upward movement as fast as possible. While this is more productive in very rapid movements, the concept of reversing the action of eccentric to concentric rapidly is useful here and enhances one’s ability to recruit more motor units and increase the rate of force development (RFD).

The upward phase (concentric action) is to move the external load as fast as possible. The steeper the upward line, the greater the RFD as well as the starting strength (initial isometric action at the beginning of the upward

in attempt to overcome the external resistance), acceler-ation strength (impulse-momentum action), and finally explosive strength. Notice that the GRF of the limbs are still about 100 newtons apart, but the RFD (impulse [F × t] and velocity) are fairly equal at the point being measured (this point is measuring the instantaneous velocity: 2579 N/s on the right foot; 2542 N/s on the left). The second phase lasts approximately .2 seconds.

The third phase is called the transition phase or sticking point (the point in the lift where the leverage is not optimal for force production, therefore there is a shift in muscle usage to complete the movement). The movement pattern slows substantially and there is zero acceleration. Movement becomes stalled and force production is the same, therefore there is a shift in segmental position to optimize position to increase force production. This phase lasts approximately .4 seconds. The final phase begins when the body position is optimal and force production resumes, thereby increasing acceleration to move the external load. Acceleration/RFD (velocity) reaches a peak at about 2.2 seconds, then decelerates until the bar comes to a stop. Total time of the lift (beginning with the initial decent), transition to lift completion, is just over 2 seconds.

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Another example measuring instantaneous velocity is a

counter-movement jump.

1

1 2 3 4

2

3

4

Linear Acceleration

Most activities are seldom performed at constant velocities. Even activities that appear to be moving at a constant velocity have variations to maintain motion and speed depending on the environment in which one is performing. In addition to how far (d) and how fast (v) a system is moving, a more detailed description of a body’s motion can be made by stating when the body is speeding up (acceler-ating) or slowing down (decelerating), or even changing its direction (which is a form of acceleration/deceleration).

To change any state of linear motion of a body, a net external force is necessary to change its state i.e. the greater the force (RFD), the greater the motion of change. How fast speed or direction is altered is based on the magnitude of the acceleration. Linear accel-eration is the time rate of change in velocity.

Acceleration = change in velocity divided by time

or

Acceleration, from a qualitative viewpoint:

• Only occurs during the time the net external force is applied

• When the net force or additional external force is removed (drops to zero), all external forces cancel out – body reaches new speed until changed by another force

• Direction of the acceleration is also in the direction of the applied force

The relation between force, mass, and acceleration is:

• Acceleration of a system is directly proportional to the net external force applied to a system, is in the same direction of the force, and is inversely proportional to the mass of the system (greater the applied force, the greater the acceleration).

• The greater the mass of the object, the more force needed to accelerate the object (thus the inverse proportion concept).

• Must consider all three components simultaneously (F, m, a).

Examples of this relationship are:

• Constant mass – if you increase the force, you increase acceleration.

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• Increase the mass and have constant force, decreased acceleration.

• Increasing mass, must increase external force to increase the acceleration.

A change in any type of motion is based on im-pulse-momentum. Impulse-momentum affects:

• Lifting a weight• Accelerating/decelerating an object

• Changing directions• Throwing/catching an object• Pushing/pulling an object• Kicking/striking an object• Anything that requires a force to move

an object from its current position• Linear Impulse consists of:• Rate of change of momentum and the

force necessary to produce change• Rearrangement of newton’s law of acceleration F = ma

• When

• Substitute a in F = ma

•

• Force = mass times its change in velocity divided by the time it took to change

• Then, multiply mass (m) by its change in velocity (a) to equal F = (mv2 – mv1)/t to equal the change in momentum/time it took to change or

•

• The momentum change is directly proportional to the force applied (change in the system’s momentum is the final momentum of the system minus the initialmomentum it had before the force was applied)

• Force multiplied by the time that force is applied to the system = the change in momentum of the system

• F(t) = mv or ∆M or I = ∆M• The Impulse-Momentum principle states:• F(t) is the impulse that the system re-

ceived to change its momentum• Force and time are the variables – these

two variables manage many different things – equipment, implements, adls, etc.

• Application of Impulse-Momentum:• Acceleration – start something moving• Decelerating – slow something down• GRF (ground reaction forces)• Shock absorption – fast and slow• ∆M = force × time (small force over long time)• ∆M = force × time (large force in a short time)• The larger the applied force or the longer the time

a force is applied or both, the greater the change in velocity of a body or object receiving that force

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Angular Kinematics

Angular kinematics is the other branch of kinematics. Angular (rotary) motion occurs when all points on an object move in circular paths about the same fixed axis. Angular motion is important because most human movements are the result of angular motions of limbs about joints. This has previously been discussed and described as part of general motion (combination of linear and rotary motion). An understanding of how angular motion is measured and described is important.

Angular kinematics is concerned with the description of angular motion. First, one must know what the definition of an angle is. Angles describe the orientation of two lines. An example is the angle of the arm to the torso.

Absolute angular position refers to the orientation of an object relative to a fixed reference line or plane, such as horizontal or vertical. Relative angular position refers to the orientation of an object relative to a non-fixed reference line or plane. Joint angles are relative, whereas limb positions may be relative or absolute. The angular movements of limbs around joints are described with terminology developed by anatomists using the anatomical position of the body as a reference.

The three principal anatomical planes (sagittal, frontal, and transverse), along with their corresponding axes (transverse, anterior-posterior, and longitudinal), are also useful for describing movements of the limbs.

When an object rotates, it undergoes an angular displacement. To define the angular displacement, the axis and plane of rotation must be known. The direction of the angular displacement (and all other angular motion and torque vectors) is

then established using the right-hand thumb rule. The definitions of angular displacement, angular velocity, and angular acceleration are similar to those for their linear counterparts. The linear displacement and distance traveled by a point on a rotating object are directly proportional to the radius of rotation. The linear distance traveled equals the product of the angular displacement measured in radians multiplied by the radius of rotation.

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Tangential linear velocity and acceleration of a point on a rotating object are directly proportional to the radius as well. The tangential linear velocity is equal to the product of the angular velocity times the radius of rotation. Lengthening the radius, while maintaining the angular velocity, is an important principle in a variety of striking skills. Tangential linear acceleration is equal to the product of angular acceleration times the radius of rotation. Centripetal acceleration (also called radial acceleration) of an object rotating in a circular path is the component of linear acceleration directed toward the axis of rotation, and is directly proportional to the square of the tangential linear velocity or the square of the angular velocity. Centripetal force is the force exerted on the rotating object to cause the centripetal acceleration.

Angular Kinetics

The basics of angular kinetics, the causes of angular mo-tion, are explained by angular interpretations of Newton’s laws of motion. We must understand angular analogs of inertia and momentum to make these interpretations. Angular inertia, called moment of inertia, is an object’s resistance to change in its angular motion. Mathematically, it is defined as the product of mass times the radius of

gyration squared. Radius of gyration is a length dimension representing, on average, how far an object’s mass is locat-ed from an axis of rotation. Objects have many different moments of inertia, one for each of their possible axes of rotation. Angular momentum, like linear momentum, is a measure of an object’s motion. Angular momentum is the product of moment of inertia and angular velocity. It is a vector quantity that is specific to an axis of rotation. Angular momentum may be constant even if angular velocity varies, so long as the variation in angular velocity is accompanied by an inverse variation in moment of inertia. The angular interpretation of Newton’s first law says that objects do not change their angular momentum unless a net external torque acts on them, which is explained by the angular interpretation of Newton’s second law. A rigid object will accelerate angularly in the direction of the net external torque, and its angular acceleration will be inversely related to its moment of inertia. For objects with variable moments of inertia, the impulse–momentum relationship is a more applicable angular interpretation of Newton’s second law. Net external torque acting over some duration of time causes a change in angular momentum in the same direction as the net external torque. An angular interpretation of Newton’s third law explains that torques act in pairs. For every torque, there is equal torque acting on another object in the opposite direction.

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Chart for comparison of linear versus angular kinetics

Quantity Symbol and Equation

SI unit

Linear

Inertia (mass) m kg

Force F N

Linear Momentum L = mv kg m/s

Impulse Ns

Angular

Moment of Inertia kg m2

Torque of moment of force

T = F r Nm

Angular momentum H = Iω kg m2/s

Angular impulse Nm s

Additional chart for all corresponding for-mulas for all concepts presented

Formula/Equation Linear Rotary (Angular)

Power P = w/t (w = work; t = time) P = w/t

Work w = f × d (f = force; d = displacement) w = T × θ (T = torque or rotational force: θ = angular displacement)

Force F = ma (m = mass; a = acceleration) T = Iα (I = inertia; α = acceleration)

Acceleration a = (vf – vi)/t (vf = final velocity; vi = initial velocity; t = time)

α = ωf – ωi/t (ωf = final velocity; ωi = initial velocity; t = time)

Velocity v = d/t (d = displacement; t =time) ω = θ/t (θ = angular dis-placement; t = time)

Momentum M = mv (m = mass; v = velocity) L = Iω (I = inertia; ω = velocity)

Impulse F(t) = ∆M = (mv) (F = force; M = momentum; m = mass; v = velocity; t = time; ∆ = the change in): F = ma or F = m(vf – vi)/t = mvf – mvi/t = mv/t = F(t) = mv or F(t) = ∆M

T(t) = ∆L = (I ω) (T = torque; L = angular momentum; I = inertia; ω = angular velocity; t = time; ∆ = the change in): T = Iα = I(ωf =ωi)/t = Iωf – Iωi/t = Iω/t = T(t) = Iω or T(t) = ∆L

Displacement Measured in meters Measured in Rads (1 rad = 57.3 degrees)

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Energy

Energy is a form of force (capacity to do work). Total energy expenditure and rate of energy expenditure (power output) are important considerations for exercise programs and training programs (Garhammer, 1993). Work done and the time taken to complete this work is the essence of power output, i.e., power flow that is present in all human movement. However, in all human movements (activities of daily liv-ing, sports, exercise programs), there is ample concern with changing the velocity of an object (remember that velocity is simply the distance an object travel in a specified time). When an object’s velocity changes, it subsequently changes the kinetic energy (KE), thus establishing the work-energy principle (KE can be changed by doing work). Increasing the work done will cause a greater increase in energy output (usage) if the average force exerted is of large enough quantity or the displacement (in line with this force) is long.

Energy is another term widely used outside of technical discussions. This usage, however, is not as frequently at variance with the technical definition of the word, as in the case of “work” (Hay, 1993). As previously stated, energy is defined as the “capacity to do work,” and when individuals state they have no energy or (alternatively) say they are full of energy, this could be interpreted as meaning they had either no capacity for work or they have a great capacity to do work. Total work done is more precise for estimating energy expenditure. These estima-tions also examine the rate at which work is utilized.

Here is an additional example of energy expenditure/power output in activities of daily living (ADL):

A person having a mass of 100 kilograms who climbs a 3-meter high ladder in 5 seconds is doing work at a rate of about 600 watts. Mass × acceleration due to gravity × height ÷ the time it takes to lift the mass to the given height gives the rate of doing work or power.

A laborer over the course of an 8-hour day can sustain an average output of about 75 watts (NOTE: this is dependent on body mass). The following is an estimation of the basic energy needs of a 75 kg person (Garhammer, 1993:

Given: Adult BMR = 1 cal/kg/hr

1 cal/Kg/hr × 75 kg × 24 hr/day = 1800 cal/day

1800 cal/day × 1 day/24 hr × 1 hr/60 min × 1 min/60 sec × 4186 J/cal = 87 J/s = 87 watts or 87 joules of energy used per second in one day. Remember – this is the metabolic value, not the mechanical (Kcals used to perform mechanical work).

Another example of sustained power output is the same 100 kg person carrying a specific load for a continuous period of time, e.g., carrying a 15 kg box 5 kilometers in 45 minutes. This is estimated to be about 2100 watts (note: force is calculated as the 100 kg body mass combined with the additional 15 kg load). High power levels can also be achieved for short intervals, and by athletes.

Work has been defined as the product of force and displacement (mechanical work), and used for estimating energy expenditure. In mechanics, energy (as previously stated) is defined as the capacity to do work. There are various forms of energy:

• Solar• Light• Heat• Mechanical• Electrical• Chemical

Mechanics is primarily concerned with mechanical energy, which comes in three forms: kinetic energy, potential ener-gy, and strain energy. Kinetic Energy is energy due to mo-tion, potential energy is energy due to position, and strain energy is stored elastic energy (elastic potential energy).

Kinetic Energy

Any moving object has the capacity to perform work based on its motion. This is what kinetic energy (KE) is. As in power output, KE is affected by the mass and velocity of an object. The formula for KE is:

KE = ½ mv2

Where

KE = kinetic energy

m = mass

v = velocity

Using the example of an overhead press, the mass of the barbell is 30 kg and the velocity is calculated as d/t (distance is .4572 meters divided by the time of 2 seconds). This equates to:

KE = ½ mv2

m = 30 kg

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v = d/t = (.4572m / 2s) = .2286 m/s

KE = ½ × 30kg × (.2286 m/s)2

KE = .784 kg × (m/s)2

The unit of KE given here derives logically from consider-ing the units used to measure the various quantities shown on the right hand side of the equation (KE = ½ mv2). This explanation is rather awkward and for this reason is rarely used. Instead, this latter quantity is measured in joules, because it is very convenient to use the same unit in measuring all forms of mechanical energy. This change in the unit is greatly enhanced by the fact that:

1 kg × (m/s)2 = 1 N m = 1 J

Thus, whenever the KE of a body is calculated, with the mass in kilograms and velocity in meters per second, the answer should be in joules.

Potential Energy

Potential Energy (PE) is the energy (capacity to do work) an object has based on that object’s position. There are two types of PE: gravitational PE (energy due to an object’s position relative the earth; and strain energy (SE) which is the deformation of an object

Gravitational PE (GPE)

Gravitational Energy is the potential energy associated with gravitational force. If an object falls from one point to another inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. From a mathematical perspective, GPE is defined as:

PE = Wh or PE = mgh

Where

PE = potential energy

W = weight

m = mass

g = acceleration due to gravity (9.81 m/s/s)

h = height

Once again, when estimating PE, newtons are used for the units of force times the length (Nm), which are equivalent to joules (which is the same for kinetic energy and work). How is PE estimated? Again, use of the mass of the barbell from the overhead barbell press (30 kg) provides a useful example.

How much gravitational potential energy does this 30 kg barbell possess when the lifter has the barbell overhead? The distance the bar traveled was 1.5 feet (.4572 meters) overhead in a positive direction. However, this is just the distance the bar traveled when the lifter moved it to a posi-tion overhead. We need to determine what the height of the barbell is when the lifter is standing upright, in reference to the ground. If we estimate this height to be approximately 76 inches (1.93 meters), then the equation becomes:

PE = Wh = (294 N) (1.93 m)

PE = (294 N) (1.93 m) = 567.42 Nm

PE = 567.42 J

This is the potential energy of the barbell in this stationary overhead position.

Strain Energy

Strain Energy (SE) is another type of potential energy used in sports and exercise train-ing. The lengthy definition of SE is:

Energy principles in structural mechanics express the relationships between stresses, strains (or defor-mations), displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and alternative means for formulating the governing equations of deformable bodies in solid mechanics.

The simpler version is:

Strain Energy: the energy contained in any material due to the deformation of an object.

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SE of any object is correlated with the material’s stiffness, material properties, and how much it will be deformed when a force is imposed on it. The formula for SE is:

SE = ½ k ∆x2

Where

SE = strain energy

k = stiffness or spring constant of material

∆x = change in the length or deformation of the object in from its un-deformed position

A material’s stiffness is expressed in N/m, therefore its strain energy is expressed in (N/m)m2. This is equivalent to joules (the same unit of measurement as GPE, KE, and work).

Please take this type of energy into serious and careful con-sideration. In sports, as well as in all human movements, there is energy stored and possessed by the individual and objects due to their motion (which is KE or kinetic energy), their position above the ground (GPE or gravitational potential energy), and the amount of deformation (SE or strain energy). Most textbooks are primarily concerned with the first two (KE and GPE), but much consideration should be given to SE (strain energy), due to the connective tissue involved in all human movement (particularly when the connective tissue is stressed beyond its capability due to injury or improper training). SE drastically affects power output and is also a factor in various materials used by athletes/competitors to increase performance.

This is an example of material strain energy used in sports: a powerlifter using a bench shirt during a competition. The shirt is made of a special type of material to enhance strain-energy, which increases the amount of weight lifted in the bench press movement.

Work-Energy Relationship

Definitions of both work and energy directly indicate a strong relationship between the two subjects. Work was de-fined as the time rate of doing work, and energy as the ca-pacity to do work. Since the two are intimately intertwined, an additional definition of work by McGinnis (2013) stated “It is the means by which energy is transferred from one object or system to another.” Both share joules as a unit of measure, indicating both are related.

How, then, are work and energy related? Again, using the overhead barbell press as an example reveals addi-tional similarities. The lifter pressed a 294 N barbell approximately 1.5 feet (or .4572 meters) overhead. The work done by the lifter was 67.2 and 134.4 J, respectively (depending on the speed of the movement example). A question to ask is: How much more energy did the barbell have after it was lifted? Since the object did not have any more kinetic energy due to its non-moving state before and after the lift/movement, what was the change in the barbell’s potential energy?

∆PE = PEfinal – PEinitial

∆PE = Whfinal – Whinitial

∆PE = W(hfinal – hinitial)

∆PE = 134.4 J

The results show the change in PE of the barbell was approximately 134 J (which is the same as the faster movement - work completed in one second). These results indicate that work done causes a change in PE, or that work may cause a change in total mechanical energy. This example of a press, as well as any movement (like a discus throw, shot put, clean and jerk, etc.), all demonstrate the work-energy principle that states that any work done by the external forces (independent of gravity) that act on an object causes a change in the energy of the object (McGinnis, 2013; Enoka, 2002; Hay, 1993). This relationship can be expressed mathematically as:

W = ∆E

W = ∆KE + ∆PE + ∆KE

W = (KEf – KEi) + (PEf – PEi) + (SEf – SEi)

W

WhereW = the work done on any object by forces other that gravity

∆E = change in the total mechanical energy

KEf = final kinetic energy

KEi = initial kinetic energy

PEf = final potential energy

PEi = initial potential energy

SEf = final strain energy

SEi = initial strain energy

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References

Baechle, T.R. and R.W. Earle. Essentials of Strength Training and Conditioning, 3rd ed. Champaign, IL: Human Kinetics. 2008.

Bompa, T., and G. Haff. Periodization: Theory and Methodology of Training. 5th ed. Champaign, IL. 2009.

Boyle, M. Advances in Functional Training Techniques for Coaches, Personal Trainers and Athletes. Aptos, CA: On- Target Publications. 2010 .

Cronin, J, and Sleivert, G. Challenges in understanding the influence of maximal pow-er training on improving athletic performance. Sports Med 35: 123–234, 2005.

Fleck, S., and W. Kraemer. Designing Resistance Training Programs. 4th ed. Champaign, IL: Human Kinetics. 2014.

Garhammer, J. A review of power output studies of Olympic and powerlifting: methodology, per-formance prediction, and evaluation tests. J Strength Cond. Res 7: 76–89, 1993.

Hay, J.G. The Biomechanics of Sports Techniques. 4th ed. San Francisco, CA: Benjamin Communings. 1993.

Komi, P. Strength and Power in Sport. London, England: Blackwell Publications. 1992. Kreighbaum, E., and K. Barthels. Biomechanics: A Qualitative Approach for Studying Human Movement. 4th ed. New York: McMillian Publishers. 1995.

Kenney, L., Wilmore, J., and Costill, D. Physiolog y of Sport and Exercise. 5th ed. Champaign, IL: Human Kinetics. 2011.

Knudson, D. Correcting the Use of the Term “Power” in the Strength and Conditioning Literature. J Strength Cond Res 23(6):1902–1908, 2009.

Knuttgen, HG, and Kraemer, WJ. Terminology and measurement in ex-ercise performance. J Appl Sport Sci Res 1: 1–10, 1987.

Komi, PV. Strength and Power in Sport. Boston, MA: Blackwell, 1992.

McGinnis, P. Biomechanics of Sport and Exercise. 3rd ed. Champaign, IL: Human Kinetics. 2013.

NESTA Biomechanics Manual. Rancho Santa Margarita, CA: JSE Publications. 2011.

NESTA CPT Manual. 3rd ed. Rancho Santa Margarita, CA: JSE Publications. 2011.

Nieman, D. Exercise Testing and Prescription. 7th ed. New York, New York: McGraw-Hill Publishers. 2010.

O’Shea, P. Quantum Strength Training. Corvallis, OR: Patrick’s Books. 1996

Siff, M. Functional Training Revisted. Strength & Conditioning Journal 24(5); 42-46, 2002.

Stone, M., M. Stone, and W. Sands. Principles and Practice of Resistance Training. Champaign, IL: Human Kinetics. 2007.

Verkhoshansky, Y. and M. Siff. Supertraining, 6th Edition: Expanded Version. SSTM. 2009.

Zatsiorsky, V. and W. Kraemer. Science and Practice of Strength Training.2nd ed. Champaign, IL: Human Kinetics. 2006.