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Biomechanics of Power in Sport

Noffal, Guillermo J. PhD, CSCS*D; Lynn, Scott K. PhD, CSCS*D

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Strength and Conditioning Journal: December 2012 - Volume 34 - Issue 6 - p 20-24
doi: 10.1519/SSC.0b013e31826f013e
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Because a few variables make up power, it is practical to define these first for a better understanding of the scientific underpinning of the variable formally termed power. One common way to calculate power involves dividing the amount of mechanical work done by the time it takes to perform that work:

The strict mechanical definition of power is the rate at which mechanical work is done (18). The measurement unit for power is the watt (W) named after James Watt who in the 18th century began to assess the capabilities of steam engines as they began to replace horses during the Industrial Revolution and coined the term horsepower. One kilowatt, which is equivalent to 1.36 horsepower, is the metabolic power corresponding to an oxygen consumption of approximately 48 mL/s (6).

For the simple movement of lifting a free weight vertically, the force (in newtons) necessary to oppose the force of gravity acting on the mass (in kilograms) of the free weight acts through a displacement (change in height in meters) during a determined time (in seconds). The product of the force and displacement determines the work (in joules) which when divided by time yields the power (in watts) (15). The force used to lift the weight should not only take into consideration the mass of the weight but also the acceleration used during the lifting task. Therefore, another way to define power is as the product of force and velocity:

However, the force-velocity relationship of muscle displays a decrease in muscle tension/force as the movement velocity is increased. Thus, peak power is achieved approximately when an individual produces one third of maximum force at one third of maximum velocity (Figure 1).

Figure 1
Figure 1:
Relationships between concentric muscle tension (force), velocity, and power (dashed line).

Also, because human movement involves angular displacement being performed by the joints, another common way of defining power is

The power produced by the joints of the body can be determined by the product of the net joint torque (in newton meters) and the joint angular velocity (in radians per second). Thus, the unit for joint power (also referred to as angular power) is newton meters or watt.

Movement in the human body is a manifestation of force exerted primarily through muscle activity. This muscular activity can result in eccentric (muscle lengthening), concentric (muscle shortening), or isometric (no muscle length changes) type of actions. The first 2 actions mentioned above will result in segmental movement, whereas the last will not. This is important because mechanical work is defined as force multiplied by displacement; thus isometric activities by definition will yield zero mechanical work. Physiologically, the body still needs to use energy to hold the static position elicited by the isometric muscle activity but without movement, no mechanical work is present. In 1978, Knuttgen (14) cautioned against calculating power when isometric muscle activities were involved since by definition, no movement was observed, and thus, no work has been produced.



Peak power, also referred to as instantaneous power, is defined as the highest power value achieved during the movement being observed. Average power is usually calculated as the product of the average force and the average velocity of the entire movement (6).


Success in many sports is dependent on the athlete's ability to produce maximum power for the duration of the event (3). However, the ability to produce power for prolonged periods is hampered by the body's in ability to generate high amounts of force repeatedly. Hence, short-duration activities are able to generate higher peak power values than those endurance or long-duration activities (6).


A simple movement of elbow flexion and extension can be used to illustrate the differences between power production and power absorption. Remember that power can be calculated as the product of torque and angular velocity, and because torque and angular acceleration are proportional to one another (torque = rotary inertia × angular acceleration), the power-time curve associated with the movement can be approximated by multiplying the angular velocity and angular acceleration curves.

When both angular velocity and angular acceleration have the same sign (that of either positive or negative), power is also positive, and it constitutes an energy flow from the muscle to the arm segment, and it is referred to as power production. Alternatively, when angular velocity and angular acceleration have different signs (one as positive and the other negative or vice versa), the energy flows from the arm segment to the muscle, and it is referred to as power absorption (6). Positive work and power production correlate with concentric muscular activity, whereas negative work and power absorption correlate with eccentric muscular activity. In the example of elbow flexion and extension, the elbow flexors initiate the upward movement of the weight being lifted through concentric activity and therefore create positive power. Before reaching its end range of motion, the weight is decelerated through eccentric activity of the elbow extensors, creating negative power. The elbow extensors initiate the start of elbow extension and create positive power; then, before reaching full extension, the weight is controlled by the elbow flexors, creating negative power through eccentric muscle activity (Figure 2).

Figure 2
Figure 2:
Angular displacement, angular velocity, angular acceleration, and angular power during an elbow flexion-extension motion.


Many strength and conditioning articles use linear position transducers to assess displacement of the body or a bar that is being lifted in their calculation of power. Displacement-time data are integrated to generate a velocity-time graph. This velocity-time graph is then integrated again to produce an acceleration-time graph. The acceleration-time graph is multiplied, typically by the system's mass (usually including both lifter and bar), to generate a force-time graph that is then multiplied by the velocity-time graph to produce a power-time curve for the movement (2). Alternatively, when a force plate is available, the transducers are used to calculate the velocity of the lifter-bar unit, and this is multiplied by the vertical force gathered from the force plate to calculate power. When only a force plate is available, both force and velocity are generated from the vertical ground reaction forces (GRFs) (5). It should be noted that the power calculated using these methods is an example of external or whole-body power.

To calculate internal or joint power, a motion analysis system that collects joint position data throughout the movement is required. This angular position data can be used to derive angular velocities and angular accelerations, which in turn will be used to calculate joint torques. The product of joint torques and angular velocities is equal to the joint power. When the pedal of a cycle ergometer is instrumented to gather forces produced from the foot, the power calculated from the product of the force and pedal velocity (external power) can be compared with that calculated from summing the joint power for the hip, knee, and ankle joints (internal power) if the joint kinematics are also obtained. Although both methods provide the power produced during 1 complete pedal revolution, the internal power calculations yield the individual joint powers and their specific contributions to the total leg power, and this has more training and performance implications (6).


Internal power is analogous to joint power and, as previously mentioned, is defined as the product of the joint torque and the angular velocity. Huijing (9) focused on ankle power during the concentric push off phase of the vertical jump. This study found that large amounts of torque were being produced by the ankle plantarflexors at the start of the push off phase 150 milliseconds before take off; however, the angular velocity and hence the power were small. Although the torque at the ankle decreased from this point until takeoff, the angular velocity and power increased to a maximum, demonstrating that maximum power at a joint does not occur when the torque is at a maximum, but it is dependent on the combination of the torque and angular velocity. External power on the other hand primarily refers to the aggregate of multiple joint powers resulting in, for example, the elevation of the center of mass as seen during a maximum vertical jump test. This is also commonly referred to as whole-body power. Knudson (13) believes that the use of cycle ergometers allows exercise physiologists the ability to measure external mechanical power during steady-state exercise, and this measures the overall external power flow from the body. This would essentially be a combination of hip, knee, and ankle power. This steady-state condition of work and power measurement provides relevant information about these continuous movements.


To better compare results from different studies, it is good practice to normalize power values to the masses of the athletes. Thus, instead of reporting absolute values in watts, the relative unit used is watts per kg (W/kg).


Unfortunately, there has been a general lack of consistency in the way studies examining peak power tests have been conducted (13). One example of this is in the research examining vertical jumping. Some experiments require participants to begin jumps from a crouched or squatted position. However, many others allow participants to start from an upright position and perform a countermovement before jumping upward. If participants use the countermovement, they can jump higher as a result of the utilization of the stretch-shorten cycle and are able to produce greater equation-calculated power output scores. In other words, more power can actually be generated with the countermovement jump technique. To be able to compare results from different studies, it is imperative that the test be standardized for a countermovement or no countermovement jump, and the type of jump be specified when reporting results (8).


There have been numerous articles published using the vertical jump as an example of whole-body power (1,2,8,11,17). Usually, a subject performs a maximal vertical jump while standing on a force plate, and GRFs are collected. From the GRF, the average force applied to the ground, and the average velocity of the center of gravity is determined, and hence, the average power produced during the jump can be calculated. This gives a good measure of the whole-body power produced during the jump. However, one needs to be careful about relating the results of the countermovement jump test to lower limb power. To be able to relate this power to the lower limbs, vertical jumps should be performed without the use of the arms and without a countermovement component to the jump (17). The arm swing is a technique that when used correctly will assist in elevating the height of the center of gravity through transfer of momentum, whereas the countermovement jump also assists jump height through the utilization of the stretch-shorten cycle in the eccentric to concentric transition. Therefore, it is important to make the clear distinction between lower limb power and whole-body power during vertical jump testing.


Many of these vertical jumping articles have derived regression equations to estimate the power during a jumping test (8,11,17). These simple formulas allow you to estimate both peak and average power without the use of expensive equipment such as force plates and motion capture technology.

One of the earlier formulas provided was the Lewis formula or nomogram (7), which was a commonly used formula by exercise practitioners many years ago. However, this formula only estimated average power and was based on a modified falling body equation. The original formula used the units of kilogram meter per second, which is not the units for power. To convert it to watts, the acceleration due to gravity (9.81 m/s2) had to be added.

Harman et al. (8) addressed many of the shortcomings of the Lewis formula and established equations for both peak and average power through multiple regression procedures. The 2 equations are listed below:

Using an even larger number of participants including both males and females, Johnson and Bahamonde (11) developed a formula for the calculation of peak and average power from the vertical jump test, using the countermovement jump.

The Sayers equation (17) also estimates peak power output (peak anaerobic power output) from the vertical jump. Keir et al. (12) developed a simple and effective nomogram for calculating peak leg power output using the Sayers equation that replaces the outdated Lewis nomogram.


As mentioned above, power is generally reported in 1 of the two ways: full-body power or as individual joint powers. Full-body power is calculated using the velocity of the body's center of gravity multiplied by the external force acting on the body (usually a GRF). Individual joint power is calculated by determining the external torque on a joint and multiplying it by the angular velocity of the joint.

For the exercise professional, it is imperative that they understand the difference between these two concepts when they read the literature because it can be useful to determine which individual joint powers most optimally result in the greatest full-body power. For example, to perform a countermovement vertical jump, there are external flexion joint torques applied to the hip/knee and external dorsiflexion torque applied to the ankle. This means the lower limb musculature must produce extension torque at the hip and knee as well as plantarflexion torques at the ankle to overcome these external torques and propel the body into the air.

If we examine the degree to which each joint is externally loaded (joint torque) and how fast it moves (angular velocity), we can determine which joints are producing the most power to create the jump. Lees et al. (16) examined this concept by having subjects perform 3 different types of jump: low, high, and maximum. Although this article did not report the joint powers, they did examine joint torques and the work done at each joint. This was measured by combining GRFs with limb kinematic data using inverse dynamics. It should be noted that the torque values would need to be multiplied by angular velocity or the work values divided by time to calculate power. Although they did not do this, they demonstrated that the external torque on the ankle did not change, no matter what jump height the subjects were trying to perform. However, the hip joint torque increased and the knee joint torque decreased as the subjects attempted to jump higher. This indicates that to jump higher, it may be beneficial to increase the power generating capabilities of the musculature surrounding the hip joint because it has a much greater cross-sectional area than the musculature surrounding the knee and ankle joints (10).

This idea is supported by the work of Crow et al. (4) who did report full-body power values in their study. They demonstrated that performing low load exercises targeting the gluteal muscles (hip extensors) before performing a dynamic task can significantly increase the whole-body power as measured during a countermovement jump test using a linear position transducer. The authors suggest that these low-level “gluteal activation” exercises may lead to further activation of these muscles during functional movements. Unfortunately, these authors did not measure the individual power contributions of each lower limb joint to the production of the countermovement jumps. It can be hypothesized that the significant increase in whole-body power may have come from an increased contribution of the hip extensors after gluteal activation exercises. As you can see, it is imperative that the exercise professional understands the difference between individual joint powers and full-body power when reading the literature.

In summary, the characteristics of power (internal/external, average/peak, production/absorption) and methodological details must be taken into account when meaningfully comparing and presenting research about the mechanical power in human movements. It is only when a common platform has been reached that significant correlations between training studies and their effect on power can be made.


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power; definitions; characteristics; application

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