During the recent Rio Olympics, I was struck by the number of times commentators used the terms “power” and “powerful”. Examples were, “That was a powerful performance”, “What a powerful run!”, “What power she displayed”. Moreover, in my latest issue of Squash Player, there was a prominent advertisement from a leading racket manufacturer that stated about its latest aerodynamic frame, “. . . provides ultimate speed and power”. Regrettably, in all of these instances, “power” was misused.
In classical mechanics, power is defined as:
The rate of doing work. (Rodgers and Cavanagh, 1984).
Both for linear and rotary motion, it is not defined as the product of force and velocity (Winter and Fowler, 2009). The unit is the watt (W), an eponymous unit that marks the contribution made by James Watt (1736 – 1819) to its development. Watt sought a way to compare the output of then recently introduced steam engines with the principal means of propulsion: horses. Strictly defined quantities, units and symbols are laid down by the Système International d’Unités, and listed by the Royal Society (1975/1981) and elsewhere (Hand, 2004). Deviations from these mandates can quickly become “chaos in the brickyard” (Forscher, 1963).
Newton’s Second Law: the Impulse-Momentum relationship
When motion occurs, objects are either accelerated or decelerated by the application of propulsive and retarding forces respectively. In both instances, the momentum of a body changes. During sport and other forms of physical activity, forces are applied by recruited muscle and transmitted via the skeleton’s lever systems. It must be remembered though, that either deliberately or unavoidably, motion is not always an outcome. Movement, for example, in gymnastics and diving can be penalised, and in sliding sports such as luge, and in sailing, the ability to hold a set body position by related isometric muscle activity is decisive.
In discrete projectile activities such as throwing a javelin, discus or shot put, horizontal and vertical jumping, hitting an object with a racket in tennis, squash and badminton, a stick in hockey or a club in golf, and kicking a ball in rugby or soccer, it is the velocity of the projectile at departure that determines performance. As “velocity” is a vector quantity, it possesses both magnitude and direction. This velocity is determined by the preceding impulse that is imparted i.e. the force history (Adamson and Whitney, 1971). The history indicates an optimisation of force and time.
The relationship (r) between impulse and velocity at departure is 1.
Techniques in throwing, jumping and hitting are designed to apply forces to a projectile for as long as possible, with the greatest forces possible.
This term can be used to describe events where repetitive generations of impulse determine performance i.e. in activities such as walking, running, swimming, rowing and cycling. Here, endurance is important and hence the body’s structural, physiological and biochemical systems become an additional focus.
In two- and four-stroke petrol engines, as well as diesel equivalents, the two most commonly used indicators of an engine’s capability are its power output and torque. However, these measures are secondary to the primary quality: the impulse that is applied to a piston by the burning fuel-air mixture (Smith, 1977).
Impulse-momentum and work-energy approaches
The principal explanation for changes in motion lies in the impulse-momentum relationship. So, rates of development of force, duration of applications of force, and magnitudes of applied force become important in understanding performance and of course, the design of effective training programmes. Energy is required, and indeed, is important, but that energy is also required when isometric muscle activity occurs – during which neither internal nor external mechanical work is done. Newton II should be the main focus not some misuse of “power” in vague, confusing and frankly otherwise incorrect ways.
A long history of concern
For at least 100 years (Hering, 1900), there have been formal expressions of concern about the misuse of mechanical constructs in sport and exercise. In the last forty years or so, during the rise and rise of sport and exercise science, concerns have grown as indicated by Adamson and Whitney (1971), Knuttgen (1978), Rodgers and Cavanagh (1984), Winter and Fowler (2009), Knudson (2009) and Winter et al. (2016). Sadly, misuse abounds. It is the responsibility of engineers and other scientists to confront malpractice, and challenge forcibly those who are either unwilling or unable to adhere to strictly-defined convention.
Adamson, G.T. and Whitney, R.J. (1971). Critical appraisal of jumping as a measure of human power. In: Medicine and Sport, 6: Biomechanics II, edited by J. Vredenbregt and J. Wartenweiler pp. 208-211. Basel: Karger.
Forscher, B.K. (1963). Letter. Chaos in the Brickyard. Science, 142: 339.
Hand, D.J. (2004). Measurement Theory and Practice. London: Arnold.
Hering, D.W. (1900). The misuse of technical terms. Science, 11, 1028-1030.
Knudson, D.V. (2009). Correcting the use of the term “power” in the strength and conditioning literature. Journal of Strength and Conditioning Research, 23, 1902-1908.
Knuttgen, H.A. (1978). Force, work, power and exercise. Medicine and Science in Sports, 10, 227-228.
Rodgers, M. and Cavanagh, P. (1984). Glossary of biomechanical terms, concepts and units. Physical Therapy, 64, 1886-1902.
Royal Society. (1975/1981). Quantities, Units and Symbols. A report by the Symbols Committee of the Royal Society. London UK: The Royal Society.
Smith, P.H. (1977). The Design and Tuning of Competition Engines (sixth edition, revised by D. N. Wenner). Cambridge, MA: Bentley.
Winter, E.M. and Fowler, N. (2009). Exercise defined and quantified according to the Système International d’Unités. Journal of Sports Sciences, 27, 447-460.
Winter, E.M., Abt, G., Brookes, F.B.C., Challis, J.H., Fowler, N. E., Knudson, D.V., Knuttgen, H.A., Kraemer, W.J., Lane, A.M., van Mechelen, W., Morton, R.H., Newton, R.U., Williams, C. and Yeadon, M.R. (2016). Misuse of “power” and other mechanical terms in sport and exercise science research. Journal of Strength and Conditioning Research, 30, 292-300.