One of the best known relationships concerning muscle action is the hyperbolic curve (Fig 1) which describes the dependence of force on velocity of movement (Hill, 1953). Although this relationship originally was derived for isolated muscle, it has been confirmed for actual sporting movement, though the interaction between several muscle groups in complex actions changes some aspects of the curve (Zatsiorsky & Matveev, 1964; Komi, 1979).
This curve implies that velocity of muscle contraction is inversely proportional to the load, that a large force cannot be exerted in very rapid movements (as in powerlifting), that the greatest velocities are attained under conditions of low loading, and that the intermediate values of force and velocity depend on the maximal isometric force. It is entirely inappropriate to take this to mean universally that large force cannot be produced at large velocities, because, as we discussed earlier, ballistic action implicating stretch-shortening and powerful neural facilitation processes exist primarily to manage such situations.
Figure 1 The relationship between force and velocity, based on the work of Hill (1953). (a) The dark curve shows the change produced by heavy strength training (b) the dark curve shows the change produced by low load, high velocity training (after Zatsiorsky, 1995).
The influence of maximal isometric strength on dynamic force and velocity is greater in heavily resisted, slow movements, although there is no correlation between maximal velocity and maximal strength (Zatsiorsky, 1995). The ability to generate maximum strength and the ability to produce high speeds are different motor abilities, so that it is inappropriate to assume that development of great strength will necessarily enhance sporting speed.
The effect of heavy strength training has been shown to shift the curve upwards, particularly in beginners (Perrine & Edgerton, 1978; Lamb, 1984; Caiozzo et al, 1981) and light, high velocity training to shift the maximum of the velocity curve to the right (Zatsiorsky, 1995). Since, in both cases, power = force x velocity, the area under the curve represents power, so that this change in curve profile with strength increase means that power is increased at all points on the curve. The term ‘strength-speed’ is often used as a synonym for power capability in sport, with some authorities preferring to distinguish between strength-speed (the quality being enhanced in Fig 1a) and speed-strength (the quality being enhanced in Fig 1b).
The graph
depicting concentric and eccentric muscle action looks like that depicted in
Figure 2. Consequently, muscular power
is determined by the product of these changes (P = FV) and reaches a maximum
at approximately one-third of the maximal velocity and one-half of the maximal
force (Zatsiorsky, 1995). In other
words, maximal dynamic muscular power is displayed when the external
resistance requires 50% of the maximal force which the muscles are capable of
producing.
Figure 2 Schematic (not to scale) of the idealised force-velocity curves for concentric and eccentric muscle contraction. The change in muscular power with speed of contraction is also depicted. Note that power is absorbed at negative velocities, i.e. under eccentric conditions.
The pattern of power production in sporting activities can differ significantly from that in the laboratory, just as instantaneous power differs from average power over a given range of movement. For example, maximum power in the powerlifting squat is produced with a load of about two-thirds of maximum (Fig 3). Power drops to 52% of maximum for a squat with maximal load and the time taken to execute the lift increases by 282%. Power output and speed of execution depend on the load; therefore, selection of the appropriate load is vital for developing the required motor quality (e.g. maximal strength, speed-strength or strength-endurance).
Figure 3 The relationship between power, load and movement time for the powerlifting squat for a group of top + 125kg lifters whose mean best squat is 407kg. If a vertical line is drawn at a given load, the intersection with the graphs gives the corresponding power and the time taken to complete the lift. e.g. the line passing through the maximum power of 1451 watts occurs for a load of 280kg moved over a period of 0.85 sec.
It is interesting
to note that the form of Hill's relationship (Fig 1) was modified by more
recent research by Perrine and Edgerton (1978), who discovered that, for in
vivo muscle contraction, the force-velocity curve is not simply hyperbolic
(curve 2 in Fig 4). Instead of
progressing rapidly towards an asymptote for low velocities, the force displays
a more parabolic shape in this region and reaches a peak for low velocities
before dropping to a lower value for isometric contraction (V = 0). In other words, maximum force or torque is
not displayed under isometric conditions, but at a certain low velocity. For higher velocities (torque greater than
about 200 degrees per sec), Hill's hyperbolic relation still applies.
In general, therefore, the picture which emerges from the equation of muscle dynamics is that of an inverse interplay between the magnitude of the load and the speed of movement, except under isometric and quasi-isometric conditions. Although this interplay is not important for the development of absolute strength, it is important for the problem of speed-strength.
Figure 4 Force-velocity relationship of isolated muscle (1) and in vivo human muscles (2) as determined in two separate experiments under similar loading conditions. The hyperbolic curve is based on the work of Hill, while the other curve is obtained from research by Perrine and Edgerton (1978).
The above studies of the relationship between strength and speed were performed in single-jointed exercises or on isolated muscles in vitro under conditions which generally excluded the effects of inertia or gravity on the limb involved. Moreover, research has shown that the velocity-time and velocity-strength relations of elementary motor tasks do not correlate with similar relations for complex, multi-jointed movements. In addition, other studies reveal that there is a poor transfer of speed-strength abilities developed with single-jointed exercises to multi-jointed activities carried out under natural conditions involving the forces of gravity and inertia acting on body and apparatus. Consequently, Kuznetsov & Fiskalov (1985) studied athletes running or walking at different speeds on a treadmill and exerting force against tensiometers. Their results revealed a force-velocity graph which is very different from the hyperbolic graph obtained by Hill (Fig 5).
Figure 5 Force-velocity relationship for cyclic activity (based on data of Kuznetsov & Fiskalov, 1982).
This figure also shows that jumping with a preliminary dip (or, counter movement) causes the F-V curve to shift upward away from the more conventional hyperbola-like F-V curve recorded under isokinetically or with squat jumps. For depth jumps, the resulting graph displays a completely different trend where the force is no longer inversely proportional to the velocity of movement. The coordinates describing the more rapid actions of running, high jumping and long jumping also fall very distant from the traditional F-V curve (Fig 6).
Figure 6 Force-Velocity curve for different types of jump (Bosco, 1982). In the squat jump, the contractile component of the muscle is primarily responsible for force production, whereas elastic energy, reflexive processes and other muscle changes play additional roles in dip (counter movement) jumps and depth jumping. The calculated values of F and V for high jump, long jump and sprints are also shown.
The reason for these discrepancies lies in the fact that movement under isokinetic and squat jumping conditions involves mainly the contractile component of the muscles, whereas the ballistic actions of the other jumps studied apparently are facilitated by the release of elastic energy stored in the SEC and the potentiation of nervous processes during the rapid eccentric movement immediately preceding the concentric movement in each case.
Studies of F-V curves under non-ballistic and ballistic conditions (Bosco, 1982) further reinforces the above findings that the traditional F-V curves do not even approximately describe the F-V relationship for explosive ballistic or plyometric action. The non-applicability of these curves to ballistic motion should be carefully noted, especially if testing or training with isokinetic apparatus is being contemplated for an athlete.
Other work reveals that the jump height reached and the force produced increases after training with depth jumps (Bosco, 1982). Whether this is the result of positive changes in the various stretch reflexes, inhibition of the limiting Golgi tendon reflex, the structure of the SEC of the muscle or in all of these processes is not precisely known yet (Zatsiorsky, 1997). What is obvious is that the normal protective decrease in muscle tension by the Golgi tendon organs does not occur to the expected extent, so it seems as if plyometric action may raise the threshold at which significant inhibition by the Golgi apparatus takes place. This has important implications for the concept and practical use of plyometrics.
References
Bosco C. (1982) Physiological considerations of strength and explosive power and jumping drills (plyometric exercise) Proceedings of Conference '82: Planning for Elite Performance, Canadian Track & Field Assoc Ottawa 1-5 Aug 1982: 27-37
Caiozzo VJ, Perrine JJ & Edgerton VR (1981) Training-induced alterations of the in vivo force-velocity relationship of human muscle J Appl Physiol 51(3):750-4
Hill A.V. (1953) The mechanics of active muscle Proc Roy Soc Lond (Biol), 141: 104-117
Komi P (1979) Neuromuscular performance: Factors influencing force and speed production Scand J of Sports Sci 1: 2-15
Kusnetsov V & Fiskalov I (1985) Correlations between speed and strength in cyclic locomotion Teoriya i Praktika Fizischeskoi Kultury (Theory & Practice of Physical Culture) 8: 6
Lamb DR (1984) The Physiology of Exercise McMillan Co
Perrine J.J. & Edgerton V.R.(1978) Muscle force-velocity and power-velocity relationships under isokinetic loading. Med Sci Sports 10(3):159-66
Zatsiorsky V.M. (1995) Science and Practice of Strength Training Human Kinetics
Zatsiorsky V.M. (1997) The Review is Nice. I Disagree with It. J of Applied Biomechs 13, 479-483
Zatsiorsky V.M. & Matveev E.N. (1964) Force-velocity relationships in throwing Teoriya I Praktika Fizischeskoi Kultury (Theory & Practice of Physical Culture) 27(8): 24-28
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