1939
DOI: 10.1113/jphysiol.1939.sp003756
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The relation between force and speed in muscular contraction

Abstract: IN a recent paper Hill [1938b] (a g.cm. being the " extra heat" for 1 cm. shortening, b g.cm./sec. the increase of the rate of energy production for 1 g. tension loss).This formula relates two variables, the speed of shortening v and the external force P, which can be determined without any heat measurements. According to this formula, which can also be written as (v+b) (P+a)=(Po+a) b=const., the relation between force and speed is a rectangular hyperbola, with asymptotes at P=-a, and v=-b. As has been ver… Show more

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Cited by 748 publications
(546 citation statements)
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“…For example, Hortobagyi et al (1995) found that eccentric torque of knee extensors was relatively maintained in a group of older adults, although the correlations of either concentric or eccentric torque with muscle mass and fiber type and size were similar. Furthermore, while the majority of studies (Hortobagyi et al, 1995;Poulin et al, 1992) report a greater degree of preservation with higher contraction velocities, consistent with the low influence of velocity of contraction on force production during eccentric contractions (Katz, 1939), the maintenance of eccentric torque is reported across a wide range of velocities (from 30°s −1 to 300°s −1 ). Thus, it appears that the preservation of eccentric torque in older adults is a well-established phenomenon, occurring indiscriminately across different muscles groups, independent of age-related architectural changes in muscle structure and the velocity of the movement.…”
Section: Evidence For the Preservation Of Eccentric Strength In Oldermentioning
confidence: 74%
“…For example, Hortobagyi et al (1995) found that eccentric torque of knee extensors was relatively maintained in a group of older adults, although the correlations of either concentric or eccentric torque with muscle mass and fiber type and size were similar. Furthermore, while the majority of studies (Hortobagyi et al, 1995;Poulin et al, 1992) report a greater degree of preservation with higher contraction velocities, consistent with the low influence of velocity of contraction on force production during eccentric contractions (Katz, 1939), the maintenance of eccentric torque is reported across a wide range of velocities (from 30°s −1 to 300°s −1 ). Thus, it appears that the preservation of eccentric torque in older adults is a well-established phenomenon, occurring indiscriminately across different muscles groups, independent of age-related architectural changes in muscle structure and the velocity of the movement.…”
Section: Evidence For the Preservation Of Eccentric Strength In Oldermentioning
confidence: 74%
“…Thus, a further problem is whether the shortening heat depends on the load or on the contractile force itself. According to KATZ (1939), the velocity of reversible lengthening was much smaller than the value calculated from Eq. (1), and the temperature coefficient (Q10) of the lengthening velocity was 1.56, while that of shortening velocity was about 2.…”
Section: Discussionmentioning
confidence: 98%
“…8A. As pointed out by KATZ (1939), the lengthening curve consists of two phases, that is, an immediate downstroke and a slow uniform lengthening, when the load is less than 1.6 Po. As the tension curve was maintained at the load level, the lengthening velocity was measured in the linear part of the lengthening curve after the immediate downstroke due to the lengthening of the series elastic component.…”
Section: Resultsmentioning
confidence: 99%
“…Active muscle offers a resistance to changes in length that varies with velocity (Hill, 1938;Katz, 1939). The afferent discharge from the muscle spindles is also known to depend on their rate of extension as well as their actual length (Matthews, 1933); furthermore, there is evidence that the response of the muscle spindles to length and to velocity of lengthening can to some extent be altered independently by fusimotor activity.…”
Section: Introductionmentioning
confidence: 99%