N. C. Heglund

The determinants of the step frequency in running, trotting and hopping in man and other vertebrates.

1. During each step of running, trotting or hopping part of the gravitational and kinetic energy of the body is absorbed and successively restored by the muscles as in an elastic rebound. In this study we analysed the vertical motion of the centre of gravity of the body during this rebound and defined the relationship between the apparent natural frequency of the bouncing system and the step frequency at the different speeds. 2. The step period and the vertical oscillation of the centre of gravity during the step were divided into two parts: a part taking place when the vertical force exerted on the ground is greater than body weight (lower part of the oscillation) and a part taking place when this force is smaller than body weight (upper part of the oscillation). This analysis was made on running humans and birds; trotting dogs, monkeys and rams; and hopping kangaroos and springhares. 3. During trotting and low‐speed running the rebound is symmetric, i.e. the duration and the amplitude of the lower part of the vertical oscillation of the centre of gravity are about equal to those of the upper part. In this case, the step frequency equals the frequency of the bouncing system. 4. At high speeds of running and in hopping the rebound is asymmetric, i.e. the duration and the amplitude of the upper part of the oscillation are greater than those of the lower part, and the step frequency is lower than the frequency of the system. 5. The asymmetry is due to a relative increase in the vertical push. At a given speed, the asymmetric bounce requires a greater power to maintain the motion of the centre of gravity of the body, Wext, than the symmetric bounce. A reduction of the push would decrease Wext but the resulting greater step frequency would increase the power required to accelerate the limbs relative to the centre of gravity, Wint. It is concluded that the asymmetric rebound is adopted in order to minimize the total power, Wext + Wint.

STORAGE AND RELEASE OF MECHANICAL ENERGY BY CONTRACTING FROG MUSCLE FIBRES

1. Stretching a contracting muscle leads to greater mechanical work being done during subsequent shortening by its contractile component; the mechanism of this enhancement is not known. 2. This mechanism has been investigated here by subjecting tetanized frog muscle fibres to ramp stretches followed by an isotonic release against a load equal to the maximum isometric tension, T(o). Shortening against T(o) was taken as direct evidence of an absolute increase in the ability to do work as a consequence of the previous stretch. 3. Ramp stretches (0.5‐8.6% sarcomere strain, confined to the plateau of the isometric tension‐length relationship) were given at different velocities of lengthening (0.03‐1.8 sarcomere lengths s‐1). Isotonic release to T(o) took place immediately after the end of the ramp, or 5‐800 ms after the end of the largest ramp stretches. The length changes taking place after release were measured both at the fibre end and on a tendon‐free segment of the fibre. The experiments were carried out at 4 and 14 degrees C. 4. After the elastic recoil of the undamped elastic elements, taking place during the fall in tension at the instant of the isotonic release, a well‐defined shortening took place against T(o) (transient shortening against T(o)). 5. The amplitude and time course of transient shortening against T(o) were similar at the fibre end and in the segment, indicating that it is due to a properly of the sarcomeres and not due to stress relaxation of the tendons. 6. Transient shortening against T(o) increased with sarcomere stretch amplitude up to about 8 nm per half‐sarcomere independent of stretch velocity. 7. When a short delay (5‐20 ms) was introduced between the end of the stretch and the isotonic release, the transient shortening against T(o) did not change; after longer time delays, the transient shortening against T(o) decreased in amplitude. 8. The velocity of transient shortening against T(o) increased with temperature with a temperature coefficient, Q10, of approximately 2.5. 9. It is suggested that transient shortening against T(o) results from the release of mechanical energy stored within the damped element of the cross‐bridges. The cross‐bridges are brought into a state of greater potential energy not only during the ramp stretch, but also immediately afterwards, during the first phase of stress relaxation.