Walking and running, the two basic gaits used by man, are very complex movements. They can, however, be described using two simple models: an inverted pendulum and a spring. Muscles must contract at each step to move the body segments in the proper sequence but the work done is, in part, relieved by the interplay of mechanical energies, potential and kinetic in walking, and elastic in running. This explains why there is an optimal speed of walking (minimal metabolic cost of about 2 J.kg(-1).m(-1) at about 1.11 m.s(-1)) and why the cost of running is constant and independent of speed (about 4 J.kg(-1).m(-1)). Historically, the mechanical work of locomotion has been divided into external and internal work. The former is the work done to raise and accelerate the body centre of mass (m) within the environment, the latter is the work done to accelerate the body segments with respect to the centre of m. The total work has been calculated, somewhat arbitrarily, as the sum of the two. While the changes of potential and kinetic energies can be accurately measured, the contribution of the elastic energy cannot easily be assessed, nor can the true work performed by the muscles. Many factors can affect the work of locomotion--the gradient of the terrain, body size (height and body m), and gravity. The partitioning of positive and negative work and their different efficiencies explain why the most economical gradient is about -10% (1.1 J.kg(-1).m(-1) at 1.3 m.s(-1) for walking, and 3.1 J.kg(-1).m(-1) at between 3 and 4 m.s(-1) for running). The mechanics of walking of children, pigmies and dwarfs, in particular the recovery of energy at each step, is not different from that of taller (normal sized) individuals when the speed is expressed in dynamically equivalent terms (Froude number). An extra load, external or internal (obesity) affects internal and external work according to the distribution of the added m. Different gravitational environments determine the optimal speed of walking and the speed of transition from walking to running: at more than 1 g it is easier to walk than to run, and it is the opposite at less than 1 g. Passive aids, such as skis or skates, allow an increase in the speed of progression, but the mechanics of the locomotion cannot be simply described using the models for walking and running because step frequency, the proportion of step duration during which the foot is in contact with the ground, the position of the limbs, the force exerted on the ground and the time of its application are all different.

The external and internal mechanical work in running has been measured through various procedures. Different from walking, in running the work due to the forward speed changes (variation of kinetic energy) and to the vertical displacement of the center of gravity (variation of potential energy), throughout the step cycle, are substantially in phase. The external work performed per kilometer is independent of speed, amounting to 0.25 kcal/kg km. The total mechanical work amounts to about 0.40–0.50 kcal/kg km. The efficiency in running has been calculated as about 40–50%: such a high value involves a contribution of a substantial amount of energy delivered at a very low cost; this appears to be identified as elastic recoil energy from the stretched contracted muscle and amounts to about half the energy spent in running. A mechanical model is given for the walking and running processes. mechanics of locomotion; kinetic and potential energy during step cycle; elasticity of contracted muscle; mechanical models for walking and running Submitted on July 29, 1963

SUMMARY1. The metabolic cost and the mechanical work at different speeds during uphill, level and downhill walking have been measured in four subjects.2. The mechanical work has been partitioned into the internal work (JWiit), due to the speed changes of body segment with respect to the body centre of mass (BCM), and the external work (WJxt), related to the position and speed changes of the BCM in the environment.3. Wext has been further divided into a positive part (W,+xt) and a negative one (Wj-xt), associated with the energy increases and decreases, respectively, over the stride period.4. For all constant speeds the most economical gradient has been found to be -102 2% (+ 0-8 S.D.). 6. Wint is constant at each speed regardless of gradient. This is partly explained by an only slight decrease in stride frequency at increasing gradient. Wint constancy implies that it has no role in determining the optimum gradient. 7. A linear multiple regression relating W,+xt and We-xt to the metabolic cost at different gradients showed that negative (eff-) and positive (eff+) efficiencies decrease with increasing speed (from 0f912 to 0726, and from 0 182 to 0 146, respectively). The eff-/eff+ ratio, however, remains rather constant (4-995 + 0-125 S.D.).8. We conclude that the measured Wext, the We+xt/We-xt partitioning and effj-/eff+ ratio, i.e. the different efficiency of the muscles used as force and brake generators, can explain the metabolic optimum gradient at about -10%.

From records obtained from a triple accelerometer applied to the trunk of a subject the displacements of the trunk in vertical, forward, and lateral directions have been calculated. With motion pictures taken simultaneously, displacements of the center of gravity within the body were measured. From these data the external mechanical work of walking was calculated. The sum of work for vertical and for forward displacements of the center of gravity of the body gives the total external work; energy for the lateral displacements was negligible. Total external work appears to be lower than that calculated from the vertical displacements alone, because work done in lifting is partly sustained by the inertial force of the forward-moving body. Total external work reaches a highest value (0.1 kcal/km kg) at the most economical speed of walking, 4 km/hr, which corresponds to an energy consumption of 0.48 kcal/km kg. At this speed the internal work appears negligible; it amounts to appreciable entities at very low speeds because of the static contractions of the muscles, and at high speeds because of considerable stiffening of the limbs and movements not involving a displacement of the center of gravity. Submitted on May 25, 1962

Tractional resistance (RT, N) was determined by towing two cyclists on a racing bike in “fully dropped” posture in calm air on a flat track at constant speed (5--16.5 m/s). RT increased with the air velocity (v, m/s): RT = 3.2 + 0.19 V2. The constant 3.2 N is interpreted as the rolling resistance and the term increasing with v2 as the air resistance. For a given posture this is a function of the body surface (SA, m2), the air temperature (T, degree K), and barometric pressure (PB, Torr). The mechanical power output (W, W) can then be described as a function of the air (v) and ground (s) speed: W = 4.5.10(-2) Ps + 4.1.10(-2) SA (PB/T)v2 s, where P is the overall weight in kg. With a mechanical efficiency of 0.25, the energy expenditure rate (VO2, ml/s) is given by: VO2 = 8.6.10(-3) Ps + 7.8.10(-3) SA (PB/T)v2 s (1 ml O2 = 20.9 J). As the decrease of VO2max with altitude is known from the literature, this last equation allows the calculation of the optimal altitude for top aerobic performance. The prediction derived from this equation is consistent with the present 1-h world record.

Five subjects walked and ran at overlapping speeds and different gradients on a motorized treadmill. At each gradient the speed was obtained at which walking and running have the same metabolic cost (Sm) and the speed of spontaneous (Ss) transition between the two gaits was measured. Ss was found to be statistically lower than Sm at all gradients, the difference being in the range of 0.5-0.9 km h-1. The motion analysis of walking reveals that at all gradients and at increasing speed: (1) the percentage of recovery, an index of mechanical energy saving related to the pendulum-like characteristic of walking, decreases; (2) the lower limb spread reaches a limit in walking; and consequently (3) both the stride frequency and the internal mechanical work, due to limb acceleration in relation to the body centre of mass, increase much more in walking than in running. Switching to a run, although implying a higher frequency, makes the internal work decrease as a result of the lower limb spread. In this paper several influences, such as the 'ratings of perceived exertion' (RPE), on the choice of beginning to run when it is more economical to walk, are discussed. A tentative hypothesis on the determinants of Ss, which is emphasized to be a speed which has to be studied in detail but is generally avoided in locomotion, is based on a comfort criterion from peripheric afferences and is reflected by the fact that at Ss a running stride costs as much as a walking stride.(ABSTRACT TRUNCATED AT 250 WORDS)

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An isolated frog gastrocnemius tetanically stimulated performs a greater amount of positive work, during shortening at a given speed, if it has been stretched immediately before it was allowed to shorten. The increase of work performed is greater, the shorter the interval between stretching and shortening. A substantial amount of the work done on the contracted muscle during the stretching appears to be available during the shortening phase, as in elastic bodies. Note: (With the Technical Assistance of G. Orlando) tension-length diagram of isolated contracted muscle; elasticity of contracted muscle; efficiency of muscular contraction Submitted on May 4, 1964