The mechanics of hopping by kangaroos (Macropodidae)

Force-platform records and films of kangaroos and a wallaby hopping have been analysed to obtain data about the energetics of hopping and about the stresses which act in muscles, tendons and the tibia. The quantitative anatomical data required for the analysis have been obtained from X-radiographs and dissections. It is shown that fluctuations of potential energy and external kinetic energy account for most of the energy cost of hopping; fluctuations of internal kinetic energy are relatively unimportant. Evidence is presented that large savings of energy are effected by elastic storage of energy in the gastrocnemius and plantaris tendons. The elastic mechanism is particularly effective at high speeds and seems to account for the observation of Dawson & Taylor (1973) that oxygen consumption is more or less constant over the whole range of hopping speeds. A mathematical model of hopping is presented. The stresses which occur in hopping are discussed. Summary Force platform records and films have been made of kangaroos and a wallaby hopping. The maximum forces exerted on the ground were about six times body weight. The force exerted on the ground changes direction, throughout the period when the feet are on the ground, so that it is always more or less in line with the centre of mass. Consequently the animal decelerates a little and then accelerates again, during the contact phase. The fluctuations of potential energy which occur in each hop are slightly smaller at high speeds than at low ones. Fluctuations of external kinetic energy increase with speed and account for most of the energy cost of hopping at high speeds. Fluctuations of internal kinetic energy (due to acceleration and deceleration of the limbs) are relatively small. While the feet are on the ground the extensor muscles of the hip do positive work, those of the knee negative work and those of the ankle negative work followed by positive work. The energy cost of hopping is reduced substantially by elastic storage of energy in the Achilles tendon. In the case of a wallaby hopping at moderate speed the calculated saving was 40%. The maximum stresses developed in leg muscles, tendons and the tibia have been calculated and are discussed in relation to the known properties of muscle, tendon and bone. The trunk pitches as the animal hops because the two legs swing forwards and back simultaneously. Appropriate tail movements reduce, but do not eliminate, this effect. A mathematical theory of hopping is presented and used to investigate the merits of different hopping techniques. Dawson & Taylor's (1973) discovery that the rate of oxygen consumption of kangaroos decreases a little, as hopping speed increases, is probably to be explained by the increased role of elastic storage of energy at high speeds.