The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic "bounce" of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.
The stride frequency at which animals of different size change from one gait to another (walk, trot, gallop) changes in a regular manner with body mass. The speed at the transition from trot to gallop can be used as an equivalent speed for comparing animals of different size. This transition point occurs at lower speeds and higher stride frequencies in smaller animals. Plotting stride frequency at the trot-gallop transition point as a function of body mass in logarithmic coordinates yields a straight line.
It is widely thought that animals switch gaits at speeds that minimize energetic cost. Horses naturally switched from a trot to a gallop at a speed where galloping required more energy than trotting, and thus, the gait transition actually increased the energetic cost of running. However, by galloping at this speed, the peak forces on the muscles, tendons, and bones, and presumably the chance of injury, are reduced. When the horses carried weights, they switched from a trot to a gallop at a lower speed but at the same critical level of force. These findings suggest that the trot-gallop transition is triggered when musculoskeletal forces reach a critical level.
Small mammals are able to run at about the same maximum speed vertically as horizontally, but larger mammals cannot do this. During level running a mouse weighing 30 grams uses about eight times as much energy per unit of body weight as does a chimpanzee weighing 17.5 kilograms (42.6 joules per kilogram meter versus 5.17 joules per kilogram meter). The additional energy required to lift 1 kilogram of body weight 1 meter while running uphill was similar for the two species (about 15.5 joules per kilogram meter). Therefore the increment in energy expenditure for mice to run uphill compared to running horizontally is about one-eighth that for a chimpanzee. Both mice and chimpanzees were able to recover about 90 percent of the energy stored running uphill on the way down.
The inferences a prospective home buyer can make about the quality of a house from the amount of time it spends on the market and the seller's optimal strategy in light of these inferences are investigated. Depending upon the information structure, the seller may have an incentive to post an inordinately high initial price (in order to ''dampen'' the signal transmitted to future prospective buyers) or an inordinately low initial price (in order to make an early sale and avoid consumer ''herding''). It is shown that the sellers of high-quality homes do best when inspection outcomes are publicly recorded and do worst when inspection outcomes are not public and the price history is not observable. Costly inspections create more adverse selection but deter consumer herding.
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