This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on April 30 , 1996 . Locomotion : Dealing with friction

To move on land, in water, or in the air, even at constant speed and at the same level, always requires an expenditure of energy. The resistance to motion that has to be overcome is of many different kinds depending on size, speed, and the characteristics of the medium, and is a fascinating subject in itself. Even more interesting are nature’s stratagems and solutions toward minimizing the effort involved in the locomotion of different types of living creatures, and humans’ imitations and inventions in an attempt to do at least as well. The Imperative to Move The world of animals—which includes all of us—is characterized by voluntary motion. It is necessary to move to find food or a mate, or to exercise the muscles needed to move. For reasons that this paper is all about, expenditure of energy always seems to be required to move, whether on land, in water, or in the air. It is only in the space between the stars that bodies—such as the members of the solar system—are able to move for eons with little or no expenditure of the energy associated with their motions. We attribute this seemingly everlasting persistence of motion—the first of Newton’s laws—to the absence of material in space, which the bodies otherwise would rub against, creating heat at the expense of their kinetic energy. For terrestrial objects, both living and inanimate, one is in continual contact with one or more of the solid, liquid, and gaseous parts of our environment, resulting in an expenditure of energy for motion even at uniform speed and at the same level. Reducing the resistance that has to be overcome, which I shall call friction, allows a greater range of travel for a given input of energy, or a greater speed for a given input of power. In the course of evolution and adaptation, one absolute requirement for survival was surely that the energy needed to move to the location of the next meal should be less on average than that acquired from consuming the last one. Similarly, that the speed required either to capture prey, or to avoid becoming one, should be achievable with the power that can be summoned at short notice from the muscles. In humans’ attempts to build vehicles capable of greater range and speed on land, in water, and in the air, nature has provided much inspiration and numerous examples, and in my attempts to understand the principles behind the functioning of craft in these different media, I have come to learn about and marvel at nature’s creations. Getting Around Friction Civilization and its manifestations often require the moving of heavy objects and undoubtedly provided the earliest opportunities for invention of devices to reduce the effort involved. The wheel is considered the greatest such invention and the three power sources used in the Middle Ages—animal, water, and wind—all were exploited by means of wheels. I presume that the earliest form in which the wheel appeared must have been logs on which heavy stones were rolled such as those of which the pyramids were built. The force, or thrust, required to move the stone is reduced from the colossal sliding friction over the ground, which it must have, to the rolling friction of the stone over the logs and that of the logs over the ground, which together still could be provided by a finite number of slaves, and presumably some form of persuasion (Fig. 1). The introduction of a simple axle in the center as in a chariot or wagon wheel was a giant leap forward, but at the expense of reintroducing sliding friction between the axle and the part of the wheel on which it rested (Fig. 2). Although the full load was still on this common surface, the distance it had to be dragged was reduced by the large ratio of the diameters, and this area could be lubricated. Lubricants magically reduce sliding friction between solids and find universal application in places where they can be contained, e.g., between axle and hub. An extraordinary example of self-lubrication, and the only case I know where sliding friction can compete with rolling friction, is that of runners on ice. They enable skaters and ice yachts to reach impressively high speeds for the input powers involved. The next ingenious step in the evolution of the wheel was to make it all rolling friction by putting back the cylindrical rollers, or equivalently spherical balls, in an annular space between the axle and the hub of the wheel, where they can remain in place. This idea was discussed in detail and illustrated in drawings by © 1998 by The National Academy of Sciences 0027-8424y98y955448-8$2.00y0 PNAS is available online at http:yywww.pnas. org. *To whom reprint requests should be addressed. e-mail: rad@rri. ernet.in. FIG. 1. Using rollers to move heavy stones as was presumably done when building the pyramids. As each roller comes out at the rear it has to be reintroduced in front, a tricky operation that must have added not a little to the agony of the slaves.