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Pushing Off

To the Editors:

In "Constructing Animal Locomotion from New Thermodynamics Theory" (July-August), Adrian Bejan and James Marden claim that in all mechanisms of animal movement "the same ground serves as a reference against which all moving bodies push, and without it no locomotion is possible."

A swimming fish does not need to push against the ground to move forward. Neither does a spacecraft need for the gases expelled from its engines to push against a solid substrate to create forward momentum. In all cases, whether it's animal or machine, thrust comes from accelerating a fluid.

Anderson Miller
San Antonio, TX

Drs. Bejan and Marden respond:

We welcome such comments, received from several readers, because they expose the difficulty that the proponents of a new paradigm face today. What could have been more obvious then the beliefs that the sun rotates above our heads, air has no weight and gravity does not matter to fish?

The assertion that a fish needs to push against the ground in order to have locomotion is not ours. It is Archimedes'; he said "give me a firm spot, and I will move the world." For an animal to propel its body one way, the animal must push another body the other way. That other body is the Earth, for all animals, whether they are runners, flyers or swimmers. The Earth's crust supports and feels everything that rests and travels on it. It must, because it is the only "firm spot" in the picture.

Mr. Miller is correct to say that the bird feels a force (the thrust) that matches the flow of momentum (the reaction, or the impulse, depending on the system selected for analysis) of the air stream accelerated (and deflected downward) by its flapping wings. But this does not mean that the ground is unaware of what goes on. The rest of the world—the steady-state control volume sandwiched between the bird and the hard ground—is in translational equilibrium. The force that the flapping bird exerts on the volume (the impulse) is met from below by pressure forces exerted by the ground.

One may ask what happens to the individual vortices (the puffs) of air that the wings hurl downstream and, necessarily, downward. All these flow structures stagnate eventually against the rest of the atmosphere and the ground.

Rocket propulsion in outer space fits in the unsteady-state scenario described above. If the system selected for analysis is the rocket engine, then the system feels a steady force (the thrust, or reaction) that accelerates the engine mass.  If the system selected for analysis is the control volume with which the engine interacts (the environment), then the system feels a steady force of opposite sign (the impulse), which is balanced by the time rate of increase of momentum inside the system. The latter is the "ma" in Newton's law F=ma, and it represents the creation of momentum (all the puffs, fast and slow) in the "space" that originally had zero momentum. The engine pushes against its environment, and the environment pushes back.

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