Summary
Flapping: Flapping propulsion uses a fin or wing to generate thrust by accelerating the surrounding fluid (pushing off of it, in a sense). Swimming strategies based on lift principles, such as thunniform swimming with lunate tails, seem to be most efficient and capable of high-speed propulsion, making them well-suited for high-speed chases or long-range migration. Generally, flapping at higher frequency or amplitude will give more thrust (appropriate for acceleration or fast swimming), but a compromise for optimal efficiency seems to exist for many fish species. Bird flight utilizes the wings for both thrust and lift production, with the angle of the wing relative to the body playing an additional role in the propulsive performance of these animals.
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Jetting: Biological jetting generally involves contracting a chamber in order to accelerate fluid out of a nozzle or orifice. Rather high velocity jets can be generated, allowing for respectable top speeds, but propulsive efficiency at suffers at lower speeds. Notably, the maximum speed of thunniform swimmers is higher than that of jetters. Squid are nevertheless capable of quite large accelerations by generating large jet velocities.
Although there are exceptions, flapping generally yields higher propulsive efficiency than jetting. The reason is primarily that flapping accelerates a large quantity of fluid a small amount (similar to airplane propellers) whereas jetting accelerates a small quantity of fluid a large amount. The net effect is that jetting adds more kinetic energy per unit mass to the flow and thus, more kinetic energy is left behind (wasted) for a given thrust. For flapping, the amount of fluid accelerated is determined by the size of the caudal fin (for swimmers) or wings (for flyers) whereas the jet diameter determines the amount of fluid accelerated for jetting. For jetters, the jet diameter is typically much smaller than the width of their body, but the caudal fins of flapping swimmers and the wings of birds are about the same size or bigger than the width of the animal body. Thus, geometry plays a big role in allowing flappers to accelerate a large quantity of fluid a small amount and achieve high efficiency. Jellyfish are a notable exception to the rule that jet diameter tends to be smaller than the body width for jetters, but the lower propulsive efficiency for jellyfish is due primarily to the fact it that ingests and ejects fluid from the same orifice, leading to the potential for rebound and higher work input for net forward propulsion.
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Common Cuttlefish.
Photographed by Bora Zont in Turkish waters.
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An interesting observation is that biological jetters do not have any speed advantage over flapping swimmers. This is in contrast to mechanical propulsion where turbojets can achieve much higher top speeds than propellers. The result for mechanical propulsion is, however, based on propulsion in air whereas the biological case refers to aquatic propulsion (there is no known aerial biological jet propulsion). Limiting ourselves to underwater propulsion, mechanical jets and propellers perform similarly, although pumpjets do have some advantage related to the delay of cavitation on the pump propeller. Thus, the lack of a speed advantage for biological jetters is related primarily to the fluid environment, not to a fundamental difference in the physics of biologically generated jets vs. mechanically generated jets.
The speed advantage for mechanical jets in air is due to the compressibility of air. Because air is a gas, a great deal of energy can be added to it simply by compressing it (reducing its volume by increasing pressure). Additional energy can be added by directly heating it. Finally, high energy air can easily be accelerated to enormous velocities simply by pushing it through a specially shaped nozzle. A high jet velocity allows net thrust to be generated for very large vehicle velocities. The same results are very difficult to achieve with liquids because they are very nearly incompressible unless extreme measures are employed.
Thermal efficiency: In terms of range and endurance, it is important to know not just the propulsive efficiency, but also the overall efficiency (how efficiently is food converted into useful propulsion?), which is determined by the product of propulsive efficiency and thermal efficiency as indicated in the discussion of efficiency found in the Principles section. In biological systems, thermal efficiency is related to how efficiently the animal's muscles covert chemical energy from food into mechanical work output (muscle movement). This in turn is related to muscle efficiency (how efficiently muscles do work) and how these muscles are connected to produce motion such as moving a fin. The latter can involve frictional forces or motion (such as mantle expansion in squid) that does not necessarily contribute directly to positive thrust, both of which tend to reduce the effective thermal efficiency.
Muscle efficiency is difficult to measure accurately, but a wide variety of techniques have been employed and generally give efficiencies in the range of 10-20% for fish, birds, and squid muscles. This may seem rather low compared to thermal efficiencies mechanical systems, but they are actually quite high considering the low temperatures at which muscles operate. A mechanical heat engine operating at these temperatures would most likely have significantly lower thermal efficiency. Moreover, biological propulsion involves distributed actuation with muscles all along the animal body doing work. In many cases this may allow improved efficiency by only activating the muscles required for the task at hand.
Further Reading
Principles of Animal Locomotion (R. McNeill Alexander, Princeton University Press, Princeton, NJ, 2003) chapters 12 and 14 – 16.
References
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