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The Flying Mechanism of Insects (from a Fluid Mechanics Point of View)

Keiji Kawachi (Research Center for Advanced Science and Technology,

the University of Tokyo)


Figure 1 compares the Reynolds numbers* and the sizes of moving parts involved in flying, swimming and other activities of organisms from as small as 107 m to airplane wings of 10 m.

These organisms use either lift or resistance or both. For example, the airplane wing shown in Fig. 2 is streamlined, with a round head and sharp tail. When an airplane equipped with this type of wing flies, both vertical power (lift) and parallel power (resistance) against the airflow are used. All of the motile organs make good use of these powers to propel the airplane.

An example of propulsion through resistance can be found in a side-wheel steamer. The direction of the water against its paddles is the same as the direction of propulsion. Thus, we can say that a side-wheel steamer is a propulsion machine that utilizes parallel power, i .e. resistance. A screw, on the other hand, uses lift: the propulsion works in a vertical direction relative to the rotation direction of the wing. Most human-made machines and meter-sized living organisms propel themselves using lift because it is more efficient than resistance in this size range.

Theoretically, a resistance 100 times greater than life can be created in the case of meter-sized motile organs. This means, for example, that a 100 kg object can be lifted when pulled with 1 kg of power. This type of power is therefore highly efficient and the secret of its efficiency is found in the shape. When the wing leans, the stream is divided into two parts at the lower surface of the front of the wing. Because the front part of the wing is rounded, one stream flows along the upper side of the wing toward the back. Likewise, because the tail of the wing is 1) sharp 2) angular, the other stream flows backwards along the lower side of the wing. This causes the upper stream to be longer than the lower one and the speed of the wing increases while the pressure decreases, creating considerable lift.

However, this phenomenon happens only in the meter-sized world; it does not occur in the case of smaller wings. The reduction of the Reynolds number causes a rise in viscosity against pressure, and the ratio between lift and resistance decreases. Therefore, small insects can effectively use both lift and resistance. Furthermore, creatures that are even smaller than insects use resistance as a parachute rather than their wings because they cannot make use of lift.

In the field of aeronautical dynamics in meter size, we try to avoid the appearance of irregular air swirls. However, when dragonflies propel themselves at a constant s peed and angle, various irregular air swirls appear. Furthermore, dragonflies take advantage of the swirl made by their front wings with their back wings.

Micrometer-sized creatures use surface tension and Brownian movement as well as resistance. These creatures can float in the air for long periods of time even if they don 't have wings. The falling speed of particles becomes slower and slower as the diameter decreases because resistance is proportional to size while weight is proportional to size cubed.

For example, when a bacterium of 1 micrometer flies out of my mouth, it takes about 7 hours for it to fall to the ground. If there is a slight updraft, the bacterium may float in the air forever. Bacteria are greatly influenced by Brownian movement, and furthermore, they do not need to make any particular effort to capture food, unlike meter-sized creatures, which must find their own nourishment. Food for these small creatures automatically enters their mouths.

Consequently, it is not necessary in the micro-sized world to overcome the natural environment to realize certain objectives. In my earlier work, I tried to control Brownian movement with micromachines. However, I have recently come to believe that it is much better to make use of the natural environment as micrometer-sized creatures use Brownian movement and surface tension.

We professors often tell our students that they can accomplish anything if they put their mind to it. However, when dealing with worlds of other sizes, perhaps we should expand this idea to doing our best regardless of the particular environment.

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