Akira Azuma

Flight performance of rotary seeds

Many samaras or winged seeds make autorotational flight during their fall. Twenty samples to each of ten species are tested in a vertical wind tunnel, and filmed by a still camera and a cinecamera with stroboscope flash and by smoked flow observation technique. Mean values of their flight characteristics as well as their geometrical configurations are listed in tables and shown in figures along with the variance in the data. Generally the seeds of simple configuration, such as those of maple and black pine, have good performance: there is a low rate of descent in spite of high wing loading (or small wing area but large seed weight) because of high rotational speed and thus a low coning angle. It becomes clear from a simple analysis that the rate of descent, spinning rate of autorotation, pitch angle and coning angle of the rotating seeds are dependent on their geometrical characteristics such as span and area of the wing, mass of the seed, airfoil configuration, position of center of mass, center of moment, and radius of gyration or moment of inertia. Important parameters that relate to the performance are also pointed out and their effects on the flight characteristics are discussed. The precise aerodynamic characteristics of rotary seeds are clarified by applying the local circulation method. Most of the lifting force is generated near the tip or outside terminal of the wing whereas the horizontal force, which is comprised of a driving force and a resistant force, is negative at the wing tip and is positive near the root. Thus the driving torque is obtained near the mid-point of the wing span. Two-dimensional aerofoil or section characteristics of the respective species are also presented. Specifically, for the seed of maple, the results obtained from the gliding flight of a swept wing formed by two seeds and from the autorotational flight of a single seed are compared and found to be in good agreement.

Experimental Study on Aerodynamic Characteristics of Unsteady Wings at Low Reynolds Number

Aerodynamic forces and moment acting on wings of AR = 6 with heaving and feathering oscillations in a wind tunnel were measured at a low Reynolds number less than 10 4 . Airfoils of the wings examined are not streamlined, but they are in various profiles such as a flat plate with and without sharp leading edge, circular arc, and corrugated airfoils. By analyzing the sinusoidal aerodynamic forces and moment, it was found that some differences among airfoils were remarkable in both the mean values and the first harmonic amplitude of aerodynamic coefficients. A large perpendicular force is obtained in some airfoils, but the thrust was almost canceled by the drag in this low-Reynolds-number range during heaving motion alone. To get the maximum thrust, the optimal phase shift of combined heaving and feathering motion was required.

Various flying modes of wind-dispersal seeds

The flight behavior of two kinds of seeds dispersed by wind, pappose seeds and winged seeds is observed and the aero- and flight-dynamics of these seeds are analysed. There are four flight modes: parachuting flight by pappi and gliding, rocking and spinning (or auto-rotational) flights utilizing a wing or wings. A bundle of pappi is applied to small seeds of flowering plants, whereas the wing is widely utilized for flowering trees. Various flight modes of winged seeds are strongly dependent on their plan form and the location of their center-of-gravity (CG). Performances as well as flight modes, specifically the rate of descent, are considered to be selective so as to depend on their environmental conditions and their way of life in their own environments.

ANALYTICAL PREDICTION OF HEIGHT-VELOCITY DIAGRAM OF A HELICOPTER USING OPTIMAL CONTROL THEORY

The autorotative landing of a single-engine helicopter following power failure is analyzed using optimal control theory. The optimization problems are formulated to minimize the unsafe region in the height-velocity diagram under the condition that the touchdown speed is within the capability of the landing gear. Nonlinear equations of motion are described using a rigid-body dynamic model with longitudinal three degrees of freedom. The aerodynamic model of the rotor takes account of the effects of blade stall during descent and increased induced flow in the vortex ring state. The present method gives a good estimation of the height-velocity boundary in comparison with the existing flight test data. It is pointed out that the test pilot started the collective flare earlier than that occurred in the optimal solution.

Flight of a samara, Alsomitra macrocarpa

The steady gliding flight of samples of Alsomitra macrocarpa samara was filmed and analysed. By using the observed data, the flight performance of the samara was made clear. The lift-to-drag ratio or the gliding ratio was about 3 ∼ 4 and the rate of descent was 0·3 ∼ 0·7 m/sec, which was smaller than those of other rotary seeds. The flight was so stable that samples were seen to take their optimal trimmed angle of attack with a value between the maximum gliding ratio and the minimum rate of descent. The aerodynamic function of the husk for the distribution of the seeds was also revealed by making wind tunnel tests of the husk.

Functional roles of the transverse and longitudinal flagella in the swimming motility of Prorocentrum minimum (Dinophyceae).

SUMMARY Equations describing the motion of the dinoflagellate Prorocentrum minimum, which has both a longitudinal and a transverse flagellum, were formulated and examined using numerical calculations based on hydrodynamic resistive force theory. The calculations revealed that each flagellum has its own function in cell locomotion. The transverse flagellum works as a propelling device that provides the main driving force or thrust to move the cell along the longitudinal axis of its helical swimming path. The longitudinal flagellum works as a rudder, giving a lateral force to the cell in a direction perpendicular to the longitudinal axis of the helix. Combining these functions results a helical swimming motion similar to the observed motion. Flagellar hairs present on the transverse flagellum are necessary to make the calculated cell motion agree with the observed cell motion.

Flight Dynamics of the Boomerang, Part 1: Fundamental Analysis

Equations of motion for boomerang flight dynamics are presented in strictly nonlinear form and solved numerically for a typical returning boomerang. The solution shows that the motion consists of both long- and short-period oscillations. The long-period oscillation originates from the exchange of potential (altitude) energy with kinetic energy mainly derived from the forward motion and the spinning motion, the latter of which is accelerated by the autorotation when the angle of attack of an apparent disk of blade rotation increases. The short-period oscillation is due to an asymmetry in the aerodynamic moment related to a large reversed-flow region and a stalled region due to high-advance-ratio flight, and a large moment of inertia or a small Lock number that is an order of magnitude smaller than that of a helicopter blade. The return flight is realized by the centripetal component of the aerodynamic force acting on the apparent disk that is tilted inwardly from the described asymmetric moment and the resulting gyro effect of the spinning motion.

Flight Dynamics of the Boomerang, Part 2: Effects of Initial Conditions and Geometrical Configuration

In Part 1, equations of motion for boomerang flight dynamics were presented in strictly nonlinear form and solved numerically for a typical returning boomerang. The solution shows that the motion consists of both long- and short-period oscillations. These oscillations were found to be the result of the aerodynamically asymmetric moment and the gyro effect of the spinning motion with high advance ratio. When either the initial conditions at takeoff or the geometrical characteristics of the boomerang were varied, various flight paths and flight performances were obtained, some of which are compared with experimental results. The detailed mechanisms of the returning path, tennis racket effect on the flight stability, and ways of throwing a boomerang to avoid dangerous flight path are presented.

Swimming by Snaking

Snaking is the most primitive way of swimming among animals. The young of most fishes swim in this mode, even though their adult locomotion may be very different. A sinusoidal deflection of either the whole body or a part of the body generates a lateral wave in the longitudinal direction. The mode of snaking used is strongly dependent on body size and body shape, because the viscous and inertial effects of the fluid surrounding the body are essentially related to the Reynolds number. The body length of microscopic organisms ranges from 1–5 μm for bacteria, to 300 μm for paramecia and spermatozoa, and their diameter is 1%–5% of the length or less. Thus, for microscopic organisms swimming in water or a slightly viscous fluid, the related Reynolds number and the reduced frequency are so small that the inertial effects of the fluid may be completely neglected. In such cases, the flow surrounding the body is said to be in the “Stokesian realm.” However, for large, elongate animals a few centimeters or meters in length swimming in fresh or salt water, the Reynolds number is large enough to introduce the inertial effects of the fluid into the hydrodynamic forces and moments. Streamlined bodies may coast for a considerable distance after having stopped their locomotion. The hydrodynamic aspects of a large, elongated body in unsteady motion can be treated either by the “slender body theory” or by the “two-dimensional flexible-wing (ribbon) theory.” In this chapter various snaking motions of different animals are presented, along with their modes of life.

Swimming by Fanning

In this chapter, let us look at the hydrodynamic aspects of fish and whales that swim with a “fanning” motion of the body, including pelvic, dorsal, anal, and caudal fins. These animals have developed streamlined bodies that are well adapted to their environment, mode of life, and movement. The body and the fin motion of slender fishes are accomplished by a rhythmic transverse oscillation of the entire body and can be treated as an unsteady motion of a slender body resembling the “snaking” or “anguilliform” motion discussed in the preceding chapter. On the other hand, a wide caudal fin can be better analyzed as an isolated wing performing a fanning motion consisting of a heaving and a feathering motion. In this case, the fanning motion can be divided into two types: “ostraciiform” and “carangiform” (Breder 1926; Gray 1968; R.W. Blake 1981c). In the former, the fanning motion is limited to the tail and is a rudderlike motion. It is seen typically in the Ostraciidae. The latter is, as seen in the Carangidae, performed by flexing the entire body with particular stress on the posterior part. The mechanical differences among these movements will be theoretically analyzed.