Chord (aeronautics)

About: Chord (aeronautics) is a research topic. Over the lifetime, 1411 publications have been published within this topic receiving 19785 citations. The topic is also known as: chord line.

The Aerodynamics of Hovering Insect Flight. III. Kinematics

Abstract: Insects in free flight were filmed at 5000 frames per second to determine the motion of their wings and bodies. General comments are offered on flight behaviour and manoeuvrability. Changes in the tilt of the stroke plane with respect to the horizontal provides kinematic control of manoeuvres, analogous to the type of control used for helicopters. A projection analysis technique is described that solves for the orientation of the animal with respect to a cam era-based coordinate system, giving full kinematic details for the longitudinal wing and body axes from single-view films. The technique can be applied to all types of flight where the wing motions are bilaterally symmetrical: forward, backward and hovering flight, as well as properly banked turns. An analysis of the errors of the technique is presented, and shows that the reconstructed angles for wing position should be accurate to within 1-2° in general. Although measurement of the angles of attack was not possible, visual estimations are given. Only 11 film sequences show flight velocities and accelerations that are small enough for the flight to be considered as ‘hovering’. Two sequences are presented for a hover-fly using an inclined stroke plane, and nine sequences of hovering with a horizontal stroke plane by another hover-fly, two crane-flies, a drone-fly, a ladybird beetle, a honey bee, and two bumble bees. In general, oscillations in the body position from its mean motion are within measurement error, about 1-2 % of the wing length. The amplitudes of oscillation for the body angle are only a few degrees, but the phase relation of this oscillation to the wingbeat cycle could be determined for a few sequences. The phase indicates that the pitching moments governing the oscillations result from the wing lift at the ends of the wingbeat, and not from the wing drag or inertial forces. The mean pitching moment of the wings, which determines the mean body angle, is controlled by shifting the centre of lift over the cycle by changing the mean positional angle of the flapping wings. Deviations of the wing tip path from the stroke plane are never large, and no consistent pattern could be found for the wing paths of different insects; indeed, variations in the path were even observed for individual insects. The wing motion is not greatly different from simple harmonic motion, but does show a general trend towards higher accelerations and decelerations at either end of the wingbeat, with constant velocities during the middle of half-strokes. Root mean square and cube root mean cube angular velocities are on average about 4 and 9% lower than simple harmonic motion. Angles of attack are nearly constant during the middle of half-strokes, typically 35° at a position 70 % along the wing length. The wing is twisted along its length, with angles of attack at the wing base some 10-20° greater than at the tip. The wings rotate through about 110° at either end of the wingbeat during 10-20 % of the cycle period. The mean velocity of the wing edges during rotation is similar to the mean flapping velocity of the wing tip and greater than the flapping velocity for more proximal wing regions, which indicates that vortex shedding during rotation is com parable with that during flapping. The wings tend to rotate as a flat plate during the first half of rotation, which ends just before, or at, the end of the half-stroke. The hover-fly using an inclined stroke plane provides a notable exception to this general pattern : pronation is delayed and overlaps the beginning of the downstroke. The wing profile flexes along a more or less localized longitudinal axis during the second half of rotation, generating the ‘flip’ profile postulated by Weis-Fogh for the hover-flies. This profile occurs to some extent for all of the insects, and is not exceptionally pronounced for the hover-fly. By the end of rotation the wings are nearly flat again, although a slight camber can sometimes be seen. Weis-Fogh showed that beneficial aerodynamic interference can result when the left and right wings come into contact during rotation at the end of the wingbeat. His ‘fling’ mechanism creates the circulation required for wing lift on the subsequent half-stroke, and can be seen on my films of the Large Cabbage White butterfly, a plum e moth, and the Mediterranean flour moth. However, their wings ‘peel’ apart like two pieces of paper being separated, rather than fling open rigidly about the trailing edges. A ‘partial fling’ was found for some insects, with the wings touching only along posterior wing areas. A ‘ near fling ’ with the wings separated by a fraction of the chord was also observed for m any insects. There is a continuous spectrum for the separation distance between the wings, in fact, and the separation can vary for a given insect during different manoeuvres. It is suggested that these variants on Weis-Fogh’s fling mechanism also generate circulation for wing lift, although less effectively than a complete fling, and that changes in the separation distance may provide a fine control over the amount of lift produced.

Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application

Abstract: This paper consists of three notes on the theory of two-dimensional thin airfoils in non-uniform motion: 1. In the first note expressions for the lift and moment of an oscillating airfoil are collected from an earlier paper and are presented in convenient forms for practical application. 2. * In the second note the lift and moment are calculated for a rigid airfoil passing through a vertical-gust pattern having a sinusoidal distribution of intensity. The lift is determined as a function of the reduced frequency (which in this case is proportional to the ratio of the airfoil chord and the wave length of the gust pattern) and is presented in the form of a vector diagram. I t is shown that the lift acts at the quarter-chord point of the airfoil at all times. 3. In the third note the results of 1 and 2 are applied to the calculation of the amplitude of torsional oscillation of a fan blade operating in the wake of a set of pre-rotation vanes. In a numerical example the amplitude is found to be small even when the vanes are spaced so tha t the exciting frequency coincides with the natural frequency of the fan blade. 1. T H E FORCES ON AN OSCILLATING AIRFOIL T SECTION consists of a summary of the results obtained by von Karman and Sears and their application to the general case of translatory and torsional oscillations about an arbitrary axis on the chord line. The principal assumptions are that the flow can be considered two-dimensional and that the airfoil thickness and the amplitude of oscillation are small compared to the chord. In the original paper, two fundamental types of oscillatory motion were considered: ''translatory" and "rotational." These are characterized by different expressions for the vertical velocity w(x) of the points along the chord of the airfoil. In the translatory oscillation this velocity is constant for all points of the chord; Received September 6, 1940.

The Aerodynamics of Hovering Insect Flight. II. Morphological Parameters

Abstract: Morphological parameters are presented for a variety of insects that have been filmed in free flight. The nature of the parameters is such that they can be divided into two distinct groups: gross parameters and shape parameters. The gross parameters provide a very crude, first-order description of the morphology of a flying animal: its mass, body length, wing length, wing area and wing mass. Another gross parameter of the wings is their virtual mass, or added mass, which is the mass of air accelerated and decelerated together with the wing at either end of the wingbeat. The wing motion during these accelerations is almost perpendicular to the wing surface, and the virtual mass is approximately given by the mass of air contained in an imaginary cylinder around the wing with the chord as its diameter. The virtual mass ranges from 0.3 to 1.3 times the actual wing mass, indicating that the total mass accelerated by the flight muscles can be more than twice the wing mass itself. Over the limited size range of insects in this study, the interspecific variation of non-dimensional forms of the gross parameters is much greater than any systematic allometric variation, and no interspecific correlations can be found. The new shape parameters provide quite a surprise, however: intraspecific coefficients of variation are very low, often only 1%, and interspecific allometric relations are extremely strong. Mechanical aspects of flight depend not only on the magnitude of gross morphological quantities, but also on their distributions. Non-dimensional radii are derived from the non-dimensional moments of the distributions; for example, the first radius of wing mass about the wing base gives the position of the centre of mass, and the second radius corresponds to the radius of gyration. The radii are called \`shape parameters' since they are functions only of the normalized shape of the distributions, and they provide a second-order description of the animal morphology. The various radii of wing area are strongly correlated, as are those of wing mass and of virtual mass: the higher radii for each quantity can all be expressed by allometric functions of the first radius. The overall shape of the distribution of a quantity can therefore be characterized by a single parameter, the position of the centroid of that quantity. The strong relations between the radii of wing area, mass and virtual mass hold for a diverse collection of insects, birds and bats. Thus flying animals adhere to \`laws of shape' regardless of biological differences. Aerodynamic and mechanical considerations are most likely to provide an understanding of these laws of shape, but an explanation has proved elusive so far. The detailed shape of a distribution can be reconstructed from the shape parameters by matching the moments of the observed distribution to those of a suitable analytical function. A Beta distribution is compared with the distribution of wing area, i.e. the shape of the wing, and a very good fit is found. With use of the laws of shape relating the higher radii to the first radius, the Beta distribution can be reduced to a function of only one parameter, thus providing a powerful tool for drawing a close approximation to the entire shape of a wing given only its centroid of area. Quite unexpectedly, the continuous spectrum of wing shapes can then be described in detail by a single parameter of shape.

Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation

Abstract: The effects of oscillatory blowing as a means of delaying separation are discussed. Experiments were carried out on a follow, flapped NACA 01115 airfoil equipped with a two-dimensional slot over the hinge of the flap. The flap extended over 25% of the chord and was detected at angles as high as 40 deg. The steady blowing momentum coefficients could be varied independently of the amplitudes and frequencies of the superimposed oscillations. The modulated blowing was a major factor in improving the performance of the airfoil at much lower energy inputs than was hitherto known. Optimum benefits in performance were obtained at reduced frequencies, based on the flap chord, of an order of unity. Significant increase in lift as well as cancellation of form drag were observed

Design of Subsonic Airfoils for High Lift

Abstract: Nomenclature c = airfoil chord CL = lift coefficient = L/!/2pV00c CLu = upper-surface lift coefficient Cp = pressure coefficient = (p -p^)/ Ap Vx 2 Mx = freestream Mach number p = static pressure Re^ = freestream Reynolds number based on airfoil chord = V^clv sp = location of leading-edge stagnation point V^ — freestream velocity v local velocity on airfoil surface x = distance along chord line F = circulation about the airfoil 7 = ratio of specific heats v = kinematic viscosity p = density () oo = freestream conditions () t e = conditions at the airfoil trailing edge