Single Wing Research Articles

Gerard Groote and the beginnings of the ‘New Devotion’ in the Low Countries

Until comparatively recently the origins of the movement known as the devotio moderna attracted curiously little attention in this country. It was judged too medieval and too orthodox in character to have had much influence upon the course of reform, and the Anglican habit of relating all reforming movements to the Reformation did not allow it its rightful place in the history of the Christian spiritual life; from another angle, the sarcasms of Erasmus in his Compendium Vitae cast doubts about the disinterestedness of its teaching, and raised among humanists suspicions that its aims and methods were ultimately obscurantist. Its reforming activities were mainly associated with the efforts of a single wing of, or group within, the movement that aimed at reforming the religious houses along the lines of the Augustinian convents of Agnetenburg and Windesheim, and small attention was paid to its appeal to the laity and its attempt to combat self-satisfied materialism among the prosperous middle classes in the towns. And the fact that it was, at any rate in its beginning, essentially a local movement, confined in the main to the western part of the ecclesiastical province of Cologne, still further confined its appeal.

A Note on the Bending Moment Induced in the Booms of a Spar at the Point of Application of a Concentrated Load

SummaryThe effect of a concentrated load, such as occurs in a wing spar at the fuselage, is to cause a discontinuity in shear strain of the spar web, which induces a bending moment in the booms through the medium of the rivets (or bolts) which attach the booms to the web. A mathematical theory is developed which shows that this bending induced in the boom is of a damped wave form starting at the point of application of the shear, and in practice the magnitude of the stresses produced by the bending moment may be appreciable at the wing root when the boom is deep compared with the spar depth (say 20 per cent.).Further experimental verification is desirable, but a single wing test suggested the original investigation, and showed a measure of agreement with the theory.

The Dynamics of a Swept Wing

I t is assumed tha t a swept wing may be represented dynamically by a plane curved rod of variable cross section with finite stiffness in torsion and in bending normal to its plane. The equations of motion for this configuration are exhibited with the restriction tha t the curvature of the elastic axis be finite. By allowing the curvature to become infinite a t a point, certain auxiliary conditions are obtained at the bend. The validity of this limiting process is examined from the physical point of view. A wing with an elastic axis consisting of a plane broken line of (n + 1) segments is denoted as an bend A method is developed for calculating the natural frequencies and modes of a single bend wing. Formulas for the natural frequencies and modes of a free-free symmetric single bend uniform rod are obtained. A generalized type of orthogonality condition between the modes of a single bend wing is proved. Based on these results, formulas are developed for the dynamic response of a single bend wing to a general system of forces. A method of generalizing the above results for a single bend wing to the n bend wing is indicated. The use of an n bend wing as an approximate representation of a wing of continuous curvature is discussed.

New Developments in the Theory of Airfoils of Infinite Span

This paper gives some supplementary developments and revisions of the two dimensional airfoil theory. (1) The chief results are reviewed and the concept of second axis of a profile is revised. (2) In discussing stability questions the theory of Hamilton's center is referred to. (3) The method of successive approximations is outlined in its relation to the so-called thinwing theory. (4) The addition of two independent lift-force systems is explained. (5) The general theorem is proved that in any case of several airfoils with mutual interference the lift force follows the same laws in its dependency on the angle of attack as in the case of a single wing. I 1917 and 1920 the author published two papers in which, for the first time, a general and complete solution of the lift problem for an airplane wing of infinite span was given. About the same time Prandtl developed his famous theory of vortex motion behind an airfoil which supplies a most valuable estimation of the influence of the finite ends. Both theories form today the basis of the practical computations in airfoil design and both are the subject matter of numerous papers continuously being published in almost all countries. In that which follows the author presents some supplementary developments and revisions to his former papers, suggested in part by recent publications. 1. T H E CHIEF RESULTS OF THE THEORY The principal results of the theory are the following. To any cross-section of an airfoil which has a sharp trailing edge (B in Fig. 1), there corresponds a point F I G . 1. Lift magnitude, direction, and line of action. F, a straight line 1° and a vector L° parallel to 1°. These elements, depending on five parameters (two coordinates of F, direction and position of /°, magnitude of L°) entirely determine the lift force for every angle of attack a. It is only necessary to draw through F Presented a t an Aerodynamics Session, Eighth Annual Meeting, I.Ae.S., New York, January 25, 1940. a parallel to the velocity V at infinity (at the angle a to the x axis). The lift L is perpendicular to Vy its line of action passes through the point of intersection of the parallel to V with 1° and its magnitude equals the projection of L° (see Fig. 1). It is easy to see that the lines of action so determined envelop a parabola with focus at F and with 1° as vertex tangent. If the direction of the flow at infinity is normal to 1°, then 1° and L° immediately give the line of action and the magnitude of the lift. The elements F, 1°, L° are connected with the crosssection of the profile through the theory of conformal transformation. If designates the complex number (or the vector) x + iy corresponding to a point x,y of the profile or its surroundings, then a function f(z) = = x' + iy' relates to the point x,y another point x',y' and this correspondence is called a conformal transformation. If the difference — z' vanishes for infinite values of and z the transformation leaves infinity unchanged. The decisive theorem is the following: There exists one and only one conformal transformation, leaving infinity unchanged, which transforms the outside of a given closed curve (the profile) into the outside of a circle. This circle, its center M and its radius a (Fig. 2), are uniquely

A Simple Method of Demonstrating Blood Circulation in the Wings and Wing-pads of the Cockroach, Periplaneta americana Linn

It has long been known that blood or hemolymph circulates in the wings of certain insects (Carus, Moseley, Brocher, and others). Most of these authors apparently observed the wing circulation with difficulty and were unable to identify completely the circulation scheme in a single insect wing at a given time. Such circulation diagrams, therefore, represent averages of a number of observations and conjectures based upon these. Brocher, until recently, saw the movement of individual blood cells only occasionally. Moseley was unable to observe blood circulation in the forewing of the cockroach, P. orientalis. The present paper reports a simple method of observing the details of blood circulation in the wings and wing-pads, as well as in the appendages and certain portions of the body, of the cockroach, P. americana. Circulation in the forewing may be observed by placing the animal in a depression made in a piece of balsa wood; the depression should just fit the insect and should be of such depth as to leave the dorsal surface of the body slightly higher than the surrounding wood. The head and pronotum are retained by a piece of paper (Fig. 1, p) pinned to the wood (w); the abdomen and all but the forewing (F) to be observed are held in a similar manner by a piece of dull black paper (b). The wing (F) should be at an angle to the black paper (b), upon which is placed a movable piece of white kymograph paper (k) with the shiny surface uppermost, so that a beam of intense light (l) from a low voltage incandescent lamp (L) can be directed downward to the edge (e) of the kymograph paper, as shown by the arrow in Fig. 1.