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Aviation History
1915
1915 - 0362.PDF
t/yGHf] |«° , I . . I'' . t . . I*' . I . f° y » - l •! 4 I l I l l t I i I I l I . • !.- Fig. 18. The first question that arises is in what manner it is desirable to initially specify the terms of restriction. The author has given preference to a form of expression involving the relative wake velocity, thus th( limiting condition is taken as defined by a con stant A representing the rearward wake velocity in terms of the velocity of flight: in the case of the marine propeller the velocity of « ® DYNAMICS THE RIGID As was ritting, considering its ration n'tSire, the third Wilbur Wright Memorial lecture, delivered before thr Aeronautical Society yesterday Thursday), was of an extremely technical character. The lecturer was Prof. G. H. Bryan, F. R.S., and he dealt with some aspects of the stability problem, to which he has given so much thought. The lecture was in fact a se<|uel to his book, " Stability in Aviation," and as the title—The Rigid Dynamics of Circling Flight— Steady Motion in a Circle—Lateral Steering of Aeroplanes— implies, it dealt with the steering of an aeroplane in a horizontal circle. The following are some notes in popular style of the lecture, drawn up officially by the Aeronautical Society. It is interesting to mote that Mr. F. W. Lanchester, who presided at the lecture, nas done notable work on aeroplane stability on different lines from those of Bryan. Familiarity with the methods of the book is assumed in the lecture. For the benefit of those who are not familiar with those methods the basis of the book will be brought out in the following remarks:— If any Ixxly or portion of matter moving steadily in a straight line is disturbed it will move in certain!directions, according to its characteristics and the forces acting on it. By means of mathematics it has been found possible to predict in what way a moving body •will behave in such cases, if we know certain things about it—for example, its weight, in what way the various masses that make up the body arc arranged about its centre of gravity, &c. By using mathematical symbols for these properties of the body and certain others we are able to build up " equations of motion " that enable us to calculate the possible behaviour of the body when its steady motion is disturbed. This branch of science is known as " Rigid Dynamics," and it is of the first importance in the study of any bodies in motion. The standardisation of " Rigid Dynamics " was largely due to Routh, who published a book with that title in i860. Strangely enough, however, although over a hundred year ago aeroplanes having nearly all the important characteristics of present-day machines, except the motor, were invented, and the evolution of the aeroplane has thus been contemporaneous with the evolution of Rigid Dynamics, the application of Rigid Dynamics to the study of the motions of an aeroplane has only been accomplished within the last decade, and that mainly owing to the labours of Professor Bryan. This is all the more remarkable for the reason that an aeroplane is dependent for its sustentation on its rapid motion through the air, and it is essential for the pilot's safety that this motion should be stable and that disturbances should be overcome. Bryan's " Stability in Aviation " was published in 1911, but he MAY 21, 1915. the vessel. If the flight velocity be represented by the symbol o, and the rearward velocity imparted by the propeller by v.:, we thus have K = vjv,. The value of A'so defined does in fact determine the diametral restriction, at least this is so if we assume the whole of the fluid passing through the disc area as being operated upon ; this is evidently the correct basis. The relation by which the constant A' and the diameter are connected is to be sought in the Newtonian theory of propulsion in accordance with the teaching of Prof. Rankine and Mr. W. Froude, but it is also controlled by the stream contraction, allowance for which may be made on the lines sug gested by the theorem of Dr. R. E. Froude, to which reference has already been made, i.e., that the velocity « at the point of passage through the propeller is equal to z>i + —. Alternatively, the author's extension of the Froude investigation might be made the basis of the allowance (see paper before I.N.A. on "Theory of Propul sion "). In the present paper this has not been thought desirable. 20. The mathematical work resolves itself into two very simple steps, supplemented by certain graphic transformations ; thus the first step is to find an expression for A'in terms of 8 and r\ ; from this expression we make a plotting in which ordinates represent values of 8 and abscissae 7/, graphs being given representing K = constant, Fig. 16; we may call these graphs iso-K lines. Next, following the method of the author's previous paper (Appendix IV.), the constant relation between r\ and C is estab lished, and 7 values are calculated or plotted, Fig. 17 (as in Fig. 18 of the paper aforesaid), with Cas abscissae, the scale chosen for C being preferably such as to correspond with the T) scale of Fig. 16. From Figs. 16 and 17 corresponditg values of 8 and 7 are read off, and these form the basis of a further plotting, Fig. 18, in which ordinates represent 8 and abscissae 7 values ; the graphs once again represent iso-K lines transformed now by the substitution of 7 for IJ as abscissae. (To be continued.) ® ® OF CIRCLING FLIGHT. had been working on the subject for some years previously. In 1903 he, in conjunction with Mr. Ellis Williams, read a paper before the Royal Society, and also before the Aeronautical Society, on the " Longitudinal Stability of Aeroplane Gliders,"in which were given the germs of the methods expounded in his later book. As long ago as October, 1897, he had directed attention (in " Science Progress") to the necessity of applying mathematics to aeroplane stability and other problems. "Stability in Aviation," then, is an application to aeroplanes of the equations of Rigid Dynamics. In this application great diffi culties had to be overcome and snares and pitfalls avoided, and one of the outstanding features of Bryan's work is the common sense way in which he has steered a true course through all these obstacles. An aeroplane is sustained by air resistance, engendered by the rapid motion through the air of the wings of the machine. It will be clear, then, that if the motion of an aeroplane is disturbed, the air pressure on the wings will be disturbed, and we have certain very complex relations to disentangle, between the natural oscillations of the machine about its centre of gravity and of that centre of gravity in space, and the various accelerating or damping forces due to the varying air pressure on the wings and other portions of the machine. Now in practical flying we want a machine that will maintain or recover its equilibrium so long as we require it to do so, but which we can turn and twist about when required. To design such a machine three courses are open to us—we may proceed by pure experiment, by pure theory, or by a combination of both experiment and theory. The latter course commends itself to the majority, and the more one considers the question of what particular theoretical methods are likely to come into general use in the future, when the design of aeroplanes is as much a matter of routine as that of, say, electric motors is now, the more is one driven to admire the fore sight of Professor Bryan in adapting the equations of Rigid Dynamics to aeroplanes, and to endorse the honour that he has received from the Aeronautical Society by the award of its Gold Medal, which will be presented before the lecture. It must not be supposed, however, that this adaptation has been completed. Very far from it, as is shown by the present lecture. It was said that certain characteristics of the moving body under investigation were denoted by symbols and that the manipulation of these symbols foretells the behaviour of the body in certain circumstances. It will be clear at once that everything depends on our choosing the essential characteristics at the outset and on giving correct numerical values to our symbols when we want quantitative results, as we must do when actually designing machines of definite 362
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