George H artley B ryan. 139 GEORGE HARTLEY BRYAN

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2 George H artley B ryan. 139 GEORGE HARTLEY BRYAN The maturity of George H artley Bryan coincided witli the birth of aviation and provided an opportunity for the exercise of his mathematical genius. So well was this opportunity taken that the principles outlined in Stability in Aviation, published by Bryan in 1911, are now universally adopted as the best means of dealing with the relations between the motions of flying craft and the air reactions producing them. The original conception behind the analytical equations presupposed rigid aircraft but natural extensions have led to the investigation of motions in which internal distortions of the craft are included a class of problem normally spoken of as flutter. The importance of Bryan s contribution to aeronautics was widely recognized by 1914 when he was presented with the gold medal of the Royal Aeronautical Society. Whilst this is the outstanding product of Bryan s ability he had earlier interests in the developments of the mathematical side of thermodynamics and hydrodynamics. George Hartley Bryan was born at Cambridge on March 1, His father, Robert Purdie Bryan, of Clare College, died whilst Bryan was young, and his education and upbringing was undertaken by his mother and grandparents. Much of his early life was spent abroad, in Italy, France, and Germany, and provided the means by which he acquired a considerable knowledge of languages, and a circle of friends of international repute. Bryan was fifth Wrangler in the Mathematical Tripos of 1886 and second Smith s Prizeman. He held a fellowship at Peterhouse from 1889 to 1895 when he was appointed Professor of Pure and Applied Mathematics in the University College of North Wales, at Bangor, an appointment held, with a special period of leave for research , until his retirement in Bryan was elected a fellow of the Royal Society in 1895, and an honorary fellow of Peterhouse in 1915 ; during his career he was also President of the Mathematical Association. Bryan married Miss Mabel Williams in 1906 ; they had one daughter, who was completing her education at Cambridge at the time of her father s death at Bordighera on October 13, 1928; Professor and Mrs. Bryan had taken a villa at Bordighera on his retirement in The final illness was short and only a fortnight before his death Bryan took part in the International Mathematical Congress at Bologna. Bryan was a friendly, kindly, very eccentric individual with a keenness for unsolved problems in dynamics and hydrodynamics. His eccentricity has been attributed largely to the circumstances of his early upbringing. Constitutionally rather delicate he was watched with great care and affection the care lasting through his undergraduate days since he was then living at

3 140 Obituary Notices. home. Bryan took a great delight in the beauties of Nature, in scenery, plants and insects and had a passion for music which led him far. At one period when piano players first appeared, a considerable amount of his time and energy was spent in developing an invention for their improvement and led bim into friendly disputation on the principles involved with musicians and physicists. In his later years Bryan found the ties of his university duties rather irksome and sought an opportunity for unfettered research ; this was provided for him in 1917 by a three years grant from the Department of Scientific and Industrial Research, which time he devoted to the dynamics of aeroplane motion and to considering methods of dealing with the motion of compressible fluids. Bryan s earliest scientific papers dealt with thermodynamics as well as hydrodynamics, and at the meeting of the British Association at Cardiff in 1891 he presented an important report on thermodynamics. Several original works led to an international reputation and Bryan was invited to contribute to the section on thermodynamics which appeared in the Encyklopadie der Mathematischen Wissenschaften of In 1901 he was awarded the gold medal of the Institution of Naval Architects for a paper on the effect of bilge keels on the oscillations of a ship. Interest in aviation started at an early date; the experimental researches of Langley in America, leading to power-driven model flights of three-quarters of a mile, had fired public imagination ; this interest was increased by Maxim s efforts in this country. Both experiments led to failure when applied to full scale. Langley s second failure occurring in Lack of any understanding of the principles of stability and control in the air was then the outstanding problem in aviation, though the development of the internal combustion engine had not then reached the stage at which the provision of sufficient power for sustained flight had been adequately solved. The problems of flight were being experimentally investigated during this period by Lanchester with a considerable measure of success. Although the work was supplemented by a certain amount of mathematical analysis this aspect of Lanchester s pioneer work was disconnected and difficult to follow. Bryan completely changed the theoretical outlook by his book Stability in Aviation. which appeared in 1911; the book was itself an extension of a paper written in 1904 with W. S. Williams as collaborator on the subject of the longitudinal stability of aerial gliders. The year 1904 was well in advance of the beginning of public flying which might perhaps be dated , whilst 1911 was a little beyond it. The dates are important, for aeronautical practice was only just ripe for Bryan s analysis at the later date ; for its satisfactory application Bryan s mathematical theory requires certain numbers derived from experiment and now spoken of as resistance derivatives ; nine were required for the longitudinal stability and a further nine for the

4 George H artley B ryan. 141 lateral stability equations of steady rectilinear flight. Some of the important items were unknown in 1911 but the apparatus for finding them had come into existence at the National Physical Laboratory, as the result of the formation in 1909 of the Advisory Committee for Aeronautics by the Prime Minister of the day Mr. Asquith. Bryan had become impatient; he said The present subject has hitherto not received so much attention as it deserves, one reason, probably, being the complexity of the algebraic formulae which present themselves at the outset, and another, doubtless, the success with which aviation has been accomplished on machines the stability of which has not been studied. And again If a lamina has in addition a motion of rotation, as when an aeroplane begins to pitch, the effects of this rotation appear, at present, to be unknown. In all existing theories of stability they have been neglected, and at the time of writing no indications have reached us of the matter receiving attention at the Government Laboratory. A few years later the position had changed entirely and gave obvious pleasure to Bryan ; the research establishments at the National Physical Laboratory and at the Royal Aircraft Factory combined in the application of Bryan s theory with the result that in 1914 an aeroplane, the B.E.2c, was constructed to illustrate the conclusions reached. On more than one occasion this aeroplane was flown from Farnborough to Salisbury a distance of 60 miles or so using only the rudder, and aviators were made aware of the possibility of producing inherent stability of an amount which gave the aeroplane a sufficient will of its own to deal with the gusts of a natural wind of moderate average value. By this time also the mathematical analysis had been extended to cover flight in gusts and to the stability of curvilinear flight; in fact little remained to be learned in the range of normal flight after this time and energy was being directed to the next stage stability and control at low speeds and to flutter. To the first of these Bryan s method is not wholly suitable owing to the rapid variation of the derivatives required by the theory to be sensibly constant throughout the disturbed motion under investigation. In the second field of investigation, flutter, Bryan s method considerably extended in detail has been fruitful; the feature which differentiates flutter from stability as dealt with by Bryan is the introduction of flexibility in the aircraft with elastic constraints between the various parts. Each extension has introduced new derivatives, as well as new equations, and the present limitations are imposed by the number of variables involved and the consequent complexity of the mathematical analysis. The introduction of the B.E.2c into the fighting area showed a defect which prompted a new investigation by Bryan. It was found that a fighting pilot desired an aeroplane completely subservient to his control and disliked the will of the very stable B.E.2c. The principles being known it was easy to produce less stable craft but Bryan conceived the idea of an aeroplane which

5 142 Obituary. was to be both inherently stable and inherently controllable. By the latter he meant an aeroplane which could be turned in any way without any permanent force being required by the pilot to maintain the manoeuvre. In his applications Bryan was mainly concerned with rapid turning. The desired effect was to be produced by twisted and bent wings but little came of this because an enormously greater control was required to change from one position to another sufficiently quickly than is necessary in the maintained turn. The ideal of light control combined with other desirable features has not yet been reached. Although he did not develop the appropriate equations Bryan pointed to essential differences between the stability of aeroplanes and airships ; arising from his general knowledge of hydrodynamics he emphasized the importance of the bulk of an airship in displacing air and so introducing virtual mass into the equations of motion. The necessary mathematical analysis has been made and the results applied to the design of airships and kite-balloons. The last modification into the stability equations which Bryan proposed was made in a paper published in 1921 on the canonical forms of the equations of motion of an aeroplane in still and gusty air. The change was that of independent variable from time to distance moved by the centre of gravity of the aeroplane. So far as the writer is aware this new work has nowhere displaced the older analysis owing to the intractibility of certain definite integrals involved. In the more general field of hydrodynamics, Bryan, in his later years, devoted attention to the movement of compressible fluids, and to the noise produced by airscrews. In the latter investigation he assumed that the acoustical effects are equivalent to those of a certain distribution of sources over the surface of an airscrew blade and starting from the velocity potential due to a fixed source extended the method to moving sources ; this was the beginning of a series of investigations by various workers which is yet far from complete. In 1918 a paper by Bryan was published under the title The effect of compressibility on stream-line motions. In it an attempt was made to proceed from the known solution for an incompressible fluid to that of an adiabatically compressed fluid, by dividing the initial field into squares by stream lines and lines of equal velocity potential, and then by distorting these squares into rectangles in accordance with the laws of adiabatic compression. The detailed analytical process was found to be too complicated for general use, but, in 1928, Gr. I. Taylor introduced an experimental equivalent using an electrical analogy. Potentials measured in a suitable electric field were successfully used to give the successive approximations visualized by Bryan. The inspiration of Bryan is still active in the world of hydrodynamics and in aviation. t -d