March 3, 19 10] 



NATURE 



II 



courses that I have been able to give any attention to 

 the subject. 



Some criticisms having- been raised by the late 

 Captain Ferber, mainly referring to the form in. which 

 the conditions of stability were stated, I suggested 

 his developing the work as I had not time to do so. 

 His results were published in the Revue d'Artillerie, 

 October and November, 1905, and include a discussion 

 of lateral as well as of longitudinal stability. 



At the beginning of last year the work of my 

 department was, for some unknown reason, exception- 

 ally light, and I had in Mr. E. H. Harper an assistant 

 well able and willing to collaborate in a much more 

 exhaustive investigation both of longitudinal and 

 lateral stability. About October I received a formal 

 letter of inquiry from the Government Committee, in 

 an envelope which I at first took for an income-tax 

 application, and in reptr stated that what I wanted 

 was a small grant to enable me to devote my whole 

 time to this work. I received a reply that the com- 

 mittee '"regretted," &c., but that "very great interest 

 was taken " in the work. The main difficulties of 

 the subject have, however, now been practicallv 

 cleared up, though a long time must elapse 

 before a detailed written account is ready for publica- 

 tion. Had any prizes been offered in England for 

 which such an investigation would be eligible, the 

 delay might have been avoided or shortened. 



Reference must be made also to Mr. Lanchester's 

 remarkable investigations, published in his "Aero- 

 donetics," and to the appearance of a German trans- 

 lation of the preceding volume, "' Aerodynamics," 

 shortly after its publication in English. 



It is here proposed to give a general idea of the 

 peculiarities of aeroplane stability as deduced from 

 my work, and a comparison with Ferber 's and Lan- 

 chester's methods; though with regard to the latter 

 it is rather difficult for any critic to be sure of not 

 misjudging the author's intended meaning. 



It is necessan,- that the distinction between equi- 

 librium and stability should be kept in mind. An 

 aeroplane is in equilibrium when travelling at a 

 uniform rate in a straight line, or, again, when being 

 steered round a horizontal arc of a circle. A badly 

 balanced aeroplane would not be able to travel in a 

 straight line. The mathematics of aeroplane equi- 

 librium is probably very imperfectly understood by 

 many persons interested in aviation, but it is com- 

 paratively simple, while the theory of stability is of 

 necessity much more difficult. 



It is necessary for stabiHty that if the aeroplane is 

 not in equilibrium and moving uniformly it shall tend 

 towards a condition of equilibrium. At the same 

 time, it may commence to oscillate, describing an un- 

 dulating path, and if the oscillations increase in ampli- 

 tude the motion will be unstable. It is necessary for 

 stability that an oscillatory motion shall have a posi- 

 tive modulus of decay or coefficient of subsidence, and 

 the calculation of this is an important feature of the 

 investigation. A slight reference to this question of 

 rolling is given by Chatley on p. 99 of "The Problem 

 of Flight," but he seems to have overlooked the fact 

 that this damping may be, and often is, negative in 

 the case of unstable aeroplanes. 



At the present time it is certain that aviators rely 

 on their own exertions for controlling machines that 

 are unstable, or at least deficient in stability, and 

 they even allege that, owing to the danger of sudden 

 igusts of wind, automatic stability is of little import- 

 ance. Moreover, even in the early experiments of 

 Pilcher, it was found that a glider with too V-shaped 

 wings, or with the centre of gravity too low down, is 

 apt to pitch dangerously in the same way that in- 

 creasing the metacentric height of a ship while 

 NO. 2105, VOL. 83] 



ircreasing its " statical " stability causes it to pitch 

 dangerously. It thus becomes important to consider 

 what is the effect of a sudden change of wind velocity 

 on an aerodrome. If the aerodrome was previously 

 in equilibrium it will cease to be so, but will tend to 

 assume a motion which will bring it into the new 

 state of equilibrium consistent with the altered cir- 

 cumstances, provided that this new motion is stable. 

 Thus an aerodrome of which every steady motion is 

 stable within given limitations will constantly tend 

 to, right itself if those limitations are not exceeded. 

 Excessive pitching or rolling results from a short 

 period of oscillation combined with a modulus of 

 decay which is either negative (giving instability) or 

 of insufficient magnitude to produce the necessary 

 damping. 



The new work depends verj- largely on the property 

 that for a system of narro'dj aeroplanes inclined at 

 small angles to the line of flight approximate methods 

 may be used, greatly simplifying the algebra, and 

 enabling the various oscillations to be separated and 

 their moduli of decay to be calculated approximately. 

 Of the six equations of motion as applied to the small 

 oscillations of a symmetrical aerodrome, three deter- 

 mine oscillations in the plane of symmetr}-, and lead 

 to conditions of symmetric or longitudinal stabilitv. 

 The other three determine asymmetric or skew svrn- 

 metric oscillations, leading to conditions of asym- 

 metric stability. The three equations in each set are 

 mutually interdependent, but independent of the other 

 three, thus accounting for the fact that Lanchester 

 found it impossible to separate "lateral " and "direc- 

 tional " stability. Failing any better terminology-, I 

 have provisionally adopted the term "asymmetric" 

 stabilit}'. 



Of the two, symmetric stability presents by far the 

 simpler problem. For the systems above mentioned 

 there are two symmetric oscillations, one of long and 

 one of short period. The short-period oscillation con- 

 sists mainly of an oscillatory motion of the centre of 

 gravity perpendicular to the line of flight (1.^. a ver- 

 tical oscillation if the aerodrome is moving hori- 

 zontally), combined with a rotaton.- oscillation about 

 the centre of gravity. To a first approximation it 

 produces no fluctuations in the velocity in the line of 

 flight, and is unaffected by head resistance or fluctua- 

 tions in the propeller thrust, provided the latter passes 

 through the centre of gravity of the aerodrome, as 

 has been assumed in many of our calculations. The 

 condition of stability depends only on the areas and 

 positions of the aeroplanes relative to the centre of 

 gravitj', and is independent of the inclinations or 

 angles of attack of the planes, the oscillations remain- 

 ing finite when the planes are parallel. This condi- 

 tion of stability is generally satisfied in any arrangre- 

 ment which satisfies the other conditions of stabilitv. 

 It must not be overlooked, though it is very unlikely 

 to give trouble. The corresponding trajectory cr 

 curve of oscillation is independent of the velocity, the 

 actual time rates of oscillation and decay being pro- 

 portional to the velocity. 



In the slow oscillations the variations of velocitj' in 

 the line of flight are a predominating feature. The 

 trajectory is wave-like, the crests of the waves being 

 more pointed than the troughs, and the descending 

 parts steeper than the ascending ones. This is 

 evidently the type of oscillation studied by Mr. Lan- 

 chester. One condition of stability is that the front 

 plane (or planes) must be inclined at a greater angle 

 than the rear ones. The second condition depends on 

 the type of machine. 



The terms "monoplane" and "biplane," as usually 

 defined, refer to the question of whether a machine 

 has not or has superposed planes. .According, ho^- 



