October 29, 1908] 



NA TURE 



67 1 



line at all, three conditions are required. It is not 

 sufficient that the drift should equal the thrust of the 

 |)ropeller (supposed horizontal), and that the lift should 

 equal the weight. There is the third condition that 

 the three forces, weight, propeller thrust, and resul't- 

 ant air resistance, must pass through one point, or an 

 equivalent condition obtained by equating moments. 

 If this condition is satisfied, but not otherwise, the 

 machine is properly balanced, and may fly straight. 

 But its flight is not necessarily stable, and it may upset 

 at any moment. To find if it is longitudinally stable 

 we must examine what happens if it deviates from its 

 course and begins to pitch. To specify its motion at 

 any instant in this case three variables are required, 

 as every student of elementary mechanics ought to 

 know. The resultant air resistance will also be 

 altered, and to specify the new resultant three other 

 variables will be required. The connection between 

 these and the pieceding three depends on the laws 

 of aerial resistance. This connection is specified by 

 certain " coefficients of stability " the values of which 

 are necessarilv based on experimental knowledge. On 

 the assumption that if these are known, and the weight, 

 position of the centre of gravity and moment of inertia 

 of the flying-machine are known, the oscillations have 

 been worked out and the condition of stability de- 

 termined. This condition is conveniently expres- 

 sible in terms of a critical velocity, it being neces- 

 sary for stabilitv that the velocity of a machine flying 

 in a given manner should not be less than the corre- 

 sponding critical velocity given by theory. In the case 

 of a balloon we have learnt, on the other hand, that 

 the velocity must not be greater than the critical 

 velocity. The existence of a critical velocity was re- 

 cently pointed out by Mr. Lanchester in a communi- 

 cation to the British Association, and it is to be hoped 

 that his remarks will carry some weight with the pre- 

 eminently vinpractical " practical men " who aliound 

 in this country. 



When these results were obtained it still remained 

 lo reduce the problem of stability to the form of rules 

 which were not beyond the ken of the ordinary work- 

 ing mechanic, and, further, to show how the necessary 

 data could be obtained from experiinents on models. 

 Had the present writer been able to give his whole 

 time to this work the problem of stability would have 

 l)een thrashed out to the bitter end long ago. Looking 

 at the matter perfectly impartially, and in view of 

 many cases of a similar kind that may occur in almost 

 any branch of science, the question may be asked 

 whether it is desirable that the completion of such 

 investigations should be delayed indefinitely because 

 those who are prepared to undertake them are de- 

 barred by their professional duties from giving the 

 necessary time? The cost of a mathematician's time 

 in working out such a problem would probably not 

 exceed the cost of building a single flying-machine, so 

 that the existing method of trial and error is certainly 

 not to be recommended on the ground of cheapness. 



The critical velocity of a machine moving in air 

 depends on the position of its centre of gravity, the 

 moment of inertia of the machine, the form, dimen- 

 sions, and position of its supporting surfaces and tail, 

 and the position of its propeller. In some cases 

 stability may be increased by increasing the moment 

 of inertia; in other cases it may be decreased. Our 

 work tended to show that a machine might become 

 unstable if the moment of inertia were either too large 

 or too small, other things being kept constant. But 

 when the mathematical theory has been worked out 

 in every detail, the coeflicients of stabilitv for any 

 given machine must necessarily depend on experi- 

 mental data. Now the average mechanic understands 

 the importance of finding the resultant thrust on an 



NO. 20; >, \OI,. , '-, ] 



aeroplane, but he does not realise the necessity uf 

 finding the centre of pressure through which this 

 thrust acts. The result is that experimental data are 

 far from complete on the very points in which they 

 are most wanted. If, however, we were to try and 

 base our stabilitv calculations entirely on the exper- 

 mental data obtained for the separate aeroplanes, we 

 should not only have a good deal of calculation to 

 perform, but at the end we should have omitted to 

 take account of the resistance of the framework, car, 

 and rider. A simpler plan would be to construct a 

 stabilimeter ' for experimenting on models as a whole 

 instead of with single aeroplanes. When a machine 

 begins to pitch and rock it has a rotatory as well as 

 a translatory motion, and the rotation may, and cer- 

 tainly does, influence the magnitude and position of 

 the resultant thrust of the air. No calculation of 

 stability can be considered valid which does not take 

 account of this influence. One might just as well 

 neglect the wedges of immersion and emersion in 

 working out the stability of ships. On this turning 

 effect, as it might be called, we have no experimental 

 data whatever. But if a model is to be tested in a 

 stabilimeter, the mechanic will require simple work- 

 ing rules for applying his results, and these must in 

 the end be laid down by mathematicians. In parti- 

 cular he will have to be told whether he can improve 

 the stability of his model by altering the positions of 

 his aeroplanes or the moment of inertia of his machine. 

 A number of questions require answering, and the 

 answers require putting in a simple form. Here is 

 one example : In a dirigible the critical velocity 

 represents the greatest velocity consistent with 

 stability ; in an aeroplane system it represents the 

 least velocity. If, starting with a dirigible, we add 

 aeroplanes and reduce the size of the balloon gradu- 

 ally down to nothing, we must come across an inter- 

 mediate type which is either always stable or always 

 unstable. What is this type? 



The recent flights show what can be done in 

 aviation bv a person possessed of skill and experience. 

 They are a necessary factor in the development of 

 artificial flight. The problem is quite in a different 

 position from what it was a year ago. But if flying- 

 machines are to be made accessible to the million, the 

 sooner English aeronauts learn mathematics or get 

 someone to do the mathematics the better. At the 

 present time a great deal of rubbish passes off as 

 mathematics which is quite unworthy of the name. 

 We may instance the use of Taylor's expansion in 

 infinite series to prove, not even that the reciprocals 

 of a harmonical progression form an arithmetical pro- 

 gression, but that the general term of this arith- 

 metical progression is of the form written down in 

 elementary text-books on algebra.- Or, again, the 

 discussion of the details of an example which would 

 be in a more proper place in a school text-book or 

 examination paper on elementary trigonometry.^ 



Mr. Lanchester's book, of which the first volume 

 has been noticed in Naturk and the second will be 

 reviewed shortly, should open the eyes of many would- 

 be aeronauts as to the complex theoretical investiga- 

 tions which have to be mastered in any attempt to 

 reduce the problem of flight to an exact science. 

 .Mthough the author has purposely avoided, so far as 

 possible, the use of mathematical formulae, the reader 

 who aspires to revolutionising the flight problem with- 

 out making actual experiments and without an ex- 

 tended study of mathematical or physical principles 

 will find the book a pretty hard nut to crack. 



The time has, however, passed when any useful 



' Cornhill Magazine, May, 1U07. 



2 Avr-07inutical Journal, -April, igo8, p. 27. 



•* Ac 07iautUal Journal, January, 1904, pp 4, 5. 



