NA TURE 



241 



THURSDAY, MAY 24, 1917. 



EXGIXEERING AEROD YNAMICS. 



The Flying-Machine from an Engineering Stand- 

 point. By F. W. Lanchester. Pp. viii-M35. 

 (London: Constable and Co., Ltd., 1916.) 

 Price 45. 6d. net. 



'X'HE greater part of this book is a reprint of 

 J- the James Forrest lecture delivered by the 

 author, and referred to already in N.ature of 

 August 13, 191 4. In the preface Mr. Lanchester 

 lays so much stress on the new section called 

 "The Theory of Sustentation " that no excuse is 

 necessary for confining the remarks of this notice 

 to the theory. 



After reading the preface and the considerable 

 claims made for the theory, a student of the sub- 

 ject will naturally look for a theory founded on 

 the equations of motion, or at least on grounds 

 not essentially experimental. It is, then, a sur- 

 prise to find an almost complete . absence of 

 mathematical formulae and reasoning, and any 

 knowledge of orthodox hydrodynamics leads to 

 questions as to the validity of many of the steps 

 taken. After a time it is inevitable that the 

 student will turn for relaxation to Kutta, whom 

 Mr. Lanchester claims as a kindred spirit. 



Kutta 's mathematical problem is not difficult 

 to follow, though doubts may be felt as to the 

 physical meaning- of his results. He takes as 

 the subject of his analysis the two-dimensional 

 flow of an inViscid fluid round a lamina in the 

 form of a circular arc. Except for the case of 

 a plane lamina moving in its own plane, it is well 

 known that the Eulerian system of equations 

 leads to a solution in which the velocity is 

 infinite at two points, the leading and trailing 

 edges of the lamina. To- meet this difficulty 

 Kutta introduces a circulation of the main mass 

 of fluid, and chooses the amount of the circula- 

 tion so as to avoid one of the infinite values for 

 the velocity. There does not appear to be any j 

 limit to the angle of incidence or the curvature of { 

 the arc beyond which Kutta 's method cannot be ' 

 applied. To deal with the second point of I 

 infinite velocity Kutta found it necessar}' to i 

 change from a lamina to a body having a rounded | 

 leading edge, and this idea was put into better 

 mathematical form by Joukowsky. 



Kutta compares his calculated forces with 

 those observed in wind chai^els, and claims 

 good agreement after makin^^n allowance for 

 skin friction. This is essentially an empirical 

 justification, and no attempt appears to have been 

 made to show that the cyclic motion of an inviscid 

 fluid has any mathematical connection with the 

 real motion of a viscous fluid. 



Having read Kutta, one returns to Mr. Lan- 

 chester. The difficult>' of two points of infinite 

 velocity is met bv saying that if the section is 

 properly shaped the flow is "conformable," i.e. 

 Includes the lamina in one of the stream lines, and 

 further attention is confined to "conformable" 

 NO. 2482, VOL. 99] 



wing shapes. In addition to a cyclic motion Mr. 

 Lanchester introduces a pair of trailing vortices, 

 which appear to extend Kutta 's analysis from 

 two dimensions to three dimensions. These 

 vortices appear as though set up in the conven- 

 tional inviscid fluid- The mechanism is not 

 shown to us, and nowhere in the theory is there 

 a clear distinction between the irrotational cyclic 

 motion and the rotational flow in the vortices, 

 nor even an estimate of the strength of the cyclic 

 component. The theory ends with a formula 

 for calculating the "sustentation" and "the 

 aerodynamic resistance." To compare the 

 results with those for a real fluid Mr, Lanchester 

 estimates from experimental data a quantity 

 which he calls "direct resistance," and which 

 he adds directly to the "aerodynamic resistance." 

 In the writer's view the theory, however excel- 

 lent as an empirical formula, has no independent 

 basis, and its utility is determined by the number 

 of experimental observations which it will hold 

 together. 



Conventional hydrodynamics is interesting 

 as a mathematical study, but work based 

 on the properties of an inviscid fluid can scarcely 

 be said to lead to results of value in explanation 

 of the observed motion of real fluids. The 

 equations of motion for a viscous fluid were given 

 to us by Stokes, and are to be found in Lamb's 

 treatise on hydrodynamics. For slow motion 

 and very viscous fluids there is reason to believe 

 that the motion is steady, and some solutions of 

 the equations have been obtained, the most 

 important being that of the flow in capillary tubes 

 which leads to our best-known method for deter- 

 mining the value of the coefficient of viscosity. 



Osborne Reynolds showed that the mathemati- 

 cal assumption of steady motion fails to acco\int 

 for observations when the fluid motion is rapid, 

 and failure has led to approximations instead of 

 to a fuller solution of the equations of motion of 

 a viscous fluid. The physical conditions of the 

 problem are usually modified by removing any 

 trace of viscosity in order to make a simpler 

 mathematical problem, Mr. Lanchester adopts 

 this method in part, and is supported by all the 

 standard treatises in the world. To a serious 

 student of fluid motion such half-hearted theories 

 produce difficulty and do not help to an under- 

 standing of the subject in its physical bearings. 



Failure to satisfy the conditions observed may 

 arise from defective equations or inability' to solve 

 correct equations. The evidence provided by 

 Stanton and Pannell's experiments on surface 

 friction in pipes appears to leave no doubt that 

 the definition of viscosity derived from slow 

 motions is sufficient for turbulent motion, and we 

 must conclude that inability to deal with the 

 mathematical analysis is the root trouble. Aii 

 examination of the problem immediately brings 

 into prominence a . fundamental difference 

 betAveen inAnscid and viscous fluids, the first of 

 which may have a tangential velocity relative to 

 a surface with which it is in contact, whilst the 

 second has no relative velocity. It is not even 



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