482 TRANSACTIONS OF SECTION G. 



two heads : one dealing with the lift and resistance of the cambered plane, the 

 other dealing with stability, which has always been the most important factor 

 making for progress in aviation. 



Calculating Lift. — In the mathematical section, an hypothesis that aeroplanes 

 are supported in flight by the inertia of the air, leads to the necessity of finding 

 plausible expressions for mass and acceleration. 



Two dimensions of the mass of air deflected are plausibly functions of the 

 span and chord of the plane; the third, which defines the depth of the stratum 

 and is known as the ' sweep ' is taken as an empirical function of the chord, but 

 this connection needs discussion. Acceleration is obviously a function of the 

 angle of the plane, but difference of opinion exists as to how that angle should 

 be measured. A suggestion is put forward in favour of the ' angle of deflection ' 

 measured at the point of intersection of tangents drawn to the leading and 

 trailing edges of the plane, which needs discussion. From the assumed premisses 

 a rough and ready formula for lift has been evolved (see summary of formulas). 



Skin Friction. — In order to extend the premisses to cover a plausible expres- 

 sion for the resistance to flight and the power expended thereon, it is necessary 

 to adopt a value for skin friction. Zahm's experiments have been accepted as 

 data (see summary of formula?), but the whole subject needs discussion. Skin 

 friction is of such fundamental importance in aerodynamics that it is imperative 

 to put it upon an accepted basis analogous to the position occupied by normal 

 pressure. 



Coefficient of Flight. — The coefficient of flight, representing the resistance per 

 unit load, may be shown to be independent of speed, but to depend on the angle 

 of the plane and to have a minimum value depending on the coefficient of skin 

 friction. On the present hypothesis, the minimum coefficient of flight obtains 

 with planes of a very small effective angle (about 5°), such as would necessitate 

 flying at much higher speeds than have hitherto been realised. The existence of 

 an angle of least resistance is very important in connection with the problem of 

 variable speed machines. 



Body Resistance. — Body resistance in a practical aeroplane is a supplementary 

 resistance to that of the planes, and should always be considered as such. It 

 stands in the way of realising the higher speeds that would lead to the use of 

 more efficient planes, but by enclosing all the principal masses in casings of stream- 

 line form a plausible means is afforded of considerably reducing this quantity. 

 A comparison of the coefficients of normal pressure and skin friction indicates a 

 very largo possible saving in this direction. In bodies of streamline form the 

 advantages of a hemispherical head are worthy of consideration. 



Stability. — Stability in a flying-machine is either natural as a result of form, 

 automatic as the result of self-acting mechanisms, or controlled by human intelli- 

 gence. No particular progress has been made along the lines of automatic stability, 

 although the use of gyroscopes and wind-vanes to operate relay mechanisms has 

 frequently been suggested. Natural stability has, however, been realised to some 

 extent and, coupled with modern expert control, the combined result has reached 

 an extraordinarily high degree of perfection considering the short period of 

 evolution. 



Natural stability in its elementary form may be readily demonstrated by 

 means of paper models. In practical aeroplanes, natural stability in the longi- 

 Indinal vertical plane is mainly based on the principle- of the dihedral angle. 

 Natural stability in the lateral vertical plane is also commonly based on the same 

 principle, but alternative systems, one of which is the arched wing, have been 

 tried. The arched wing and the dihedral being apparently diametrically opposite 

 in principle, attention is drawn to two orders of stability, 'stiff' and 'rollincr.' 

 The relative possibilities of successful development along each line is well worthy 

 of discussion. 



The ascentric centre of gravity, in which the principal masses are placed well 

 below the centre of pressure, is frequently suggested as a stabilising principle, 

 but the permanent existence of a couple between the centre of gravity and the 

 centre of pressure indicates liability to pronounced oscillation, and the system 

 does not find general favour. In connection with the under-carriages of aero- 

 planes, the advantage of landing direct on skids is urged, and in connection with 

 the power-plant, the possible disturbing influence of the gyroscopic force of 

 heavy revolving masses is worthy of notice. 



