Frederick William Lanchester

“ There is not only equilibrium between the angle of the plane and its direction of motion as above demonstrated, but also between the gliding angle and the velocity of flight; thus if the velocity is deficient, so that the weight is insufficiently sustained, the gliding angle and the component of gravity in the line of flight automatically increase and the aerodrome undergoes acceleration. Conversely, if the velocity is excessive, the gliding angle (and so the propulsive component) diminishes, and the velocity is thereby reduced. [13] ”

“ The pressure on a circumscribed area of the surface of a solid cannot be given by any formula, or, in fact, at all, unless the form of the remainder of the solid be known; any equation or theory that attempts to give a solution for the individual elements of the surface of a body independently of its whole form, is of necessity unreliable and in general entirely misleading. ”

“ A limiting width will evidently be approached asymptotically when the number of planes becomes very great, and the limiting condition is that which most nearly resembles that of our hypothesis, for the whole depth of the fluid is then acted on with approximate uniformity, and the sweep of each plane will be fairly represented by the area included between any two adjacent planes. Hence the value of deduced from experiments with pairs of superposed planes may he less than its true value according to the requirements of hypothesis. ”

“ The Newtonian Theory Modified; the Hypothesis of Constant “Sweep.”—In the theory of the Newtonian medium, for a given velocity the mass of fluid dealt with is proportional to the sine of the angle \beta ; in a real fluid it is evident that the particles cannot cross each other's paths as depicted in Fig. 92, but will be constrained to move in a congruent manner. Thus if one layer be supposed to strike the plane and follow its surface, the next layer will be in turn deflected and move parallel to the first, and so on. ”

“ In actual planes it is impossible to do away with thickness, so that in addition to skin friction there must be the possibility of a longitudinal pressure component due to the shape of the plane. Thus, if the plane be of “fair” form, i.e., a stream-line solid based on an axis plane (Fig. 104) , the pressure distribution, not being in any sense symmetrically disposed, may conceivably possess a longitudinal component of quite considerable value ”

“ Likewise if the angle become too great the centre of pressure will recede and the resulting couple will tend to diminish the angle, and again the equilibrium is restored; thus the conditions are those of stable equilibrium, the plane tends to maintain its proper inclination to its line of flight. ”

“ The most direct disproof of the Newtonian law is to be found in experiments with the falling plane. It is found that if a horizontal plane, suitably mounted in vertical guides, be allowed to fall freely, the time of fall may be increased almost indefinitely by imparting to it a simultaneous horizontal motion. ”

“ Our knowledge of the behaviour of the plane inclined to its direction of motion is in the main confined to the immediate results of experiment, extended it may be by the drawing of smooth curves through the observed points plotted on a co-ordinate chart. ”

“ It is probable that for planes of less than a certain proportionate thickness the augmentation due to the edge area is imperceptible, and that for such thin planes edge effect can be ignored. Equally it is probable that for planes of rectangular section of more than a certain proportionate thickness the skin-friction disappears and the total resistance may be assessed as edge effect. ”

“ The determination of the value of the coefficient of skin-friction, .
The most satisfactory results can be obtained by employing planes of mica, of only a few thousandths of an inch in thickness, the ballasting being effected by a split lead shot, as shown in the figure. Such planes show a perfection of equilibrium that appears to be unattainable with any other material than mica; it is also important that the ballast should be applied in a compact mass centrally and not distributed along the front edge. ”

“ It appears to the author that the augmentation of pressure will be greater than might be supposed from the foregoing reasoning, for the abandoned air, having motion in the same direction as the plane, will impede the flow of air round the following edge and so maintain a greater pressure difference between its two faces ”

“ It is found that for the normal plane the geometric and pressure centres are coincident, but that as the plane is inclined the latter is displaced towards the leading edge, the displacement of the centre of pressure increasing as the angle made by the plane to its line of flight becomes less and less. This is shown in the form of a diagram in Fig. ”

“ In a case such as the present, where a high degree of accuracy is not important, and not attainable, such a range may be said to extend to as much as ten or fifteen degrees, and thus include practically the whole range of angle that can be usefully employed in the application of the aeroplane to aviation. ”

“ The square plane may be taken as the type of greatest simplicity which includes generally planes of square proportion; such planes are not affected seriously by considerations of “aspect,” although doubtless a square plane will not give exactly the same results in diagonal as in square presentation. The latter is always assumed in the absence of an explicit statement to the contrary.
In Fig. 93, in which ordinates represent the relative pressure on the plane for all angles from degree 0 to 90 degrees, we have curves plotted as follows:—
Fig. ”

“ In order to improve the “sense of direction” it is found to be advantageous to “dog-ear” the front corners, slightly turning them upwards. It may be further noted that the rectangular form is very advantageous; in general other forms give inferior stability. ”