Frederick William Lanchester

“ To be definite, we may say that the general nature of the fluid motion can be shown to depend upon the major function of the wing, i.e., the support of the weight; the wing form must then conform to the motion so derived, and the detail of the fluid motion in turn will depend upon the more minute character of the wing form. Such indefinite process of adaptation and readaptation as the above implies is one to which the methods of evolution appear to be eminently adapted, but to which the methods of calculation are ill suited ”

“ Consider a fluid prismatic column formed by imaginary vertical surfaces touching the edges of the aerofoil and continued downwards to the earth's surface and upwards indefinitely. Adopting the hypothesis that the fluid is inviscid, all forces acting on the column from the surrounding fluid must be normal to its surface, and have no vertical component. The only vertical forces acting on the column are therefore the weight of the loaded aerofoil, acting downwards, and the pressure on the base of the column due to the distribution of the weight W on the earth's surface. ”

“ There is at first a circulation of air round the edge of the plane from the under to the upper side, forming a kind of vortex fringe (Fig. 61) , the air all round the edges of the plane being in a state of rapid upward motion. If now we impress upon the plane a simultaneous horizontal motion, it is evident that the air encountered by its leading edge will be in a state of upward motion, and it would appear probable that this up-current, in front of the advancing plane, would only cease to exist when the horizontal velocity of the plane becomes equal to the velocity of sound. ”

“ When a loaded aerofoil is dynamically supported by a fluid, we know that its weight is eventually sustained by the surface of the earth, and that the transmission of the stress is effected by the communication of momentum from part to part, and is thereby distributed over a considerable area as a region of increased pressure. ”

“ The features in common may be taken, on the doctrine of natural selection, as consequent on the form of the fluid motion essential to flight, although, physically speaking, it is the fluid disturbance that depends upon the form of the wing. ”

“ When the amplitude of motion becomes sensible, there is no doubt that the streamlines react on one another in a manner not accounted for by the form of field contemplated, i.e., that of the quiescent state. ”

“ Therefore, adopting a method of expression common in mathematical work (but not so frequently employed in direct physical demonstration) , we may say that if we take as hypothesis a small finite load, so that the actual motions of the fluid be small finite quantities, the expenditure of energy in sustaining the load will be zero, neglecting small quantities of the second order. ”

“ Reverting to the case of a body supported by the communication of momentum to a number of independent material particles, it is evident that the particles projected downwards eventually give up their momentum on striking the surface of the earth. ”

“ Now the factor that must limit the thickness of this stratum is evidently the size and shape of the plane, for the more remote layers of the fluid only escape by the fact that a circulation takes place from the side of greatest to the side of least pressure, which circulation depends chiefly upon the size and shape, and but little upon the angle of the plane. The elasticity of the air might become sensible if the velocity were sufficient, but at ordinary velocities this factor is unimportant. ”

“ We can conceive that these vortices are formed after the manner indicated in Fig. 83, in which an aerofoil is represented in end elevation with the flow indicated diagrammatically. We may suppose that the air skirting the upper surface of the aerofoil has a component motion imparted towards the axis of flight,
Fig. 84. and that skirting the under surface in the opposite direction, so that when the aerofoil has passed there exists a Helmholtz surface of gyration. This surface of gyration will, owing to viscosity, break up into a number of vortex filaments or vortices after the manner shown. ”

“ Energy in the Periptery.—A body in motion in a fluid is known to carry with it kinetic energy due to the fluid disturbance in addition to that due to its proper mass (§§ 81, 84) . A superposed cyclic motion adds to the energy so carried. A cyclic motion around a cylinder or cylindrical filament, or round about a plane, in an infinite expanse of fluid contains an infinite quantity of energy (§ 85) , and the resulting peripteroid motion for these cases will consequently require an infinite quantity of energy for its production. ”

“ The immediate function performed by the sectional form of the aerofoil is to receive a current of air in upward motion and impart to it a downward velocity, the whole air being dealt with possessing relatively to the aerofoil a superposed motion of translation. It would appear that any appropriate smoothly curved form, whose leading and trailing angles (Fig. 68) are conformable to the lines of flow, might be regarded as fulfilling the necessary conditions, the essential feature evidently being that neither edge shall give rise to a surface of discontinuity. ”

“ Fig. 57. The discovery appears to have been made as a matter of practical experience, and, as often takes place under these circumstances, the theory given by the inventor in his specification is erroneous. Just, however, as in patent law an inventor's theory, however unsound, is not held to invalidate an invention, so in the matter of discovery, the fact that a discoverer does not fully understand the fact that he has been the first to ascertain, does not in any way detract from the credit due. ”

“ In § 90 it was shown that the disturbance peculiar to the neighbourhood of the aerofoil possesses angular momentum, and it was inferred that this being the case, the disturbance comprises a cyclic motion, for otherwise it must involve rotation, which is excluded by the nature of the hypothesis. We are consequently confined, in an inviscid atmosphere, strictly to the case where the aerofoil is of infinite lateral extent, for a cyclic motion is only possible in a multiply connected region. ”

“ The consequence is that peripteroid motion is theoretically possible in the case of a cylinder of infinite extent, no matter what its cross-section. This conclusion applies naturally only in the case of the inviscid fluid; in a real fluid we are threatened with discontinuity. The position is analogous in every way to that of simple translation. In the inviscid fluid all bodies are of stream-line form, in real fluids only those that in their motion do not set up a discontinuity. ”

“ Thus in the case of a loaded aerofoil of finite lateral extent, there is a continual loss of energy occurring, and a source of power is consequently necessary to maintain the aerofoil in horizontal flight.
In addition to the residual vertical motions of the fluid, of which the causes have just been discussed, there must also be horizontal counter-currents formed simultaneously with those in a vertical direction, the horizontal and vertical motions being the horizontal and vertical components of the actual resultant motion of the fluid. ”

“ Let us then assume for our convention that the depth of the layer affected for a plane of given shape depends upon its linear dimension and is constant in respect of angle, the latter being supposed to be of small magnitude. Then, since under the pre- sent supposition the lines of flow will require to follow the surfaces of the plane (the fluid being unable to bounce off as in the previous case) , we have
where is a constant, and by (1) we obtain:—
This result for planes of certain general proportions, at small angles to the line of flight, agrees closely with experiment. ”

“ Peripteroid Motion in a Simply Connected Region.—The problem presented in the case of an aerofoil of finite lateral extent is, from the present standpoint, one of some difficulty, inasmuch as the region under these circumstances becomes simply connected, so that cyclic motion can no longer exist, and rotation in some form constitutes the only solution. ”

“ The fluid in the vicinity of the aeroplane is in a state of motion, and consequently possesses energy, but under the conditions of hypothesis the quantity is less than any assignable finite magnitude, that is to say, infinitesimal, but the motion remaining in the fluid and the continued energy expenditure are of zero value considered as infinitesimals of the same order. ”

“ Following out this idea, we should obtain, for an inviscid atmosphere, a system consisting primarily of a vortex hoop or halfring, loaded in the centre by the aerofoil (Fig. 81) , and whose energy will be perfectly conserved, the aerofoil and its supporting vortex lying in a plane at right angles to the direction of flight. Such a system in a fluid that is truly inviscid would be uncreatable and indestructible, just as in such a fluid a vortex ring is uncreatable and indestructible. The system of static forces called into play is represented diagrammatically in Fig. ”

“ In practice, it will be shown later in the work, the question of wing-form, especially with regard to the extremities, is not decided by aerodynamic considerations alone, and that the question of equilibrium is involved. ”

“ Wing Form,—Arched Section.—The most salient characteristics of wing form are common to birds of widely different species and habit of life. In spite of variations in detail and in general proportions, there is a certain uniformity of design and construction that cannot fail to impress even the most superficial observer. ”