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Aviation History
1922
1922 - 0689.PDF
NOVEMBER 23, 1922 Involuntarily we now ask how it happens that the air does not separate on even a moderate increase in the diameter of the cross-section. The explanation lies in the viscosity of the air or, in most cases, more correctly, in an apparent viscosity, which m turbulent phenomena is conditioned by the turbulence itself. The case may be pictured qualitatively as follows :—The fluid has a tendency, on account of its inertia, to flow straight ahead, instead of following the curved surface, but then there must exist, between it and the surface of the wing, a quiet or an eddying " dead-water " region. This " dead water " is now carried along by friction (or the effect of viscosity), and must be constantly replaced (Fig. 4) Now, when the viscosity is so great that, in a given time more fluid is carried away than can flow in, the " dead water " ia&$ therefore be assumed that the influence of the curvature of the flow plays a role of some importance with a given wing section with a moderately large camber, but nothing further is thereby gained than would be gained by a larger camber. The extraordinarily large increase in the maximum lift cannot therefore be thus explained. The following consideration may be of more importance. The front wing lies in a region of increased velocity. Now, since the force of the air is proportional to the square of the velocity, it is evident that the lift on the front wing is thereby considerably increased. This argument has but one excep tion, namely, that the reverse is true of the rear wing, so that for the combination of the two wings the two effects neutralise each other. In calculating the relations for an Fig. 3.—Flow about a wing section at an angle of attack of 8 degrees. disappears and the flow follows the surface of the wing (Fig- 3)- Such are the general outlines of the phenomena which produce lift and which also limit its magnitude. Unfortu nately, these phenomena cannot be treated quantitatively by theoretical methods. We must therefore content our selves with qualitative illustrations, and will now endeavour to explain, on this basis, the action of the slotted wing. For the sake of simplicity, we will assume that there is only one slot. Such a wing section may be imagined as a biplane with a very great positive stagger and a very small distance between the wings. Some justification for this conception proceeds from the fact that, even with an ordinary biplane, the maximum lift is increased by a positive stagger. According to biplane measurements published by myself in the fourth volume of " Zeitschrift fur Flugtechnik und Motorluftschiffahrt," the maximum CL without stagger was 100, with a positive stagger of 300 it was'no and for one wing alone it was 106. Similar results were also obtained in England (Technical Report of the Advisory Committee for Aeronautics, 1915-16, Rep. 196, Sect. II). Though the differences are not great, they would evidently be greater Fig. 5.—Change in pres sure distribution due to mutual influence of both wing sections. 1. Undis turbed pressure distri bution. 2. Disturbed pressure distribution with unchanged angle of attack. 3. Pressure distribution with increased angle of attack. For rear wing curves 1 and 3 coincide. Fig. 4.—Flow about a wing section at an angle of attack of 19 degrees. unstaggered biplane we even obtain a smaller maximum lift than for the two wings alone, and this result is confirmed by experiments. The relations are, however, somewhat changed by staggering. We must go into this more thoroughly. We will first consider the arrangement with two wings of about the same size, in which the relations stand out the clearest. The front wing, taken alone, would have a pressure distribution somewhat as shown by the fine line on the left of Fig. 5. Now, if we bring the rear wing, which has about the same pressure distribution by itself, into proximity with the front wing, the trailing edge of the latter will lie in a region of great velocity, and correspondingly small pressure, produced by the rear wing. The leading edge of the front wing, on account of its greater distance from the rear wing, lies in air that is much less disturbed, and consequently in a region of nearly normal pressure. The leading edge of the front wing is, accordingly, not much affected by the pressure on the rear wing, while the pressure on the trailing edge of the front wing is diminished. We will therefore obtain, for the front wing, a lift distribution corresponding somewhat to the dash curve in Fig. 5. Through this modification of the pressure curve, the pressure FIG. 6 ^^z^^^^ V77777777T7TTTTT^. Fig 6. Double Venturi tube with corresponding pressure distribution. Pressure in outer tube shown in plain line, in inner tube in dash line. if the stagger were increased and the interval between the wings diminished. , ,. , We will first consider only the front wing, and discuss how its characteristics are affected by the rear wing, from tne theory of the biplane, we know that the flow is here obliquely upward. This affects the lift-drag ratio, but not tne maximum coefficient of lift, which here alone interests us We also know that, at this point, the flow is obliquely upwards. This has about the same effect as increasing By increasing the latter the maximum increase on the suction (upper) side becomes much flatter- On the other hand, we know that the limit of the lift is determined by the steepness of the pressure curve. It is therefore evident that we may now further increase the angle of attack until the inclination of the pressure curve again reaches its limit value (heavy line in Fig. 5). Since the velocity has become greater everywhere, the pressure curve may climb steeper than before. As is obvious, the lift, which is represented by the area enclosed by this curve, has become considerably greater. Let us now turn our attention to the rear wing. Here we the wing camber. &y IMUC<KU.6 «— -- limited lift may actually be increased though only to.a. ve y ^ ^ corresponding phenomena. The front wing produces on degree and at the expense of the lirt-drag^^ ^ ^^ ^ leading edge o the rear wing a decrease in vel0city and wing is similarly affected by the curvature 689
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