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Aviation History
1914
1914 - 0769.PDF
JULY 17, 1914. water, are in substantial agreement—in tact, in very close agreement —provided that they are put in their proper perspective, with due consideration to the laws of dynamic similarity. (Compare memo randum cited, also addendum to same by Lord Rayleigh ) The final conclusion given in the memorandum under discussion is expressed in graphic form in Figs. 38a and 38A, in which abscissa; represent the quantity LV (the product of the linear dimension * (/OGHT) Fig. 39. in feet by the velocity in feet per second), and in which ordinates represent the coefficient of skin friction. Three curves are shown ; the upper curve is the double-surface coefficient for air, for which I employ the symbol g, the lower curve (solid line) is the single-surface coefficient (half the value of the former), the dotted curve is the coefficient for water. In Fig. 38a, LV values may be read from 20 to 1,400. In Fig. 38b is given a graph for lower values. tSlt is a point not without interest that, for geometrically similar aerofoils, the weight sustained varies as (LV)1, consequently for any given- value of LV the weight is constant. In other words, as already shown, for least resistance P = Cp V2, where C is a constant whose value is round about 0*32, or if k LP represents the area, and W=weight, W=0*32 kp (LV)2. Therefore assuming good design (max. lift/drift), and some definite value of aspect ratio (to fix the value of the constant k), the coefficient of skin friction is determined by the weight of the machine, and is the same whatever the designed velocity may be. Skin-friction has a habit of playing an elusive part in actual resistance phenomena, and the subject in practice is full of pitfalls. In the case of a plane moving edgewise, it may frequently happen that skin frictional resistance will virtually disappear, the leading edge of a plane such as used by the late Professor Langley will by its bluffness set in motion a certain quantity of air, and this moving air subsequently washing the surfaces of the plane will reduce the skin-frictional resistance to something immeasurably small; as pointed out by me in discussing Langley's work, this was one of the causes that led him into error. Another case where the coefficient of skin friction may be abnormally low is that of the inclined plane at a small angle of incidence; in Aerial Flight, vol. i, the matter is dealt with on page 264, article 182 ; it is pointed out that as a deduction from gliding experiments made with the ballasted plane, and calculations based on same, the coefficient of skin-friction is in effect less than is ordinarily the case, and the explanation is offered that the upper surface of the plane being to a certain degree a " dead-water region " the coefficient may in this case be only that of the single surface. This conclusion has received striking confirmation in connection with some experimental work recently carried out at the National Physical Laboratory. I consider it probable that in the case of the pterygoid aerofoil, that is to say, the aerofoil of arched section, such as shown at the foot of Fig. 39, the skin friction may in effect be abnormally high * Ordinarily the linear dimension, represented in the laws of dynamic similarity by L, presupposes geometrical similarity, i.e., geometrical form as an invariable. In the present usage, owing to the thinness of the layer of air affected, L may be taken as the linear dimension of the plane in the direction of •motion. owing to the augmented velocity with which the air flows over the upper surface. This, speaking generally, is not altogether compen sated by the lower velocity on the under side. The velocity of the air in the vicinity of the aerofoil can be deduced approximately from the ordinary laws of fluid motion from the local pressure. Now pr:ssure curves have been made of several different sections of aero foil by the N. P. L. ; the curve shown in Fig. 39 may be taken as cu u U I Fig. 40. roughly typical of the pressure graph for mid section of any well- shaped aerofoil at or about its angle of least resistance. The ordinates downwards from the zero datum line being the negative pressures on the upper surface of the foil, and the ordinates measured upwards from the said datum line being the positive pressures on the under surface, in both cases measured above and below atmo sphere. Plotting the same curve in Fig. 40 and taking a datum line corresponding to zero motion, ordinates will represent fluid tension (negative pressure) and the velocity at every point is repre sented by the square root of its ordinate ; hence the skin friction will vary as the ordinate itself, and, referring to Fig, 40, the effective coefficient of skin-friction will be greater than normal in the relation of the mean of the ordinates a b a c to the ordinate a d. Referring again to Fig. 39, it may be observed that the mean pressure increase on the under face is approximately one-fourth of the mean pressure decrease on the upper face ; taking this proportion as a basis, I give, in Fig. 41, graphs _ of the augmenta- •* tion of the skin ' friction as a func tion of the aerofoil pressure constant; the normal coeffi cient proper to the LV value in ques tion being read on the ordinate corre sponding to pres sure constant = zero, on the left hand of the Figure. In the case, for example, of the normal value of the coefficient being 0-008, it will be seen that for a pressure constant=0'32 the aug mented coefficient will be nearly o-oi. We thus begin to obtain values approaching those that I have found to apply in connection with the theory of least resistance. If, in addition to the above, we allow an addition to represent form resistance, as has been found by Prandtl in the case of the ichthyoid body, and which is due to the degeneration of the stream-line system consequent on the appearance of the frictional wake, we might expect the effective direct resistance of the aerofoil expressed in terms of skin friction equivalent to a coefficient of 0"oi75, which is in full and complete agreement with experience. The assumption here is that the proportion of the added form resistance bears the same ratio to the true skin friction, approxi mately 3 : 4, as commonly found in the case of the ichthyoid body. 769
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