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Aviation History
1938
1938 - 0267.PDF
JANUARY 27. 3 THE ATRCRAFT ENGINEER SUPPLEMENT TO FLIGHT 96c against the position of maximum camber in Fig. 4.Ki ®*^ aureate that IOT a ^vveu camber Cl^ n isgreatest when the maximum camber occurs at .4c. The jnean curve drawn through the points of Fig. 4 has been used to calculate those of Fig. 5, on the assumption that this curve applies in form to all thickness ratios. The final relationship for CLOPT by this method is CLOPT = (1.7 - tt) yA .. .. (5) where t = maximum thickness in terms of the chord length y = maximum camber in terms of the chord length A = constant dependent upon the position of the maximum camber—given by Fig. 4. Having established some connection between the drag due to camber and the zero-lift moment, it is interesting to note that Fig. 6 shows a similar relationship between CLOPT and CM0. Here again it is clearly shown that the 230 series of aerofoils differ from the other aerofoils. This is not brought out by the method just previously considered : By plotting CLOPT against A ICD0 some idea is obtained of the relative value of the different centre- line forms from the point of view of drag for a given value of CLOPT- Fig. 6a clearly shows that for a given CLOPT no centreline form is of outstanding merit. It must be remembered that the 230 series have a smaller CM0 for a given CLOPT than any of the other sections. It must be pointed out here that, although the 230 series of aerofoils have some admirable characteristics at low angles of attack, they invariably have very sudden stalls, and although CLmax/CDmin may be large, the pilot cannot take full advantage of the maximum lift available for fear of " dropping a wing " in the event of an inadvertent stall. The question of the stalling of wings is beyond -K future article. In the previous article the writer suggested the possi- bility of using a generalised curve to express, for practical aerofoils, the variation of drag from the minimum value in the form of: ^CL -CLQPT\ \GLJJ OLQPT The N.A.C.A. Report showed that when their tests were completed the variation in drag could not be repre- sented by a single curve. Probably due to the higher Reynolds Number, and also to the fact that many im- practical sections have been discarded, they now feel that for practical purposes the variation expressed by 6 can be adopted using a single curve. The revised values for A2CD0 are given in Fig. 7, which is actually a copy of Fig. 45 of N.A.C.A Report No. 586, with the two graphs from the previous article added for comparison. A set of empirical corrections (Ref. 4) to the theory of thin aerofoils (Ref. 5) has been published by the present writer. Since the scale effect on the zero-lift conditions is negligible, these can still be applied with confidence. LIST OF REFERENCES.1. W. R. ANDREWS : The Estimation of Profile Drag. Aircraft Engineer, June and July, 1932. 2. E. N. JACOBS, K. E. WARD and R. M. PIKKERTQN : The Characteristics of78 related aerofoil sections from tests in the Variable Density Tunnel. N.A.C.A. Report, 400.3. E. K. JACOBS and A. SHERMAN : Aerofoil section characteristics as atlected by variations of the Reynolds Number. N.A.C.A. Report 5864. W. R. ASIIREWS: The design of aerofoils and the prediction of character- istics. The Aircraft Engineer. Oct., Nov., and Dec, 1933. Jan., 1834.5. H. GLAUERT : The theory of thin aerofoils. R. & M. 910. IMPROVED LAMINATED WOOD in TORSION By EDGAR REISSNER, B Sc., D.I.C. G.R.Ae.S.I IN recent years improved laminated wood, which is ofhigh strength, rigidity and moisture proofness, hasfound considerable use in aircraft and airscrew con- struction. It consists of thin wood veneers glued together under high pressure and temperature. In order to make the best use of this material with regard to safety and light- ness in construction, it is necessary to take into account the different behaviour of the material in the different directions (the aeolotropy) and to determine the elastic constants of this aeolotropic material and the ultimate ' stresses. These figures must then be applied in the stress calculations lor the structural members built up from laminated wood. As will be formulated later, the propeitics ol laminated wood referred to the three planes of symmetry are repre- sented by nine elastic constants, viz., 3 moduli of elasticity E,, E,, Ez. 3 Poisson ratios vT, v v, vz and 3 moduli of rigidity, Gx, Gv, Gz. The determination of these constants constitutes two independent problems. The first is solved by tension and compression experiments, the second by pure shear. This article will occupy itself only with the question regarding the moduli of rigidity and the ultimate shear stresses and, in order to have a case of pure shear, with the application of torsion experiments on the determination of said quantities. For the sake of completeness, and as an introduction, a short and slightly simplified derivation of the torsion formul.p is given. The justifiable assumption is made that the material dealt with here has three planes of symmetry (which arc the three co-ordinate planes). Reference throughout is made to :Navier, St. Venant.— Resistance des Corps solides 1864 ;. Paris. .—Theory of elasticity, early edition about 1870. Symbols used':— Pa ~px = stress in z direction perpendicular to x axis Ptt = pt = stress in x direction perpendicular to z axis P..P,. G., G., Yxi = />. = />, = G= G = y, = Y — stress in z direction perpendicular to y axis = stress in y direction perpendicular to z axis = modulus of rigidity in xz plane = modulus of rigidity in yz plane = decrease of original rectangle in xz plane , — decrease of original rectangle in vz plane u — displacement of any point in x direction v — displacement of any point in y direction = displacement of any point in z direction to = angle of twist per unit length of rod 8 — angle of twist = wt 1 „ —- polar moment of inertia of cross-section. w The condition of equilibrium (see Fig i) is A A. - o i)r 0y and the stress strain relations ?:=&:;„ •• •• •• (1) (2) The influence of the aeolotropy is expressed by G, T G,. Y is the decrease of original rectangle of an elemental prism (see Fig. 2). - = *•-J7 + U+ y a (3) It is assumed, and later justified by the solution (as in the theory of isotropic bodies), that every cross-section, or better its projection in an xy plane turns as a whole through some angle 0. The displacement PP1 of the point P can be written (see Fig. 3). u = - 6V , v = + 6X = — °>IV — W!X • • • • • • (4) Substituting equations (2), (3). (4) in equation (1)—
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