FlightGlobal.com
Home
Premium
Archive
Video
Images
Forum
Atlas
Blogs
Jobs
Shop
RSS
Email Newsletters
You are in:
Home
Aviation History
1936
1936 - 2103.PDF
SUPPLEMENT TO FLIGHT 2 THE AIRCRAFT ENGINEER JULY 30, i93o the one more easily determined from loading tests on a wing, and if the ratio of IF/IR and E remain sensibly con stant along the span the line so found will approximate to the flexural line. The integration necessary for determining the flexural line, for a two-spar wing, is as follows :—(Ref. 1.). £)r-+(S)f" .' 1 J 1 m = loading per unit span. = distance of flexural axis from rear spar in terms of distance between the spars. = distance out from root. IR COS 3aF wr = Zw + 2 where w r w dx)2 (1) Z I R COS 3aR -+- IF COS 3aF 1 = Semi span. aF & aR = Angle of front and rear spar to C.L. of wing in plan. It will be noticed that this integration is carried out from the tip inwards. ' Point of Application of Aerodynamic Loading Due to the more general use of the C.P. for the stressing of a wing, it is impossible to use the stresses from one case and easily determine those for another. The following method, although somewhat more refined in certain respects than may be found necessary in practice, provides a means of obtaining quickly and accurately the stresses for all other cases from those found for one case. The method is to apply certain unit loads in the manner laid down and calculate the stresses induced by these loads by standard methods. The stresses in the particular cases are then obtained by proportion and addition. Another great advantage of the method lies in the ease with which major modifications (changes of speed and weight) can be allowed for accurately. Where the stressing cases are few the method offers little advantage, but so far as British requirements are concerned the number of stressing cases cannot usually be considered as few. The only way of accomplishing the end in view is to replace the C.P. position by some fixed line about which the, moment is known. The only line which satisfies the requirements of simplicity is that about which the moment coefficient is constant. Usually this line is referred to as the " Quarter Chord," but from empirical data the following relationship is obtained. dKm /(/Kt •25 .4t' (2) where / = maximum thickness — chord ratio of the aero foil section. As difficulty is sometimes experienced in changing over from the conception of C.P. to that of a constant moment coefficient about the quarter chord, the following notes may help. Consider only the approximate relationship for C.P. ^ ^ — Km * CP. = ^- •• .. -. .. (3) where C.P. is in terms of chord. It can be shown on empirical evidence that the Km — KL curve is invariably a straight continuous line from no-lift to very near KL max. so that we may write Km = — eKL + Km„ . . . . .. (4) where Km0 is the no-lift moment. The C.P. expression then becomes C.P. = e-1g» (5) This is still with respect to the L.E. If now we take moments about the C.P. position on the chord we get the moment about ec as :—- (Km ) Km(ec) = K L(C.P. - e) - - KL^^ = -Km0 by substitution from Equation 5. This leads us to a fixed line on the wing about which the moment coefficient is constant and at which the lift is applied. The Untwisted Wing For the aerodynamically untwisted wing the load co efficients about the flexural line can be split up as follows :— (a)Km0 transferred directly from ec. (b) A Km due to transferring KL from ec to flexural line. (c) The lift KL applied at the flexural line. (d) The drag. Let f.c. be the distance, at any point, from the " quarter chord " to the flexural line. Assuming the normal force coefficient to be equal to KL (as is customary) then the total moment on the wing at any section is - M = poV2!* Km0C*dx + paY^j f KL CHx .. ((>) The first part of the right-hand expression is independent of the span wise loading and remains constant (except for V) for all the cases. Since for an untwisted wing it is customary to use the same loading distribution curve for all values of lift we may write C2dx for the second part of the right-hand side of equation 6 where K£ is the mean lift coefficient. The integral is then a constant for all values of KL and finally M = paV2 i: Km, C* dx sfr* ~C*dx L (7) A special case arises where the C.P.B. has the over riding value of C.P.F. -f- .1. In this case the Km0 must be artificially increased to :— Km'0 = (1—KL) Km, + 10 The loads due to Km0 alone must then be increased in the ratio Kw'n Km0 i-KL) + KLm KL 10 • Km„ The shear and B.M. for the front and rear spars can then be expressed as follows :— Shear B.M For Front Spar. dx, J ;/ \ KL EF IF ^r - ^V" KL r cos a/ dxf ' 1/ J if \ KL / Similarly for the Rear Spar. Shear — ER IRS— = p<ATi KL / ( ^-~) (1 — r) cos oRdxR COS OR^R)2 (8) The spar stresses due to direct and differential bending can be expressed in terms of KL/>CTV2 and Km0paV2 only. This article is not concerned with the determination of absolute stresses due to bending and torsion. The stressing has been taken only as far as is necessary to show that a particular case can be obtained from a general case in unit loadings. The final stresses in the member can be expressed as follows :— Stress = ApcV2 + BKLpoV2 + GKDPaV2 Where \/oV is I.A.S. (fps) and p = .002378. If the wing loading is w, and KL = —^ then for straight flying (i.e. without gusts) Stress = ApaV2 + Bw, + GKDPaV2 .. • • (9) Where A, B and G vary along the span, A depends upon Km0 and B depends upon the sum of the stresses induced by differential bending through moving point of applica tion of Kj[ from the quarter chord to the flexural line, plus
Sign up to
Flight Digital Magazine
Flight Print Magazine
Airline Business Magazine
E-newsletters
RSS
Events
