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Aviation History
1936
1936 - 0765.PDF
SUPPLEMENI ro FLIGHT MARCH 26, 1936 THE AIRCRAFT ENGINEER • In any method which is based on the resilience of the members, the sizes have to be first obtained and then the method applied as a check to see how close is the first approximation to the sizes required. The object of this article is to show— (1) How the spar sizes can be estimated by a first approximation. (2) How to obtain the loads in the members allowing for the contribution of the covering in taking torsion. (3) How to check the result. Sheers and Bending Moments The first estimation of the shears and bending moments on the spars is made as follows :—The curve of load grading along the spar for the particular plan form of wing under consideration is obtained by the method as given in A.P. 970 Chapter VIII (Ref. 3a) (Chapter VII 1035 Edition) (Ref. 36). If for any particular stressing case the loading as found is placed along the line of centre of pressure, the spar loadings can be obtained by taking moments about either spar and so obtaining the loading along one spar. The loading along the other spar then follows by difference. This, however, neglects the effect of any load being trans ferred from the spar most heavily loaded relevant to its strength, to the other spar, so the spar loadings need to be modified in the first approximation, so that finally the sizes required will not differ greatly from those found by the first approximation. The front spar size is usually fixed by the C.P. Forward Case. In this case the torque on the wing, due to the line of applied load not being on the line of flexure, is usually small. The front spar sizes can therefore be provisionally fixed on the loads obtained as above. In the C.P. Back Case, however, the wing has usually a large torque, and it is this case, therefore, which needs a correction before fixing provisionally the sizes of the rear spar. The writer has found that the following gives a method of allowing for load being transferred from one spar to the other, which, when the final calculations are done, will result in showing that the spars so found are the most economical PROPORTION OF IOTAL &M & SHEAR ON REAR SPAR TRANSFERRED TO FRONT SPAR IN C P &ACKCASE FIG 2. -,20 13 « 5 At the inner end of the wing the result of the loading along the centre of pressure gives definite reactions at the fuselage attachments, which depend on the position of the load on the wing and are not affected by any load transfer ence from one spar to the other. It is seen, therefore, that at the wing root the transference must vanish. It is a reasonable assumption that the full transference will not be obtained until a length along the spar equal to the root chord is reached, and that the transference varies linearly over this portion of the wing. From this point out to the tip the full transference can be assumed to be a uniform proportion of the bending moment or shear on the rear spar. For the bending this transference is taken as 25 per cent, and for shear as 20 per cent. Fig. 2 is a diagram showing this. Several of the other cases have a large torque, but the two cases mentioned are usually satisfactory for pro visionally fixing the spar sizes. The above is based on an aerofoil section with a moderate C.P. movement and may need some modification to suit an extreme case. For instance, with a constant C.P. section the spars may be positioned so that the torque 04 the wing is negligible, or in the other extreme a very large C.P. movement may require more transference for economical design, but the above is a guide for the general case. It is now possible to get the spar sizes fixed. It is necsssary to make an approximation oi this kind for, until the sizes of the spars are known, it is impossible to proceed with the method that follows or with the method obtained in (1). The preliminary sizes of the spars having now been fixed the calculations can be proceeded with as outlined below . NOTATION DIAGRAM RF —*= ~-Zt- IgNTSPAR ' CP LOCUS ? i nPWWL, LIME "" gj* s— "^R ___———^ FIG.I. i ll NOTATION DIAGRAM. ZE ZR is an axis defined by the wing root. 7-i ZT is an axis at Wing Tip parallel io ZR ZR X X is an axis norma! to Z Z. » is a distance along X X from ZT ZT defining a general section of the wing parallel to Z Z. d is the distance between the spars measured,parallel to Z Z at the general section. aF & oR are the inclinations of the front and rear spars respectively to X X. As drawn aF is positive. IF IR are the moments of inertia of the front and rear spars respeetivelv. w is tha loading per unit run of X X applied normal to the plane of the wing structure along A.B. and is positive upwards. t is the torque per unit run of X X due to non-coincidence of the C.P. locus and the flexural line of the wing and is positive when producing elevation of the front spar. Mf & MR are the bending moments on the front and rear spars respectively at the general section and are positive when causing concavity when the spars are viewed from above. Explanation of Method (See Notation Diagram, Fig. 1). It is first necessary to obtain the flexural line. The flexural line is a line along the span such that, if the load is applied along the line, the spars will deflect equally at all points along the span. The equation to the flexural line is fully investigated in R. & M. 1617 (1) and is as follows— Equation (1). dR Cx , d2R wr = R» + 2—1 wax + —— dxj0 dx'-, w dx . dx R Where r = distance from the rear spar to the flexural line x = distance along X X from ZT ZT R = distance from the rear spar to the " R " line' w = load intensity along the span. When the spars are parallel IF \ This is dealt with later for non- IF 4. iR j parallel spars. IF = moment of inertia of front spar. IR = moment of inertia of rear spar. A loading of w per unit run of X X applied in the direction of lift can be regarded as a loading of u> Per unit run of X X applied in the same direction along the flexural line CD. together with a distributed torque. The increment of torque at any point is equa to the load at that point multiplied by the distance between the line of centre of pressure A B and the
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