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Aviation History
1936
1936 - 1414.PDF
MAY 28, 1936 35 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT 576* increases when moving along the x x axis from the tip. The shear curves with corrections are shown in Fig. 3. Integration of these curves gives the curves of B.M. for pure flexure of the spars. These are shown in Fig. 4. An interesting means of checking the B.M.s curves so obtained, and so checking the load curves for the spars, is now possible. Reference R. <&&gt; M. 1617 (1) Page 4. Equation 7. wr (dx)2 = R w (dx)2 (Equation 4). or M (spar) = R (spar) x M where M is the total wing moment. i.e., The moment on a spar at any point is equal to the Total Wing Moment at the point multiplied by the value of " R " for the spar at that point. Point on Spar. Tip .1 .2 •3 •4 •5 .6 •7 .8 •9 Root la i-5 1.48 1.46 1.44 1.42 1.4 1.36 1.32 1.28 1.24 1.2 16 i-5 152 1-54 1.56 1.58 1.6 1.64 1.68 1.72 1.76 1.8 TABLE 1. Ic •5 •52 •54 •56 •58 .6 .62 .64 .66 .68 .70 S = Ia+Ib + Ic 3 5 3-52 3-54 3-56 3-58 3-6 3.62 3-64 3.66 3.68 3-7 la S 429 421 413 4°5 397 389 376 363 35 337 323 lb S •429 •432 •435 •439 .442 •445 •454 .462 .471 .478 .486 U s 143 148 353 L57 162 167 17. 175 179 185 191 TABLE 2. Point on Spar. Tip .1 .2 •3 •4 •5 .6 •7 .8 9 Root Spar B.M.s. a 0 1.2 2.2 3-5 5-o 7-i 93 11.8 *43 17.1 b 0 i-7 2.6 4.0 5-6 8-5 11.7 15-7 20.2 25-9 c 1 2 3 4 6 7 10 3 f>5 9 5 15 3 5 0 7 Check on B.M.s (by Equation 4). a 2-3 3-57 4-95 7-i 925 11.7 14.2 17.1 b 2 4 5 8 11 15 20 25 5 15 67 6 8 7 2 7 c .89 1-52 2.13 3.22 4.46 5-96 7-7 10.i X ^.Mb ^JliX ^Mc SPAR BM. CURVES (FLEXURE) FIG. 4. ROOT « TIP This method is perhaps the quickest way of finding the moments on the spars, but it is necessary to know the loadings on the spars to obtain the flexural line, and so obtain the torque system on the wing. As it is difficult to obtain load curves with any accuracy by double differentiation of the B.M curves, E'quation 4 is only used to check the results obtained. Table 2 gives the values of B.M. for the spars (a) (b) and (c) at various points along the span, and a check on the results, obtained by Equation 4, is also given. It is now possible to obtain the flexural line for the wing. This is the line of the centre of gravity of the spar loadings, and is obtained by taking moments about any datum parallel to the X X axis. The values are derived in Table 3 by taking moments about spar (c). TABLE 3. POSITION OF FLEXURAL LINE. (MOMENTS OF SPAR LOADS ABOUT SPAR (c)). Point on Spar. Tip .2 •4 •5 •7 •9 Root wa .429 •391 •355 •34 .192 .12 .085 ». •429 •45 •405 •475 •573 .62 •645 da 5 5 5 5 5 5 5 db 2 2 2 2 2 2 2 ">„ da 215 I.96 I.78 i-7 •9.6 .6 •43 Wi db .86 .90 •93 •95 115 1.24 1.29 D 30 2.86 2.71 2.65 2.11 1.84 1.72 The flexural line is plotted on Fig. 1. It could have been drawn by the method used in the article on a two-spar wing (1) as follows— (1) Obtain values of R for spars (a and b). (2! (3) (4) (5) Plot these values R (a + b). Use this line as an equivalent spar Ic = la + U and combining with spar (c) obtain Final " R " line R (a + b + c). Treating the equivalent spar and spar (c) as a two- spar wing, draw the flexural line as described in the previous article. The flexural line by this method checks with the calculated flexural line. This completes the Flexural system and it is now possible to deal with the torque system. ROOT 9 The Torque System The increment of torque at any point is equal to the load at that point multiplied by the distance between the line of centre of pressure, and the flexural line. The integral of this, from the tip to any section, is the torque at that section. For.the purpose of the example, a line of centre of pressure is drawn on Fig. 1 (C.P.). The curve of torque is given in Fig. 5. This torque is now shared between the skin in shear, and the spars in differential bending. The amount of torque taken by the skin can be found by the method of R. & M. 1617, or if the srinj has some other form of torque bracing, an estimate of the torque taken by this will have to be made. For the purpose of the example the torque left to be taken in the spars is as shown in Fig. 5. When a wing has two spars, torque is taken by the spars as a couple, the T load on each spar at any point beinj — where T is the torque at the section and d is the distance between the spar
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