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Aviation History
1936
1936 - 1415.PDF
SUPPLEMENT TO FLIGHT 576/ 36 THE AIRCRAFT ENGINEER MAY 28, 1936 centres. The method for a multi-spar wing will now be outlined. Fig. 6 shows the spars at any section of the wing. The centre of rotation under a pure torque at any section of the wing is a point which is the centre of resistance of the spars. This is the point R(a + b + c) shown on Fig. 1. and obtained when checking the flexural line. This will be proved later when it is shown that the loads obtained from this satisfy the following conditions :— These allow for the difference in deflections required to satisfy (3) and are the final ratios of the spar loads. The actual spar shears are obtained by multiplying these ratios by the value of the torque at each section under consideration and correcting for scale. As the torque at any section is the integral of the increments of torque from the tip, up to the section under consideration, the values so found are the shears on the spars. The spar B.Ms, are the integral of the shears so found. The values for the example will be obtained and checked to see that they satisfy the three conditions. It will be found that the values of shear for the spars so obtained will satisfy the three conditions. To check con- 1 f' x Cx IV! dition (3) obtain values of — — dx dx for each spar a.L JL I and these should be equal at any point along the wing. If the twist of the wing is required it can now easily be obtained by evaluating the spar deflections by the usual methods for beams, remembering that I is a variable. As FIG. 7. v^^S. -. 1^ ' | TORQUE SYSTEM SPAR SHEARS Note. Sa is opposite sign to Sb a Sc. - N V. - >^Ma S<Mt FI6.8. 1 TORQUE SYSTEM SPAR S.Hs ' Ma is opposite sign to Mb&Mc 1 TIP ROOT 9 (1) Sa -f S6 -f Sc = o at any section. (2) Sa da + S„ d„ -f Sc dc = Torque at any section. (3) The deflections of the spars are proportional to the distances from the centre of rotation. The loads on the spars to satisfy these conditions are obtained as follows— Take the values -^- —* -^ for the spars from Table 1. These are the ratio of the loads for equal deflections. I„ da Ie dt Ie de "s s s~ Derive the values the deflections so found are those due to the part of the torque taken in the spars, and do not include flexure loads, from these deflections the true angle of twist of the wing at any point can be obtained. The methods outlined in this article have been checked by using values for an actual wing, and gave very close results to those obtained by more elaborate calculations. LIST OF REFERENCES. (1) The Design of Monoplane Wings, by H. N. Home, •' The Aircraft Engineer," March 26 and April 30, 1930. (2) Report and Memoranda 1017. May 1934. Aeronautical Research Committee. TABLE Point on Spar. Tip .2 •4 .6 .8 Root la ~s .429 •413 •397 •376 •35 •323 16 S .429 •435 .442 •454 .471 .486 Ic S •M3 •153 .162 •17 .179 .191 da 2.0 2.07 2.14 2.2 2.3 2.4 db 1,0 •93 .86 .80 .70 .6 dc 3-o 2-93 2.86 2.80 2.70 2.60 ek -858 .856 •85 .826 .805 •775 (-) .429 •4°5 •38 • 364 .328 .292 Uk .429 •447 •463 .476 .482 .496 T 0 .21 •44 .76 1.16 1.58 True values of Sa 0 •053 .112 .188 .28 •37 S6- 0 .0255 .O"502 .083 .114 •135 Sc 0 .0281 .0611 .108 .168 •235 To obtain the scale correction find Sa, S6 and Sc at the root. Calculate Sa dtt + Sb d„ + Sc de and equate to the torque at the root. This gives a correction factor to give the correct values for Sa, S6 and Sc. #(1.23 x 2.4 + .451 x .6 + .785 x 2.6) m 1.58 #(2.96 + .27 + 2.04) = 1.58 _ 1-58 X = mm 0.3 5-27 3 The shear values for the spars are therefore (— da T J 0.3, using the correct values for each spar. These are shown as S», Sb, Sc and are plotted in Fig. 6. ^
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