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Aviation History
1936
1936 - 2106.PDF
J'JLY 30, 1936 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT TABLE 3. 1 CULATION OF DIRECT SHEAR AND BENDING MOMENT ON THE FKC WING APPLIED ALONG THE X Feet Tip 25 24 22 20 18 16 14 12 10 8 f> 4 2 0 '1 0.620 0.637 0.672 0.707 0.744 0.774 0.811 0.848 0.883 0.920 0.957 0.987 1.032 1073 w, 0 7-25 11.6 14.0 *5;5 16.7 17.8 18.8 19-75 20.6 21-35 22.0 22.4 22.6 »tf, 0 4.62 7-79 9.90 ii-54 12.93 14-43 15-95 17-43 18.94 20.46 21.70 23.12 2425 FLEXURAL LI rX — wxrxdx I K"L„ 0 2 31 I4.94 32.76 54.20 78.67 I06.O I30 4 I69.8 206.2 245.6 287.7 3325 379-9 NE ('.)• -X -X . 1- 1 _KL1 x-o O 1.6 18.0 65.2 152.2 285.0 469.7 712.0 IC18 1394 1846 2369 2990 3602 Shear q KL = 2.86.5. a B.M. iv,r,dx ; / 1 KL_ KL„ 1 . Wjr^dx)2; TABLE 4 CALCULATION OF DIRECT SHEAR AND BENDING MOMENT ON THE FRONT SPAR DUE TO ADDED LOADING WITH 50 WASH IN AT TIP. LOADING APPLIED AT FLEXURAL LINE r2. X Feet Tip 25 24 22 20 18 16 M 12 10 8 6 4 2 0 2 '2 0.620 0.637 0.674 0.713 0-753 0.798 0.847 0.902 0.967 1.049 1.158 1.301 1.454 1527 Shear <? HI, 5° wash in J 0 0.50 0.742 0.819 0.846 0.837 0.802 0.750 0.676 0.588 0.49S o-393 0327 0.314 W**! O 0.3I9 O.5OO O.584 O.637 0.668 0.678 0.677 0.653 0.617 °-577 0.472 0.476 0.480 — 'x wtr^Lx •> i 0 0.160 1.002 2.094 3-32 4.62 5-97 7-3-2 8.64 9.91 II.II 12.15 13.10 14.06 r*f 'x w,r 2(dx)- J/-/ 0 .08 1-197 4.27 9.69 17.62 28.21 41.50 57-40 76.01 96.03 ii93 1445 171.7 rx Bendiner Moment w2r^x ; 1 q ' X 1 fx . I dx)2. TABLE 5. CALCULATION OF MOMENT ON WING DUE TO APPLYING LOADING FOR UNTWISTED WING AT FLEXURAL LINE r[ INSTEAD OF AT THE " QUARTER CHORD." x Feet Tip 25 24 22 20 18 16 M 12 10 8 6 4 2 O Feet wjtc 0.666 0.495 0.450 0.304 0.150 0.013 — 0.129 -0.283 -0.429 -0.582 -0737 -0.861 — 1.050 -1.230 0 7-25 11.6 14.0 155 16.7 17.8 18.8 1975 20.6 21 35 22.0 22.4 22.6 0 3-59 5.22 4-25 2-33 0.21 - 2.30 - 5-33 - 8.47 - 11.98 - '5-74 -18.95 -23-5° -27-75 M KL ? KL 1 79 H-35 21.00 27-58 30.12 30.10 24-54 10.74 9.71 37-43 72.12 114.6 1658 M Kr o 0.63 3-96 7-33 9.62 10.52 10.51 8-57 3-75 — 3-39 — 13.06 — 25.2 — 40.0 -57-9 NOTES. M -KL Po\r* ; — = = *v .Qs.Wyfidx ; KL = KL at 1 rad. from no-lift for A = 2a0 (per rad.) at which aspect ratio curves of A.P. 970 are calculated = 2.865. TABLE 6. CALCULATION OF MOMENT PRODUCED BY THE NO-LIFT MOMENT PLUS THAT DUE TO MOVING POINT OF APPLICATION OF ADDED LOADING WITH 50 TWIST FROM 0.25C TO FLEXURAL LINE tt. X Feet 25 24 O ~> 20 18 16 14 12 10 8 6 4 2 0 /sc u>. Feet k" at tip 0.666 0.495 0.442 0.279 0.121 — Q.079 — 0.279 — 0.508 — 0.780 — 1.120 -1-575 — 2.170 — 2.810 -3.110 0 0.50 0.742 0.819 0.846 0.837 0.802 0750 0.676 0.5S8 0.498 0.393 0-327 0314 f2wtC 0 0.247 0.328 0.229 0.102 — 0.066 — 0.223 — 0.381 — 0-527 -0.658 — 0.780 -0.852 —0.919 —0.977 Km0C — O.IOD — 0.104 — 0.112 — 0.120 -0.128 —0.136 —0.144 — 0.152 — 0.160 -0.168 —0.176 —0.184 —0.192 —0.200 (/•jjt'2 + Kwj0)C — 0.10 + 0.143 0.216 0.109 — 0.026 — 0.202 -0.367 -0533 — 0.687 -0.826 -0.956 — 1.036 —1.111 — 1.177 M — ? 0 0.02 0435 0.867 0.950 0.722 O.I53 - 0.747 — 1-967 - 3.480 — 5-262 - 7-254 — 9.401 — 11.6S9 M <! (/jtflj + Km0) C dx ; Km0 = — 0.02 radian) of 2.86 the aspect ratio is 5.74. As, however, the shape of the load distribution is not appreciably affected by small changes in aspect ratio the curves of A.P. 970 are applied without correction. Serious error might be introduced by adopting this procedure if the loads in members are expressed in terms of the angle from no-lift instead of the mean KL. This error is caused by the change in the slope of the lift curve for the actual' wing b<-mg different from that for the wing of aspect ratio 2 a 0 upon which the load distribution is based. 1 we position of the spars assumed is shown in Fig. 2 and the calculation oi the flexural lines is carried out as shown in lables 1 and 2, the results being plotted in Fig. 4. It will be noticed that for ease of computation equation 1 is divided through by w giving „ , 2 dz [x r==z + wTxLud* fcfl * 1 dh . Since the Z line is assumed to be straight -3—^ is zero 0 dx2 and the second differential vanishes, "vxtiere possible it is a great advantage to approximate to the Z line by a series of straight lines as suggested by Mr. Home (Ref. 3) and use equation 17 in preference to 1. The correction for the discontinuity due to Mr. Burton where the straight line approximations meet is also given in Ref. 3. The direct shears and bending moments on the spars due to the loading for an untwisted wing follow auto matically in Table 3 and for the added load with twist in Table 4. These have been calculated for the front spar only. The loads due to the untwisted wing at any value of KL are obtained directly by proportion (Fig. 5) and are then added to the constant loads induced by the twist on the wing (Fig. 6). The overall moment calculation proceeds as in Tables 5
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