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Aviation History
1934
1934 - 1455.PDF
SEPTEMBER 27, 1934 67 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT IOO2C 2.—Height of NA above x x = 2 Zart 3.—Moment of Inertia of an arc about x x .. • . I., =/ trddr* sin20 . J *i /««— rH] sin2 Odd j_2 4 jBl 92 — 61 sin 2 0, — sin 2 02~|~^—+ ~ A J Since the arc is symmetrical about YY we have : sin 2 0j — sin 2 02 sin 2 0j 4 ~ 2 and sin 2 (?j = cos (a j .'. I** =— a + COS (a -- Moment of Inertia of arc about NA : rcc*(H - h)2INA = lxx - It has been found convenient, in order to expedite the work, to plot curves of cross sectional areas, heights of cg's and moments of inertia of circular arcs of various radii. These are shown in Figs. 11, 12 and 13 (Figs. 11 and 13 are for t = .iin.) Diameter == 28in. / = .o8in. Developed width 1.7 P. 1st top arc, 23 radians Equivalent thickness 1.7 X .048 = .0817m. 2nd top arc 1.2 radians Equivalent thickness 1.7 X .064 = .io88in. Bottom arc 1.0 radian. Equivalent thickness, .io88in. Element. Shell 1st top arc 2nd top arc Bottom arc Cross Sectional Area. sq. in. 7-°52.70 1.87 i-55 Height above XX. in. 0 11.42 3 3-52 - 1381 Moment of Area about XX. 0 3O-85 25-3 - 21.4 Total area 13.17 sq. in. Total moment 34.75 in. h = 3475 =n*7 Element. Shell 1st top arc 2nd top arc Bottom arc Moment of Inertia about XX. 690 373 346 300 Moment of Inertia about N.A. 739-5 228.5 225.7 4239 Total I about N.A. 1,617.6 in.4 MOMENTS OF INERTIA OF CIRCULAR ARCS 16 * 17 g,-6 S 15 IK 1-3 12 D< >• K A- y.not y Zc-KD!t FIG.15 •1 « 1-1 1-4 1-5 1-6 17 1-8 19 20 2-1 2-2 21 BENDIN6 MODULUS COEFFICIENT K 1617.6Z c = '— = 137.5m. 3 " 11.76 o/ J 7 1617.6 . Z, = = 95.0m.3 The Zc of this particular section may be expressed in terms of a coefficient x D2 x /. 137-5The coefficient for this section is = 2.19 The following example is worked out to illustrate the application of the above method to a section of the pro- posed spar near the wing root. . 282 X .08 The section considered has a cross sectional area of 13.17 sq. in., is 28in. diameter and the shell thickness is .o8in. A plain tube of the same cross sectional area would be = .1495 thick.•n X 28 .I495 The thickness ratio is therefore —=- = 1.869 ,Oo
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