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Aviation History
1933
1933 - 1327.PDF
DECEMBER 28, 1933 89 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT TABLE X Column r, ,. t rm DI rr, T L'K T-E- Kw„ calculated . No OrdinatesofC.L. Slope of C.L. at S]ope S]ope by method of Kw„ (empirically «/o= any point ^ ^ R & M fll0 corrected) 1 h x (1 - x) (a - x) ' h [a -2(1+ a)x 2 h x(l - xf j h (1 — 4* + 3x2) 3 Si(l-i) A (1 - 2x) 4 /t(l-*)[l-(l-a;)3] j h (3-12x+l2x2-<lx3' h(l-x) [1—(1—a;)4] ' h (4—20* + 30a:2 -20a:3 + 5a-4) h (l—x) [l-(l-x)»] ! ah h I, U llli h (1-a) i jn h (7 - 8 a) 0-3436 A (1-4-9/2) a-10-8675 - «| 0 -h -h -h -h l" -\" 1" 64 70rt h 512 -0-0455 A (1-4-9*8) -0-3436// (l-4-9<a) -0-3855 A(l-4-9^) -0-370A(l-4-9<<) FIG.I3 • g,-hx(i-x)(a-x) / 3 -32 '34 -36 38 40 42 44 46 x' •POINT OF MAX CAMBER a^-hXii-xKa-x) FIG. 14 30 32 34 -36 38 -40 42 -44 46 48 X'» POINT OF MAX. CAMBER Ft - l-4-9t* FIG.I5 0 -02 04 06 08 10 12 14 16 -18 -20 t SERIES y^.hlixxJtHl-x)"] > *«<« EMPIRIC* 910 oiy cofRarreo FIG. 16 0 -5 1-0 IS 20 2-5 JO J5 40 VALUES OF n Aerofoil Centreline Shapes Taking first the series having the maximum rise of centreline at half the chord, the value of F2 = yofz(x)dx for this series is zero, since the centreline J.° is symmetrical about 0.5 of the chord. Therefore, one would expect that the no-lift angle and the moment at no-lift will be dependent upon one another as suggested by theory. The following table gives the result of such an analysis. TABLE XI Section 4500 4509 4512 4515 4518 4521 6500 650!) 6512 6515 8818 6521 —KntQ 0 0535 0-0535 0 0505 0-0485 0-047 0-041 0 079 0-076 0'074 0 060 0064 — 57-3 x4K»«o •n 3-90 3-90 3-68 3-54 3-43 2-99 5-75 5-54 5'30 503 4-67 —»0 observed 4-32 4-13 403 4-07 3-85 3-40 0-35 6-35 6-27 5-91 6-70 5-23 —Difference degrees 0-42 0-23 0-35 0-53 0-42 0-41 0-6 0-73 0-52 0-67 0-56 It will be seen from this thati the mean difference in degrees is approximately 10 x camber ratio. Where the value of F„ is not zero this relationship does not hold. To get an agreement an amount corresponding to F, (see Fig. 15) must first be added to Km,. 1-4.9 t2 This same function of thickness appears in the empirical correction for Km,, Its physical significance in that connection was not clear, but its re-appearance here is even less so. The following table shows the final variation when TABLE XII Section — K«o •57-3 It L v jyJ -no observed — Difference — — (oo — a\) 4306 09 12 15 18 21 6306 09 12 15 18 21 4406 09 12 15 18 21 6406 09 12 15 18 21 0 0375 0 0375 0 036 0 034 0-0325 0-0285 -— 0-0555 0 0545 0-0520 0-0485 0-0455 -— 0 042 0 0435 0 0415 0-039 0 036 — 0 0665 0-0645 0 0625 0 0595 0-0555 2-74 4-0-68=3-32° 2-74+0-59 = 3-35° 2-63+0-61-3-24° 2-48+0-64 = 3-12° 2-37-t-0-68 = 305° 2-08+0-73=2-81° 4-05 + 0-89=4-94° 3-98+0-92 = 4-90° 3-80 + 0-96 =-4-76° 3-54 + 1-01=4-55° 3-32 + 1-09 = 4-41° 3-14+0-30-3-44° 3-17+0-31-3-48° 3-03+0-33-3 36° 2-85+0-34 = 3 19° 2-63+0-37=300° 4-76 + 0-44 = 5-20° 4-71+0-46 = 5-17° 4-56+0-48 = 5-04° 4-35 + 0-51 =4-86° 4-06 + 0-55 = 4-60° 3-79° 3-54° 3-60° 3-58° 3-44' 3-55° 4-82° 5-35" 5-35° 5-30" 5 18° 5-*0° — 3 6° 3-8° 3-8° 8-7" 3-5° — 5-25° 5-75° 5-75° 5-75° 5-3° 0-47° 0-19° 0-36° 0-46" 0-39° 0-74° 0;41° 0-45° 0-54° 0-63" 0-59° 0 12° 0 32° 0-44° 0-51° 0-5° — 0-75° 0-58° 0-71° 0-89° 0-70° 1310c
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