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Aviation History
1933
1933 - 1109.PDF
NOVEMBER 30. 1933 81 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT One of the most important relationships brought out by these tests is the proportionality of Km,, to the camber ratio. This is as suggested by the theory of thin aerofoils, and although the value of the moment falls below the calculated value for any thickness ratio, the ratio of calculated to observed remains the same for any camber at constant thickness ratio. For any camber ratio the Kwi0 falls off as a function of the square of the thickness ratio as shown by Fig. 7, TZVm where ° is plotted against t2. Y Where y = Maximum camber of centreline. t = Maximum thickness-to-chord ratio. Table 3 gives the laws for the mean curves drawn through the points for the three series. TABLE 3 Series Observed Km„ 43—63 44—64 45—65 - 0-967 (1-4-9 V) v -115 (1^-9 <2)y - 1-375 (1-4-9 f-)y The physical significance of the function (1-4.9 i2) is a little obscure, but its recurrence greatly assists the investigations. It is now only necessary to compare the extrapolated value of Km, for t = o with the value calculated for the centreline by means of R. & M. 910. Since it has been shown that both the observed and the calculated Km, are proportional to camber, we may eompil* Table 4, giving the relationships between Km,, and camber for the cambered sections. TABLE 4 Series Calculated Kmn AKm0 (calculated-observed) 43—63 44—64 45—65 112 y 1-319 y 1-57 Y -0-153 Y -0-169 Y -0-195 Y An empirical correction to the calculated value of Km0 was suggested in a previous article (Ref. 7) based •02 •01 o E a: < 0 -01 <• Sj A.F. 52 KJ !F26 Nj RA R.A F.SI F.2^ A Kny OBSERVED Km„ - CALCULATED .. » -• 0 RA. F.25 FIG.8. R&M 9l0)Kmo ( R ) 3R. A.F. V.F.; X® •A •1 0 ifr- SLOPE AT TRAILIN6 EDGE on the camber ratio of the section. This correction only applied to non-reflexed sections which, if the sections have somewhat similar shapes of centreline, may be considered as being expressed in terms of the trailing edge slope. Table 5 and Fig. 8 give the results of expressing this difference between calculated and observed Km, in terms of the trailing-edge slope (ty) for the It.A.F. Series of Aerofoils, tested at low value of Reynolds Number. TABLE 5 Aerofoil = T.E. slope of Centreline Km0 Observed Calc. by j R. & M.910 AK.m„ R.A.F. 25 26 28 :si 33 -0041 -0-082 -0-05 -0-082 -0-202 +0-0516 +0-0207 0 016 -0-028 -0-022 -0-029 -0 067 -0 009 -0-005 0016 -0-031 0022 0 032 0-078 0 0 0 0 003 0 0003 0011 -0009 -0005 These low-pressure tunnel tests give a linear variation of AK»i„ with trailing-edge slope. Warner suggests (Ref. 8) an approximate relationship between trailing- edge slope and Km,,, which will be shown later as only possible when the shapes of the aerofoils are similar and the thickness ratios the same. With the V.D. tunnel tests the effect of trailing-edge slope can be separated from that due to the slope of the leading edge in the following manner: — Since Km, is proportional to camber, it is possible to forecast Km, for any camber of any of thei series from the known value of Km, at another camber. If, there fore, we choose one particular camber for one series and adjust the camber of the other series to give the same trailing-edge angle, then by the aid of Table 4 we can compile Table 6, which gives Km0 for a con stant trailing-edge slope of —0.16. TABLE 6 Series T.E. Slope lyt?^e = + ! -0-16 L.E. Slope AKm0 -0 16) 43—63 -Y -*- 0-3 44—64 -149 Y -49 45—65 -r^O-25 0 056 0-048 Y-+-0-15=0-373 Y-^-0-2=0-24 0040 i Y=0-25=016 0-0086 0-0081 0 0078. The values of AK», refer to the extrapolated values when f = o. Fig. 9 gives the plot of these interesting results, the law to the curve drawn being AK»n„ = +0-00725 - 0-0036 <j> [for y = -0- 16and< = t>](7). on 010 009 |°0O8 < 007 006 005 CONSTANT TE. ANGLE —16 ci(C; Q n v. J, w. •05 •15 -2 L.E. SLOPE •25 35 The Effect of Trailing Edge Slope on No-lift Moment Variation of No-lift Moment with Slope of Centreline of Correction. Low-pressure Wind Tunn»l Tests Leading Edge 1198e
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