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Aviation History
1937
1937 - 1111.PDF
APRIL 29, 1937 25 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT 420s LONGITUDINAL STABILITY An Investigation with Particular Reference to Low-wing Monoplanes By W. R. ANDREWS, A.F.R.Ae.S. (Continued from page 19.) Loading of Biplane Wings (A) Equal-wing Biplane—no Decalage. I T has been customary to use a single curve (Reference 4) giving the ratio of lift on the upper to that of the lower plane for any biplane. This ratio has been expressed in terms of the angle of stagger of the wings. Diehl (References 5 and 6) has shown that a semi-rational method is possible, using the aspect ratio, gap and stagger from no-lift as parameters. The method is developed for any wing arrangement. For an equal-wing biplane a possibly simpler expression is obtainable. Using Diehl's data and references he gives Munk's expressions for the additional lift coefficient of staggered wings as KL = ± 2KL k- b R C T where b S = span = area s = stagger with respect to the no-lift line k = equivalent monoplane span factor R = a distance used in calculating induced down- wash. This can be re-written as follows s /I ± 2 — I -x RVA J5 Ara kW-where A = '-—— = equivalent monoplane aspect ratio of the wing arrangement Am= monoplane aspect ratio of each wing sepa rately. This relationship can be easily expressed in terms of known quantities obtainable from wind tunnel data, and the equivalent monoplane aspect ratio thus A K, KT ~ i-5 A. g on the assumption that R is a function of c/g and (<j>), where <f>1 = angle of stagger to no-lift, and g = gap. This is done in the following table, where, from test results, Am = 6 and -5/Am =* .09 in each case. These results are plotted in Fig. 3. It will be noticed that the grouping of the points is quite equal to that of Fig. 13 of Diehl's report (Reference 5). The points of Fig. 3 actually fall into three main groups, each represented approximately by a straight line. The figures of Table II of Diehl's report follow the approximate relationship AKL • vC/i A L= 0 = (.29 JL.0228^)- -- H K, £VA the values for Diehl's Table III e = (.27 + .0186 ,j £ (I - -£) and the third from the value of Table IV 9 = (.2 + .oi m-B Tables II and IV represent direct force measurements ln American and British wind tunnels respectively and Stagger Degrees. (!—j &-•*) = B TABLE II—DATA. Ik' - (<M -25.2 -36.5 1.2 1.2 1.8 2.3 9.7 14.6 19.3 19.8 28.4 35.8 -19.3 9.3 32.6 -.104 -.104 .127 .088 .06 .038 .157 .116 .104 .236 .178 .147 -.03 .077 .198 3.84 4.04 3.63 3.77 3.90 4.04 3.63 3.84 4.04 3.63 3.84 4.04 3.84 — — .17 .158 .186 .175 .167 .158 .180 . .170 .158 .186 .170 .158 .170 — — - .61 - .66 .683 .502 .359 .24 .845 .682 .657 1.27 1.048 .93 - .177 .45 1.165 .9 1.2 .6 .8 1.0 1 4> .6 .9 1.2 .6 .9 1.2 .9 — — - .55 - .792 .41 .402 .359 ..288 .506 .614 .788 .761 .943 1.116 - .159 .405 1.050 TABLE III—DATA- 2.3 4.0 17.2 29.25 9.15 5.2 18.8 30.6 40.0 6.3 19.85 31.35 7.4 10.2 .017 .06 .111 .160 .009 .076 .096 .141 .172 .064 .088 .096 .050 .040 3.54 3.73 — — 3.9 — — — — 4.06 — — 4.22 4.39 .193 .178 ,— — .166 — — — — ' .157 — — .147 .138 .0881 .337 .624 .90 • .0542 .458 .578 .850 1.035 .408 .561 .612 .34 .29 .5 .75 .75 .75 1.0 — — — — 1.25 — — 1.5 2.0 .044 .253 .408 .67.) .054 .458 .578 .850 1.035 .51 .70 .765 .51 .58 32.1 1.1 - 28.3 1.1 30.1 16.7 -14.1 3.5 S9.0 .130 .027 -.115 .036 .146 .091 0 .088 .221 TABLE IV— 3.9 — — — — — — 3.67 .166 — — — — — — .162 DATA. .785 .16 - .695 .217 .88 .55 0 .543 1.305 1.0 — — — — — — .667 — .79 .16 - .70 .22 .88 .55 0 .362 .91 Table III is for pressure distribution tests in the American wind tunnel. Considering the difficulties of this last series of tests, it seems remarkable that such close-agree ment is obtained. The full line drawn on the.graph represents the mean of the values. This line represents the relationship f 4>) = (-25 + -020^,) - so that finally and C/i 6 = (.25 + .020^) - h^ KL upper 1 + 0 ' Am/ (12) KL lower 8 Diehl shows that the top and bottom wings do not come to their no-lift angles simultaneously due to a venturi effect between the bottom surface of the top and the top surface of the bottom wing. This might be likened to an equivalent change in the aerodynamic decalage and is neglected for the purpose of the present investigation. (b) Unequal Wings and Wings with Decalage. No attempt has been made to simplify Diehl's method of dealing with unequal wings and wings with decalage and reference should be made to his work except for all but equal-wing biplanes. Diehl's treatment is probably as simple as such a complicated problem allows.
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