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Aviation History
1936
1936 - 0531.PDF
SUPPLEMENT TO FLIGHT 8*8/ 14 THE AIRCRAFT ENGINEER FEBRUARY 27, 1935 TAPERED WINGS and SAFETY M Dr. G. V. Lachmann, A.F.R.Ae.S., Replies to Mr. W. R. Andrews' Criticisms of His Previous Article picture and then produce Presenting certain definite [Y article in Flight of January 2 on the stalling of tapered wings seems to have created the impression on Mr. W. R. Andrews (to judge by his article in The Aircraft Engineer of January 23) that the object was to paint a dark and pessimistic the slot as a dens ex machina. physical facts can hardly be compared with the painting of a picture. Besides, my short article never claimed more than to touch on certain aspects of the problem and the presentation of a particular technical solution which has been found to be practicable and to fulfil in full scale certain theoretical predictions. The object of my article was to show how the distribu tion of induced velocity across the span of a fully tapered wing, especially when the latter is fitted with a partial flap, can utilise to the fullest extent the beneficial aero dynamic characteristics of the slot. The result is a com pound wing comprising all the advantages of high taper for normal flight combined with a high maximum lift and satisfactory stability in roll at and near the stall. The second misapprehension on Mr. Andrews' part is that my article only considered wings having the same aerofoil section along the span, which limitation " is hardly in accordance with universal practice as far as cantilever wings are concerned." The wing considered in my article—which has been subjected to wind-tunnel tests, theoretical analysis and full-scale trials—is not of constant thickness/chord ratio along the span, but quite " in accordance with the rules of general practice " it has been designed with a skeleton line of constant camber and thickness/chord ratio of 17 per cent, at the root and 10 per cent, at the tip. This wing is actually used on a certain type of service aircraft now in production. I shall show later on that the influence of varying thick ness/chord ratios is unable to alter noticeably the stalling characteristics of wings having higher taper ratios than A = 0.75 and that sections of unusually high camber are necessary to produce a shght effect on wings of a taper ratio of X : 0.5, which is the maximum taper considered by Mr. Andrews in his article. A rather hair-splitting method has to be applied to not very reliable data (bearing in mind the elusiveness of KL max.) in order to show off an improvement which, when expressed in definite units and compared with the effect of a slight rate of roll, melts away very rapidly. For some reason, which I fail to see, Mr. Andrews con nects maximum KL with Km0 (zero lift moment) as if maximum KL were a function of the zero lift moment. Maximum KL as well as zero lift moment are, of course, functions of physical parameters, namely, camber and thickness. However, this method of linking up KL max. with Km0 has at least the advantage of showing off certain structural consequences to which I shall refer later on. It would appear that Mr. Andrews bases most of his conclusions—in regard to KL max.—on wind tunnel tests obtained in the high-compression tunnel in U.S.A. It is well known, however, that these figures are not too reliable, because of the influence of turbulence. However, for the following discussion I shall accept these figures on their face value. I find it a little difficult to follow Mr. Andrews' theoretical interpretations, and es_ pecially his remarks on damp ing in roll. Mr. Andrews chooses as a criterion for damping in roll the expres sion KL x c which, of course, is the load per unit span. -; Now, as far as damping in roll is concerned, the absolute loading is of no importance ; what matters, of course is the plan form of the wing and the slope of the lift curve dKhjda for infinite aspect ratio. Damping in roll for a constant and positive dK, can be expressed by : L, pv> da ./, (C).. dx /dK \~~da :l VARIATION of R0LUN6 MOMENT WITH ASPECT RATIO I I I 7 6 ? where : fm — downwash factor according to Munk dependent on lift distribution and aspect ratio. p == rate of roll. C x = chord at distance x from centre line. The value of the integral for a trapezoidal wing with root chord Ci and tip chord c0 becomes : ./» -S- I 1 — .5 -— —) p.v .p In Diagram 1 the rolling moment due to roll has been plotted for wings of various taper ratios on the basis of constant span, area, forward speed and rate of roll. The slope of the lift curve dK^/da has a constant value for any section quite independent of camber and thickness/ chord ratio. The theoretical value is w and the actual value is slightly below this. American results (N.A.C.A. Report No. 460) indicate a small influence of the thickness/chord ratio on dKhlda; however, this effect is doubtful and may be due to other causes and in any case is negligibly small. It follows, therefore, that damping in roll below the stall, i.e., when the slope of the lift curve for each section is still positive, is always less for a tapered wing than for a rectangular one and the higher the taper ratio the smaller will be the damping in roll. This is really one of the advantages of the highly tapered wing from the point of view of con trollability which has enabled large monoplanes with tapered wings to compete successfully with biplanes of constant chord. Apart from being impossible it would be quite absurd trying to develop a tapered wing giving the same degree of damping in roll as a straight wing. The only reliable way of determining damping in roll for a wing near stalling incidence is to measure the rolling moment due to roll on a rolling balance for various rates 0 roll. The calculation of rolling moment due to roll near the stall, in other words, damping moment for a partially stalled wing, gives very hypothetical and unreliable nsv^s' because the influence of the rate of spreading of the stalled area is unpredictable. . , I understand that tests of this kind have been carnea out at the N.P.L. with wings of various plan ten^dj^ sw these results are published they will shed more light on problem in question. . te In discussing damping in roll one has to difleren 1 ^ between the degree of rolling moment or the magnitu e rolling moment produced at a certain angle of mcid at a certain rate of roll, and the angle of incidence at wnu^ for a given rate of roll, damping becomes negative. latter point is of great practical interest because it
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