An Experimental Investigation on the FlutterCharacteristics of a Model Flying Wing

NATIONAL A£RO~i;\: ",'Ci ,L ESIABI..ISI-lMEN'I LIBRARY R. & M. No. 2626 (HI,509) A.RC. Technical Report An Experimental Investigation on the Flutter Characteristics of a Model Flying Wing By N. C. LAMBOURNE, B.Sc., of the Aerodynamics Division, N.P.L. CVGWn Copyright ReslWVod LONDON : HER MAJESTY'S STATIONERY OFFICE 1952 PRICE 6s 6d NET Reports and Memoranda No. April, 1947 r\lATiONAL ,,\ F,:():",J·I... E..:> ~ j·\l3i-1SH1Vd::.ll.r1 liBRARY An Experimental Investigation on the Flutter Characteristics of a Model Flying Wing By jl N. c. -LAMBOURNE, B.Sc., of the Aerodynamics Division, N.P.L. l r li.vaIiJ\l. ( .~ -. --- ,ml/ L t~~~\ 1.~,5~ \ • ... "'. _..." Summary.-This report describes some preliminary experimental work that has been carried out in an attempt to gain information on the flexural-torsional flutter characteristics of flying wing types of aircraft. Tests were made with two flexible tip-to-tip models:- A Rectangular plan form. B Cranked and tapered plan form. The method of supporting the models in the wind tunnel allowed certain bodily freedoms to be present either singly or simultaneously, and measurements were made of critical speeds and frequencies, and in a few cases the flutter motion was analysed by means of cinematograph records. The experimental results are in no way conclusive and cannot be directly applied to full-scale problems, but they do point to some of the difficulties in the treatment of the flutter of flying wings. Further, the difficulties encountered during the flutter tests themselves lead to suggested modifications in the technique of providing a model in a wind tunnel with the bodily freedoms appropriate to free flight conditions. 1. General Lntroduction.e-Yx: the problem of wing flutter of conventional single-engined aero- planes it is usually assumed that the critical speed that will be met in practice is only slightly different from that which would be obtained were the fuselage immobile. Frazer and Duncan' (1931) investigated theoretically the effect of fuselage mobility on binary flexural-aileron flutter for one particular aeroplane that was typical of practice at that time. Their conclusions were that the critical speed for longitudinal-symmetrical flutter differs little from that which is obtained when the fuselage is regarded as immobile, and that the critical speed for lateral-anti- symmetrical flutter is considerably higher than that corresponding to a fixed fuselage. The same authors also give one calculation to show that freedom of the fuselage in roll raises the critical speed for anti-symmetrical flutter of the ternary flexural-torsional-aileron type. More recently W. P. jones" (1944) has examined the case of anti-symmetrical flutter of a large transport aero- plane when the ailerons are mass underbalanced. He treats, inter alia, the cases of binary flexural-aileron flutter and of ternary flexural-torsional-aileron flutter, and concludes that the critical speeds for both types are raised by the introduction of rolling mobility. As far as pure flexural-torsional flutter is concerned the effect of fuselage mobility in roll has been investigated theoretically by Pugsley, Morris and Naylor" (1939). They conclude that for a single-engined aeroplane anti-symmetrical flutter is the least probable in practice, and they point out that in symmetrical flutter the vertical motion of the fuselage is likely to be small since the associated mass is large compared with the wings. Similarly, since the pitching moment of inertia of the fuselage is large compared with that of the wings, it may also be concluded that the pitching motion of the fuselage will be small during symmetrical flexural-torsional flutter. Published with the permission of the Director, National Physical Laboratory. 1 Although most of the foregoing evidence refers to flutter involving aileron movements, it has been usual to regard the effect of fuselage mobility on the flexural-torsional flutter speed as negligible, at least with single-engined aeroplanes. Valuable experimental investigations with half-span model wings rigidly held at their roots have been carried out on this basis. Not only were the experiments able to provide controls on critical speed calculations, but the results could, with a considerable measure of truth, be directly applied on a basis of dynamical similarity to the flutter of actual aircraft. In the case of an aeroplane with wing engines, where up to roughly three-quarters of the total weight may be located in the wings, the mobility of the fuselage becomes important. Experi- mentation using model cantilever wings rigidly attached at the root is still able to provide controls on calculations, but the results of the experiments are no longer directly applicable to the flutter which might occur in flight. With the advent of the flying wing type of aircraft in which there is a relatively uniform distribution of mass over a single lifting surface a more general approach to the flutter problem must be sought. The instabilities which may occur in flight can no longer be conveniently separated into those that do not involve structural distortions (i.e., the bodily oscillations dealt with by classical aircraft stability theory) and those that only involve structural distortions and control surface movements (i.e., flutter). The flutter problem of practical flying wings is also complicated by the sweep back (or forward) which will be present for the purposes of attaining both 'rigid body' stability and high speeds. The investigation to be described was concerned mainly with the problem of mounting a model flying wing in a wind tunnel so as to provide satisfactory allowances for true bodily freedoms which are present in flight. In the main the system of supporting the model was designed on the lines suggested by Frazer;' the models themselves consisted of flexible wings attached to a central body which could be supported in either of two manners for separate study of the sym- metrical and the anti-symmetrical types of oscillations. The two interchangeable suspension systems provided the following alternative sets of bodily freedoms (see Fig. 1):- (i) Appropriate to symmetrical flutter. Pitching. Vertical translation. (ii) Appropriate to anti-symmetrical flutter. Rolling. Yawing. Lateral translation. Tests were carried out with two tip-to-tip models* (see Fig. 2) as follows:- (A) Rectangular. (B) Tapered and cranked. The experiments with A were intended primarily as a simple approach to the more general problem. . '" Tests with a further model (tapered without sweep back) were originally intended, but on the completion of the work with the other two models it was not considered worthwhile to proceed with the construction of the third, The original experimental programme was ambitious in including provision for the variation of the stiffness and mass loading of the wings. In practice, however, the adjustments necessary to match the stiffnesses of the port and starboard wings were so tedious that no attempt was made to vary the wing stiffnesses once these matching adjustments were complete; nor was any attempt made to vary the wing inertias, and the flutter tests all relate to the effect of the freedoms of the central body. 2. Description of Model Wings.-The plan forms of the models are shown in Fig. 2. Each wing (root to tip) consisted of two separate parts, an inner and an outer bay, the inner bay being common to both the rectangular and the cranked model. The internal wing structure was designed to provide easily definable stiffness properties, and was of course not representative of actual practice. The general layout of the rectangular wings is shown in Fig. 3, whilst the outer bays of the cranked wings were constructed on similar lines except that the spars were swept back. Wooden spars at the leading and trailing edges of the inner bay were independently hinged by means of small ball bearings to an aluminium box (the central body) which is described in section 3. The spars were also connected to the central body by flat steel strips, C and D, which acted as torsion springs and constrained the hinging of the spars. The leading and trailing edge spars of the outer bay were similarly hinged to the outer ribs of the inner bay and were constrained by the steel strips A and B. The spars themselves were T-sectioned, quite stiff in bending but flexible in torsion, so that, whilst the flexure of the wing was controlled directly by the 4 springs A, B, C and D, wing torsion took place by the differential hinging of the leading edge spars. Thus, the torsional stiffness of the wing was dependent not only on the 4 springs but also on the characteristics of the wooden structure itself. Provision was also made for cross- connection of the leading and trailing edges by flat steel strips E and F at the outer sections of both bays, so that the torsional stiffness of the wing could be adjusted independently of the flexural stiffness. The leading and trailing-edge spars were also cross-connected at a number of points by light wooden ribs parallel to the longitudinal axis of the complete model and defining the aerodynamic sections. The inner and outer bays were separately covered with vaseline- doped silk and access to the springs was gained by removal of portions of the coverings (see Fig. 4). 3. Description of Support System.-The two interchangeable support systems shown in Fig. 1 have been described in outline in section 1. The apparatus as arranged for the case of symmetrical flutter and with all the possible spring attachments is shown diagramatically in Fig. 5. Rod AB was mounted in ball bearings bb attached to the walls of the wind tunnel. Rod CD, which was integral with AB, was arranged along the wind axis and supported by springs S", A light aluminium box which formed the central body to which the wings were attached, could pitch . about an axis through the ball bearings P,P; these small bearings were carried by a fitting E clamped to a sleeve R at the upstream end of rod CD, (see also Fig. 6). This sleeve was itself mounted on small ball bearings and could turn about its own axis to provide a rolling freedom for the model. During tests involving symmetrical flutter this last degree of freedom was of course locked. The wing-body combination then had two possible bodily freedoms as follows:- 1 Pitching about PP. 2 Pitching about AB (approximately a freedom in vertical translation and subsequently referred to as such). Independent clamps were provided so that either or both of these freedoms could be eliminated, and the majority of the tests described in this report refer to pitching freedom about PP only. In this case the central body was supported in the horizontal position by the pitching springs as shown in the diagram. It may be noted that if both the freedoms had been present simul- taneously a cross stiffness would have been introduced by the pitching springs. 3 It was possible to fix the pitching axis at various positions behind the leading edge of the model and the pitching inertia could be varied by masses clamped to rod F. Fig. 7 shows the aluminium box with one wing attached. During the flutter tests the box was shielded by a plywood cover, and Fig. 8 shows the complete apparatus mounted in the wind tunnel. For the case of anti-symmetrical flutter it was intended to keep the plane of the wings hori- zontal with the supporting apparatus reorientated as follows:- 1 Axis PP vertical, to form the axis of yawing. 2 Axis AB vertical, to provide approximately lateral translation. 3 Rolling freedom unlocked. The experimental difficulties encountered during the tests with freedoms appropriate to sym- metrical flutter led to the conclusion that the alternative arrangement of the apparatus would not be satisfactory for tests involving anti-symmetrical flutter. In fact, rolling was the only freedom appropriate to anti-symmetrical flutter that was used. 4. Experiments with Rectangular Wings.--Elastic Stiffness and Flexibility ColJ.7fcients.-The elastic properties were determined by means of flexibility coefficients referring to points 1, 2,3, 4 on each wing (see Table 1). From these measurements the flexural and torsional stiffnesses and the positions of the flexural centres were obtained on the assumption that the chordwise sections do not distort. The loads were applied to the spars themselves, and the vertical displacements of needles attached to the spars near the loading points were measured by means of micrometer heads. During these measurements the central body was clamped as effectively as possible and equal loads were applied at corresponding positions in both the port and starboard wings, so that any deflection due to the slight residual flexibility in roll was eliminated. There was, however, some movement of the central body in the vertical plane, and displacements were also measured at two additional points 5, 6, so that corrections could be applied to the wing deflections. It was found that creep occurred after a load had been applied, and to obtain consistent sets of coefficients the wings were allowed to settle for 4 minutes before readings were taken. Although the port and starboard wings were constructed in the same manner and similar flat steel springs were fitted in each, it was found at the outset that the two wings had vastly different stiffnesses. Much time was spent in altering the stiffnesses of the steel springs by modifying either their width or thicknesses until the wings had approximately equal stiffnesses. The method of carrying out these adjustments was firstly to remove the outer bays, and modify springs C and D (see Fig. 3) by trial and error until the flexural stiffnesses and positions of the flexural centre at sections (3, 4) were approximately the same for both wings. It was then found that the torsional stiffnesses of the inner bays were also in reasonable agreement, and no alteration of spring F was necessary. The outer bays were then attached and springs A and B were modified until the flexural stiffnesses and positions of the flexural centres as measured at sections (1, 2) were the same for both wings. It was again found that the torsional stiffnesses measured at these sections were in agreement, and no alteration of spring E was necessary. The final elastic properties of the two wings are contained in Table 1, where aij is the deflection at position i due to unit load at position i The measuring and loading positions did not quite coincide and they are given in Table 2. A more convenient picture of the final elastic state of the wings is provided by Table 3 which gives the flexural and torsion stiffnesses and the positions of the flexural centre for sections (1, 2) and (3, 4). 4 5. Inertial Properties and Natural Frequencies.-As a means of comparing the inertial properties of the port and starboard wings, each wing in turn was forced sinusoidally through a weak spring connected to the appropriate tip rib whilst the central body was held as firmly as possible. The reasonance frequencies were as follows:- ]Dort Starboard 1st resonance (mainly flexure) 2nd resonance (mainly torsion) 4·27 c.p.s. 8·17 c.p.s, 4·06 c.p.s. 8·22 c.p.s, It should be noted that since a metal fitting and a spring were attached to each wing during these measurements, the above frequencies are not the natural frequencies applicable to the con- ditions of the flutter tests; they merely serve to provide a comparison of the oscillatory characteristics of the two wings. This comparison was considered to be satisfactory and no adjustment of the mass properties was made. In order to determine approximately the natural frequencies of the wings without attachments the central body was forced inexorably in pitching. The measured frequencies which are appli- cable to the "body clamped" condition were as follows:- ]Dort Starboard 1st resonance (mainly flexure) 2nd resonance (mainly torsion) 3·21 c.p.s, 6·82 c.p.s. 3·17 c.p.s. 6·92 c.p.s, The nodal lines at the second resonance were found to be approximately at 0·5 chord aft of the leading edges of both wings. , 6. Flutter Experiments.-The critical speed for flutter was in each case measured by finding the lowest speed at which the system would continue to oscillate after a disturbance. The disturbance was initiated by padded levers which were normally clear of the wing, but could be operated to strike either or both wings. Clamps were also provided so that the wings might be held. As a preliminary experiment all the freedoms of the central body were locked, and the critical speed and frequency were measured for each wing in turn whilst the other was held in its clamp. The following results were obtained:- ]Dort Starboard Critical speed 43·0 42·9 (it/sec) Flutter frequency 4·68 4·98 (c.p.s.) 5 With the central body locked, but with both wings free, independent oscillations of both wings were obtained at the following critical speeds and frequencies:- Port Starboard Critical speed 42·7 42·4 (ft/sec) Flutter frequency 4·66 4·94 (c.p.s.) A more detailed description of these tests may be of interest. When the wind speed was adjusted to 42·7 ft/:::ec and the port wing was disturbed flutter of this wing occurred. At the same time a small amplitude oscillation was picked up by the starboard wing due to some slight freedom of the central body. This forced oscillation of the starboard wing was, however, not sufficient to initiate growing flutter oscillations. Similarly, when the starboard wing was dis- turbed at a wind speed of 42-4 it/sec it fluttered whilst the port wing picked up a small oscilla- tion in sympathy. If both wings were disturbed simultaneously at the higher wind speed, they fluttered at their different frequencies, and a small amount of beating was noticeable in the amplitudes. When this experiment was repeated on later occasions it was sometimes found that the wings, instead of fluttering independently oscillated symmetrically; on no occasion was anti-symmetrical flutter observed. Whether or not independent flutter occurred seemed to depend very critically on the effectiveness of the clamping of the central body. The critical speed for wing divergence appeared to be only slightly above the critical speed for flutter, but no accurate determination of the divergence speed was made. Effect of Bodily Freedoms.-6.1. Pitching Freedom.-The central body was allowed freedom to pitch about an axis PP 0·2-chord aft of the leading edge, which was the most forward position that could be obtained with the apparatus. It was found that the system became statically unstable almost as soon as the wind stream was started and remained so at least up to 50 ft/sec; this suggested that the aerodynamic centre was forward of the 0·2-chord position. It was thought at first that this might be caused by the aerodynamic moment due to the rod and inertia weight which projected forward of the central body, but tests with these removed showed that the wing-body combination was itself aerodynamically unstable. Therefore, it was necessary to provide some stability in pitching, and springs were attached to the central body from above and below. Critical speeds and frequencies were measured for variations of both the pitching inertia of the central body 1