MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER OGEE WINGS

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December 1, 1964
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Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Measurements, at Mach Numbers up to 2.8, of the Longitudinal Characteristics of One Plane and Three Cambered Slender ' Ogee ' Wings By C. R. TAYLOR COMMUNICATED BY TIIE DEPUTY CONTROLLER AIRCRAFT (RESEARCH AND DEVELOPMEN r), MINISTRY OF AVIATION Reports and Memoranda No. 3328* December, 1961 Summary. Measurements have been made of the longitudinal characteristics of one plane and three cambered slen ler ogee wings (p = 0.45, = 0208). at two subsonic and eight supersonic Mach numbers up to 2.8. he tests also included measurements of the zero-lift pressure drag and support interference of the plane wing. The results have been analysed to give data for estimating the performance of supersonic transport aircra r. LIST OF CONTENTS Section 1. Introduction 2. Description of the Models 3. Details of the Tests 4. Presentation and Discussion of the Results 4.1 Introductory remarks 4.2 Results for subsonic speeds 4.3 Zero-lift drag of the plane wing 4.4 Drag-due-to-lift at supersonic speeds 4.5 Lift and pitching moment at supersonic speeds 5. Conclusions 6. Acknowledgements List of Symbols List of References Appendix I--Corrections to measured lift and pitching moment for asymmetry ot the sting shroud Appendix II?Kell's free-flight measurements of the zero-lift drag of the plane wing Table?Details of the models Illustrations Figs. 1 to 40 Detachable Abstract Cards * Replaces R.A.E. Report No. Aero. 2658--ARC. 23,776. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 LIST OF ILLUSTRATIONS Figure 1. The planform 2. Variation of leading-edge sweepback across the span 3. Variation of thickness/chord ratio across the span 4. The thickness distribution-chordwise sections 5. The thickness distribution spanwise sections 6. Cross-sectional area distribution 7. Centre-line camber, wings 16, 17 and 18 8. Chordwise variation of camber loading for wings 16, 17 and 18 9. Details of wings 16, 17 and 18 10. Details of model supports 11. Lift vs. incidence, 114 = 0.3 12. Pitching moment vs. lift, M 0? 3 13. Drag vs. lift, M 0?3 14. Lift vs. incidence, M 0.8 15. Pitching moment vs. lift, M O? 8 16. Drag vs. lift, M 0-8 17. Lift vs. incidence, M == 1.4 and 1.8 18. Lift vs. incidence, M = 2.2 and 2.6 19. Pitching moment vs. lift, M = 1.4 and 2.6 20. Pitching moment vs. lift, M 1.8 and 2.2 21. Drag vs. lift, M = 1.4 and 1-8 22. Drag vs. lift, M = 2.2 and 2.6 23. Variation of aerodynamic-centre position with lift coefficient, M 0.3 24. Variation of aerodynamic-centre of non-linear lift, wing 15, M 0? 3 25. Analysis of zero-lift drag of wing 15 26. Variation of K, with Mach number 27. Comparison of measured pressure distribution for wing 15, at CI, = 0, with t k4'0 theoretical distributions, M = 2.2 28. Variation with Mach number of zero-lift pressure distribution for wing 15 29. Variation of drag-due-to-lift factors with Mach number 9 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 LIST OF 11,I,USTRAT ONS?continued Figure 30. Lift-dependent drag of the plane wing, C1 = 0.10 31. Variation of 7rAa/C, with p for plane wings 32. Variation of 0C1/acx with Mach number, wing 15 33. Variation of ? ac?,iac, with Mach number, wing 15 34. Variation with Mach number of ACm at constant CL, wings 16 to 18 35. Effective C for C = 0.075, wings 16 to 18 36. Variation of CL and Cm at design attitude with Mach number, wings 16,17 and 18 37. Notation for Appendix I 38. Free-flight measurements of zero-lift drag of wing 15 39. Free-flight model 40. Comparison of free-flight measurements with tunnel results 1. Introduction. The purpose of this report is to describe tests, in the 8 ft x 8 ft Tunnel at Bedford, on tot r slender ogee wings. All four wings had the same planform (p 0.45, ST/Co = 0-208) one ?51 plane and three were cambered to give varying amounts of centre-of-pressure shift at superson:e speeds. Measurements of lift, drag and pitching moment were made at two subsonic and eight supersonic speeds up to M = 2.8 and the tests also included pressure measurements to determine the zero-lift pressure drag and support interference for the plane wing at supersonic speeds. The present tests contribute to an extensive investigation of the aerodynamics of slender shap( s and their suitability for long-range supersonic transport aircraft. As a result of earlier work in aus investigation it has been suggested that it should be possible to design an aircraft having a acceptable performance and flight characteristics, utilizing wing flows which are both computabL and physically realizable, provided that: (a) its planform is slender with streamwise tips (at all flighi speeds the leading edges are 'subsonic') and the trailing edge is either straight or only slightl, swept; (b) it is integrated, in the sense that the wing and body are smoothly blended together t form a single smooth wing-like shape, capable of lifting over its entire length; and (c) the leadin edges are sharp and if the wing is cambered (in order to bring the centre of lift at cruising condition-. near the position of the aerodynamic centre at low speeds), the camber loading is zero at the leadin edges, so that the leading edges are attachment lines at the design incidence and at other incidencei the flow separations are either wholly above or wholly below the wine, 2.3 A fundamental featur of the flow past these wings is that at all flight conditions there is primary separation from all edge; and, under cruising conditions, the wing surface is free from shock waves. It should be noted that th 3 (87542) A 2 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 aerodynamic design point is not normally a flight condition. This is because, for wings with sharp and highly swept leading edges, the existing methods of design are only valid when du eading edges are attachment lines and it has been found that lower cruising drags are obtained by iisir 9 design lift coefficients lower than the cruise value. Earlier work in the slender-wing programme concentrated on wings of simple shape (e wings with rhombic transverse cross-sections, having planforms and centre-line sections Jefined b.! simple polynomials), and the principal object of the tests described here, was to deterrrime to vkt.t; r extent changes towards what was considered to be a more realistic shape would affea the high-speed drag and the ability of a simply designed camber to trim the wing: Thus, although the present wings conform to the restrictions of the preceding paragraph, considerations of an rircrait.t.towage, balance and structural requirements have influenced the choice of planform and thickness c istribu- tion. Consequently, they have much of their volume concentrated near the centre-line and, eonipared with most of the earlier wings, the position of maximum cross-sectional area is farther aft, tht mean trailing-edge angle and the minimum leading-edge angle are greater, and the planform oatarneter, p elco, has been reduced by 'waisting' the planform. For these wings the cruise concition is assumed to be C.,, = 0075, M = 2.2. 2. Description of the Models. Four shapes were tested, one plane, the others cambered; all four had the sar le plain and thickness distribution. The planform, which is defined by the equation .s3 XA 4:7.? --= 1 ? 2 ? 24- 2.2 -1- 3 ?3 ? CO C0 Co ST L= 0208,. co is shown in Fig. 1, where it is compared with two gothic wings and two other o7lee wings of the same slenderness parameter (s/c0). It will be seen that the lower p-value for the present ?;): pe has been obtained by waisting the planform while maintaining an apex angle comparable with that of the gothic wing with p = 7/12. This has resulted in a shape having two points of Inflexion ud an uneven variation of leading-edge sweepback across the span (see Fig. 2). The thickness distribution (Figs. 3, 4 and 5) is a 'lofted' shape without a defining eq,iation. It is an example of how a smooth integrated fairing could enclose a realistic pressure cabin and outboard fuel tanks. For these wings it was proposed that the engines should be enclosed in under-wing boxes whose shapes followed those of the clean-aircraft streamlines. Me stramwise variation of cross-sectional area is less smooth than those of earlier wings, the position of maximum area is farther back, and both the slope and curvature at the trailing edge are larger (see 1og 6). The camber surfaces for these wings were designed by the slender-wing-th( ory method of Ref. 4*. Inboard of the 'shoulder lines' the streamwise slope of the mean surface i:. consttit Along the span but outboard of the shoulders it varies parabolically with the spanwise c )-ordim,te. The * A computing programme for calculating the camber shape by linearized thin-wing theor\ vtai not available at the time. Slender-wing theory was chosen in preference to not-so-slender thew-117. 21 te7ause of its simplicity. 4 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 ratio between the values of the slope at the leading edge and at the centre is chosen such that the load vanishes at the leading edge. The ordinates of the mean surfaces have been obtain( d by integrating the surface slopes from a straight hinge-line at 95% root chord. The equation of the shoulder position is th)(x) = 05 0.5 + fax _1\2 co 2/ The shoulder position was chosen to be well inboard near the apex in order to avoid large ac verse pressure gradients; it was chosen to be farther outboard near the trailing edge to obtain a low l ortex drag'. The wings were cambered to give the following lift and pitching-moment coefficients: Wing CL(/ Cmd ad 0 15 (plane wing) 0 0 0 0 0 16 0 0-00853 0 30? 0.00853 17 0.025 0-00800 10 500 0-00853 18 0.025 0.00435 10 40? 0-00487 The design incidence ad is the inclination of the central part of the mean surface at the trailing edge (a = 0 corresponds to the no-lift attitude according to slender-wing theory). The values of 0 quoted are the maximum angles of leading-edge droop. At a lift coefficient of 0.075 the cambered wings are intended to have their centres of lift either 40/0 co (wing 18) or 7% co (wings 16 ar d 18% forward of that of the plane wing. In order to be able to use slender-wing (i.e. M = 1) theory to design a camber surface to live a prescribed shift of centre of pressure at a cruise Mach number of 2.2, it has been assumed that even though the centre-of-pressure positions of the wings may change with Mach number, th( difference in Cm between the plane and cambered wings, at the cruise CL, will not change an -1 wil' be equal to the difference. at the design lift coefficient. To decide the centre-of-pressure movement needed, it was also assumed that the aerodynamic centre at low speeds would not be affect:td 13N, wing camber. With these assumptions it was expected that the ACm required for this planform at CL = 0.075 would fall between the two values chosen (i.e. between 000487 and 0.00853) Details of the camber loadings and the shapes of the cambered wings are shown in Figs. 7, 8 and 9 Except for the nose sections, wings 15 and 16 were machined from steel, whereas wings 17 and 18 were fabricated from glass-cloth bonded with Araldite. For the force tests the models were supported by a sting of 2. 1 in. diameter and included a six-component strain-gauge balance (Fit. 10) On all the models the cylindrical sting shroud was symmetrically disposed at the trailing edge An additional model of wing 15 was used for the pressure measurements; this was connecte i to a cranked sting by a thin yoke near the trailing edge (Fig. 10), which was designed to leave the ippei surface of the wing free from support influence for M 1.4. The pressure holes (100 in nu nber) were distributed along five chordwise stations, located so that they represented equal amounts of frontal area, i.e. at yls,,, ---- 0.032, 0096, 0-176, 0-336 and 0656. A dummy sting shroud was available for the tests to investigate the shroud effect on zero-lift drag. Table 1 lists all the model dimensions. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 3. Details of the Tests. In the force tests, measurements of normal force, pitching moment and axial forct were m2cle at Mach numbers 0- 3 (approximately), 0.8 (approximately) and 1.4 (0.2) 2.8, at a con ;tant Rey.iolds number of 107, based on root chord. 'File incidence range used was: A = ? 6(10)0(,0)60(10)120 except at M 0.3 where = ? 60(10)200 . The models were tested both right-way-up and inverted in order to isolate the offects f flow deflections in the airstream (all the graphs in this Report refer to the mean of right-way -up and model-inverted results). All force coefficients are based on the plan area of the wings; the reference length for C?, is e (the second mean chord) and the moment reference point is at 0.5, i.e. at the centre of the plan area. The pressure measurements on wing 15 were made at M = 1.4, 1- 8, 2.2 and 2.6 mv the Reynolds number again being 107, with an additional test at M = 2.2, R = x . The incidences tested were a = - 2'(1?)2' and A = 0 model inverted. The tests with the curium/ ,lit-oud fitted were done only at zero incidence. At M = 2.0 additional force measurements were made at Reynolds numbers of 5 aid 15 nTilions, and the results were used to estimate the effects of model distortion under load. The iesults fo- the metal models showed no change with dynamic pressure (apart from the expected sh ft in th,T level of the drag polars), whereas for models 17 and 18 there were measurable changes in pit,:hing m mn,Trit and lift. The distortion corrections, at M = 2.0, for R = 107 were found to be: AAP = - SC,?,/CL = ? 0.010; these corrections have been applied to the results for all supersonic Mach numbers. The drag results in Figs. 13, 16, 21 and 22 are not corrected for the presence of the sting sl,rolid, except that the axial force has been corrected to free-stream static pressure at the shroud bam. The correction to the zero-lift drag of the plane wing has been derived from the pressure measure merits, it is closely approximated by A C,? = 0.00088 ? 0.00053 log and is taken into account n The analysis of the zero-lift drag measurements on wing 15 in Section 4.3. On the carAlered wings, ? except at the trailing edges, the sting shroud protruded from the upper and lower surfacs by different amounts, in effect distorting the camber surface. The estimated corrections for this are (see Apneldi 1 for details): Wing 16 AC?, -= 00003/p 17 000843 18 0.0005/p these are included in all the plotted results for supersonic speeds. The following tunnel-constraint corrections were applied to the results for subsom speecs: M 0.3 M 0-8 Aa/ C1, 0-72? 082? 0-056 0-093 A C?/CL2 0-010 0-010 where a is measured from the no-lift attitude. These figures were derived by applyin.?, the rthTtn,Td of Ref. 5 to this planform. The small blockage effect of these wings was allowed for !)y corn eing the values of p, and .121)172 given to the computer. 6 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Estimates of the accuracy of the tests suggest that the errors in the plotted results are within the following limits: C1: + 0.001 + 0?01CL Cm: + 0.0002 + 0 ? 01 Cm : + 0.0003 + 0?008CL2 except for M 0.3, where, due to the low dynamic pressure, the errors may be three times these values. For the pressure coefficients the random scatter, due to errors in pressure measurement. is thought to be less than 0.004; an additional error, due to uncertainty in the measurement of the true static pressure in the tunnel, is probably about + 0.005 (this would affect all the readings at one Mach number by the same amount and would not affect the measured pressure drag). An additional error in pitching moment may arise from the unaccounted-for variation with Mach number of the distortion correction. To promote boundary-layer transition near the leading edges, bands of 60 grade carborundum in Araldite were applied to the wings; these were in. wide and were located Tiu in. from the leading edges. This size of roughness (approximately 0.010 in.) was that required to cause transition at M = 2.8; it is estimated that at M =- 1-4 it is 1.7 times, and at M = 0.3 twice, the size needed. It did not cause transition at M = 2-0, R = 5 x 106. Further measurements of the zero-lift drag of wing 15 were made while this report was being prepared, using a more sensitive balance which has recently become available. The conditions for these tests were: (a) R = 107, M = 1.4,1.8,2.2,2.4,2.6, and (b) R = 1.5 x 107, M = 1-4 (0.2) 2.2. The errors in C, for these tests are thought to be less than 0.0002. 4. Presentation and Discussion of the Results. .4.1. Introductory Remarks. The results of the force measurements at subsonic speeds are plotted in Figs. 11 to 16; Figs. 17 to 22 contain a selection of the force results for supersonic speeds and Figs. 27 and 28 show the measured pressure distributions for the plane wing. In the analysis of wind-tunnel results for performance estimation it is current practice to divide the drag of the aircraft into three separate, and additive, components, via. = -4- C CD DWI" + CM; (1) of which only one, the skin-friction drag Cm., is sensitive to changes in Reynolds number*. Of the remaining terms, CDory is the wave drag due to thickness and CDL is the drag increment due to lift. For the present series of tests, C Dow is the zero-lift wave drag as measured on the plane wing and if this is expressed as 128 V2 CDOTT 4K0, (2) IT Sen then K, is the ratio of the zero-lift wave drag of a wing to that of the minimum-drag body of revolution having the same length and volume. No distinction is made between zero-lift wave drag and zero-lift pressure drag. * The Reynolds number, based on length, for the full-scale aircraft at cruise is approximately 3.5 -; 108. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 The lift-dependent drag, C?,,, may be expressed in the forms*: CDL - C 2 7T A CI 2 (Kr 2 " +2/32 -- h?.), ITAc?2 where, in theory, K,. = 1 for an elliptic spanwise distribution of lift and K?. 1 in the approximation of not-so-slender-wing theory for slender wings having an elliptic streamwise distribi.r ion (1 The values of C?, for Kr = 1 ? K?, are sometimes known as R. T. Jones's lower hot nd foi the drag due to lift l,2,6. In general, K? and K,r will vary with Mach number and lift coeffi,ient. In the following sections we consider first the subsonic characteristics of the wing., then the breakdown of the drag, according to equation (1), and finally the lift and pitchit g-momr.a- t characteristics. 4.2. Results for Subsonic Speeds. In this section we consider those aspects of the results for subsonic speeds which are ,-elevaia t ) the performance of the aircraft, particularly those which affect the interpretation of the results tor supersonic speeds. It should he noted that, for these wings: (a) the incidence corresponding to ih landing-approach condition is about 14? and (b) the lift coefficient for 'hold' or `diversh.n' at bign subsonic speeds is approximately 0.10. The lift vs. incidence plots for M 0? 3 arid M 0.8 (Figs. 11 and 14) show an increas in lift-curve slope with incidence as is usual for slender wings, the curves for all four w ngs being virtually parallel in the region of interest. The 'approach' incidence can be seen to correq)ond to lift coefficient of approximately 0-45. At M 0-3 the lift curve of the plane wing is clo-wk, approximated by C?fa = 1-21 {1 + 1-45a2/31, where a is in radians, a similar, but larger vari.iti )1, of lift with incidence is given by the slender-wing theories of Adams and Edwards (cf. Ref. 7). The measured lift is approximately 7% more than that given by Peckham's generalised curve tor flat-plate delta and gothic wings", if a small allowance for Mach number is made by repha i CL by ,8'2CL, a by p'cx and sTico by g'sTlco; 13' = v/(1? M2). An important feature of the results for M 0?3 is the severe pitch-up (Figs. 12 and 22). For tlt- plane wing the aerodynamic-centre position moves forward about 4% e with an increase i,i CL iron- zero to the approach value; the movements are greater for the cambered wings and inci ease kith increasing amounts of leading-edge droop. The aerodynamic centre of the non-linear lift on ta( plane wing has been estimated by assuming that the aerodynamic centre of the linear lin reniailF fixed at 0-5, its position at C1 = 0, and the linear and non-linear lift components are given in 1.21a (rad) and 1.7606513(rad) respectively. This shows, Fig. 24, that the aerodynamic centre or the non-linear lift is always ahead of that of the linear lift and moves forward rapidly with nereasnig lift coefficient. At M 0.8, camber again has a destabilizing effect, but the pitch-up is less Than at M 0.3 and only occurs at lift coefficients greater than the flight value. At both subsonic Mach numbers camber has little effect on drag due to lift; at M 0-3 lie cambered wings have slightly more drag than the plane wing, at M 0.8 slightly less. At M 1, the drag polar for the plane wing is a parabola with K? = 1.54. The cambered wings have vor7cx drag factors, at C1, = 0.1, based on the C,o of the plane wing, of 1?44 (wings 16 at d 18) or ? 36 (wing 17). * Throughout the analysis C111, is the difference between CD of the cambered wing and C,,, of the fiane win z. 8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 4.3.. Zero-Lift Drag of the Plane Wing. In this section we consider the first two terms in the drag breakdown {equation (1)}, i.e. we consider the division of the zero-lift drag of the plane wing into the skin-friction and pressure-drag components. The pressure tests on the plane wing were specifically designed to facilitate this analysis by providing measurements of the effects of the sting shroud and a direct measurement of the zero-lift pressure drag. A comparison of the measured pressure distributions with those given by slender-wing theory and linearised thin-wing theory was also intended. Earlier tests in the slender-wing programme, mainly those on delta wings with rhombic cross sections and Newby or Lord V area distributions (cf. Fig. 6), have shown that the friction drag of these wings can be accurately estimated by calculating the drag of a flat plate of the same planform, assuming the boundary layer is locally two-dimensional, and multiplying this value by the ratio of the wetted area of the model to that of the flat plate. This method of estimating the skin friction has also been used here. The pressure drags of these earlier models are in close agreement with both linear-theory and slender-body-theory estimates of wave drag at low values of ,8s/c0, where the results from the two theories agree; but at higher values of the slenderness parameter, where the theoretical values diverge, the experimental drags followed the lower (i.e. slender-body) estimate. The breakdown of the zero-lift drag of wing 15 is shown in Fig. 25. The measured total-drag coefficients are increased by the correction for the masking effect and pressure field of the sting shroud. The difference between this corrected C,? and the estimated friction-drag coefficient should be equal to the measured pressure drag but it is, in fact, 0-0003 to 0.0006 higher. The errors in the various measurements are thought to be within the following ranges: C,? + 0.0003 (? 0.0002 for later tests) Shroud correction + 0.0001 Pressure drag + 0.0001 so that the most adverse combination of these errors cannot entirely account for the discrepancies. It must be concluded therefore, that the friction drag is at least 5% higher than estimated.* A comparison of the measured pressure drag with slender-body theory9f and linearized thin-wing theorymt estimates of the wave drag, Fig. 26, shows good agreement with linearized theory at all Mach numbers, and poor agreement with slender-body theory, thus reversing the trend of earlier results. However, the general level of K, is higher than that for wings with Newby or Lord V area distributions. It should be noted that, for wing 15, the difference between linearized and slender- body theories at the higher values of/3s1/c0 is much larger than for Newby and Lord V area distribu- tions and that Weber" has shown that differences of this order are typical of wings with comparably large values of ? c02S/(x)/I7 and ? c03S"(x)/17 at the trailing edge. For these locally 'non-slender' wings one must expect the zero-lift wave drag to be much closer to the linearized-theory value than to the slender-body-theory value. Recent calculations of the zero-lift wave drag of a family of delta wings with rhombic cross-sections'', using linearized theory, have shown that, even for the * In the light of more recent tests this conclusion should be modified. It now appears that the friction drag is no greater than was estimated. The discrepancies noted arc due to the drag of the bands of carborundum grit used to fix transition (cf. Appendix II). t See Acknowledgements, 9 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 'optimum'* wings, the values of K, increase when the position of maximum cross-sectional ar _.a is moved aft beyond 0?65c0. Thus, it can be expected that the relatively high drag of wing 15 is manly due to the relatively rearward position of the maximum cross-sectional area (see Fig. 6), which is partly a result of the low p-value of the planform. Further confirmation of the accuracy of linearized theory' is given by the excellent agreement of the theoretical pressure distribution with the measured values for M = 22, shown in Fig_ 27. The agreement here appears to be much better than, for example, that normally found between pressure distributions in two-dimensional flow over aerofoil sections at low speeds and the corresponding linearized approximations. By comparison, the slender-thin-wing-theory" estir late, while giving reasonable accuracy over the front of the wing, is seriously in error over the rear 25% c0, where the shape becomes non-slender. It should be noticed that the measured pre sure coefficients are quite small (Figs. 27 and 28) and therefore an important assumption in linearized theory, viz, that the perturbations are small, is genuinely satisfied. 4.4. Drag-due-to-Lift at Supersonic Speeds. We turn now to the last term in the drag breakdown and consider the lift-dependent drag f all four wings. In the absence of any theoretical method of estimating the lift-dependent drag for wings with leading-edge separation we rely entirely on wind-tunnel measurements and their analysis in terms of simple geometric parameters. Such an analysis of early measurements of the lift-dependent drag of plane slender wings has been made by Courtney". He found that if he plotted K=77-A(C )? Cm)/ CL2, for CL = 0.1, against gA, all the points for sharp-edged plane wings with streamwise tips lay close to the line K 075 + 0- 64/3A , 1.2 SA 3.2. These values of K, and also those for sharp-edged delta wings, are, in general, lower than the ;e for round-nosed delta wings collected and analysed by Cane and Collingbourne some years earlier , implying that the loss of leading-edge thrust due to sharpening the leading edge is more than compensated by the resulting leading-edge flow separation, (a) increasing the lift for a given inci-lence and (b) producing higher over-wing suctions than under-wing pressures on the forward-lacing surfaces near the leading edges. For camber distributions with attached flow at a CI, lower thi,n tht cruise C, the high loadings near the leading edges act on the drooped parts of the wing, wi- h th( result that, although the minimum drag coefficient may be increased slightly, the curvature -if tilt drag polar is reduced sufficiently to give a lower CD, and hence K, at the cruising C1, (as in Figs. 21 and 22). Thus the values of K given by Courtney's curve form an upper limit to the range of -alue, we would expect for cambered wings; a lower limit is given by R. T. Jones's lower boun:11,2,6 although this is no real physical limit and lower values may, in principle, be obtainable. The values of K derived from a comparison of the drags of the cambered wings with the zero-lift drag of the plane wing are shown in Fig. 29. It should be noted that although the potential errors iti these plots are quite large (e.g. AK = + 0045 + 0? 0018/C,2 for the worst combination of the errors listed in Section 3) the actual uncertainty in the points plotted is thought to be no more th in the * The 'optimum' wings are those members of the family having the smallest drag for a fixed post non of the maximum cross-sectional area, at a given gs,,fro. 10 Approved For Release 2002/10/16: CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 scatter about the mean lines shown on the figures. For all the wings the variation of K with M ich number is of the form K = K, 2K,d32?,7, 02 2/cwith the following values for Kr and Wing ? K, 0.075 K. C = K 0.100 K?, C,= K? 0.125 K?. 15 1.28 2-10 1.44 1.94 1-48 1-94 16 1.33 1.70 1-39 1.57 1-41 1-64 17 1-18 2.04 l? 22 1.76 1.22 178 18 1.23 1.74 1.22 1.76 1-30 1-56 All the cambered wings have lower values of K, and Ku., and hence lower values of K, than he plane wing. For the range of leading-edge droop angle covered by the cambered wings (i.e. 30? to .5 r) an increase in droop decreases increases K? and, in general, decreases K. For = O? 10 it is only the more highly cambered wings which have values of K lower than those of Courtne: 's curve. The drag factors for the plane wing are at least 0 ? 15 higher than his values but, neverthekss, they are still 0.25 lower than the value for zero axial force (i.e. 7rAoc/cr, in Fig. 30), which is better than average for wings of this V/Se*, implying that the main reason for the high lift-dependent drag of this family of wings is the low lift-curve slope of the planform. This is a direct consequence of the low value of p; as is shown in Fig. 31, where values of 77-Acil Cr, for CI, = 0-1, obtained from recent tests on plane gothic and ogee wings15, 16, 17, 18, are compared with the value for wing 15 at the same f3sT/co and the same A. 4.5. Lift and Pitching Moment at Supersonic Speeds. In this section we discuss the supersonic lift and pitching-moment characteristics and assess the effectiveness of the camber designs as means of trimming the wings at the cruise condition. In the previous section it was shown that for lift coefficients greater than about 0.07 the cambered wir gs have lower drags than the plane wing. It is also known that conventional trailing-edge controls may be very inefficient trimming devices (e.g. wind-tunnel tests of a model of the F.D.2 delta-wing research aircraftn have shown that, at supersonic speeds, the lift-dependent drag factor of the trimmed configuration is twice that for the fixed-elevator cases). Thus there is a considerable incentive to trim a supersonic aircraft, at cruising conditions, using camber alone. A comparison of the lift vs. incidence curves of the four wings shows that the cambers tested hAel no significant effect on the development of lift with departures from the design incidence (to make this comparison in Figs. 17 and 18 the curves for wings 17 and 18 should be displaced 1? to the left). Similarly, if allowance is made for the possible errors in the distortion correctiOns for wings 17 and 18, it is found that the camber has very little effect on the aerodynamic-centre position at supersonic speeds. The variations of aCjace and - ac?,lac,, for the plane wing, shown in Figs. 3 2 and 33, therefore may be regarded as representative of all four wings. At all Mach numbers the lift vs. incidence curves become straight for [3(a. ? ocd) greater than about 3? and two values of ac,,-), are plotted in Fig. 32. It is noticeable that, at the lower supersonic Mach numbers, where there is * e.g. (7rAolICL? K) varies varies from 0?10 to 0.30 for the wings of Refs. 16 to 19. 11 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16: CIA-RDP71600822R000100080002-8 more lift due to leading-edge separation, the Cm vs. CL curves are quite straight, implyin that tt e centres of linear and non-linear lift are virtually coincident. At the higher Mach number i there ,s less non-linear lift but the aerodynamic-centre position moves forward with increasing C. . Figs. 32 and 33 also show values of these two derivatives given by two approximate theones, both of which assume that the flow remains attached at the leading edge. Not-so-slender-wing theory", which has given good agreement with linear theory for conical wings and r,asonaitle agreement with experimental results for sharp-edged gothic wings21, is clearly of limited use for the present planform, with its highly curved leading edge. On the other hand Evvard's approxirnaa: theor y22, 237 which was not expected to be of much use for this slender highly curved planform, appears to give a fair estimate of the lift-curve slope at zero incidence and a quite reasonable estimate of the aerodynamic-centre position at zero lift. Turning to the trimming effectiveness of the wings, we recall that the cruising conuition was assumed to be CL = 0.075 at M = 2.2* and at this condition the wings should give centre-of- pressure shifts of either 4% c? (wing 18) or 7% co (wings 16 and 17). Further, the low-speed results have shown that, at approach conditions, there is a progressive forward movement of the aer.)- dynamic-centre position with increasing leading-edge droop. Thus in considering the trimming effectiveness of the camber we must take into account the fact that each wing will have ;. differeit most rearward e.g. position, dictated by the low-speed longitudinal stability requirement-i. Reference to the Cn, vs. CL curves for M = 2.2 in Fig. 20 shows immediately that none 01 the cambered wings achieves a satisfactory trimmed CL. The values of AC (i.e. C?, ? (Cm)wing at the same CL) and the shift of the centre of pressure for CL = 0.075 actually obtained ;,re showr in Fig. 34. It appears that, without allowing for the low-speed characteristics, wings 17 and 18 givt about half the C.P. shift assumed and wing 16 about one third. However, when the pitching-moinens reference points are moved forward to coincide with the low-speed aerodynamic-centre position: for CL = 0.45, as in Fig. 35, then, at M = 2.2, the effective centre-of-pressure movements art only 1-Mc0 for wing 16, 2% co for wing 17 and 1% co for wing 18, when a shift of *X, c? needed to trim. Some indication of the manner in which the camber designs have failed to give their desiox performance is given by the variation of lift and pitching moment with Mach number at desigri attitude (Fig. 36). These plots show that, if the design CL and Cm are attained at fls;r/co = 0, then there must be a very rapid increase in CL at ad with Mach number for 1 M 1- 4, due, no doubt, to loss of the designed negative lift near the trailing edge (see Fig. 8)?wing 16, which c.11s for the largest amount of negative lift, being the most sensitive to changes in Mach number. Mea-wreniciit:; of the load distribution on wing 1724 confirm that for this wing the designed negative lit near ttit trailing edge is not achieved, even at M = 1 ? 4, and also show that, at low Mach numbers, ttp: region near the apex develops considerably more than the design lift. The rearward movement or the centre of pressure with further increases in Mach number is due to increasing liit near tit trailing edge and decreasing lift near the apex. On any non-conical cambered wing one must expect a rearward movement of the centre ot pressure of the camber loading with increasing Mach number above M = 1; one must iiso expect a rearward movement of the aerodynamic-centre position. Whether the changes in these two quantities follow one another in such a way that the value of Cm, remains constant must depend (id * Higher lift coefficients, of the order 0.10, are now being considered. 12 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 both the planform and the camber loading. Clearly, the planforms with higher values of p, their larger chords near the tips, will have larger movements of aerodynamic-centre posit on (e.g. for a gothic wing, the change in x?(. in going from M 1 to M = 2 is 12% c015, compa ed with 3% c, for wing 15) and correspondingly larger changes in the centre-of-pressure position of the camber loading can be tolerated. The present wings failed to maintain their designed A because the changes in the centres of pressure of the camber loadings outstripped the shift in aei ?- dynamic centre (which was not as large as expected), mainly due, as we have seen, to the rapillv varying camber loadings near the trailing edge being too sensitive to changes in Mach numLer. A more-favourable result could be expected from wings with less-curved planforms and hiver values of p, using smoother camber loadings. However, it may not be possible to utilize planforms and camber loadings which are smooth enough to justify the use of slender-wing theory and, in general, it would seem necessary to calculate the shape of the mean surface by linearized theory for the cruise Mach number. 5. Conclusions. Analysis of the results to provide data for performance estimation, and comparisons with ear ler results, has shown that: (i) the zero-lift wave drag and zero-lift pressure distribution for the plane wing are both in cl se agreement with predictions of linearized thin-wing theory; (ii) the zero-lift wave drag of the plane wing is higher than the values for wings of the same volume and length obtained in the earlier tests; this is attributed to the relatively rearward posit on of the maximum cross-sectional area, which partly results from the relatively low value of :he planform shape parameter, p (iii) the lift-dependent drag factors of the wings are higher than those of other slender wings, when compared at the same value of /3A; this is mainly due to the low lift-curve slope of the wings, which, in turn, is due to the low value of p; (iv) the camber shapes designed by slender-wing theory do not give the desired changes in centre of pressure at M = 2.2, the 'non-slender' camber loadings being more sensitive to changes in A/Leh number than the incidence loading; (v) the trimming effectiveness of the cambered wings is significantly reduced by 'pitch-up' at the low-speed approach condition, the more-cambered wings being more affected. An obvious implication of these conclusions is that a better aerodynamic performance would be obtained from a wing with a less-curved planform, having a higher value of p. Such a wing would be expected to have: (a) a more forward position of maximum cross-sectional area and therefore a lover zero-lift wave drag, (h) a higher lift-curve slope and therefore a lower lift-dependent drag, and (c) less pitch-up at low speeds. A better trimming effectiveness of the camber for such a wing would also be expected if a smoother camber loading were used and the mean surface were calculated by linearized theory. 6. Acknowledgements. The author is indebted to Dr. J. Weber (R.A.E. Farnborough) for her calculation of -he slender-body-theory and linear-theory wave drags for wing 15 (Fig. 26), to Mr. J. H. B. Smith (R.A.E. Farnborough) for the linear thin-wing-theory pressure distribution and to Dr. C. S. Sinnott (Hawker-Siddeley Aviation Limited) for the slender-thin-wing pressure distribution for wing 15 (Fig. 27). 13 Approved For Release 2002/10/16 : CIA-RDP711300822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 LIST OF SYMBOLS A Aspect ratio, 4s7,2/S c(y) Local wing chord c, Root chord First mean chord Second (aerodynamic) mean chord CD Drag coefficient CD0 Zero-lift drag coefficient of plane wing CDT, CD - C?,, where C?, is zero-lift drag of plane wing CL Lift coefficient C10, Design lift coefficient Pitching-moment coefficient (based on -e) Design pitching-moment coefficient Pressure coefficient Lift-dependent drag factor (see Fig. 29) L(x) Spanwise integral of loading/4U' Mach number of free stream Planform parameter, elco Reynolds number based on c, s(x) Local semi-span s,, Semi-span Plan area S(x) Cross-sectional area (Fig. 6) I(Y) Local maximum wing thickness V Wing volume x, y, z Cartesian co-ordinates with origin at wing apex Incidence (in degrees unless stated otherwise) LY,t Incidence at design attitude g / _ 1) -V(1 ?1112) A Angle of sweepback of leading edge Volume parameter, V/S""2 = C?, ? ?, at constant CL (AC,,,) = AC,,,, referred to low-speed A.C. for CL = 0.45 e = tx + c(y) c0}/c(y), non-dimensional chordwisc co-ordinate 7/(x) = S(X) 14 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 No. Approved For Release 2002/10/16: CIA-RDP71600822R000100080002-8 REFERENCES Author(s) Title, etc. 1 D. Kuchemann . Aircraft shapes and their aerodynamics for flight at supersoni speeds. Advances in Aeronautical Sciences, Vol. 3, p. 221. Pergarno Press. 1961. Proc. 2nd int. congr. Aero. Sci., Zurich. 12 to 16 September, 1960. 2 E. C. Maskell and J. Weber On the aerodynamic design of slender wings. J. R. Ae. Soc., Vol. 63, No. 588, p. 709. December, 1959. 3 J. H. 13. Smith . The problem of trim for a supersonic slender-wing aircraft. Unpublished M.o.A. Report. 4 J. Weber Design of warped slender wings with the attachment line alohg the leading edge. A.R.C. 20,051. September, 1957. 5 S. B. Berndt Wind-tunnel interference due to lift for delta wings of small aspect ratio. K.T.H. Aero. Tech. Note 19. Sweden. 1950. 6 R. T. Jones The minimum drag of thin wings in frictionless flow. J. Ae. Sci., Vol. 18, No. 2, p. 75. February, 1951. 7 J. Weber . Some effects of flow separation on slender delta wings. A.R.C. 18,073. November, 1955. 8 D. H. Peckham Low-speed wind-tunnel tests on a series of uncambered dent er pointed wings with sharp edges. A.R.C. R. & M. 3186. December, 1958. 9 M. J. Lighthill . The wave drag at zero lift of slender delta wings and similar configurations. J. Fluid Mech., Vol. 1, Part 3, p. 337. September, 1956. 10 H. Lomax .. The wave drag of arbitrary configurations in linearized flow, as determined by areas and forces in oblique planes. N.A.C.A. Research Memo. A55A18. March, 1955. 11 J. Weber .. Some notes on the zero-lift wave drag of slender wings with unswept trailing edge. A.R.C. R. & M. 3222. December, 1959. 12 J. H. B. Smith and W. Thomson The calculated effect of the station of maximum cross-secticiial area on the wave drag of delta wings. A.R.C. C.P. 606. September, 1961. 13 J. Weber . Slender delta wings with sharp edges at zero lift. A.R.C. 19,549. May, 1957. 14 A. L. Courtney . A collection of data on the lift-dependent drag of uncambi red slender wings at supersonic speeds. Unpublished M.o.A. Report. 15 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 No. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 R EFERENCES--continued Author(s) Title, etc. 15 L. C. Squire . ? An experimental investigation at supersonic speeds of the characteristics of two gothic wings, one plane and one cambered. A.R.C. R. & M. 3211. May, 1959. 16 L. C. Squire 'I'he characteristics of some slender cambered wings a Mac numbers from 0- 4 to 2-0. Unpublished M.o.A. Report. 17 D. G. Mabey and G. P. Ilott . The characteristics of three slender 'mild ogee' wings a Mach numbers from 0- 4 to 20. Unpublished M.o.A. Report. 18 A. L. Courtney and A. 0. Ormerod Pressure plotting and force tests at Mach numbers up to 2-8 of an uncambered slender wing of p srlc? -- (1 landley Page Ogee). A.R.C. 23,109. May, 1961. 19 C. R. Taylor and T. A. Cook .. Six component force measurements on a 1/9th scale modei of the Fairy Delta 2 research aircraft at Mach numbers up to 2 ? 0. Unpublished M.o.A. Report. 20 MacC. Adams and W. R. Sears .. Slender-body-theory review and extension. J. Ae. Sci., Vol. 20, No. 2. August, 1959. 21 L. C. Squire Some applications of 'not-so-slender' wing theory to winf.-,s vvitn curved leading edges. A.R.C. R. & M. 3278. July, 1960. 22 J. C. Evvard The effects of yawing thin pointed wings at supersonic seeds. N.A.C.A. Tech. Note 1429. September, 1947. . 23 J. Gilbert .. Approximate method for computing the pressure distribu7ion on wings with subsonic leading edges in a steady stream. English Electric Aero. Tech. Memo. AM18. 1956. 24 J. Britton . Pressure measurements on a cambered ogee wing (p = 0 45) at Mach numbers up to 2.6. Unpublished M.o.A. Report. 25 W. R. Sears (editor) . General theory of high speed aerodynamics. (Vol. VI of Speed Aerodynamics and Jet Propulsion.) Princeton University Press. 1955. 26 J. C. Evvard Use of source distributions for evaluating theoretical aerody ainic of thin finite wings at supersonic speeds. N.A.C.A. Report 951. A.R.C. 13,821. 1950. 27 C. Kell Free-flight measurements of the zero-lift drag of a slende, winf at Mach numbers between 1.4 and 2.7. A.R.C. 23,511. August, 1961. 28 R. J. Monaghan .. Formulae and approximations for aerodynamic heating rites iii high speed flight. A.R.C. C.P. 360. October, 1955. 29 J. B. W. Edwards Free-flight measurements of the zero-lift drag of a slendef oget wing at transonic and supersonic speeds. A.R.C. 24,448. October, 1962. 16 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 200,41)Ini6D:n11-RDP711300822R000100080002-8 Corrections to Measured Lift and Pitching Moment for Asymmetry of the Sting Shroud The asymmetry of the sting shroud distorts the mean surface. In the notation of Fig. 37 the distortion is Az(x, y) = -{Azu(x, y) ? Azdx, y)} and the corresponding additional incidence is 0 Aa(x, y) - ? y). (6) To calculate the additional lift AL(x) induced by the distortion on the segment of the w ng between x' = 0 and x' = x we utilize a flow-reversal theorem (cf. p. 235 of Ref. 25) which, or the present application, states that: AL(x) = 0 fr Aa(x', y') x) dy' dx' -r a 7) where Lip(x', y': x) is the loading, at a point (x', y'), on a flat-plate wing, of the same planform as the wing segment 0 x' < x, at incidence a in reverse flow. It follows from relations (5) and (6) that d r , y')dy' 1 2 dx; (Az,? Az2)dy' -r - 2 dx' where a(x') is the difference between the additional cross-sectional areas on the upper and low er surfaces. We may approximate Ap(x", y': x) in the region 0 ty' I r(x) by its value in the cent re and thus obtain for AL-(x) the approximate value AL(x) = ? f dx' J o a The wing segments in reversed flow are wings with supersonic leading edges and subsonic trailing edges. If x ? x' < ,es(x), then the loading is the same as in two-dimensional flow: 2 Ap 4 pU2 a p- ? If ,Bs(x) x ? x' ,Bs(x) + 2gs(x0), then the loading on the centre-line can be determined I- y Evvard's26 method. The solution which satisfies the Kutta-Joukowski condition at the suhson trailing edges reads: (87542) 2 Ap pU2 8 Ft sgn y, - {(x _ x,)2 isoy2}-1/2dy 77 ? 0 8 , Py, s n X - 17 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 When the upper- and lower-surface distortion fields do not interact, i.e. when x < Ps(x), 2 _ 2 AL(x) o(x) pU2 and, since the loading Ap/a is constant over the entire area of the distortion, this exp ession s exact. In other cases yi must be found by geometrical construction and AL(x) by integration. The corrections to measured lift and pitching moment are: A CL = 2 AL(x) p S and, for moment coefficients about 1/2, based on e, A Cfl, = ? A CL ? p---U2 2 ? fxT AL(x)dx. S1 For wings 16 to 18, xr/sT = 1.5 so that for M ?-? 1.8: AC1 = 2o-(x) I3S and AC? = -2 xT a(x)dx IRS'e - 0-0003//3 for wing 16 - 0-0008/f3 for wing 17 - 0-0005//3 for wing 18. At M = 1.4 and 1.6 the calculated differences from the above values were less than the probable experimental errors. 18 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 APPENDIX II Kell's free-flight measurements of the zero-lift drag of the plane wing In Ref. 27 Kell describes his free-flight measurements of the zero-lift drag of the plane w rig (i.e. wing 15) between M = 1-4 and 2.7. His results are reproduced in Fig. 38; also shown in this figure are his estimates of the drag of the small sting and stabilising fin (see Fig. 39) and the w ng friction drag. The model was flown with transition fixing bands of 0-007 in. carborundum crit 0.5 in. wide, located in. from the leading edges. The turbulent-skin-friction drag was estima' ed using the intermediate-enthalpy methods of Ref. 28. Estimates of the probable heating rates of he model were based on the flight history and the known thermal properties of the model. In order to illustrate the significance of the heat-transfer rate, Kell estimated values of skin-friction d ag assuming full and zero heat transfer; these are also plotted in Fig. 38. These last two estimates ire only intended to illustrate the significance of the heat-transfer conditions, they are not intended to indicate the limits of accuracy of the skin-friction estimates. The Reynolds number during the test varied from 42 x 106 at M = 1-4 to 105 x 106 at M = 2 7. The comparison of the 'apparent wave drag' deduced from the free-flight results with that fn)rri the tunnel force measurements for R = 107 and with the tunnel measurements of pressure dr4 is shown in Fig. 40. The 'apparent wave drag' is the total measured drag less the sum of the estimated friction drag and the sting drag, and fin drag (if any). In the region of principal interest, i.e. near M = 2.2, the free-flight results are about 0.0005 higher than the tunnel force results and 0-0( 08 higher than the measured pressure drag. It is now recognised that, in both the tunnel and f1.4 ht tests, there were significant drag increments due to the roughness bands which were not taken into account in the analyses of zero-lift drag.* The roughness drag increment in the free-flight tests is expected to be larger than that for the tunnel tests since the grit used in flight was excessively coarse for the high Reynolds number of the tests. In view of the surprisingly large drag increments in the tunnel-0.0003 at R = 107 and 0.0005 at R = 1-5 x 107 for a grit which did not prow- ke transition completely at R = 0.5 x 107- --it could be anticipated that the drag of the transition trip accounts for, at least, a major part of the discrepancy between the apparent wave drag derived frc,rn the flight measurements and the tunnel measurement of pressure drag. * See footnote in Section 4.3 and Section 4.5 of Ref. 29. (87542) 19 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 TABLE Details of the Models Length (c0) 60 in. Span (2sT) 24.96 in. Plan area (S) 674 in.2 Volume (V) 726 in.3 (excluding sting shroud) Surface area 1420 in.2 (including sting shroud) Sting-shroud diameter Sting diameter 2.60 in. 2-10 in. Planform parameter (p) 0-45 Aspect ratio 0.924 c/co 0.616 T V/S3 2 0-0415 vis-e 0.040 4 '77' Co KCILD? = S 406.5 128 V2 Moment reference point at 0.5e (i.e. at centre of plan area) 20 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 I \ \ I\ \ \ I \ \ V\ I \ \ \ p= 57/3 UoTH1C p .;12. Gomic p /15 OGEE (COURTNEY) p a OGEE (COLLINGSOURNE) WINGS 5-81 ('; 0.45) 5T/.. = 0.208 ii FIG. 1. The planform. 0 IS SA.tori A0 1 0 0'5 0 008 0.06 0.04 0-02 1 WiNG5 15-18 .0 .45) ? ? QUARTIC OGEE 1...0.5) ?COLLINGBOURNE. OGEE 0 '5) ? ? ? 'COURTNEY' MILO 0G52 .0. 533) 0 0-2 0.4 0-6 0-5 o FIG. 2. Variation of leading-edge sweep- back across the span. 0.040 0 05 04 0.6 043 1.0 WsT FIG. 3. Variation of thickness, chord ratio across the span. 8-Z00080001?000tIZZ80081./dCltl-VI3 : 91./01./ZOOZ eseeletl JOd PeA0AdV Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 FIG. 4. The thickness distribution?chordwise sections. 22 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16: CIA-RDP71600822R000100080002-8 ? 0-4 NOTE THE VERTICAL AND SPANN/10E? OIMEN5ION5 ARE MAGNIFIED 42.4.) FIG. 5. The thickness distribution-- spanwise sections. 23 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 2.0 15-18 g -14.2 0: g -75 WINGS LORD -7 -14 -12 -48 NEWBY - - o.s 0.1 02 0-3 0.4 0.5 0.6 0.7 3C/c. FIG. 6. Cross-sectional area distribution. 24 0.8 0-9 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 1 0 " Approved-For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0 04 0.02 WING 16 WING 17 WING 18 0.10 -E 0.05 LOE.) ST 0.2 04 08 G /C0 0.8 ID FIG. 7. Centre-line camber, wings 16, 17 and 18. / __, --...\\\:\ \ \ ? \ ? /1 iii I, FIG. 8. Chordwise variation of camber loading for wings 16, 17 and 18, as assumed in slender-wing theory. NOTE: VERTICAL GPANWISE DIMENSIONS MAGNIFIED (2.4) -- WING 16 WING 17 WING 18 10 FIG. 9. Details of wings 16, 17 and 18. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 STING SUPPORT (FORCE TESTS ONLY) 24% STING SHROUD (2.6 DIA) --------- H.7\ MOMENT REFERENCE PT 60. / SUPPORT FOR PREStURE -PLOTTING MODEL FIG. 10. Details of model supports. 26 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP711300822R000100080002-8 / / , Y / / , / / , / / r / //// i wiNG i5 WING 17 WING le ? ? / I . i 4' e 1 . I 1 i a. le d. a, FIG. 11. Lift vs. incidence, A/ 0.3. 0 OS 0 04 003 0 02 001 -0 I 1 WING IS WING 16 WING 17 WING IS -- --- . / / ? / . / ,..., ?.?--,-- /?.., / 77/ .> 7 -- ,- .... ,...- r ..-- - ., ,--? --.-- -001 + 0.1 2 0.3 0.4 CI. 0.5 .6 07 FIG. 12. Pitching moment vs. lift, _11= 0.3. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0 24 0 20 0 15 co 0 12 0.0e 04 I.__ -0.1 0 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 WiNG 15 WING 16 WING r7 WING le I ? ? -- -- . 7 . / . . - 04 FIG. 13. Drag vs. lift, M 0.3. 04 0.7 0 0 0 0 0 0 0 .40 .35 / .. 2 WING WING WING IS 17 le / / 20 / / ,. r / II /? /// / / )5 - 400 FIG. 14. Lift vs. incidence, Al 0.8. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0 012 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 WING IS WINO Pe WING WING 18 FIG. 15. Pitching moment vs. lift, M 0.8. -- ?0035 win* 15 WING IG WING n WING IS / ? --- ? / r 0 025 co ?0.020 ,, , 0.015 . ?0010 ???%,......... ?0 005 ci -0.05 +0-05 0.10 0-15 oeo FIG. 16. Drag vs. lift, M 0.8. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 25 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 w NG 15 WING 16 WING 17 WING A / . ......,,, , 0I5 012 -0 -08 .7/ 77-X" ......X.77/ ,4 ./....4"./.. / M?t-6 0 3' 4 5' 7' 'GU / 16 t 12 Z" -08 , 1-01 _...007/t1.1?4 5 6 FIG. 17. Lift vs. incidence, 31 =-- 1.4 and 1.8. a- 0-2 0 c? 0 To -r _ WING 15 WING 16 WING I? WING ...."- ...," ...--- ...-"" ....." .../ ...." ....". ...." ..., ../ / el t -6 +16 2" 4' 5' .c 6' ucv 016 CI. 0 -12 / ../ ./' .-- ../..".." . ..../. .----- /''' 0 .05 ...," ....." ....1".'4 0.04 ....../.2". :1622. +I. e- 3' 4." S. 6 FIG. 18. Litt vs. incidence, M = 2,2 and 2.6. Approved For Release 2002/10/16 : CIA-RDP711300822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 -.0.0080 -0-04 -0. c,? --0-0040 ?.6008 MZ 6 -1- 0 12 0 6 ............. CL,.."-z MUM YANG 15 WING 16 WING 17 WING 18 ,c1-Lneg NN. i M ? 1.4 N.\\N,s. N. N.., 'N.........\\ ? .\\ ? N 0 04 +604 016 0- C, -0-0040 Cm. 'N -600120 =0-0160 FIG. 19. Pitching moment vs. lift, M = 14 and 2.6. 0 0 1?1+2?2 0 -0-04 N 0040 00080 0-0120 N. .?......... + 0 12 .......N.N \ \ .".".... ......,_ ? ........_ .... \ ::"... ......_ - ..... -\ .....7.. ....i 0-IS 010 CL ?,60080 - -0-04 WING 15 WING 16 WING 17 WING 18 0 -?60040 -60-0060 -60-0120 -.0-0160 N. + 0-04' 001ir ? 612 N. 010 0-20 CL FIG. 20. Pitching moment vs. lift, M = 1-8 and 2.2. A roved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0 -024 0 020 ?0-012 14?1-4 ?0006 ?0004 II ?0-024 ?0-020 0-016 ?0-00$ ?0-004 ?1-8 WING 15 WING 16 WING 17 WING IA 0 -0.04 0 #0-04 006 0-12 0-16 -0-04 0 +0.04 006 CL c, FIG. 21. Drag vs. lift, M = 14 and 1.8. 0 024 -0020 0 016 Co -0004 -0.04 2- 2 WING 15 W1N4 16 WINO 17 WING 1B 0.04 0.013 0'12 GL 012 ?0-004 0-16 -0-04 + 0-04 002 012 CL FIG. 22. Drag vs: lift, M = 2.2 and 2-6. 32 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0.16 (87542) Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0 10 004 002 ?64 % ?65 77., - ? A.C.(% c) ' ?72. ?66 X; ,..?..,"... ?67 ..-'--2 .../ ,,-- ,/ "?666, ?69 0 1 0.2 03 04 CL FIG. 23. Variation of aerodynamic-centre positions with lift coefficient, M 0-3. 05 0.6 I i '-------\,,,,N.N...1................................... Ci..1.21 it 4 MIK % eCaYaC,)0 .0 42 664 6 60 0402 0, FIG. 24. Variation of aerodynamic centre of non-linear lift; wing 15, M 0-3. 33 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0.010 0.006 CD 0004 0.002 O MEASURED Co. o MEASURED Co. + SHROUD CORRECTION - ESTIMATED Cr O MEASURED PRESSURE DRAG DASHED SYMBOLS DENOTE LATER TESTS --SHROUD CORRECTION 1.2 I 4 1:6 I 8 2.0 2.2 0.010 0-008 0-006 Co 0-004 0-002 (a) R = 107. 24 26 2-8 ? MEASURED CD. 111 MEASURED Co. + SHROUD CORRECTION - ESTIMATED CF ? MEASURED PRESSURE DRAB 0 I 2 CORRECTION t 4 I? 6 1'8 2.0 2.2 2-4 (b) R = 1.5 X 10 7 (later tests). FIG. 25. Analysis of zero-lift drag of wing 15. 34 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 K0 -e-- MEASURED PRESSURE DRAG - SLENDER -WIN q-THEORY WAVE DRAG - LINEAR - THEORY } 1.2 0.8 04 K0 ? Trziza C04/0 0wz9, _ `.. N.N.. g I I. C ''''`............. 1111 l? 8 E.0 ....., 2.2 -"-.........., 2-4 2-6 .......T........"-. 2.8 M = 1.4 0.1 FIG. 26. 0-2 03 04 ST/c. 0.5 0.6 Variation of K, with Mach number, wing 15. 35 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 LINEAR THIN - WING THEORY SLENDER-THIN -WING THEORY MEASURED VALUES (R .1.5 .107) - 0 05 0 ?176 cp -0.05 Op -0.05 ,/sT . 0.656 cp vsT"'336 0.9 ? .0.05 0.3 0.4 0.5 0.6 0.7 0.8 FIG. 27. Comparison of measured pressure distribution for wing 15, at CL -= 0, with two theoretical distributions. M = 2.2. 36 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 - 010 - 0.05 c, Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 ? o /er'r 1-0.05 04 +0.10 , x100?5 0.6 010 005 C, 4-005 + 010 + 015 06 08 0.7 08 9./s.r. 0.336 d9 JO - 0 I 0 cp 0 05 +0051 , Dc/0.. 0.75 080 085 ? M.1-4 ? M? 1.6 ? M? 2.6 ......?..--ir ,---s- /V ----- 0-4 06 08 0 656 ST 090 095 to m?1-4 ? 11?2.6 ^ ...".. .-....-C- ? 4- ar' ----&? a o(O 03 . 4-.... . _ - 06 07 0.8 0-9 ill E/ sr '0.03 2 X/c.. 01 0-2 0.3 0-4 0.5 0.6 0-7 0.8 0.9 10 Fro. 28. Variation with Mach number of zero-lift pressure distribution for wing 15. 37 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 K ? it A (Co - WHERE Co. is ZERO-LIFT DRAG COEFF. OF WING 15 WiNG 15 WING 16 o ? WING 17 ? WINO 18 25 20 O.. 0-10 I 00 25 20 IS I0 0 0-1 02 03 04 0-5 201840.a I I II- I 4 16 I- 2-0 2-2 2-4 2-6 2-5 20 5 to ..?-?"'" ' t-----. ..------ ......--o? -*---- ?.Jo' _......t-r- ....?...- ,...------ ,c,....-.0 - ---- ..-1... , -a> -3.-......--- ...:-..C---- K?12751-0-640A 0-1 2/6 ST/ 0-4 0 5 M 1-4 1-6 1 B 2-0 2-2 2-4 26 CL. 0-075 --. -- 2 ?????".....d.891..5.:-......4 ? ...-- ,?*4 ...--- ....?....ArP .--;;;---. III 1 I I 1 14 s 1-4 1-6 I-8 00 2- 2 04 2-, 01 0-2 0-5 ZA ST/Coa FIG. 29. Variation of drag-due-to-lift factors with Mach number. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0-4 6 05 30 25 20 Is 10 s 2.0 '5 I0 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 ..../- --le" ...-..'" -,-----3 - ------"'-ji , -- .... .- - n A.5.c.../... K--..- . ..-"" ..... ,-.- ? ../.. . FIG. 30. 01 02 Lift-dependent drag of the plane wing, CL = 0.10. O WING 1 IMF. 15 A WING 8 REF St. ? WING 9 REF I 7 37/0.?0'25 + WING 15 PM 18 X %ONG 15 5 0.433 0.40 045 fiA?1.30 060 065 0/0 P ? a 5%. A ? a/Co r 'c, " 20 16 I 2 KL PER RAO 08 0 -e- MEASURED VALUES o.0 - MEASURED VALUES /3 > 3' 'NOT-50 -SLENDER' THEORY EVVARD'S APPROX. THEORY \ \ ? ? \ a. M' 1 1.4 1 1.6 1 1.11 1 20 I i 2.2 .2.4 21.6 2.. ii 0.05 0.10 0.15 0.20 /3157a FIG. 32. Variation of CCL/aa with Mach number, winv 15. ? 30 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0.16 0.12 - bet, 0 05 Approved For Release 2002/1.0/16 : CIA-RDP71600822R000100080002-8 MEA5LRE0 VALUES CL MEASURED 'VALUES 'NOT- 50- SLENDER THEORY EVVARD'S APPROX. THEORY 004; M 1.6 1.8 0.05 010 2.0 2-2 2.4 0' '5 0- 20 s FIG. 33. Variation of ? Jicmiac,, with Mach number, wing 15. 211 025 030 0-012 0-008 0-004 0- 0 CL ? 0-075 4 2 0 1 6 1. 6 I-6 2.0 2 2 2-4 2.6 IA FIG. 34. Variation with Mach number of AC?,, at constant CL, wings 16 to 18. v WING 16 WING 17 WING 16 MINIMUM (A C.X170 TI AT CL .0-075 wig ooe :,,$)*-t ......... -----'s? ? A 1 4 6 13 20 22 24 5 FIG. 35. Effective AC for CI, = 0.075. -ripnc 16 tn 1Q !Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 8 6 4 2 0 CP SHIFT (% C.) CL 0-04 0-02 0 010 0-006 0.004 0-002 0 'Approved For Release 2002/10/16 : CIA-RDP711300822R0001000800028 0 005 010 a 0-15 pa S-ric: 020 0.25 M2 1-4 1-6 I-5 2-0 2-2 2.4 2.6 ? I 1 WING 16 WING 17 WING le DESIGN P75 ? ?. ? ?. 0 \\NN ... \ 22 NN's \ ? ? '....?........,?.?,.......... '.:::?-?....---?? 1 N ? ? ? ? ? ? ? ..--Z-....---,.... .... ? ..... ..... _ 0-05 0-10 015 (31 C 20 0 25 FIG. 36. Variation of Cr, and Cm at design attitude with Mach number, wings 16, 17 and 18, UNDISTORTED MEAN SURFACE ? ......_ "i2I3.(x-24)?/' DISTORTED MEAN SURFACE STING SHROUD (RAOILIS ?r) 17Tr. 1'7 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 tont 1- 0 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0-010 0-008 0-006 CD? 0-004 0.002 .- MEASURED TOTAL DRAG MAX 4_ MOST 7.- ZERO HI. H.T. _ PROBABLE ........ I HEAT TRANSFER -- ESTIMATED FIN -I- STING DRAG 1 14 1-6 II 20 22 2.4 2.6 STIMATED WING FRICTION DRAG 211 k FIG. 38. Free-flight measurements of zero-lift drag of wing 15. FIG. 39. Free-flight model. 42 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 0-006 0.006 CD 0.004 0-002 APPARENT WAVE DRAG, FREE FLIGHT APPARENT WAVE DRAG. TUNNEL, R 2z104 MEASURED PRESSURE DRAG 1.4 (87542) Wt. 64,11857 1s.5 8/63 1.6 16 29 p,A 2.2 24 26 26 FIG. 40. Comparison of free-flight measurements with tunnel results. 43 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8 A.R.C. R. & M. No. 3328 December, 1961 C. R. Taylor 533.693.3: 533.6.011.34/.5: 533.6.013.12/.13: 533.6.013.15 MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER 'OGEE' WINGS Measurements have been made of the longitudinal characteristics of one plane and three cambered slender ogee wings (p = 0.45, sr/co = 0-208) at two subsonic and eight supersonic Mach numbers up to 28. The tests also included measurements of the zero-lift pressure drag and support interference of the plane wing. The results have been analysed to give data for estimating the performance of supersonic transport aircraft. A.R.C. R. & M. No. 3328 December, 1961 C. R. Taylor 533.693.3: 533.6.011.34/.5: 533.6.013.12/.13: 533.6.013.15 MEASUREMENTS, AT MACH NUMBERS UP TO 2-8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER 'OGEE' WINGS Measurements have been made of the longitudinal characteristics of one plane and three cambered slender ogee wings (p = 0-45, sr/co = 0-208) at two subsonic and eight supersonic Mach numbers up to 2.8. The tests also included measurements of the zero-lift pressure drag and support interference of the plane wing. The results have been analysed to give data for estimating the performance of supersonic transport aircraft. A.R.C. R. & M. No. 3328 December, 1961 C. R. Taylor 533.693.3: 533.6.011.34/.5: 533.6.013.12/.13: 533.6.013.15 MEASUREMENTS, AT MACH NUMBERS UP TO 2.8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER 'OGEE' WINGS Measurements have been made of the longitudinal characteristics of one plane and three cambered slender ogee wings (p = 045, sr/co = 0.208) at two subsonic and eight supersonic Mach numbers up to 2.8. The tests also included measurements of the sero-lift pressure drag and support interference of the plane wing. The results have been analysed to give data for estimating the performance of supersonic transport aircraft. A.R.C. R. & M. No. 3328 December, 1961 C. R. Taylor 533.693.3: 533.6.011.34/.5: 533.6.013.12/.13: 533.6.013.15 MEASUREMENTS, AT MACH NUMBERS UP TO 2-8, OF THE LONGITUDINAL CHARACTERISTICS OF ONE PLANE AND THREE CAMBERED SLENDER 'OGEE' WINGS Measurements have been made of the longitudinal characteristics of one plane and three cambered slender ogee wings (p = 0.45, sr/co = 0.208) at two subsonic and eight supersonic Mach numbers up to 2-8. The tests also included measurements of the zero-lift pressure drag and support interference of the plane wing. The results have been analysed to give data for estimating the performance of supersonic transport aircraft. Approved For Release 2002/10/16 : CIA-RDP71600822R000100080002-8