Free Flight Measurements at Supersonic Speeds of the Drag of a Particular Delta Wing having a l Simple Prkssure Distribution

Transcription

1 C.P. No p A.R.C. Technical Report MlNlSiRY OF SUPPLY AERONAUTICAL RESEARCH COUNCIL CURRENT PAPERS -WX. EliT&YLis~t,+ 1, 1 Free Flight Measurements at Supersonic Speeds of the Drag of a Particular Delta Wing having a l Simple Prkssure Distribution P. J. Herbert, B.Sc. Crown Copyright Reskrved LONDON: HIS MAJESTY S STATIONERY OFFICE 1951 Price 2s. Od. net.

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3 C.P. 57 ROYAL AIRCRAFT FSTABLISHMETJT Report NO. Aero 2406 November, 1950 Free Flight Measurements at Supersonic Speeds of the Drag of a Particular Delta Wing having a Simple Pressure Distrlbutlon P. J. Herbert, B.Sc. SUMMARY Squire has drawn attention to a farmly of delta wings, having aerofoil-like sectlons with a rounded leading edge, whose supersonic wave drag at zero lncldence is theoretxally determinable, so long as the leading edge 1s subso 1~. Drag measurements have been made, at a Reynolds number of 7 x 10 it, on one member of this family usug the ground-launched rocket-boosted mods1 technxque. The experimental wave drag is In good agreement wth tunnel measurements on another wing of the family, both methods giving values less than theory.

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5 LIST OF CONTENTS m 1 Introduction 2 Test Vehwle an4 Test 3 Results and Comparison with Theory and other tests 4 Conclusions References LIST OF ILLUSTRATIONS Figure Geometric Characterutics of the Wing 1 Test Vehicle Dunensions Test Vehxle Drag Coefficient of the Test Derived Wing Drag Coefficient Comparison of Theoretical and Experimental Wave Drags Comparison mth a Similar Wing -2-

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7 1 Introduction As yet little theoretical work exists on the drag of round-nosed aerofo11s at supersonic speeds. Using linearised theory, Squire' has determined the pressure distribution, when the leading edge is subsonic, for a flat elliptic cone with the equation Jc= x2-y 2 tan*a % 2to ( c2 i and for a flat 'elliptic hype+cone' with the equation where x = upstream distance from the apex, Y = &stance to starboard., z = distance downwrds, c = root chord, A = sweepback angle, and to = constant determining the thickness, Squire has canbined the results for these two surfaces and obtarned the pressure distribution for a wing-like surface with the equation z = 0 _ l$)( - f;aa y 2t0 This is a delta wing with round--nosed sections except at the root, where the section is biconvex. It has a root thickness/chord ratio of to/o. In a corrigendum to the original report, Squire applies a correction to this linearised theory solution to allow for the high pressures at the rounded leading edge. This correction is due to R. T. Jones2. To obtain an experimental chsck on the theory the drag has been measured, in free-flight, of a 45O sweptback delta wing of this family having a root thickness/chord ratio of The theoretical geometric characteristics of the design wing and the actual characteristics of the wing tested are shown in Fig.1. The result and a comparison with theory are given in this report. Comparison is also made with tunnel tests on another member of the family having 600 sweepback and a root thickness/chord. ratio of 0.10, and with a wing having R.A.E.lO1 section and a uniform thickness/ohor3 ratio of 0.06 throughout. The flight test of this report was made in July

8 2 Test Vehicle and Test The test vehicle (Figs. 2 an3 3) was based on a 5 inch L.A.P. solid fuel rocket, The rocket was encased m a bakelised paper tube, to which VA.? attached a h-calibre ogival head of moulded perspex with a wooden nose. The two lvlngs, which had a root chord of xi inches, were made of wood with tufnol trailing edges. Stability in yaw was achieved by fittug two stabilising fins rearward of the wings and at rightangles to them. These fins were flat plat6.s of duralurmn tith chamfered leading and tralllng edges. The vehule was launched at the Larkhill range by Trials Wing, Guded Weapons Dept. The flight path was observed by km&theodolites which gave the trajectory. The velocity along the 1ln.e of sight was given by the radzo rcfltictlon doppler method. These and atmospheric data permitted the evaluation of the total drag of the test vehicle3 over the Mach number ryge 0.95 < M6< 1.6. The Reynolds number of tho test varied from 5 x IO to IO x 10 as Id increased from 0.95 to 1.6 (See Fig&). 3 Results and Comparison with Theory and other Tests The total drag coeffxient of the test vehxcle is plotted y1 Fig& The hag coefficient of the body and stsbilzsing fins, as obtalnad from separate testd, is also shown. From these the drag coefficient of the wzng 1s derived by subtraction and 1s shown in Flg.5, where it 1s based on exposed wing area. Fig.6 gxves a comparison rplth theory an2 also with some tests, as yet unpublished, made zn the R.A.E. 9" supersonx tunnel. In this figure the results are plotted in the form CD 4527 WC 2 against cot A cot+, where C, is the wave drag coefficient based on sxposed wing area, to/c the root thickness/chord ratlo, A the sweepback angle and p the Mach angle. This method of plotting enables direct comparuon to be made with the tunnel tests; these tests were ma?c on a wng of different sweepback and thickness. The theoretical curve 1s that &v-en by Squire'. The wave drag coefflclent used In tks free-flight curve was derived fmm the experimental drag coefflczent by s<btrac'ilng 0.005, to allow for the probable w&e of skln friction &a[; coefficzent. The tunnel wave drag coeffxzunts wre obtained frorl pressure dlstrlbution measurements on a half wing. A sumnary of the relax-ant test data 1s given below. wmg Ma& No. Reynolds No. I / I Free Flight II = 45 O x40 6 mean to/, = 0.06 TUIDSl A = f 60' ) to/c = x IO6, -6 2 x x IO6 It is seen that the free-flight results are in good agreement with the tunnel tests, and the experimental curve has the same general shape as the theoretxal,although the linearised theoq overestimates the drag. In the range 0.3 < cota cotp < 0.7 my, where a closer agreement rmth theory was eqx&x& the theory overestimates the wave -L -

9 drag coefficient by 35% or more. No explanation can at present be given for this lack of quantltatlve agreement between theory and experiment. Linearised theory breaks down as sonx velocity 1s approached and also as the Mach number at which the leading edge becomes sonic is approached, so the lack of agreement in these regions was not unexpected. It is worth pointing out that at the Mach number at whohlch the leading edge becomes sonic there is no tendency for a peak In the drag ooefflcient against Mach number curve (see Fig.5). This 1s m agreement with prewous experience rnth pnngs havwg leading edge sweepback. In order to complete the picture a oomparzson is given in Flg.7 between the drag of the present wing and of a wing of identical planform, having a standard round-nosed sectxon (R.A.E.lO1) and a uniform thickness/chord ratlo (0.06 throughout). The thickness/chord ratio of the present wing varies across the span and if It is assumed that the drag at any spanwise station is proportional to the product of the square of the local thickness/chord ratio and the local chord, it can be shown, that this wing has a mean weighted thxkness/ohord ratio* of In Flg.7 the results are plotted An the form I&/T* against Mach number, is the wave drag coeffxient based on exposed ting area and 7 is the mean thickness/chord (0.06 for the R.A.E.lO1 section wing and for the Squre section wing). The maximum thckness Line of the present wing is shown in Flg.1, the m-mum thickness being at 0.5 chord at the root, chord at mid span and chord at the tip. The R.A.E.lOl section has its maximum thickness at 0.31 chord. It 1s seen that on this basis of comparison the supersonic drags are in good agreement. 4 Conclusions 1 The flight test on the present wxng 1s In good agreement with tunnel tests on another wing of the family. 2 Both methods give wave drags less than theory. 3 If allowance IS made for the spanwlse variation U-I thickness/ chord ratio of the present wing the experimental total drag at supersonic speeds (1.0~ M < 1.4) IS in good agreement with the drag of a wing of identical planform having R.A.E,lOl section and a uniform thidcness/ chord ratio. *T= [[(t,c)2cdy/[cdyr -5-

10 p& Author 1 Squire 2 Jones, R.T. 3 Lawrence, swan and Warren 4 Poulter Title, etc. iin Example in Wing Theory at Supersonic Speeds. R& M.2549, Feb Leading Edge Singularities in Thin drofoil Theory. Jour. Acre. SC. Vol.17 No.5 pp May, 19%. Development of a Transonic Research Technique using Ground-launched Rocket-boo&cd Moodols. Pt.11 Dram: Measurements. A.R.C. 14,167 - March, Comparative Drag Tests on Three Related 15O Delta Wings using Ground-Launched Rocket-boosted Models. RAE Tech. Memo. No. &I-O 117, :,up Xt.2078.CP57.m. PTintad WI h-eat tritazn. -6-

11 FIG. I,A /I / / / d / PLANFORM SECTIONS 1.2E T I - DESIGN. EXPTL WINGS I oc c 0.25 C FOOT I.0 DISTANCE ALONG SPAN TIP FIG.1 GEOMETRIC CHARACTERISTICS OF THE WING.

12 SQUIRE AT ROOT SECTION 2 STASILISING FINS 0.13* THICK WITH CHAMFERED LEADING AND TRAILING EDGES. FIG. 2 TEST VEHICLE DIMENSIONS.

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14 FIG. 4 &5 I fi >I % > * TEST VEHICLE, O-2 / I- 0 3 IO BODY AND FINS REYNOLD5 NUMBER X IO b 1 b I i t IO 1.1 I I 5 16 MACH NUMBER FIG.4. DRAG COEFFICIENT OF THE TEST VEHICLE , BASED ON IO I I I2 l-3 l-4 15 I-6 MACH NUMBER FIG.5. DERIVED WING DRAG COEFFICIENT. (THIS INCLUDES SKIN FRICTION.)

15 FIG, 6 &7 IC -X I REYNOLDS FREE FLIGHT - A= 45 lqc = X106 MEAN : / 0 TUNNEL 0.85 X IO6 + k60 td/,*o-10, i 2x10 2x10= NQ l I I / I f c 6 4 h : SWEEPBACK ANGLE 2 C FIG.6 COMPARISON OF THEORETICAt. AND - EXPERIMENTAL WAVE DRAGS. N HAS BEEN SUBTRACTED FROM THE FREE -FLIGHl- CD TO ALLOW FOR SKIN FRICTION. 2. THE TUNNEL RESULTS WERf OBTAINED FROM PRESSURE DISTRIBUTION MEASUREMENTS m-rae SECTION - SQUIRE SECTION 4 2 r = MEAN WEIGHTElf w 0 IQ I.1 I.2 I.3 14 MACH NUMBER FIG.7 COMPARISON WITH A SIMILAR WING. : HAVING AN LDENTICAL PLANFORM AND RAE 101 SECTION WITH UNIFORM THICKNESS / CHORD * 0 06.

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