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Experimental investigation of the flow field about sharp-edged delta and rectangular wings Sun, Yung-chiun 1961

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EXPERIMENTAL INVESTIGATION OF THE FLOW FIELD ABOUT SHARP-EDGED DELTA AND RECTANGULAR WINGS by YUNG-CHIUN SUN B . S c , N a t i o n a l Taiwan U n i v e r s i t y , 1957 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A, Sc. i n the Department of Mechanical Engineering We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard The U n i v e r s i t y of B r i t i s h Columbia December I961 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y • a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permission. Department The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date - 11 -ABSTRACT. When a t h i n delta wing with high leading-edge sweep i s placed at incidence i n a stream, the f l u i d separates from the surface at the leading edges and c o i l s up to form a pair of symmetrically placed vortices above the upper surface of the wing. This flow pattern i s stable up to high incidence, but at extreme high incidence, the stable vortex core appears to burst or rapidly d i f f u s e . The present research was done as part of a general program to study the vortex bursting phenomenon about sharp-edged delta wings. The aim was to determine the"bursting position at d i f f e r e n t angles of attack and the e f f e c t on the wing performance. I t was found that the bursting oocurs f i r s t downstream of the t r a i l i n g edge and then moves rapidly upstream with increasing incidence. The wing s t a l l s when the bursting point occurs at a position upstream of the wing's t r a i l i n g edge. The pressure d i s t r i b u t i o n s on a sharp-edged rectangular wing were also measured i n the present research and the o v e r a l l normal force c o e f f i c i e n t was obtained by the graphical integration of surface pressures. I t was found from the pressure d i s t r i b u t i o n s that the flow pattern changes from one type to another i n the range from <=>(,= 10° to o(= 15°. The o v e r a l l normal force c o e f f i c i e n t reaches its f i r s t maximum value at 17° incidence. i i i -CONTENTS . . ~ Page. INTRODUCTION .' . . . . 1 HISTORICAL BACKGROUND AND CURRENT THEORIES . . . . . . . . . . . k TEST FACILITIES AND APPARATUS .13 MEASUREMENT TECHNIQUES . . . . . . . . . . 17 TEST RESULTS - 19 DISCUSSION OF TEST RESULTS . . . . . . . 24 CONCLUSIONS vi-^fv* 31 RECOMMENDATIONS • • * 32 REFERENCES 33 ILLUSTRATIONS 36 - i v -ILLUSTRATIONS Fig u r e Number 1. WIND TUNNEL AERODYNAMIC OUTLINE 2. SKETCH OF MODELS I AND I I 3. SKETCH OF MODEL I I I k. SKETCH OF MODELS IV, V, VI AND VII.. 5. SKETCH OF MODEL V I I I 6. SKETCH OF MODELS IX, X AND XI 7. SKETCH OF MODEL X I I ' 8. SKETCH OF PROBES 9. TRAVERSING APPARATUS 10. POSITION OF VORTEX CORE MEASURED WITH VORTOMETER MODELS I AND I I 11. VORTEX CORE POSITION FOR FLAT DELTA WINGS 12. TIP VORTEX CORE ABOUT MODEL I I I AT 15° ANGLE OF ATTACK, 13. VORTEX SYSTEM ABOUT MODEL V I I I AT 10° ANGLE OF ATTACK Ik, SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL .IX 15. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL IX 16. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX 17. SPANWISE PRESSURE DISTRIBUTIONS AT STATION k MODEL IX 18. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL IX 19. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL IX 20. "SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL IX 21. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C w WITH x INCIDENCE MODEL IX. 22. CHORDWISE VARIATION OF C H MODEL IX 23. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL IX ILLUSTRATIONS CONTINUED Fi g u r e Number 2k. SPANWISE PRESSURE DISTRIBUTIONS MODEL IX (COMPARISON WITH RESULTS OF BROWN AND MICHAEL, MANGLER AND SMITH) . 25. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL X. 26. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL X 27. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL X 28. SPANWISE PRESSURE DISTRIBUTIONS AT. STATION 9 MODEL X .'. 29. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 10 MODEL X 30. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 11 MODEL X 31. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C w WITH :INCIDENCE MODEL X 32* CHORDWISE VARIATION OF C N MODEL X 33, VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X . 3k.' . SPANWISE PRESSURE:DISTRIBUTIONS AT STATION 1 MODEL XI 35. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL XI 36. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL XI 37. SPANWISE PRESSURE DISTRIBUTIONS AT STATION k MODEL XI . 38... SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL XI 39. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL XI kO. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL XI kl. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C N x WITH INCIDENCE MODEL XI k2. CHORDWISE VARIATION OF C w MODEL XI k3. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH . INCIDENCE MODEL XI - v i ILLUSTRATIONS CONTINUED Fig u r e Number kh. . COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE COEFFICIENTS OF DELTA WINGS 45. SPANWISE VARIATION OF C p AT STATION 1 MODEL X I I k-6. SPANWISE VARIATION OF C p AT STATION 2 MODEL X I I hf. SPANWISE VARIATION OF C p AT STATION 3 MODEL X I I kQ. SPANWISE VARIATION; OF C p AT STATION k MODEL X I I 1+9. SPANWISE VARIATION OF Cp AT STATION 5 MODEL X I I 50. SPANWISE VARIATION OF C p AT STATION 6 MODEL X I I 51. SPANWISE VARIATION OF C p AT STATION 1^ . i n . FROM L.E. MODEL X I I 52. PRESSURE DISTRIBUTIONS ON THE UPPER SURFACE OF MODEL X I I AT 10° ANGLE OF ATTACK 53. VARIATION OF SECTIONAL NORMAL FORGE COEFFICIENT C„ WITH x INCIDENCE, MODEL X I I $k. CHORDWISE VARIATION OF C w MODEL X I I 55. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X I I 56. COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE CHARACTERISTICS OF A = 2 RECTANGULAR WINGS 57- VARIATION OF VORTEX BREAKDOWN-POSITIONS WITH INCIDENCE MODEL IX 58. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MODEL X. 59. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MODEL XI 60. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH SWEEP 61. VARIATION OF LIFT COEFFICIENT C L WITH INCIDENCE MODELS IX,X AND XI - v i i -ACKNOWLEDGMENT The author wishes t o acknowledge the advice and encouragement given by Dr. G. V. Parkinson who supervised the research. He a l s o wishes to thank the Mechanical Engineering Department f o r the extensive use of the U n i v e r s i t y of B r i t i s h Columbia wind t u n n e l . F i n a n c i a l a s s i s t a n c e was re c e i v e d from the Defence Research Board of Canada. - v i i i SYMBOLS Aspect r a t i o Span ( t r a i l i n g edge) Root chord .; P - P~ Pressure c o e f f i c i e n t ir.pu: S t a t i c pressure S t a t i c pressure i n the undisturbed stream Density Free stream v e l o c i t y Pressure c o e f f i c i e n t at zero incidence = C - C P P lower upper 2 s L o c a l normal f o r c e c o e f f i c i e n t . / L o c a l semi-span Normal f o r c e L i f t f o r c e ,c> O v e r a l l normal f o r c e c o e f f i c i e n t = - * N 6 Cf-L i f t c o e f f i c i e n t Wing area C a r t e s i a n co-ordinates x measured chordwise y measured spanwise SYMBOLS CONTINUED Angle of a t t a c k Leading edge sweepback Serai apex angle of d e l t a wings = t a n ^ 3 = cot A EXPERIMENTAL INVESTIGATION OF THE FLOW FIELD ABOUT SHARP-EDGED DELTA AND RECTANGULAR WINGS INTRODUCTION . During the nineteen f o r t i e s , i t was recognized that sweepback could appreciably delay the transonic drag r i s e on. a i r c r a f t wings. Also i n the lower supersonic regime, the wave drag could be reduced i f the l i f t i n g surface were kept inside the Mach cone. I t was also known that the drag of high speed a i r f o i l s is•proportional to the square of t h e i r thickness. Under these considerations, th i n swept wings and t h i n delta wings were developed for high speed a i r c r a f t . Although t h i s class of - l i f t i n g surfaces has excellent high speed performance ch a r a c t e r i s t i c s , i t s low speed behavior, important for taking off and landing, poses serious problems. In order to f i n d out what the r e a l flow f i e l d around t h i s class of wings looks l i k e and the reason for poor low speed performance, many investigators have studied t h i s problem by experimental or theoretical methods. Observations show that, when th i n wings with high leading-edge sweep are placed at.incidence i n a stream, the f l u i d separates from the surface along l i n e s near the leading edges and c o i l s up to form pairs of symmetrically placed vortices above the upper surface of the wing. This flow pattern, which has been found by many investigators, has a stable char-acter even at high incidence and gives higher l i f t than would resu l t from a flow pattern without leading edge separation. I t i s also found that the - 2 -f l o w i s not s e n s i t i v e t o Mach number and i n consequence many i n v e s t i g a t i o n s of t h i s type of f l o w may be -performed i n the low speed wind tun n e l or water : t u n n e l . When a c e r t a i n high incidence i s reached, the s t a b l e vortex core appears t o b u r s t or r a p i d l y d i f f u s e at some di s t a n c e downstream. As-incidence i s i n c r e a s e d the b u r s t moves forward towards the apex. The p o s i t i o n along the vortex at which b u r s t i n g occurs depends p r i m a r i l y on a combination of the angle of sweepback of the l e a d i n g edge and the incidence of the wing. For l a r g e angles of sweepback and low incidence the b u r s t occurs i n the vortex downstream of"the wing, but w i t h an increase of incidence or a decrease of e f f e c t i v e sweepback the b u r s t moves upstream t o a p o s i t i o n above the surface of the wing. Observation of the b u r s t i n g process r e v e a l s t h a t i t i n v o l v e s r a p i d d e c e l e r a t i o n of the f l u i d moving along the a x i s of the vortex f o l l o w e d by what appears t o be s p i r a l l i n g of the vortex core be-f o r e the f l o w becomes completely i r r e g u l a r . This phenomenon i s not f u l l y understood so f a r and i t i s s t i l l the subject of much t h e o r e t i c a l and ex-perimental research. The f i r s t p a r t of the present research was done as part of a general program t o study the l e a d i n g edge separation and vortex b u r s t i n g phenomenon f o r sharp-edged d e l t a wings. The aim was t o determine t h e , b u r s t i n g p o s i t i o n at d i f f e r e n t angles of a t t a c k on.three h a l f model d e l t a wings and the e f f e c t of vortex b u r s t i n g on the surface pressure d i s t r i b u t i o n . Normal f o r c e c o e f f i c i e n t s on the 65°, 70° and 75° l e a d i n g edge sweepback models were worked out by the g r a p h i c a l i n t e g r a t i o n of surface pressures. Vortometers ware used t o l o c a t e the s t a b l e vortex core. The data were then c o r r e l a t e d w i t h r e s u l t s from other sources. I t d i d not prove easy to i n t e r p r e t ana-l y t i c a l l y a l l the f e a t u r e s of the f l o w f i e l d and t o c o n s t r u c t a s a t i s f a c t o r y . theory f o r the f l o w . Recent developments i n a i r c r a f t and m i s s i l e s f o r high speed f l i g h t have r e s u l t e d i n a tren d toward u s i n g t h i n a i r f o i l s of short span among which r e c t a n g u l a r wings pla y an important r o l e . Consequently, i t i s necessary t o understand the f l o w p a t t e r n s about t h i s k i n d of wing both ax hi g h speed and low speed. When a t h i n r e c t a n g u l a r wing i s set at &• small.angle of a t t a c k i n a uniform stream, the f l o w remains attached t o the wing surface so th a t a l l the shed v o r t i c i t y l i e s i n a sheet which contains the wing planform and proceeds t o r o l l up g r a d u a l l y ' a f t e r l e a v i n g the wing t r a i l i n g edge. As the angle of a t t a c k i s i n c r e a s e d , the si d e edges become more oblique t o the f r e e stream, the f l u i d can no longer n e g o t i a t e the l8o° t u r n at the side edges and side^edge s e p a r a t i o n occurs, g i v i n g r i s e to two a d d i t i o n a l • v o r t e x sheets which b e g i n t o r o l l up even ahead of the wing t r a i l i n g edge. F i n a l l y at s t i l l higher angles of a t t a c k , the f l o w separates from the l e a d i n g edge, •. g i v i n g r i s e t o v o r t i c e s whose axes are e s s e n t i a l l y normal t o the f r e e stream d i r e c t i o n . The angles o f a t t a c k at which the fo r e g o i n g phenomena occur and the r a t e of r o l l i n g up and shedding depend on the aspect r a t i o of the wing and the sharpness of i t . In the second part" of the present research an i n v e s t i g a t i o n i s made of the flow p a t t e r n and pressure d i s t r i b u t i o n on a sharp-edged r e c t a n g u l a r wing at low speed. The main o b j e c t i v e was t o o b t a i n the vor t e x system.about the wing a t 10° angle of a t t a c k by u s i n g a vortometer. Surface pressure d i s t r i b u t i o n s were measured from the pressure taps on the wing and the over-a l l normal force, c o e f f i c i e n t was obtained by the g r a p h i c a l i n t e g r a t i o n of surface pressures. The data were c o r r e l a t e d w i t h other a v a i l a b l e data.and theory. - 4 -HISTORICAL BACKGROUND AND CURRENT THEORIES The f l o w f i e l d about d e l t a wings has been i n v e s t i g a t e d by many experimenters over the l a s t f i f t e e n y e a r s . I n the f i r s t few years, they d i s c o v e r e d the n o n - l i n e a r property of l i f t and moment curves by means of wind t u n n e l balance measurements. In order t o i n t e r p r e t t h i s n o n - l i n e a r i t y , a number of experimental s t u d i e s have been performed t o l o c a t e vortex cores and t o f i n d the d i r e c t i o n of f l o w w i t h i n the i n n e r core of the boundary l a y e r by u s i n g d i f f e r e n t techniques such as t u f t g r i d , vortometer, vapor screen, lamp-black and china c l a y c o a t i n g s . Recently a t t e n t i o n has been drawn t o the phenomenon of vortex b u r s t i n g which occurs when a c e r t a i n incidence i s reached and which may have d e t r i m e n t a l e f f e c t s . A b r i e f summary of the experimental work i s given i n the f o l l o w i n g paragraphs. In 19^ 7> Anderson 1 i n v e s t i g a t e d the low speed c h a r a c t e r i s t i c s of a l a r g e - s c a l e t r i a n g u l a r wing w i t h symmetrical double wedge s e c t i o n . He found t h a t there are two types of f l o w over the wing; smooth fl o w at low angle of a t t a c k and f l o w w i t h s e p a r a t i o n o f f the sharp l e a d i n g edge at h i g h angle of a t t a c k . The t r a n s i t i o n from one type of f l o w t o the other was i n d i c a t e d by breaks i n the f o r c e and moment curves, which occurred at d i f f e r e n t values of angle of a t t a c k , depending upon the wing c o n f i g u r a t i o n . A f t e r t e s t i n g s i x plane d e l t a wings i n 19^8, Berndt a l s o found that both the l i f t and moment curves show a t y p i c a l n o n - l i n e a r form. The l i f t curve slope has one value at low angle of a t t a c k ( <K < 10°) and another l a r g e r value at high angle of a t t a c k . The increase of l i f t curve slope i s accompanied by a backward s h i f t of the aerodynamic center. This e f f e c t increases w i t h decreasing aspect ..ratio. • The n o n - l i n e a r i t y i s due t o the t i p v o r t i c e s not l e a v i n g at the t r a i l i n g edge, but at the forward p a r t of the t i p p r o f i l e s u c t i o n s i d e . The r e s u l t s of h i s stream-flow t e s t s show a boundary l a y e r movement towards the wing t i p s and a s e p a r a t i o n beginning at the wing - 5 -t i p s and growing inwards w i t h i n c r e a s i n g angle of a t t a c k . The e a r l i e s t systematic t u f t g r i d t e s t s on t h i s problem were made by B i r d and R i l e y i n 1952. T h e i r t e s t s i n d i c a t e d t h a t the c h a r a c t e r of the, f l o w f i e l d i s i n general agreement w i t h what has been a n t i c i p a t e d on the basis, of l a r g e s c a l e t e s t s u t i l i z i n g other techniques. The r e s u l t s i n d i c a t e d a l s o that q u a n t i t a t i v e analyses of t r a i l i n g - v o r t e x s t r e n g t h and l o c a t i o n and approx-imate downwash ap.& sidewash angles over a l a r g e area behind l i f t i n g surfaces and other aerodynamic forms-may be s a t i s f a c t o r i l y conducted w i t h data obtained by t h i s technique. I n 195^; Ornberg^' found t h a t on h i g h l y swept d e l t a wings the l e a d i n g edge se p a r a t i o n produces concentrated, s t a t i o n a r y , edge v o r t i c e s which induce high s u c t i o n peaks on the surface under them. The most important parameters governing the appearance of these edge v o r t i c e s at a given angle of a t t a c k are the angle of l e a d i n g edge sweep and the shape of wing p r o f i l e , e s p e c i a l l y nose r a d i u s and t h i c k n e s s . The boundary l a y e r f l o w i n g round the l e a d i n g edges separates e a s i l y at the very edge when the nose r a d i u s i s small and r o l l s up r a p i d l y i n t o f r e e concentrated v o r t i c e s which grow i n s i z e and i n t e n -s i t y towards the t r a i l i n g edge as long as they are f e d w i t h v o r t i c i t y from the l e a d i n g edge. The i n c r e a s e i n l i f t curve slope, which became more marked as the angle of sweep increased, may be e x p l a i n e d by the s u c t i o n induced by the v o r t i c e s . In order t o determine the extent t o which the f l o w was approximately c o n i c a l , F i n k and T a y l o r ^ measured the pressure along generators i n 1955• They found that the i n f l u e n c e . o f the t r a i l i n g edge d i d not spread a p p r e c i a b l y forward of the a f t t h i r d of the wing i n the range of incidence of the t e s t s . 'The spanwise pressure d i s t r i b u t i o n s were measured at two chord s t a t i o n s f o r s e v e r a l angles of i n c i d e n c e . A f t e r an extensive s e r i e s of t o t a l pressure - 6 -surveys over the s u c t i o n side of the wing, i t was found t h a t the f l o w separated from the wing at the sharp l e a d i n g edges f o r a l l but the smallest angles of incidence and i t was more complicated than expected i n t h a t f u r t h e r s e p a r a t i o n of the cross f l o w took place on the s u c t i o n side of the wing somewhat inboard of the l e a d i n g edges. I n 1957, J a s z l i c s and T r i l l i n g ^ deduced a number of u s e f u l conclusions from t h e i r measurements. They pointed out t h a t v o r t i c i t y i s generated at the l e a d i n g edge at a r a t e independent of p o s i t i o n along the span. The amount of v o r t i c i t y generated per u n i t l e n g t h measured i n the streamwise d i r e c t i o n i s a f u n c t i o n of angle of a t t a c k only and a n e a r l y l i n e a r f u n c t i o n . The edge of the r e s u l t i n g vortex sheet forms a ray through the wing apex, which remains i n a h o r i z o n t a l plane through the apex. The r a t i o of the h o r i z o n t a l d i s t a n c e from root chord to v o r t e x edge t o the distance from root chord to l e a d i n g edge i s a unique l i n e a r f u n c t i o n of angle of a t t a c k f o r a wide range of sweep angles and angles of a t t a c k . The c o n i c a l f l o w p a t t e r n remains v a l i d f o r narrow d e l t a wings up t o the c l o s e neighbourhood of the t r a i l i n g edge. By doing both wind t u n n e l and water t u n n e l experiments on s i m i l a r d e l t a wings w i t h sharp l e a d i n g edges i n 1958, E l l e found t h a t the s t r u c t u r e of the s p i r a l vortex sheets and the l o c a t i o n of t h e i r c e n t e r l i n e s are not . d i f f e r e n t t o any extent i n a i r f l o w and i n water :.flow when the water contains a considerable amount of" u n d i s s o l v e d a i r . He a l s o concluded that the theory, of Brown and M i c h a e l " ^ f o r sharp-edged'slender d e l t a wings i s b a s i c a l l y sound and a p p l i c a b l e t o d e l t a wings which are not a c t u a l l y s lender. The breakdown of the s p i r a l vortex sheet at high incidence was discovered. He thought t h a t i t may occur because the f i e l d of v o r t i c i t y i n the s p i r a l develops i n such a way t h a t the t r a n s p o r t of the f l u i d down-stream along the v o r t e x c e n t e r l i n e f a i l s . - 7 -I n 1958, Marsden's group r e a l i z e d the ex i s t e n c e of secondary v o r t i c e s . They i n d i c a t e d t h a t secondary v o r t i c e s of opposite s i g n t o the main v o r t i c e s e x i s t on the upper, surface of the wing outboard of andibelow the main v o r t i c e s . The secondary v o r t i c e s are formed as a r e s u l t of separation of the boundary l a y e r developing outboard of the top surface attachment l i n e s . The secondary separation regions are f a i r l y e x tensive on f l a t narrow d e l t a wings and cause an inboard and upward displacement of the v o r t e x cores compared t o the p o s i t i o n given by the theory of Mangier and Smith"^. The t r a i l i n g edge e f f e c t present at subsonic speed was found t o be considerable even at s m a l l angles of a t t a c k . The normal f o r c e developed by spanwise s t r i p s exceeded t h a t p r e d i c t e d by Mangier and Smith' - near the apex, but f e l l p r o g r e s s i v e l y as the t r a i l i n g edge was approached. The center of pressure i s approximately independent of incidence up t o angles of a t t a c k i n excess of the semi apex angle. In 1958, Peckham^ d i d a s e r i e s of t e s t s t o i n v e s t i g a t e the e f f e c t of planform shape, t h i c k n e s s , and aspect r a t i o on the aerodynamic charac-t e r i s t i c s at low speed. A number of i n t e r e s t i n g r e s u l t s can be deduced from h i s experiments. The f l o w w i t h c o i l e d l e a d i n g edge vortex sheets i s p e r f e c t l y steady and gives a smooth v a r i a t i o n of o v e r a l l f o r c e s and moments" over the whole range of a t t i t u d e s l i k e l y t o be encountered i n f l i g h t con-d i t i o n s . I n c r e a s i n g aspect r a t i o , i n c r e a s i n g t h i c k n e s s , and i n c r e a s i n g convexity of the l e a d i n g edge planform shape, a l l have the e f f e c t of moving the attachment l i n e , peak s u c t i o n l i n e and secondary se p a r a t i o n l i n e f u r t h e r outboard. They a l s o have the e f f e c t of moving the cores of the c o i l e d v ortex sheets f u r t h e r away from the wing chordal plane. The t h e o r e t i c a l l i n e a r l i f t slope given by Weber^-O f o r d e l t a wings agrees reasonably w e l l - 8 -w i t h the experimental r e s u l t s f o r f l a t p l a t e d e l t a wings near zero i n c i d e n c e . To a c l o s e approximation, the over a l l l i f t of g o t h i c and d e l t a planform shapes i s p r o p o r t i o n a l t o the square root of sle'nderness r a t i o , d e f i n e d as (l/2 span/cr). The center of pressure on f l a t p l a t e d e l t a wings of aspect r a t i o 1. i s at 40$ aerodynamic mean chord. Recently, Lambourne and Brye r 1 1 performed a s e r i e s of water t u n n e l t e s t s t o i n v e s t i g a t e the vortex b u r s t i n g phenomenon about d e l t a and sweptback wings. A number of v a l u a b l e conclusions were obtained from t h e i r t e s t s . T h e i r r e s u l t s show t h a t b u r s t i n g i n v o l v e s a sudden d e c e l e r a t i o n of the a x i a l f l o w accompanied b y expansion of the v o r t e x around a stagnant core. A short d i s t a n c e f u r t h e r down-stream a breakdown t o t u r b u l e n t f l o w occurs. There i s u s u a l l y , between the p o s i t i o n of a x i a l d e c e l e r a t i o n and the t u r b u l e n t breakdown, a r e g i o n of p e r i o d i c f l o w i n which the a x i a l f i l a m e n t performs a r e g u l a r w h i r l i n g motion. The presence of a b u r s t above the wing causes a l o s s of s u c t i o n l o c a l l y at the surface and a m o d i f i c a t i o n t o the p o s i t i o n of s e p a r a t i o n of the surface f l o w beneath the v o r t e x . When the b u r s t i s upstream of the t r a i l i n g edge i t s p o s i t i o n depends on a combination of incidence and l e a d i n g edge sweepback and i n r e l a t i o n t o the geometry of the wing, i t s p o s i t i o n i s l a r g e l y independent of Reynolds number. The b u r s t p o s i t i o n i s s e n s i t i v e t o the pressure gradient along the v o r t e x , a r e d u c t i o n i n the gradient b e i n g conducive to a longer laminar v o r t e x . Two other experiments on v o r t e x b u r s t i n g were c a r r i e d out by Harvey-'-2 i n i960. I n h i s f i r s t experiment, the o r i g i n a l problem of the vortex b u r s t i n g a s s o c i a t e d w i t h h i g h l y swept wings was i n v e s t i g a t e d by u s i n g a 20° apex angle sharp-edged d e l t a wing mounted i n a 5' x 4' low speed wind t u n n e l . His second experiment was performed i n a p a r a l l e l - w a l l e d vortex tube. He concluded t h a t the f l o w p a t t e r n a f t e r the b u r s t i n g p o i n t remains - 9 -axisymmetric about the vortex o r i g i n a l center line.. The flow near the burst was characterised by a pocket of almost stagnant a i r which was of a closed approximately spherical shape i n the vortex tube experiment but only exhibited the hemi-spherical forward end on the wing. The complete formation of the pocket on the wing might have been impeded by the vortex sheet which continued to add v o r t i c i t y to the core i n a non-axisymmetrical fashion after the breakdown. In the vortex tube experiment the conventional vortex was reformed downstream of the spherical pocket and t h i s form was retained for a distance roughly equal to the pocket's length whereupon a second burst took place. There are three a n a l y t i c a l studies of delta wings with leading edge separation, due to Legendre-L3, Brown and Michael^", and Mangier and Smith"'"''.. Their method, . i n b r i e f , i s to consider the problem as a potential flow. The slender body or low aspect r a t i o approximation i s made, the flow i s considered to be non-viscous" and conical, a Kutta condition i s applied at the leading edge and the vortex sheet that separates from the leading edge i s replaced by d i f f e r e n t vortex systems. The f i r s t theory"was due to Legendre who replaced the s p i r a l vortex sheets i n the f l u i d by a p a i r of isol a t e d vortices l y i n g along streamlines. This s i m p l i f i c a t i o n only gives a q u a l i t a t i v e representation of the flow f i e l d which can be observed at moderate incidences near the apex of highly swept wing'f.. Legendre' s potential f i e l d does not: s a t i s f y the law of conservation of circulationaround a vortex. Therefore, the solution i s not e n t i r e l y satisfactory and could be regarded merely as a f i r s t approximation. In order to s a t i s f y Kelvin's theorem, Brown and Michael elaborated the i s o l a t e d vortex model by considering two feeding vortex sheets connecting the source of v o r t i c i t y (leading edge) and the - 10 -concentrated l i n e v o r t i c e s . One of the boundary conditions i n t h e i r analysis i s that the f l u i d pressure i s continuous which i s impossible to s a t i s f y with the assumed model. They made t h i s condition less detailed by considering that the i n t e g r a l of pressure around the assumed vortex system vanish. That i s they assumed the forces on the feeding vortex sheet to be cancelled by equal but opposite forces on the concentrated vortex. Their mathematical model i s expected to give a reasonable agreement with the r e a l flows at least at moderate Mach numbers and for slender enough wings. This analysis also shows that leading edge separation on slender delta wings leads to nonlinear l i f t curves with l i f t greater than predicted by R. T. Jones'-^ theory. In 1958, Mangier and Smith'j- refined Brown and Michael's model by assuming a curved vortex sheet feeding the concentrated vortex core. They have translated the exact three dimensional boundary conditions back into the cross flow plane, and solved the r e s u l t i n g problem by s a t i s f y i n g the condition that the pressure difference across the vortex sheet i s zero at selected points on the sheet. The f i r s t : t h e o r e t i c a l investigation of vortex breakdown was given by Squire-*-? i n i960. He thought that i f standing waves can ex i s t i n the flow f i e l d , disturbances, which are generally present down stream, w i l l spread forward along the vortex and cause the breakdown. The problem i s to f i n d the possible conditions f o r the existence of standing waves. He considered three cases of uniform a x i a l v e l o c i t y and di f f e r e n t s w i r l v e l o c i t y d i s t r i b u t i o n s and found that very long waves may be present when the maximum, s w i r l v e l o c i t y i s rather larger than the a x i a l v e l o c i t y . This condition i s proposed as the c r i t e r i o n f o r vortex breakdown. Harvey's experiments made with a vortex i n a tube (Ref. 12) show that breakdown i s present for (Max. s w i r l v e l . ) / ( a x i a l vel.) ='1.22. - 11 --i Q In I960, J . P. Jones a l s o e s t a b l i s h e d a t h e o r e t i c a l a n a l y s i s of vor t e x breakdown. In h i s a n a l y s i s , the v e l o c i t y components and pressure appropriate t o the mean f l o w were assumed t o r e c e i v e small p e r t u r b a t i o n s which vary i n both time and space. N e g l e c t i n g higher powers of the p e r t u r b a t i o n s a set of l i n e a r d i f f e r e n t i a l equations was obtained i n which the time r a t e of change of the disturbance i s a parameter. I n s t a b i l i t y occurs when the disturbance tends t o grow without l i m i t . Then the vortex breakdown i s assumed t o occur at some p o s i t i o n along the core where c o n d i t i o n s ( i n f a c t the v e l o c i t y d i s t r i b u t i o n s ) are of the'unstable type. For r e c t a n g u l a r wings of s m a l l aspect r a t i o , BoUay-^ e s t a b l i s h e d a theory under the assumption t h a t a l l shed v o r t i c e s l i e i n two planes normal t o the wing surface and c o n t a i n i n g the s i d e edges. Thus the wing i s repre-sented by a continuous d i s t r i b u t i o n of horseshoe v o r t i c e s , l y i n g at some angle to the wing s u r f a c e . The angle i s assumed constant and the vortex strengths are assumed t o be constant across the span b u t . c o n t i n u o u s l y v a r y i n g i n the chordwise d i r e c t i o n . . This mathematical model i s l i m i t e d t o r e c t a n g u l a r wings of s m a l l aspect r a t i o i n incompressible f l o w and i s not s u i t e d t o the c a l c u l a t i o n of q u a n t i t i e s other than normal f o r c e s . However, the agree-ment between the c a l c u l a t e d and measured normal f o r c e s i s e x c e l l e n t at very low aspect r a t i o up t o angles of a t t a c k of about 40°. For extending the theory of B o l l a y to higher aspect r a t i o , Gersten^O presented an a n a l y t i c a l method i n 1959» He considered the a c t u a l wing t o be made up of a number, of B o l l a y ' s wings pla c e d side by side and' assumed t h a t the shedding angle of a l l the horseshoe v o r t i c e s remained constant a t the l i m i t i n g value of °^ -/2. This model has v o r t i c e s shed over the e n t i r e wing s u r f a c e , but i n order t o make the problem mathematically t r a c t a b l e , he d i v i d e d the wing i n t o a f i n i t e number of spanwise s t r i p s . - 12-A c t u a l l y h i s model c o n s i s t s of a d i s c r e t e number of l i f t i n g l i n e s , each having .an u n s p e c i f i e d spanwise l o a d i n g and shedding a f l a t continuous vortex sheet at h a l f the angle of a t t a c k . This method i s r e s t r i c t e d t o s m a l l angle of a t t a c k but appears t o give an improvement of B o l l a y 1 s theory f o r aspect r a t i o s from 2 t o k and angles of a t t a c k up t o about 15°» In a d d i t i o n , h i s a n a l y s i s i s s u i t e d t o the c a l c u l a t i o n of l o a d d i s t r i b u t i o n and p i t c h i n g moment i n a d d i t i o n t o l i f t and drag. Pi More r e c e n t l y , Sacks and N i e l s e n developed a mathematical theory f o r r e c t a n g u l a r wings of any aspect r a t i o at low speed w i t h side edge s e p a r a t i o n . I n t h e i r theory, the wing i s represented mathematically by a l i f t i n g l i n e of u n s p e c i f i e d spanwise c i r c u l a t i o n d i s t r i b u t i o n w i t h i t s a s s o c i a t e d t r a i l i n g v ortex sheet l y i n g i n the plane of the wing and a continuous system of horseshoe v o r t i c e s r e p r e s e n t i n g the separated vortex system. I t was a l s o as:sumed t h a t s e p a r a t i o n occurs a l l along the side edges and t h a t a l l of the shed v o r t i c e s l i e i n the two planes c o n t a i n i n g the f r e e stream d i r e c t i o n and the side edges. The K u t t a c o n d i t i o n i s s a t i s f i e d along the side edges and the boundary c o n d i t i o n of no f l o w through the wing i s s a t i s f i e d by a s u i t a b l e choice of spanwise c i r c u l a t i o n d i s t r i b u t i o n along the l i f t i n g l i n e . The r e s u l t i n g theory i n c l u d e s the c l a s s i c a l l i f t i n g l i n e theory of P r a n d t l and provides a means of c a l c u l a t i n g the dowriwasti anywhere i n the plane, of the l i f t i n g l i n e . The agreement between experiment and theory i s good up t o :the onset of l e a d i n g edge s t a l l . This a n a l y s i s can be extended t o d e l t a wings by r e p r e s e n t i n g the a c t u a l wing as a system of elementary r e c t a n g u l a r wings of v a r y i n g aspect r a t i o s . Thus sep a r a t i o n along the e n t i r e l e a d i n g edge i s approximated and the theory leads t o an i t e r a t i v e technique f o r c a l c u l a t i n g the aerodynamic c h a r a c t e r i s t i c s of d e l t a wings w i t h l e a d i n g edge s e p a r a t i o n . - 13 -TEST FACILITIES AND APPARATUS 1. Wind Tunnel A l l the t e s t s d e s c r i b e d i n t h i s r e p o r t were c a r r i e d out i n the U n i v e r s i t y of B r i t i s h Columbia low-speed, c l o s e d - c i r c u i t , s i n g l e r e t u r n wind t u n n e l (see F i g . l ) . The t e s t s e c t i o n i s foctagpnal.., formed by a 27 i n c h by 36 i n c h r e c t a n g l e w i t h 45° f i l l e t s , and i s 104 inches i n l e n g t h . The f i l l e t s decrease from 6.0 inches at the upstream end t o 4.75 inches at the downstream end t o o f f s e t the e f f e c t of boundary l a y e r growth. The f l o w i s smoothed by three screens placed as shown, and enters the t e s t s e c t i o n through a 7:1 c o n t r a c t i o n cone which a c c e l e r a t e s the f l o w and improves i t s u n i f o r m i t y . I n the t e s t s e c t i o n , the s p a t i a l v a r i a t i o n i n v e l o c i t y i s approximately 0.25$, and the turbulence l e v e l i s l e s s than 0.5$» The tu n n e l i s capable of p r q y i d i n g a steady f l o w i n d e f i n i t e l y at an ai r s p e e d which may be v a r i e d continuously from 4.0 fps t o 140 f p s . 2. D e s c r i p t i o n of Models Twelve h a l f - s p a n models have been t e s t e d , a l l of which were made of f l a t p l a t e and had sharp edges. Models I and I I were two f l a t p l a t e d e l t a wings w i t h 65.8° l e a d i n g edge sweep and ro o t chord 24.5 inches. Both of the two models were made of 1/2 i n c h t h i c k f l a t wood..plate. Model I had a completely f l a t . u p p e r surface and was b e v e l l e d on the underside t o provide sharp edges. Model I I was b e v e l l e d on the upper surface. These two models were only used f o r p r e l i m i n a r y vortometer measurements, (see F i g . 2). Model I I I was a sharp-edged r e c t a n g u l a r wing w i t h lower surface b e v e l l e d . The thi c k n e s s and m a t e r i a l of t h i s model are i d e n t i c a l w i t h those of Model I . The chord l e n g t h and h a l f span were 11 inches and - Ik -16 inches r e s p e c t i v e l y . This model was a l s o used f o r p r e l i m i n a r y vortometer measurement (see F i g . 3). Models IV, V, VI and VI I were fo u r d e l t a wings w i t h leading-edge sweeps of 850, 80°, 75°'and-70° r e s p e c t i v e l y . They a l l were made of l/k i n , t h i c k f l a t b r a ss plate.and had a b e v e l l e d lower surface t o form the sharpy edges. The root chord of these models was 2k inches (see F i g . k). Model V I I I , a metal r e c t a n g u l a r wing w i t h lk° b e v e l l e d lower surface was made of l/k i n c h t h i c k f l a t brass p l a t e and had a r o o t chord and- h a l f span of 11 i n c h e s , (see F i g . 5)« . Models IX, X and'XT, designed f o r surface pressure measurements, were three sharp-edged d e l t a wings w i t h 75°, 70° and 65 0 l e a d i n g edge sweep, r e s p e c t i v e l y . The p r o f i l e and m a t e r i a l were the same as. i n Model IV. On the lower s u r f a c e , i n the middle of these models, l/8 i n c h of the brass was cut out by a m i l l i n g machine t o give space f o r f i t t i n g pressure tubing.. Pressure taps were d r i l l e d through the p l a t e i n t o p l a s t i c t u b i n g cemented t o the p l a t e under the s u r f a c e . There are seven s t a t i o n s of pressure taps on Models IX and X and eleven s t a t i o n s on Model X I . The d i s t a n c e between holes along each s t a t i o n i s l/k i n c h which i s c l o s e enough t o give the exact l o c a t i o n of the su c t i o n peak e s p e c i a l l y near the t r a i l i n g edge. A sheet metal cover was used on the under side- t o make the lower surface as f l a t as Model IV. (see F i g , 6), Model X I I , a r e c t a n g u l a r wing of 11 inches chord l e n g t h and ! h a l f span, had the same c o n s t r u c t i o n as Models IX, X and X I . S i x s t a t i o n s of pressure taps were d r i l l e d t o give the s t a t i c pressure on the model sur f a c e . The diameter of the pressure o r i f i c e s was 0.02 inches (see F i g . 7). - 15 -The models were r i g i d l y mounted on a simple turntable on the tunnel f l o o r . The incidence could be varied e a s i l y outside the tunnel. The boundary layer displacement thickness at the turntable i s 0.22 inches at the vel o c i t y of 60 fps. 3* Probes Two vortometer probes were used i n the tunnel f o r qu a l i t a t i v e investigation of the flow f i e l d and to determine the vortex-paths over these experimental models. They were sim i l a r to the one recently described by Hopkins and Sorensen 2^ and were made e n t i r e l y of brass for ease i n machining. The c y l i n d r i c a l propeller was l/2 inch long by l / l 6 inch i n diameter. One end of the propeller was painted black i n order to f a c i l i t a t e stroboscopic reading of the rpm. The dimensions of these two vortometers appear i n Figure 8. k. Traverse Apparatus The traverse apparatus was designed to locate the probe anywhere around the model and e a s i l y to control three degrees of freedom. I t allowed tr a n s l a t i o n along the f u l l length of the model and 3 feet downstream from the model. I t could also move the probes 33 inches hor- -i z o n t a l l y i n a dir e c t i o n perpendicular to the stream and 27 inches v e r t i c a l l y . The possible error i n the location of points of measurement' i s about l/32 inches along the longitudinal and l a t e r a l axes and about l / l 6 inch along the v e r t i c a l axis. The traverse apparatus consisted of a carriage s l i d i n g on three horizontal•shafts at the middle of the test section. The f i r s t shaft had a keyway along it,engaged by a key on a hollow cylinder. The cylinder drove a gear rack system by wires to control the v e r t i c a l motion of the probe. The second shaft was a brass screw meshed with a nut on the carriage to control the l a t e r a l motion. - 16 -The t h i r d shaft had a gear on both ends meshed with two racks f i x e d on the r a i l s outside of the tunnel to give the longitudinal motion. The ro t a t i o n a l motion could be adjusted manually after stopping the tunnel. (see F i g . 9)» 5« Manometers For pressure measurement, three manometers were used. The f i r s t , a Betz micromanometer which could be read to t 0.005 ™n* w.g. was used as the tunnel speed gauge. The second, a Lambrecht i n c l i n e d micro-manometer, was used f o r the t o t a l head measurements i n the boundary layer-on the tunnel f l o o r . The t h i r d , a 50-tube in c l i n e d manometer, was used for a l l pressure measurements associated with the models and the f l o o r pressure taps. This manometer was constructed with 3/l6 inch 0. D. Pyrex glass tubes mounted on a r i g i d frame. The frame was balanced i n precision l i n e -bored pivots on the r i g i d stand. Manual adjustment screws on the top of the board could f i x the frame at any desired angle of i n c l i n a t i o n between 5° and ^ 5° of horizontal. A l l tubes were manifolded to a single brass reservoir of i n f i n i t e l y adjustable height- on a v e r t i c a l guide rod. The reading length of t h i s manometer was 18 inches. Alcohol was used as manometer o i l . 6. Strobotac The angular vel o c i t y of the vortometer was determined by vi s u a l observation by using a G. R. Strobotac. The range of t h i s instrument i s from 110 rpm to 25000 rpm. I t could be read to t 5 rpm. - 17 -MEASUREMENT TECHNIQUES 1. L o c a t i o n of the Vortex Core The vortex cores about the d e l t a and r e c t a n g u l a r wing models were obtained by a vortometer d e s c r i b e d i n the preceding s e c t i o n . The vortometer was placed i n the f l o w f i e l d w i t h i t s a x i s of r o t a t i o n a l i g n e d i n the f r e e stream d i r e c t i o n . When i t moves across a vo r t e x core i t s r o t a t i o n a l speed changes because of the l a r g e f l o w angle g r a d i e n t s near the core. The r o t a t i o n a l speeds of the vortometer a t va r i o u s p o s i t i o n s w i t h i n the vortex core were measured w i t h a st r o b o t a c . These r e s u l t s were p l o t t e d i n the form of contours of constant r o t a t i o n a l - s p e e d . At the center of the vortex core, the r o t a t i o n a l speed i s maximum. As the vortometer-moves away from the vortex core, i t s r o t a t i o n a l speed decreases to zero. Thus, the center of the vortex core and i t s s i z e can be d e f i n e d a c c u r a t e l y i n each transverse plane. A f t e r measuring the core i n s e v e r a l t r a n s v e r s e planes ahead of and behind the t r a i l i n g edge, l o c a t i o n of the core as w e l l as i t s o r i g i n s can be e s t a b l i s h e d . 2. P o s i t i o n of the B u r s t i n g P o i n t Vortex b u r s t i n g about: a d e l t a wing i s considered to be a sudden s t r u c t u r a l change of the vortex core when the incidence reaches a c e r t a i n high v a l u e . The b u r s t i n g ! occurs f i r s t f a r downstream of the t r a i l i n g edge and moves r a p i d l y upstream w i t h i n c r e a s i n g i n c i d e n c e . P r e l i m i n a r y " experiments i n d i c a t e d that' the peak s u c t i o n on a wing surface at s t a t i o n s which are ahead of the b u r s t f o r each incidence increases w i t h i n c i d e n c e . When the incidence i s high enough t o move the b u r s t forward of those s t a t i o n s , the pressure d i s t r i b u t i o n becomes much f l a t t e r than would be expected i n the absence of the b u r s t . This experience of e f f e c t of b u r s t . on pressure d i s t r i b u t i o n leads one to hope th a t the b u r s t i n g p o i n t can - 18 -be detected by measuring the pressure d i s t r i b u t i o n on the wing. The three d e l t a wing pressure models were used f o r these measurements. The 50-tube manometer was connected t o the pressure taps t o measure the pressure d i s t r i b u t i o n a t each s t a t i o n . The s u c t i o n peak.increases g r a d u a l l y w i t h incidence to a maximum value and then s t a r t s t o drop r a p i d l y . The b u r s t i s assumed t o occur above the s t a t i o n where maximum peak s u c t i o n i s reached at t h a t p a r t i c u l a r angle of a t t a c k . 3. Normal Force C o e f f i c i e n t s The normal f o r c e c o e f f i c i e n t s were obtained i n d i r e c t l y by the g r a p h i c a l i n t e g r a t i o n of surface pressures. Although t h i s i s not a good method, i t gives very u s e f u l i n f o r m a t i o n where there i s no, tunne l balance a v a i l a b l e . The v a r i a t i o n of pressure d i s t r i b u t i o n w i t h angle of a t t a c k i s shown l a t e r t o have great importance w i t h regard to the vor t e x b u r s t i n g phenomenon. Models IX, X, X I , and X I I were used f o r these t e s t s . Since the pressure taps were on the s u c t i o n sides of the models, the pressure d i s t r i b u t i o n s on the pressure sides were obtained by i n v e r t i n g the models. The models were r i g i d l y f i x e d on the t u r n t a b l e i n the t e s t s e c t i o n . When the model was adjusted t o a p a r t i c u l a r angle of a t t a c k , f o u r screws on the t u r n t a b l e were t i g h t e n e d to prevent the model from moving d u r i n g a t e s t . The pressures were measured by the 50-tube i n c l i n e d manometer. - 19 -TEST RESULTS 1 1. Vortometer Measurements a. Tests on Model I P r e l i m i n a r y vortometer measurements were performed on Model I f i x e d on the t u n n e l f l o o r w i t h a 3/4" gap between the model and f l o o r . Because small angles of a t t a c k were not p o s s i b l e as the vortometer could not get c l o s e enough t o the wing f o r a complete survey, the wing was set at 15° angle of a t t a c k . The a i r s p e e d was 80 f p s , corresponding t o a Reynolds Number of 9*78 x 10^ based on the root chord. The number of r e v o l u t i o n s per minute of the vortometer was measured by u s i n g a s t r o b o t a c . u n i t . Near-the t r a i l i n g edge of the wing the r o t a t i o n a l speed was not constant due to s l i g h t v i b r a t i o n of the"wing. The v o r t e x core obtained i s p l o t t e d i n F i g . 10. I t was noted t h a t the height of vortex core above the wing surface agrees f a i r l y w e l l w i t h p u b l i s h e d .data, but the h o r i z o n t a l distance fronr wing t i p to the vortex core i s s m a l l e r . The reason i s considered to be the gap between model and t u n n e l f l o o r . Because of the gap a vortex core forms near the r o o t chord which tends t o push the vortex core at the l e a d i n g edge" outboard. A f t e r the gap was sealed, the vortex core p o s i t i o n agreed w i t h other r e s u l t s very w e l l (see F i g . l l ) . I t i s c l e a r t h a t the e f f e c t . o f t u n n e l f l o o r boundary l a y e r i s smaller than t h a t due t o the gap between " -model and t u n n e l f l o o r . In order t o e l i m i n a t e the gap e f f e c t , i t was de-c i d e d t o s e a l the gap. b. Tests on Model I I Some measurement was done on Model I I t o check the e f f e c t of b e v e l at the l e a d i n g edge on the p o s i t i o n of vortex core. The model was set. at the same c o n d i t i o n as Model I . Model I I had a b e v e l l e d upper surface. - 20 -I t was found t h a t the p o s i t i o n of vortex core was s l i g h t l y outboard i n comparison w i t h t h a t about Model I and the f l o w f i e l d was not so c o n s i s t e n t as t h a t above Model I.. Based on these experiences, a l l the models designed f o r the f o l l o w i n g t e s t s had a f l a t ' u p p e r surface and were b e v e l l e d on the lower surface to provide the sharp edges. I n a l l cases the models were set on the t u r n t a b l e without gaps between the models and tu n n e l f l o o r . c. Tests on Model I I I -For angle of a t t a c k of"15° and air s p e e d of 80 fps,. measurements were made i n s e v e r a l planes around the wing t i p . The angular speeds of the vortometer were v e r y ' c o n s i s t e n t i n the f l o w f i e l d ' d u r i n g the t e s t s . This suggests t h a t there i s a steady vortex core formed about the wing t i p . The p o s i t i o n of v o r t e x core i s shown i n F i g . 12. d. Tests on Model V I I I I n order t o i n v e s t i g a t e the f l o w f i e l d about r e c t a n g u l a r wings, a more accurate metal model was made. This was a t h i n model w i t h lk° b e v e l on the lower s u r f a c e . The t e s t s were c a r r i e d out i n the wind t u n n e l a t an airs p e e d of 72.6 f p s . and the wing was set at angles of a t t a c k of 3 and 10 degrees. The minimum angle of a t t a c k a t which the wing gives a dete c t a b l e t i p v ortex core i s 3 degrees. For angles of a t t a c k l e s s than 3 degrees, the f l o w remains attached t o the wing surface. A thorough measurement was made at 10° angle, of a t t a c k . I n a d d i t i o n t o the side edge se p a r a t i o n , separation was found a t the l e a d i n g edge. The pl a n view of the vor t e x system on t h i s model i s given i n F i g . 13• • - 21 -2. Pressure D i s t r i b u t i o n a. Measurements on Model IX Spanwise pressure d i s t r i b u t i o n s were measured at seven stations on th i s model by using the 50-tube manometer. An incidence range up to 40° was covered i n 5° steps at a speed of 72-6 fps. Both pressure and suction surface readings were obtained by inverting the model. Figures l 4 to 20 give the pressure d i s t r i b u t i o n at each station. The figures show the incremental pressure d i s t r i b u t i o n C_ - C , where pressure c o e f f i c i e n t at zero P p c* = o / incidence was i n the range 0.02 ^ C < 0.04 at a l l test points. I t P o<. = 0 was noted that the magnitude of the pressure d i s t r i b u t i o n changes as the t r a i l i n g edge i s approached and the flow f i e l d for low speed flow i s c l e a r l y f a r from conical due to the upstream effect of the t r a i l i n g edge. However, for angles of attack under 10° the pressure v a r i a t i o n along y/s = constant i s small over the forward two thirds of the model. This means that the flow f i e l d may be taken approximately as conical at lower angles of attack. Spanwise integration of the pressure c o e f f i c i e n t d i s t r i b u t i o n s gives the l o c a l normal force coefficient curves shown i n F i g . 21. A chord, wise plot of the l o c a l normal force c o e f f i c i e n t i s shown i n F i g . 22. Chordwise integration of the l o c a l normal force coefficient.gives the o v e r a l l normal force c o e f f i c i e n t shown i n F i g . 23• The l i f t c o e f f i c i e n t i s given i n Fig.6l. The wing reaches i t s s t a l l i n g point at 3^° angle of attack. b. Measurements oh Model X Static pressure d i s t r i b u t i o n was obtained on the upper surface" of t h i s model under the same test conditions as for Model IX. The incidence range covered was 10° to 35°• Figures 25 to 30 show the di s t r i b u t i o n s of pressure c o e f f i c i e n t . The pressure d i s t r i b u t i o n s on the lower surface were not measured on t h i s model. For the purpose of obtaining the ov e r a l l - 22 -normal forc e c o e f f i c i e n t , estimates were made by r e f e r r i n g to the data presented by R a i n b i r d ' s group (Ref. 8 ) . Because the pressure c o e f f i c i e n t curves on the lower surface a t d i f f e r e n t angles of a t t a c k are e q u a l l y spaced and of s i m i l a r shape, and the magnitude of pressure c o e f f i c i e n t . i s s m a l l i n comparison w i t h the s u c t i o n on the upper surface, i t i s reasonable t o b e l i e v e t h a t the e r r o r introduced by t h i s estimate i s s m a l l . Then the l o c a l normal f o r c e c o e f f i c i e n t curves were obtained by g r a p h i c a l i n t e g r a t i o n shown i n F i g ure 31« Chordwise p l o t s of l o c a l normal f o r c e c o e f f i c i e n t are shown i n Figure 32• The v a r i a t i o n of o v e r a l l normal f o r c e c o e f f i c i e n t i s given i n Figure 33« The l i f t c o e f f i c i e n t i s given i n F i g . 6 l . The s t a l l i n g p o i n t f o r t h i s model was found a t 32° i n c i d e n c e . .. c. Measurements on Model XI The same measurements as f o r Model X were made on t h i s model at seven s t a t i o n s . Measurements of pressure c o e f f i c i e n t were taken every 5° from o< = 5° t o c < = 30°. The pressure d i s t r i b u t i o n s a t those s t a t i o n s are shown i n F i g u r e s 3*+ t o 1+0. . Based on the data given by F i n k and T a y l o r , (Ref. 5) , R a i n b i r d ' s group (Ref. g) and the present t e s t s on Model IX, estimates of pressure d i s t r i b u t i o n s on the lower surface were made. G r a p h i c a l i n t e g r a t i o n was. a p p l i e d again to t h i s model to give the l o c a l normal f o r c e c o e f f i c i e n t s shown i n Figure hi. F i g u r e 1+2 gives the chordwise p l o t of C^and Fi g u r e 1+3 shows the o v e r a l l normal f o r c e c o e f f i c i e n t versus i n c i d e n c e . The l i f t c o e f f i c i e n t i s shown i n F i g . 6 l , The wing s t a l l e d at 29° i n c i d e n c e . d. Measurements on Model X I I Re s u l t s of surface pressure d i s t r i b u t i o n s on t h i s model are given i n F i g u r e s 1+5 to 51 • The a i r speed was 72.6 fps and the incidence range covered was 5° t o 30°, measurements b e i n g made at 5° steps. At 10° angle - 23 -of attack, the effect of the t i p vortex became apparent and a suction peak was found on the pressure d i s t r i b u t i o n curves. The differences between the upper and lower surface pressure -coefficients have been integrated with respect to y/s at s i x stations to give C^x shown i n Figure 53* The chord-wise v a r i a t i o n of C J J x i s shown i n Figure 54 f o r the range of incidence up to 30°• Figure 55 gives the o v e r a l l normal force c o e f f i c i e n t versus incidence. 3. Position of Vortex Bursting Positions of vortex bursting obtained from the change of pressure d i s t r i b u t i o n are shown i n Figures 57, 58 and 59 ^or Models IX, X and XI, respectively. The res u l t s presented by E l l e and Lambourne and Bryer are also shown i n the figures for comparison. On these three models, the bursting occurs at the t r a i l i n g edge at the incidences plotted i n Figure 60. 4. Floor Static Pressure Measurements Static pressures "on the tunnel f l o o r behind Models IV, V, VI and VII were measured at two stations. I t was expected that there must be an effect on the pressure d i s t r i b u t i o n s due to the vortex bursting while i t occurs above the measured station. Because of the boundary layer on the tunnel f l o o r and the distance between the vortex core and the f l o o r , no clear evidence was found behind Models V, VI and VII. For Model IV, some evidence was found. The suction peak increases gradually with incidence and then drops down quickly at a certain high incidence. - 2k -DISCUSSION OF TEST RESULTS DELTA WINGS Spanwise pressure d i s t r i b u t i o n s on Models IX, X and XI have the same character at each t e s t s t a t i o n . On the upper surface of the wing, -a high s u c t i o n peak was found near -the l e a d i n g edge due t o the vortex core above the wing and the s u c t i o n i s comparatively s m a l l i n the r e g i o n around the r o o t chord. This phenomenon i n d i c a t e s t h a t the vortex l i n e has a strong e f f e c t on the l i f t i n g and s t a b i l i t y p r o p e r t i e s of such wings. At 5° angle of a t t a c k , the s u c t i o n peak i s n o t i c e a b l e . This means t h a t l e a d i n g edge sep a r a t i o n happens e~ven a t such a low angle of a t t a c k . The s u c t i o n peak which corresponds t o the vortex core p o s i t i o n moves inboard w i t h i n c r e a s i n g angle of a t t a c k . The magnitude of the p'eak s u c t i o n i n c r e a s e s g r a d u a l l y w i t h incidence t o a c e r t a i n value and then s t a r t s t o drop r a p i d l y due to the sudden s t r u c t u r a l change of the. vortex core above the wing known as vortex b u r s t i n g . At 5° i n c i d e n c e , a poin t of minimum s u c t i o n was found a t each s t a t i o n . This p o i n t represents the reattachment of the r o l l i n g up shear l a y e r on the upper surface of the wing. On Model IX at a l l s t a t i o n s , the reattachment occurs near y/s = 0.55* F i g u r e 2k shows a comparison of the pressure c o e f f i c i e n t d i s t r i -b u t i o n a t s t a t i o n 6 of Model IX w i t h those p r e d i c t e d by Mangier and Smith and Brown and M i c h a e l . I t i s ' seen that the t h e o r e t i c a l pressure peaks are much greater and narrower than the experimental results.- The p o s i t i o n of the t h e o r e t i c a l peaks i s a l s o outboard of the experimental data. No evidence of secondary separation was found on Models IX and X, because the pressure taps were not clos e enough t o the l e a d i n g edge. On Model XI at s t a t i o n s i t and 2, an a d d i t i o n a l s u c t i o n peak was found a t y/s = 0.9 which i n d i c a t e s the secondary s e p a r a t i o n . -- 25 -Static pressure measurements on the lower surface of Model IX were made (see Figures lh to 20)„ I t was found that the effect of flow pattern on the lower surface pressure d i s t r i b u t i o n i s not marked. The shape of.pressure d i s t r i b u t i o n curves remains the same at a l l angles of attack-and the curves are equally spaced, but the magnitude of pressure increases with incidence. I t was also noted that as the t r a i l i n g edge i s approached, the magnitude of s t a t i c pressure decreases- For example, at station 6 of Model IX, the average s t a t i c pressure i s +0.5 at °C = 40°, but at station 1 the s t a t i c pressure i s only +0-3". Therefore the t r a i l i n g edge effect on the lower surface pressure i s als'o considerable. A lower pressure reading was obtained i n the region near the root chord at high angle of attack. This i s due to the effect of tunnel w a l l boundary layer. Local normal force c o e f f i c i e n t curves for Model IX are shown i n Figure 21. When a comparison i s made with the curves given by Brown and Michael, (Ref. l U ) , Mangier and Smith (Ref. 15), and Jones (Ref. 16), i t i s seen that the experimental results f o r a l l stations f a l l progressively below Brown and Michael's t h e o r e t i c a l curve. The C^x curves for the forward stations 5 and 6 l i e above Mangier and Smith's curve. The curves for a l l stations except station 1 l i e above Jones' the o r e t i c a l curve. I t was noted from t h i s family of curves that at a l l stations except station 1, the l o c a l normal force c o e f f i c i e n t increases" with incidence to a maximum value and then drops rapidly as the incidence increases further.. This i s the effect of vortex bursting on l o c a l normal force c o e f f i c i e n t . There are two factors to influence the normal force c o e f f i c i e n t . The f i r s t i s the t r a i l i n g edge effect and the second i s due to the vortex bursting i n the flow f i e l d . I t i s believed that the presence of a subsonic t r a i l i n g edge would have a small effect at small incidence and a progressively greater effect at large incidence.. - 26 -At station 1, the normal force increases with incidence even when vortex bursting occurs ahead of t h i s station* This suggests that the effect of t r a i l i n g edge i s greater than the bursting effect there. The s t a l l i n g points at a l l stations except station 1 are at pC - 3^°. The s t a l l i n g point i s the incidence at which CT = C t . By ° Mnax J examining the l i f t curves f o r Models IX, X and XI, the s t a l l i n g points on these three models were found at 3^ °> 32° and 29° incidence, respectively^ For ordinary subsonic a i r f o i l s s t a l l i s due to separation of flow on the upper surface. Separation f i r s t occurs at the t r a i l i n g edge and then moves forward with incidence. When the point of separation moves close to the leading edge, the a i r f o i l s t a l l s . For sharp-edged delta wings, flow separates-at the leading edge, even at very low angle of attack and i t i s clear from the l i f t curves that the separation does not cause the wing s t a l l but rather gives a higher l i f t than the wing without separation. Therefore, separation i s not the reason for s t a l l on sharp-edged delta wings. Probably the reason i s the st r u c t u r a l change of the vortex system or vortex bursting i n the flow f i e l d . Bursting, which occurs downstream of the t r a i l i n g edge at small angle of attack, moves upstream towards the apex with incidence and causes the wing s t a l l . For Model IX, see Figures 6l and 57 • The wing .s t a l l s at 3^° incidence for which bursting occurs at 6C$ c r. This suggests that the wing s t a l l s when the bursting point reaches a position upstream of the t r a i l i n g edge. The same phenomenon was found on Model X, as shown i n Figures 6l and 58, and Model XI, as . shown i n Figures 6l and 59-Comparison between the present test results and theories f o r normal force c o e f f i c i e n t of these three wings i s shown i n Figure kk. I t i s seen that the experimental results are lower than the t h e o r e t i c a l r e s u l t s . Some experimental results from other sources are shown i n the figure f o r comparison. - 27 -RECTANGULAR WINGS Spanwise pressure d i s t r i b u t i o n s show that' the average Cp on the upper,surface of the wing increases r a p i d l y w i t h incidence t o a maximum value and then, drops g r a d u a l l y w i t h i n c r e a s i n g i n c i d e n c e . For example, at s t a t i o n ' 6 of Model X I I , the average C increases from -0.3 at <=< = 5° "to -0.7 at <=«£_ = 10° and then drops tor-0.5 at o< = 20°. When the incidence i n c r e a s e s again, the average C^ drops g r a d u a l l y to -0.45 at °^-= 30° and almost remains constant t h e r e . On the lower s u r f a c e , the average inc r e a s e s c o n t i n u o u s l y from +0.1 at oC = 5° "to +0.6 at &<. = 30°. The same behavior was found at other s t a t i o n s . I t was found that the d i f f e r e n c e of C between s t a t i o n s i s • P n o t i c e a b l e at lower angle of a t t a c k . S t a t i o n s near the t r a i l i n g edge give a smaller reading. At higher angle of a t t a c k , Cp on the upper surface i s almost the same at a l l s t a t i o n s . :For'example, Cp i s around -0.6 at a l l s t a t i o n s at o< = 20°. At =< = 10° and oC = 15°, a s u c t i o n peak near the wing t i p was found which i s caused by the side edge s e p a r a t i o n . For angles of a t t a c k more than 15°, no evidences of t i p v o r t e x core were found from the pressure d i s t r i b u t i o n s . F i g ure 53 shows the v a r i a t i o n of l o c a l normal f o r c e w i t h incidence at each s t a t i o n . I t was found t h a t the shapes of the curves are the same; They a l l increase w i t h incidence t o a maximum , value and then decrease a l i t t l e b i t and then r i s e again. For given angle of a t t a c k , s t a t i o n 6 gives the l a r g e s t l o c a l normal f o r c e c o e f f i c i e n t . C^x f o r ..other s t a t i o n s decreases p r o g r e s s i v e l y as the t r a i l i n g edge i s approached. The maximum qccurs at d i f f e r e n t angles at d i f f e r e n t s t a t i o n s . , C J J reaches i t s maximum at o£ - ne-at s t a t i o n 6, but at oC = 19° at s t a t i o n 1. The. maximum occurs at other s t a t i o n s i n the range from.; c< = 11° t o o< = 19°. For angles of a t t a c k greater than 25°, the normal f o r c e increases again w i t h incidence at a l l - 2b -stations. I t can be imagined that Cjj - w i l l reach a maximum at o( = 90° and the curves f o r stations 1 and 6 w i l l meet there. From the o v e r a l l normal force curve, i t i s seen that C,T = Cm at c*C = 17° (see Figure 55) • - N INmax 23 I t i s known that forc< = 90° i s about 1.20 f o r a f l a t , plate of A = 2. Reference to the chordwise va r i a t i o n of C-^  (see Figure 5*0 shows . 0 that the character of v a r i a t i o n for °C = 15 i s di f f e r e n t from that f o r o< - 10°. For o< less than 10°, concave upward curves were obtained, but for o£ larger than 15°, a l l the "curves are concave downward. This suggests that the flow pattern changes from one type to another i n the range from .cx£ = 10° to oC = 15°« Preliminary vortometer tests indicate that there i s a stable t i p vortex core about the wing t i p and a vortex core at the leading edge at 10° incidence. Therefore, the flow pattern about the rectangular wing i s dominated by a t i p vortex core and a leading edge vortex core above the wing. These vortex cores produce the high suction at the wing t i p and the leading edge as seen on the pressure d i s t r i b u t i o n curves. When angles of attack exceed • 15° the leading edge vortex passes downstream with the free stream, producing an unsteady flow pattern with vortex shedding i n the' manner of flow past a b l u f f body. The vortex core at the wing t i p also changes i t s structure at high angle of attack. This unstable flow pattern does not produce high suction peaks around the leading edge and wing t i p as shown on the pressure d i s t r i b u t i o n curves f o r angles of attack above 20°. Comparison of the o v e r a l l normal force c o e f f i c i e n t with the results" of other Investigators indicates very good agreement 'for angles of attack less than 15°> but disagreement at high angles of attack (see Figure 56). Discrepancies are. due to the d i f f e r e n t a i r f o i l sections of the experimental models. The theory of Sacks and Nielsen does not show close agreement for - 29 -angles of a t t a c k greater than 14°, because they d i d not consider the l e a d i n g edge se p a r a t i o n on the. wing-. They a l s o d i d not analyze the unstable f l o w p a t t e r n at extremely high angles of attack.,.. VORTEX BURSTING . -Vortex b u r s t i n g , which occurs at high angles of a t t a c k , was known as a sudden s t r u c t u r a l change of the vo r t e x core. For a given l e a d i n g edge sweep d e l t a wing, the b u r s t i n g p o s i t i o n depends on the angle of a t t a c k * From F i g u r e s 57, 58 and 59, i t was noted t h a t the b u r s t i n g p o s i t i o n i s very s e n s i t i v e t o angle of a t t a c k when b u r s t i n g occurs around the t r a i l i n g edge. On the three models, the b u r s t i n g p o s i t i o n moves q u i c k l y forward to 50$ c r and g r a d u a l l y moves again towards the apex, w i t h i n c r e a s i n g i n c i d e n c e . No e f f e c t of Reynolds number i s n o t i c e a b l e i n the range of Re = 7-l6 x 10^ t o 9"i5 x 10-*. Leading edge sweep i s another important parameter of b u r s t i n g p o s i t i o n . For 75° l e a d i n g edge sweep, b u r s t i n g occurs at the t r a i l i n g edge at c< = 33°, but i t occurs there at o ( = 21° on 65° l e a d i n g edge sweep wings. The p l o t of l e a d i n g edge sweep against °< at which b u r s t i n g occurs at the t r a i l i n g edge i s a s t r a i g h t l i n e (see Figure 6o). This curve i s i d e n t i c a l w i t h E l l e ' s r e s u l t s obtained by smoke t e s t . Compar-i s o n between the present t e s t r e s u l t s and other a v a i l a b l e data i s shown i n F i g u r e s 57 and 59* For Model XI, 'Lambourne and Bryer showed t h a t the b u r s t i n g occurs a t the t r a i l i n g edge at l6.5° incidence by smoke t e s t , but the present t e s t gave a value of 21°, which i s i d e n t i c a l w i t h E l l e 1 s r e s u l t . For incidence g r e a t e r than 22°, t h e i r r e s u l t s are i n good agreement w i t h the present t e s t s . For Model IX, the d i f f e r e n c e between E l l e ' s r e s u l t s o and the present t e s t s i s of the order 1.5 • The reason f o r and the a c t u a l mechanism of vortex b u r s t i n g have not yet been found. Based on the a v a i l a b l e experimental data, i t i s reasonable t o speculate that b u r s t i n g occurs: 1 . due t o the disturbance produced at the t r a i l i n g edge, t r a i l i n g edge e f f e c t . . 2. ' due to a. f o r c e unbalance on the vortex system at high i n c i d e n c e . - 31 -CONCLUSIONS From the i n t e r p r e t a t i o n of the data which have been presented, the f o l l o w i n g conclusions are drawn: 1. The vor t e x b u r s t i n g occurs f i r s t downstream of the t r a i l i n g edge and then moves r a p i d l y upstream w i t h i n c r e a s i n g i n c i d e n c e . 2. At a given angle of a t t a c k , the p o s i t i o n of vortex b u r s t i n g depends on the angle of sweep. For higher l e a d i n g edge sweep wings, b u r s t i n g occurs f u r t h e r downstream. 3« The p o s i t i o n of vortex b u r s t i n g i s not s e n s i t i v e to Reynolds number. ' ' k. The vor t e x b u r s t i n g makes the surface s u c t i o n peak much f l a t t e r than t h a t produced by a concentrated vortex core. 5. The ' forward movement of the b u r s t i n g p o i n t i s the reason f o r s t a l l . The wing s t a l l s when the b u r s t i n g occurs at a p o s i t i o n upstream of the t r a i l i n g edge. 6. The f l o w p a t t e r n about the sharp-edged r e c t a n g u l a r wings o . o changes from one type to another i n the range from ©(. = 10 t o °< = 15 . " 7» This change s h i f t s the center of pressure backward, 8. This change a l s o causes the wing s t a l l . - 32 -RECOMMENDATIONS The f o l l o w i n g recommendations are made f o r f u t u r e i n v e s t i g a t i o n s : 1. In order to understand the vortex b u r s t i n g phenomenon, i t i s necessary t o measure the t o t a l head, s t a t i c pressure and the f l o w d i r e c t i o n a t v a r i ous s t a t i o n s along the vortex core r i g h t up t o the b u r s t i n g p o i n t . 2. For the purpose of c a r r y i n g out the t e s t s i n ( l . ) new measurement techniques must be developed. 3. The e f f e c t of t r a i l i n g edge r e q u i r e s some d e t a i l e d i n v e s t i g a t i o n . h. The f l o w f i e l d around the corners of the re c t a n g u l a r wing a l s o r e q u i r e s d e t a i l e d measurement. - 33 -REFERENCES 1. Anderson, A. E. An i n v e s t i g a t i o n a t low speed of a l a r g e - s c a l e t r i a n g u l a r wing  of aspect r a t i o two, ~~ NACA RM A7F06 . 19^ 7 2. Berndt, S. B. • Three component measurement and f l o w i n v e s t i g a t i o n of plane d e l t a wings a t low speeds and' zero yaw. K.T.H. Aero. TN 4 1949. 3. B i r d , J . D. and R i l e y , D. R. Some experiments on v i s u a l i z a t i o n of fl o w f i e l d s behilnd low- a s p e c t - r a t i o wings by means'of a " t u f t g r i d . NACA TN 2674 May 1952. 4. Ornberg, T. A. A. note on the f l o w around d e l t a wings. K.T.H. Aero. TN No." 38, 1954. 5. F i n k , P. T. and T a y l o r , J . T. Spme- low speed experiments w i t h 20 degree d e l t a wings. ''•Imperial College Rep." F. M. 2339 Sept., 1955. 6. J a s z l i c s , . 1. and T r i l l i n g , L. An experimental study of the,f l o w f i e l d about swept and d e l t a  wings w i t h sharp 'leading edges. ~~ 0SR- TN-58-6 October, 1957. " 7. E l l e , B. J . An i n v e s t i g a t i o n at low speed of the flow-near the apex of t h i n  delta.wings w i t h sharp l e a d i n g edges. ARC F. M. 2629 January7 1958. 8. Marsden, D. J . , Simpson, R. W. and R a i n b i r d , W. J . An i n v e s t i g a t i o n i n t o the f l o w over d e l t a wings at low speeds w i t h  l e a d i n g edge s e p a r a t i o n . The College of Aeronautics Report No. 114 February, 1958.. 9. Peckham, D. H. •Low-speed wind tun n e l t e s t s on a s e r i e s of uncambered slender  pointed wings w i t h sharp edges. R.A.E. Report Aero. 2613 December, 1958. 10. Weber, J . • ,• • Some e f f e c t s of f l o w s e p a r a t i o n on slender d e l t a wings. R.A.E. Tech.' Note "No. Aero 2425. ' ~~' November, 1955 11. Lambourne, N. C. and Bryer, D. J . The b u r s t i n g of leading-edge v o r t i c e s -Some observations and d i s c u s s i o n of the phenomenon A.R.C.- R.M. 3085 A p r i l , 1961.. - 3^  -12. Harvey, J . K. An a l y s i s of vor t e x breakdown phenomenon, Pa r t I I Im p e r i a l College of; Science and Technology Report 103 September, i960. 13- Legendre, R. Vortex formation a t the l e a d i n g edge, of. an a i r f o i l . C.R. Acad. S c i . P a r i s , 23^, 12, September, 1956. Ik. Brown, C. E. and Mi c h a e l , W. H. J r . E f f e c t of leading-edge s e p a r a t i o n on the l i f t of a d e l t a wing. J.A.S. V o l . 21, No.' 10, P 609, October, 195^. ' 15. Mangier, K. W. and Smith, J . H. B. A theory of slender d e l t a wings w i t h l e a d i n g edge s e p a r a t i o n . Proc. Roy. Soc, London (A) 251,1265, pp 200-217 May, 1959 16. Jones, R. T. Pr o p e r t i e s of l o w - a s p e c t - r a t i o pointed wings at;speeds below  and above the speed of.sound. NACA Report No. 835, I945. 17. Squire, H. B. A n a l y s i s of the vor t e x breakdown phenomenon, P a r t I . Im p e r i a l College of Science and Technology . Report No. 102 i960. 18. Jones, J . P. The breakdown of v o r t i c e s i n separated f l o w . U. S.A. A. Report No".' lh-0 ~ " J u l y , i960. "" " 19. B o l l a y , W. • . ' A no n - l i n e a r wing theory and i t s a p p l i c a t i o n to r e c t a n g u l a r  wings of small aspect r a t i o . • Z. Angew Math. Mech, Bd. 19, February, 1939* 20. Gersten, K. Non-linear a i r f o i l theory f o r r e c t a n g u l a r wings i n compressible f l o w . NASA RE 3-2-59W Feburary 1959-21. Sacks, A. H. and N i e l s e n , J . N. An a n a l y t i c a l study of the low speed aerodynamics of s t r a i g h t and  swept wings w i t h f l o w s e p a r a t i o n . VIDYA, Report No. "38, -January I961.' 22. Hopkins, E. J . and Sorensen, N. E. A device f o r vortex core measurements. J . A. S. V o l . 23/ No." k, pp 396-398 A p r i l , 1956. 23. Hoerner, S. F. F l u i d dynamic drag, p. 3 -l6. P u b l i s h e d by the author, 1958* TABLE I P o s i t i o n of Pressure Taps on Models IX, X, XI and X I I . Model IX Model XI — S t a t i o n x/.cr 1 .9375 2 .8125 3 .6875 4 .6oko i 5 .5210 6 .4375 7 .3540 S t a t i o n x / c r 1 • 9375 2 .8125 3 .6875 4 .6o4o 5 .5210 6 .^375 : 7 •35+0 Model X Model. X I I S t a t i o n x / c r S t a t i o n x / c r 1 .936 1 .866 2 • 914 2 .727 •3 .87 3 .636 4 .83 4 • 5^ 5 5 .786 5 .364 6 . .744 6 .182 7 8 .700 .658 9 • 573 10 .486 11 .402 TURNING THIRD POWER FOURTH PIP7H VASES DIP7USSR SECTION l>IPPUSEIi DIPP'JSKR SECTI Yd 53.50' PIUIUE 1 WIND TUMEL AERODTJAXIC G:v:i I'.IE - 3 8 4 ~~! A J 1" - SXE^H DP KPDEL I I I - 39 -- 40 -24" • PIRURE 4b - SKETCH OP MODELS IV, V, VI AMD VI I 11"-- i 1 1/4" y SECTION A-A 11" - 41 -FIGURE 5 - SKETCH OP MODEL VIII - 4 2 -STATIONS MODEL IX 1/4 14° SECTION A-A STATIONS MODEL X - 4 3 -STATIONS PIS'JHE 6b - SKETCH OP MODELS IX, X AND XI STATIONS 1 ? 3 4 r — * 1 n J 0 0 —I 11"_ y v///////z^/y/^/^^ 14° SECTION A-A PI GUPS 7 - SI'ET'CH OP XII I'D 4 3-(a) h i ' 1*" ! CYLINDER (b) FIGURE 8 - SKETCH OF PROBES - 4 6 -FIGURE 9 - TRAVERSE APPARATUS - 4 7 FIGURE 10 - POSITION OP VORTEX CORE MEASURED WITH VORTOMETER MODEL I AND I I - 4 8 -0.4 O PUBLISHED DATA © PRESENT TESTS MODEL I a = 10? 15? 22.5° LEGENDRE BROWN & MICHAEL MANGLER & SMITH 0.5 0.6 0.7 0.8 0.9 y/s FIGURE 11 - VORTEX POSITION FOR PLAT DELTA WINGS 1.0 - 5 0 -TRAILING EDGE H 2 LEADING EDGE -6 8 i n . 10 ROOT CHORD FIGURE 13 - VORTEX SYSTEM ABOUT MODEL V I I I AT 10° ANGLE OF ATTACK +0.4 1.0 0.8 0.6 0.4 0.2 0 y / e FIGURE 14 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL IX -1.50 +0.75 U 1 1 1 1 1 1.0 0.8 0 o6 0.4 0.2 0 y/s FIGURE 15 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL IX - 5 3 1.0 0.8 0.6 0.4 0.2 0 y/s FIGURE 16a - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX UPPER SURFACE - 5 4 -FIGURE 16b - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX LOWER SURFACE FICURE 17a - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 4 MODEL IX UP?:O< 'CT.JKJ'ACK - 5 6 -FIGURE 17b - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 4 MODEL IX LOWER SURFACE y / s FIGURE 18 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL IX - 58 --3.0 + 1.0 | I I | ; . 1.0 0.8 0o6 0 e4 0.2 0. y / s FIGURE 19 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL IX FIGURE 21 - VARIATION OF SECTIONAL NORMAL FORCE . . COEFFICIENT C„ WITH INCIDENCE MODEL IX MODEL IX - 63 -- 2 . 5 ._ BROWN & MICHAEL _ MANGLER & SMITH PRESENT TESTS FIGURE 24 - SPANWISE PRESSURE DISTRIBUTIONS MODEL IX ( COMPARISON WITH RESULTS OP BROWN AND . MICHAEL, MANGLER AND SMITH ) - 6 4 -- 65 -•1.50 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 26 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL X - 66 -3.0 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 28 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 9 MODEL X 3.0 30° FIGURE 29 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 10 MODEL X FIGURE 30 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 11 MODEL X 1.75 1.50 1.25 1.00 0.75 0° 10 c 20° 30° a 40 c 50< FIGURE 33 - VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X - 74 FIGURE 35 - SPAIWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL XI 2.00 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 36 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL XI 76 -3.0 2.5 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 38 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL XI - 7 8 -. -3.0 1«0 0.8 0.6 0.4 0.2 0 y / s FIGURE 39 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL XI - 7 9 -1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 40 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL XI - 80 -3.0 2.5 - 81 -- 82 1.75 1.50 - 8 3 — 18 16 14 12 °N/K 2 10 8 O 9 9 A 4-e JONES BROWN & MICHAEL MANGLER & SMITH PRESENT TESTS MODEL IX MODEL X MODEL XI DATA PROM REP. 15 PINK & TAYLOR p = 10° MICHAEL p = 10°,M =1.9 LAMPERT p = 7.5°, M = 1.46 MICHAEL p = 7. LAMPERT p = 12°, M = 1.46 MICHAEL p = 10°, M = 1.9 V 0.2 0.4 0.6 0.8 1.0 1.2 1.4 a/K FIGURE 44 - COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE COEFFICIENTS OF DELTA WINGS .0.3 -0.6 -0.4 -0.2 +0.2 +0.4 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 C y/s FIGURE 45a - SPANWISE VARIATION OP C ? AT STATION 1 MODEL X I I -0.8 -0.6 -0.4 *0.2 +0.2 +0,4 1.0 0.9 0.8 0.7 0.6 0.5 y / s 0.4 0.3 0.2 0.1 FIGURE 45b - SPANWISE VARIATION OF C AT STATION 1 MODEL X I I P ( a - 10°, 20°, 30° ) 0 00 FIGURE 46a - SPANWISE VARIATION 0? C AT STATION" 2 MODEL X I I P FIGURE 46b - SPANWISE VARIATION OF C AT STATION 2 MODEL X I I P ( «!== 10°, 20°, 30° ) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 " 0.3 0.2 0.1 y/s 0 FIGURE 47a - SPANWISE VARIATION OF C AT STATION 3 MODEL X I I I P ( a = 5°, 15°, 25° ) -0.8 +0,6 1.0 0.9 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1 0 y/s 1 vo ro FIGURE 49a - SPANWISE VARIATION OF C AT STATION 5 MODEL X I I . P 1 ( a = 5°, 15°, 25° ) FIGURE 49b - SPANWISE VARIATION OF C AT STATION 5 MODEL X I I P ( a = 10°, 20°, 30° ) - 99 FIGURE 55 - VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C„ WITH INCIDENCE MODEL X I I - i o i -- 102 -20 28° 30° 32° 34° 36° 38° o ANGLE OP ATTACK -40° 42'° FIGURE 57-~ VARIATION OF VOPTEX R^FAIGDCWN. POSITIONS WITH INCIDENCE HOTEL-J7. -.103 -100 60 40 20 ol • ELLE V 0 PRESENT TESTS >^ i > *» ?6° 28° 30° 32° 34° 36° 38° 40° « ANGLE OP ATTACK . PICUPE 58 ~ VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MCDEL X - 104 -FIGURE 59 - VARIATION OF VOHTFX BREAKDOWN POSITIONS WITH INCIDENCE MODEL XI FIGURE 61 - VARIATION OF LIFT COEFFICIENT C T h WITH INCIDENCE MODELS I X , X AND XI 

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