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UBC Theses and Dissertations

An experimental investigation of the pointed forebody aerodynamics Stewart, Alan Charles 1988

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A N E X P E R I M E N T A L I N V E S T I G A T I O N O F T H E P O I N T E D F O R E B O D Y A E R O D Y N A M I C S B y C A P T A I N A L A N C H A R L E S S T E W A R T B . E n g . , T h e R o y a l M i l i t a r y C o l l e g e o f C a n a d a , 1981 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R S O F A P P L I E D S C I E N C E i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S ( D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A A u g u s t 1988 © C o p y r i g h t A l a n C h a r l e s S t e w a r t , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mechanical Engineering The University of British Columbia Vancouver, Canada Date 2 August, 1988  DE-6 (2/88) i i ABSTRACT A n e x p e r i m e n t a l i n v e s t i g a t i o n i n t o t h e p o i n t e d f o r e b o d y a e r o d y n a m i c s h a s b e e n c o n d u c t e d w i t h p a r t i c u l a r e m p h a s i s o n t h e h i g h a n g l e o f a t t a c k , z e r o y a w , s i d e f o r c e e x p e r i e n c e d b y f i g h t e r a i r c r a f t a n d m i s s i l e s . T o w a r d s t h i s e n d , a s l e n d e r c o n e - c y l i n d e r m o d e l w a s t e s t e d i n t h e low s p e e d w i n d t u n n e l w i t h v a r i o u s p a s s i v e a n d a c t i v e s i d e f o r c e a l l e v i a t i o n d e v i c e s i n s t a l l e d . T h e a s y m m e t r i c f low f i e l d , i n d u c e d b y t h e t i p g e n e r a t e d p a i r o f h e l i c a l v o r t i c e s , a n d i t s e f f e c t s o n t h e m o d e l a r e i n v e s t i g a t e d i n t h e p r e s e n c e o f s e v e r a l c o n e t i p g e o m e t r i e s : a f a m i l y o f n o s e - b o o m s ; a s e t o f d e l t a s t r a k e s ; a p o r o u s t i p ; s p i n n i n g n o s e - b o o m t i p s ; a s w e l l a s t h e s t a n d a r d c o n e t i p . T h e e f f e c t i v e n e s s of e a c h t i p i n r e d u c i n g t h e s i d e f o r c e i s a s s e s s e d o v e r a r a n g e o f f l i g h t c o n d i t i o n s , a n d c o m p a r e d w i t h t h e c o r r e s p o n d i n g s t a n d a r d t i p d a t a . R e d u c t i o n s i n t h e s i d e f o r c e o f u p t o 50% w i t h n o s e - b o o m s ; 88% w i t h d e l t a s t r a k e t i p s ; 50% w i t h a p o r o u s t i p ; a n d u p t o 75% w i t h s p i n n i n g n o s e - b o o m s h a v e b e e n a c h i e v e d . T h e a p p l i c a b i l i t y a n d p r a c t i c a l i t y o f t h e s e d e v i c e s i n a i r c r a f t a p p l i c a t i o n s a r e a l s o c o n s i d e r e d , h o w e v e r , o n l y i n a p r e l i m i n a r y f a s h i o n . i i i TABLE OF CONTENTS 1 INTRODUCTION 1 1.1 Preliminary Renarks 1 1.2 A B r i e f Review of the Relevant L i t e r a t u r e 4 1.3 Purpose and Scope of the Investigation 13 2 MODELS AND TEST PROCEDURES 15 2.1 Cone Model 15 2.2 Tip Geometries 17 2.3 Wind Tunnel 21 2.4 Instrumentation 23 2.5 Test Procedures 25 3 RESULTS & DISCUSSIONS 28 3.1 Standard Cone Tip R o l l Tests 28 3.2 Nose-Boom Tests 37 3.3 Delta Strake Tests 43 3.4 Porous Tip Tests 52 3.5 Spinning T ip Tests 56 4 CONCLUDING REMARKS 65 4.1 Conclusions 65 4.2 Recommendations 69 BIBLIOGRAPHY 73 APPENDIX I: INTEGRATION OF PRESSURE DATA 78 iv LIST OP FIGURES Figure 1-1 E f f e c t of angle of attack on the lee-Bide flow f i e l d Figure 2-1 The standard cone mounted in the wind tunnel at an angle of attack of 30° 1 Figure 2-2 An exploded view of the cone-model 1 Figure 2-3 A section view of the cone model Figure 2-4 The brass apex cone t i p containing 16 pressure taps Figure 2-5 The porous cone t i p Figure 2-6 The bearing housing cone segment Figure 2-7 A family of nose-boom t i p s with the standard t i p shown for comparison Figure 2-8 A family of d e l t a strake t i p s used in the t e s t program Figure 2-9 A schematic diagram of the low speed wind tunnel used in the experiments Figure 2-10 The scanivalve pressure l i n e switching arrangement Figure 2-11 The Barocel pressure transducer and e l e c t r o n i c manometer Figure 2-12 Instrumentation layout for pressure measurements using a Scanivalve and a Barocel transducer Figure 3-1 Pressure d i s t r i b u t i o n at a reference s t a t i o n P, as affected by the angle of attack, for the standard t i p at zero r o l l angle Figure 3-2 Pressure d i s t r i b u t i o n at a reference s t a t i o n P, as affected by the angle of attack, for the standard t i p at a r o l l angle of 300° Figure 3-3 V a r i a t i o n of the side force c o e f f i c i e n t f or the standard t i p model with p i t c h and r o l l V Figure 3-4 Variation of the normal force coefficient for the standard tip model with pitch and ro l l . 33 Figure 3-5 Effect of the standard tip roll position on the side force at a pitch angle of 50° 35 Figure 3-6 Effect of the standard tip roll position on the normal force 36 Figure 3-7 Effect of boom length on variation in the side force coefficient with pitch and roll attitudes: a) Lb = 4.13 cm, Lb/L = 0.27; b) Lb = 3.18 cm, Lb/L = 0.21; c) Lb = 2.54 cm, Lb/L = 0.17 38 d) Lb = 1.91 cm, Lb/L = 0.125; e) Lb = 1.27 cm, Lb/L = 0.083; f) Lb = 0.95 cm, Lb/L = 0.063 40 g) Lb = 0.64 cm, Lb/L = 0.042; h) Lb = 0.32 cm, Lb/L = 0.031; i) Lb = 0.16 cm, Lb/L = 0.010 41 Figure 3-8 Magnitude of the maximum side force coefficient with varying nose-boom length including the standard tip case 42 Figure 3-9 Normal force variation with pitch angle and roll orientation for the 4.13 cm nose-boom 44 Figure 3-10 Normal force coefficient variation with pitch incidence and nose-boom length 45 Figure 3-11 Variation of the Bide force coefficient with pitch and roll angles for the 3.18 cm delta strake 46 Figure 3-12 Pressure distribution, at the reference station P, for the standard tip at a yaw incidence of: a) (3 = -10° 48 b) B = +10° 49 Figure 3-13 Variation of the side force coefficient with pitch and yaw angles as affected by the delta strake length (aspect ration = 1): a) standard tip, Ls/L = 0; b) Ls = 0.32 cm, Ls/L = 0.021; c) Ls = 0.64 cm, Ls/L = 0.042 50 d) Ls = 1.27 cm, Ls/L = 0.083; e) Ls = 1.91 cm, Ls/L = 0.125; f) Ls = 2.54 cm, Ls/L = 0.167; g) Ls = 3.18 cm, Ls/L = 0.208 51 v i Figure 3-14 E f f e c t of the strake length on the magnitude of the side force 53 Figure 3-15 Va r i a t i o n of the normal force c o e f f i c i e n t with p i t c h and yaw angles for a strake of 3.18 cm. . . . 54 Figure 3-16 E f f e c t of the strake length on the normal force c o e f f i c i e n t .55 Figure 3-17 Side force v a r i a t i o n as affected by the p i t c h angle and nose-boom length at t i p spin of 2000 rpm 57 Figure 3-18 E f f e c t of the nose-boom length on the side force c o e f f i c i e n t at 2000 rpm 59 Figure 3-19 Side force v a r i a t i o n as affected by the p i t c h angle and spin rate f o r a 1.27 cm nose-boom 60 Figure 3-20 E f f e c t of spin rate on the side force c o e f f i c i e n t for a 1.27 cm nose-boom 61 Figure 3-21 The normal force c o e f f i c i e n t as affected by: a) the nose-boom length at a spin rate of 2000 rpm. . . .63 b) the spin rate f o r a 1.27 cm nose-boom 64 Figure 1-1 D i v i s i o n of the cone surface into area segments 78 v i i L I S T O F S Y M B O L S Ab base area of cone, TCD 2 /4 a local speed of sound C perimeter of a regular polygon of n sides CN coeff icient of normal force , normal f o r c e / ( q « A b ) Cp coeff icient of p r e s s u r e , P / q Cs coeff icient of side force , Side Force/ (qAb) D cone base diameter L total cone length Lb nose-boom length L i length of the cone to the station i Ls strake length M Mach number, V / a n an integer , number of s ides of a po lygon P, P« local and reference free stream static p r e s s u r e s , respect ive ly q free stream dynamic p r e s s u r e head, (1/2JPV** Re Reynolds number, V D / u Ri rad ius of the cone at the station i S i length of the side of a regular polygon V, V» local and free stream velocit ies, respect ive ly a angle of attack 0 yaw angle 6 cone hal f -angle viii P density 0 roll angle (in the circumferential direction) to reference point on the surface of the cone 8 angular position in roll w.r.t. a fixed reference frame 6j circumferential position on the cone surface at the point i u viscosity ix ACKNOWLEDGEMENTS The timely completion of this thesis would not have been possible without the assistance of many individuals and organizations. F i r s t and foremost gratitude is expressed for the guidance and counsel of Dr. V.J. Modi. His clear insight into the technical part of the thesis and his invaluable editorial skills are greatly appreciated. The comraderie and occasional brainstorming sessions with my fellow graduate students have made my entire masters program including the thesis, both more enjoyable and progress faster. The machine and instrumentation shop technicians have helped me with their expertise when needed. Their assistance has been invaluable. In particular, Len Drakes contributed his exceptional model making skills. The Canadian Armed Forces completely covered all financial costs of this post-graduate education and to them I am grateful for both the financial assistance and the opportunity. Many local agencies of the Canadian Armed Forces have been particularly helpful over the last years. Sargent Daniels of Jericho Detatchment and the Photo Section of Canadian Forces Base Chilliwack deserve special mention. 1 1 INTRODUCTION 1 • 1 PreliminaryRemarks It is well known that certain flight vehicles, particularly the STOL and fighter airplanes, often undertake maneuvers at relatively high angles of attack. It has been observed that, depending upon the geometry of the aircraft and its angle of attack, it may experience a large side force, of uncertain direction, resulting in a yawing moment that may prove difficult to control. Association of a side force with an object that has a plane of symmetry intrigued aerodynamicists, however, it was quickly established to be related to the fluid mechanics of pointed forebodies. In the case of an aircraft, it would be the nose of the fuselage. Tip-tanks, bombs, missiles, launch vehicles, hubs of propellers, etc., also present pointed forebody geometries. Normally, such a pointed forebody is incorporated as a part of the streamlined structure to reduce drag, increase stability and aid in generating lift. Although a simple cone geometry is sometimes used, a more common pointed forebody is a tangent ogive or its variation. As discussed by Ericsson and Reding [1], an object with a slender forebody, depending upon its attitude in pitch, exhibits four distinctly different types of flow patterns as shown in Figure 1-1. At low angles of attack the flow field is usually symmetric and essentially attached. As the pitch angle increases the streamlines are swept downstream from the windward to the leeward side of the body symmetrically about the pitch plane. Figure 1-1. Effect of angle of attack on the lee-side flow field. 3 A t h i g h e r a n g l e s o f a t t a c k t h e f l o w b e c o m e s s e p a r a t e d . T y p i c a l l y , t w o c o u n t e r r o t a t i n g , s y m m e t r i c , s t a t i o n a r y v o r t i c e s f o r m o n t h e l e e w a r d s i d e o f t h e o b j e c t , s t a r t i n g a t o r n e a r t h e a p e x a n d c o n t i n u i n g w e l l d o w n s t r e a m o f t h e o b j e c t . A t s t i l l h i g h e r a n g l e s o f a t t a c k t h e v o r t i c e s b e c o m e a s y m m e t r i c . O n e v o r t e x o f t h e p a i r c h a n g e s s t r e n g t h a n d p o s i t i o n s u c h t h a t i t e x e r t s a l o w e r a e r o d y n a m i c p r e s s u r e o n t h e b o d y t h a n t h e o t h e r . T h i s r e s u l t s i n a n e t s i d e f o r c e w h i c h i s t h e s u b j e c t o f s t u d y i n t h i s t h e s i s . A l t h o u g h t h i s f l o w p a t t e r n h a s b e e n d e s c r i b e d a n d a n a l y z e d i n t h e l i t e r a t u r e i n t e r m s o f t w o v o r t i c e s , e f f e c t i v e l y t h e r e c a n be f o u r , s i x o r m o r e s t a t i o n a r y q u a s i s t e a d y v o r t i c e s . A t a n g l e s o f a t t a c k a p p r o a c h i n g f l o w n o r m a l t o t h e s l e n d e r b o d y t h e s t a t i o n a r y v o r t i c e s s t a r t t o s h e d . A v o r t e x s t r e e t o r a m o r e r a n d o m w a k e r e s u l t s a n d t h e s i d e f o r c e b e c o m e s o s c i l l a t o r y o r d i s a p p e a r s e n t i r e l y . T h e o n s e t o f a s i g n i f i c a n t s i d e f o r c e u s u a l l y o c c u r s a t a n a n g l e o f a t t a c k a p p r o x i m a t e l y t w i c e t h e c o n e h a l f - a n g l e , a n d a t i t s p e a k c a n be o f t h e same o r d e r o f m a g n i t u d e a s t h e l i f t g e n e r a t e d b y t h e f o r e b o d y . O n a i r c r a f t t h i s w o u l d c o r r e s p o n d t o a n a n g l e o f a t t a c k w h e n t h e r u d d e r i s p a r t i a l l y s h a d o w e d b y t h e w a k e o f t h e f u s e l a g e . T h i s m a y l e a d t o t h e s i t u a t i o n w h e r e t h e s i d e f o r c e i s a n o r d e r o f m a g n i t u d e l a r g e r t h a n t h e c o r r e c t i n g f o r c e a v a i l a b l e f r o m t h e r u d d e r . A s t h e o n s e t o f t h e s i d e f o r c e i s u s u a l l y a t a f a i r l y h i g h a n g l e of a t t a c k , i t i s n o t a p r o b l e m f o r m o s t a i r c r a f t . O n l y h i g h l y m a n e u v e r a b l e c r a f t c a p a b l e o f f l i g h t s a t l a r g e a n g l e s o f a t t a c k h a v e e x p e r i e n c e d t h e s i d e f o r c e p h e n o m e n a . I n c l u d e d w i t h i n t h i s g r o u p a r e t h e l a t e s t 4 fighters, the F-16, F-18, etc., together with air-to-air and surface-to-air missiles. For reasons of nose shape, flight attitude and the Mach number the Space Shuttle largely avoids the side force phenomena. The effectiveness of tip geometry in partial alleviation of the side forces experienced by pointed forebodies is the topic of investigation here. The flow field is fully three-dimensional, unsteady, vortex dominated, and primarily governed by the boundary layer. It also exhibits puzzling, seemingly random characteristics thus making this problem of contemporary interest and significance, rather challenging. 1.2 AJBrieL-BeYJew QL.the.JRekvant Literature The side force phenomenon was f i r s t noticed and documented by Allen and Perkins [2] in 1951. Since then many researchers have experimented with various aspects of the problem. Most of the early investigations [2-4] concentrated on flow past slender cylinders with various nose geometries. They focused their study on the flow field aft of the nose. Only more recently [5-13] has the focus moved to the forebody nose itself. A review of the literature suggests that the early research efforts can be broadly divided into two groups. On one hand, we have investigators who consider the side force phenomenon to be boundary layer governed and treat it as a logical extension of the two-dimensional cylinder flow. The Reynolds number dependence and the effectiveness of some of the side force alleviation devices seem to support this view. Other researchers suggest that the side force is caused by a basic hydrodynamic instability of the leeward flow. Some experimental results, 5 s u c h a s t h e d i r e c t i o n s w i t c h i n g of t h e s i d e f o r c e a n d e f f e c t s o f n o r m a l b l o w i n g , s u b s t a n t i a t e t h i s c o n c e p t . I t a p p e a r s t h a t t h e s e t w o h y p o t h e s e s a r e n o t m u t u a l l y e x c l u s i v e . A h y d r o d y n a m i c i n s t a b i l i t y o f t h e l e e w a r d f l o w c o u l d be q u i t e s e n s i t i v e to a n a s y m m e t r i c b o u n d a r y l a y e r u p s t r e a m . C o n v e r s e l y , t h e h i g h p r e s s u r e g r a d i e n t s i n t h e s t r e a m w i s e d i r e c t i o n may m a k e t h e b o u n d a r y l a y e r s e p a r a t i o n s e n s i t i v e t o t h e e x t e r n a l f l o w . T h o m p s o n a n d M o r r i s o n [3] s t u d i e d t h e s p a c i n g , p o s i t i o n a n d s t r e n g t h o f v o r t i c e s b e h i n d s l e n d e r c y l i n d e r s . T h e y u s e d s c h l i e r e n p h o t o g r a p h y a n d y a w m e t e r t r a v e r s e s t o i n v e s t i g a t e t h e f l o w f i e l d i n t h e w a k e o f a c o n e - c y l i n d e r m o d e l . T h e i r c o n c e r n w a s m o s t l y i n t h e d r a g a n d v o r t e x s h e d d i n g f r o m t h e c y l i n d r i c a l b o d y , a n d t h e y h a v e p r e s e n t e d u s e f u l d a t a o n t h e s u b j e c t u p t o a M a c h N u m b e r o f o n e . L a m o n t a n d H u n t [4] t e s t e d a s l e n d e r c y l i n d e r i n l a m i n a r f l o w w i t h f o u r d i f f e r e n t n o s e g e o m e t r i e s . T h e i r p r e s s u r e t a p p e d c y l i n d e r c o u l d b e f i t t e d w i t h a 2 , 4 , o r 6 c a l i b r e o g i v e n o s e o r a n o s e - c o n e o f L / D = 2. T h e r e s u l t s d e m o n s t r a t e d a c l e a r d e p e n d e n c e o n t h e R e y n o l d s n u m b e r , h o w e v e r , t h e y w e r e p l a g u e d b y a l a c k o f r e p e a t a b i l i t y . I t w a s p o s t u l a t e d t h a t t h e f l o w w a s u n s t e a d y a s i t e x h i b i t e d c l e a r e v i d e n c e o f s w i t c h i n g o f p a t t e r n b e t w e e n t w o c o n f i g u r a t i o n s . A c h a n g e i n t h e r o l l a n g l e w a s u s e d t o f u r t h e r d e m o n s t r a t e t h e u n s t e a d i n e s s . R a o [5] s u g g e s t e d t h a t a p r o p e r l y d e s i g n e d b o u n d a r y l a y e r t r i p c o u l d s t a b i l i z e t h e s i d e f o r c e b y d i s r u p t i n g t h e v o r t e x f e e d i n g m e c h a n i s m . He i n s t a l l e d a p a i r o f s y m m e t r i c a l h e l i c a l t r i p s o n t h e n o s e o f a n F - 5 a i r c r a f t m o d e l a n d t e s t e d i t s s t a t i c a n d d y n a m i c r e s p o n s e a t h i g h a n g l e s o f a t t a c k . H i s r e s u l t s s h o w e d b e t t e r r e s p o n s e i n a l l f l i g h t 6 conditions except sideslip where the trips decreased the directional stability. The trips, however, did not disrupt the vortex feeding mechanism but did keep the separated vortices symmetrical throughout a much larger flight envelope. Oberkampf and Bartel [14] studied the wake of an ogive nosed cylinder in a supersonic flow. Although they demonstrated some interesting characteristics of the wake, the investigation was confined to symmetric flows at relatively low incidence. Ericsson and Reding have contributed rather extensively to the field. Their best known papers [1,6,7,15] are reviews of the existing literature, and critical analysis of the results with conclusions based upon both the previous work and their own. In particular, reference [6] focuses on the vortices created by the nose and methods of alleviating the side force. It suggests the usefulness of nose bluntness, nose-boom, and various geometries of boundary layer trips, in reducing the side force and presents results showing the effectiveness of the trips with an F - l l l aircraft model. They concluded that nose bluntness and nose-boom can alleviate the side force to various degrees. On the other hand, trips and strakes, although more effective, have a disadvantage for an aircraft not flying coordinated maneuvers. Further evidence of the leeside flow instability hypothesis was presented by Oberkampf, Owen and Shivananda [16] in their investigation of high subsonic flow past a pointed slender body. They used a Laser Doppler Velocimeter (LDV), force and moment measurements, surface hot wires and laser vapour screen photography in their experiments. The results clearly showed that more than one asymmetric 7 v o r t e x w a k e c o n f i g u r a t i o n c a n e x i s t f o r t h e same a n g l e o f a t t a c k a n d r o l l a n g l e . A n o t h e r p a p e r b y E r i c s s o n a n d R e d i n g [15] c o n c e n t r a t e d o n m o v i n g w a l l e f f e c t s . T h e i n f l u e n c e o f s p i n , c o n i n g a n d p i t c h r a t e o n t h e s i d e f o r c e p h e n o m e n o n w e r e a n a l y z e d . T h e e f f e c t s o f v a r y i n g t h e R e y n o l d s a n d M a c h n u m b e r s o n t h e s i d e f o r c e w e r e a l s o d i s c u s s e d . A c l e a r d e p e n d e n c e o f t h e d i r e c t i o n o f t h e s i d e f o r c e o n t h e b o d y m o t i o n was d e m o n s t r a t e d p a r t i c u l a r l y w i t h i n a c r i t i c a l R e y n o l d s n u m b e r r a n g e . T h e s t u d y s h o w e d a p o s i t i v e c o u p l i n g b e t w e e n t h e c o n i n g m o t i o n a n d t h e v o r t e x s h e d d i n g s u c h t h a t t h e p r e s s u r e d i s t r i b u t i o n i n c r e a s e d t h e c o n i n g r a t e . P e a k e , O w e n a n d J o h n s o n [8] c o n d u c t e d s t u d i e s w i t h a n L D V , t h e L a s e r V a p o u r S c r e e n V i s u a l i z a t i o n , p r e s s u r e m e a s u r e m e n t s a n d b u r i e d w i r e i n s t r u m e n t s o n a 5 ° c o n e a n d a 1 6 ° t a n g e n t o g i v e . B e s i d e s c o n j e c t u r i n g u p o n t h e m e c h a n i s m s t r i g g e r i n g t h e i n i t i a l a s y m m e t r y , t h e y a l s o p r o p o s e d a n o v e l m e a n s o f c o n t r o l l i n g t h e o r i e n t a t i o n o f t h e s i d e f o r c e u t i l i z i n g a s m a l l a m o u n t o f b l o w i n g q u i t e c l o s e to t h e n o s e . It w a s d e m o n s t r a t e d t h a t b l o w i n g o n o n e s i d e o f t h e n o s e c o u l d r e v e r s e t h e s i d e f o r c e , a n d t h a t t h e n o r m a l b l o w i n g w o r k s b e t t e r t h a n e i t h e r t h e u p s t r e a m o r t h e d o w n s t r e a m t a n g e n t i a l b l o w i n g . S k o w , M o o r e a n d L o r i n c z [9] c a r r i e d t h e c o n c e p t o f a c t i v e b l o w i n g a s t e p f u r t h e r . T h e y c o m p l e t e d a c o m b i n e d e x p e r i m e n t a l a n d a n a l y t i c a l s t u d y t o c o n t r o l a s y m m e t r i c v o r t e x f o r m a t i o n f r o m a n a i r c r a f t f o r e b o d y w i t h t h e a im o f d e v e l o p i n g a n a u t o m a t i c s p i n r e c o v e r y s y s t e m . F r o m t h e r e s u l t s o f t h e w i n d t u n n e l t e s t s w i t h t a n g e n t i a l b l o w i n g a s i x d e g r e e o f f r e e d o m d i g i t a l s i m u l a t i o n o f a i r c r a f t p e r f o r m a n c e w a s d e v e l o p e d t o s h o w 8 t h a t t h e c o n c e p t c o u l d s u b s t a n t i a l l y i m p r o v e t h e s p i n r e c o v e r y o f f i g h t e r s . T h e y a l s o s h o w e d t h a t a s m a l l a a m o u n t o f b l o w i n g a t h i g h a n g l e s o f a t t a c k c a n p r o d u c e m o r e y a w i n g moment t h a n t h a t o b t a i n e d t h r o u g h t h e r u d d e r . E r i c k s o n a n d L o r i n c z [10] s t u d i e d t h e e f f e c t s o f h e l i c a l t r i p s o n a m o d e l o f a f i g h t e r a i r c r a f t , t h e F - 5 . T h e i r w a t e r t u n n e l a n d w i n d t u n n e l t e s t s c o n c l u d e d t h a t p r o p e r l y d e s i g n e d h e l i c a l t r i p s s i g n i f i c a n t l y r e d u c e d t h e a s y m m e t r i c l o a d s a t z e r o s i d e s l i p , h o w e v e r , a l a r g e d e c r e a s e i n l a t e r a l - d i r e c t i o n a l s t a b i l i t y w a s a l s o n o t e d . Y a n t a a n d W a r d l a w [17] c o n d u c t e d some f u n d a m e n t a l r e s e a r c h o n t h e f l o w f i e l d s t r u c t u r e s a s s o c i a t e d w i t h s l e n d e r b o d i e s . It w a s f o u n d t h a t t h e maximum l o c a l s i d e f o r c e o c c u r s a s t h e f i r s t v o r t e x i s s h e d , a n d is t o w a r d s t h e s i d e o f t h e r e m a i n i n g v o r t e x . U n f o r t u n a t e l y t h e r e s u l t s w e r e p l a g u e d w i t h t h e r e p e a t a b i l i t y p r o b l e m s , a l s o f a c e d b y m a n y o t h e r r e s e a r c h e r s , h e n c e t h e i r o b s e r v a t i o n s c a n o n l y b e c o n s i d e r e d q u a l i t a t i v e i n n a t u r e . A l m o s n i n o a n d Rom [18] e x p e r i m e n t e d w i t h s y m m e t r i c a l b l o w i n g a n d c i r c u l a r t r i p s o n a s l e n d e r b o d y . T h e y f o u n d b o t h t h e d e v i c e s e f f e c t i v e i n r e d u c i n g t h e s i d e f o r c e b u t t h e b l o w i n g r a t e r e q u i r e d to s i g n i f i c a n t l y a l l e v i a t e t h e s i d e f o r c e b e c a m e v e r y l a r g e a t t r a n s o n i c a n d s u p e r s o n i c s p e e d s . It w a s c o n c l u d e d t h a t s y m m e t r i c a l b l o w i n g i s a s i m p l e a n d e a s y p r o c e d u r e t o i m p l e m e n t i n e x i s t i n g a n d f u t u r e a i r c r a f t . P e a k e , F i s h e r a n d M c R a e [19] s t u d i e d s e p a r a t e d f low b e h i n d a 5* c o n e a t M a c h n u m b e r s o f 0.6, 1.5 a n d 1.8 i n f l i g h t , a s w e l l a s t h r o u g h w i n d t u n n e l a n d n u m e r i c a l e x p e r i m e n t s . T h e y f o u n d a r e a s o n a b l e 9 agreement between the three sets of results, however, the experiments avoided test angles of attack which might produce an asymmetric flow. Lamont [20] contributed an article which has proven very important to the understanding of the side force phenomenon. He conducted wind tunnel tests with an extensively instrumented ogive-cylinder in laminar, transition and turbulent separation conditions. The results clearly demonstrated a need to vary roll angle in any series of comprehensive tests. He conjectured that microscopic surface asymmetries at the apex of the body were sufficient to trigger large scale flow asymmetries further downstream. Keener et al. [21] further substantiated Lamont's thoughts on the cause of the side force onset. His experiments involved measuring the side force while first rolling his entire model and then rolling the tip alone. The results, nearly identical in the two tests, support the microasymmetry hypothesis. Woolard [22] used a conformal mapping technique to add weight to the hydrodynamic instability argument. Some researchers have postulated that boundary layer effects, associated with asymmetric separation points, cause vortex asymmetry. Others, by comparing the forebody vortices to the slender wing vortices, postulate a hydrodynamic instability resulting from the crowding of vortex lines at the apex despite symmetric separation. Woolard, by successfully comparing cone side force onset angles, through the appropriate mappings, to slender delta wing experimental data, concluded that the separation lines are unimportant in relation to the basic hydrodynamic instability. 10 A p a r t f r o m t h e n u m e r i c a l w o r k o f P e a k e t a l . [19] m e n t i o n e d p r e v i o u s l y , o t h e r a v e n u e s o f c o m p u t e r m o d e l i n g o f t h e a i r f l o w a r o u n d s l e n d e r b o d i e s h a v e a l s o b e e n a t t e m p t e d . A l m o s n i n o a n d Rom [23] u s i n g p o t e n t i a l f l o w t h e o r y , w i t h a c o m b i n a t i o n o f s o u r c e a n d v o r t e x - l a t t i c e e l e m e n t s t o r e p r e s e n t t h e b o d y , s u c c e s s f u l l y m o d e l e d r e a l s y m m e t r i c a l f l o w s . A l m o s n i n o [24] e x t e n d e d t h i s c o m p u t e r m o d e l to a s y m m e t r i c f l o w s a t h i g h e r a n g l e s o f a t t a c k . T h e o n l y i n p u t n e e d e d f o r a r e a l i s t i c m o d e l i n g w a s t h e l o c a t i o n o f t h e s e p a r a t i o n l i n e s o n t h e b o d y . Newsome a n d A d a m s [25] h a v e s o l v e d t h e R e y n o l d s - a v e r a g e d N a v i e r - S t o k e s e q u a t i o n s f o r f low a b o u t a n e l l i p t i c a l b o d y m i s s i l e . N u m e r i c a l r e s u l t s w e r e o b t a i n e d f o r t h e v o r t e x d o m i n a t e d f low a t 1 0 ° a n d 2 0 ° a n g l e s o f a t t a c k w i t h 0 ° a n d 4 5 ° r o l l . T h e y u s e d a h i g h s p e e d v e c t o r - p r o c e s s o r c o m p u t e r , t h e C y b e r 205. E x c e l l e n t a g r e e m e n t w a s f o u n d w i t h t h e i r e x p e r i m e n t a l r e s u l t s . C h a n [26] u s e d a f a r f i e l d a p p r o a c h t o s t u d y t h e s i d e f o r c e o n a s l e n d e r b o d y . He n u m e r i c a l l y m o d e l e d t h e f a r f i e l d w a k e b y a s y s t e m o f t r a i l i n g v o r t e x f i l a m e n t s , a n d e s t a b l i s h e d a r e l a t i o n s h i p b e t w e e n t h e f o r c e d i s t r i b u t i o n a n d t h e s t r u c t u r e o f t h e w a k e . T h e g e o m e t r y a n d s t r e n g t h o f t h e f i l a m e n t s w e r e d e r i v e d f r o m e x p e r i m e n t a l d a t a a n d t h e d y n a m i c s o f t h e s y s t e m . T h e p r o c e d u r e a p p e a r s q u i t e p r o m i s i n g a s t h e n u m e r i c a l p r e d i t i o n s s h o w e d e x c e l l e n t c o r r e l a t i o n w i t h t h e e x p e r i m e n t a l r e s u l t s . In t h e r e v i e w a r t i c l e b y R e d i n g a n d E r i c s s o n [7] t h r e e h y p o t h e s e s w e r e p r o p o s e d w h i c h w e r e s u p p o r t e d b y t h e n e w e v i d e n c e : t h e max imum s i d e f o r c e o c c u r s w h e n a B u b c r i t i c a l s e p a r a t i o n i s e x p e r i e n c e d o n o n e s i d e o f a b o d y a n d a s u p e r c r i t i c a l s e p a r a t i o n a p p e a r s o n t h e 11 o t h e r ; t h e b o d y m o t i o n c a n l o c k i n a d r i v i n g v o r t e x a s y m m e t r y to p r o d u c e a s e l f - i n d u c e d r o t a t i o n ; a n d a l a m i n a r s e p a r a t i o n c a n o c c u r o n a c y l i n d e r w h e n t h e p o i n t e d n o s e i s e x p e r i e n c i n g a t u r b u l e n t f low . In a p a p e r c o n c e n t r a t i n g o n t h e c o u p l i n g o f b o d y m o t i o n a n d v o r t e x s h e d d i n g r e f e r r e d t o e a r l i e r , E r i c s s o n a n d R e d i n g [1] p r e s e n t some i n t e r e s t i n g r e s u l t s . T e s t s w i t h a s p i n n i n g t i p a t t h e c r i t i c a l R e y n o l d s n u m b e r s h o w e d t h a t t h e d i r e c t i o n o f t h e s p i n d e t e r m i n e s t h e d i r e c t i o n o f t h e s i d e f o r c e . T h e c o n i n g a c t i o n s h e d s v o r t i c e s s u c h t h a t t h e m o t i o n i s s u s t a i n e d r e g a r d l e s s o f t h e d i r e c t i o n o f t h e s t a t i c s i d e f o r c e . H e n c e i t a p p e a r s t h a t t h e v e h i c l e m o t i o n i n d u c e s a s y m m e t r i c v o r t i c e s w h i c h e a s i l y o v e r p o w e r a n y s t a t i c a s y m m e t r y . S e g i n e r a n d R i n g e l [27] e x p l o r e d t h e M a g n u s e f f e c t a t h i g h a n g l e s o f a t t a c k a n d i n t h e c r i t i c a l R e y n o l d s n u m b e r r a n g e . It w a s o b s e r v e d t h a t t h e f o r c e r e v e r s a l c a n o c c u r w h e n , d u e to t h e b o u n d a r y l a y e r e f f e c t s , t h e l i f t i s o p p o s i t e t o t h e c l a s s i c a l M a g n u s c o n t r i b u t i o n . T h e i r e x p e r i m e n t s d e m o n s t r a t e d a c o m p l e x i n t e r d e p e n d e n c e o f t h e s p i n r a t e , a n g l e o f a t t a c k , R e y n o l d s n u m b e r a n d l i f t . E r i c s s o n [28] e x p l o r e d t h e f l a t s p i n o f Blender b o d i e s a n d t h e i r r e c o v e r y . He d i s c u s s e s i n d e p t h t h e t y p e s o f s e p a r a t i o n p o s s i b l e , t h e e f f e c t o f b o d y m o t i o n o n s e p a r a t i o n , i t s a t t e n d a n t l i f t a n d t h e M a g n u s e f f e c t . I n a m o r e r e c e n t p a p e r o n t h e s u b j e c t [29] h e s h o w s c o n c l u s i v e l y t h a t t h e b o d y m o t i o n l o c k s i n a n a s y m m e t r i c v o r t e x p a t t e r n , w h i c h d r i v e s t h e s l e n d e r b o d y i n t o a f l a t s p i n . V i s w a n a t h a n d N a r a y a n [11] c o n d u c t e d t e s t s w i t h a 20" c o n e a t p i t c h a n g l e s u p to 47* a n d o v e r a w i d e r a n g e o f t h e R e y n o l d s n u m b e r . T h e i n f o r m a t i o n w a s c o n f i n e d o n l y t o t h e f o r c e b a l a n c e d a t a . 12 M o d i e t a l . [12] c a r r i e d o u t e x p e r i m e n t s w i t h a c i r c u l a r c y l i n d e r t o w h i c h a s e t o f c o n i c a l f o r e b o d i e s c a n b e a t t a c h e d . T h e y e x p l o r e d t h e e f f e c t s o f s u r f a c e r o u g h n e s s , h e l i c a l t r i p s , m o d i f i e d t i p g e o m e t r i e s a n d t i p r o t a t i o n . A m o n g t h e s i d e f o r c e a l l e v i a t i o n d e v i c e s t e s t e d , t h e n o s e -boom a n d t i p r o t a t i o n p r o v e d to b e t h e most p r o m i s i n g . I n a n u n p u b l i s h e d f o u r t h y e a r e n g i n e e r i n g p r o j e c t r e p o r t b y B i s h o p , T a r n a i , a n d T h o r n t h w a i t e [13] , t e s t s o n a 2 8 ' c o n e i n s u b s o n i c f low i n d i c a t e t h a t , a m o n g t h e v a r i o u s n o s e g e o m e t r i e s t r i e d , t h e d e l t a -s t r a k e t i p h a d t h e m o s t p r o m i s e i n t e r m s o f t h e s i d e f o r c e r e d u c t i o n . F i d d e s [30] h a s p r e s e n t e d a n e x c e l l e n t s u m m a r y o f s e v e r a l p o t e n t i a l f l o w l i n e v o r t e x a n d v o r t e x s h e e t m o d e l s f o r f low p a s t a n i n c l i n e d c o n e . He d i v i d e s t h e n u m e r i c a l r e s u l t s i n t o two c a t e g o r i e s . T h e f i r s t f a m i l y o f s o l u t i o n s r e q u i r e a s y m m e t r i c s e p a r a t i o n l i n e s t o p r o d u c e a s y m m e t r i c f low r e s u l t s . T h e s e c o n d f a m i l y o f s o l u t i o n s a r e c a p a b l e o f p r o d u c i n g a s y m m e t r i c v o r t e x c o r e l o c a t i o n s e v e n w h e n f e d f r o m s y m m e t r i c s e p a r a t i o n p o s i t i o n s . H i s o w n c o n t r i b u t i o n to t h e p r o b l e m w a s t h e d e v e l o p m e n t o f a n u m e r i c a l s c h e m e u s i n g v o r t e x s h e e t m e t h o d s , some c l e v e r f o r m u l a e a n d p a r a m e t r i c m a n i p u l a t i o n s w h i c h p r o d u c e d t h e s e c o n d f a m i l y o f r e s u l t s . T h e n u m e r i c a l r e s u l t s c o m p a r e d q u i t e f a v o u r a b l y w i t h t h e e x p e r i m e n t a l d a t a . M a r c o n i [31] h a s a l s o c o n t r i b u t e d some i n t e r e s t i n g n u m e r i c a l r e s u l t s , f o r h i g h l y v o r t i c a l f l o w s p a s t c o n e s a n d d e l t a w i n g s i n t h e s u p e r s o n i c r e g i m e , u s i n g a n E u l e r e q u a t i o n m o d e l . T w o s o u r c e s o f v o r t i c i t y a r e s t u d i e d : t h e f low f i e l d s h o c k s y s t e m ; a n d t h e s e p a r a t i n g b o u n d a r y l a y e r . S o l u t i o n s o b t a i n e d w i t h b o t h t h e s o u r c e s o f v o r t i c i t y 13 are studied in detail, and compared with each other, with the potential flow calculations and the experimental data. It is apparent from the literature that the problem of side force experienced by high performance aerospace vehicles has received active attention relatively recently. Some progress has been made in understanding of the phenomenon at a fundamental level and there are several hypotheses which seem to explain some aspects of the mechanism of the side force generation. On the other hand, the experimental results are often not reproducible, suggesting that the models used in explaining the phenomenon are, at best, incomplete. 1.3 E.urpQ.s.e._.an.d__S.cope. o l ...the Investigation With this as background, the thesis aims at providing more precise information, obtained through a set of carefully planned experiments, assuring repeatable and reliable data, to better understand the side force phenomenon. It aims at studying the asymmetric flow field associated with a slender cone and assessing effectiveness of several tip devices in alleviating the side force. As apparent from the review the flow field is unsteady, boundary layer sensitive, turbulent, vortex dominated and highly configuration dependent. Furthermore, it is somewhat affected by the Reynolds and Mach numbers. Hence, the problem of high angle of attack forebody aerodynamics does not lend itself to the known analytical or numerical procedures. The present investigation, therefore, purely relies on a carefully planned experimental program. 14 S e v e r a l i n v e s t i g a t o r s i n t h e p a s t [5,6,9,12,13,18] h a v e t r i e d n o s e -b o o m s , s t r a k e s , t r i p s a n d s u r f a c e r o u g h n e s s w i t h v a r y i n g d e g r e e s of s u c c e s s a s t o t h e i r e f f e c t i v e n e s s i n r e d u c i n g t h e s i d e f o r c e . In m o s t c a s e s t h e t e s t s h a v e b e e n r a t h e r p r e l i m i n a r y i n n a t u r e w i t h r e s u l t s m o s t l y q u a l i t a t i v e i n c h a r a c t e r . T h e p r e s e n t s t u d y a t t e m p t s to l a y a f i r m f o u n d a t i o n f o r t h i s c l a s s o f p r o b l e m s t h r o u g h a s y s t e m a t i c s t u d y w i t h s e v e r a l p a s s i v e d e v i c e s w h i c h a p p e a r p r o m i s i n g i n r e d u c i n g t h e s i d e f o r c e . T h e e m p h a s i s i s p u r p o s e l y o n p a s s i v e d e v i c e s a s t h e y a r e d e e m e d t o b e m o r e p r a c t i c a l . O b v i o u s l y , t h e a p p l i c a b i l i t y o f t h e d e v i c e i n r e a l - l i f e s i t u a t i o n w o u l d be t h e u l t i m a t e c r i t e r i o n o f i t s s u c c e s s . A l t h o u g h t h i s a s p e c t i s o f i m p o r t a n c e , i t i s n o t t h e p r i m e c o n c e r n h e r e , t h e f o c u s b e i n g o n t h e f u n d a m e n t a l i n f o r m a t i o n o n p e r f o r m a n c e o f t h e s i d e f o r c e a l l e v i a t i o n d e v i c e s . I t i s r e c o g n i z e d t h a t a s t h e n o s e o f a n a i r c r a f t o r a m i s s i l e i s f r e q u e n t l y u s e d t o h o u s e a r a d a r , some o f t h e d e v i c e s w h i c h a p p e a r p r o m i s i n g i n a l l e v i a t i n g t h e s i d e f o r c e m a y p r o v e i m p r a c t i c a l to i m p l e m e n t . T h e r a d o m e , w h i c h f o r m s t h e n o s e o f s u c h a i r c r a f t , i s u s u a l l y a t h i n , u n i f o r m , n o n m e t a l l i c c o m p o s i t e s h e l l w i t h n o m o v i n g p a r t s . O f p a r t i c u l a r i m p o r t a n c e a r e i t s s p e c t r a l t r a n s m i s s i o n c h a r a c t e r i s t i c s , w h i c h a r e r e q u i r e d t o b e a s u n i f o r m a s p o s s i b l e , d i r e c t i o n a l l y . H e n c e , f r o m t h e r a d a r p e r f o r m a n c e c o n s i d e r a t i o n s , a c t i v e m o v i n g d e v i c e s a p p e a r i m p r a c t i c a l . W a t e r a b s o r p t i o n a n d i t s a t t e n d a n t a t t e n u a t i o n o f m i c r o w a v e s i s l i k e l y t o m a k e a p o r o u s t i p a l l e v i a t i o n d e v i c e u n s u i t a b l e a s w e l l . O n t h e o t h e r h a n d , d e v i c e s s u c h a s n o s e -b o o m s a n d s t r a k e s d e g r a d e r a d a r p e r f o r m a n c e o n l y m a r g i n a l l y a n d h e n c e h a v e r e c e i v e d p a r t i c u l a r a t t e n t i o n i n t h i s t h e s i s . 15 2 M O D E L S A N D T E S T P R O C E D U R E S T h i s c h a p t e r b r i e f l y d e s c r i b e s t h e m o d e l s u s e d i n t h e w i n d t u n n e l e x p e r i m e n t s , t e s t a r r a n g e m e n t , i n s t r u m e n t a t i o n a n d t e s t p r o c e d u r e s . T h e c o n v e n t i o n a l w i n d t u n n e l e q u i p m e n t b e i n g s t a n d a r d i n a n y a e r o d y n a m i c s l a b o r a t o r y n e e d s n o e x p l a n a t i o n . M o s t o f t h e w i n d t u n n e l t e s t p r o c e d u r e s a r e a l s o w e l l e s t a b l i s h e d . O n l y d i s t i n c t i v e m o d e l s a n d i n s t r u m e n t s w i t h s p e c i f i c r o l e a r e t o u c h e d u p o n h e r e . 2.1 Cone - M o d e l F o r t h e e n t i r e e x p e r i m e n t a l p r o g r a m a c y l i n d r i c a l b a s e , 7 c m i n d i a m e t e r a n d 10 c m l o n g , w i t h a c o n i c a l f o r e b o d y f o r m e d t h e b a s i c t e s t m o d e l . T h e h o l l o w a l u m i n u m c o n e w i t h a n a p e x a n g l e o f * 28" w a s 15.25 cm (6 i n . ) l o n g a n d h a d a b a s e d i a m e t e r o f 7.62 cm (3 i n . ) . I t a c c o m m o d a t e d u p t o 40 p r e s s u r e t a p s . T h e a p e x o f t h e c o n e c a n b e s e p a r a t e d a t t w o l o c a t i o n s t o r e p l a c e i t w i t h d e s i r e d t i p g e o m e t r i e s . T h e c y l i n d r i c a l a f t b o d y h o u s e d a v a r i a b l e s p e e d d . c . m o t o r t o r o t a t e t h e t i p a t a c o n t r o l l e d s p e e d d u r i n g o n e p h a s e o f t h e e x p e r i m e n t a l p r o g r a m . T h e a f t b o d y w a s a l s o c o n n e c t e d t o a y o k e t y p e v e r t i c a l s u p p o r t , i n t u r n m o u n t e d o n t h e w i n d t u n n e l b a l a n c e p l a t f o r m , s u c h t h a t t h e a n g l e o f a t t a c k a n d y a w i n c l i n a t i o n c a n b e a d j u s t e d a s r e q u i r e d . T h e m o d e l , t h o u g h m o d i f i e d a n d r e f i n e d , i s e s s e n t i a l l y t h e same a s t h e o n e u s e d b y B i s h o p e t a l . [13 ] . F i g u r e s 2 -1 a n d 2 - 2 s h o w t h e t e s t a r r a n g e m e n t f o r t h e m o d e l a n d i t s e x p l o d e d v i e w , r e s p e c t i v e l y . 16 Figure 2-2 An exploded view of the cone-model. 17 T h e p r e s s u r e t a p s f o r t h e s t a n d a r d c o n e m o d e l , i .e. w i t h n o t i p m o d i f i c a t i o n , w e r e e q u a l l y s p a c e d c i r c u m f e r e n t i a l l y a t s i x s t a t i o n s a l o n g i t s l e n g t h . In a l l t h e r e w e r e 40 p r e s s u r e t a p s d i s t r i b u t e d o n t h e c o n e s u r f a c e a s i n d i c a t e d i n F i g u r e 2 - 3 . T h e b r a s s a p e x o f t h e c o n e c a r r y i n g 16 p r e s s u r e t a p s ( F i g u r e 2-4) c a n be r e m o v e d a n d r e p l a c e d w i t h a p o r o u s t i p ( F i g u r e 2-5) o r a b e a r i n g h o u s i n g ( F i g u r e 2-6) p r o v i d e d w i t h t h r e e p r e s s u r e t a p s . T h e b e a r i n g h o u s i n g , w i t h t h e p r e s s u r e t a p s , s u p p o r t s d i f f e r e n t n o s e - t i p s , w h i c h c a n now be t e s t e d a t d e s i r e d r o l l o r i e n t a t i o n s , a s w e l l a s i n t h e s p i n n i n g m o d e . T h e s t a t i c p r e s s u r e a t a t a p , t y p i c a l l y 0.64 mm i n d i a m e t e r , i s c o n v e y e d b y a p o l y e t h y l e n e t u b e , 1.7 mm i n s i d e d i a m e t e r , to a n e x t e r n a l l y l o c a t e d p r e s s u r e t r a n s d u c e r . T o m in imize t h e e f f e c t o f t h e s u r f a c e r o u g h n e s s o n t h e b o u n d a r y l a y e r i n s t a b i l i t y , a n d h e n c e b e t t e r i d e n t i f y t h e i n f l u e n c e of t i p g e o m e t r y o n t h e s i d e f o r c e , t h e c o n e m o d e l w a s p r o v i d e d w i t h a s m o o t h m i r r o r f i n i s h . W i th t h e e x c e p t i o n o f some o f t h e s m a l l e r n o s e t i p s , t h e e n t i r e c o n e w a s p o l i s h e d t o w i t h i n a 5-7 m i c r o n s u r f a c e r o u g h n e s s . A l t h o u g h t h e r o u g h n e s s w a s n e c e s s a r i l y h i g h e r a t j u n c t i o n s o f t h e v a r i o u s c o m p o n e n t s o f t h e c o n e , t h e m o d e l m a y be c o n s i d e r e d e s s e n t i a l l y s m o o t h . 2.2 T i p .Gjeoinetries T h e t e s t p r o g r a m m a d e u s e o f s e v e r a l t i p g e o m e t r i e s . B e s i d e s t h e s t a n d a r d t i p s h o w n i n F i g u r e 2 - 3 , a s m a l l e r t i p ( F i g u r e 2 -7 ) w a s a l s o e m p l o y e d , w h i c h c a n b e r o t a t e d a b o u t i t s a x i s q u i t e r e a d i l y t o a s s e s s t h e s i d e f o r c e d e p e n d e n c e o n t h e r o l l a n g l e . A s d i s c u s s e d i n C h a p t e r 1, 15.25-SECTION A-A CONE MODEL WITH STANDARD TIP RING OF 3 'I 3.18-^—4.32 -5.59 BEARING HOUSING WITH ROTATABLE STANDARD TIP Figure 2-3 A section view of the cone model ( a l l dimensions i n centimeters) %19 Figure 2-5 The porous cone tip. Figure 2-7 A family of nose-boom tips with the standard tip shown for comparison. 21 L a m o n t [20] a n d K e e n e r e t a l . [21] d i d o b s e r v e s u c h r o l l d e p e n d e n c e o f t h e s i d e f o r c e . T h e t e s t s h a v e f o c u s e d p r i m a r i l y o n t w o f a m i l i e s o f t i p g e o m e t r i e s : n o s e - b o o m ( F i g u r e 2 - 7 ) a n d d e l t a s t r a k e ( F i g u r e 2 - 8 ) . T h e l i t e r a t u r e r e v i e w s u g g e s t s b o t h t h e d e v i c e s t o a f f e c t t h e s i d e f o r c e [5 ,6 ,8 ,9 ,12 ,13 ] . T h e n o s e - b o o m l e n g t h s u s e d i n t h e e x p e r i m e n t s v a r i e d f r o m 2.7 cm t o 0.16 c m ( a s p e c t r a t i o v a r i a t i o n b a s e d o n t h e m a x i m u m boom d i a m e t e r w a s 46 a n d 2 , r e s p e c t i v e l y ) . T h e l e n g t h o f t h e d e l t a s t r a k e v a r i e d f r o m 3.2 c m t o 0.32 c m w i t h a n a s p e c t r a t i o o f 1. A s s e v e r a l e a r l i e r i n v e s t i g a t o r s [5 ,6,8,9] h a v e o b s e r v e d a l o s s o f l a t e r a l - d i r e c t i o n a l s t a b i l i t y w i t h t h e d e l t a - s t r a k e , t h e t e s t s w e r e a l s o c o n d u c t e d a t y a w a n g l e s o f ± 1 0 " . 2.3 W i n d Tunnel T h e c o n e m o d e l w a s t e s t e d i n a l o w s p e e d , l o w t u r b u l e n c e r e t u r n t y p e w i n d t u n n e l w h e r e t h e a i r s p e e d c a n b e v a r i e d f r o m 1 t o 46 m/s w i t h a t u r b u l e n c e l e v e l l e s s t h a n 0.1%. T h e p r e s s u r e d i f f e r e n t i a l a c r o s s t h e c o n t r a c t i o n s e c t i o n o f 7:1 r a t i o c a n be m e a s u r e d o n a B e t z m i c r o m a n o m e t e r w i t h a n a c c u r a c y o f 0.2 mm o f w a t e r . T h e t e s t s e c t i o n v e l o c i t y i s c a l i b r a t e d a g a i n s t t h e a b o v e p r e s s u r e d i f f e r e n t i a l . T h e r e c t a n g u l a r c r o s s - s e c t i o n , 91 cm w i d e X 69 cm h i g h , i s p r o v i d e d w i t h 4 5 " c o r n e r f i l l e t s w h i c h v a r y f r o m 15 cm X 15 cm t o 12 cm X 12 cm t o p a r t l y c o m p e n s a t e f o r t h e b o u n d a r y l a y e r g r o w t h . F i g u r e 2 - 9 s h o w s t h e t u n n e l o u t l i n e . 22 F i g u r e 2 - 9 A s c h e m a t i c d i a g r a m of t h e low s p e e d w i n d t u n n e l u s e d i n t h e e x p e r i m e n t s . 23 2.4 Instmmentetiojni A l t h o u g h t h e p r i m a r y i n t e r e s t w a s i n t h e p r e s s u r e m e a s u r e m e n t s , t h e m o d e l w a s m o u n t e d o n a c u s t o m b u i l t A e r o l a b s u p p l y b a l a n c e t u r n t a b l e . B e s i d e s s u p p o r t i n g t h e m o d e l , t h e t u r n t a b l e c a n be a d j u s t e d t o p r o v i d e a n y d e s i r e d a n g l e o f a t t a c k . T h e s t r a i n g a u g e b a l a n c e i n c o r p o r a t e s a n a r r a y o f s i x l o a d c e l l s w h i c h p r o v i d e t h e t h r e e o r t h a g o n a l c o m p o n e n t s o f t h e r e s u l t a n t f o r c e ( l i f t , d r a g a n d s i d e f o r c e ) , a n d m o m e n t ( p i t c h , r o l l a n d y a w ) i n c o n j u n c t i o n w i t h a L e e d s a n d N o r t h r u p m i c r o v o l t a m p l i f i e r . D u e t o e x c e s s i v e d r i f t o f t h e i n s t r u m e n t , i t w a s u s e d o n l y a s a q u a l i t a t i v e i n d i c a t o r a n d h e n c e t h e b a l a n c e r e s u l t s a r e p u r p o s e l y n o t r e p o r t e d . T h e m o d e l h a d 24, 27, o r 40 p r e s s u r e t a p s d e p e n d i n g u p o n t h e t i p c o n f i g u r a t i o n . A s c a n i v a l v e t y p e 48J9 ( F i g u r e 2-10) s w i t c h i n g d e v i c e w a s u s e d , w h i c h c o n n e c t e d t h e p r e s s u r e t a p s s e q u e n t i a l l y t o a D a t a m e t r i c s B a r o c e l P r e s s u r e S e n s o r , t y p e 5 1 1 J - 1 0 . T h e B a r o c e l i s a h i g h p r e c i s i o n , s t a b l e , c a p a c i t i v e v o l t a g e d i v i d e r w h i c h m e a s u r e s a d i f f e r e n t i a l p r e s s u r e u p t o ± 10 mmHg. T h e r e s u l t i n g v o l t a g e w a s t r a n s m i t t e d t o a D a t a m e t r i c s E l e c t r o n i c M a n o m e t e r , t y p e 1018B ( F i g u r e 2 -11) . T h e a c c u r a c y o f t h e c o m b i n e d B a r o c e l a n d E l e c t r i c M a n o m e t e r s y s t e m i s 0.001 mmHg a n d t h e s y s t e m w a s f o u n d t o be i n c a l i b r a t i o n w i t h t h e B e t z M a n o m e t e r . A s t h e f r e e s t r e a m f l u c t u a t i o n s w e r e r e l a t i v e l y i n s i g n i f i c a n t a n d f o r r e a s o n s o f c o n v e n i e n c e , t h e B a r o c e l r e a d i n g s w e r e r o u n d e d o f f t o t h e n e a r e s t 0.01 mmHg. A s c h e m a t i c d i a g r a m o f t h e i n s t r u m e n t a t i o n s e t - u p i s p r e s e n t e d i n F i g u r e 2 -12 . F o r t h e s p i n n i n g t i p t e s t s t h e r a t e o f r o t a t i o n w a s m e a s u r e d w i t h a h a n d h e l d S h i m p o t a c h o m e t e r . 24 F i g u r e 2 -11 T h e B a r o c e l p r e s s u r e t r a n s d u c e r a n d e l e c t r o n i c m a n o m e t e r . 25 Electronic Manometer F i g u r e 2 -12 I n s t r u m e n t a t i o n l a y o u t f o r p r e s s u r e m e a s u r e m e n t u s i n g a S c a n i v a l v e a n d a B a r o c e l T r a n s d u c e r . 2.5 Test Procedures E a r l i e r t e s t s w i t h a s i m i l a r m o d e l [13] h a d i n d i c a t e d a n e e d f o r a s t r o n g e r m o d e l s u p p o r t a s i t w a s f o u n d t o b e s u s c e p t i b l e t o v i b r a t i o n s c a u s e d b y h i g h l y t u r b u l e n t s e p a r a t e d f low a t h i g h e r s p e e d s a n d a n g l e s o f a t t a c k . P r e l i m i n a r y t e s t s w i t h t h e i m p r o v e d s u p p o r t s y s t e m d e l a y e d t h e o n s e t o f v i b r a t i o n t o a > 50* w i t h t h e f r e e s t r e a m s p e e d a s h i g h a s 25.8 m/s. H e n c e , f o r t h e p r e s e n t t e s t p r o g r a m t h e w i n d s p e e d w a s s e t a t 22.7 m / s w h i c h (w i th o n e e x c e p t i o n ) e l i m i n a t e d v i b r a t i o n o v e r t h e e n t i r e r a n g e o f i n t e r e s t . T h i s i s m o r e t h a n d o u b l e t h e s p e e d p r e v i o u s l y a c h i e v e d w i t h o u t v i b r a t i o n . T h e c o r r e s p o n d i n g R e y n o l d s n u m b e r b a s e d o n t h e maximum c o n e d i a m e t e r i s 1.1 X 10 s , w h i c h c o m p a r e s w i t h t h a t u s e d b y t h e e a r l i e r i n v e s t i g a t o r s [1,4,11,20] a n d h e n c e f a c i l i t a t e s c o m p a r i s o n o f t h e d a t a . I t i s i n t h e r a n g e w h e r e t h e R e y n o l d s n u m b e r 26 d e p e n d e n c y i s n e g l i g i b l e a n d t h e f low s e p a r a t i o n i s l a m i n a r . A t a h i g h e r R e y n o l d s n u m b e r i n t h e r a n g e o f 3 X 1 0 5 - 2 X 10 6 , a l a m i n a r s e p a r a t i o n m a y s t i l l o c c u r o n o n e s i d e w h i l e t h e f low o n t h e o t h e r s i d e m a y e x h i b i t a l a m i n a r s e p a r a t i o n f o l l o w e d b y a t u r b u l e n t r e a t t a c h m e n t a n d s e p a r a t i o n . In t h i s c r i t i c a l r a n g e o f t h e R e y n o l d s n u m b e r m u c h h i g h e r l e v e l s o f s i d e f o r c e h a v e b e e n r e p o r t e d , h o w e v e r , a s p o i n t e d o u t b e f o r e , t h e r e s u l t s h a v e b e e n l e s s p r e d i c t a b l e a n d r e p e a t a b l e . It s h o u l d b e e m p h a s i z e d t h a t t h e r e p e a t a b i l i t y p r o b l e m h e r e i s d i s t i n c t l y d i f f e r e n t i n o r i g i n f r o m t h a t a s s o c i a t e d w i t h t h e r o l l o r i e n t a t i o n . T h e s e r i e s o f s t e p s d u r i n g a t y p i c a l t e s t m a y be s u m m a r i z e d a s f o l l o w s : i ) s e t t h e b a l a n c e t a b l e to a = 0; i i ) s e t t h e y a w a n g l e (3 a s d e s i r e d ; i i i ) s e t t h e n o s e t i p to t h e r e q u i r e d r o l l a n g l e 0; i v ) s e t t h e t u n n e l t o a p r e s e l e c t e d w i n d s p e e d ; v ) r e a d p r e s s u r e s a t t h e t a p s w i t h t h e S c a n i v a l v e a n d t h e e l e c t r o n i c m a n o m e t e r ; v i ) i n c r e a s e t h e a n g l e o f a t t a c k a b y 10* u p to 5 0 ' , r e s e t t i n g t h e t u n n e l s p e e d i f n e e d e d . O n c e t h e r e p e a t a b l e c h a r a c t e r o f t h e d a t a w a s e s t a b l i s h e d t h r o u g h a s e r i e s o f t e s t s , t h e a b o v e p r o c e d u r e w a s s h o r t e n e d a n d t h e m e a s u r e m e n t s w e r e l i m i t e d t o a = 30" , 4 0 ° , a n d 5 0 * . D u r i n g t h e a s s e s s m e n t o f r o l l a n g l e e f f e c t s w i t h t h e s t a n d a r d t i p , t h e w h o l e m o d e l w a s r o t a t e d a b o u t i t s a x i s a s t h e t i p c o u l d n o t b e r o l l e d i n d e p e n d e n t l y . F o r t h e s m a l l e r s p i n a b l e t i p s o n l y t h e t i p p o s i t i o n w a s 27 c h a n g e d . T h i s i s e x p e c t e d t o g i v e r e s u l t s s i m i l a r to t h o s e o b t a i n e d w i t h t h e r o l l i n g o f t h e e n t i r e b o d y a s s h o w n b y K e e n e r e t a l . [21]. T h e d y n a m i c h e a d q = ( 1 / 2 ) p V t 2 a n d i n d i v i d u a l Pi - P* p r e s s u r e r e a d i n g s b e i n g a v a i l a b l e f r o m e a c h t a p , a p r e s s u r e c o e f f i c i e n t c a n be o b t a i n e d d i r e c t l y , Cpi - (Pi - Pm)/q. T h e p r e s s u r e c o e f f i c i e n t s w e r e i n t e g r a t e d o v e r t h e c o n e s u r f a c e to o b t a i n t h e f o r c e c o e f f i c i e n t s . T h e i n t e g r a t i o n r o u t i n e i s s u m m a r i z e d i n A p p e n d i x I. 28 3 R E S U L T S fc D I S C U S S I O N S T h e a m o u n t o f i n f o r m a t i o n o b t a i n e d t h r o u g h a p l a n n e d v a r i a t i o n o f t h e s y s t e m p a r a m e t e r s s u c h a s t h e t i p g e o m e t r y ; r o l l , y a w a n d p i t c h a n g l e s ; t i p r o t a t i o n ; s c a n n i n g o f 40 p r e s s u r e t a p s a n d t h e i r i n t e g r a t i o n ; e t c . , i s r a t h e r e x t e n s i v e . T h e r e a r e s e v e r a l o p t i o n s a v a i l a b l e f o r t h e p r e s e n t a t i o n o f d a t a . A n e f f o r t i s m a d e t o c o n v e y t h e i n f o r m a t i o n a s c o n c i s e l y a s p o s s i b l e w i t h a n e m p h a s i s o n d i s c e r n a b l e t r e n d s . T h e s t a n d a r d c o n e - t i p d a t a a r e p r e s e n t e d f i r s t , w h i c h s e r v e a s r e f e r e n c e t o a s s e s s e f f e c t i v e n e s s o f o t h e r t i p g e o m e t r i e s . T h e r e s u l t s w i t h t h e n o s e - b o o m , d e l t a - s t r a k e a n d p o r o u s t i p f o l l o w . F i n a l l y , t h e e f f e c t o f t h e t i p r o t a t i o n i s e v a l u a t e d . S u c h c a r e f u l l y p l a n n e d e x p e r i m e n t s w i t h r e p e a t a b l e r e s u l t s , a i m e d a t s i d e f o r c e a l l e v i a t i o n t h r o u g h a d j u s t m e n t o f t h e t i p g e o m e t r y a r e n o t r e p o r t e d i n t h e l i t e r a t u r e . 3.1 SfcftiJicliftr d J C o n e . J I ip_^o l I_ j £ 3 . t s . T h e p l a i n c o n e t i p ( F i g u r e 2-4) o f 4:1 l e n g t h t o r a d i u s r a t i o w a s t e s t e d i n t h e r a n g e o f a n g l e o f a t t a c k f r o m O t o 5 0 ° i n 12 d i f f e r e n t r o l l p o s i t i o n s . T h e p r e s s u r e c o e f f i c i e n t a t e a c h p r e s s u r e t a p w a s c a l c u l a t e d a n d i n t e g r a t e d o v e r t h e c o n e s u r f a c e t o e v a l u a t e t h e s i d e f o r c e a n d n o r m a l f o r c e c o m p o n e n t s . F o r b o t h s y m m e t r i c a n d a s y m m e t r i c f low p a t t e r n s t h e p r e s s u r e d i s t r i b u t i o n v a r i e d o n l y s l i g h t l y i n t h e a x i a l d i r e c t i o n , i .e. f r o m t h e n o s e t o t h e b a s e o f t h e c o n e . O n t h e o t h e r h a n d , l a r g e p r e s s u r e v a r i a t i o n s w e r e n o t i c e d i n t h e c i r c u m f e r e n t i a l d i r e c t i o n e s p e c i a l l y f o r t h e a s y m m e t r i c f low s i t u a t i o n s . T h u s , a p l o t o f p r e s s u r e v a r i a t i o n a t a n y p a r t i c u l a r a x i a l s t a t i o n c a n s e r v e a s a 29 q u a l i t a t i v e p r e s s u r e l o a d i n g f o r t h e e n t i r e c o n e . T h e ax ia l s t a t i o n P a t 25.3% o f t h e t o t a l c o n e l e n g t h w a s s e l e c t e d t o t h i s e n d a s i t h a d t h e l a r g e s t n u m b e r o f p r e s s u r e t a p s . F i g u r e 3-1 s h o w s a t y p i c a l Cp p l o t f o r z e r o r o l l a n g l e . In g e n e r a l t h e l i f t i n c r e a s e s w i t h a n i n c r e a s e i n t h e a n g l e o f a t t a c k . N o t e , i n t h e r a n g e a = 0 - 3 0 * , t h e c i r c u m f e r e n t i a l p r e s s u r e d i s t r i b u t i o n a t t h e s t a t i o n P i s e s s e n t i a l l y s y m m e t r i c a b o u t t h e ax ia l v e r t i c a l p l a n e . T h e a s y m m e t r y a p p e a r s a t a = 4 0 ° s u g g e s t i n g t h e p r e s e n c e o f a n e t s i d e f o r c e . F i g u r e 3-2 s h o w s a s i m i l a r a s y m m e t r i c p r e s s u r e d i s t r i b u t i o n c a s e , f o r a r o l l a n g l e o f 3 0 0 ° , b u t n o w t h e n e t s i d e f o r c e i s i n t h e o p p o s i t e d i r e c t i o n . F o r t h e t w e l v e r o l l p o s i t i o n s t e s t e d t h e s i d e f o r c e a t a g i v e n a n g l e o f a t t a c k c h a n g e d d i r e c t i o n w i t h o u t s u g g e s t i n g a n y t r e n d (w i th r e s p e c t t o t h e r o l l a n g l e ) . T h i s i s u n d e r s t a n d a b l e a s t h e b o u n d a r y l a y e r i n s t a b i l i t y i s g o v e r n e d b y t h e t i p s u r f a c e r o u g h n e s s , a r a n d o m p a r a m e t e r . F i g u r e 3 -3 p r e s e n t s t h e s i d e f o r c e v a r i a t i o n f o r 12 d i f f e r e n t r o l l p o s i t i o n s . It c l e a r l y s h o w s a l a r g e i n c r e a s e i n s i d e f o r c e s t a r t i n g a t a c l o s e t o 3 0 ° . T h i s i s a p p r o x i m a t e l y t h e v a l u e o f t h e c o n e a n g l e a n d c o m p a r e s w e l l w i t h t h e r e s u l t s o f o t h e r i n v e s t i g a t o r s [ 1 - 5 , 11, 12, 15, 17, 20, 21] . It i s a p p a r e n t t h a t t h e s i d e f o r c e c h a n g e s d i r e c t i o n r a t h e r r a n d o m l y a s e x p l a i n e d b e f o r e . I ts m a g n i t u d e f o r a g i v e n a i s a l s o a f f e c t e d , p e r h a p s d u e t o t h e e x t e n t o f a s y m m e t r y i n t h e f l o w , i n d u c e d b y t h e s u r f a c e r o u g h n e s s a t t h e t i p . T h i s w o u l d r e q u i r e m o r e e x t e n s i v e i n s t r u m e n t a t i o n to a n a l y s e t h e f low f i e l d a c c u r a t e l y . F i g u r e 3 -4 s h o w s t h e n o r m a l f o r c e c o e f f i c i e n t v a r i a t i o n f o r t h e t w e l v e r o l l p o s i t i o n s . Note t h e r e s u l t s s h o w a m a r k e d s c a t t e r , a t a a, deg. o - 0 A - 10 + = 20 X = 30 o = 40 V = 50 360.0 Figure 3-1 Pressure distribution at a reference station P, as affected by the angle of attack, for the standard tip at zero roll angle. ' i I 1 1 1 ! 0.0 60.0 120.0 180.0 240.0 300.0 360.0 e , d e g . Figure 3-2 Pressure distribution at a reference station P, as affected by the angle of attack, for the standard tip at a roll angle of 300*. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 a , d e g . Figure 3-4 Variation of the normal force coefficient for the standard tip model with pitch and roll. 34 g i v e n a , s i g n i f i c a n t l y l a r g e r t h a n t h a t o b s e r v e d f o r t h e s i d e f o r c e . T h i s c a n b e e x p l a i n e d b y t h e f low f i e l d v a r i a t i o n s w i t h t h e r o l l a n g l e . A l t h o u g h t h e p r e s s u r e p l o t s o f F i g u r e s 3-1 a n d 3-2 a r e r e p e a t a b l e a n d e a s y t o i n t e g r a t e , t h e c o n e m o d e l i s n o t c o v e r e d w i t h t h e same p r e s s u r e t a p d e n s i t y . H e n c e , t h e p r e s s u r e i n t e g r a t i o n o v e r t h e c o n e s u r f a c e c a n s h o w some v a r i a t i o n d e p e n d i n g u p o n t h e o r i e n t a t i o n o f t h e p r e s s u r e t a p s . T h i s w a s c h e c k e d b y i n t e g r a t i n g o n l y t h e s e c o n d r i n g o f p r e s s u r e t a p s (12 t a p s r o l l e d t h r o u g h 12 p o s i t i o n s ) . Now t h e n o r m a l f o r c e r e s u l t s s h o w e d d i s t i n c t l y l e s s s c a t t e r . A l l s u b s e q u e n t t e s t s w e r e c o n d u c t e d a t o n e b o d y r o l l p o s i t i o n , w i t h t h e t i p a l o n e r o t a t e d t o d i f f e r e n t r o l l p o s i t i o n s . T h u s t h e r o l l i n d u c e d e x p e r i m e n t a l e r r o r i s e l i m i n a t e d i n f u r t h e r t e s t s . F i g u r e 3 -5 s h o w s t h e s i d e f o r c e v a r i a t i o n a s a f f e c t e d b y t h e r o l l p o s i t i o n a t a f i x e d p i t c h i n c i d e n c e o f 5 0 ° . T h e s e r e s u l t s w e r e o b t a i n e d w i t h t h e b e s t p o l i s h e d a n d n e a r l y s y m m e t r i c n o s e t i p . N o t e , t h e m i n o r v a r i a t i o n s i n t h e m a g n i t u d e o f t h e s i d e f o r c e c o e f f i c i e n t m a y be a t t r i b u t e d t o t h e p r e s s u r e i n t e g r a t i o n p r o c e d u r e a s p o i n t e d o u t b e f o r e . T h e e f f e c t o f m i c r o a s y m m e t r y o f t h e t i p s u r f a c e p r o f i l e i s s t r i k i n g l y v i s i b l e . T h e s i d e f o r c e v a r i a t i o n f o l l o w s a s q u a r e w a v e t y p e p a t t e r n s i m i l a r to t h e o n e o b s e r v e d b y L a m o n t [20]. T h e f a c t t h a t F i g u r e 3 - 5 s h o w s t w o s q u a r e w a v e s d i s c o u n t s t h e p r o b a b i l i t y o f a n y l a r g e a s y m m e t r y i n t h e m o d e l c o n s t r u c t i o n . N o t e , a l t h o u g h t h e s i d e f o r c e s w i t c h e s d i r e c t i o n t h e n o r m a l f o r c e i s n e a r l y c o n s t a n t ( F i g u r e 3 -6 ) . T h e f l u c t u a t i o n s i n t h e n o r m a l f o r c e c o e f f i c i e n t i s e n t i r e l y d u e t o t h e r o l l i n d u c e d p r e s s u r e i n t e g r a t i o n e r r o r . T h e m o d e l w a s r o l l e d i n s t e p s o f 3 0 ° w h i l e m o s t o f t h e p r e s s u r e t a p s h a d a 6 0 ° s p a c i n g . T h i s r e s u l t s i n a p o s i t i v e o r n e g a t i v e b i a s i n g o f t h e r e s u l t a b o u t i t s t r u e v a l u e . 0.0 60.0 120.0 180.0 240.0 300.0 360.0 0, d e g . Figure 3-5 Effect of the standard tip roll position on the side force at a pitch angle of 50". Figure 3-6 Effect of the standard tip roll position on the normal force. 37 T h e maximum r e c o r d e d s i d e f o r c e c o e f f i c i e n t f o r t h e s t a n d a r d t i p w a s 1.22. T h i s i s of t h e same o r d e r o f m a g n i t u d e a s t h e n o r m a l f o r c e c o e f f i c i e n t (1.5). T h i s n o m i n a l v a l u e of t h e s i d e f o r c e i s u s e d a s a r e f e r e n c e to a s s e s s t h e e f f e c t i v e n e s s of o t h e r t i p g e o m e t r i e s . It m a y be p o i n t e d o u t t h a t t h i s n o m i n a l v a l u e o f t h e s i d e f o r c e c o e f f i c i e n t c o m p a r e s w e l l w i t h t h a t o b t a i n e d b y s e v e r a l e a r l i e r r e s e a r c h e r s . F o r e x a m p l e , K e e n e r e t a l . [21] i n h i s e x p e r i m e n t s w i t h a 2 0 ° c o n e f o u n d Cs t o b e 1.25, w h i l e V i s w a n a t h a n d N a r a y a n [11] o b t a i n e d Cs = 1.10 f o r a s i m i l a r c o n e m o d e l . 3.2 NQs.e-.Bpom T e a t s E a c h n o s e - b o o m w a s m a d e f r o m a 0.89 mm d i a m e t e r t a p e r e d d a r n i n g n e e d l e . A f a m i l y o f n i n e d i f f e r e n t n e e d l e s , v a r y i n g i n l e n g t h (Lb) f r o m 4.13 c m t o 0.16 cm (4.13, 3.18, 2.54, 1.91, 1.27, 0.95, 0.64, 0.32, 0.16 cm) w a s u s e d i n t h i s t e s t - p r o g r a m . E a c h t e s t w i t h a n o s e - b o o m w a s c a r r i e d o u t a t s i x r o l l p o s i t i o n s . In t h e s e t e s t s j u s t t h e t i p w a s r o l l e d i n s t e a d of t h e e n t i r e c o n e b o d y . A s p o i n t e d o u t b y K e e n e r e t a l . [26] , t h i s i s e x p e c t e d t o p r o d u c e t h e same e f f e c t a s t h a t o b t a i n e d b y r o l l i n g t h e e n t i r e m o d e l . T h e e x p e r i m e n t s d i d s u b s t a n t i a t e t h i s o b s e r v a t i o n . F i g u r e 3-7(a) s h o w s t h e s i d e f o r c e v a r i a t i o n w i t h t h e p i t c h i n c i d e n c e a n d t h e n o s e r o l l p o s i t i o n w h e n t h e t i p i s f i t t e d w i t h a 4.13 c m n o s e - b o o m ( the l o n g e s t u s e d i n t h e t e s t - p r o g r a m ) . A m a r k e d d e p e n d e n c e o n t h e t i p r o l l o r i e n t a t i o n c o n t i n u e s t o be p r e s e n t a t h i g h e r a n g l e s o f a t t a c k (a > 3 0 ° ) , s i m i l a r to t h a t o b s e r v e d w i t h t h e s t a n d a r d t i p . T h e m a g n i t u d e o f t h e maximum s i d e f o r c e d i d s h o w a s i g n i f i c a n t 38 Figure 3-7 Effect of boom length on variation in the side force coefficient with pitch and roll attitudes: ( a ) , ( b ) , ( c ) . 39 (50%) r e d u c t i o n . In f a c t d u r i n g t h i s s e t o f t e s t s , t h e l a r g e s t n o s e - b o o m d i d r e s u l t i n t h e max imum s i d e - f o r c e r e d u c t i o n . F i g u r e s 3 -7 (b ) t o 3-7( i ) s h o w s i m i l a r v a r i a t i o n s i n t h e s i d e f o r c e c o e f f i c i e n t f o r t h e o t h e r n o s e - b o o m s t e s t e d . T h e b o o m s l a r g e r t h a n 0.95 c m s h o w e d a r e d u c t i o n i n t h e s i d e f o r c e w h i l e t h o s e s m a l l e r t h a n 0.95 c m s h o w e d a n i n c r e a s e i n C s . It i s o f i n t e r e s t t o n o t e t h a t t h e d i r e c t i o n o f t h e s i d e f o r c e i s d e p e n d e n t o n b o t h t h e p i t c h a n g l e a n d t h e r o l l o r i e n t a t i o n . In g e n e r a l , t h e c h a n g e s i n m a g n i t u d e a c c o m p a n y i n g t h e c h a n g e s i n d i r e c t i o n , w i t h a a n d 0, w e r e l a r g e r f o r s h o r t e r b o o m - l e n g t h s (Lb < 0.95 c m ) . It i s i m p o r t a n t t o p o i n t o u t t h a t e v e n f o r i d e n t i c a l t e s t c o n d i t i o n s , i .e. f o r a g i v e n m o d e l a t f i x e d p i t c h a n d r o l l o r i e n t a t i o n s , a n d a f i x e d R e y n o l d s n u m b e r , r e p e a t i n g t h e t e s t m a y l e a d to a d i f f e r e n t d i r e c t i o n o f t h e s i d e f o r c e ( w i t h o u t a f f e c t i n g i t s m a g n i t u d e ) . T h i s b i s t a b l e c h a r a c t e r o f t h e p h e n o m e n o n i s u n d e r s t a n d a b l e c o n s i d e r i n g i t s s e n s i t i v i t y t o t h e f r e e s t r e a m t u r b u l e n c e c h a r a c t e r , a s w e l l a s t h e s u r f a c e r o u g h n e s s d i s t r i b u t i o n . F i g u r e 3 -8 s u m m a r i z e s t h e a b o v e i n f o r m a t i o n i n a u s e f u l w a y t o b e t t e r a p p r e c i a t e t h e e f f e c t o f n o s e - b o o m a n d i t s l e n g t h . It s h o w s v a r i a t i o n s o f t h e a b s o l u t e max imum s i d e f o r c e c o e f f i c i e n t a n d i t s p e r c e n t a g e c h a n g e ( f r o m t h e n o n o s e - b o o m c a s e ) a s a f f e c t e d b y t h e boom l e n g t h . A l t h o u g h t h e l o c a l v a r i a t i o n s d o n o t e x h i b i t a n y we l l d e f i n e d p a t t e r n t h e o v e r a l l t r e n d s a r e w e l l e s t a b l i s h e d . T h e s h o r t e r boom l e n g t h s ( L b / L < 0.7) t e n d t o i n c r e a s e t h e s i d e f o r c e , h o w e v e r , f o r l o n g e r boom l e n g t h s t h e r e i s a d i s t i n c t r e d u c t i o n i n t h e maximum C s . It 40 i n o 1 1 1 I 1 1 ' 0.0 10.0 20.0 30.0 40.0 50.0 60.0 a f d e g . Figure 3-7 Effect of boom length on variation in the side force coefficient with pitch and roll attitudes: (d), (e), (f). o F i g u r e 3-7 E f f e c t o f b o o m l e n g t h o n v a r i a t i o n i n t h e s i d e f o r c e c o e f f i c i e n t w i t h p i t c h a n d r o l l a t t i t u d e s : ( g ) , (h ) , ( i ) . F i g u r e 3-8 M a g n i t u d e o f t h e maximum s i d e f o r c e c o e f f i c i e n t w i t h v a r y i n g n o s e - b o o m l e n g t h i n c l u d i n g t h e s t a n d a r d t i p c a s e . 43 is possible to achieve a reduction in maximum side force coefficient by around 50% through the appropriate choice of the nose-boom length. Figure 3-9 shows normal force variations with the pitch angle for the case of a 4.13 cm nose-boom. It is nearly linear with little scatter. The normal force plots for the other boom lengths show similar trends. Variation of the normal force with the nose-boom length is shown in Figure 3-10. It is apparent that effect of the boom length on the normal force coefficient is relatively small. 3.3 De.lt^„stmke_. Tests Tests with 3.18 cm delta strake tip shown in Figure 2-8 were conducted at 6 different roll positions. Of primary interest was the effect of the strake when perpendicular to the pitch plane, as this configuration was expected to be successful at minimizing the side force. However, the tests were also conducted at roll angles of ± 10*, ± 20° and 90°. The small roll angles would be of interest for noncoordinated flight maneuvers, while the 90° position was tried to compare its effectiveness in side force alleviation with the more conventional orientations of the strake. Results of the side force variation with pitch and roll attitudes for the 3.18 cm delta strake are presented in Figure 3-11. Note, both zero and 90° roll orientations of the strake seem to promote symmetric flow fields with the zero position proving a little better. For a given pitch angle, particularly with a > 30°, the presence of a small roll angle (± 10°, ±20°) seems to reduce effectiveness of the strake in promoting the flow symmetry. However, it is encouraging that the side force remains relatively low over the entire range of the pitch angle tested. o i 1 1 1 1 1 r 0.0 10.0 20.0 30.0 40.0 50.0 60.0 a , d e g . Figure 3-9 Normal force variation with pitch angle and roll orientation for the 4.13 cm nose-boom. F i g u r e 3-10 N o r m a l f o r c e c o e f f i c i e n t v a r i a t i o n w i t h p i t c h i n c i d e n c e a n d n o s e - b o o m l e n g t h . deg. 8 - 0 10 • - 10 o - 20 • - 20 • = 90 1 1 1 1 1 1 f 0.0 10.0 20.0 30.0 40.0 50.0 60.0 of deg. Figure 3-11 Variation of the side force coefficient with pitch and roll angles for the 3.18 cm delta strake. 47 A s s e v e r a l i n v e s t i g a t o r s h a v e r e p o r t e d a l o s s o f l a t e r a l - d i r e c t i o n a l s t a b i l i t y w i t h s t r a k e a l l e v i a t i o n d e v i c e s , i t w a s d e e m e d i m p o r t a n t to c o n d u c t t e s t s a t n o n z e r o y a w a n g l e s a s w e l l a s t h e n o r m a l z e r o s i d e s l i p c o n d i t i o n . P r e s s u r e d i s t r i b u t i o n p l o t s o v e r t h e c o n e s u r f a c e w i t h t h e s t a n d a r d t i p , a s a f f e c t e d b y t h e p i t c h f o r B = ± 1 0 ° a r e p r e s e n t e d i n F i g u r e 3 -12 . In F i g u r e 3-12(a) t h e c o n e i s y a w e d t o t h e r i g h t (as v i e w e d b y t h e p i l o t ) . A t z e r o a n g l e o f a t t a c k , t h e p r e s s u r e d i s t r i b u t i o n s h o w s a c l e a r s i d e l o a d t o t h e r i g h t . H o w e v e r , a s t h e p i t c h a n g l e i n c r e a s e s t h e s i d e f o r c e r e v e r s e s d i r e c t i o n a n d i s t o t h e l e f t . T h i s s u g g e s t s a s t r o n g p o s i t i v e s t a b i l i t y . O n t h e o t h e r h a n d , p r e s s u r e p l o t s f o r B = 1 0 ° i n F i g u r e 3 -12 (b ) s h o w t h e r e v e r s e t r e n d i n d i c a t i n g a n e g a t i v e s t a b i l i t y . T h e r e s u l t a n t s i d e f o r c e c o e f f i c i e n t s a r e p l o t t e d a g a i n s t t h e p i t c h a n g l e f o r B = 0 ° a n d ± 1 0 ° ( F i g u r e 3 -13a) f o r t h e s t a n d a r d t i p . In t h i s s e r i e s o f t e s t s i t s e e m s t h e s i d e f o r c e d i r e c t i o n i s n o t a f f e c t e d b y t h e y a w d i r e c t i o n . It a p p e a r s t h a t m i c r o a s y m m e t r y o f t h e c o n e t i p s u r f a c e e a s i l y o v e r p o w e r s a n y i n h e r e n t d i r e c t i o n a l s t a b i l i t y o f t h i s f o r e b o d y c o n f i g u r a t i o n . R e s u l t s f o r t h e p r e s s u r e i n t e g r a t e d s i d e f o r c e d a t a f o r t h e v a r i o u s l e n g t h s o f d e l t a s t r a k e t e s t e d a r e p r e s e n t e d i n F i g u r e s 3 -13 (b ) t h r o u g h 3 - 1 3 ( g ) . E v i d e n c e o f a w e a k b u t p o s i t i v e d i r e c t i o n a l s t a b i l i t y i s a p p a r e n t f o r t h e 3.18 c m s t r a k e t i p ( F i g u r e 3 - 1 3 g ) . It i s o f i n t e r e s t t o n o t e t h a t t h e s t a b i l i t y g e t s p r o g r e s s i v e l y w e a k e r a s t h e s t r a k e s i z e d e c r e a s e s a n d b e l o w L s = 1.27 c m t h e m o d e l b e c o m e s i n c r e a s i n g l y m o r e u n s t a b l e i n y a w . It i s i m p o r t a n t t o p o i n t o u t t h a t a l l t h e s t r a k e t i p s l a r g e r t h a n 0.32 c m s h o w e d p r o m i s e i n t e r m s o f t h e s i d e f o r c e r e d u c t i o n . O n t h e o = 0 A = 10 + = 20 X = 30 o = 40 V = 50 1 1 1 I I I 0.0 60.0 120.0 180.0 210.0 300.0 360.0 e , d e g . Figure 3-12 Pressure distribution, at the reference station P, for the standard tip at a yaw incidence of: a) B = -10'. Figure 3-12 Pressure distribution, at the reference station P, for the standard tip at a yaw incidence of: b) 0 = +10*. 0.0 10.0 20.0 30.0 40.0 50.0 60.0 o., deg. F i g u r e 3 -13 V a r i a t i o n o f t h e Bide f o r c e c o e f f i c i e n t w i t h p i t c h a n d y a w a n g l e s a s a f f e c t e d b y t h e d e l t a s t r a k e l e n g t h ( a s p e c t r a t i o =1): (a) , (b ) , (c ) . 51 d) Ls = 1.27 cm, L s / L - 0.083 1 I i i i 1 0.0 10.0 20.0 30.0 40.0 50.0 60.0 o.f d e g . F i g u r e 3 -13 V a r i a t i o n o f t h e s i d e f o r c e c o e f f i c i e n t w i t h p i t c h a n d y a w a n g l e s a s a f f e c t e d b y t h e d e l t a s t r a k e l e n g t h ( a s p e c t r a t i o =1): ( d ) , (e ) , ( f ) , (g ) . 52 w h o l e t h e y p e r f o r m e d m u c h b e t t e r t h a n t h e n o s e - b o o m s . T h e maximum r e d u c t i o n i n t h e s i d e f o r c e c o e f f i c i e n t a c h i e v e d w a s a r o u n d 88% o f t h e n o m i n a l v a l u e w i t h t h e d e l t a s t r a k e o f L s = 3.19 c m ( F i g u r e 3 -14) . A s w i t h t h e n o s e - b o o m s t u d y , t h e v a r i a t i o n o f t h e n o r m a l f o r c e w i t h t h e p i t c h a n g l e i s e s s e n t i a l l y l i n e a r . H o w e v e r , t h e p r e s e n c e o f y a w d o e s t e n d t o s c a t t e r t h e r e s u l t s a t a g i v e n a. F i g u r e 3 -15 s h o w s t h e n o r m a l f o r c e c o e f f i c i e n t r e s u l t s f o r t h e 3.18 c m d e l t a s t r a k e a s a f f e c t e d b y p i t c h a n d y a w a n g l e s . F i g u r e 3-16 s u m m a r i z e s t h e n o r m a l f o r c e r e s u l t s f o r t h e f a m i l y o f d e l t a s t r a k e s . A s l i g h t d e c r e a s e i n t h e n o r m a l f o r c e i s n o t e d a s t h e s t r a k e l e n g t h i s i n c r e a s e d . If t h e f o r e b o d y l i f t c o n t r i b u t i o n i s a s i g n i f i c a n t p o r t i o n o f t h e t o t a l l i f t o f a m i s s i l e o r a n a i r c r a f t , t h e n t h e i m p o r t a n c e o f t h i s l o s s o f l i f t w o u l d h a v e t o be a n a l y s e d . It s e e m s , h o w e v e r , a s m a l l p e n a l t y t o p a y f o r t h e l a r g e r e d u c t i o n s i n t h e s i d e f o r c e o b t a i n e d w i t h t h e s e t i p s . 3.4 EQrou.s_. T i p . T e s t s T h e p o r o u s b r a s s t i p u s e d i n t h e t e s t p r o g r a m ( F i g u r e 2 -5 ) w a s e q u i p p e d »w i th a 3.18 c m n o s e - b o o m , a n d p e r f o r a t e d w i t h 0.64 mm h o l e s . T h e p e r f o r a t e d p o r t i o n c o m p r i s e d a p p r o x i m a t e l y 20% o f t h e t o t a l c o n e l e n g t h . T h e maximum r e c o r d e d s i d e f o r c e c o e f f i c i e n t w a s 0.62, a 38% r e d u c t i o n f r o m t h e n o s e - b o o m c a s e a n d a 49% r e d u c t i o n f r o m t h e s t a n d a r d t i p v a l u e . O n t h e o t h e r h a n d , t h e p o r o u s t i p r e c o r d e d a s l i g h t l y h i g h e r (6%) n o r m a l f o r c e t h a n t h a t w i t h t h e s t a n d a r d t i p . It s e e m s l o g i c a l t h a t a n e f f i c i e n t p o r o u s t i p w i t h n e a r i n s t a n t a n e o u s c o m m u n i c a t i o n o f p r e s s u r e a c r o s s i t s s u r f a c e w o u l d e n h a n c e s y m m e t r i c v o r t e x f o r m a t i o n , a s w e l l a s n e g a t e t h e e f f e c t s o f Figure 3-14 Effect of the strake length on the magnitude of the side force. OJ 0.0 10.0 20.0 30.0 40.0 50.0 , 60.0 ex, d e g . Figure 3-15 Variation of the normal force coefficient with pitch and yaw angles for a strake of 3.18 cm. o CM Ls / L Figure 3-16 Effect of the strake length on the normal force coefficient. 56 a s y m m e t r i c v o r t i c i e s . T h e p o r o u s t i p u s e d i n t h e p r e s e n t t e s t p r o g r a m h a d s e v e r a l l i m i t a t i o n s : (i) t h e t a p s i z e i s r a t h e r l a r g e c o n t r i b u t i n g to t h e s u r f a c e r o u g h n e s s t h u s p a r t l y c a n c e l l i n g i t s d e s i r e d i n f l u e n c e ; (ii) t h e p o r o u s l e n g t h i s p e r h a p s too l o n g , t h u s p r e s e n t i n g a l a r g e r i n t e r n a l v o l u m e r e s u l t i n g i n t h e a v e r a g e p r e s s u r e t h a t i s d i f f e r e n t f r o m t h e l o c a l v a l u e ; ( i i i ) t h e p r o b l e m i n (ii) i s f u r t h e r a c c e n t u a t e d h e r e a s t h e i n t e r n a l g a p e x t e n d s to t h e b a s e o f t h e c o n e a n d c o m m u n i c a t e s w i t h t h e p r e s s u r e t h e r e . H o w e v e r , e f f e c t i v e n e s s o f t h e p o r o u s t i p i n r e d u c i n g t h e s i d e f o r c e i s c l e a r l y e s t a b l i s h e d , e v e n b y t h i s p r e l i m i n a r y t e s t . B e t t e r p l a n n e d e x p e r i m e n t s i n t h i s d i r e c t i o n a r e l i k e l y t o be f r u i t f u l . 3.5 S i n n i n g . J i p . . T e s t s T h e e a r l i e r p r e l i m i n a r y i n v e s t i g a t i o n b y M o d i e t a l . [12] h a d s u g g e s t e d a p o s s i b l e r e d u c t i o n i n s i d e f o r c e w h e n t h e t i p o f t h e c o n e w a s s p u n . S e v e r a l c a r e f u l l y p l a n n e d t e s t s w e r e c o n d u c t e d t o a s s e s s m o r e p r e c i s e l y t h e e f f e c t o f t i p r o t a t i o n . T h e f i r s t s e t o f t e s t s i n v o l v e d s p i n n i n g t h e s t a n d a r d t i p a n d t h e n o s e - b o o m s o f u p t o 1.27 c m l e n g t h . A l l t h e s e t e s t s w e r e c o n d u c t e d a t 2000 r p m , t h e max imum s p e e d o f t h e s m a l l D . C . m o t o r u s e d . V a r i a t i o n s i n t h e s i d e f o r c e w i t h t h e p i t c h a n g l e a r e s h o w n i n F i g u r e 3 -17 . F o r e a c h t i p t e s t e d t h e m o d e l w a s p i t c h e d t h r o u g h t o 5 0 ° a n d t h e t e s t r e p e a t e d w i t h t h e s p i n r e v e r s e d . T w o o b s e r v a t i o n s o f i n t e r e s t c a n be made: i) T h e d i r e c t i o n o f t h e s p i n d e t e r m i n e s t h e d i r e c t i o n o f t h e s i d e f o r c e . A c l o c k w i s e r o t a t i o n l e a d s t o a n e t l e f t s i d e f o r c e (as LO O LD i n o _ I 0.0 10.0 20.0 30.0 o., d e g . 40.0 50.0 60.0 Lb / L o A + X o V 0.0 0.010 0.032 0.041 0.063 0.083 F i g u r e 3-17 S i d e f o r c e v a r i a t i o n a s a f f e c t e d b y p i t c h a n g l e a n d n o s e - b o o m l e n g t h a t t i p s p i n r a t e o f 2000 r p m . 58 v i e w e d b y t h e p i l o t ) . T h e o p p o s i t e i s t r u e f o r t h e a n t i c l o c k w i s e s p i n . T h i s i s i n a g r e e m e n t w i t h t h e r e s u l t s o f E r i c s s o n a n d R e d i n g [15]. i i ) T h e t i p r o t a t i o n c a n l e a d t o a s i g n i f i c a n t r e d u c t i o n i n t h e s i d e f o r c e . F i g u r e 3 -18 d e m o n s t r a t e s e f f e c t i v e n e s s o f v a r i o u s n o s e - b o o m s i n r e d u c i n g t h e s i d e f o r c e a t 2000 r p m . T h e s e r e s u l t s s h o w t h a t r e d u c t i o n i n t h e r a n g e o f 50% t o 75% of t h e n o m i n a l v a l u e c a n be o b t a i n e d b y s p i n n i n g t h e t i p w i t h a n o s e - b o o m . T h e maximum s i d e f o r c e r e d u c t i o n w i t h a 0.318 n o s e - b o o m t i p s p i n n i n g a t 2000 r p m , w a s a r o u n d 25% (of t h e n o m i n a l v a l u e ) . N o t e , t h e same boom l e n g t h i n t h e n o n s p i n n i n g t e s t s a c t u a l l y i n c r e a s e d t h e s i d e f o r c e f r o m t h e n o m i n a l v a l u e . It i s i n t e r e s t i n g t o n o t e t h a t t h e s p i n n i n g s t a n d a r d t i p w a s q u i t e e f f e c t i v e w i t h t h e s i d e f o r c e r e d u c e d b y 71%. T h e s e c o n d s e t o f t e s t s i n v o l v e d s p i n n i n g a 1.27 c m n o s e - b o o m o v e r a r a n g e o f s p e e d . T h e s i d e f o r c e v a r i a t i o n w i t h t h e p i t c h a n d t h e s p i n r a t e a r e s h o w n i n F i g u r e 3 -19 . A g a i n t h e s e n s e o f r o t a t i o n h a s d e t e r m i n e d t h e s i d e f o r c e d i r e c t i o n . Wi th t h e p r e s e n t m o t o r i t w a s n o t p o s s i b l e t o o b t a i n a s t a b l e s p i n r a t e b e l o w 100 r p m . F i g u r e s 3 -20 s h o w s t h e maximum s i d e f o r c e v a r i a t i o n w i t h s p i n r a t e f o r a 1.27 c m n o s e - b o o m . N o t e , a c l e a r m i n i m u m i n t h e s i d e f o r c e a t 200 r p m . In f a c t , a n y s p i n s e e m s to r e d u c e t h e s i d e f o r c e w i t h 200 r p m y i e l d i n g 25% o f t h e n o m i n a l v a l u e a n d 46% o f t h e z e r o s p i n c a s e , f o r t h e same t i p . I n v e s t i g a t i o n s b y o t h e r r e s e a r c h e r s [12, 15] s u g g e s t s t h a t t h e maximum r e d u c t i o n i n t h e s i d e f o r c e o c c u r s a t s p i n r a t e s i n t h e r a n g e o f 100-400 r p m . Figure 3-18 Effect of the nose-boom length on the side force coefficient at 2000 rpm. IT) O LO LT) I 0.0 CLOCKWISE SPIN RPiTE, RPM o = 2000 v = 2000 v = 1200 a - 1200 a - 700 x - 700 x - 525 • - 525 • - 410 © = 410 © = 300 a = 300 a = 200 a = 200 a = 100' B = 100 10.0 20.0 30.0 a , d e g . 40.0 50.0 60.0 Figure 3-19 Side force variation as affected by pitch angle and spin rate for a 1.27 cm nose-boom. (] (0) ( B r a c k e t t e d numbers a r e % r e d u c t i o n f rom t h e 1.27 cm n o s e - b o o m ' s s t a t i o n a r y v a l u e ) 1 1 1 0.0 500.0 1000.0 1500.0 2000 SPIN R A T E , RPM F i g u r e 3-20 E f f e c t o f s p i n r a t e o n t h e s i d e f o r c e c o e f f i c i e n t f o r a 1.27 c m n o s e - b o o m . Results for the normal force length and spin rate are presented Cn is virtually unaffected by these 62 coefficient as affected by the boom in Figure 3-21. It iB apparent that parameters. o Figure 3-21 The normal force coefficient as affected by: a) the nose-boom length at a spin rate of 2000 rpm. Figure 3-21 The normal force coefficient as affected by: b) the spin rate for a 1.27 cm nose-boom. 65 4 C O N C L U D I N G R E M A R K S T h e s u b j e c t o f v o r t e x d o m i n a t e d f o r e b o d y f l o w s h a s p r o v e n t o be f a r m o r e c o m p l e x t h a n t h e f i r s t i m p r e s s i o n s w o u l d i n d i c a t e . A s o f t e n h a p p e n s i n i n v e s t i g a t i o n s o f a e r o d y n a m i c p h e n o m e n a , m a n y u n c o n t r o l l a b l e p a r a m e t e r s a p p e a r w h i c h n o t o n l y c o m p l i c a t e , b u t s o m e t i m e s i n v a l i d a t e t h e t e s t r e s u l t s . T h e p r e s e n t s t u d y p r o v e d t o be a n e d u c a t i o n , n o t o n l y i n t h e s u b j e c t m a t t e r , b u t i n p r o c e d u r e s a n d p r o b l e m s o f a n i n v o l v e d a e r o d y n a m i c t e s t i n g s c h e m e . 4.1 CpnclMSiplQS T h e c a r e f u l l y p l a n n e d e x p e r i m e n t s w i t h r e p e a t a b l e r e s u l t s p r o v i d e s , f o r t h e f i r s t t i m e , r e l i a b l e i n f o r m a t i o n c o n c e r n i n g t h e e f f e c t i v e n e s s o f s e v e r a l t i p g e o m e t r i e s a n d t h e i r r o t a t i o n o n t h e s i d e f o r c e r e d u c t i o n . T h e t e s t s w i t h a 2 8 ° c o n e - c y l i n d e r m o d e l , p r o v i d e d w i t h t h e s t a n d a r d t i p , n o s e - b o o m s w i t h o u t a n d w i t h p o r o u s a p e x , d e l t a s t r a k e s a n d t i p r o t a t i o n , h a v e g i v e n f u n d a m e n t a l i n f o r m a t i o n l e a d i n g t o a b e t t e r a p p r e c i a t i o n o f t h e c o m p l e x f l o w . B a s e d o n t h e r e s u l t s f o l l o w i n g g e n e r a l c o n c l u s i o n s c a n be m a d e : i) A c o m p l e t e a n d a u t h o r i t a t i v e s t u d y o f s i d e f o r c e c h a r a c t e r i s t i c s a t h i g h a n g l e s o f a t t a c k c a n n o t be c o m p l e t e w i t h o u t a c o m p r e h e n s i v e s t u d y o f e f f e c t s o f t h e r o l l a n g l e . T e s t s m u s t be r e p e a t e d a t a s m a n y r o l l o r i e n t a t i o n s a s p o s s i b l e t o e n s u r e t h a t t h e w o r s t c o n f i g u r a t i o n i s c o v e r e d , i i ) R e g a r d l e s s o f t h e h y p o t h e s e s c o n c e r n i n g t h e s i d e f o r c e o n s e t , i t i s u n d e n i a b l y t r u e t h a t m i c r o a s y m m e t r y o f e i t h e r t h e t i p s u r f a c e o r t h e f r e e s t r e a m t u r b u l e n c e i s s u f f i c i e n t t o t r i g g e r a s y m m e t r i c v o r t e x d e v e l o p m e n t . T h e s i d e f o r c e d i r e c t i o n s w i t c h i n g w i t h r o l l p o s i t i o n s , s u g g e s t s s u r f a c e r o u g h n e s s t o be a n i m p o r t a n t p a r a m e t e r i n i n i t i a t i n g a n a s y m m e t r i c f low p a t t e r n a n d t h e a t t e n d a n t s i d e f o r c e , i i i ) T h e e f f e c t o f r o l l o r i e n t a t i o n c a n b e a s s e s s e d b y e i t h e r r o l l i n g t h e e n t i r e b o d y o r t h e t i p a l o n e . T h i s s u p p o r t s t h e h y p o t h e s i s t h a t s u r f a c e a s y m m e t r i e s r e s p o n s i b l e f o r t r i g g e r i n g m a j o r f low a s y m m e t r i e s a r e c o n f i n e d t o t h e t i p r e g i o n . i v ) P l o t s o f p r e s s u r e o v e r t h e c o n e s u r f a c e a t h i g h a n g l e s o f a t t a c k s h o w i t t o be q u i t e low o n o n e h a l f o f t h e l e e w a r d s i d e . B a s e d o n t h e l i t e r a t u r e s u r v e y a n d f low v i s u a l i z a t i o n s t u d i e s b y o t h e r r e s e a r c h e r s , t h e low p r e s s u r e a r e a i s a t t r i b u t e d t o t h e p r e s e n c e o f a v o r t e x l i n e c l o s e to t h e c o n e s u r f a c e . T h e o t h e r h a l f o f t h e l e e w a r d s i d e o f t h e c o n e h a s a n e a r l y u n i f o r m p r e s s u r e i n d i c a t i n g a f u l l y s e p a r a t e d f low , v ) T h e o n s e t o f t h e s i g n i f i c a n t s i d e f o r c e o c c u r s a t a p i t c h a n g l e a p p r o x i m a t e l y e q u a l t o t h e c o n e a n g l e . T h e maximum s i d e f o r c e i s o f t h e Bame o r d e r o f m a g n i t u d e a s t h e n o r m a l f o r c e . v i ) T h e n o r m a l f o r c e i s r e l a t i v e l y u n a f f e c t e d b y t h e r o l l o r i e n t a t i o n . 67 Nose-Boom i) A B in the case of the standard tip, the roll orientation continues to affect the side force, even in the presence of a noBe-boom. ii) By properly choosing the size of a nose-boom, the side force can be reduced by as much as 50%. However, it appears that too short a nose boom is worse than none at all as a 34% Increase in the side force was recorded with a 0.32 cm nose—boom (Lb/L = 3.1%). In fact, the nose—booms shorter than 7% of the cone length increased the maximum side force while the opposite was true for the nose-booms with Lb/L > 0.07. iii) Tests with the nose-booms of lengths less than 7% of the cone length exhibited a greater instability of the flow field. Large changes in the side force magnitude and direction with roll orientations were frequent with shorter booms. This agrees with the trend observed by several investigators in their studies with slender cones. iv) The normal force is relatively insensitive to both the nose-boom length and roll orientation. Eorpus .Tip_wifch.NQse-Boora i) A side force reduction of nearly 50% is possible with the addition of a porous tip having a 3.18 cm nose-boom. i) A side force reduction by at least 88%, and possibly greater, is achievable with an appropriate delta strake. The largest strake used in the test program (21% of the cone length) e x h i b i t e d t h e b e s t s i d e f o r c e a l l e v i a t i o n . A l l s t r a k e s , i r r e s p e c t i v e o f t h e i r l e n g t h s , e x c e p t t h e s h o r t e s t (2.1% o f t h e c o n e l e n g t h ) , r e d u c e d t h e s i d e f o r c e . T h e m o d e l w i t h t h e s h o r t e s t s t r a k e b e h a v e d a l m o s t l i k e t h e s t a n d a r d t i p c o n f i g u r a t i o n . ii) A n o r i e n t a t i o n o f t h e s t r a k e p e r p e n d i c u l a r t o t h e p i t c h p l a n e i s p r e f e r a b l e t o t h a t p a r a l l e l t o t h e p i t c h p l a n e . A s l i g h t l y l o w e r s i d e f o r c e c o e f f i c i e n t r e s u l t s f r o m t h i s m o r e c o n v e n t i o n a l c o n f i g u r a t i o n , i i i ) A sma l l r o l l o r i e n t a t i o n o f t h e d e l t a s t r a k e , a s e n c o u n t e r e d i n a n o n c o o r d i n a t e d f l i g h t , l e a d s t o a s l i g h t l y h i g h e r s i d e f o r c e b u t s t i l l f a r l e s s t h a n 50% o f t h a t e n c o u n t e r e d w i t h t h e s t a n d a r d t i p . i v ) Y a w t e s t s w i t h t h e d e l t a s t r a k e s , a t B = ± 1 0 ° , i n d i c a t e t h a t t h e l a r g e s t t i p p r o m o t e s a w e a k b u t p o s i t i v e d i r e c t i o n a l s t a b i l i t y . T h e s t a b i l i t y d e c r e a s e s a n d t h e s y s t e m b e c o m e s s t r o n g l y u n s t a b l e a s t h e d e l t a s t r a k e i s r e d u c e d i n s i z e . T h e s t r a k e s l a r g e r t h a n 12% o f t h e c o n e l e n g t h a p p e a r e d t o p r o m o t e d i r e c t i o n a l s t a b i l i t y . I n c i d e n t a l l y , t h e same t r e n d w a s o b s e r v e d f o r t h e s t a n d a r d t i p m o d e l , v ) A s l i g h t d e c r e a s e i n t h e n o r m a l f o r c e w a s o b s e r v e d w i t h t h e a d d i t i o n o f a d e l t a s t r a k e . T h e n o r m a l f o r c e d e c r e a s e s w i t h a n i n c r e a s e i n t h e s t r a k e l e n g t h . F o r a l l p r a c t i c a l p u r p o s e s , t h i s n e g l i g i b l e r e d u c t i o n i n l i f t i s o f l i t t l e c o n s e q u e n c e c o m p a r e d t o t h e a s s o c i a t e d l a r g e r e d u c t i o n s i n t h e s i d e f o r c e . 69 .Spinning .Tips i) Spin direction determines the direction of the side force. For the test Reynolds number of 1.1 X 105, there is no Magnus lift reversal and the side force is always to the left for clockwise spin and to the right for anticlockwise rotation (as viewed by the pilot). ii) Reductions in the side force of up to 75% were possible with spinning tips. Tests with various sizes of the nose—booms spinning at 2000 rpm showed that a smaller boom length is more effective in alleviating the side force. A seventy-five percent reduction in the side force was achieved at 2000 rpm with a 0.32 cm nose-boom, iii) Spinning of the nose-tip does not increase the side force. iv) A clear minimum side force coefficient (75% reduction) was observed at 200 rpm for the 1.27 cm nose-boom (Lb/L = 0.318). v) A complex interdependence of the spin rate, tunnel test speed, angle of attack and nose-boom length is evident. A separate more elaborate and carefully planned test-program is necessary to fully appreciate these interactions. 4.2 Recommendations As in any study aimed at understanding a phenomenon at the fundamental level, more new questions arise as one has better appreciation of the process. This experimental program trying to understand the side force phenomenon is no exception. Most of the following recommendations involve extension of the present test-program. 70 S e v e r a l o f t h e s i d e f o r c e a l l e v i a t i o n d e v i c e s s t u d i e d h e r e ( s p i n n i n g a n d p o r o u s t i p s ) a r e o f c o n s i d e r a b l e f u n d a m e n t a l i n t e r e s t i n t e r m s o f t h e a s s o c i a t e d f l u i d m e c h a n i c s a n d h e n c e m e r i t f u r t h e r i n v e s t i g a t i o n o n t h a t b a s i s a l o n e . O t h e r s ( n o s e - b o o m s a n d d e l t a s t r a k e s ) , i n a d d i t i o n , h a v e c o n s i d e r a b l e s c o p e f o r p r a c t i c a l a p p l i c a t i o n s . D e p e n d i n g u p o n t h e i n d i v i d u a l ' s i n t e r e s t , o n e o r t h e o t h e r g r o u p m a y r e c e i v e s p e c i a l a t t e n t i o n . O n t h e o t h e r h a n d , o n e m a y p r e f e r to n a r r o w t h e w i d e r a n g e o f t h e r e s e a r c h t o p i c s . I n d u s t r i a l , m a n u f a c t u r i n g a n d o p e r a t i o n a l r e q u i r e m e n t s m a y be p o l l e d i n o r d e r t o d i s t i n g u i s h f e a s i b l e s i d e f o r c e a l l e v i a t i o n d e v i c e s f r o m t h o s e w h i c h h a v e l i t t l e p r o m i s e i n t e r m s o f p r a c t i c a l a p p l i c a t i o n . T o t h i s e n d a g e n c i e s s u c h a s N A S A , a i r c r a f t a n d m i s s i l e m a n u f a c t u r e r s , p i l o t s a n d m a i n t e n a n c e e n g i n e e r s s h o u l d a l s o be c o n s u l t e d t o e v o l v e a r a t i o n a l p l a n of f u r t h e r s t u d y . E v e n i n a b s e n c e s u c h c o o r d i n a t e d c o n s u l t a t i o n t h e f o l l o w i n g r e c o m m e n d a t i o n s s e e m a p p r o p r i a t e : i) T w e l v e p r e s s u r e t a p s p e r r i n g i s a m i n i m u m t o a d e q u a t e l y d e s c r i b e t h e p r e s s u r e d i s t r i b u t i o n . T h e a d d i t i o n o f m o r e p r e s s u r e t a p s a t c e r t a i n s t a t i o n s s h o u l d be s e r i o u s l y c o n s i d e r e d . i i ) T h e m o d e l s u p p o r t , a l t h o u g h m u c h i m p r o v e d f r o m i t s p r e v i o u s s t a t e [13] , c o u l d s t a n d f u r t h e r m o d i f i c a t i o n . M o d e l v i b r a t i o n s l i m i t e d t h e t e s t s to t h e w i n d s p e e d (22.7 m / s ) a n d t h e maximum a n g l e o f a t t a c k o f 5 0 ° . i i i ) T h e u s e of a r e l i a b l e a n d c a l i b r a t e d f o r c e b a l a n c e t a b l e i s r e c o m m e n d e d a s a c h e c k o n t h e p r e s s u r e i n t e g r a t i o n p r o c e d u r e . T h e D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g h a s 71 j u s t a c q u i r e d s u c h a s y s t e m w h i c h , u n f o r t u n a t e l y , w a s n o t o p e r a t i o n a l a t t h e t ime of t h e p r e s e n t p r o g r a m . i v ) T h e u s e o f m o r e c o m p l e t e i n s t r u m e n t a t i o n i s r e c o m m e n d e d to b e t t e r u n d e r s t a n d t h e f low f i e l d s t r u c t u r e a r o u n d t h e m o d e l . T h e u s e o f L D V , h o t w i r e s a n d f low v i s u a l i z a t i o n , a l t h o u g h t ime c o n s u m i n g w o u l d g r e a t l y i m p r o v e t h e u n d e r s t a n d i n g o f t h i s f low p h e n o m e n o n , v ) T h e a p p l i c a t i o n o f v a r i o u s l e n g t h s o f n o s e - b o o m t o a n a i r c r a f t m o d e l w o u l d p r o v e a n i n t e r e s t i n g a n d u s e f u l s u b s t a n t i a t i o n o f t h i s w o r k . It i s r e c o m m e n d e d t h a t a n F - 1 6 o r F - 1 8 a i r c r a f t f o r e b o d y be made o r a c q u i r e d f o r t h i s p u r p o s e a s t h e y d o n o t p r e s e n t l y i n c o r p o r a t e a n o s e - b o o m . v i ) It i s r e c o m m e n d e d t h a t f u r t h e r s t u d y o f t h e d e l t a s t r a k e t i p e f f e c t i v e n e s s b e c a r r i e d o u t . T h i s w a s f o u n d to be t h e b e s t g e o m e t r y f o r s i d e f o r c e a l l e v i a t i o n a n d a s y e t h a s n o t b e e n o p t i m i z e d . D i f f e r e n t l e n g t h s , a s p e c t r a t i o s a n d s h a p e s c o u l d b e t e s t e d t o a r r i v e a t t h e o p t i m u m g e o m e t r y . T h e a p p l i c a t i o n o f t h i s d e v i c e t o a m o d e l o f a n a i r c r a f t n o s e i s a l s o r e c o m m e n d e d f o r s u b s t a n t i a t i o n o f t h e r e s u l t s , v i i ) F u r t h e r s t u d y o f t h e p o r o u s t i p c o n c e p t a s a s i d e f o r c e a l l e v i a t i o n d e v i c e i s r e c o m m e n d e d . P a r a m e t e r s s u c h a s p o r o u s l e n g t h , p o r o s i t y , a n d i t s u s e w i t h o t h e r d e v i c e s r e q u i r e f u r t h e r e x a m i n a t i o n . A f u e l f i l t e r m a d e o f p o r o u s b r o n z e w a s p u r c h a s e d b u t p r o v e d to be o f t h e w r o n g s h a p e a n d s i z e t o i n c o r p o r a t e i n t o t h e e x i s t i n g m o d e l . P e r h a p s a n e w m o d e l t o m a t c h t h e t i p m a y be c o n s t r u c t e d to a s s e s s i t s e f f e c t i v e n e s s . 72 v i i i ) T h e p o r o u s t i p u s e d i n t h e t e s t p r o g r a m w a s ho l low a n d c o n n e c t e d to t h e ho l low c o n e m o d e l . P r e s s u r e w a s c o m m u n i c a t e d n o t o n l y c i r c u m f e r e n t i a l l y b u t a l s o to t h e w a k e o f t h e b o d y t h r o u g h t h e c e n t e r o f t h e m o d e l . It i s r e c o m m e n d e d t h a t t h e e f f e c t o f t h e b a s e p r e s s u r e o n t h e s i d e f o r c e a l l e v i a t i o n c h a r a c t e r i s t i c s b e e x a m i n e d b y i s o l a t i n g t h e p o r o u s t i p c a v i t y f r o m t h e r e s t o f t h e m o d e l , ix) A s t h e s i d e f o r c e r e d u c t i o n t h r o u g h t i p r o t a t i o n i s a n i n t e r e s t i n g p h e n o m e n o n , i t m e r i t s f u r t h e r s t u d y . T h e o p t i m i z a t i o n o f s p i n r a t e a n d n o s e - b o o m l e n g t h h a s n o t b e e n a c h i e v e d i n t h e p r e s e n t s t u d y . It i s r e c o m m e n d e d t h a t t h e s e r e s u l t s be n o n d i m e n s i o n a l i z e d w i t h r e s p e c t t o t h e w i n d s p e e d . x) F i n a l l y , a s t a t e m e n t s h o u l d be made o n a n a n a l y t i c a l / n u m e r i c a l i n v e s t i g a t i o n . E a r l i e r , d u r i n g t h e l i t e r a t u r e r e v i e w , c o m p u t e r m o d e l i n g o f t h e c o m p l e x f low s h o w e d l i t t l e p r o m i s e . H o w e v e r , r e c e n t l y s e v e r a l a u t h o r s h a v e d e v e l o p e d c o m p u t e r c o d e s , a n d c o m p a r e d t h e r e s u l t s o f t h e n u m e r i c a l m o d e l s w i t h t h e e x p e r i m e n t a l d a t a , w h i c h a r e e n c o u r a g i n g . xi) It i s s u g g e s t e d t h a t t h e a p p r o a c h e s p r e s e n t e d b y Newsome a n d A d a m s [25] , a n d F i d d e s [30] s h o u l d b e e x p l o r e d f u r t h e r , p a r t i c u l a r l y w i t h r e s p e c t t o t h e v a r i o u s t i p g e o m e t r i e s a n d t i p r o t a t i o n . If s u c c e s s f u l , t h i s w o u l d f a c i l i t a t e t h e d e s i g n p r o c e s s s i g n i f i c a n t l y . 73 B I B L I O G R A P H Y [1] E r i c s s o n L . E . , a n d Reding J . 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Hussaini and M.D. Salas, Springer-Verlag, New York, 1987, pp. 311-364. 78 A P P E N D I X I: I N T E G R A T I O N O F P R E S S U R E D A T A A s p o i n t e d o u t e a r l i e r , t h e c o n e m o d e l w a s p r o v i d e d w i t h 24 t o 40 p r e s s u r e t a p s d e p e n d i n g u p o n t h e n o s e t i p u s e d . T h e c o n e s u r f a c e w a s d i v i d e d i n t o a n u m b e r o f s e g m e n t s , e a c h s u r r o u n d i n g a p r e s s u r e t a p , w h e r e t h e p r e s s u r e w a s a s s u m e d t o b e c o n s t a n t . T h u s , t h e f o r c e c o n t r i b u t i o n f r o m e a c h s e g m e n t o f t h e c o n e s u r f a c e i s t h e p r e s s u r e m e a s u r e d a t t h e t a p t i m e s t h e a r e a o f t h a t s e g m e n t . T h e p r e s s u r e d o e s v a r y c o n s i d e r a b l y a r o u n d t h e c o n e e s p e c i a l l y i n t h e c i r c u m f e r e n t i a l d i r e c t i o n , h e n c e t h e u s e o f t h i s c o a r s e i n t e g r a t i o n p r o c e d u r e d o e s i n t r o d u c e a d e g r e e o f e r r o r o f a p p r o x i m a t e l y 10%. E a c h p r e s s u r e t a p i s s u r r o u n d e d b y a t r a p e z o i d a l s h a p e d a r e a s e g m e n t . T h e u n e q u a l e d g e s a r e d e s c r i b e d b y a r e g u l a r p o l y g o n o f n s i d e s i n s c r i b e d i n a c i r c l e ( F i g u r e 1-1). T h e p e r i m e t e r (C) o f t h e p o l y g o n a t a r e f e r e n c e l o c a t i o n i i s C i = 2 n R i « S i n ( n / n ) , h e n c e e a c h s i d e (Si) i s g i v e n b y , S i = 2 R i * S i n ( n / n ) , w h e r e t h e r a d i u s (Ri) i s R i = L i * T a n ( 5 ) a n d L i i s t h e c o n e l e n g t h a t s t a t i o n i. T h e a r e a (Ai) o f e a c h t r a p e z o i d i s A i = S i + S(bn) • Hi , w h e r e t h e h e i g h t o f t h e t r a p e z o i d Hi i s : 2 H i = L i - L»»n) T h u s : C o s ( 6 ) A i = ( L i 2 - L ( „ n ) 2 ) T a n ( 6 ) S i n ( n / n ) C o s ( 6 ) 79 T h e r e s u l t a n t p r e s s u r e f o r c e s e x e r t e d u p o n t h e c o n e c a n now b e r e s o l v e d i n t o n o r m a l a n d s i d e f o r c e c o m p o n e n t s a s f o l l o w s : F H = N O R M A L F O R C E * 2 P i • A i • S i n 6i • C o s ( 6 ) ; F s = S I D E F O R C E = 2 P i • A i • C o s 6i • Cos(8); w h e r e 0 i i s t h e c i r c u m f e r e n t i a l a n g u l a r p o s i t i o n o f e a c h p r e s s u r e t a p . E x p r e s s i n g f o r c e s i n t e r m s o f c o e f f i c i e n t s : C N = 2 Cpi • A i • S i n 81 • Cos(6) — ^ — — ^ — — — — — — — — ^ — ; AB C s = 2 C p i • A i • C o s 8t • Cos(6) AB w h e r e AB i s t h e c o n e b a s e a r e a * D 2 / 4 . A s d r a g a n d a x i a l f o r c e s w e r e n o t m e a s u r e d , t h e u s e o f n o r m a l f o r c e i n s t e a d o f l i f t f o r c e i s m o r e l o g i c a l a n d c o n v e n t i o n a l i n t h i s t y p e o f i n v e s t i g a t i o n . T h e F O R T R A N p r o g r a m u s e d t o i n t e g r a t e t h e p r e s s u r e d a t a i s a t t a c h e d . F i g u r e 1-1 D i v i s i o n o f t h e c o n e s u r f a c e i n t o a r e a s e g m e n t s . C PROGRAM TO R E S O L V E FORCES ON A CONE C INTO L I F T DRAG AND S I D E FORCE REAL A ( 4 0 ) , C P ( 4 1 ) , L ( 4 0 ) , T ( 4 0 ) . L I F T , T T ( 1 2 ) , C P P ( 1 2 ) INTEGER ALPHA1.ALPHA2,NOSE,ROLL CHARACTER T E S V 3 0 C A I S THE ARE SURROUNDING EACH PRESSURE TAP C CP I S THE C O E F F I C I E N T OF PRESSURE FOR EACH TAP C L I S THE LENGTH OF EACH AREA SEGMENT MEASURED C FROM THE T I P C T I S THE O R I E N T A T I O N IN ROLL OF EACH TAP C CA I S THE CONE HALF ANGLE C ALPHA 1 I S THE F I R S T ANGLE OF ATTACK FOR EACH T E S T C ALPHA2 I S THE L A S T ANGLE OF ATTACK FOR EACH T E S T C NOSE I S THE NOSE ROLL P O S I T I O N C ROLL I S THE BODY ROLL P O S I T I O N C T E S T I S THE T I T L E OF EACH EXPERIMENT C C C F I R S T FOR THE AREAS P I = 3 . 1 4 1 5 9 2 6 C A = A T A N ( . 2 5 ) L ( 1 ) = 6 . 0 L ( 7 ) = 5 . 0 L ( 1 3 ) = 4 . 1 2 5 L ( 1 9 ) = 3 . 2 5 L ( 2 5 ) = 2 . 2 5 L ( 3 7 ) = 1 . 2 5 DO 1 N=1,5 L ( 1 + N ) = L ( 1) L ( 7 + N ) = L ( 7 ) L ( 1 3 + N ) = L ( 1 3 ) L ( 19 + N ) = L ( 1 9 ) 1 L ( 4 1 - N ) = L ( 3 7 ) DO 6 N=1.11 6 L ( 2 5 + N ) = L ( 2 5 ) DO 2 N=1,24 2 A ( N ) = ( L ( N ) * * 2 - L ( N + 6) "2)'TAN(CA)/COS(CA)/2. DO 3 N=25,36 3 A ( N ) = ( L ( N ) ' * 2 - L ( 3 7 ) * ' 2 ) * T A N ( C A ) ' S I N ( P I / 1 2 . ) / C O S ( C A ) DO 12 N=37 ,40 12 A ( N ) = L ( N ) • * 2 * T A N ( C A ) / C 0 S ( C A ) * S I N ( P I / 4 . ) C C DO LOOP FOR VARIOUS T E S T S C DO 7 J = 1 . 2 4 C C DO LOOP FOR VARIOUS ANGLES OF ATTACK C INPUT ROLL A N G L E , ANGLE OF A T T A C K , NOSE P O S I T I O N C R E A D ( 5 , 7 0 ) T E S T 70 F O R M A T ( A 3 0 ) W R I T E ( 7 . 7 0 ) T E S T READ*.ROLL,ALPHA 1,ALPHA2 WRITEC 7 , 2 5 ) R O L L , A L P H A 1.ALPHA2 25 F O R M A T ( 3 ( I 5 ) ) C C C A L C U L A T E TAP ROLL P O S I T I O N C T ( 1 ) = ( 3 . 0 + R 0 L L ) * P I / 6 . 0 T ( 2 ) = ( 5 . 0 + R 0 L L ) ' P I / 6 . 0 T ( 3 ) = ( 7 . 0 + R O L L ) ' P I / 6 . 0 T ( 4 ) = ( 9 . 0 + R 0 L L ) ' P I / 6 . 0 T ( 5 ) = ( 11 . O + R O L D ' P I / 6 . 0 T ( 6 ) = ( 1 . 0 + R O L L ) * P I / 6 .0 DO 4 N=1.3 T ( 6 * N + 1 ) = T ( 1 ) T ( 6 * N + 2 ) = T ( 2 ) T ( 6 * N * 3 ) = T ( 3 ) T ( 6 * N + 4 ) = T ( 4 ) T ( 6 ' N + 5 ) = T ( 5 ) 4 T ( 6 * N + 6 ) = T ( 6 ) T(25)=T(1)-.3578 DO 9 N=1 ,11 9 T(25+N)=T(24+N)+PI/6. T(37)=T(25) DO 11 N=1,3 11 T(37+N)=T(36+N)+PI/2. DO 21 N=1,40 PI2=2."PI 21 IF(T(N).GE.PI2) T(N)=T(N)-PI2 C C INPUT PRESSURE MEASUREMENTS C DO 7 K=ALPHA1,ALPHA2, 10 READ(5,20)CP 20 FORMAT(12(F10 . 4) ) Q=CP(41) DO 5 N=1,41 5 CP(N)=CP(N)/0 C SORTING OF ANGLES AND PRESSURES LF = 25 DO 22 N=26,36 22 IF(T(LF).GT.T(N)) LF=N DO 23 N=1,12 LFF=LF+N-1 IF(LFF.GT.36) THEN KK=LF+N-13 ELSE KK=LF+N-1 ENDIF TT(N)=T(KK) 23 CPP(N)=CP(KK) WRITE(7,35 )TT 35 FORMAT(12(F10.4) ) WRITE(7,35)CPP C C INTEGRATE FORCES C LIFT=0.0 SIDE=0.0 DO 6 N=1,40 LIFT=LIFT+A(N)"CP(N)*COS(CA)*COS(T(N)) 6 SIDE=SIDE + A(N)'CP(N)'COS(CA)'SIN(T(N) ) CL=LIFT/(2.25'PI) CS=SIDE/(2.25'PI> C C NOW FOR SOME RESULTS C C WRITE(6.60) TEST 60 FORMAT(2X,A30) C WRITE(6,40) ROLL.K.CL.CS 40 FORMAT(5X,'FOR ROLL POSITION ',13,' AND FOR ANGLE 2'0F ATTACK ',13, 3' CL AND CS ARE ',2(F10.4) ) WRITE(7,45)CL , CS 45 F0RMAT(2(F10.4) ) C WRITE(6,50) C 50 FORMAT(' PRESSURE COEFFICIENTS FOR EACH TAP') C WRITE(6.30) CP C 30 FORMAT(6(F10.4)) 7 CONTINUE STOP END 

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