Analytic investigation of helicopter rotor blade appended aeroelastic devices

NASA Contractor Report 166525 I I UTRC Report R84-915774-24

Analytic Investigation of

Helicopter Rotor Blade Appended

Aeroelastic Devices

Richard L. Bielawa United Technologies Research Center EastHartfond, CT m1iN Prepared for Ames Research Center under Contract NASZ-11008 T National Aeronautics and Space Administration Amas Research Center MoftettField. California 94035 PREFACE The results described h e r e i n were performed by United Technologies Research Center (UTRC) under c o n t r a c t NAS2-11008, "Analytic I n v e s t i g a t i o n of Helicopter Rotor Blade Appended A e r o e l a s t i c Devices.'' This c o n t r a c t was through the Ames Research Center of N A S A with M r . Robert H. Stroub a c t i n g a s c o n t r a c t monitor. The program manager f o r t h i s s t u d y was D r . Richard L . Bielawa.

The s t u d y made e x t e n s i v e use of the GOOOPA a e r o e l a s t i c a n a l y s i s developed by UTRC f o r NASA Langley Research Center and the S t r u c t u r e s Laboratory of the USRTL (AVRADCOM) under c o n t r a c t NAS1-16058.

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TABLE OF CONTEXTS Page i ii PREFACE vii LIST OF FIGURES AKD TABLES SUMMARY J INTRODUCTION Background Description of Aeroelastic Devices Analysis Requirements LIST OF SYMBOLS 2 3 MATHEMATICAL DEVELOPMEKT 2 3 Torsionally Active Devices Harmonically Dilational Airfoil Tip 3 7 RESULTS Baseline Rotor Configuration Trimmed Flight Conditions Passive Tuned Tab Control Coupled Tab All-Flying Torsion Tip Harmonically Dilational Airfoil Tip CONCLUSIONS AND RECOMMENDATIONS REFERENCES

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L I S T OF FIGURES AXD TABLES Figure No. T i t l e Page 1. P i c t o r i a l of Tuned T r a i l i n g Edge Tab 2. P i c t o r i d of T r a i l i n g Edge Tab Coupled t o Blade Control Loads 3. P i c t o r i a l of All-Flying Torsion Tip 4 . P i c t o r i a l of H e l i c o p t e r Rotor Disk i n Forward F l i g h t Showing C o n f l i c t i n g Requirements f o r Blade Tip S e c t i o n s 5 . P i c t o r i a l of Harmonically Deformable A i r f o i l Tip 2 5 6. Geometrical and Mechanical Modeling of t h e T o r s i o n a l l y Active Devices 7 . Schematic of E x c i t a t i o n Scheme f o r Harmonically Deformable A i r f o i l Tip Spanwise V a r i a t i o n of 1/2PTP F l a t w i s e Bending Moment f o r 8 .

Trimmed Baseline Cases 4 4 Spanwise V a r i a t i o n of 1/2PTP Edgewise Bending Moment f o r 9.

Trimmed Baseline Cases 10. Spanwise V a r i a t i o n of 4P F l a t w i s e Bending Moment f o r Trimmed Baseline Cases 11. Spanwise V a r i a t i o n of 4P Edgewise Bending Moment f o r Trimmed Baseline Cases 12. S i m p l i f i e d Conceptualization of t h e P a s s i v e Tuned Tab 13. R e s u l t s of S i m p l i f i e d Analysis--Effect of P a s s i v e Tab Spanwise Location on Root Vertical Shears, p 0 . 4 , C /0=.09 T V a r i a t i o n s i n Components of 4P Hub Shear w i t h P a s s i v e 14.

Tuned Tab Mass, 90 m / s F l i g h t Speed ( ~ 0 . 4 ) 15. V a r i a t i o n s i n Components of 4P Hub Shear w i t h P a s s i v e Tuned Tab Uncoupled Tab Frequency, 90 m/s F l i g h t Speed (v-0.407)

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L I S T OF FIGURES A N D TABLES cont inued Figure No. T i t l e Page 16. 5 4 V a r i a t i o n s i n Components of 4P Hub Shear with Passive Tuned Tab Mass Center Location, 90 m / s F l i g h t Speed ( p - 0 . 4 ) 1 7 . E f f e c t of O f f s e t Moment and Spring Rate on Operation of

All-Flying T i p - Preliminary A n a l y s i s

18. E f f e c t of L i n e a r l y Combined O f f s e t Moment and Spring Rate

on Equilibrium Loading Moment f o r All-Flying Tip -

Preliminary Analysis 6 2

19. V a r i a t i o n of LID, with Spring Rate f o r All-Flying Tip -

Preliminary Analysis 20. Comparison of L/D, C h a r a c t e r i s t i c s of All-Flying Tip Using 65 Quasi-Static v s . Unsteady A i r l o a d s Formulations, 90.0 m / s F l i g h t Speed (u=0.407), 0.15R Tip Span.

21. Comparison of Equilibrium Moment C h a r a c t e r i s t i c s f o r All- 67 Flying T i p Using A l t e r n a t e Applied Moments, 90 m/s F l i g h t Speed ( v = 0 . 4 0 7 ) , 0.10R T i p Span 22. Comparison of L/De C h a r a c t e r i s t i c s of All-Flying Tip Using 68 A l t e r n a t e Offset Moment Schedules, 1~10.407, 0.10R Tip Span 23. Comparison of Equilibrium Moment C h a r a c t e r i s t i c s of 69 All-Flying Tip f o r Alternate F l i g h t Speeds and Tip Spans 24. Comparison of L/De Characteristics of All-Flying Tip f o r 70 A l t e r n a t e F l i g h t Speeds and Tip Spans Time-History Responses of All-Flying Tip f o r Alternate 25.

Spring Rates, 0.15R Tip Span, ~ 0 . 4 0 7 v i i i LIST OF FIGURES A?D TABLES continued Page Figure No. Title 7 2 Time-History Responses of All-Flying Tip for Alternate 26, I .

Spring Rates, 0.10R Tip Span, ~ 0 . 4 0 7 7 3 Variation of Time-History Responses of All-Flying Tip 27,

I -

with Flight Speed, Maximum L/De Configuration, 0.15R Tip Span 7 4 28. Variation of Time-History Responses of All-Flying Tip with Flight Speed, Maximum L/De Configuration, 0.10R Tip Span Angle-of-Attack Time-Histories at r = 0.925R for All- 29.

Flying Tip, Maximum L/De Configuration, 0.15R Tip Span, PO. 338 7 7 Angle-of-Attack Time-Histories at r = 0.925R for All- 30.

Flying Tip, Maximum L/De Configuration, 0.15R Tip Span, p=0.407 7 9 Vibratory Blade Bending and Torsion Moment Charac- 31.

teristics for All-Flying Tip, 0.15R Tip Span, p=O. 338, Maximum L/De Conditions 32. Vibratory Blade Bending and Torsion Moment Charac- teristics for All-Flying Tip, 0.15R Tip Span, u-0.407, Maximum L/De Conditions 8 3 Variation of L/De Characteristics of Harmonically 33.

Dilational Tip with Amplitude of Perturbational Thickness Ratio, 0.15R Tip Span, p-0.407.

Comparison of L/De Characteristics of Harmonically 3 4 .

Dilational Tip for Variations in Flight Speed and Tip Span TABLES Table No. Title Page I. Baseline (UH-60A) Rotor Blade Physical Parameters 38 11. Distributions of Geometric and Mechanical Properties for Baseline Rotor Blade 3 9 111. Selected Basic Trim Conditions for the UH-60A Blackhawk Rotor 4 2 Summary of GOOOPA Trim Calculations Achieved for IV .

UH-60A Blackhawk Rotor V. Partial Derivatives of Performance Parameters with Respect 56 Coupling Gain for Control Coupled Tab, ~'0.338 to X -- AXALYTIC IhT'ESTIGATIOK OF HELICOPTER ROTOR BLADE APPENDED AEROELASTIC DEVICES By Richard L. Bielawa United Technologies Research Center S U M M A R Y Analytic e v a l u a t i o n s of f o u r d i f f e r e n t p a s s i v e a e r o e l a s t i c devices appended t o h e l i c o p t e r r o t o r blades i s presented. The devices c o n s i s t of a passive tuned t a b , a c o n t r o l coupled t a b , an a l l - f l y i n g t i p and a harmonic t i p ; each device was conceived f o r improving e i t h e r d i l a t i o n a l a i r f o i l aerodynamic performance, o r reducing v i b r a t o r y c o n t r o l l o a d s o r hub s h e a r s .

The e v a l u a t i o n was performed using a comprehensive r o t o r a e r o e l a s t i c analysis ( t h e G400PA code with a p p r o p r i a t e m o d i f i c a t i o n s ) , t o g e t h e r w i t h d a t a f o r a r e a l i s t i c h e l i c o p t e r r o t o r blade (the UH-60A Blackhawk) i n high s p e e d f l i g h t (90 m / s , 175 k t s ) . The r e s u l t s of t h i s study show t h a t s i g n i f i c a n t performance R e s u l t s f o r t h e (L/De) g a i n s can be achieved with t h e a l l - f l y i n g f r e e t i p .

harmonic d i l a t i o n a l a i r f o i l t i p show t h e p o t e n t i a l f o r moderate improvements i n LID,.

F i n a l l y , t h e r e s u l t s f o r the passive tuned t a b and t h e c o n t r o l coupled t a b , as configured f o r t h i s s t u d y , show these devices t o be i m p r a c t i c a l .

Sections are included which describe t h e o p e r a t i o n of each device, t h e required GOOOPA modifications, and t h e d e t a i l e d r e s u l t s obtained f o r each device.

I NTRODU CT I ON Background It has long been appreciated t h a t so-called conventional h e l i c o p t e r r o t o r s , both a r t i c u l a t e d and h i n g e l e s s , are I n of themselves less than optimal l i f t i n g elements f o r VTOL a i r c r a f t systems. Indeed, t h e b a s i c elements of such conventional r o t o r s o f f e r few design o p t i o n s f o r improvements i n dynamlc/aeroelastic r e l a t e d performance parameters.

t o enhancing t h e s e parameters have t y p i c a l l y State-of-the-art approaches c o n s i s t e d of recourse t o some s o r t of ingenious gadgetry.

One form of such gadgetry c o n s i s t s of i n c o r p o r a t i n g innovative dynamic f e a t u r e ( s ) i n t o the blades themselves, such as a e r o e l a s t i c conformality (Ref. l), o r i n t o t h e i n t e g r a t e d r o t o r system.

Examples of t h e l a t t e r are t h e Advancing Blade Concept (Ref.2) o r the t i l t - r o t o r concept (Ref. 3). A second form of gadgetry c o n s i s t s of t h e appending of a s p e c i a l i z e d aeromechanical device t o a n otherwise conventional (or i t s e l f a e r o e l a s t i c a l l y enhanced) r o t o r blade.

The p r e s e n t emergence of high performance, high s t r e n g t h m a t e r i a l s , t o g e t h e r w i t h an improved a b i l i t y t o analyze and understand t h e physics involved have .

made t h e implementations of such devices more a t t r a c t i v e as design s o l u t i o n s .

An example of a r o t o r blade appended mechanical device which can be r e a d i l y assumed t o be state-of-the-art is the blade pendular absorber ( R e f . 4 ) .

The blade pendular absorber is c h a r a c t e r i z e d by being a purely dynamic device with no d i r e c t aerodynamic i n t e r a c t i o n s and tuned t o o p e r a t e a t n x r o t o r speed frequencies. As such, t h e pendular absorber is i n h e r e n t l y only a p a s s i v e v i b r a t i o n suppression device.

Other blade appended dynamic devices which do involve d i r e c t aerodynamic i n t e r a c t i o n have been conceived, b u t have not a s y e t been subjected e i t h e r t o in-depth a n a l y s i s or experimental proof-of-concept. Reasons f o r t h i s l a c k of t e c h n i c a l underpinning would i n c l u d e the l a c k of a p p l i c a b i l i t y of state-of-the- a r t production o r i e n t e d a n a l y s i s codes, and the d i f f i c u l t i e s i n designing and t e s t i n g workable experimental hardware. A meaningful a n a l y t i c a l study of such devices would r e q u i r e an a p p r e c i a t i o n of their germane c h a r a c t e r i s t i c s and t h e implementation of t h e s e c h a r a c t e r i s t i c s i n a proven comprehensive a e r o e l a s t i c a n a l y s i s of the type p r e s e n t l y u s e d for state-of-the-art r o t o r systems.

The o b j e c t i v e of t h e p r e s e n t study was, t h e r e f o r e , t o determine t h e p r a c t i c a l i t y , both a b s o l u t e and r e l a t i v e , of f o u r (4) d i f f e r e n t passive a e r o e l a s t i c devices appended t o h e l i c o p t e r r o t o r b l a d e s f o r improving r o t o r performance, c o n t r o l l o a d s and/or v i b r a t i o n a l l e v i a t i o n . It w a s believed t h a t the f o u r devices s e l e c t e d f o r t h i s study could o f f e r s i g n i f i c a n t p o t e n t i a l f o r achieving t h e s e improvements. It w a s hoped t h a t t h e study might achieve a s i g n i f i c a n t advance i n h e l i c o p t e r a e r o e l a s t i c s technology through t h e e x p r e s s s e l e c t i o n of only devices which are both p a s s i v e and a e r o e l a s t i c a l l y responsive.

The emphasis on p a s s i v i t y r e f l e c t s t h e d e s i r e t o achieve g a i n s in performance, c o n t r o l l o a d s r e d u c t i o n and v i b r a t i o n a l l e v i a t i o n through the s i m p l i c i t y afforded by fundamental r o t o r blade a e r o e l a s t i c responses i n forward f l i g h t . There undoubtedly e x i s t e q u a l l y f e a s i b l e and p o t e n t i a l l y a t t r a c t i v e concepts f o r b l a d e appended devices which u t i l i z e a c t i v e c o n t r o l schemes t o achieve t h e s e same improvements. However, active c o n t r o l i m p l i e s complexity i n t h e form of a d d i t i o n a l e l e c t r o n i c s and/or h y d r a u l i c s which must u l t i m a t e l y r e s u l t i n i n c r e a s e d c o s t and less a t t r a c t i v e m a i n t a i n a b i l i t y and r e l i a b i l i t y c h a r a c t e r i s t i c s .

"Passive" appended devices would have p o t e n t i a l l y powerful advantages accruing from c o n f i g u r a t i o n s i m p l i c i t y . However, t h e a c t u a l operation of these devices is n e c e s s a r i l y complex s i n c e i n t i m a t e a e r o e l a s t i c i n t e r - a c t i o n between t h e blade proper i s i n t e n t i o n a l l y introduced, This complexity, eoupled with t h e long-standing inadequacies of state-of-the-art r o t o r aero- e l a s t i c s methodology, and t h e l i m i t s of materials and f a b r i c a t i o n techniques have most l i k e l y been t h e major arguments a g a i n s t t h e incorporation o r even s e r i o u s c o n s i d e r a t i o n of these devices i n h e l i c o p t e r blade designs h e r e t o f o r e .

While t h e argument of l i m i t e d material and f a b r i c a t i o n resources i s an important one, i t is deemed beyond the scope of t h e p r e s e n t study. Nevertheless, i t i s t h e r e c e n t emergence of more e f f i c i e n t materials and c o n s t r u c t i o n techniques which has l e d , i n p a r t , t o t h e challenging of t h i s argument and a renewed i n t e r e s t i n such devices. It i s f u r t h e r believed t h a t with t h e s u b s t a n t i a l g a i n s made i n r o t o r a e r o e l a s t i c s methodology w i t h i n t h e l a s t few y e a r s , t h e argument of a n a l y s i s inadequacy is no longer v a l i d .

Description of Selected A e r o e l a s t i c Devices ( 4 ) a e r o e l a s t i c devices were s e l e c t e d f o r a n a l y s i s based upon Four t h e i r conformity t o t h e c h a r a c t e r i s t i c s discussed above. The devices a r e a l l passive i n t h e sense that they are a c t i v a t e d by t h e r o t o r o p e r a t i n g i n its normal f l i g h t envelope without r e q u i r i n g o v e r t a c t i v a t i o n by t h e p i l o t , and t h a t they do n o t use any other energy source except t h a t a r i s i n g from r o t o r r o t a t i o n . The devices seek e i t h e r t o enhance performance, reduce c o n t r o l loads, and/or a l l e v i a t e v i b r a t i o n .

1. Tuned T r a i l ing Edge Tab_ One scheme which could provide v i b r a t i o n a l l e v i a t i o n i s a Tuned ( T r a i l i n g Edge) Tab concept. The o b j e c t i v e of t h i s t a b i s t o create harmonic a i r l o a d i n g of favorable amplitude and phase t o v e c t o r a l l y cancel .

the inherent harmonic a i r l o a d i n g which a c t s as a source of main r o t o r v i b r a t i o n .

P h y s i c a l l y , A schematic of the p a s s i v e t a b concept i s shown i n Figure 1.

t h e p a s s i v e blade t a b i s appended near t o t h e t r a i l i n g edge of a standard r o t o r blade by some hinge c o n f i g u r a t i o n so t h a t t h e t a b can d e f l e c t f r e e l y about e t c . , t h e hinge. The hinge could be mechanical i n n a t u r e w i t h bearings, or it could be made of a composite material t h a t has a l a r g e s t r a i n allowable such t h a t t h e t a b is a c t u a l l y "taped" t o the blade by t h e composite hinge. The l a t i t u d e i n s e l e c t i n g t h e s p r i n g rate of t h e t a b about the hinge would provide dynamic tuning c a p a b i l i t y ; t h e s p r i n g r a t e could be provided e i t h e r mechanically or by t h e e l a s t i c i t y of t h e material f o r a composite hinge.

The b a s i s of t h e concept as o u t l i n e d i n Figure 1 i s simple: When a r o t o r blade t a b d e f l e c t s i t c r e a t e s an incremental a i r l o a d and p i t c h i n g moment on t h e r o t o r blade as a r e s u l t of t h e increased camber. The p i t c h i n g moment a l s o c r e a t e s an a d d i t i o n a l a i r l o a d on t h e r o t o r blade by e l a s t i c t w i s t i n g t o create an incremental angle-of-attack. The importance of t h i s source of a i r l o a d i n g i s c l o s e l y t i e d t o the blade t o r s i o n a l s t i f f n e s s and n a t u r a l frequency, This source of incremental a i r l o a d i n g i s secondary t o t h a t obtained from t h e e f f e c t i v e camber change for t h i s concept. When t h e t a b d e f l e c t s harmonically, t h e a i r l o a d s and p i t c h i n g moment c r e a t e d by t h e t a b d e f l e c t i o n are a l s o harmonic. Therefore, t o d e r i v e b e n e f i t from t h e t a b , the t a b motion m u s t be c o r r e c t l y phased t o cancel t h e i n h e r e n t harmonic a i r l o a d i n g t h a t excites t h e blade f l a t w i s e modes and produces v i b r a t i o n .

The d r i v i n g f o r c e s on t h e t a b are its own i n e r t i a l loading as t h e blade f l a p s and p i t c h e s (both as a r i g i d body and f l e x i b l y ) and t h e aerodynamics a r i s i n g from blade and t a b motion. By i n c r e a s i n g t h e o f f s e t of t h e t a b center of g r a v i t y from t h e hinge t h e i n e r t i a l f o r c i n g can be increased.

For a t a b l o c a t e d a t t h e blade t i p , most of t h e vertical harmonic motion would come from t h e response of t h e f l e x i b l e f l a t w i s e modes and n e a r l y a l l of t h e t o r s i o n motion would be due t o t h e response of t h e blade first t o r s i o n mode. Hence, t h e r e is a d i r e c t r e l a t i o n s h i p between t h e motion t h a t i s i n e r t i a l l y f o r c i n g t h e t a b t o d e f l e c t and t h e v i b r a t i o n t h a t i s a r e s u l t of that same motion.

Therefore, t h e success of t h i s concept hinges on c o r r e c t l y s i z i n g and p l a c i n g t h e t a b along t h e r o t o r blade span and choosing its mass and n a t u r a l frequency so t h a t t h e maximum v e c t o r a l c a n c e l l a t i o n of inherent harmonic a i r l o a d i n g is achieved.

ALTERNATE IMPiEMENTATlON SCHEMES MECHANICAL HINGE COMPOSITE MATERIAL HINGE Figure 1. Pictorial of Tuned Trailing Edge Tab 2. T r a i l i n g Edge Tab Coupled t o Blade Control Loads is l i m i t e d The s e l e c t i o n of a i r f o i l s f o r h e l i c o p t e r main r o t o r blades t o those a i r f o i l s which have low p i t c h i n g moments because a i r f o i l s having .

high p i t c h i n g moments cause excessive blade p i t c h c o n t r o l system v i b r a t o r y loads and high blade t o r s i o n a l d e f l e c t i o n s i n forward f l i g h t , The s e l e c t i o n of a i r f o i l s has t h e r e f o r e been constrained t o t h e use of symmetrical I n a d d i t i o n t o a i r f o i l s or at b e s t , a i r f o i l s having 2 percent of camber.

t h i s fundamental c o n s t r a i n t , h e l i c o p t e r maximum speeds are f r e q u e n t l y l i m i t e d by t h e r a p i d growth of v i b r a t o r y c o n t r o l loads as blade s t a l l i s approached, p a r t i c u l a r l y i n maneuvering f l i g h t . I f t h e s e c o n s t r a i n t s could be eliminated, a i r f o i l s w i t h high camber could be employed and could be s e l e c t e d t o o p e r a t e a t t h e i r optimum l i f t c o e f f i c i e n t s t o delay s t a l l i n g and consequently i n c r e a s e t h e maximum h e l i c o p t e r c r u i s e speed f o r a given The achievement of higher blade loadings through r o t o r blade loading.

t h e use of cambered a i r f o i l s would a l s o permit o p e r a t i o n of t h e r o t o r a t reduced r o t o r n o i s e . Reduction of r o t o r n o i s e i s emerging a s a major requirement f o r c i v i l h e l i c o p t e r s , p a r t i c u l a r l y those i n t h e 20,000 pounds and l a r g e r s i z e c l a s s e s because of l o c a l and f e d e r a l noise r e g u l a t i o n s , The reduction of blade c o n t r o l s y s t e m loads has t h e p o t e n t i a l f o r providing s e v e r a l a d d i t i o n a l advantages. Because of high c o n t r o l s y s t e m v i b r a t o r y c o n t r o l l o a d s many elements of the c o n t r o l system and a i r f r a m e support s t r u c t u r e are l i f e - l i m i t e d . A s i g n i f i c a n t r e d u c t i o n of t h e s e loads would provide unlimited l i f e f o r such components and would probably permit l a r g e weight reductions as well. Furthermore, t h e s e n 0 a c t u a t o r s i z e , weight and power requirements could be reduced. This is p a r t i c u l a r l y s i g n i f i c a n t where redundant c o n t r o l s y s t e m s are required. C o n c o m i t a n t l y , a l a r g e i n c r e a s e i n c o n t r o l s y s t e m r e l i a b i l i t y should be achievable.

A c o n t r o l f o r c e r e d u c t i o n device based on t h e use of a c o n t r o l load coupled t a b system o f f e r s t h e p o t e n t i a l f o r r e l a x i n g t h e c o n s t r a i n t s on t h e use of hinhly cambered a i r f o i l s and of DrOVidinR more r e l i a b l e and l i g h t e r c o n t r o l systems. The control load coupled t a b r o t o r blade as conceived is described below w i t h r e f e r e n c e t o Figure 2. This c o n t r o l f o r c e r e d u c t i o n device o p e r a t e s p r i m a r i l y by sensing t h e c o n t r o l load required t o f e a t h e r t h e r o t o r blade and, through a mechanical l i n k a g e , d e f l e c t i n g t o counter t h e b l a d e p i t c h i n g moment i n a d i r e c t i o n t o reduce t h e c o n t r o l load toward zero. As shown i n Figure 2 t h e f r e e l y f e a t h e r i n g blade i s constrained i n p i t c h a n g l e by means of a c o n t r o l rod which i s a t t a c h e d t o t h e blade p i t c h horn a t one end and t o t h e r o t a t i n g swashplate a t the o p p o s i t e end. The c o n t r o l rod c o n t a i n s a s p r i n g c a p s u l e which d e f l e c t s i n proportion t o t h e c o n t r o l load by an amount which depends on t h e s p r i n g rate. By t h i s means the c o n t r o l rod s h o r t e n s when t h e s p r i n g is compressed and lengthens when t h e s p r i n g is extended.

‘ 6 TAB HINGE AXIS, .

W E PITCH TAB PITCH TAB EKCRANKIN 5 CONTROL ROD SPRING CAPSULE SWASHPLATE DEFLECTED TAB DEPICTION Figure 2. Pictorial of Trailing Edge Tab Coupled to Blade Control Loads A second, but r i g i d , c o n t r o l rod i s a t t a c h e d i n p a r a l l e l w i t h t h e s p r i n g capsule and d r i v e s a tab torque tube. I f t h e spring d e f l e c t i o n I s zero, t h e t a b does n o t d e f l e c t . I f t h e s p r i n g i s compressed, t h e t a b d e f l e c t s t o produce a p i t c h i n g moment i n a d i r e c t i o n t o r e l i e v e t h e load i n t h e c o n t r o l rod. A p a r t i c u l a r advantage of t h i s system i s t h a t t h e c o n t r o l load is driven toward zero r e g a r d l e s s of t h e cause of t h e blade p i t c h i n g moment.

3. All-Flying Torsion Tip This concept, a s analyzed h e r e i n , I s a g e n e r a l i z a t i o n of t h e Free- Tip Rotor concept o r i g i n a l l y s t u d i e d i n Reference 5 , and i s p i c t o r i a l l y depicted i n Figure 3 . The o v e r - a l l o b j e c t i v e of t h i s device i s t h e improvement of r o t o r aerodynamic e f f i c i e n c y by t h e c r e a t i o n of a more uniform a i r l o a d d i s t r i b u t i o n around t h e azimuth of t h e t i p region of t h e blade. This concept i s p r i m a r i l y d i r e c t e d t o t h e a i r l o a d i n g of t h e blade t i p region owing t o t h e recognized p o t e n t i a l f o r n e g a t i v e l i f t i n g l o a d s i n t h i s blade r e g i o n on t h e advancing s i d e i n forward f l i g h t , The attainment of t h e o v e r - a l l o b j e c t i v e f o r t h i s device i s t o be achieved by c o n s t r a i n i n g t h e a l l - f l y i n g t i p t o g e n e r a t e p o s i t i v e l i f t through a c o n t r o l l e d a p p l i e d moment.

A s shown i n Figure 3 , an i n t e n t i o n a l l y introduced o f f s e t between t h e hinge ( p i t c h ) a x i s and t h e aerodynamic c e n t e r , Achord, would e n a b l e t h e l i f t on t h e t i p t o be c o n t r o l l e d by means of t h e applied moment t o t h e t i p : l i f t x Achord = c o n t r o l l e r a p p l i e d moment.

The c o n t r o l l e r a p p l i e d moment i s i n t u r n determined by t h e placement of t h e aerodynamic and mass c e n t e r s of t h e t i p r e l a t i v e t o t h e p i t c h a x i s of t h e t i p , and t h e type of r e a c t i o n moment provided by t h e t i p moment.

I n t h e o r i g i n a l conception of t h e device, a c o n s t a n t t o r s i o n a l moment (preload) r e s t r a i n t is placed on t h e t i p p i t c h a x i s and t h e t i p , t h e r e f o r e , t e n d s t o f l y so as t o provide a nominally c o n s t a n t l i f t .

As analyzed h e r e i n , t h e t i p i s a d d i t i o n a l l y mounted w i t h a f i n i t e t o r s i o n s p r i n g restraint t o be s i z e d relative t o t h e e f f e c t i v e aerodynamic s p r i n g .

Although t h i s d e p a r t s somewhat from t h e c o n s t a n t moment r e s t r a i n t concept defined i n Reference 5 , it n e v e r t h e l e s s r e p r e s e n t s a reasonable g e n e r a l i z a t i o n of t h e o r i g i n a l concept. The p e r t i n e n t performance payoff parameter f o r t h e a l l - f l y i n g t o r s i o n t i p is L/De.

.

AERODYNAMIC CENTER 1 25% CHORD!

RESTRAINT SPRING INBOARD PORTION OF BLADE TIP IN DEFLECTED POSITION Figure 3. Pictorial of All*Flying Torsion Tip ’ 80-4- 13-2 4 . Harmonically Deformable Airfoil Tip As indicated in Figure 4 , the outboard portion of a helicopter rotor blade in forward flight ideally requires two conflicting characteristics for optimal aerodynamic performance: thin sections are required on the advancing side to minimize transonic compressibility effects, and relatively thick, cambered sections are required on the retreating side to achieve high unstalled lift coefficients in low subsonic conditions.

Furthermore, a compromise airfoil with camber would ideally be needed for hovering flight.

The harmonically deformable airfoil tip is a device which seeks to accommodate these conflicting requirements. It could consist of a tip portion of the blade whose airfoil section is so flexibly constructed and tuned as to harmonically deform in response to 1P dynamic pressure variations, As illustrated in Figure 5, the harmonic deformations of the device would be in the thicknesswise directions and would be tailored to produce both overall thickness and/or camber variations.

As conceived, and depicted in Figure 4 , one implementation of the device could be accomplished using an airfoil section construction whose thicknesswise rigidity is controlled by the differential pressure within internal pressure cells attached to the inside of the flexible outer skin.

Increased differential pressure within the cells would cause a thicknessvise contraction (and chordwise elongation) of the airfoil, Camber variations could be obtained by unsymmetric attachments to the inside surface of the flexible airfoil contour skin. Because of the inherently high fatigue stress environment of this device, and the need for high dynamic strains, such.a construction scheme would benefit from composite material techniques.

Of greater importance than the construction techniques, however, are the required dynamic characteristics. Clearly, to produce significant harmonic variations in thickness at lP, the device must be tuned to that frequency. The difficulty arises, however, in the proper phasing of the resonant response. The required response must be approximately 180 deg out-of-phase with the excitation rather than the 90 deg which normally occurs at resonance. That is, the airfoil must contract at the same instant that the 1P dynamic pressure is trying to dilate it.

FREESTREAM VELOCITY REGION OF TRANSONIC FLOW.

~= 180" LOW INCIDENCE ANGLES .*.THIN AIRFOILS NEEDED. LITTLE REGION OF LOW SUBSONIC FLOW.

HIGH INCIDENCE ANGLES r L = O (HIGH Cp S) 2. THICK.

CAMBERED SECTIONS NEEDED Figure 4. Pictorial of Helicopter Rotor Disk in Fonnard Flight Showing Conflicting Requiromonts for Blade Tip Soctions .

80-4- 13-4 TIP SECTION AT k ! ' = 90 ' FLEXIBLE OUTER SKlhi (TYP ) ATTACHMENT POINT INTERNAL CELLS PRESSURiZED TIP SECTION AT IL= 270' I LOCAL DYNAMIC PRESSURE ACTS AS A 1 SUCTION TO DILATE AIRFOIL

INTERNAL CELLS DEPRESSURIZED Y

Figure 5. Pictorial of Harmonically Deformable Airfoil l i p I t i s expected that appropriate gadgetry involving interblade coupling i s required t o achieve passive operation.

S p e c i f i c means f o r achieving t h i s operation are discussed i n the appropriate r e s u l t s subsection. A s with the a l l - f l y i n g t o r s i o n t i p , the pertinent performance payoff parameter f o r t h i s device i s the l i f t t o (equivalent) drag r a t i o , LID,, .

Analysis Requirements Requirements for Present Study As the descriptions of the selected appended aeroelastic devices offered in the above sub section demonstrate, these devices share iden- tifiable characteristics which pertain intrinsically to the requirements , for their successful analysis: The devices each generally comprise a simple dynamic element 1.

(spring-mass-damper) with a single degree-of-freedom descriptor which couples with the aeroelastics of an otherwise conventional state-of-the- art rotor blade.

2. The direct dynamic influence of the aeroelastic devices on the hub harmonic loads is subordinate to their indirect influence via modifi- Hence, cations to blade responses and resulting blade generated hub loads.

rotor-fuselage aeroelastic analysis would provide whereas a fully-coupled, maximum rigor to the analysis, a more simple, conventional hub-fixed approach should yield adequate insights into the relative efficiencies of the devices.

3. Over some spanwise portions(s) of the blade, the incremental aerodynamic loading description must account for the motion of the aeroelastic device. Typically, this incremental loading modifies the basic aerodynamic excitations of the blade (incremental section coefficients) as well as generating airload excitations of the device itself, Furthermore, because the devices would generally be expected to produce abrupt deviations from the otherwise smooth blade geometries, abrupt and concentrated airloadings at these deviations would ensue.

4.

The aerodynamic environment in which these devices (as well as the basic blade itself) operate is essentially unsteady.

Multi-harmonic blade motions and potentially high reduced frequency transient phenomena impact on the operation of the three torsionally active devices and, hence, on their potential merit.

This impact requires an attention to the attenuations and phase lags in both the stalled and unstalled aerodynamic loadings.

5 . The operation of any blade appended device with respect to any one specific performance index cannot be isolated from the inherent of the device. Thus, the aeroelastic analysis must aeroelastic stability be sufficiently comprehensive as to be able to demonstrate any inherent lastability condition caused by a selection of parameters which might otherwise demonstrate superior performance in specific selected payoff parameter.

G4OOPA Rotor Aeroelastic Analysis The analysis selected as the tool for analyzing the four appended devices is the "PA" version of the United Technologies Corporation G400 Rotor Aeroelastic Analysis. As first reported in Reference 6, this basic analysis has evolved into a family of multi-purpose programs directed to the analysis of all major rotor types and complexities with application to helicopters, wind turbines and propellers.

Generally the G400 analyses are formulated on a beam bending-torsion basis and include a rigorous modeling of large, nonlinear and time-varying structural twist. The differential equations of blade bending (flatwise and edgewise) and torsion incorporate the salient features of Reference and are solved using a Galerkin procedure wherein normal "uncoupled" vibration mode shapes and their spanwise derivatives along with the spanwise derivative of the blade (nonlinear) twist are combined to approximate "coupled" blade deflections. The aerodynamic description includes the use of predetermined static airfoil data, constant or variable (multiply harmonic and spanwise variable) inflow and unsteady airload effects (both unstalled and stalled), An important capability of the G400 analysis to the present study is the implementation of a rigorous method f o r including detailed inertial and aerodynamic loadings and internal structural (elastic) characteristics with unlimited attention to nonlinearities. An important contribution to this implementation and to the ability to calculate dynamic loads arising from concentrated load sources such as pendulum absorbers and the herein considered appended devices is the force-integration method for calculating blade stresses and hub loads (Reference 8).

The "PA" version of G400, as reported in Reference 9, was selected for the present study because it provided the best basis for meeting the above itemized requirements. In particular, by virtue of the explicit modeling of pendulum absorbers, this version already incorporated the structuring required to accommodate the differential equations for a single degree-of-freedom dynamic system attached to the rotor blade.

Beyond this existing capability, however, explicit modifications were required and are described in a subsequent section.

LIST OF SYMBOLS Spanwise aerodynamic diffusion matrix for six outermost blade [AI segments. ND.

a a , a Components of inertial acceleration in the "5" coordinate

x5D ' 5 2 5 system. m/s 2 , b Number of blades C Theodorsen function CL/c, C I C Rotor aerodynaxic lift and propulsive force coefficients over PF solidity, respectively.

Damper rate of explicit restraint of torsionally active device, cT Nms/rad.

C Blade section chord, n.

C Chord of appended device, rc T Rotor equivalent drag (see Eq. 19), N.

' e e x2 coordinate of coincident flat-lag hinge or hingeless blade off set point m.

f Equivalent flat plate area for defining aerodynamic drag, K.

Coupling gain for tab motion per root deflection, ED.

GT If Rotor horsepower.

Spring rate of explicit restraint of torsionally active KTD K6T device, (alternate forms), Nm/rad.

Blade root torsion spring to account for control system

Ke

R flexibility, Nm/rad Gain constants used for passive dynamic implementation of the K1' K2 hannonic dilational airfoil tip.

k r k Mass radii of gyration of tab (or tip) mass center inertia ' T ' T about axes parallel and normal to tab chordline, respectively, IC.

c LIST OF SYMBOLS cont inued Uass r a d i i of g y r a t i o n of blade s e c t i o n about axes through and k P k z

y l o 10 perpendicular t o the spanwise (x5) a x i s and i n the chordvise and

thicknesswise d i r e c t i o n s , r e s p e c t i v e l y , m.

L Rotor l i f t , N.

Distance from t a b device hinge a f t t o t a b mass c e n t e r , m.

1, M Mach number M Constant applied moment about hinge f o r t o r s i o n a l l y a c t i v e aPPT device, Xr.

M Residual e l a s t i c moment about hinge r e s i s t i n g aerodynariic res i d and i n e r t i a l o a d s , Nm.

Uass of t h e t o r s i o n a l l y a c t i v e device, kg.

MT M Moment about hinge a x i s of t h e t o r s i o n a l l y a c t i v e device.

X 6T m Reference blade mass d i s t r i b u t i o n , taken t o be t h a t of t h e 5 t h blade segment, kglm.

-

m Blade mass d i s t r i b u t i o n , (ND) n Blade segment index P Per r o t o r r e v o l u t i o n PF Rotor propulsive f o r c e , h’.

Section shear load d i s t r i b u t i o n 6 In d i r e c t i o n s of axes i n t h e 5- c o o r d i n a t e system, (ND) S t a t i c a i r f o i l p r e s s u r e s d e f i n i n g t h e o p e r a t i o n of the harmonic d i l a t l o n a l a i r f o i l t i p , Pa.

LIST OF SYMBOLS cont inued

Q

Q u a s i - s t a t i c a i r f o i l downwash v e l o c i t y f u n c t i o n f o r a i r f o i l s w i t h t a b s , m/s.

E f f e c t i v e a i r f o i l dcrwnwash v e l o c i t y f u n c t i o n f o r a i r f o i l s QE w i t h t a b s , m/s.

A i r f o i l downwash v e l o c i t y f u n c t i o n f o r a i r f o i l s w i t h t a b s , c o r r e c t e d using unsteady decay parameter algorithm, m/s.

Blade j ' t h t o r s i o n modal response v a r i a b l e .

9, R Rotor r a d i u s , m.

m.

Spanxise e x t e n t of appended device, LRT

-

Blade spanwise coordinate, measured from o f f s e t , e, i n x r d i r e c t i o n , (h?))

-

r E f f e c t i v e ( a r e a c e n t e r ) r a d i u s of t h e planform of t h e ef f harmonic d i l a t i o n a l t i p , ND w i t h r e s p e c t t o R .

C r , Cx n ' t h blade spanwise segment ( a r c ) l e n g t h , (KD)

n n F r i c t i o n (Coulomb) damping moment about hinge f o r t o r s i o n a l l y a c t i v e device, Nm.

Components of Blade Root Shears i n (nonrotatin&) l o n g i t u d i n a l ,

s , s 9 s

'1 1 l a t e r a l and v e r t i c a l d i r e c t i o n s , r e s p e c t i v e l y , N.

6 Aerodynamic time Trimmed r o t o r f l i g h t rpeed, m/s 8nd (kts) " T L I S T OF SYMBOLS c m t h u e d Vector of components of incremental displacement of a point In the "5" coordinate system, m.

X Nondimensional blade spanwise station measured from center cen of rotation.

Components of the 5-coordinate system, defined to be rotating with the hub, but at the blade coned and lagged position, (hT) Y Chordwise distance of blade section mass center forvard from " C G the elastic axis, (ND).

Perturbational thickness ratio response for the i'th blade.

'i D Section angle-of-attack, deg and rad Effective aerodynamic section angle-of-attack, Including of unsteady decay parameter, deg.

effects a Quasi-static angle-of-attack, rad.

Q a Aerodynamic section unsteady decay parameter, rad.

k' Prantl-Glauert transformation factor, ( = - 1 E Torsion deflection of torsionally active device, positive @T TE up, rad.

Steady component of torsion related device deflection, rad.

ET Component of tab torsion motion due to ganging with root 8T1 torsion motion, rad.

Deflection mode shape for the j'th torsion normal mode, (hi) LIST OF SYMBOLS continued 0 Total local blade pitch angle, radians.

Rotor advance ratio, (= flight speed/RR) IJ Rotor solidity ( = bc/rR).

TIC Airfoil thickness ratio.

(T/c)~ , (TIC) First hannonic cosine and sine components of perturbational

C Is thickness ratio.

Generalized Wagner function, with compressibility corrections.

eC $ Blade azimuthal (angular) position, rad and (deg) R Rotor rotational frequency, or speed (rpm)

- - -

'*I ~ u V s u E (Nondimensional) uncoupled natural frequencies of i'th f 1acr;ise

'

bending mode, k'th edgewise bending mode and j'th torsion modi, 2 1 Subscripts Arising from aerodynamic loading a Relating to the appended device (tip or tab) ( )T Superscript s Pertaining to dynamic inertia loads Pertaining to elastic restraints Differentiation with respect to (r/R) Perturbational quantity

Kondimensionalization by combinations of m , R and/or C

Differentiation with respect to (at) MATHEMATICAL DEVELOPMEKT For purposes of t h i s study, the required modifications of the G4OOPA a n a l y s i s f a l l i n t o two main c a t e g o r i e s : those needed f o r t h e t h r e e t o r s i o n a l l y a c t i v e devices (tuned t a b , c o n t r o l coupled t a b , and the a l l - f l y i n g t i p ) , and those f o r t h e d i l a t i o n a l s e c t i o n t i p . The first p a r t of t h i s s e c t i o n d e s c r i b e s t h e a d d i t i o n a l formulations r e q u i r e d t o convert t h e e x i s t i n g G400PA formulations f o r a purely mechanical conventional blade appended, pendular absorber t o those f o r an aerodynamically a c t i v e pendular mass whose hinge i s now o r i e n t e d p a r a l l e l t o t h e blade p i t c h axis. These formulations a r e more o r l e s s common t o a l l t h r e e t o r s i o n a l l y a c t i v e devices.

Where noted, some a r e a p p r o p r i a t e l y p e r t i n e n t t o only one o r two of these l a s t p a r t of devices. The t h i s s e c t i o n d e a l s w i t h design c o n s i d e r a t i o n s r e l e v a n t r e l e v a n t t o the d i l a t i o n a l s e c t i o n t i p and w i t h those GOOOPA modifications necessary f o r i t s a n a l y s i s w i t h i n t h e scope o f t h e present study.

Torsionally Active Devices Four b a s i c formulations and subsequent modifications of t h e G400PA were required : Development of the i n e r t i a loadings f o r a pendular mass with an a x i a l l y mounted hinge.

I n c l u s i o n of e l a s t i c and/or coupling c o n s t r a i n t s of the device about t h e hinge.

Extension of c l a s s i c (frequency domain) unsteady a i r l o a d s formulations t o a time-history s o l u t i o n format.

Development of a method for accounting f o r spanwise aerodynamic cross- t a l k e f f e c t s . These arise from t h e abrupt loadings changes a t the boundaries of t h e devices.

Supplementary Assumptions To achieve a s u c c e s s f u l modeling of the t o r s i o n a l l y active devices the following list of assumptions were made ( i n a d d i t i o n t o those s t a t e d i n Reference 9) : 1. The device is a r i g i d body attached t o t h e blade proper a t two p o i n t s as defined by the spanwise c e n t e r s of two s e l e c t e d blade segments, a s t y p i c a l l y used f o r blade segmentation.

The hinge l i n e defined by t h e s e two p o i n t s is nominally p a r a l l e l t o t h e blade (reference) p i t c h a x i s .

2 . The t o r s i o n a l device i s uniform i n p r o p e r t i e s i n the spanwise d i r e c t i o n .

3. For purposes of d e f i n i n g t h e incremental i n e r t i a loads on t h e blade proper due t o device motion, t h e device is approximated by two incremental mass d i s t r i b u t i o n s a t each of t h e two attachment segments, each defined by h a l f t h e device mass.

4. The device is mechanically r e s t r a i n e d t o t h e blade by a p a r a l l e l combination of s p r i n g , damper, f r i c t i o n , constant valued and c o n t r o l coupled moments (see Figure 6 ) .

5 . The normal (uncoupled) mode i n p u t p r e p a r a t i o n c a l c u l a t i o n s f o r t h e blade proper are t o be performed with a blade mass d i s t r i b u t i o n a p p r o p r i a t e t o t h e blade ( a s designed t o i n c l u d e t h e device) but with t h e a c t u a l moveable device mass removed. This moveable device m a s s must then be e x p l i c i t e l y added i n t h e G400PA equation d e s c r i p t i o n .

6. The aerodynamic d e s c r i p t i o n s f o r both t h e device and blade proper should include unsteady e f f e c t s . Because s t a l l f l u t t e r r e p r e s e n t s a "higher-order" dynamic phenomenon beyond t h e scope of t h e p r e s e n t study, t h e a p p r o p r i a t e unsteady e f f e c t s are those two-dimensional formulations based on u n s t a l l e d p o t e n t i a l flow. The c l a s s i c theory of Theodorsen and Garrick (Reference 10) i s an a p p r o p r i a t e b a s i s .

7. Aerodynamic spanwise c r o s s t a l k e f f e c t s are l i m i t e d t o those c i r c u l a t o r y a i r l o a d s accruing only from t h e incremental l i f t l o a d s due t o device d e f l e c t i o n . These c r o s s t a l k e f f e c t s are approximated by a c o n s t a n t (cross- t a l k ) matrix premultiplying t h e (two-dimensional) s t r i p theory incremental spanwise a i r l o a d d i s t r i b u t i o n .

I n e r t i a Load D i s t r i b u t i o n s f o r Pendular Mass The d e r i v a t i o n of t h e dynamic l o a d s a c t i n g on t h e t o r s i o n a l l y a c t i v e device follows from a s t r a i g h t f o r w a r d a p p l i c a t i o n of a p p r o p r i a t e coordinate transformations and d i f f e r e n t i a t i o n s of a p o s i t i o n v e c t o r . Using Equation (35) of Reference 6 a s a s t a r t i n g p o i n t and r e f e r r i n g t o F i g u r e 6, one can write t h e c 83-6-1034 i incremental (nondimensional) p o s i t i o n vector f o r a mass element on t h e t o r s i o n a l device as:

-

- 2 : cos&

sinPT cos@ sinp, - s i n 0 cosp, {ax,} U T - Y ) - cos@ cosp, - sin@ sin@, I sin@sinp, + ~ ~ s @ c o s p ,

- sin@ COS^, + cos@ sin&

0 and f! a r e , r e s p e c t i v e l y , t h e t o t a l p i t c h angle of t h e blade s e c t i o n and t h e (T.E. up) d e f l e c t i o n of t h e t o r s i o n device about the hinge. From Equation (1) can be derived t h e components of incremental i n e r t i a l

a c c e l e r a t i o n , 1AaX5, Aayj, Aaz5j , which arise s o l e l y from the pendular

motion of t h e t o r s i o n a l l y a c t i v e device. Combination of t h e s e incremental a c c e l e r a t i o n components w i t h those components a r i s i n g from motion of the blade i t s e l f d e f i n e s t h e t o t a l i n e r t i a loads a c t i n g on t h e point mass of t h e t o r s i o n a l device.

The inertia moment acting on t h e torsional device about the hinge is obtained by i n t e g r a t i n g the d i f f e r e n t i a l i n e r t i a moments over t h e device c o r s s s e c t i o n a r e a :

Upon expansion of t h e i n e r t i a a c c e l e r a t i o n components (a, , aygB and

az5) i n a Taylor S e r i e s i n t h e chordwise and thicknesswise p o s l t i o n v e c t o r components, y and 2 , r e s p e c t i v e l y , Equation (2) can be w r i t t e n i n t e n n s of conventional mass d e s c r i p t o r s : I Equation (3) i s then used as t h e b a s i s for d e f i n i n g t h e dynamic equation f o r t h e t o r s i o n a l device.

The modifications t o t h e blade modal dynamic equations u t i l i z e supplementary assumption 3 given above. A t each of the two blade spanwise segments wherein t h e device is a t t a c h e d , the i n e r t i a load d i s t r i b u t i o n i s modified t o include t h r e e e f f e c t s : o The incremental load due t o t o r s i o n device motion about t h e hinge using t a b mass and t h e incremental i n e r t i a l a c c e l e r a t i o n components, The combined masses of o t h e blade proper and t h e device t o g e t h e r with the i n e r t i a a c c e l e r a t i o n s of t h e blade proper.

o The e f f e c t i v e change i n combined s e c t i o n center-of-gravity l o c a t i o n (both chordwise and thicknesswise) caused by t a b d e f l e c t i o n .

Elasto-mechanical Torsion R e s t r a i n t s As shown i n Figure 6, f o u r types of elasto-mechanical c o n s t r a i n t s a r e used t o a t t a c h t h e t o r s i o n a l device t o the blade. The t h r e e passive elements, (spring, damper, and f r i c t i o n ) a r e common t o a l l t h r e e t o r s i o n a l l y a c t i v e devices: For t h e a l l - f l y i n g t i p , an a d d i t i o n a l constant moment c o n s t r a i n t ,

M , i s added. This c o n s t a n t applied moment could be implemented through

aPPT t h e use of i n t e r n a l gadgetry which might u t i l i z e t h e c e n t r i f u g a l f o r c e f i e l d , o r by combining t h e t o r s i o n s p r i n g rate, $, t o g e t h e r w i t h a b u i l t - i n t i p d e f l e c t i o n . The combined p a s s i v e restraint is then given by: As can be seen i n Figure 2 , t h e motion of t h e t a b is a c t u a l l y comprised of two p a r t s : a gross motion p a r t , B T ~ , . d i r e c t l y geared by a p p r o p r i a t e b e l l c r a n k i n g to t h e elastic t o r s i o n d e f l e c t i o n of t h e blade a t t h e r o o t , and % a p e r t u r b a t i o n a l p a r t , 8F, governed by t h e p a s s i v e impedances ( s t i f f n e s s and damping) of t h e bellcranking i t s e l f .

The g r o s s motion p a r t of t h e t a b d e f l e c t i o n is, t h e r e f o r e , defined u s i n g blade t o r s i o n mode shapes which are c a l c u l a t e d using r o o t t o r s i o n s p r i n g s .

Such mode shapes have nonzero r o o t (O), which can be geared ghrough a gain parameter, GT, t o d e f i n e j Thus, t h e t o t a l c o n t r o l coupled t a b motion is defined by: the gross motion.

4- P,, + 4

where Time Domain Unsteady Airloads Each of t h e t h r e e t o r s i o n a l l y a c t i v e devices e n t a i l s a s i g n i f i c a n t degree of coupling between the blade f l a t w i s e bending modes and t h e t o r s i o n a l response of t h e device i t s e l f . Consequently, t h e p o t e n t i a l e x i s t s f o r a e r o e l a s t i c i n s t a b i l i t y with t h e s e devices. Such i n s t a b i l i t i e s , moreover, could occur a t response f r e q u e n c i e s s u f f i c i e n t l y high t o warrant t h e i n c l u s i o n s of the l a g s and a t t e n u a t i o n s due t o unsteady aerodynamic e f f e c t s . This is e s p e c i a l l y t r u e f o r t h e p a s s i v e tuned t a b which is t o o p e r a t e a t blade passage frequencies.

The presence of a t r a i l i n g edge t a b w i t h two of t h e t o r s i o n devices, a s a d i s t i n c t aerodynamic element, f u r t h e r d e f i n e s an aerodynamic modeling over and above t h e u s u a l q u a s i - s t a t i c s t r i p theory t y p i c a l l y used for t h e nonappended blade. F i n a l l y , t h e i n c l u s i o n of t h e s e unsteady a i r l o a d i n g and t r a i l i n g edge tab f e a t u r e s is r e q u i r e d i n a time-domain format. A l l t h e G400PA response c a l c u l a t i o n s are performed by (time) i n t e g r a t i n g t h e n o n l i n e a r dynamic equations and t h e aerodynamics must t h e r e f o r e be defined by a p p r o p r i a t e d i f f e r e n t i a l equations.

U n s t e a 3 Decg Parameter

--- -- -----

The approach followed h e r e i n draws upon t h e use of t h e unsteady decay parameter, ow, described i n d e t a i l in R e f . 1 1 and defined as follows: I I 28 This parameter is an equivalent embodiment of t h e Wagner f u n c t i o n (and i t s F o u r i e r transform c o u n t e r p a r t , t h e Theodorsen f u n c t i o n - see Ref. 1 2 ) .

This aw parameter when taken t o g e t h e r w i t h t h e q u a s i - s t a t i c angle-of-attack d e f i n e s an e q u i v a l e n t angle-of-attack: Q ~ = Q ~ - Q , which when used q u a s i - s t a t i c a l l y produces a i r l o a d s which c l o s e l y approximate t h e unsteady l o a d i n g s r e s u l t i n g from i n d i c i a 1 responses (Wagner problem) as w e l l a s s i n u s o i d a l ones (Theodorsen problem).

T r a i l i n g Edge Tab E f f e c t s

- - - - - - - - - - - - -

I n t h e Ref. 10 formulation f o r t h e unsteady aerodynamic loading f o r a two-dimensional a i r f o i l w i t h t a b , t h e e f f e c t s of c i r c u l a t o r y unsteady e f f e c t s are seen t o be contained i n t h e s i n g l e product CQ. This product c o n s i s t s of t h e f a m i l i a r Theodorsen f u n c t i o n , C , and a f u n c t i o n Q which i s analogous t o a product of t h e q u a s i - s t a t i c angle-of-attack (without t a b ) , aQ, and t h e f r e e s t r e a m v e l o c i t y , V . This analogy s u g g e s t s t h e h e u r i s t i c approach s e l e c t e d h e r e i n f o r combining t h e unsteady decay parameter approach described above w i t h t h e formulations of Theodorsen and G a r r i c k (Ref. 10).

S p e c i f i c a l l y , but f o r t h e CQ terms i n t h e e q u a t i o n s f o r l i f t , moment and t a b moment given by Theodorsen and Garrick, a l l o t h e r terms are a l r e a d y d e f i n e d i n t h e t i m e domain. The CQ term is r e d e f i n e d i n t o t h e time domain by means of a n e q u i v a l e n t Q : Q , = Q - Q , where J u s t as aE is used q u a s i - s t a t i c a l l y t o i n c l u d e unsteady e f f e c t s , so t o o is t h e QE parameter used as a s u b s t i t u t i o n f o r t h e CQ frequency-domain defined product .

Spanwise C r o s s t a l k E f f e c t s As demonstrated by References 13 and 1 4 , t h e s o l e use of s t r i p theory cannot adequately d e s c r i b e t h e a i r l o a d i n g i n t h e v i c i n i t y of e i t h e r boundary I n such i n s t a n c e s t h e incremental loadings p r e d i c t e d over t h e of t h e t a b .

span of t h e t a b are r e a l i s t i c a l l y d i f f u s e d over t h e a d j a c e n t p o r t i o n s of t h e blade (or wing). This has t h e r e s u l t t h a t t h e a c t u a l e f f e c t i v i t y of t h e t a b is somewhat reduced from what would be c a l c u l a t e d u s i n g s t r i p t h e o r y .

The r i g o r o u s accounting of t h e three-dimensional c h a r a c t e r i s t i c s of a d e f l e c t e d t a b on a h e l i c o p t e r r o t o r blade i n forward f l i g h t does n o t y e t e x i s t and some form of " f i r s t order" approximation is r e q u i r e d . The approach used h e r e i n is based on a "spanwise d i f f u s i o n " m a t r i x , which when post- m u l t i p l i e d by t h e two-dimensional loading d i s t r i b u t i o n v e c t o r g i v e s an approximation t o t h e three-dimensional loading. As p e r supplementary assumption 7 given above, t h i s spanwise d i f f u s i o n matrix, A, is a p p l i e d only t o t h e incremental loading caused by device d e f l e c t i o n : The a c t u a l spanwise d i f f u s i o n m a t r i x used f o r the c a l c u l a t i o n s t o be discussed i n t h e next s e c t i o n was c a l c u l a t e d using NASA s u p p l i e d test d a t a f o r a Blackhawk h e l i c o p t e r r o t o r blade f o r t h e s i x (6) outboard segments s e l e c t e d : .510 .094 .0285 .0239 .0096 .500 .160 .080 .028 .187 .493 .148 ,056 ,180 .370 .002 .050 .146 ,080

.050 .0563 . l o 7 . .170 .243

,120 .150 ,205 .395 .600 ,100 where d d i s t r i b u t i o n due ( t a b ) d e f l e c t i o n { ApZr 1 = Incremental a i r l o ~~ 3 f l a p -'a f o r segments 10 through 15. Note t h a t t h e selected spanwise segmentation is as follows: = [ 0 . 0 5 , 095, . 0 5 , - 0 5 , .04, .01 J 10-15 Harmonically Dilational Airfoil Tip In contrast to the three torsionally active devices the operation of the harmonically dilational airfoil tip does not involve potential encounters with any known unstable aeroelastic phenomena. Thus, any aeroelastic or rather aeromechanical instabilities of this device would be governed by the type of excitation scheme used and would not necessarily be inherent in the concept itself. Thus, the focusing of the analysis on the dynamics of any one type of excitation scheme would appear to be inappropriate to the intent of the present study (i.e., to assess the aerodynamic performance payoff of the device). For this reason no incorporation of the dynamics of a potentially practical excitation scheme was made in the GOOOPA program. Instead, the response of the dilational tip was modeled directly wherein the amplitude and phases were input for parametric variation, For completeness, however, a potential scheme for excitation was conceived as part of this study. In the subsections to follow the actual program modifications incorporated are first discussed. Then, the potential scheme for passive excitation is described.

Variable Airfoil Thickness Ratio The original GOOOPA storage and utilization of static airfoil data consisted of multi-variable tables of CQ, Cd, and aerodynamic coefficients.

Interpolation table look-up was based on selected radial station (airfoil type variation), Mach number, and angle-of-attack. For analysis of the harmonically dilational airfoil tip, the table look-up organization and interpolation with regard to radial station variation, rn, was replaced by thickness ratio variation, T / C : C q ( M 9 Q 9 rn ) -.I Cq ( M 3 Q 9 r / C ) Further, the total where q refers to either aerodynamic type ( a , d , mc/4).

thickness ratio was assumed to consist of a steady value, (T/C)~ which is dependent on span, and a perturbational part which varies dynamically in accordance with the operation of the device.

Assuming the total thickness ratio to be limited by minimum and maximum values, the total thickness ratio is expressible as: where The implementation of Eq. (14b) r e q u i r e s t h e d e f i n i t i o n and i n p u t of a spanwise d i s t r i b u t i o n a r r a y , ( T / c ) ~ ~ , f o r t h e d e s c r i p t i o n of t h e b a s e l i n e r o t o r blade, and a d e f i n i t i o n of a harmonic r e p r e s e n t a t i o n f o r the p e r t u r b a t i o n p a r t : The c o e f f i c i e n t s , A ( T / c ) l C and A(T/C)lS, a r e t h u s t h e c y c l i c components of harmonic a i r f o i l d i l a t i o n . Together w i t h t h e spanwise e x t e n t of t h e d i l a t i o n a l t i p , t h e s e c y c l i c components f o r n the p r i n c i p a l parameters t o be v a r i e d i n t h i s study.

Preliminary Conception f o r Implementation As schematically depicted i n Fig. 7 , a preliminary concept f o r implemen- t a t i o n of t h e device would u s e an a i r f o i l c o n s t r u c t i o n whose thicknesswise r i g i d i t y i s c o n t r o l l e d by t h r e e pressures: The p r e s s u r e p1 p1, p2, and p3.

i s t h e s t a t i c p r e s s u r e o u t s i d e t h e f l e x i b l e o u t e r s k i n and is chordwise l o c a t i o n dependent.

The p r e s s u r e i n s i d e t h e i n t e r n a l p r e s s u r e cells is denoted as p2 and t h a t i n s i d e t h e a i r f o i l , but o u t s i d e t h e i n t e r n a l p r e s s u r e cells is denoted as p3.

Increased d i f f e r e n t i a l p r e s s u r e s w i t h i n and o u t s i d e t h e p r e s s u r e cells (Ap = pz-p3) would cause a thicknesswise c o n t r a c t i o n (and chordwise elongation) of t h e a i r f o i l .

3 2 l h i T E 9 1 0 4 OF TYPICAL INTERNAL CELL P EXTERIOFi OF INTERNAL CELL P3

2 7 A -

EXTERIOR OF SKIN. P1

< - & + -

\ / ', ' '. #'

(ADVANCING SIDE, SECTION A-A A / ARE CONNECTED TO INNER PORTIONS OF INTERNAL CELL AIR BLADE ARE RIGID VOLUMES OF RESPECTIVE FOLLOWING B L ~ D E S EXTERIOR TO CELL AIR VOLUMES OF OPPOSING TIPS ARE C O Y k E Z T E C BLADE RAM (TOTAL) PRESSURE

ORIFICE (TYP) r

' 0 PRAM = P, + 1QP UT WHERE UT, = I!R [ r + Fsn (4 + 1x12) 1 HAS 1P AND 2P COMPONENTS "TI 1=4

I (RE1 'REATING SIDE)

Figure 7. Schomatic of Excitation Scheme for Harmonically Doformabie Airfoil Tip 81 -1 2-0-1 Because of the i n h e r e n t l y high f a t i g u e s t r e s s environment of t h i s device and the need f o r high dynamic s t r a i n s , a c o n s t r u c t i o n scheme u t i l i z i n g compo- s i t e materials might be employed, Furthermore, because the device must main- t a i n a reasonably smooth a i r f o i l contour w i t h i n the d i l a t i o n a l range, t h e o u t e r a i r f o i l s k i n would have t o be s t r u c t u r a l l y r e i n f o r c e d between the i n t e r n a l c e l l t o s k i n attachment p o i n t s .

O f equal importance t o t h e s e c o n s t r u c t i o n c o n s i d e r a t i o n s , however, a r e t h e required s t a t i c and dynamic c h a r a c t e r i s t i c s . S t a t i c a l l y , the a i r f o i l m u s t maintain i t s "compromise" thickness r a t i o , roughly halfway between t h e f u l l y d i l a t e d and contracted p o s i t i o n s ( a s defined i n hovering f l i g h t ) , i n a l l f l i g h t conditions. That i s , i t must n o t become d i l a t e d due t o t h e b a s i c s t e a d y component of dynamic p r e s s u r e . Dynamically, t h e a i r f o i l must o s c i l l a t e with s i g n i f i c a n t harmonic v a r i a t i o n s i n thickness a t a once p e r r e v (1P) frequency, and, hence, must be tuned t o r e s o n a t e a t t h a t frequency. A requirement i n implementing such a device s u c c e s s f u l l y arises, however, i n t h e proper phasing of t h e resonant response. The required response m u s t be approximately 180 degrees out-of-phase w i t h t h e e x c i t a t i o n from t h e o u t e r s t a t i c p r e s s u r e , p l , r a t h e r than the 90 degrees which would normally occur from t h i s e x c i t a t i o n .

An implementation of t h i s device which p o t e n t i a l l y s a t i s f i e s t h e s e requirements i s based on a four-bladed r o t o r c o n f i g u r a t i o n as shown i n Fig. 7.

This implementation c o n s i s t s of t h e following elements: (1) t o t a l o r "ram" p r e s s u r e o r i f i c e s l o c a t e d on each blade a t o r near t h e s t a g n a t i o n p o i n t on the leading edge, as f a r outboard along the blade as i s p r a c t i c a l ; ( 2 ) connections of t h e s e ram p r e s s u r e o r i f i c e s t o t h e i n t e r n a l c e l l s of t h e i r r e s p e c t i v e following blades; and (3) i n t e r c o n n e c t i o n s of t h e p3 i n t e r n a l p r e s s u r e s between opposite blades.

This Implementation s a t i s f i e s t h e phasing requirement i n t h a t t h e c o n t r a c t i o n a l e x c i t a t i o n , 1P v a r i a t i o n i n P 2 - ~ 3 , is applied 90 deg i n phase ahead of when t h e c o n t r a c t i o n i s t o occur. Furthermore, t h e use of r a - pressure f o r t h e I n t e r n a l c e l l p r e s s u r e , p2, acts t o s t a b i l i z e t h e a i r f o i l s t a t i c a l l y i n hover. The interconnection of t h e p3 p r e s s u r e of t h e opposing blades serves t h e f u n c t i o n of g i v i n g t h e i n t e r n a l (p=p3) air, i n e f f e c t , a harmonic accumulator so t h a t t h e a i r f o i l can undergo a 1P volume change w i t h n e g l i g i b l e impedance, I n e f f e c t t h i s implementation i n s u r e s t h a t t h e ApCpz-p3) p r e s s u r e d i f f e r e n t i a l is p r o p o r t i o n a l t o t h e dynamic p r e s s u r e (=%pV2) a t t h e preceding b l a d e , A s i m p l i f i e d mathematical modeling of t h e p e r t u r b a t i o n a l t h i c k n e s s r a t i o , ( Z = A ( - K / C ) ) assumes t h a t f o r t h e i t h blade, Zi is governed by a b a s i c a l l y second order l i n e a r d i f f e r e n t i a l equation w i t h e x c i t a t i o n sources from s t a t i c and blade advanced ram p r e s s u r e s : where t h e e x c i t a t i o n components a r e given by: Note t h a t t h e dynamic e x c i t a t i o n of t h e i t h blade given i n Eq. (17) uses t h e o r i f i c e ram p r e s s u r e from t h e ( i + l ) t h blade. Note a l s o that t h e s t a t i c p r e s s u r e e x c i t a t i o n i s p r o p o r t i o n a l t o t h e t o t a l t h i c k n e s s r a t i o , ( T / c ) . Thus, t h e s e c t i o n d i l a t i o n a l p r e s s u r e i s i t s e l f p r o p o r t i o n a l , i n p a r t , t o t h e perturba- t i o n a l d i l a t i o n , Z i .

The above mathematical modeling r e p r e s e n t s a f i r s t c u t a t d e f i n i n g t h e physics of t h e device. The v a r i o u s c o n s t a n t s used i n E q s . (16) through (18) can p r e s e n t l y only be roughly estimated.

These e q u a t i o n s could have been implemented i n t h e GOOOPA a n a l y s i s and, with a p p r o p r i a t e e s t i m a t i o n s of t h e c o n s t a n t s , solved as p a r t of t h e aeromechanics of t h e d i l a t i o n a l t i p . This approach, however, was deemed o u t s i d e t h e p r i n c i p a l scope of t h i s study and was, t h e r e f o r e , deferred t o a more i n t e n s i v e d e s i g n study and e v a l u a t i o n of t h i s device.

RESULTS Baseline Rotor Configuration For t h e purpose of providing a numerical v e h i c l e f o r e v a l u a t i n g t h e f o u r a e r o e l a s t i c appended d e v i c e s , t h e Blackhawk UH-60A r o t o r blade w a s s e l e c t e d .

This p a r t i c u l a r s e l e c t i o n was made based on t h e timely a v a i l a b i l i t y of t h e d a t a , and on t h e f a c t t h a t t h i s r o t o r r e p r e s e n t s a r e l e v a n t , s t a t e - o f - t h e - a r t , conventional ( a r t i c u l a t e d ) b l a d e design. The a p p r o p r i a t e basic b l a d e geometry and dynamic d a t a f o r t h i s blade are summarized i n Tables I and 11. Table I p r e s e n t s t h e b a s i c g r o s s d e s i g n parameters which s i z e and dynamically d e f i n e t h e b a s e l i n e r o t o r blade. A s t h i s t a b l e Implies, t h r e e f l a t w i s e (uncoupled) modes, one edgewise mode and one t o r s i o n mode, were used t o approximate t h e elasto-mechanics of t h e blade. Table I1 p r e s e n t s t h e d e t a i l e d d i s t r i b u t i o n of p e r t i n e n t geometric and mechanical ( r e f e r e n c e ) blade p r o p e r t i e s used i n t h e c a l c u l a t i o n s . I n subsequent c a l c u l a t i o n s f o r each of t h e d e v i c e s under c o n s i d e r a t i o n , v a r i o u s of t h e s e e n t r i e s were a p p r o p r i a t e l y altered t o accommodate t h e p h y s i c a l c o n s t r a i n t s r e q u i r e d by t h a t device.

T r i m e d F l i g h t Conditions S e l e c t i o n of Cases Each of t h e f o u r appended d e v i c e s w a s conceived f o r a t t a i n i n g improvements i n some type of performance index, e i t h e r dynamic o r aerodynamic, g e n e r a l l y a t t h e high speed end of t h e f l i g h t envelope. Accordingly, two b a s i c trimmed f l i g h t c o n d i t i o n s , which a c c e n t u a t e t h e high speed a s p e c t , were selected f o r e v a l u a t i n g t h e p o t e n t i a l g a i n s a c h i e v a b l e w i t h t h e s e l e c t e d d e v i c e s . Table 111 below summarizes t h e t r i m c o n d i t i o n s s e l e c t e d f o r t h e UH-60A r o t o r . Note t h a t t h e trims are defined f o r c o n d i t i o n s a t 1219 m (4000 f t ) altitude and 95 d e g temperature : TABLE I BASELIh’E (UH-60A) ROTOR BLADE PHYSICAL PARAMETERS Design Parameters Full Scale Values Tip Speed, RR, m ! s (f/s) 221.0 (725) Rotor Speed, R , rpm 258.0 No. of Blades, b Radius, R, m (ft) 8.179 (26.833) Chord, c, m (ft) 0.527 (1.73) Solidity, u 0.0821 Blade Root Offset, e 0.0466R Pitch-Flap Coupling, 8 -0.0170 Pitch-Lag Coupling, 86 -0.030 Lag Damper Rate, Nms/rad (lbf-ft-s/rad) 3401.7 (2509) Effective Blade Twist, el, deg -12.8 Parameters Calculated or Estimated 1st Flatwise, uw1, Hz 12.08 (2.809P) 2nd Flatwise, Ww2, Hz 21.14 (4.915P) 3rd Flatwise, L’w3, Hz 33.09 (7.696P) 1st Edgewise, %I, Hz 19.80 (4.604P) 1st Torsion, Hz 18.14 (4.218P) Is t Edgewise Mode 0.02 Other

---

2 2 10.642 (0.22226) Reference Mass Distribution, mo, kg/m (lb-sec /ft ) Root Torsion Motion, 1st Torsion Mode, Y e . (0) 0.4104 TA2LE I1 DISTRIBUTIONS OF GEOMETRIC AND MECHANICAL PROPERTIES FOR BASELINE ROTOR BLADE .

t l c n o c g

T ; ; I -

I

1 .1434 ,1183 .0186 3 ,0945 -. 0001

3.0249 ,00570 2 ,1100 ,2450 .06447 .0945 .9496 -.0033 .01320 .0945

3 .loo0 .3500 ,06447 ,9638 - -0033 .01340

4 .06447

.loo0 ,4500 ,0945 .9683 - 0033 ,01350

.5250 .06447 .0955 1.0000 -. 0019 ,01360

6 .0500 ,5750 .06447 .0955 -. 0016

,9779 .01370 7 .0500 ,6250 .06447 .0955

.9903 -. 0016 ,01365

8 ,0500 .6750 .06447 .0955 1.0520 .0014 .01350 9 ,0500 ,7250 .06447 .0955 1.2324 .0015 ,01440 10 .06447 .0955 .0500 .7750 1.2331 ,0015 .01466 ,0500 ,8250 .06447 .0955 1.2270 ,0013 .01470 12 .0500 .8750 .06447 .0950 1.4755 .0030 01388 13 .0500 .9250 .06447 ,0945

1.6298 - . 0010 .01410

.0400 ,9700 .06447 ,0945 1.2923 -. 0010 .01340

15 ,0100 .9950 ,06447 .0945 0.3784

- .OOlO .01390

TABLE I11 SELECTED B A S I C TRIM CONDITIONS FOR THE U P 6 0 A BLACKHAWK ROTOR Case Prop Force L i f t VT 2 f 2 No. m/s(kts) m (ft 1 N (1bf) N(lbf) C L I U 1 5275(1186) 77404(17401) 0.09314 74.6(145) 2.54(27.4) 2 90.0(175) 1.84(19.8) 5553(1248) 77404(17401) 0.09314 Rolling and p i t c k i n g moments a r e each t o be trimmed t o zero with a t o l e r a n c e of 4067 Nm (3000 l b f f t ) .

These b a s i c t r i m c a s e s were f u r t h e r expanded depending on t h e type, of o p t i o n a l aerodynamic refinement included i n t h e c a l c u l a t i o n , For each f l i g h t speed, t h r e e subcases were defined as A, B, o r C i n accordance w i t h t h e aero- dynamic d e s c r i p t i o n , r e s p e c t i v e l y , being (A) q u a s i - s t a t i c a i r l o a d s , no v a r i a b l e inflow, (B) u n s t a l l e d unsteady a i r l o a d s , no v a r i a b l e inflow, and (C) u n s t a l l e d unsteady a i r l o a d s , w i t h (quasi) v a r i a b l e inflow. These t h r e e subcases were a l t e r n a t e l y used f o r gaging t h e a p p r o p r i a t e performance i n d i c e s of t h e devices according t o t h e accuracy refinements, r e s p e c t i v e l y , r e q u i r e d by each. The q u a s i - s t a t i c (A) subcases were used f o r t h e harmonically deformable t i p . The unsteady a i r l o a d s (B) subcases were g e n e r a l l y used f o r t h e t h r e e t o r s i o n a l l y a c t i v e d e v i c e s and t h e (C) subcases were used f o r i s o l a t e d c a l c u l a t i o n s f o r t h e a l l - f l y i n g t o r s i o n t i p . For t h e (C) subcases, t h e v a r i a b l e inflow c a l c u l a t i o n s were performed using t h e UTRC P r e s c r i b e d Wake Rotor Inflow Analysis (RIA) described i n Ref. 15.

The v a r i a b l e inflow d a t a i n p u t t o G4OOPA were f i r s t c a l c u l a t e d i n t h e R I A with a trimming procedure using t h e Table I11 values. By t h i s procedure, v a r i a b l e i n f l o w d a t a c o n s i s t e n t w i t h t h e trimmed c o n d i t i o n s were obtained f o r use i n G400PA. It should be s t r e s s e d t h a t t h i s procedure r e p r e s e n t s a n a d hoc method f o r i n c l u d i n g v a r i a b l e inflow i n t h e a e r o e l a s t i c code. The u s u a l , more a few i t e r a - r i g o r o u s method f o r i n c l u d i n g v a r i a b l e inflow t y p i c a l l y r e q u i r e s t i o n s between t h e r o t o r inflow a n a l y s i s and t h e a e r o e l a s t i c code u n t i l convergence (consistency) i s reached. This procedure, however, is q u i t e CPU t i m e i n t e n s i v e even without t h e f u r t h e r onus of having t o t r i m t h e two analyses. Consequently, because of t h e l i m i t e d r e s o u r c e s a v a i l a b l e t o t h i s study t h e h e r e i n ad hoc method was i n s t e a d used, i n hopes of o b t a i n i n g a t least a " f i r s t - c u t " i n d i c a t i o n of t h e e f f e c t s of v a r i a b l e inflow. To d i s t i n g u i s h t h e r e s u l t s obtained h e r e i n from those which would be obtained u s i n g t h e more r i g o r o u s procedure they a r e r e f e r r e d t o as "quasi" v a r i a b l e i n f l o w r e s u l t s , It should be f u r t h e r s t r e s s e d t h a t t h i s a d hoc method f o r i n c l u d i n g v a r i a b l e inflow would produce r e s u l t s which are approximately c o r r e c t In G400PA only a t t h e r e s p e c t i v e trimmed f l i g h t c o n d i t i o n s .

Calculated R e s u l t s The r e s u l t s of t h e s i x t r i m c a l c u l a t i o n s are summarized i n Table I V and Table I V p r e s e n t s t h e actual hub f o r c e s and moment F i g u r e s 8 through 11.

achieved ( t o be compared with r e s p e c t i v e v a l u e s from Table 111). Generally, t h e hub moments could be obtained t o w i t h i n t h e s e l e c t e d t o l e r a n c e s only f o r t h e lower 145 k t f l i g h t c o n d i t i o n . Obtaining convergent trims a t t h e higher 175 k t f l i g h t .speed c o n d i t i o n s was a c o n s i s t e n t l y d i f f i c u l t procedure through- o u t t h i s study. The d i f f i c u l t y experienced i n achieving s y s t e m a t i c convergence i s believed t o be r e l a t e d t o t h e increased e x t e n t of s t a l l experienced on t h e r e t r e a t i n g blade s i d e a t t h i s f l i g h t speed, which thereby r e n d e r s t h e t r i m p r o c e s s h i g h l y n o n l i n e a r . O f p a r t i c u l a r u s e f u l n e s s i n t h i s t a b l e are t h e b a s e l i n e v a l u e s of l i f t p e r e q u i v a l e n t drag, LID,, of median and &PTP r o o t t o r s i o n moment, M, (0), and of t h e 4P amplitudes of t h e components of hub s h e a r s , Sxl, Syl, and Szl.

Note t h a t t h e l i f t p e r e q u i v a l e n t drag, LID,, accounts f o r r e q u i r e d r o t o r power and is d e f i n e d as: L

‘Oe = 325.647 W / VT - PF

Table I V c l e a r l y shows t h e s t r o n g impact of v a r i a b l e i n f l o w on LID,, median r o o t t o r s i o n moment, and 4P v e r t i c a l hub load c a l c u l a t i o n s . F i g u r e s 8 and 9 show t h e %PTP f l a t w i s e and edgewise bending moments, r e s p e c t i v e l y , f o r t h e s i x t r i m c o n d i t i o n s defined i n Table I V . Since t h e %PTP v a l u e s i n c l u d e c o n t r i - f r o m all harmonics, F i g u r e s 10 and 11 p r e s e n t only t h e 4P amplitudes b u t i o n s of f l a t w i s e and edgewise bending moments, r e s p e c t i v e l y , as a n a l t e r n a t e b a s i s f o r i n t e r p r e t i n g and e v a l u a t i n g t h e performance of t h e appended devices. I n the s u b s e c t i o n s t o f o l l o w t h e r e s u l t s w i l l be nondimensionalized, where p o s s i b l e , by t h e a p p r o p r i a t e b a s e l i n e v a l u e s given i n e i t h e r Table I V o r Figure 8 through 11.

TABLE I V SUMMARY OF G4OOPA TRIM CALCULATIONS ACHIEVED FOR UH-60A BLACKHAWK ROTOR T r i m Case 1 A

1 B 1c 2A 2 B

2c 74.6 90.0 (145) (175) Advance Ratio, u 0.338 0.407 Unsteady Airloads N Y Y N Y Y Quasi-Variable I n f l o w K N Y N N h’ Hub Moment, Nm, 2252 764 348 4603 5300 3626 (lbf-f t ) (1661) (563) (25 7 1 (3394) (3909) ( 2 6 7 4 ) CLi u 0.0885 0.0944 0.0915 0.0961 0.0950 0.0881 0.00661 0.00633 0.00643 0.00764 0.00679 0.00653

‘PF’ ‘

L/D, 7.184 7.417 9.919 6.684 6.572 5.405 -580.0 -542.1 - 4 1 7 . 1 -661.8 -655.0 -492.7

$5 : ; : ; - : )

(-5133) (- 47 98) (-3692) (-5857) (-57 97 ) (-4361) 694.4

9p 04x5 (0) 1 , h, 656.8 668.0 984.3 903.4

809.0 ( l b f - i n ) (6146) (5813) (5912) (8712) (7996) (7160) (4), N 1157 1312 78 3 2082 1948 1517 (260) (295) (176) (468) (4 38 1 (341) 930 54 7 1366 1 4 7 2 (117 1 (209) (123) (307) (331) (268) 351 377 816 314 234 94 0 (78.9) (84.8) (183.4) (70.7) (52.8) (211.21)

levice ---- AEp&aiiliLy

? a s s i v e Tuned Tab X X X X :ontrol Coupled Tab X X X X Ul-Flying Tip krmonic D i l a t i o n a l X X A i r f o i l c CASES 1A. 1B. IC V T = 7 4 6 m/s

-

CASES 2A. 28. 2C VT = 90 0 mis 2c 2A ’ I I I I 1.o 0 0.2 0.4 0.6 0.8 NONDIMENSIONAL SPANWISE STATION, r Figure 8. Spanwire Variation of 1IZPTP Fiatwise Bending Moment for Trimmed Baseline Cases 4 3 03-6- 103- 10 5c C A S E S l A 18 1C V T = 7 4 6 m / s 4c

‘\ \\

“b -

X E ’0

‘\ \

z b- z w I 0 0

z

/- -

\ CASES 2A. 2 8 2C V T = 90.0 m/s / \ /

28 ’

I I I I OO 0.2 0.4 0.6 0.8 1 .o NONDIMENSIONAL SPANWISE STATION, r Figure 9. Spanwire Variation of 1lPPTP Edgewise Bending Moment for Trimmed Basoline Cases 4 4 83-6103-11 4 r CASES 1A. 18. 1C V T = 74 6 m/s 3 - 2 - I I I 0 0.2 0.4

0.6 0.8 1 .o

NONDIMENSIONAL SPANWISE STATION, r Figure 10. Spanwise Variation of 4P Flatwise Bending Moment for Trimmed Baseline Cases 1: CASES 1A, 18 IC VT = 74.6 m/s I C

5 \

I I I

’I 5

I I I I 0.2 0.4 0.6 0.8 1 NONDIMENSIONAL SPANWISE STATION, r Figure 11. Spanwire Variation of 4P Edgewise Bending Moment for Trimmed Baseline Cases 83-6-103-12 Passive Tuned Tab Background The preliminary development of t h i s device was performed using a s e p a r a t e s i m p l i f i e d a e r o e l a s t i c a n a l y s i s which was only l o o s e l y coupled with the G400PA a n a l y s i s (see Reference 1 6 ) . As described i n t h i s r e p o r t , t h e b a s i s of t h e p a s s i v e tuned t a b was s i m p l y conceptualized as shown i n Figure 1 2 .

Generally, t h i s c o n c e p t u a l i z a t i o n assumes t h a t the e f f e c t of t h e t a b motion on t h e blade proper is l i m i t e d t o t h e incremental a i r l o a d s derived from t h e t a b motion. A s shown i n t h e f i g u r e , one incremental normal a i r l o a d resu!ts from an e f f e c t i v e camber induced s h i f t of t h e l i f t c o e f f i c i e n t f o r a f i x e d s e c t i o n angle-of-attack. The camber change a l s o c r e a t e s a s h i f t i n the blade p i t c h i n g moment c o e f f i c i e n t which i n t u r n c r e a t e s an a d d i t i o n a l a i r l o a d by t w i s t i n g the blade t o c r e a t e a change i n the s e c t i o n angle-of-attack i t s e l f . When t h e t a b responds harmonically, the r e s u l t i n g incremental a i r l o a d s can add t o or s u b t r a c t from t h e i n h e r e n t (blade alone) a i r l o a d i n g depending on the amplitude and phase of t a b motion.

The e x c i t a t i o n of t h e t a b w a s assumed t o be l i m i t e d t o t h a t induced i n e r t i a l l y by t h e blade as i t f l a p s (both as a r i g i d body and f l e x i b l y ) and p i t c h e s . The r o l e of t h e G400PA a n a l y s i s i n t h i s s i m p l i f i e d t a b a n a l y s i s was t o provide t h e b a s i c blade a e r o e l a s t i c responses used t o e x c i t e t h e t a b . The f i n a l harmonic hub s h e a r s can then be c a l c u l a t e d using t h e incremental t a b l o a d s (both i n e r t i a l and aerodynamic) together with those p r e d i c t e d by the G400PA a n a l y s i s .

A n example of t h e v e r t i c a l hub shear loads as p r e d i c t e d by t h i s s i m p l i f i e d a n a l y s i s f o r t h e Blackhawk r o t o r i s presented i n Figure 1 3 (taken from Reference 16). It is the favorable f i n d i n g s r e p o r t e d i n t h i s r e f e r e n c e t h a t i d e n t i f i e d t h e p o t e n t i a l f o r t h i s device. As r e p o r t e d i n t h i s r e f e r e n c e , the i n t e r p r e t a t i o n of t h e Figure 13 r e s u l t s are as follows: "TO study t h e e f f e c t i v e n e s s of t h e p a s s i v e tuned t a b , a b a s e l i n e t a b c o n f i g u r a t i o n w a s s e l e c t e d and v a r i a t i o n s i n t a b design parameters from the b a s e l i n e c o n f i g u r a t i o n was selected and v a r i a t i o n s i n t a b design parameters from t h e b a s e l i n e c o n f i g u r a t i o n were inveatigated...

Placement of t h e t a b along t h e blade span is c r i t i c a l f o r t a b e f f e c t i v e n e s s .

This i s shown i n Figure (13). The p r e d i c t e d v i b r a t o r y r o o t v e r t i c a l s h e a r s a r e shown as a f u n c t i o n of t a b spanwide l o c a t i o n f o r a t a b with l e n g t h equivalent t o 1 C p e r c e n t of t h e blade r a d i u s . are shown f o r two t a b tunings: R e s u l t s 5 / r e v and lO/rev. The t a b l o c a t i o n f o r maximum e f f e c t i v e n e s s is between 50 and 70 4 7 -

t

W cn Z

g

v) W a W

Q

W cn

z

C K

-T-

00-12-29-1 iii

z

W a

-

U .

I cn

B

> W K

2o t

A W

z

-J w a

s

U .

6o t

a W I TAB CONFIGURATION cn I 3 R T = 0.81 3 m

5 =10.67cm

B

M~ = 2.268 kg p T = - 2 5 4 c r n E v 01 I 1 I I W

z

W

e

K I cn

's a

TAB SPANWISE LOCATION ('lo RADIUS)

Figure 13. Results of Simplified Analysis - Effect of Passive Tab Spanwise Location on

Root Vertical Shears, p L : 0.4, CT/U = 0.09

81-4-31-1 4 9 percent blade r a d i u s . This r e s u l t is a t t r i b u t e d d i r e c t l y t o the i n f l u e n c e of the f l a t w i s e mode shapes on the e x c i t a t i o n of t h e tab. Both first and second f l a t w i s e modes have antinodes i n t h i s r e g i o n , and s i n c e t h e t a b is i n e r t i a l l y excited by the blade f l a t w i s e motion, more e x c i t a t i o n occurs a t f l a t w i s e antinodes than a t f l a t w i s e nodes. The node p o i n t s f o r these same two f l a t w i s e modes a r e between 75 and 90 percent and Figure 1 3 shows t h a t t h i s i s the region of lowest t a b e f f e c t i v e n e s s . I n f a c t , a m p l i f i c a t i o n of the 4Irev r o o t v e r t i c a l s h e a r s a l s o occurs i n t h i s region. The blade t i p i s a l s o an antinode f o r the blade f l a t w i s e modes but Figure 13 shows t h a t e f f e c t i v e n e s s f o r a t a b l o c a t e d a t the blade t i p i s n o t as good as f o r a t a b near midspan. The reason f o r t h i s apparent anomaly i s related t o t h e i n f l u e n c e of t h e r i g i d body f l a t w i s e mode on t a b e x c i t a t i o n . Even though t h e r i g i d body f l a t w i s e mode c o n t r i b u t e s l i t t l e t o the r o o t v e r t i c a l s h e a r , i t s motion is a p p r e c i a b l e a t 3, 4, and 5/rev. I n f a c t , t h e r i g i d body f l a t w i s e mode has more motion a t 3, 4 , and 5 / r e v than the second f l a t w i s e mode (~'"5.1 r e v ) . The i n f l u e n c e of the r i g i d body mode on the t a b e x c i t a t i o n i s t h e r e f o r e d e t r i m e n t a l because t h e t a b responds t o n u l l the v e r t i c a l shear caused by the v e r t i c a l motion. From t h i s i t i s clear t h a t , based on t h e r i g i d body f l a t w i s e mode shape, an inboard t a b l o c a t i o n i s b e t t e r than an in order t o reduce t h e t a b response t o t h e r i g i d body mode.

outboard t a b l o c a t i o n For example, a t m i d span the r i g i d body f l a t w i s e mode s h a p e has only half the d e f l e c t i o n a t the blade t i p , so t h e i n f l u e n c e of t h e r i g i d body f l a t w i s e mode on t h e t a b response is a l s o c u t i n h a l f .

of t a b tuning on the v i b r a t o r y r o o t v e r t i c a l Figure 1 3 a l s o shows t h e e f f e c t shears. Overall, the 5 p e r rev tuning provides b e t t e r v i b r a t i o n a l l e v i a t i o n than the 10 per rev tuning. This is because t a b angular motion i n c r e a s e s w i t h a decrease i n t a b n a t u r a l frequency, and increased t a b motion provides increased c o n t r o l a u t h o r i t y . For a t a b l o c a t e d a t 60 p e r c e n t r a d i u s w i t h a 5 / r e v tuning, t h e percent reductions i n v i b r a t o r y s h e a r s are 54, 15, and 88 p e r c e n t f o r 3, 4 and S/rev, r e s p e c t i v e l y . However, t h e t a b angular motions a s s o c i a t e d w i t h t h i s l e v e l of r o o t shear r e d u c t i o n may v i o l a t e design c o n s t r a i n t s . " Limitations of Simglified Analysis

--------- ----- --

A s a r t i c u l a t e d i n a n above s u b s e c t i o n , t h e s i m p l i f i e d a n a l y s i s omits two forms of blade-to-tab coupling: t h e aerodynamic e x c i t a t i o n o f t h e t a b due t o blade motion, and t h e i n e r t i a e x c i t a t i o n of t h e blade proper due t o t h a t motion, The latter type of coupling i n l a r g e measure d e f i n e s t h e e l a s t o - mechanical "pendular absorber" dynamics which t h e t a b imposes on t h e blade because of i t s mass. A p o t e n t i a l l y weak element of ,$he s i m p l i f i e d a n a l y s i s is t h e ad hoc combining of some c a l c u l a t i o n s of t h e (nonlinear) G400PA c a l c u l a t i o n s with those of t h e ( l i n e a r ) e i m p l i f i e d t a b equations. A major l i m i t a t i o n of t h e forced response s i m p l i f i e d a n a l y s i s is t h a t i t only o b t a i n s response solution at integral order harmonics of rotor speed. As such, the flutter eigenvalue solution is eliminated. Thus, this simplified analysis cannot identify aeroelastically unstable configurations.

Parameter Selection For GOOOPA Calculations Based on the results of the Reference 16 simplified calculations, an initial design tab configuration was selected and variations were made in four of the primary parameters.

Initial Desip Configuration

------ --- - - -

The initial design configuration was defined by the following paraneter selection:

o nominal span, ART . . . . . . . . . . . . . . . . . . 0.15R

o mass, MT . . . . . . . . . . . . . . . . . . 1.612 kg

o (aft) hinge location, y1oH . . . . . . . . . . . . . 0.290 m

o tab chord, cT . . . . . . . . . . . . . . . . . . 0.105m

o coincident tab L.E. and hinge

o (aft) tab c.g. location from hinge . . . . . . . . . . -0.026 m (-.25 CT)

o chordwise radius of gyration (about c . g . 1 . . . . . . 0.030 m

o viscous damper rate . . . . . . . . . . . . . . . . . 0.122 Nms/rad

o torsion spring rate . . . . . . . . . . . . . . . . . 653.5 Nm/rad

This combination of parameters gives an uncoupled, undamped natural frequency of 13.105P.

Parametric Variations

----------

The parametric variations used are as follows:

o ( 2 ) spanwise c.g. locations . . . . . . . . . . . . . (0.5751, 0.913R)

o (2) masses (and proportional spring rates to

maintain uncoupled frequency) . . . . . . . . . . . (3.225 kg, 0.806 kg)

o (3) uncoupled frequencies . . . . . . . . . . . (3.91P, 7.62P, 11.37P)

(maintaining constant mass)

o ( 3 ) chordwise c.g. locations . . . . . . . . . . .(-.125 cT, 0, +.125 cT)

5 1 1 2 1 .o

-- -

-

0.8 E

0.6 0 4 0 2 1 I I I 1 2

1 0 - 1

I ' 1.0

-

0.8

"E

TAB SPANWISE LOCATION

1 0 5 R - 0 65R)

0.2

- - - (0 a 5 ~ - 0 97%)

1 I I I I I

4 t

L I I I I 4 5 Figure 14. Variations in Components of 4P Hub Shear with Passive Tuned Tab Mass, 90 mls Flight Speed (u =0.4) 5 2 83--6103-1 1.2 1 .o I I I 1.2 1 .o 0.8 0.6 0.4 0.2 a

I I I I I

5 10 15 20 25

TAB FREQUENCY, +, PER ROTOR REV

Figure 15. Variations in Components of 4P Hub Show with Passivo Tuned Tab Uncoupled Tab Frequency, 90 mls Flight Speed (p =0.407) 5 3 0 3 - 6 1 03-6 1 .i I 1 .c 0.e 0.6 0.4 0.2 0.E 0.4 0.2 01 I I 1 I 1 1 2 i o tk I 1 I I I 4.3 4.2 -0.1 0 0.1 0.2 0.3 (ND) TAB C.G LOCATION FROM HINGE, Y&C T Figure 16. Variations in Compononts of 4P Hub Shear with Passive Tuned Tab Mass Center Location, 90 mls Flight S p e d (cc 00.4) 5 4 83-6-1 03-7 Generally, t h e results are c o n s i s t e n t l y poor. While some modest g a i n s (reductions i n v i b r a t o r y shear) a r e noted f o r t h e l o n g i t u d i n a l and l a t e r a l component p r e d i c t i o n s , t h e major i n c r e a s e s i n t h e vertical component would c l e a r l y be unacceptable. Note t h a t because of t h e e x t e n t of t h e s e counter- productive r e s u l t s , o t h e r lesser parameters which could have been v a r i e d , such as t a b chord and f l i g h t speed, were not.

Since t h e major parameter v a r i a t i o n s d i d n o t r e s u l t i n a design enhancing p r e d i c t i o n , t h e resources of t h i s study were d i r e c t e d t o more productive purposes.

The reason f o r t h e highly counter-productive r e s u l t s a c t u a l l y obtained, i n view of t h e o p t i m i s t i c r e s u l t s from t h e s i m p l i f i e d a n a l y s i s , is n o t f u l l y understood, however. One p o s s i b l e explanation is that t h e t a b , a t t h e s e parameter v a l u e s , is o p e r a t i n g as a badly mistuned pendular absorber.

Another reason is t h a t t h e proper, more f u l l y coupled a n a l y s i s of t h i s device (as afforded by t h e G400PA a n a l y s i s ) r e q u i r e s a more d e t a i l e d accounting of a l l t h e v a r i o u s balancing f o r c e s and moments than t h e s i m p l i f i e d a n a l y s i s i s capable o f . These q u e s t i o n s , however, are beyond t h e scope of t h e p r e s e n t study.

Control Coupled Tab I n i t i a l Parameter S e l e c t i o n f o r G O O O P A C a l c u l a t i o n s

.................... -----

Because of t h e high degree of mechanical s i m i l a r i t y between t h e c o n t r o l coupled t a b (CCT) and t h e p a s s i v e tuned t a b (PTT), t h e nominal design configu- r a t i o n s e l e c t e d f o r t h e CCT w a s t h e same used for t h e PTT. The t a b was l o c a t e d a t t h e outboard p o s i t i o n ( r C G -0.913R) and t h e minimum mass (.806 kg), T z e r o c.g. o f f s e t c o n f i g u r a t i o n was used throughout. O f t h e remaining p r i n c i p a l parameters impacting on t h e CCT, t h e blade r o o t t o r s i o n s t i f f n e s s , K g R , (as d e f i n e d by c o n t r o l system s t i f f n e s s ) , and the c o n t r o l coupling gain, GT were s e l e c t e d f o r major parameter variation. S p e c i f i c a l l y , v a r i a t i o n s i n Kg were R

-

s e l e c t e d t o y i e l d uncoupled b l a d e t o r s i o n f r e q u e n c i e s , ue,, of 2.25P, 3.19P and 4.73P (compared w i t h 4.22P f o r t h e b a s e l i n e c o n f i g u r a t i o n ) . The s e l e c t e d v a r i a - t i o n s i n coupling g a i n , GT, were determined by matching i n nondimensional u n i t s t h e dimensional g a i n v a r i a t i o n s used i n Reference 16 (0, -.00885, and -.01770 deg/Nm) .

I n c o n t r a s t t o t h e i n t e n t of t h e p a s s i v e tuned t a b , t h e "tab alone" dynamics of CCT about i t s hinge are n o t germaine t o its o p e r a t i o n and, t h e hence, should be i s o l a t e d from t h e dynamics due t o coupling. Accordingly, t h e s p r i n g r e s t r a i n t of t h e t a b t o t h e coupling attachment was set t o a

-

s u i t a b l y high v a l u e t o i n s u r e t h a t t h e uncoupled t a b frequency, weT, would be i n excess of 2OP. The a c t u a l v a l u e achieved was 26.7P. Since t h e c o n t r o l loads would be expected t o be a f u n c t i o n of t h e trim c o n d i t i o n s , i t w a s concluded that a l l c a l c u l a t i o n s f o r t h e CCT would n e c e s s i t a t e t h e use of t h e t r i m procedure.

G4OOPA C a l c u l a t i o n R e s u l t s

-------------

Using t h e parameter s e l e c t i o n s t r a t e g y defined above, i n i t i a l c a l c u l a t i o n s were made with combinations of r o o t t o r s i o n s t i f f n e s s and t h e r e s u l t i n g v a l u e s of coupling gain. I n every i n s t a n c e , i t w a s found t h a t t r i m c a l c u l a t i o n s could not be achieved due t o g r o s s l o s s e s of r o t o r l i f t . I n a n a t t e m p t t o shed l i g h t on t h i s phenomenon, non-trim c a l c u l a t i o n s were made f o r s i m p l e p e r t u r b a t i o n s of

t h e coupling g a i n , GT = - + 0 . 5

(deg/deg) with t h e nominal r o o t t o r s i o n s t i f f n e s s , These t r e n d s are presented i n t h e form of p a r t i a l d e r i v a t i v e s of v a r i o u s p e r t i n e n t performance parameters w i t h r e s p e c t t o coupling g a i n , GT.

TABLE V PARTIAL DERIVATIVES OF PERFORMANCE PARAMETERS W I T H RESPECT TO COUPLING GAIN FOR CONTROL COWLED TAB, p = 0.338

a (Parameter) / a G T

Parameter Dimensional Value % Baseline ,00943 10.4 CT/ 0.403 LIDe 5 . 6

Nm - 8 . 7 1 -1.2

N -231.3 -7 :2

N - 57.8

-4.4

N - 1.4

-0.2 The p r i n c i p a l r e s u l t t o be gleaned from Table V is that, f o r the t a b geometry used, the device is functioning almost e x c l u s i v e l y a s a generator of a d d i t i o n a l r o t o r l i f t rather than a s a r e l i e v e r of v i b r a t i o n a l push-rod l o a d s .

S u r p r i s i n g l y , t h e p o t e n t i a l f o r changes i n v i b r a t i o n a l push-rod load l e v e l per coupling g a i n is n o t only q u i t e low i n magnitude ( r e l a t i v e t o t h e l i f t change p o t e n t i a l ) , but is of t h e opposite s i g n from what would normally be expected based on t h e f i n d i n g s of Reference 16.

Two explanations have been i d e n t i f i e d f o r t h e disagreement of t h e p r e s e n t f i n d i n g s with those of Reference 16: 1. The c o n f i g u r a t i o n used h e r e i n has t w i c e t h e t a b c h o r d / a i r f o i l chord r a t i o a s t h a t used i n Reference 16 (20% vs. 10%). The twofold i n c r e a s e i n t h i s r a t i o should have a comparable i n c r e a s e i n Acg, should be r e l a t i v e l y less but t h e accompanying increase i n A% c / 4 because of the shortening of moment arm. Indeed, for f l a t p l a t e theory i n the l i m i t of u n i t chord r a t i o , t h e increment i n moment c o e f f i c i e n t approaches zero.

2 . The c a l c u l a t i o n f o r incremental moment due t o t a b d e f l e c t i o n used h e r e i n was made using the a n a l y t i c formulation of Theodorsen and Garrick (Reference l o ) , whereas t h a t used i n Reference 16 was made Except f o r t h e using experimental v a l u e s as given i n Reference 17.

f a c t t h a t t h i s experimental d a t a was l i m i t e d t o a chord r a t i o of n o t more than 0.10, t h e experimental d a t a source would have been a b e t t e r a l t e r n a t i v e than t h e a n a l y t i c one used. Within t h e context of t h e unsteady a i r l o a d s methodology adapted h e r e i n , however, t h e i n c l u s i o n of such experimental s t a t i c data would result i n an ad hoc formulation r e q u i r i n g some engineering judgment.

CCT is t h a t aeromechanically i t One observation which can be made of t h e bears a s t r o n g resemblance t o t h e Kaman servo-tab r o t o r system.

I n t h a t r o t o r concept a t a b is used t o produce blade t o r s i o n a l moments f o r t h e purpose of r o t o r c y c l i c c o n t r o l . Although t h e i n t e n t is somewhat d i f f e r e n t from t h a t of the CCT, t h e aerodynamic p r i n c i p l e invoked is t h e same: t o r s i o n moment c o n t r o l using a t r a i l i n g edge tab. I n t h e Kaman system, which a f t e r several y e a r s of development can be assumed t o be reasonably optimized, t h e t a b is of small chord r a t i o and l o c a t e d an exaggeratedly a f t d i s t a n c e so as t o be removed from the blade proper e n t i r e l y . This c o n f i g u r a t i o n would c l e a r l y maximize t h e incremental aerodynamic moment generation while minimizing the incremental l i f t generation.

5 7 Thus, f o r purposes of t h e CCT, t h e s e l e c t e d t a b c o n f i g u r a t i o n is f a r from optimal and a complete e v a l u a t i o n of t h i s concept would r e q u i r e an Optimization study of t h e design parameters. This a d d i t i o n a l optimization s t u d y , w a s beyond the resources of the p r e s e n t study.

All-Flying Torsion T r i p Preliminary Analysis I n i t i a l G400PA c l c u l a t i o n s were made f o r t h e a l l - f l y i n t o r s i o n t i p using q u a s i - s t a t i c a i r l o a d s and a straight-forward implementation of a nominal s e l e c t i o n of t i p dynamic parameters. Included i n i n p u t parameters f o r t h e b a s i c b l a d e (without t i p ) was a 95% r e d u c t i o n i n mass d i s t r i b u t i o n over t h e t i p span r e g i o n s where t h e t i p was t o be l o c a t e d . T h i s s u b t r a c t e d m a s s w a s then included i n t h e t i p mass d e s c r i p t i o n . With t h e s e s e l e c t e d dynamic parameters, t h e c a l c u l a t i o n s uncovered a number of problem areas. As shown i n F i g u r e 3, t h e concept n e c e s s a r i l y e n t a i l s o f f s e t s of t h e t i p aerodynamic c e n t e r from both the hinge a x i s and t h e mass c e n t e r . Nominally, t h e m a s s c e n t e r would be located c o i n c i d e n t w i t h t h e hinge a x i s .

Preliminary c a l c u l a t i o n s were made using t h e nominal c o n f i g u r a t i o n rrLth t h e aerodynamic c e n t e r maintained a t t h e q u a r t e r chord p o i n t . This r e s u l t s i n a s i g n i f i c a n t forward mass c e n t e r c o n s i s t e n t w i t h a placement of t h e t a b hinge a x i s 1 2 % of t h e chord i n f r o n t of t h e blade p i t c h ( e l a s t i c ) a x i s . I n t h i s were c a l c u l a t e d which were subsequently c o n f i g u r a t i o n , s e v e r e o s c i l l a t i o n s a s c e r t a i n e d t o be f l u t t e r involving t h e second f l a t w i s e bending and f i r s t t o r s i o n modes. A temporary f i x f o r t h i s c o n d i t i o n w a s t o d i s p l a c e t h e t i p a f t so t h a t t h e hinge l i n e (and mass c e n t e r ) were c o i n c i d e n t w i t h t h e e l a s t i c a x i s . This c o n f i g u r a t i o n was found t o be s t a b l e and convergent responses were thereby achieved.

Subsequent a t t e m p t s t o r e t u r n t o t h e o r i g i n a l c o n f i g u r a t i o n , w i t h t h e forward t i p mass c e n t e r , were e v e n t u a l l y s u c c e s s f u l l y made. The s t a b i l i z a t i o n of t h i s o r i g i n a l c o n f i g u r a t i o n was achieved by a d j u s t i n g t h e mass c e n t e r s of blade segment numbers 2, 7 and 11 t o n u l l t h e i n e r t i a l coupling of t h e second f l a t w i s e bending and t o r s i o n modes. It i s of interest t o note that t h e aero- mechanical s t a b i l i t y a n a l y s i s o f Chopra (Reference 18), w h i l e p r e d i c t i n g some low frequency i n s t a b i l i t i e s a s s o c i a t e d w i t h r i g i d f l a p p i n g and lead-lag motions, does n o t p r e d i c t o r a n t i c i p a t e t h i s e s s e n t i a l l y classic bending-torsion f l u t t e r .

Probable reasons f o r t h e discrepancy i n f i n d i n g s of t h e p r e s e n t work w i t h those of Reference 18 are t h a t t h e p r e s e n t a n a l y s i s included t h e a e r o e l a s t i c e q u a t i o n s f o r e l a s t i c modes, a t i p hinge a x i s d i s p l a c e d from t h e e l a s t i c a x i s , and used r e a l i s t i c amounts of damping, both s t r u c t u r a l and t h a t from t h e lead- l a g damper, i n t h e c a l c u l a t i o n s . The a n a l y s i s of Reference 18, however, u s e d a s i m p l i f i e d modeling without e l a s t i c i t y d i r e c t e d t o t h e f l a p - l a g - t o r s i o n i n s t a b i l i t y problem, and considered no s t i f f n e s s r e s t r a i n t t o t h e f r e e t o r s i o n sect ions.

A second d i f f i c u l t y experienced i n t h e p r e l i m i n a r y c a l c u l a t i o n s w a s t h a t t h e expected i n c r e a s e i n L/De d i d n o t m a t e r i a l i z e w i t h t h e d e v i c e a c t i v a t e d even w i t h s u f f i c i e n t ( c o n s t a n t ) a p p l i e d moment about t h e t i p axis t o m a i n t a i n p o s i t i v e l i f t on t h e advancing s i d e . I n t h e s e c a l c u l a t i o n s , no attempt was made t o retrim t h e r o t o r and t h e c o n t r o l s e t t i n g s and i n f l o w v a l u e s a p p r o p r i a t e t o t h e trimmed unappended blade were used d i r e c t l y . I n t h i s c o n d i t i o n , t h e c o n s t a n t a p p l i e d moment was found t o be a g g r a v a t i n g t h e s t a l l c o n d i t i o n on t h e r e t r e a t i n g blade s i d e of t h e r o t o r d i s k , thereby i n c r e a s i n g t h e e q u i v a l e n t drag It w a s subsequently found t h a t t h e p o t e n t i a l f o r i n c r e a s e d LIDe could be De.

obtained, however, only when t h e r o t o r w a s r e t r i m e d .

A d d i t i o n a l p r e l i m i n a r y c a l c u l a t i o n s were performed t o e s t a b l i s h t r e n d s w i t h regard t o t h e i n t e r p l a y between t h e o f f s e t a p p l i e d (zero d e f l e c t i o n ) t o r s i o n moment and t h e t o r s i o n s p r i n g rate. The r e s u l t s of t h e s e c a l c u l a t i o n s are shown i n F i g u r e s 17 t h r u 19. Figure 17 p r e s e n t s t h e b a s i c t r e n d s achieved w i t h s e p a r a t e v a r i a t i o n s i n o f f s e t moment and s p r i n g rate. The f o u r c a l c u l a t i o n p o i n t s i n t h i s f i g u r e (denoted by t h e s q u a r e symbols) d e f i n e t h e range of mean t i p d e f l e c t i o n a n g l e s achieved t o g e t h e r with t h e r e s u l t i n g average e q u i l i b r i u m ( i n e r t i a l a n d aerodynamic) l o a d i n g moments, MEQUIL . The equilibrium l o a d i n g moment i s a d i r e c t measure of t h e s t e a d y l i f t s u s t a i n e d on t h e b l a d e s e c t i o n s comprising t h e t i p . The p r i n c i p a l f i n d i n g presented by t h i s f i g u r e i s t h e r e l a t i v e i n s e n s i t i v i t y of t h e performance i n d i c a t o r (L/De) t o o f f s e t moment, %, and t h e s t r o n g s e n s i t i v i t y t o s p r i n g rate, Kg . A r e l a t e d secondary r e s u l t shown i n t h e f i g u r e i s t h e small v a r i a t i o n i n equilibrium l o a d i n g w i t h o f f s e t moment. The o f f s e t moment is s e e n t o a f f e c t p r i n c i p a l l y o n l y t h e v a l u e of t h e mean t i p d e f l e c t i o n angle, *TO F i g u r e 18 p r e s e n t s t h e r e s u l t s achieved by l i n e a r l y ganging t h e o f f s e t moment and s p r i n g rate so t h a t a l l combinations would tend t o e q u i l i b r a t e a t a s e l e c t e d t i p d e f l e c t i o n a n g l e and e q u i l i b r i u m l o a d i n g moment. The v a l u e s so s e l e c t e d f o r F i g u r e 18 are, r e s p e c t i v e l y , -1.07 d e g r e e s and 381 Nm. With 5 9 VT = 90.0 mls (r = 0 407) M, = 691 M ~ ~ ~ t ~ = M ~ + K ~ T DP, 70(

- K = 11524 NmlRAD

- - - t T = 3 3 9 0 NmlRAD

Jl 65C 60C E z

+-

z

r

Z

g 500

e

a_ + 'EQUILIBRIUM LOADING MOMENT, MEOUIL 0 1 I I I I I I

-1.6 -1.4 -1.2 -1 .o

-0.8 -0.6 -0.4 -0.2 0

MEAN TIP DEFLECTION, + , deg

Figun 17. Effects of Offset Momont and Sphng Rat0 on Opontion of Ail-Flying Tip-Preliminary Analysis E z a- c I I z m U

e

a

I- 2000 4000 6000 8000 ’ 10000 12000 14000 TIP TORSION SPRING RATE, K , NmlRAD BT Figure 18. Effect of Linearly Combined Offset Moment and Spring Rate on Equilibrium Loading Moment for All.Flying TipPreliminary Analysis

- -

83-6-1 03-1 5 8.5 VT = 90 0 m/s (F = 0 407) I SEGMENTS 12 TO 15 8.0 I SPRING RATE, K NmlRAD BT'

Figure 19. Variation of U D , with Spring Rate for Ali=FLyingTipPreiiminrty Analysis

?

v a r i a t i o n s i n t h e s p r i n g rate (and, commensurately, i n o f f s e t moment) the a c t u a l r e s u l t i n g equilibrium loading moment is seen t o vary i n v e r s e l y and i n t e r s e c t the o f f s e t moment a t a s p r i n g r a t e of approximately 2373 Nmlradian (applied moment of 426 Nm). This r e s u l t suggests t h a t , f o r t h i s l i n e a r combination, s p r i n g rates below t h i s value would r e s u l t i n mean t i p d e f l e c t i o n angles, BT,, which were p o s i t i v e (LE nose down) and, hence, counterproductive. I n a l l o t h e r c a l c u l a t i o n s applied moment and s p r i n g rate, a involving d i f f e r e n t l i n e a r combinations of minimum s p r i n g rate w a s g e n e r a l l y defined by the i n t e r s e c t i o n of t h e two curves.

The e f f e c t i v e n e s s of t h e s e p r i n c i p l e s t o o b t a i n a more n e a r l y optimized L/De i s shown i n Figure 19; a 20 percent improvement is i n d i c a t e d . These r e s u l t s include the concurrent use of v a r i a t i o n s i n o f f s e t moment, and are based on the r e l a t i v e i n s e n s i t i v i t y of LIDe t o o f f s e t moment, Aerodynamic Refinements

-----------

Based on t h e favorable r e s u l t s obtained using only q u a s i - s t a t i c a i r l o a d s and uniform inflow shown i n Figure 19, a more in-depth a n a l y s i s of the a l l - f l y i n g t i p appeared j u s t i f i e d . The s u c c e s s f u l o p e r a t i o n of and, hence, payoff f o r the device appear t o be c l o s e l y dependent on t h r e e f a c t o r s : (1) the e x t e n t t o which t h e l i f t , L, is influenced by t h e inflow c o n d i t i o n s on the advancing blade s i d e , ( 2 ) the e x t e n t t o which t h e equivalent drag, De, i s influenced by inflow c o n d i t i o n s on t h e r e t r e a t i n g blade s i d e , and (3) t h e e x t e n t t o which the dynamic o p e r a t i o n of the device i s influenced by t h e l a g s and a t t e n u a t i o n s of t h e unsteady c h a r a c t e r of t h e a i r l o a d s .

Reference 1 shows t h a t t h e s u b s t a n t i a l downloads t y p i c a l l y predicted on the advancing s i d e using simple uniform inflow become s i g n i f i c a n t l y diminished with t h e use of v a r i a b l e inflow. A s t h a t r e f e r e n c e demonstrates, the L/De c a l c u l a t e d can depend i n l a r g e measure on t h e o p t i o n a l use of v a r i a b l e inflow o r uniform inflow. For use w i t h t h e GOOOPA, however, t h e r i g o r o u s usage of v a r i a b l e inflow i n a combined t r i m i t e r a t i o n program i n t e r a c t i o n a l mode i s extremely computer CPU t i m e i n t e n s i v e . Such a complete usage of v a r i a b l e inflow as beyond t h e scope of t h e p r e s e n t study and only a cursory assessment of t h e impact of v a r i a b l e inflow was t h e r e f o r e attempted. The i n c l u s i o n of w a s e a s i l y accomplished and was used unsteady aerodynamics, on t h e o t h e r hand, i n a l l t h e f i n a l c a l c u l a t i o n s .

Parameter S e l e c t i o n f o r G400PA C a l c u l a t i o n s For all t h e f i n a l c a l c u l a t i o n s t h e unsteady a i r l o a d s o p t i o n w a s invoked and the t i p hinge a x i s and mass c e n t e r were maintained a t a chordwise l o c a t i o n .13c behind t h e leadingedge (.12c i n f r o n t of t h e blade p i t c h a x i s ) , The mass of each of t h e t i p s e c t i o n s w a s chosen t o be approximately 95% of t h e c o r r e s - ponding unappended blade s e c t i o n mass. The parameter v a r i a t i o n s used i n t h e f i n a l c a l c u l a t i o n s are as follows: o t o r s i o n s p r i n g rate: (W14000 Nm/rad) o moment c o n s t r a i n t r e l a t i o n between o f f s e t moment and s p r i n g rate: (Mg = 381 + .0187 K B ~ ,

267 + e0187 K B ~ )

o spanwise e x t e n t : * ( O . l O R , 0.15R)

o f l i g h t a i r s p e e d : (74.6, 90.0 m/s) I n a d d i t i o n , f o r t h e best c o n f i g u r a t i o n obtained from t h e parameter v a r i a t i o n s , t h e approximate e f f e c t s of v a r i a b l e inflow were i n v e s t i g a t e d f o r t h e two f l i g h t speeds.

G400PA C a l c u l a t i o n R e s u l t s The c a l c u l a t e d r e s u l t s f o r t h e a l l - f l y i n g t i p c o n s i s t predominantly of a s i n g l e performance index: l i f t t o e q u i v a l e n t drag r a t i o ( s e e Equation 1 9 ) .

For i s o l a t e d c o n d i t i o n s , r e s u l t s a r e a l s o presented f o r 1/2PTP blade bending and t o r s i o n moment d i s t r i b u t i o n s . Generally, t h e c a l c u l a t i o n procedure defined i n t h e above Preliminary Analysis Subsection i s adhered t o . The r e s u l t s are presented i n Figures 20 t h r u 32.

a t Unsteady A i r l o a d s E f f e c t s

--------- - - - -

F i g u r e 20 compares t h e p r e d i c t e d L/De v a r i a t i o n s w i t h r e s t r a i n t s t i f f n e s s as made w i t h and without t h e e f f e c t s of unsteady a i r l o a d s f o r t h e high speed (p 0.407) f l i g h t c o n d i t i o n and t h e 15% r a d i u s t i p span c o n f i g u r a t i o n . The comparison a p p e a r s t o be reasonably c l o s e w i t h no s i g n i f i c a n t changes i n c h a r a c t e r . The f a v o r a b l e g a i n s obtained w i t h a q u a s i - s t a t i c a i r l o a d s fonnu- l a t i o n discussed above are maintained and even improved upon w i t h t h e i n c l u s i o n of unsteady a i r l o a d s . On a p e r c e n t improvement over b a s e l i n e b a s i s , t h e impact of unsteady a i r l o a d s appears t o be advantageous.

* Note t h a t t h e corresponding t i p masses are: (11.32 kg, 13.07 kg)

8.5 VT = 90 0 m k 01 = 0 407)

----- OUASI-STEADY AERODYNAMICS

UNSTEADY AERODYNAMICS Mo = 381 + 0.01 87 K a, 8.0 / / /

-

7.5

/

/ I 1 / a 2 0 7.0 6.5

I I II Y

6.0

I I I I I I

0 2000 4000 6000 8000 10000 12000 14000 SPRING RATE, K NmlRAD BT' Figure 20. Comparison of UD, Characteristics of All=FlyingTip Using Quasi-Static vs.

Unsteady Airloads Formulations, 90.0 mla Flight S p e d =0.407), 0.15 Tip Span 6 5 83-6-103-17 Performance c h a r a c t e r i s t i c s f o r t h e reduced span (.10R) a r e presented i n Figures 2 1 and 22. The p r i m a r y comparison made i n t h e s e f i g u r e s is w i t h regard t o the v a r i a t i o n i n t h e o f f s e t moment schedule w i t h s p r i n g rate.

The reduced value of o f f s e t moment a t zero s p r i n g rate, 267 Nm, corresponds t o t h a t f o r t h e 15% span r a t i o e d by t h e areas weighted by r 2 . The p r i n c i p a l e f f e c t of t h e reduced o f f s e t moment i s seen t o occur a t t h e low s p r i n g rate c o n d i t i o n s , wherein t h e g r e a t e s t d i f f e r e n c e s i n equilibrium moment and s t e a d y t i p d e f l e c - t i o n s would occur. As Figure 22 shows, however, t h e maximum LID, v a l u e s are obtained a t s p r i n g rates wherein t h e equilibrium moments are very n e a r l y e q u a l .

The r e s u l t s shown i n Figure 22 confirm t h e e x p e c t a t i o n t h a t t h e lower (area s c a l e d ) a p p l i e d moment would produce a more n e a r l y optimal performance index than would t h e moment a p p r o p r i a t e t o t h e 15% span c o n f i g u r a t i o n . F i g u r e s 21 and 22 a l s o show t h e optimum L/De v a l u e s t o occur a t s i m i l a r v a l u e s of e q u i l i - brium moment.

----- Reduced Flakt-SEe - e d

Figure 23 c o n t r a s t s t h e equilibrium moments obtained f o r each of t h e two 15% span) a t t h e two f l i g h t speeds. Generally spanwise c o n f i g u r a t i o n s (10% and i n t h a t t h e h i g h e r e q u i l i - f o r e i t h e r spanwise e x t e n t t h e t r e n d s are similar, brium moment occurs a t t h e h i g h e r f l i g h t speed. As would be expected, t h e 15% span c o n f i g u r a t i o n would o p e r a t e a t a commensurately h i g h e r e q u i l i b r i u m moment. Figure 24 p r e s e n t s a summary of t h e b e s t c a l c u l a t i o n s f o r t h e two spanwise e x t e n t c o n f i g u r a t i o n s each a t t h e two f l i g h t speeds.

Figures 25 t h r u 28 p r e s e n t time-history responses of t h e t i p s e c t i o n s f o r v a r i o u s o f f s e t moment/spring r a t e schedules, t i p spans and f l i g h t speeds.

Figures 25 and 26 each compare the responses r e s u l t i n g from v a r i o u s s p r i n g rates (and concomitant o f f s e t moments) a t t h e same high speed f l i g h t c o n d i t i o n s .407) but f o r t h e 15% and 10% t i p spans, r e s p e c t i v e l y . Both t h e s e f i g u r e s (p show t h e s u b s t a n t i a l o s c i l l a t o r y c h a r a c t e r i s t i c s of t h e t i p a t t h e lower s p r i n g rates and t h e subsequent s t a b i l i z a t i o n induced by t h e h i g h e r s p r i n g rates.

The f i g u r e 8 a l s o g r a p h i c a l l y show t h e n e g a t i v e peaks which occur a t t h e JI- 90 advancing b l a d e p o s i t i o n , r e f l e c t i n g t h e r e q u i r e d o p e r a t i o n of t h e t i p i n augmenting t h e a i r l o a d i n g i n t h i s p o r t i o n of t h e r o t o r d i s k . Note t h a t t h e higher o s c i l l a t o r y c o n t e n t i n responses f o r t h e lower s p r i n g rates g e n e r a l l y allow p o s i t i v e (leading edge down) d e f l e c t i o n excursions and an o v e r l y negative peak a t t h e 90 deg azimuth p o s i t i o n . Both of t h e s e excessive response FREE-TIP. SEGMENT 13 TO 15 FLIGHT SPEED = 90 0 mls

/

-

-

-

-

E z i Z -/ / Mo=267.r00187 Kj,

400 1

w I I z

E !

v, I - & c

- / \ EOUlLlBRlUM AERODYNAMIC MOMENT M,,, ,,, FOR

(M,=267+00187 K ) J 0 2000 4000 6000 8000 10,000 12,000 14,000 16.000 TIP TORSION SPRING RATE. K Nmlrad BT' Figure 21. Comparison of Equilibrium Moment Characteristics for All-Flying l i p Using Alternate Applied Moments, 90 mls Flight Speed =0.407), O.iOR l i p Span 83-6 103-4 8.C FREE-TIP. SEGMENT 13 TO IS FLIGHT SPEED. VT = 90.0 mls 7.5 7.c Q,

/ / - M,=381 +0018667 K

s

6.!

I 1 I I I I 10,000 12,000 14,000 16,000 400 0 6000 8000 TIP TORSION PRING RATE, KsT, Nm/rad Figure 22. Comparlson of UD, Characteristics of All=FlyIgTip Using Alternate Offset

Moment Schedules, p = 0.407,O.lOR Tip Span

- - -

FREE-TIP, SEGMENT 12 TO 15. M,=381 +00187 K dT

- - -

FREE-TIP, SEGMENT 13 TO 1 5 , M, =267 + 0.0187 K BT E z b- z 74.6 m/s 1

r"

H 300 \

- - , - - - - - -

2oo t

I 74.6 mls I I I I 0' TIP TORSION SPRING RATE, KB , Nmlrad T Figure 23. Comparison of Equilibrium Moment Characteristics of All=FlylngTip for Alternate Flight Speeds and Tip Spans 6 9 83-6-103-2 1 '

- BASELINE (TIP LOCKED UP)

--

FREE-TIP. SEGMENT 12 TO 15.

M,=381 +00187 K BT 1c

---

FREE-TIP. SEGMENT 13 TO 15, M, = 267 + 0.0107 K I I I I I I I I I I 0 2000 4000 6000 8000 10,000 12,000 14,000 16,000 18000 20000 22000 Figure 24. Comparison of UD, Characteristics of All-Flying Tip for Alternate Flight Speeds and Tip Spans B L b l O 3 - 9

!

*\ d ,yo-

I N

(. / *

''t.c..

\

\

1 I 83-8-61 -3

E

cu m N N aD c m (3

-

L n P

83-8-61 - 1

/ \ I I I I ? T P 6aP 'lo' '319NV NO11331330 d l l 7 3 83-8-61 -4 / I 6ap 'l&f '319NV N01133133Q d l l 7 4 83-8-61 -2 features would detract from conditions favorable to optimum L/De: reduction of local lift due to positive tip deflection and increase in equivalent L/De: reduction of local lift due to positive tip deflection and increase in equivalent drag due to too high an angle-of-attack on the advancing side.

Generally, the observed trends shown in Figure 2 5 for the 15% tip span carry Included on both of over to the 10% tip span responses shown in Figure 26.

these figures are the tip responses for the maximum L/De configurations.

Each of these optimal responses are characterized by a well-damped signature, a negative peak at the 90 degree azimuth position and a generally negative mean value of about 1 deg. for the remainder of the rotor period. Figures 27 and 28 show the variations of the tip time-history responses with flight speed for the 15% and 10% tip span optimal configurations, respectively. For both of these spanwise extent configurations, the same spring rate (K =13560 Nrn/rad) BT was used. The higher oscillatory content in the 10% span responses can be attributed to (1) a higher natural frequency (resulting from a reduced torsion inertia) and ( 2 ) a reduction in aerodynamic damping (resulting from a reduced aerodynamic area and the less effective airloading of the tip sections).

Generally, the response characteristics of the tip section are not strong functions of flight speed.

Tig Section Ankle-of-ALtack Dnamic Characteristics

- ----- --- -- -----------

Figures 29 and 30 present the time-histories of the effective angle-of- attack, u characteristics of the T = 0.925 radial station (corresponding to E ' the center section of the 15% tip span configuration), f o r the two flight

conditions, u= 0.338 and 0.407, respectively. In each of these figures are

(1) the appropriate baseline results (no tip), (2) the results for the tip section activated but responses with the increment due to tip motion arti- ficially subtracted out, and ( 3 ) with the tip motion included.

The responses clearly show the reductions in negative angle-of-attack at the advancing blade portions of the disk provided by the device. The figures also show that the blade proper responses with the tip activated are even more negative than the baseline values in this portion of the disk.

A probable reason for this response characteristic is the blade's response to the reaction moment imparted by the tip device.

Observations and Interzretations

----------- ----

Observations which can be made from the non-variable inflow results are as follows:

' I

I '

I I

N 0 c c 83-8-61 -5 83-8-61 -6 1. The i n c r e a s e i n performance obtained f o r t h e device t r a c k s t h e performance v a r i a t i o n w i t h respect t o a i r s p e e d f o r t h e unappended device.

2. The e f f e c t of increased t i p span on performance i s a monotonic f u n c t i o n of t h e t i p span.

3. The s p r i n g r a t e f o r maximum LIDe v a r i e s w i t h f l i g h t speed; t h e off-optimum p e n a l t y does n o t appear g r e a t , however.

4 . (again n e g l e c t i n g v a r i a b l e The maximum performance g a i n s f o r t h e device inflow f o r t h e moment) are approximately 20% f o r t h e 0.15R c o n f i g u r a t i o n and 10% f o r t h e 0.10R c o n f i g u r a t i o n .

The o p e r a t i o n of t h e device i s t r u l y dynamic i n t h a t i t n o t only provides 5.

a more o r less steady i n c r e a s e i n angle-of-attack over most of t h e r o t o r azimuth, but w i t h a n incremental dynamic peak where i t i s most needed on t h e aximuthal period.

t h e advancing blade p o r t i o n s of 6 . Off-optimal responses a t t h e reduced s p r i n g rates are c h a r a c t e r i z e d by e x c e s s i v e o s c i l l a t o r y motion.

As d i s c u s s e d i n a n above s u b s e c t i o n , t h e v a r i a b l e inflow d i s t r i b u t i o n s a p p r o p r i a t e t o trimmed f l i g h t a t t h e two f l i g h t speeds were c a l c u l a t e d and input t o GOOOPA, without interprogram i t e r a t i o n . These d i s t r i b u t i o n s were used t o provide a p r e l i m i n a r y estimate of t h e e f f e c t of v a r i a b l e i n f l o w on one c l o s e l y optimized c o n f i g u r a t i o n . Generally, t h e r e s u l t s o b t a i n e d w i t h t h e use of q u a s i - v a r i a b l e inflow are s u s p e c t . Comparison of t r i m cases 1 B w i t h l C , and 2B w i t h 2 C shows a d e t e r i o r a t i o n i n t h e incremental performance due t o v a r i a b l e i n f l o w where t y p i c a l l y t h e reverse i s t h e norm. On t h e o t h e r hand, r e s u l t s f o r t h e r o t o r w i t h t h e s e l e c t e d optimized a l l - f l y i n g t i p c o n f i g u r a t i o n , a t t h e two advance r a t i o s , both showed s u b s t a n t i a l aerodynamic g a i n s : L/De v a l u e s w e l l i n excess of 10. The most v a l i d o b s e r v a t i o n t o be drawn from t h e s e r e s u l t s i s t h a t t h e t r u e e f f e c t of v a r i a b l e Inflow on t h e performance of t h e a l l - f l y i n g t i p i s moot and r e q u i r e s a more r i g o r o u s i n c l u s i o n of t h i s methodology.

F i g u r e s 31 and 32 p r e s e n t comparisons of i n t e r n a l v i b r a t o r y blade l o a d s f o r a c o n f i g u r a t i o n s e l e c t e d f o r b e s t L/De a t t h e two f l i g h t speeds. Discernable t r e n d s from t h e s e r e s u l t s are a s follows: .

5.c WITH TIP ACTIVATED

-----

BASELINE CASE IC

-

4.c CL i 2.0

k g

2 0 ' I 1 .o m 1 .o 2'ol ,

------

0 1

- -

u.2 0 0.4 0.6 NONDIMENSIONAL SPANWISE STATION, r Figure 31. Vibratory Blade Bending and Torsion Moment Characteristics for All-FLying lip, 0.15R Tip Span, p r0.338, Maximum UD, Conditions 3.0

I

.

I I I 5.0 \ /-- \ / \

4.0 L

/ \ .

# /

I

WITH TIP ACTIVA TED

-----

BASELINE CASE

1.0 -

0 1 1 1 m z o

-

g 2.0

5 5

c NONDIMENSIONAL SPANWISE STATION,T Figure 32. Vibratory Blade Bending and Tonion Moment Characteristics for All-Flying Tip,

0.15R Tip Span, 1 - 0.407, Maximum UDe Conditions

83-6-103-20 o The p r i n c i p a l impact of t h e device on t h e 1 / 2 PTP f l a t w i s e bending moment d i s t r i b u t i o n i s the l o c a l i n c r e a s e j u s t inboard of the device attachment. This would be expected based on t h e increased loading of t h e t i p s e c t i o n s .

o A p a r t from t h e t i p regions the device produces n e g l i g i b l e i n c r e a s e s , where i n c r e a s e s are noted, i n t h e bending moments.

o The 1/2 PTP t o r s i o n moments are, as would be expected, r e l a t i v e l y unaffected by t h e o p e r a t i o n of the device.

Harmonically D i l a t i o n a l A i r f o i l Tip The aeromechanical o p e r a t i o n of the Harmonically D i l a t i o n a l A i r f o i l T i p (HDAT) is assumed t o be more benign than those f o r the t o r s i o n a l l y a c t i v e devices, which are p o t e n t i a l l y s u s c e p t i b l e t o aeromechanical and/or a e r o e l a s t i c i n s t a b i l i t y . In t h e absence of test, no known i n s t a b i l i t i e s can be linked with the HDAT a t t h i s time. Consequently, the GOOOPA c a l c u l a t i o n s f o r t h i s device pose no s p e c i a l c o n s i d e r a t i o n s and a r e r e l a t i v e l y r o u t i n e . The device is aerodynamic performance r e l a t e d and, hence, a l l G400PA c a l c u l a t i o n s g e n e r a l l y r e q u i r e t r i m computations.

Parameter S e l e c t i o n f o r G400PA Calculations The G400PA c a l c u l a t i o n s of t h e HDAT u t i l i z e a i r f o i l aerodynamic d a t a look-ups based on thickness r a t i o i n s t e a d of r a d i a l s t a t i o n . The t h i c k n e s s r a t i o n d i s t r i b u t i o n for t h e b a s e l i n e (UH-60A) h e l i c o p t e r r o t o r blade i s given i n Table 11. This d i s t r i b u t i o n based on t h e SC1095 a i r f o i l series is g e n e r a l l y c o n s t a n t and r e f l e c t s a c u r r e n t trend t o cambered, r e l a t i v e l y t h i n n e r s e c t i o n s . For s u c c e s s f u l o p e r a t i o n of t h e HDAT, the a i r f o i l must c o n t r a c t t o as t h i n a s e c t i o n as is p o s s i b l e on t h e advancing side and commensurate d i l a t i o n must be implemented on t h e r e t r e a t i n g blade s i d e .

The p r i n c i p a l parameter s e l e c t i o n r e q u i r e d f o r t h e G400PA XDAT c a l c u l a t i o n s t h e r e f o r e c o n s i s t e d of a c q u i r i n g and preparing f o r G400PA i n p u t aerodynamic t h i c k n e s s r a t i o s .

a i r f o i l d a t a a t a v a r i e t y of The following t a b l e lists t h e a i r f o i l used t o c o n s t r u c t t h e required a i r f o i l d a t a t a b l e : Thickness Ratio A i r f o i l

0.080 . . . . . . . . RC-08

0.0945 . . . . . . . . SC1095

0.0955 . . . . . . . . SC1095/R8

0.120 . . . . . . . . sc1012

0.150 . . . . . . . . NACA 0015

Note t h a t t h e t h i c k n e s s r a t i o range thus a v a i l a b l e i n d i c a t e s t h a t more is a v a i l a b l e than c o n t r a c t u a l (.0945+.08).

d i l a t i o n a l range (.0945+.15) Thus, t h e t o t a l t h i c k n e s s r a t i o s c a l c u l a t e d assuming a harmonic p e r t u r b a t i o n were truncated t o minimum and maximum v a l u e s of .08 and .15, r e s p e c t i v e l y .

The parameter v a r i a t i o n s u s e d i n the G4OOPA c a l c u l a t i o n s are as follows:

o amplitude of p e r t u r b a t i o n a l thickness r a t i o s , A T / C . . . (0+.06)

o r o t o r azimuth angle f o r minimum thickness r a t i o s , JI ( 7 0 , 90, 110 Ceg) ‘/emin o spanwise e x t e n t : * * (0.10R, 0.15R)

o f l i g h t a i r s p e e d : . . . . . . . . . . . . . . . . . . . (74.6, 90.0 m / s )

G400PA Calculation R e s u l t s The a p p r o p r i a t e performance index f o r t h e DHAT as f o r t h e a l l - f l y i n g t i p i s t h e l i f t p e r e q u i v a l e n t drag r a t i o , L/De, (see Equation 1 9 ) . The c a l c u l a t i o n results f o r t h e DHATarepresented i n Figures 31 and 32. These f i g u r e s show t h e comparisons of t h e LID, with v a r i a t i o n s i n t h e parameters discussed above.

The r e s u l t s shown i n F i g u r e s 33 and 34 confirm t h e expected r e s u l t t h a t the HDAT is capable of i n c r e a s i n g t h e aerodynamic performance of h e l i c o p t e r r o t o r s i n forward f l i g h t . S p e c i f i c o b s e r v a t i o n s and i n t e r p r e t a t i o n s of t h e s e r e s u l t s are as follows: 1.

Maximum performance g a i n s i n L/De of approximately 11% and 9% are i n d i c a t e d a t t h e ~ 0 . 3 3 8 and 0.407 advance r a t i o s , r e s p e c t i v e l y .

2. The maximum performance g a i n s occur, as would be expected, f o r configura- t i o n s w i t h a minimum t h i c k n e s s aximuth a n g l e of 90 deg. ( f u l l advancing blade c o n d i t i o n ) .

V T = 9 C O m l s ( r = 0 4 0 7 ) BASELINE CASE 2A

I

l R T $ , , , T I C . deg 0 15R 90

- - - - - - - _ - _ _ _

0 15R 110

- - - 0 1 5 R 70

6.0 6'1

01 I I I I I 0 0.1 0.2 0.3 0.4 0.5 0.6 AMPLITUDE OF A r k Figure 33. Variation of UD, Characteristics of Harmonically Dllational Tip with Amplitude of Perturbational Thickness Ratio, O.15R Tip Span, p -0.407 a 3 8 3 - 6 1 03-19 8.5 .

VT t 74 6 mls @ = 0.338) 8.0

u

7.:

f

7.c aJ

s

6.5 7.E (b) VT = 90.0 m/s ( p = 0 407) 7.( BASELINE CASE 2A

\

6.: I I I I I 6.C 1 6 0.01 0.02 0.03 0.04 0.05 c AMPLITUDE OF Ark

Figure 34. Comparison of UD, Characteristics of Harmonically Dllational Tip for Variations

I n Flight Speed and Tip Span

a4 83-6- 1 03- 1 8 3 .

The maximum performance g a i n s occur a t p e r t u r b a t i o n a l t h i c k n e s s r a t i o amplitudes of .03 t o .035.

4 . The g a i n i n performance between 0.10R and 0.15R t i p span c o n f i g u r a t i o n s ! .

is i n excess of what would be expected from the r a t i o of t i p areas.

One p o s s i b l e explanation of t h i s r e s u l t i s t h e secondary g a i n s obtained from the increased thickness on the r e t r e a t i n g blade s i d e .

I '

CONCLUSIONS AND RECOMMENDATIONS An a n a l y t i c study has been performed of t h e p r a c t i c a l i t y of f o u r d i f f - e r e n t p a s s i v e a e r o e l a s t i c devices appended t o h e l i c o p t e r r o t o r blades f o r improving r o t o r aerodynamic performance, reducing c o n t r o l loads and/or a l l e v i a t i n g a i r f r a m e v i b r a t i o n . Since t h i s study was s t r i c t l y a n a l y t i c , the v a l i d i t y of t h e conclusions is heavily dependent on the accuracy of the modeling assumptions employed and on the depth of the study performed h e r e i n , Conclusions General Assessment of Devices 1. The p a s s i v e tuned t a b a s configured i n t h i s study is i m p r a c t i c a l . This is based on the s i g n i f i c a n t l y amplified 4P v e r t i c a l hub shear loads and t h e r e l a t i v e l y small a t t e n u a t i o n s achieved i n t h e l o n g i t u d i n a l and l a t e r a l loads.

2 . The c o n t r o l coupled t a b as configured i n t h i s study i s i m p r a c t i c a l .

This is based on t h e r e l a t i v e l y excessive incremental r o t o r l i f t changes p e r coupling gain (and consequently tab d e f l e c t i o n ) obtained as compared with the incremental blade t o r s i o n moment changes forming t h e b a s i s of t h i s device.

3. The a l l - f l y i n g t i p o f f e r s t h e p o t e n t i a l f o r s i g n i f i c a n t i n c r e a s e s i n aerodynamic performance. P r e s e n t f i n d i n g s p r o j e c t an approximately 20% i n c r e a s e i n LID, f o r t h i s device w i t h no s i g n i f i c a n t i n c r e a s e s i n blade bending o r t o r s i o n moments.

. 4.

The harmonically d i l a t i o n a l a i r f o i l t i p o f f e r s t h e p o t e n t i a l f o r moderate P r e s e n t f i n d i n g s p r o j e c t an i n c r e a s e s i n aerodynamic performance.

approximately 10% i n c r e a s e i n L/De f o r t h i s device.

Favorable f i n d i n g s f o r t h e a l l - f l y i n g t i p and t h e h a r n o n i c a l l y d i l a t i o n a l 5 .

This is because a i r f o i l t i p should be a d d i t i v e t o a s i g n i f i c a n t degree.

the former device achieves performance g a i n s by e l i m i n a t i n g performance robbing i n e f f i c i e n c i e s i n l i f t (notably r o t o r areas of negative l i f t , whereas t h e l a t t e r d e v i c e achieves g a i n by reducing l o s s e s accruing from drag rises due t o advancing blade c o m p r e s s i b i l i t y .

S p e c i f i c Conclusions R e l a t i n g t o Device Operation 1. For both performance r e l a t e d devices ( a l l - f l y i n g t i p and d i l a t i o n a l is a i r f o i l t i p ) t h e g a i n i n performance a r i s i n g from increased t i p span i n excess of t h e i n c r e a s e I n t i p a r e a . A p o s s i b l e explanation is t h a t t h e i n c r e a s e i n area occurs a t the inboard, aerodynamically more e f f i c i e n t end of t h e t i p .

The b e n e f i t s from t h e devices a r e n o t monotonic with f l i g h t speed and 2 .

a r e g e n e r a l l y more optimal a t t h e moderate advance r a t i o (~30.3 t o 0,35) f l i g h t speeds than a t t h e high advance r a t i o ones.

i n aero- 3 . The e f f e c t s of unsteady a i r l o a d s do n o t d e t r a c t from t h e g a i n s dynamic performance p r e d i c t e d f o r t h e a l l - f l y i n g t i p .

4 . The r e s u l t s from t h e use of a q u a s i - v a r i a b l e inflow procedure were inconclusive.

5 . The i n c l u s i o n of unsteady aerodynamics i s c r i t i c a l t o a s a t i s f a c t o r y modeling of t h e t o r s i o n a l l y a c t i v e devices for purposes of p r e d i c t i n g a e r o e l a s t i c i n s t a b i l i t y ( f l u t t e r ) .

6 . A l l implementations of t o r s i o n a l l y a c t i v e d e v i c e s on a b l a d e should be configured such t h a t t h e combined blade is a p p r o p r i a t e l y configured w i t h chordwise mass balancing t o decouple c r i t i c a l f l a t w i s e and t o r s i o n modes and thereby preclude f l u t t e r .

Recommendations Any f u t u r e work t o r e f i n e t h e assessment of the p a s s i v e tuned t a b should 1.

be d i r e c t e d t o parameter v a r i a t i o n s on an a c t i v e implementation of t h e harmonic t a b responses t o e s t a b l i s h what amplitudes and phases of those i f any, a c t u a l l y a t t e n u a t e t h e v i b r a t o r y hub loads.

responses, 2 , A rigorous interactional calculation, using the G4OOPA and Rotor Inflow Analysis (RIA) Programs should be made for the all-flying tip to more fully assess the impact of variable inflow on the improved L/De predictions for this device. This would require modification of the RIA to include the kinematics of the dynamic response of the all-flying tip.

3. Additional parameter variations, with regard to hinge location and the geometry of aerodynamic sweep should be made for the all-flying tip.

4. The detailed dynamic modeling and evaluation of an implementation for passive excitation of the dilational airfoil tip should be made. This evaluation would indicate (1) how practical and obtainable the ideal response is, and ( 2 ) what potential aeromechanical instabilities might exist for this device.

5 . A study should be made to detennine the extent to which the gains of the all-flying tip and the harmonic dilational airfoil tip are additive.

6. Future work on the control coupled tab should be directed to tab config- urations which maximize the section moment/lift characteristics such as a nonattached tab located as far aft of the balde section proper as is practical.

r REFERENCES 1 . Blackwell, R. H.: Investigation of the Compliant Rotor Concept.

USMlRDL Technical Report 77-7, June 1977, '.

2. Ruddell, A. J. : Advancing Blade Concept (ABC)m Development. Proceedings of the 23rd Annual National Forum of the American Helicopter Society, May 1976.

3. Wernicke, K. G.: Performance and Safety Aspects of the VX-15 Tilt Rotor Research Aircraft. Proceedings of the 33rd Annual National Forum of the American Helicopter Society, May 1977.

4 . Gabel, R.: Pendulum Absorbers Reduce Transition Vibration. Proceedings of the 31st Annual National Forum of the American Helicopter Society, May 1975.

5 . . Stroub, R. H: Performance Improvements With the Free-Tip Rotor.

Proceedings of the Specialists' Meetings on Rotor System Design of the American Helicopter Society, Philadelphia, PA., October 1980.

6. Bielawa, R. L.: Aeroelastic Analysis for Helicopter Rotor Blades With Time-Variable, Nonlinear Structural Twist and Multiple Structural Redundancy

- Mathematical Derivation and Program User's Manual. NASA Contractor Report

CR-2638, October 1976.

7. Houbolt, J. C. and G. W. Brooks: Differential Equations of Motions for Combined Flapwise Bending, Chordwise Bending, and Torsion of Twisted ' Nonuniform Rotor Blades. NACA Report 1346, 1958.

8 . Bielawa, R. L . : Blade Stress CalculaEions - Mode Deflection vs. Force

Integration. J. of the American Helicopter Society, Vol. 24, No. 3, July 1978.

9 . Bielawa, R. L . : Aeroelastic Analysis for Helicopter Rotors With Blade

Appended Pendulum Vibration Asorbers -- Mathematical Derivations and

Program User's Manual. NASA CR-165896, June 1982.

e 10. Theodorsen, T . and I. E. Garrick: Nonstationary Flow About a Wing- NACA Technical Aileron-Tab Combination Including Aerodynamic Balance.

Report 736, 1941.

P R a J D e 3 G PAGE BLANK NO!I' FILMED

11. Bielawa, R. L., S. A. Johnson, R. ti. Chi, and S. T. Gangwani:

Aeroelastic Analysis for Propellers - Mathematical Formulation and

Program User's Manual. NASA CR-3729, December 1983.

12. Bisplinghdff, R. L., H. Ashley, and R. L. Halfman: Aeroelasticity.

Addison-Wesley Publishing Co., Inc., Reading, MA., 1955, p p 281-286.

13. Reissner, E . : Effect of Finite Span on the Airload Distributions f o r

Oscillating Wings, Vol. I - Aerodynamic Theory of Oscillating Wings of

Finite Span. NACA TN 1194, March 1947.

14. Rowe, W. S., J. D. Sebastian, and M. C. Redman: Recent Developments in Predicting Unsteady Airloads Caused by Control Surface Notions. J. of Aircraft, Vol. 13, No. 12, December 1976, pp 955-961.

15. Egolf, T. A. and A. J. Landgrebe: A Prescribed Wake Rotor Inflow and - Flow Field Prediction Analysis - User's Manual and Technical Approach.

NASA CR 165894, June 1984.

16. Blackwell, R. H., et al.: Predesign Study for an Advanced Flight Research Rotor. Sikorsky Aircraft Report SER-510105, NASA CR-166405, December 1982.

17. Prouty, R. W.: A State-of-the-Art Survey of Two-Dimensional Airfoil Data, Journal of the American Helicopter Society, Vol. 20, No. 4, pp 14-25.

October 1974, 18, Chopra, I.: Dynamic Analysis of Constant-Lift and Free-Tip Rotors.

J. of the American Helicopter Society, Vol. 28, No. 1, January 1983.

3. R u p . n t ' s cnrlog No 2. Covunmont L o n No.

1. R m t No.

NASA CR166525 4 Tclo md Subtitlo 1 . O.tr A n a l y t i c I n v e s t i g a t i o n of H e l i c o p t e r Rotor Blade Appended A e r o e l a s t i c Devices 7. AuthorW 0. Worming Orvirrtion A ~ p o r t No R84-915774-24 Richard L. Bielawa 10. Work Unit No.

9 Rforning Olgll)imtMn Nrmr rd M d r r s United Technologies Research Center 11 - u t or Grrnt No East H a r t f o r d , CT 06108 NAS2-11008 13 T v p of R m md hid c0vu.d 1 : Soornoring bqmcv N D ~ M md A d d r a C o n t r a c t o r Report NASA-Ames Research Center 14 Soonsonng *glncv Code M o f f e t t F i e l d , CA 94035 505 42 11 16 A @ S l ' X t A n a l y t i c e v a l u a t i o n s of f o u r d i f f e r e n t p a s s i v e a e r o e l a s t i c d e v i c e s appended t o h e l i c o p t e r r o t o r b l a d e s is p r e s e n t e d . The d e v i c e s c o n s i s t of a p a s s i v e tuned t a b , a c o n t r o l coupled t a b , and a l l - f l y i n g t i p and a harmonic d i l a t i o n a l a i r f o i l t i p ; each d e v i c e w a s conceived f o r improving e i t h e r aerodynamic performance, or reducing v i b r a t o r y c o n t r o l l o a d s o r hub s h e a r s . The e v a l u a t i o n w a s performed u s i n g a comprehensive r o t o r a e r o e l a s t i c a n a l y s i s ( t h e G400PA code w i t h a p p r o p r i a t e m o d i f i c a t i o n s ) , t o g e t h e r w i t h d a t a for a r e a l i s t i c h e l i c o p t e r r o t o r b l a d e ( t h e UH-60A (90 m/s, 175 k t s ) . The r e s u l t s of t h i s Blackhawk), i n h i g h speed f l i g h t s t u d y show t h a t s i g n i f i c a n t performance (L/De) g a i n s can be achieved w i t h t h e a l l - f l y i n g free t i p . R e s u l t s f o r t h e harmonic d i l a t i o n a l a i r f o i l t i p show t h e p o t e n t i a l f o r moderate improvements i n L/D,. F i n a l l y , t h e r e s u l t s f o r the p a s s i v e tuned t a b and t h e c o n t r o l coupled t a b , as c o n f i g u r e d for t h i s s t u d y , show t h e s e d e v i c e s t o be i m p r a c t i c a l .

S e c t i o n s are i n c l u d e d which d e s c r i b e t h e o p e r a t i o n of e a c h d e v i c e , t h e r e q u i r e d G400PA m o d i f i c a t i o n s , and t h e d e t a i l e d r e s u l t s o b t a i n e d f o r each d e v i c e .

7. KY WorL ISuJlmOd k Author(rI1 la. Omribtian Stmonunt Tip C o n f i g u r a t i o n s Harmonic Unlimited Tuned Tab D i l a t i o n a l Tip S t a r Category 05 C o n t r o l Coupled Tab All-Flying Tip H e l i c o p t e r Rotor 0. Scuritv onrlf (of tknf0poftl 20 SICurirv ulruf. lof m t s -1 21. No of Pogos 22 Rice.

N o ne None 100