Analysis of the free-tip rotor wind-tunnel test results

NASA Technical Memorandum 86751 .

(NASA-TH-8675 1) ANALYSIS G? T H E EBEE-TIP N87-i 19 15 l j O l O H YXliD-TULNEL TEST EESULIS ( N A S A ) 7 0 p A v a i l : NTIS H C AGU/BF 8 0 1 CSCL O l C U n c l a s

Analysis of the Free-Tip Rotor

Wind-Tunnel Test Results

Robert H. Stroub

May 1985 I .

National Aeronautics and

I Date for general release

Space Ad ministration NASA Technical Memorandum 86751

Analysis of the Free-Tip Rotor

Wind-Tunnel Test Results

Robert H. Stroub, Ames Research Center, Moffett Field, California May 1985 National Aeronautlcs and Space Administration Ames Research Center Moffett Field California 94035 SYMBOLS lateral cyclic control, deg coefficients of Fourier equation A N yBp.J a aerodynamic center a.c.

longitudinal cyclic control, deg B1.S b span of free tip, m aerodynamic damping moment, N - m sec/rad bA friction damping moment, N - m b f lift deficiency factor C1 drag C t i p drag coefficient, Dt 0.5pStV lift tip lift coefficient, CLt 0.5pStV rate of change of lift with angle of attack, deg-’ cL a rotor lift CL/a rotor lift coefficient, PS(QR)~ itching moment tip pitching moment coefficient, positive nose-up, Cmt 0.5pStctV rate of change of tip pitching moment with angle of attack, positive ‘ m a

nose-up , deg-

(torque)n c / a rotor power coefficient, P pS(QRI3 C blade chord, m i i i c e n t e r of g r a v i t y c . g .

r e f e r e n c e c h o r d of t i p , m r a t e of change of t o r s i o n a l moment w i t h e l a s t i c twist of t e n s i o n t o r s i o n d M /d4 SP s t r a p , N.m/deg c e n t r i f u g a l f o r c e , N FCF moment of i n e r t i a of t h e t i p a b o u t t h e p i t c h a x i s , kg-m I i n c i d e n c e a n g l e , d e g it p S t c t V 2 , N.m/rad K e q u i v a l e n t a e r o d y n a m i c s p r i n g c o n s t a n t , 0.5Cm a a k s p r i n g c o n s t a n t o f c o n t r o l l e r , N.m/rad l e n g t h of t h e u n t w i s t e d t o r s i o n s t r a p s , m a.

c o n t r o l moment, N - m MC p i t c h i n g moment i n d u c e d by f l a p p i n g , N - m M 0 M p i t c h i n g moment i n d u c e d by l e a d - l a g , N - m m mass of t i p , kg R rotor r a d i u s , m r r a d i u s from p i t c h axis c e n t e r l i n e , m r a d i a l d i s t a n c e from r o t o r hub c e n t e r l i n e t o measurement s t a t i o n , m r b r e v o l u t i o n s p e r m i n u t e r Pm S p l a n f o r m area of rotor b l a d e s , m t i p planform area, m S t wing planform area, m 2 sw T p e r i o d of o n e c y c l e , sec TR i n e r t i a l f e a t h e r i n g moment w i t h p i t c h a n g l e , N-m/rad V free-stream v e l o c i t y , m/sec R rotor p r o p u l s i v e force c o e f f i c i e n t , -drag/2pV S / a i v angle of attack of tip, deg at wing angle-of-attack, deg a w blade flapping angle, deg B first and second time-derivative of blade flap angle, radlsec, rad/sec 2 , li, B respectively pitch axis and aerodynamic center offset, rn Ac Aa angle-of-attack change, deg tip pitch angle relative to the inboard portion of blade, positive A 0 nose-up, deg

A i , A 0 first and second time-derivative of A e , rad/sec, rad/sec2, respectively

blade lead-lag angle, deg first and second time-derivative of blade lead-lag angle, rad/sec, rad/sec2, respectively total pitch angle of tension-torsion strap, deg pitch angle of inboard portion of blade relative to rotor-disk plane, deg tip pitch angle relative to rotor-disk plane, deg pitch angle at 0.75 R , deg '0.75 A sweep angle, deg exponential decay coefficient, s e c ' 1 density of air, kg/m 3 strap helical angle, deg azimuth angle, deg Y tip speed, m/sec Q R damped natural frequency, rad/sec w V SUMMARY The results from a wind-tunnel test of a small-scale free-tip rotor are analyzed. The free-tip rotor has blade tips that are free to weathervane into the tip's relative wind, thus producing a more uniform lift around the azimuth. The free tip extended over the outer 10% of the rotor blade and included a simple, passive controller mechanism. The free-tip assembly, which includes the controller, functioned flawlessly throughout the test. In a test of the free-tip's response after passing through a vertical air jet, the tip pitched freely and in a controlled manner. Analysis of the tip's response characteristics showed the free-tip system's damped natural frequency to be 5.2 per rev. Tip pitch-angle responses to the local airstream are presented for an advance-ratio range of 0.1 to 0.397 and for a solid- ity weighted rotor lift-coefficient range of 0.038 to 0.092. Harmonic analysis of the responses showed a dominance by the first harmonic. Only at low advance ratios were there significant contributions from the higher harmonics. As a result of the tip being free, forward flight power requirements were reduced by 8% or more.

Considerably more power reduction was recorded for high-thrust conditions. The reduction in power requirements was attributed to a favorable influence of the tip's negative pitch angle relative to the inboard portion of the blade; a hypothesis i s presented to account for that favorable effect. The lessening of tip drag because of its negative relative pitch angle was also supported by fixed-wing wind-tunnel test of the same tip shape. In addition to the power reduction, flatwise blade bending moments were reduced by as much as 30% at the inboard blade stations.

Chordwise loads, however, were not reduced by the free tip. Loads going into the control system were reduced at all speeds and rotor lift levels. Details of tip and controller design and construction are included.

INTRODUCTION It is a major objective of helicopter research to develop means of improving performance and reducing vibration. Since performance and vibration can be affected by the blade tip, the tip has been the subject of considerable study. The free tip i s one of the proposed design changes, and it holds considerable promise for improv- ing performance and lessening oscillatory loads and vibration.

The free tip (fig. 1 ) i s characterized by ( 1 ) being separated from the rest of the blade, (2) by having the pitch axis forward of the aerodynamic center, and ( 3 ) by a control moment that is applied about the pitch axis. These characteristics add a new pitch degree of freedom t o the tip's motion. With the added pitch degree of freedom, the tip weathervanes into its relative wind to produce a moment balance about the pitch axis. The tip weathervanes about a prescribed null point that results in a finite pitch moment and, consequently, in a finite lift. Therefore, the free tip may generate a lift level that is nearly constant as it goes around the az imuth .

The free-tip design was derived as an offshoot from the constant-lift rotor described in reference 1 . The constant-lift rotor had many free pitching segments along the blade radius, and it included a pilot-controlled mechanism to vary the lift both collectively and cyclically. For the free-tip design, only one free pitching segment was included and there was no mechanism to vary the lift either collectively or cyclically by the pilot.

An analytical investigation of the free-tip was carried out to quantify a potential gain in rotor forward flight performance (ref. 2). That investigation concluded that a 10% reduction in power could be realized if the free tip would eliminate the negative lift on the advancing tip.

Although the free tip seemed attractive on a performance-improvement basis, there was considerable concern about the practicality of building it. Could the tip mass be balanced about the pitch axis at the 0.125 chord line? Could the polar moment of inertia be low enough to allow reasonable dynamic response? Could a simple controller be built? These questions were addressed under a contracted preliminary design study (ref. 3). It was concluded that a tip could be mass- balanced about the 0.125 chord line, with a resulting moment of inertia that would enable an undamped natural frequency of 7 to 8 per rev, based on its aerodynamic spring rate; moreover, a simple controller could be easily built.

Given the high performance-improvement potential and the feasibility of con- structing the tip and controller, an investigation was undertaken to explore experi- mentally the result of having a free tip on a rotor blade. A small-scale model rotor was modified to accept the first free tip. The rotor blade was modified by installing a steel pitch shaft at 13% chord to carry the free tip. A helical groove, cut into the steel shaft, accepted a guide pin which was inserted through the leading edge of the free tip and held in place by a retaining screw. This arrangement allowed the tip to pivot freely within the limits of the groove and still remain secured on the shaft. In addition, this arrangement causes the guide pin to carry the full centrifugal-force loading with the potential of having very high friction between the pin and the groove. To minimize friction, the guide pin and groove were lubricated by an oven-bonded dry lubricant. The pin in the helical groove was the tip's radial restraint and also served as the "controller," the device which produces a pitching moment about the pitching axis. The pin in the helical groove produced the pitching moment by creating a component of the tip's centrifugal load parallel to the helical groove in the shaft. Because this force component was acting at a radial distance from the centerline of the shaft, a torque was produced.

The model was built, bench tested, and then tested in the wind tunnel. In the wind-tunnel test, the tip did not pitch freely. In fact, it hardly pitched at L ~ a l l . The t i p went t o a nominal p i t c h a n g l e t h a t was 10" g r e a t e r t h a n t h e i n b o a r d p o r t i o n of t h e b l a d e a n d o s c i l l a t e d o n l y 20.5" a r o u n d t h e n o m i n a l s e t t i n g . The t i p ' s m o t i o n was l i m i t e d , e v e n though t h e a d v a n c i n g - t i p Mach number was as much as 0.83. The t e s t r e s u l t s were r e p o r t e d i n r e f e r e n c e s 4 and 5.

P o s t - t e s t a n a l y s i s r e v e a l e d a number of s h o r t c o m i n g s i n t h i s d e s i g n . F i r s t , t h e 0.05 R s p a n of t h e free t i p was t o o s h o r t , which made it i m p o s s i b l e t o u t i l i z e t h e l i f t i n g p o t e n t i a l of i n b o a r d s t a t i o n s t o i n c r e a s e t h e w e a t h e r v a n i n g c a p a b i l - i t y . S e c o n d , t h e c e n t r i f u g a l force of t h e t i p was c a r r i e d across s u r f a c e s i n s l i d - i n g c o n t a c t , which i n c r e a s e d t h e t i p ' s s u s c e p t i b i l i t y t o h i g h f r i c t i o n losses t h a t i n h i b i t e d m o t i o n . T h i r d , t h e c o n t r o l l e r was d e s i g n e d s o t h e c o n t r o l moment c o u l d n o t b e a d j u s t e d from t h e d e s i g n v a l u e . T h i s made it i m p o s s i b l e t o e v a l u a t e t h e d e s i g n o v e r a b r o a d r a n g e of t i p aerodynamic l o a d i n g .

S i n c e t h i s f i r s t w i n d - t u n n e l test d e m o n s t r a t e d d e s i g n s h o r t c o m i n g s of t h e model r o t o r t e s t e d b u t n o t of t h e f r e e - t i p i d e a , a new f r e e - t i p e v a l u a t i o n program was commenced. I n t h a t program, s e v e r a l p o t e n t i a l c o n t r o l l e r s a n d t i p s h a p e s were c o n s i d e r e d and tested. The b e s t c o n t r o l l e r and t h e b e s t t i p s h a p e were t h e n i n c o r - p o r a t e d i n t o a model r o t o r which was t e s t e d i n t h e Boeing Vertol wind t u n n e l .

The p u r p o s e of t h i s r e p o r t is t o p r e s e n t t h e a n a l y s i s and r e s u l t s of t h e f i r s t s u c c e s s f u l f r e e - t i p w i n d - t u n n e l test. Also p r e s e n t e d are t h e r e s u l t s of d e v e l o p - m e n t a l tests of t h e f r e e - t i p s y s t e m t h a t p r e c e d e d t h e w i n d - t u n n e l tests. A c o m p l e t e s e t of d a t a from t h e w i n d - t u n n e l t e s t is p r e s e n t e d i n r e f e r e n c e 6 .

MODEL DESCRIPTION A n e x i s t i n g f o u r - b l a d e d , 5.09-m-diam, Mach-scaled model rotor was m o d i f i e d t o i n c o r p o r a t e t h e f r e e - t i p d e s i g n . The c o m p l e t e r o t o r w i t h t h e free t i p is shown i n T h i s rotor was m o d i f i e d by f i g u r e 2 ; f i g u r e 3 shows a c l o s e - u p of t h e t i p s .

i n s t a l l i n g a s t e e l p i t c h s h a f t a t t h e t i p on t h e 13% c h o r d l i n e . The s h a f t t r a n s - f e r r e d t i p b e n d i n g and shear l o a d s t o t h e i n b o a r d p o r t i o n of t h e b l a d e ; it also s e r v e d as t h e p i t c h a x i s a b o u t w h i c h t h e t i p was free t o o s c i l l a t e .

p i t c h s h a f t was h o l l o w t o allow a c o n c e n t r i c i n n e r s h a f t t o g r i p t h e free The t i p and e x t e n d i n t o t h e i n b o a r d p o r t i o n of t h e b l a d e s where it a t t a c h e d t o t h e c o n t r o l l e r mechanism. The i n n e r s h a f t s e r v e d t o r e t a i n t h e t i p a g a i n s t c e n t r i f u g a l force and t o t r a n s m i t t h e p i t c h - c o n t r o l moment. F i g u r e 4 shows t h e t o t a l c o n f i g u r a - t i o n . The t i p is r e t a i n e d , u s i n g a l o c k n u t a r r a n g e m e n t i n which t h e " n u t " is a n i n t e g r a l p a r t of t h e free t i p and is clamped t o t h e t h r e a d e d end of t h e s h a f t . A Rulan b e a r i n g a p p l i e d t o t h e s h a f t minimized t h e f r i c t i o n a l forces between t h e free t i p a n d t h e p i t c h s h a f t .

The c o n t r o l l e r mechanism is a s i m p l e wire-wound, t e n s i o n - t o r s i o n s t r a p . A c o n t i n u o u s h i g h - s t r e n g t h wire, 0.152 mm diam, was wrapped 275 times a r o u n d two s p o o l s p l a c e d 5 . 7 1 c m a p a r t . One s p o o l was f i x e d t o t h e i n b o a r d p o r t i o n of t h e blade a n d t h e o t h e r s p o o l was a t t a c h e d t o t h e i n b o a r d end of t h e i n n e r s h a f t w i t h a c l e v i s j o i n t . The s t r a p s were e n c a s e d i n a n elastomer material which k e p t t h e s t r a p s s e p a r a t e d when s u b j e c t e d t o a n g u l a r d e f l e c t i o n s g r e a t e r t h a n 90". W i t h o u t t h e elastomer between the s t r a p s , t h e s t r a p s would come t o g e t h e r , and t h e o u t p u t t o r q u e would d e c r e a s e t o a n u n a c c e p t a b l y low v a l u e . L a r g e a n g u l a r p i t c h d e f l e c t i o n s between t h e two spools were a n i n t e g r a l p a r t of t h e d e s i g n c r i t e r i a . The s t r a p s were f a t i g u e - t e s t e d t o o v e r 2 m i l l i o n c y c l e s of + l o " p i t c h c h a n g e s w h i l e c a r r y i n g t h e f u l l d e s i g n t e n s i o n load a n d p r e t w i s t e d t o 125".

The c o n t r o l l e r c a r r i e s t h e t i p ' s f u l l c e n t r i f u g a l force a n d u s e s it t o p r o d u c e

I

most of t h e d e s i r e d c o n t r o l moment. C o n t r o l moment is p r o d u c e d by t h e c e n t r i f u g a l force a c t i n g on t h e t o r s i o n a l l y t w i s t e d s t r a p s as i n d i c a t e d i n f i g u r e 5. An a d d i - t i o n a l c o n t r o l moment component was t h e m e c h a n i c a l b e n d i n g of wires and t w i s t i n g of elastomer t h a t accompanied t w i s t i n g t h e s t r a p s . The t o t a l t o r s i o n a l moment is compu t e d by M = r F t a n 4 + [dM / d 4 ] $ C CF SP Although t h i s e q u a t i o n r e f l e c t s t h e p r o p e r p h y s i c a l r e l a t i o n s h i p , t h e t o r s i o n a l I twist a n g l e term 4 is n o t c o n v e n i e n t t o u s e . A more c o n v e n i e n t term is e C , t h e p i t c h a n g u l a r d e f l e c t i o n of t h e o u t b o a r d s p o o l r e l a t i v e t o t h e i n b o a r d spool. The r e l a t i o n s h i p between 9 a n d 4 is o b t a i n e d by e q u a t i n g a n arc l e n g t h y as I d e f i n e d by t h e t o r s i o n a ? twist a n g l e a n d by t h e p i t c h a n g l e B e : y = %4 ( 2 )

y = 4 G - j T Z

( 3 ) where A Q is t h e change i n s t r a p l e n g t h w i t h a n g u l a r d e f l e c t i o n . The c h a n g e i n s t r a p l e n g t h is t h e decrease or f o r e s h o r t e n i n g w i t h . To e v a l u a t e t h e m a g n i t u d e of A Q , A Q w i l l b e d e t e r m i n e d by computing t h e s t r a i g h t l i n e d i s t a n c e between p o i n t A a n d p o i n t B i n f i g u r e 5. I t is assumed t h e s t r a p d o e s n o t e l o n g a t e u n d e r t e n s i o n l o a d s o d i s t a n c e between p o i n t A and p o i n t B is t h e l e n g t h o f t h e u n t w i s t e d s t r a p .

2 2 + (n, - = ( X B - X A ) + ( Y e - YA) or 2 2 2 2 A X + A Y + ( Q - A Q ) = 9 , R e d e f i n i n g A X a n d AY t o i n c l u d e e C , A Y = r s i n 0 A X = r - r cos 0 c ' C and e q u a t i o n ( 5 ) becomes

( r - r cos e c ) 2 + ( r s i n e ) 2 + ( Q - A Q ) 2 = Q 2

C Expanding equation ( 6 ) and rearranging yields Solving for A t using the binomial theorem, the minimum value for A % is expressed as

A % = a - d a 2 - 2r(r - cos e )

C with 0 = 1 0 0 ' and the strap geometry parameters defined as a = 57.1 mm, and r = 6.85 mm, With A % defined, equation (3) can be evaluated. For ec = looo = 1.745 rad then, ( 1 - 0 ~ ) ~ = 142.9 term is very large compared to = 0.706, the (AEI2 term can be Since (re ) 2 C neglected amd equation ( 3 ) can be simplified to y = rec Equating arc length y as defined by equations (2) and (91, and If 41 is a small angle, then further modifications of equation ( 1 ) are simpli- fied. The angle (0 can be defined from the following expression based on geometry.

I$ = 2 sin 2Q = 9.76" With 41 only 9.76", then Also, the additional control moment term can be redefined as (dM / d + ) + = (dM /dec)ec SP SP Substituting equations (ll), (13), and (14) into equation ( 1 ) yields Mc = [ ( r /a)FCF + (dMc/dOc)]ec With e c = O P T + A e , t h e n T h u s , t h e c o n t r o l moment is e x p r e s s e d i n terms of t h e p i t c h - a n g l e d e f l e c t i o n of t h e c o n t r o l l e r o u t b o a r d end.

I n t h e a p p l i c a t i o n o f c o n t r o l moment t o t h e free t i p , a c o n t r o l moment i n v a r i - a n t w i t h t i p p i t c h d e f l e c t i o n was t h e ideal g o a l . However, t h e control-moment v a r i a t i o n from f i g u r e 6 , which is 9% of t h e maximum d e s i g n v a l u e of 6 . 7 8 N - m , was a c c e p t a b l e . Also, t h e 21.9% v a r i a t i o n owing t o h y s t e r e s i s was c o n s i d e r e d t o b e a c c e p t a b l e .

The c a l c u l a t e d uncoupled b l a d e n a t u r a l f r e q u e n c i e s a r e p r e s e n t e d i n f i g u r e 7 as a f u n c t i o n of r o t o r s p e e d . These f r e q u e n c i e s were c a l c u l a t e d u s i n g t h e t r a n s f e r e a c h mass h a v i n g matrix method. This method employed 2 5 lumped masses w i t h 5 d e g r e e s of freedom: f l a p p i n g , l e a d - l a g t o r s i o n , f l a p b e n d i n g , and c h o r d w i s e b e n d i n g . Although t h e s e f r e q u e n c i e s r e f l e c t a f i x e d - t i p c o n f i g u r a t i o n , t h e f l a t w i s e and c h o r d w i s e f r e q u e n c i e s are also a p p l i c a b l e t o t h e f r e e - t i p c o n f i g u r a t i o n , s i n c e t h e mass, c e n t e r - o f - g r a v i t y l o c a t i o n , and moments of i n e r t i a p r o p e r t i e s a r e t h e same, The s p a n w i s e d i s t r i b u t i o n of b l a d e mass a n d its o f f s e t from e l a s t i c a x i s are p r e s e n t e d i n f i g u r e 8. Another d e s i g n c r i t e r i o n was t h a t t h e t i p c e n t e r of g r a v i t y t o b e on t h e p i t c h a x i s a t 0.13 c. S p a c e and volume r e s t r i c t i o n s p r e s e n t e d t h e a c h i e v e m e n t of t h a t g o a l , however, a n d t h e t i p c . g . was located a t 0 . 1 4 c . The b l a d e had a 0.171-m c h o r d , a c o n s t a n t V23010-1.58 a i r f o i l , and -9.45' of l i n e a r twist from c e n t e r o f r o t a t i o n o u t t o and i n c l u d i n g t h e t i p . The f r e e t i p had a V23010-1.58 a i r f o i l w i t h a 5.8% c h o r d t a b added t o match t h e basic b l a d e a i r f o i l .

The 0.1 R t i p was c o n s t r u c t e d of Nomex core and magnesium s p a r c o v e r e d w i t h f i b e r - g l a s s . The u p p e r and lower s u r f a c e s were c o v e r e d cJith 0.013-mm-thick Mylar t o p r e v e n t a i r t r a n s f e r from t h e lower t o t h e u p p e r s u r f a c e . For c h o r d w i s e mass b a l - a n c e , t a n t a l u m balance w e i g h t s were i n s e r t e d i n t h e s p a c e ahead of t h e p i t c h a x i s .

T a b l e 1 p r e s e n t s a summary of t h e r o t o r d i m e n s i o n a l c h a r a c t e r i s t i c s .

Boeing Vertol's dynamic r o t o r t e s t s t a n d , which i n c o r p o r a t e s a n e l e c t r i c a l power s u p p l y and a six-component b a l a n c e , was u s e d f o r t h e t e s t . The t e s t was c o n d u c t e d i n t h e Boeing Vertol 20- by 2 0 - f t V/STOL wind t u n n e l . The w i n d - t u n n e l test s e c t i o n was c o n f i g u r e d w i t h s l o t t e d walls, s l o t t e d c e i l i n g , and s l o t t e d f l o o r t o g i v e 10% p o r o s i t y for f o r w a r d f l i g h t t e s t i n g .

I n s t r u m e n t a t i o n for t h e main b l a d e c o n s i s t e d of f o u r f l a p - b e n d i n g g a u g e s a t 0.13 R , 0.18 R , 0.38 R , 0.53 R a n d o n e c h o r d - b e n d i n g g a u g e a t 0.18 R . A d d i t i o n a l f l a p w i s e a n d chordwise b e n d i n g g a u g e s were l o c a t e d a t 0.9 R and o n t h e base of t h e shaft a b o u t which t h e t i p p i t c h e s . S h a f t t o r q u e was measured u s i n g t o r q u e g a u g e s o n t h e rotor d r i v e s h a f t .

B l a d e - f l a p p i n g motion a b o u t t h e f l a p h i n g e was c o n t i n u o u s l y measured by t r a n s - d u c e r s p l a c e d a t t h e f l a p h i n g e o f t h e i n s t r u m e n t e d b l a d e . The a n g l e of t h e t i p r e l a t i v e t o t h e main b l a d e was measured by a Hall-effect d e v i c e . I n t h a t d e v i c e , a t i n y m a g n e t i c o n t h e free t i p is used t o m o d u l a t e a n e l e c t r i c c u r r e n t t h r o u g h a s e m i c o n d u c t o r mounted on t h e inboard p o r t i o n of t h e b l a d e .

AERODYNAMIC DESIGN OF THE TIP for fast The p r i n c i p a l a e r o d y n a m i c d e s i g n c r i t e r i o n was h i g h ' m OL r e s p o n s i v e n e s s t o v e l o c i t y p e r t u r b a t i o n . For fast r e s p o n s i v e n e s s t o v e l o c i t y p e r - t u r b a t i o n , a minimum v a l u e for of -0.012 was selected. T h i s was b a s e d on ' m a s t u d i e s r e p o r t e d i n r e f e r e n c e s 2 and 7. I n t h o s e s t u d i e s , t i p - r e s p o n s e c h a r a c t e r i s - t i c s were e v a l u a t e d f o r b o t h a s i m p l e segment a n d a n i n t e g r a t e d s y s t e m of t h e r o t o r p l u s free t i p . Although a Cm = -0.012 was shown to allow s u f f i c i e n t a r e s p o n s i v e n e s s t o p r o v i d e performance improvement and r e d u c e d v i b r a t o r y l o a d s , t h i s d i d n o t p r e c l u d e d e s i g n i n g t o a g r e a t e r m a g n i t u d e i n C t o e n a b l e faster r e s p o n s e m t o a n g l e - o f - a t t a c k p e r t u r b a t i o n . a The s y s t e m n a t u r a l f r e q u e n c y and damping c h a r a c t e r i s t i c s were e x p e c t e d t o b e s u f f i c i e n t t o n e g a t e t h e p o s s i b i l i t y of f l u t t e r . However, t h e f i n a l p l a n f o r m con- f i g u r a t i o n was e x p e c t e d t o h a v e a g r e a t i n f l u e n c e on t h e t i p damping c h a r a c t e r i s - t i c s , e s p e c i a l l y when sweep is i n c l u d e d .

Aerodynamic d e s i g n was a l s o i n f l u e n c e d by s t r u c t u r a l r e q u i r e m e n t s . The p a r a - mount s t r u c t u r a l c o n s t r a i n t s were the flatwise b e n d i n g moment a t t h e i n b o a r d e d g e of t h e p i t c h shaft and t h e c e n t r i f u g a l force o n t h e c o n t r o l l e r a s s e m b l y . T h e s e two c o n s t r a i n t s n e c e s s i t a t e d t i p c h o r d t a p e r t o r e d u c e maximum l i f t c a p a b i l i t y , t o move t h e s p a n w i s e c e n t e r of p r e s s u r e i n b o a r d , a n d t o lower t h e w e i g h t a n d t h e p i t c h i n e r t i a of t h e t i p . T r a n s m i t t a l of t h e c h o r d w i s e and flatwise b e n d i n g moment from t h e t i p t o t h e p i t c h s h a f t n e c e s s i t a t e d t h e p i t c h s h a f t e x t e n d i n g t o h a l f t h e s p a n of t h e t i p . T h i s a l l o w e d t h e r e a c t i o n forces t o b e w i t h i n s t r u c t u r a l limits of t h e t h i n - w a l l t i p s e c t i o n , b u t forced chord t a p e r and sweep t o b e i n c o r p o r a t e d o n l y o v e r t h e o u t b o a r d 50% of t h e t i p . T i p chord t a p e r of 0.3 was r e q u i r e d t o s a t i s f y t h e s t r u c t u r a l r e q u i r e m e n t s . Sweeping t h e t i p 35" was more t h a n s u f f i c i e n t t o meet Cm = -0.012 c r i t e r i o n , as determined from t h e w i n d - t u n n e l t e s t d a t a p r e s e n t e d i n a f i g u r e 9.

PRETEST CHECKOUT Before w i n d - t u n n e l e n t r y , t h e f r e e - t i p rotor was r u n i n a test c e l l t o d e t e r - mine e x p e r i m e n t a l l y t h e n a t u r a l f r e q u e n c y of t h e f r e e - t i p s y s t e m and t o d e t e r m i n e i f T h i s would show t h e q u i c k n e s s of t h e s y s t e m was c r i t i c a l l y damped or underdamped.

the free-tip's reaction to flow perturbations. Satisfaction of these quanitative objectives would determine the readiness of the free tip for a wind-tunnel test.

The experimental natural frequency and damping characteristics were determined by analyzing the response to an abrupt change in angle of attack. An abrupt Aa input was obtained by driving the blades through a vertical airjet that caused the tip to pitch nose-down. After leaving the air jet, the tip saw an abrupt negative change in angle of attack, to which it responded by pitching nose-up to some equi- librium pitch angle. A schematic of the test setup is presented in figure 10, which also shows the tip angle-of-attack change and the deflection as it passes by the jet. Tip response after leaving the air jet was used to determine frequency and damping characteristics because the air-velocity states were better known. Although the air-velocity characteristics are better known, they cannot be considered analytically constant, because of recirculation in the room. Blade pitch, e o was varied from 0" to 8", but this produced considerable recirculation within'z?; test chamber. The recirculation was probably uneven across the rotor disk and around the azimuth. This unevenness was attributed to the rectangular shape of the of the rotor to the walls (one wall being about 25% open to test cell, the proximity the outside atmosphere), and blowing at only one small area of the disk.

Experimentally derived frequency and damping characteristics were compared with analytically derived characteristics to evaluate the weathervaning capabilities of the tip.

Analytical Derivation of Tip Dynamic Response The analytical characteristics were derived using the response of a second- order system. From the free-body model shown in figure 1 1 , the response equation is derived as

bf(bt - e , )

- Kaat - TROt + Mc

- k(et - e , ) + M + M = 0 ( 1 7 ) -Iet - bAat -

B 5

lit - e a t

is the damping moment produced by aerodynamics that include the effect where bAat is damping from friction forces generated

of tip planform, [bf(it - iL)]/1it - 6,l

by the tip oscillating about the pitch shaft, K is the rate of change of aerody- a namic pitching moment with angle of attack, TROt is the feathering moment produced by centripetal acceleration on the mass located forward and aft of the pitch axis, and where M and M are inertial moments produced by the tip's c.g. offset from 6 5 the pitch axis in conjunction with flap and lead-lag angles plus their respective velocities and accelerations.

A e = e t - e , , R e a r r a n g i n g e q u a t i o n (7) a n d i n c l u d i n g t h e i d e n t i t y t h a t s i m p l i f y t h i s moment e q u a t i o n . First, A number o f a s s u m p t i o n s were made it was assumed t h a t t h e i n b o a r d p o r t i o n of t h e blade d i d n o t t o r s i o n a l l y deflect while p e n e t r a t i n g t h e j e t . T h i s is a r e a s o n a b l e a s s u m p t i o n s i n c e t h e a i r j e t was f o c u s e d on t h e t i p i t s e l f w i t h l i t t l e e f f l u x i m p i n g i n g on t h e i n b o a r d p o r t i o n of t h e b l a d e , and t h e i n b o a r d section t o r s i o n a l i n e r t i a was a b o u t 10 times t h a t of t h e t i p . S e c o n d , it was assumed t h e eo.75 was z e r o . For t h i s t e s t of t i p r e s p o n s i v e - n e s s , 9 c o u l d h a v e been any v a l u e . Z e r o eo.72 was selected t o m i n i m i z e 0 . 5 r e c i r c u l a z i o n effects. T h i r d , at was assumed t o e a p p r o x i m a t e l y t h e same as 88. F o u r t h , it was assumed t h a t t h e a i r j e t effects c a u s e d no s i g n i f i c a n t blade f l a p p i n g o r l e a d - l a g . F i f t h , K was assumed t o be n u m e r i c a l l y t h e r a t e of c h a n g e Q of p i t c h i n g moment w i t h r e s p e c t t o t i p i n c i d e n c e , K i , rather t h a n w i t h r e s p e c t t o t h e a n g l e of attack of t h e b l a d e . T h i s is r e a s o n a b l e s i n c e t h e i n b o a r d p o r t i o n of t h e b l a d e does n o t e x p e r i e n c e t h e e f f l u x d u r i n g j e t p e n e t r a t i o n and therefore would n o t h a v e a n a n g l e - o f - a t t a c k c h a n g e d u r i n g t h a t time. Neither would there be a n a n g l e - o f - a t t a c k c h a n g e on t h e inboard s e c t i o n coming o u t o f t h e a z i m u t h a l z o n e o f t h e j e t a n d d u r i n g t h e t i p r e s p o n s e . With t h e a b o v e a s s u m p t i o n s , e t = e , = o a = A 8 t

A t = A 6

6 = 8 B = 0 , a n d t h e r e f o r e M = 0 5 = 5 = 5 = 0 , and t h e r e f o r e M = 0 K = K a i S i n c e e t e + A e and e , = 0 , then e t = Ae, e t = 8 8 , and e t = A B . I n s e r t i n g % these terms i n t o e q u a t i o n (81, I A B + ( b A + bf)A6 + ( K i + k + T R ) A O = Mc ( 1 9 ) T h i s e q u a t i o n was s o l v e d u s i n g L a p l a c i a n t e c h n i q u e s which a c c o u n t for i n i t i a l c o n d i - of A i = 0 , M, = 0 , a n d AB = 4 " .

t i o n s The expression f o r the response is then determined to be where + k + TR 1/2

I 3

a = bf + b A

x =

wIAB0 - 1 X = tan ~ 1 Aio Numerical estimates of the parameters are as follows: where dCm/dA8 i s a static value (from R. H. Stroub and J . van Aken, "Tip Aerody- namic Characteristics from a Wind-Tunnel Test of a Semispan Wing," proposed NASA TM) and C 1 is an estimated correction f o r dynamic oscillation from reference 7. For dCm/dAO = 0.01, Q R = 213.4 m/sec, C1 = 0.825, and the tip geometry Ki = 80.22 N-m/rad.

L b A = (dCm/d6)(p/4)aRStct, The aerodynamic damping coefficient is defined as where dCm/dC) is from reference 8. For dCm/d6 = 2.6, bA = 0.1734 N-m/rad/sec.

With tip lift load and flapping near zero, then bf = 0, k = 3.519 N.m/rad from I = 2.84x10-' kg-m2 (from geometry).

figure 6, TR = 0.369 N.rn/rad, and The coefficients of the response equation (10) are now determined: w = 443.18 rad/sec a = 443.18 rad/sec x = 314.1 sec-' X , = 1.5708 rad After the coefficients are substituted into equation (10) the response equation for 796 rpm, o r QR = 213.4 m/sec, becomes -314. It A9 = Ago e sin(443.18t + 1.571) = A e e -314.1t cos(443.18t) Likewise, at 740 rpm, A9 = be e -292 cos (428.28t) and at 600 rpm, A0 = A9 0 e -236 * 7t cos ( 353.95t) Comparison of Analytical and Experimental Values From these three analytical response equations, the frequency and damping characteristics will be compared to experimental values determined from the time- histories shown in figure 12 for three rotational speeds. Figure 13 shows the techniques used in determining the frequency and damping characteristics from the experimental data. A comparison of analytical and experimental values is presented below.

Test Analytical x rpm w / Q , per rev 1 w/n, per rev - 796 5.2 159 5.32 314.1 5.53 292.0 740 5.2 29 1 600 5.45 150 5.63 236.7 Test results showed good agreement with the analytical model for the natural frequency, but damping characteristics did not correlate well.

Although damping was less than expected, the free tip was a well-damped system. This test of the free tip's responsiveness showed the free-tip system to be a responsive, stable, and well-damped system ready for a wind-tunnel test. With the free-tip system shown to be underdamped with a damped natural frequency of 5.2, the free-tip rotor was ready for a wind-tunnel test.

TEST CONDITIONS AND PROCEDURES The prime objective of the wind-tunnel test was to evaluate the free-tip con- figuration to determine its advantages over a similar fixed-tip configuration. In 1 1 o r d e r t o make a n e f f e c t i v e c o m p a r i s o n , b o t h f i x e d - t i p a n d f r e e - t i p c o n f i g u r a t i o n s were e v a l u a t e d a t a p r e s c r i b e d p r o p u l s i v e f o r c e c o e f f i c i e n t a n d m i n i m i z e d b l a d e f l a p p i n g , w i t h t h e r o t o r l i f t c o e f f i c i e n t o r a d v a n c e r a t i o b e i n g t h e v a r i a b l e .

R o t o r l i f t sweeps were made a t V / Q R = 0.3 a n d 2 = 0.05, w i t h m i n i m i z e d c y c l i c of t h e maximum l i f t c o e f f i c i e n t a t t a i n a b l e f l a p p i n g . T h e s e d a t a g a v e a n i n d i c a t i o n w i t h a f r e e - t i p r o t o r . To o b t a i n a c o m p a r i s o n w i t h f o r w a r d s p e e d , a n a d v a n c e - r a t i o sweep was c o n d u c t e d from 0 . 2 t o 0 . 4 a t CL/a = 0 . 0 7 , 2 = 0.05, a n d m i n i m i z e d f l a p - T h i s p r o v i d e d a s i m u l a t e d speed-power p o l a r a t a c o n t e m p o r a r y d e s i g n l i f t p i n g .

c o e f f i c i e n t and a t a p r o p u l s i v e - f o r c e c o e f f i c i e n t r e p r e s e n t i n g a n e q u i v a l e n t f l a t - p l a t e d r a g area o f a r e l a t i v e l y low-drag h e l i c o p t e r . R o t o r - t i p s p e e d was h e l d c o n s t a n t a t 213 m/sec, t h e n o r m a l t i p s p e e d f o r t h i s r o t o r . I n a d d i t i o n t o t h e s t a n d a r d a d v a n c e - r a t i o sweep, t h e f r e e - t i p - r o t o r t e s t e n v e l o p e was expanded t o i n c l u d e a d v a n c e r a t i o s down t o 0.1 i n o r d e r to test t h e t i p ' s b e h a v i o r i n t h a t t u r b u l e n t e n v i r o n m e n t .

Data from t h i s t e s t were l i m i t e d b e c a u s e of r e s o n a n c e p r o b l e m s i n the t e s t r i g i t s e l f . The r i g d e v e l o p e d a n i n - p l a n e r e s o n a n c e p a r t way t h r o u g h t h e t e s t . With t h e b l a d e s o f f , t h e r e s o n a n c e was found t o be s e n s i t i v e t o rpm, w i t h t h e t e s t rpm o f 796 b e i n g v e r y n e a r t h e a m p l i f i c a t i o n p e a k . I n a d d i t i o n , a m p l i f i c a t i o n i n c r e a s e d f u r t h e r when t h e r o t o r s h a f t was t i l t e d f o r w a r d from t h e z e r o s h a f t - a n g l e p o s i - t i o n . The r e s o n a n c e a m p l i f i c a t i o n was r e d u c e d t o z e r o a t 552 rpm, which is a t i p This t i p s p e e d was too low t o p e r m i t t h e o b t a i n m e n t o f s p e e d of o n l y 147 m/sec.

v a l i d rotor p e r f o r m a n c e and l o a d s i n f o r m a t i o n s u i t a b l e f o r r e a l i s t i c e v a l u a t i o n of t h i s f r e e - t i p c o n f i g u r a t i o n . For e v a l u a t i o n p u r p o s e s , l o w e r t i p s p e e d d o e s n o t e n a b l e e v a l u a t i o n of c o m p r e s s i b i l i t y e f f e c t s , which are s i g n i f i c a n t c o n t r i b u t o r s t o t h e t i p ' s aerodynamic moment c h a r a c t e r i s t i c s . Because d a t a for 147-m/sec t i p s p e e d d o e s n o t i n c l u d e c o m p r e s s i b i l i t y e f f e c t s , t h e o n l y u s e f u l t e s t d a t a are l i m i t e d t o t h e 213-m/sec d a t a set i n c l u d e d h e r e i n .

The p r o c e d u r e f o r s e t t i n g e a c h d a t a p o i n t was as f o l l o w s : ( 1 ) s e t r o t o r t i p s p e e d and d e s i r e d advance r a t i o , and ( 2 ) a d j u s t c o l l e c t i v e p i t c h , c y c l i c c o n t r o l s , a n d s h a f t a n g l e t o a c h i e v e d e s i r e d r o t o r l i f t and p r o p u l s i v e force c o e f f i c i e n t , a n d to m i n i m i z e f i r s t - h a r m o n i c f l a p p i n g . A l l these d e p e n d e n t v a r i a b l e s were v i s u a l l y d i s p l a y e d i n real time f o r t h e r o t o r p i l o t t o u s e i n s e t t i n g t h e test p o i n t .

DATA CORRECTIONS AND PRESENTATIONS The d a t a o u t p u t from t h i s t e s t reflect c o r r e c t i o n s for hub tares. Hub tares were o b t a i n e d f r o m blades-off t e s t i n g o v e r t h e r a n g e o f dynamic p r e s s u r e s and s h a f t tilt a n g l e s u s e d i n b l a d e s - o n t e s t i n g . I n c l u d e d i n t h e hub tares were t h e i n t e r f e r - e n c e effects of t h e n o n m e t r i c t e s t r i g on t h e hub d r a g itself. Hub tares d i d n o t i n c l u d e effects of t h e r o t o r downwash.

N o w i n d - t u n n e l wall c o r r e c t i o n s were a p p l i e d t o t h e d a t a , b u t b l o c k a g e correc- The r o t o r power d a t a p r e s e n t e d t i o n s were a p p l i e d t o c o r r e c t f r e e - s t r e a m v e l o c i t y .

h e r e i n reflects s t a n d a r d i z e d trim c o n d i t i o n s b a s e d on p r o p u l s i v e force l e v e l and lift level when appropriate. Corrections were applied to the data to compensate for small increments from the standardized conditions. The applied corrections are presented as follows: 1. To correct for rotor lift increment from CL/u = 0 . 0 7 : = 0.05: 2. To correct for rotor propulsive force increment from Since test lift and propulsive force values were very close to the standardized condition, corrections were 1 % o r less for the whole test.

Dynamic loads, bending moments, and tip-deflection angles are the averaged data taken over ten rotor revolutions. The averaged data were then processed to determine mean values, peak-to-peak amplitudes, and harmonic content. Figures depicting tip At3 variation around the azimuth are the data for one revolution repeated over two revolutions. This was done to aid visualization over the azimuthal sector between 270" and 90".

RESULTS Tip Pitching Behavior at V / Q R = 0.305 The free tip's weathervaning capability produced pitch angle time-histories that demonstrate the varied aerodynamic environment in which it operates. Figure 1 4 shows the azimuthal variation of the tip's A0 over two rotor revolutions at an advance ratio of 0.305 and f o r various rotor thrust coefficients; rotor propulsive force coefficient was held constant at 0.05. The At3 has a general overall nega- tive magnitude which was probably caused by a combination of controller output moment (6.0 N-m) and local flow conditions. The tip was probably still producing positive lift, but less than it would had it been fixed.

The free-tip weathervaning enabled it to provide easy identification of vor- tices it may have encountered. To accomplish this, it must be assumed the tip encounters a shed vortex with counterclockwise rotation. The encounter is such that the counterclockwise rotation results in the tip experiencing a downward velocity increment first and an upward velocity increment second. This order of velocities encountered causes the free tip to pitch up at it approaches the vortex center and then pitch down as it retreats from the center. Therefore, an encounter with a counterclockwise vortex would be identified by a positive At3 increment followed by a n e g a t i v e A8 i n c r e m e n t . F i g u r e 14 may show a n example of t h i s r e s p o n s e a t a b o u t Y = 75" when CL/a - < 0.07. Over a 45" a z i m u t h a l r e g i o n c e n t e r e d a t Y = 7 5 O , t h e A 8 t r a c e h a s small u n d u l a t i o n s . With i n c r e a s i n g C /a, t h e u n d u l a - L t i o n s , o r w a v i n e s s , become more s e v e r e . For two r e a s o n s , t h i s g r o w t h i n w a v i n e s s w i t h C / a c o u l d b e i n d i c a t i v e of a v o r t e x e n c o u n t e r : L 1 . The s t r e n g t h o f t h e e n c o u n t e r e d v o r t e x is d i r e c t l y r e l a t e d t o t h e r o t o r t h r u s t l e v e l : t h e h i g h e r the rotor t h r u s t , t h e s t r o n g e r t h e v o r t i c i t y .

2 . The r o t o r - t i p - p a t h p l a n e was t i l t e d more a f t a t h i g h CL/a t h a n a t low C / a i n o r d e r t o m a i n t a i n t h e same p r o p u l s i v e force a t b o t h t h r u s t l e v e l s . With L more a f t tilt, a r o t o r b l a d e is closer t o a p r e v i o u s l y g e n e r a t e d v o r t e x , and g r e a t e r v o r t e x i n d u c e d v e l o c i t i e s a r e e n c o u n t e r e d .

T h e s e two e f f e c t s o f t e n combine where, a t h i g h e r C /a, t h e v o r t i c e s g e n e r a t e d are L s t r o n g e r , h a v e h i g h e r v e l o c i t i e s , and are closer t o t h e t i p - p a t h p l a n e . Now, i f t h e free t i p were t o e n c o u n t e r e s these v o r t i c e s , t h e t i p A8 trace would e x h i b i t a growth i n w a v i n e s s with i n c r e a s i n g CL/a. T h e r e f o r e , t h e i n c r e a s e d w a v i n e s s e x h i b - i t e d a t a b o u t Y = 75" s u g g e s t s t h a t a t i p v o r t e x was e n c o u n t e r e d .

Harmonic a n a l y s i s of t h e free t i p ' s waveform is p r e s e n t e d i n f i g u r e 15. The 1 p e r r e v d o m i n a t e s by f a r , w i t h t h e h i g h e r h a r m o n i c terms b e i n g of t h e o r d e r o f 0.5" o r less. The magnitude of t h e 1 p e r r e v is s e e n t o b e p r o p o r t i o n a l t o t h e r o t o r l i f t c o e f f i c i e n t .

W e h a v e s e e n t h e t i p ' s A8 a z i m u t h a l and h a r m o n i c c h a r a c t e r i s t i c s for a C / a sweep a t V / Q R = 0.3. With some v a r i a t i o n owing t o p o s s i b l e b l a d e - v o r t e x L e n c o u n t e r s , t h e g e n e r a l c h a r a c t e r of these t i m e - h i s t o r i e s was n e a r l y t h e same f o r a l l l i f t l e v e l s . T h i s r e l a t i v e e q u i v a l e n c e for a l l CL/a is a r e s u l t of the gen- eral flow state being v i r t u a l l y e s t a b l i s h e d by t h e a d v a n c e r a t i o , making v a r i a t i o n w i t h CL/a a s e c o n d a r y i n f l u e n c e . With v a r i a t i o n i n a d v a n c e r a t i o , t h e s i t u a t i o n is d i f f e r e n t .

T i p P i t c h i n g B e h a v i o r w i t h Advance Ratio The t i p ' s A B a z i m u t h a l c h a r a c t e r i s t i c s w i t h a d v a n c e r a t i o are d e p i c t e d i n f i g u r e 16. The waveform for V / Q R = 0.1 shows what h a p p e n s when t h e t i p e n c o u n t e r s two l a r g e d i s t u r b a n c e s , o n e a t a b o u t Y = 72O and t h e o t h e r a t a b o u t Y = 3 2 0 " .

One o r b o t h of t h e s e d i s t u r b a n c e s may b e a t i p v o r t e x s h e d from a p r e v i o u s l y p a s s i n g b l a d e . T h i s is p a r t i c u l a r l y p o s s i b l e a t t h e r e g i o n a r o u n d Y = 72O. The r e s p o n s e of t h e t i p t o t h e s e d i s t u r b a n c e s is q u i c k and s t a b l e . With i n c r e a s i n g a d v a n c e r a t i o , t h e t i p ' s r e s p o n s e d i m i n i s h e d i n these two a z i m u t h a l r e g i o n s . T h i s s u g g e s t s t h a t t h e i n t e n s i t y of b o t h d i s t u r b a n c e s was a l s o r e d u c e d , and t h e d i s t u r b a n c e s n e a r l y d i s a p p e a r e d a t V / Q R = 0.3. Only a small r e m n a n t of t h e e f f e c t s of t h e t h i r d - q u a d r a n t d i s t u r b a n c e r e m a i n s . The peak-to-peak a m p l i t u d e of t h e o v e r a l l trace a l s o d i m i n i s h e s , w i t h a d v a n c e r a t i o i n c r e a s i n g t o 0.3. Beyond V / Q R = 0.3, t h e peak-to-peak a m p l i t u d e i n c r e a s e s a g a i n . t h e s e a m p l i t u d e i n c r e a s e s are d u e t o t h e l a r g e c h a n g e s i n t h e b a s i c a e r o d y n a m i c e n v i r o n m e n t a s s o c i a t e d w i t h h i g h e r - s p e e d f l i g h t . The t i p ' s A B becomes more p o s i t i v e on t h e a d v a n c i n g side n e a r Y = 120" as t h e i n b o a r d p o r t i o n o f t h e b l a d e r e d u c e s p i t c h t o a c h i e v e r o t o r trim. On t h e r e t r e a t i n g s i d e a t a b o u t Y = 270", t h e A B becomes more n e g a t i v e , as c y c l i c p i t c h d r i v e s t h e i n b o a r d s e c t i o n t o h i g h e r p i t c h a n g l e s f o r r o t o r trim.

I n f i g u r e 16, t h e waveform f o r V / n R = 0.1 a l s o d e m o n s t r a t e s t h e h i g h - p i t c h - rate g e n e r a t i n g c a p a b i l i t y o f t h e f r e e t i p . The p i t c h rate o f 1857"/sec (32.4 r a d l s e c ) is i n f e r r e d by t h e 10.5" A B c h a n g e t h a t o c c u r r e d o v e r a 27" azi- m u t h a l i n c r e m e n t c e n t e r e d a t a b o u t I = 72".

F i g u r e 17 p r e s e n t s a c o m p i l a t i o n of t h e A B waveforms for a l l t h e a d v a n c e ratios. T h i s c o m p i l a t i o n shows t h e a e r o d y n a m i c e n v i r o n m e n t c h a n g i n g o v e r d i f f e r e n t sectors of t h e rotor d i s k , a s t h e r o t o r is a t v a r i o u s f o r w a r d s p e e d s .

The harmonic c o n t e n t of t h e t i p ' s d i f f e r e n t i a l p i t c h a n g l e v a r i e d c o n s i d e r a b l y w i t h a d v a n c e r a t i o . F i g u r e 1 8 shows t h i s v a r i a t i o n . A t V / Q R < 0 . 2 , t h e t i p r e s p o n s e h a s s i g n i f i c a n t c o n t e n t i n h a r m o n i c s 1 t h r o u g h 8, w i t h t h e f i r s t a n d s e c o n d h a r m o n i c s h a v i n g t h e l a r g e s t a b s o l u t e m a g n i t u d e . The r e m a i n i n g h a r m o n i c s , 3 t h r o u g h 10, t a k e n as a c o m p l e t e g r o u p , r e f l e c t c o n s i d e r a b l e g r o w t h w i t h d e c r e a s i n g a d v a n c e ratio. T h i s g r o w t h is p r o b a b l y a r e s u l t o f t h e free t i p coming c l o s e r t o , o r e n c o u n t e r i n g , t i p v o r t i c e s s h e d from t h e p r e v i o u s p a s s a g e of a b l a d e . T h i s is s u g g e s t e d by t h e waveforms shown i n f i g u r e 19, where o n l y h a r m o n i c s 3 t h r o u g h 10 were summed t o p r o d u c e waveforms f o r V / Q R = 0.1 t o 0.2. A t t h e s e low a d v a n c e ratios, t h e s u s p e c t e d i n f l u e n c e of shed v o r t i c e s is v e r y s t r o n g , b e c a u s e t h e t i p - p a t h - p l a n e tilt is v e r y low a n d t h e s t r e n g t h of t h e t i p v o r t e x is v e r y h i g h . T h e r e - fore, t h e h i g h e r h a r m o n i c c o n t e n t of t h e A B waveform is p r o b a b l y a r e s u l t of t h e p r o x i m i t y o f t i p v o r t i c e s when the advance r a t i o is less t h a n 0.2.

With a d v a n c e ratios g r e a t e r than 0.2, t h e r e is c o n t i n u e d g r o w t h a n d dominance o f t h e f i r s t h a r m o n i c c o n t e n t ( f i g . 18). I t is l i k e l y t h a t a t least p a r t of t h i s g r o w t h was c a u s e d by t h e i n c r e a s e i n l o n g i t u d i n a l c y c l i c p i t c h b e i n g i m p r e s s e d upon t h e i n b o a r d p o r t i o n o f t h e b l a d e . While t h e i n b o a r d p i t c h is b e i n g i n c r e a s e d by c y c l i c p i t c h , t h e free t i p a p p e a r s to n u l l i f y t h a t i n c r e a s e i n l o n g i t u d i n a l c y c l i c .

F i g u r e 16 shows t h a t a t V / Q R = 0.391, A B h a s a l a r g e n e g a t i v e v a l u e a t Y = 270" when l o n g i t u d i n a l c y c l i c p i t c h is d r i v i n g t h e i n b o a r d b l a d e t o a maximum is programmed t o a t t e m p t t o m a i n t a i n n e a r l y u n i - v a l u e . Keep i n mind t h a t t h e t i p form l i f t a r o u n d t h e a z i m u t h a n d , therefore, it n e e d s a h i g h a n g l e o f a t t a c k a t Y = 270", as d o e s t h e r e s t o f t h e b l a d e . Also n o t e t h a t t h e r o t o r d i s k is t i l t e d f o r w a r d 5". When t h e r o t o r tilt is added t o t h e local downwash a n g l e , t h e r e is a n e g a t i v e i n f l o w a n g l e , p e r h a p s of the o r d e r of -8" t o -10". And when t h a t n e g a t i v e i n f l o w a n g l e is added t o t h e 9" a b s o l u t e p i t c h a n g l e a t 0.95 R (from rotor c o n t r o l s e t t i n g s ) , t h e n e t is a b o u t 0" p i t c h a n g l e o r a 0" e f f e c t i v e a n g l e of a t t a c k f o r t h e free t i p . But i f t h e e f f e c t i v e a n g l e o f a t t a c k is O " , how c o u l d t h e t i p b e l i f t - i n g ? P r o b a b l y t h e t i p is l i f t i n g because a p o s i t i v e c o n t r o l moment was b e i n g a p p l i e d t o t h e c o n t r o l l e r . I f the t i p is l i f t i n g , two e v e n t s are o c c u r r i n g , e i t h e r s i n g u l a r l y o r i n c o m b i n a t i o n : e i t h e r t h e i n b o a r d p o r t i o n of t h e b l a d e is e x p e r i e n c - i n g dynamic twist t h a t is of t h e order o f 7" nose-up a t V / Q R = 270°, o r t h e h i g h of the i n b o a r d b l a d e c a u s e d a l a r g e u p f l o w a t t h e t i p . U n f o r t u n a t e l y , n e i t h e r CL

I

Both events are probably occurring, event can be ascertained from the test data.

however, to a lesser degree. I t would be well to establish the dynamic twist of the blade in the next wind-tunnel test.

In figure 18, the second harmonic magnitude decreased with increasing advance ratio until V / Q R = 0.3, and then it increased again. The magnitudes of harmonics 3 through 10, taken as a group, had the usual expected distribution as advance ratio At advance ratios beyond 0.3, the magnitude of harmonics 4-6 grew increased to 0.3.

No particular significance can be attached to the changes in higher har- larger.

monic magnitudes at this time.

Oscillatory Lift Calculation The motion of the free tip is in response to changes in the aerodynamic environment that produce oscillatory lift loading in a fixed-tip configuration. A question arises as to how much loading change is alleviated by the free tip. This question is answered by reviewing an analytical loading calculation based on the tip pitch angle and on the local velocity normal to the tip. The primary hypothesis here is that all A e tip response is generated by lift-loading perturbations. The analytical expression used to define the lift loading is Loading = C AaSt0.5pV L L a

Loading = CL bo + (AN sin NY + BN cos N Y ) [ Q R ( 1 + p sin Y ) ] 0.50St

I

a N = 1 (A sin N Y Loading = 0.5pS C [ ( O R ) 2 + 2p(QR)* sin Y + ( p Q R ) sin I] A . +

[ N=l N

La + BN cos NY) where A O = + ( A ~ sin NY + B~ COS N Y ) N= 1 is assumed equal to Ba.

The lift curve slope, CL , reflects the situation that the whole tip, and at

a least part of the inboard section of the blade, are subjected to the local angle-of- attack change. Also, the CL reflects a lift deficiency factor of 0.827 for a consideration of unsteady aerodynamics. Using CL = 0.065 per degree from Stroub a and van Aken and C 1 = 0.827 from reference 8, the effective CL is 0.0537 per a

Based on this effective CL , the resulting calculated lift loading per

degree.

a unit tip area, that is, the lift loading parameters, is presented in figure 20 for

x = 0.05 and at an

two rotor lift coefficients, CL/u = 0,0708 and 0.0915 at advance ratio of 0.305. The loadings for the two lift levels are about the same in character but different in magnitude. The negative values shown reflect a response to a positive change in local angle of attack. Likewise, positive values represent a response to a negative angle-of-attack change. These data show the tip reducing the loading around the azimuth, with the larger reduction on the retreating side of the rotor disk. More important though are the changes related to higher harmonic loading, which contributes to vibratory loads in the nonrotating system. The fixed- system vibratory loads are affected by higher harmonics above 2 per rev and, mainly, by harmonics 3 through 10 per rev. Calculated higher harmonic air-load changes caused by the free tip are depicted in figure 21 as the summation of magnitudes and phases of harmonics 3 through 10 at two rotor lift coefficients. At C / a = 0.0708,

the resulting curves show the largest perturbation occurring over an 80 k azimuthal

sector centered at about O o azimuth. The major discernible effect with rotor lift coefficient is that higher lift appears to increase the amplitude of lesser peaks.

The maximum overall peak-to-peak amplitude was not changed, but there are more high magnitude peaks occurring at C L / u = 0.0915 than at CL/a = 0.0708.

The same approach was taken for the free tip at different advance ratios.

CL/a = 0.0708, x = 0.05, at

Figure 22 presents the calculated total air loading for advance ratios of 0.305 and 0.392. In figure 23, harmonics 3 through 10 are summed and presented for the same two advance ratios. Increasing the advance ratio from 0.305 to 0.392 changes some peaks around the azimuth, but the biggest effect is the amplitude change over the front part of the disk, at about the 180' azimuth. The greatest potential for aerodynamically induced oscillatory loads appears to come from the fore and aft sector of the disk and from the advancing-blade zone centered near 120' azimuth. With this approach, we are able to identify greas that might be major sources of the vibratory loads that affect fixed-system vibration.

Even at near-equivalence in force and speed settings, the free-tip lift loading parameter shows considerable variation between the data from the lift sweep in figure 21 and the data from the speed sweep in figure 23. Figure 24 presents the lift-loading parameter from figures 21 and 23 for CL/a = 0.0708, 2 = 0.05, and V / Q R = 0.3. At near-equivalence in force and speed setting, the character of the harmonic content shows large, distinct differences, especially at 100' azimuth. The data from the lift sweep show that the advancing blade produces a 40% greater peak- to-peak amplitude than the other case. This suggests that small differences in orientation of the tip-path plane can greatly change the aerodynamic environment This would make the synthesis of that aerodynamic through which the tip must pass.

environment a difficult task and its validation more difficult as well.

CORRELATION WITH THEORY A rotor mathematical model was modified to include the free tip. This mathe- matical model incorporated blade-element theory, an unsteady aerodynamics model, a modal approach to structural dynamics, and a prescribed wake with nonuniform down- wash. The model was run to match a wind-tunnel test condition of an advance ratio

of 0.3 with the rotor at = 0.07, x = 0 . 0 5 , and a tip speed of 213 m/sec. The

correlation between the tes data and the model is shown in figure 25, with tip cP

A0 azimuthal variation being the correlation parameter; the correlation is very The differences between test and model are so large that this mathematical poor.

model could not be used in the evaluation of the results of this test.

We have seen the responsiveness of the free tip to airflow perturbation and have examined how it changes its loading characteristics around the azimuth. Next, let us see what are the benefits of its free pitching capability--how it affects power required, blade loads, and control loads.

POWER Comparison at Various Rotor Lift Coefficients In forward flight, the free-tip rotor required less power than the comparable fixed-tip rotor configuration. This is shown in figure 26 for a C / a sweep at V/QR = 0.3. The free-tip configuration required less power for C L ) u greater than 0.045 and appears to be a more power efficient configuration with increasing thrust. For example, if the free tip were at the same power coefficient associated with the fixed tip at C / a = 0.07, the free-tip lift capability would be 15% L greater. The primary reason the free tip requires less power is the pitch-down or A0 of the tip relative to the inboard portion of the blade.

negative There are two reasons the negative A B reduces the power requirement. First, negative A9 lowers tip lift owing to just reducing the at and, therefore, lowers the induced drag of the tip. Secondly, negative Ae causes the tip's "drag due to lift" characteristics to be less severe. These two reasons for lower power from lowered tip drag were demonstrated with wind-tunnel test data from a metric tip on a The tip was mounted on its own six-component semispan wing (Stroub and van Aken).

strain gauge balance. The drag due to lift characteristics from that test are presented in figure 27 for 30" and for 35" tip sweep angles. The data presented include those at 0' and -5" incidence angles for the 3O0-swept tip and at 0" for the 35O-swept tip.

There were no data taken for 35O-swept tip at -5" incidence angle, but trends with incidence angle associated with the 30°-sweep angle are expected to carry over to the 35O-swept-tip configuration as well. The data in figure 27 show the general sensitivity of tip drag with tip lift and show the relief of that sensitivity with a 1 8 -5" i n c i d e n c e a n g l e o r A B . The two r e a s o n s for r e d u c e d d r a g and power are demon- strated i n f i g u r e 26 by n o t i n g t h e f o l l o w i n g : ( 1 ) p o i n t A is t h e u n d e f l e c t e d t i p l i f t a n d d r a g state; ( 2 ) p o i n t B shows less d r a g r e s u l t i n g j u s t from r e d u c i n g t i p ( 3 ) p o i n t C shows less drag a t t h e same l i f t when t h e i n c i d e n c e a n g l e was l i f t ; a n d n e g a t i v e .

From these data it is e a s i l y seen t h a t there is a d e f i n i t e d r a g a d v a n t a g e when t h e t i p is a t a n e g a t i v e A0 b u t a t t h e same l i f t . A q u a n t i t a t i v e p e r s p e c t i v e is g a i n e d from table 2 , which shows what h a p p e n s t o t i p d r a g when t i p i n c i d e n c e a n g l e is changed from 0" t o -5" and when wing l i f t is e q u a l i n b o t h cases. Two w i n g - l i f t c o e f f i c i e n t s are i n c l u d e d i n t a b l e 2 . W i n g - l i f t c o e f f i c i e n t s reflect t h e l i f t o f t h e whole w i n g , i n c l u d i n g t h e t i p .

T a b l e 2 shows t h a t t h e t i p - d r a g r e d u c t i o n w i t h wing l i f t is t h e same f o r i n c i - d e n c e a n g l e s o f 0" and - 5 " . I t s h o u l d b e n o t e d t h a t d r a g o f t h e c o m p l e t e wing was a b o u t t h e same i n b o t h cases, o r at least w i t h i n t h e a c c u r a c y of t h e wing b a l a n c e .

I t is l i k e l y t h a t t h e i n b o a r d p o r t i o n o f t h e wing i n c r e a s e d its d r a g l e v e l w i t h n e g a t i v e t i p i n c i d e n c e a n g l e , b u t t h a t it a p p r o x i m a t e l y b a l a n c e d o u t t h e d e c r e a s e d d r a g of t h e t i p . T h e r e f o r e , f o r a f i x e d wing, t h e d r a g r e d u c t i o n a s s o c i a t e d w i t h n e g a t i v e t i p i n c i d e n c e a n g l e may be o f small n e t c o n s e q u e n c e . For r o t o r s , t h e o p p o s i t e is t r u e . For a rotor, s h i f t i n g t h e d r a g i n b o a r d would r e d u c e t h e radial arm of t h e d r a g c e n t r o i d , c a u s i n g less power t o be r e q u i r e d .

The mechanism f o r r e d u c e d t i p drag is h y p o t h e s i z e d as a n i n t e r a c t i o n between t h e t i p v o r t e x a n d t h e d e f l e c t e d t i p . With t h e t i p a t a s t r o n g n e g a t i v e i n c i d e n c e a n g l e , there w i l l be a s u b s t a n t i a l l i f t d i f f e r e n c e between t h e t i p a n d t h e i n b o a r d p o r t i o n o f t h e wing. T h i s l i f t d i f f e r e n c e would n o t b e accommodated i n a g r a d u a l s p a n w i s e l i f t g r a d i e n t , b u t there would b e a s h a r p l i f t d i s c o n t i n u i t y w i t h t h e l a r g e s t g r a d i e n t a t t h e j u n c t i o n between t h e t i p and t h e i n b o a r d wing. T h i s l a r g e g r a d i e n t i n s p a n w i s e l i f t d i s t r i b u t i o n c a u s e s a v o r t e x to be shed from t h a t junc- t u r e . The shed v o r t e x i n d u c e s a n upwash which c a u s e s t h e t i p l i f t v e c t o r t o be i n c l i n e d more forward, t h u s r e d u c i n g t h e i n d u c e d d r a g .

Another factor is t h a t t h e t i p i n c i d e n c e a n g l e itself also c o n t r i b u t e s t o t i p d r a g r e d u c t i o n . With a n e g a t i v e i n c i d e n c e a n g l e a t t h e t i p , t h e u p p e r s u r f a c e of t h e a i r f o i l is i n c l i n e d more f o r w a r d . The s u c t i o n s u r f a c e p r e s s u r e s , a s s o c i a t e d w i t h t i p - v o r t e x s w e e p i n g t h e a i r f o i l ' s u p p e r s u r f a c e , which is n o t i n c l u d e d more f o r w a r d . T h u s , a lower t i p d r a g would r e s u l t . Both t h e effect of t h e u p p e r - s u r f a c e i n c l i n a t i o n a n d t h e effect of v o r t e x shed from t h e j u n c t u r e would be p r e d o m i n a t e l y p r o p o r t i o n a l t o t h e l i f t c o e f f i c i e n t o f t h e wing, n o t t h e l i f t c o e f f i c i e n t of t h e t i p i t s e l f .

A n e g a t i v e i n c i d e n c e a n g l e a t t h e t i p , or - d e , lowers t h e t i p d r a g on t h e s e m i s p a n wing, and likewise lowers the d r a g of t h e t i p on the r o t o r a n d r e d u c e s the r o t o r ' s power n e e d s as well.

Comparison at Various Forward Speeds Speed power polars for the free- and fixed-tip configuration are presented in figure 28. The polar for the fixed tip has been adjusted to correlate with the fixed tip data in the C / a sweep shown in figure 26. In figure 28 the free tip is L shown to require less power than the fixed tip. The reasons for the free tip pertain requiring less power were discussed earlier, and those reasons generally here as well. The one exception is the highest advance-ratio case in which the fixed tip exhibits a sharp increase in power demand. The free tip, on the other hand, exhibits a more gradual increase in power required. The fixed tip's sharp increase in power suggests it is experiencing compressibility effects at the advanc- ing-tip Mach number of 0.83, whereas the free-tip configuration appears less suscep- tible to compressibility effects, perhaps because it is less loaded. This could be one of the most significant aspects of the comparison between these two rotor con- figurations: the free tip may be less susceptible to compressibility power rise.

OSCILLATORY LOADS Comparison at Various Forward Speeds Loads data from this test are presented to provide insight into the effect of one free-tip configuration on oscillatory blade loads and control-system oscillatory loads. It was found that the free tip reduces most out-of-plane vibratory loads, but not in-plane loads. The reduction of out-of-plane blade loads is shown in figure 29, where half peak-to-peak oscillatory bending moments are presented over the test advance-ratio range. Comparisons are shown f o r the free- and fixed-tip.

configurations, using several measurement stations along the blade. For advance ratios greater than 0.25, the free tip is effective in reducing the oscillatory amplitudes 30% or more at stations inboard of 0.53 R. Insight into the vibratory- load suppression is gained by harmonic analysis of the oscillation load. Figure 30 presents the harmonic analysis for the four measurements stations with the rotor Figure 30 shows that the operating at an advance ratio of 0.305 and CL/a = 0.0708.

free tip markedly reduced the first- and second-harmonic bending moments. Other harmonics were reduced as well, but the third, sixth, and eighth harmonics were increased somewhat. Although some harmonics were increased, the large suppression of the first harmonic played a dominant role in reduced peak-to-peak amplitude In figure 29, a rise in peak-to-peak amplitude is shown for both tip configura- tions at advance ratios greater than 0.35. This was probably a reaction to compres- sibility effects that had similarly increased the power required. A t advance ratios less than 0.25, the inboard measurement stations report a rise in free-tip oscilla- tory load, especially around V/aR = 0.1. This rise is probably a result of an encounter with strong tip vortices, as indicated by the A 9 response at about P = 80" and 320" in figure 16. Unfortunately, data were not obtained on the fixed- tip blade at the low advance ratios. However, helicopter flight-test data have shown that the fixed-tip blade undergoes a large rise in oscillatory loads at the lower advance ratios, and one can only guess whether the fixed-tip oscillatory loads would be greater o r less than those of the free-tip configuration. Nevertheless, the free-tip weathervaning capability needs to be enhanced through new design.

Comparison at Various Lift Coefficients We have seen that the free-tip suppresses oscillatory flatwise bending moments We will now review the free-tip's suppression of at cruise speed and at high speed.

oscillatory loads at lift coefficients with the advance ratio held constant at presents half peak-to-peak flatwise bending moment from various 0.305. Figure 31 measurement stations for both tip configurations. Rotor propulsive force and advance ratio were held constant while thrust level was varied. The data of fig- ure 31 show that the free tip caused oscillatory load reduction only at measurement stations inboard of Also, more reduction resulted at the lower rotor rb/R = 0.53.

lift levels. One reason the free tip could be more effective at the low lift levels was that the rotor disk is tilted more forward at the low lift. By tilting forward, the rotor tip operated farther from the main part of the rotor wake, thus reducing the high harmonic content of the perturbations in the velocity vector. With the resulting increased dominance of the lower harmonics, this particular free tip can pitch effectively to deal with the oscillatory loads. At higher thrust levels, the rotor disk is tilted more aft and operates closer to its wake and its influences.

This subjects the tip to higher harmonic velocity perturbations, only some of which the free tip could effectively counter.

Blade chordwise bending-moment measurements were limited to one inboard station at 0.18 R. The measurements for both the free- and fixed-tip configurations are presented in figure 32 for the forward speed sweep and in figure 33 for the rotor lift sweep. The speed sweep data set shows the free-tip configuration producing generally larger oscillatory loads than the fixed-tip configuration, except at V/nR = 0 . 3 . At V/QR = 0.3, the fixed- and free-tip oscillatory loads for C / a 0.07, f = 0.05 The rotor lift sweep data in figure 33 are nearly the same.

L confirm this near-equivalence at but it also shows the free tip CL/a = 0.0708 CL/a > 0.0708. Evaluating these limited data having higher oscillatory loads when from this test suggests that the free tip generally increases oscillatory chordwise bending moments over the most important segments of the test envelope. Reasons for the free tip generating the higher chordwise bending moments are not discernible from the available data.

Tip Oscillatory Loads Sufficient oscillatory loads data were not obtained that would allow comparison between free-tip and fixed-tip configurations. Oscillatory loads were obtained from of the inboard edge of the strain gauges applied to the pitch shaft and just inboard tips. Although the instrumentation was the same for both tip configurations, this instrumentation was sufficient to measure the free-tip oscillatory load but not for t h e f i x e d - t i p l o a d s measurement. The m i s s i n g i n f o r m a t i o n is l o a d s d a t a from t h e p i n u s e d t o p r e v e n t t h e t i p from p i t c h i n g .

For t h e free-tip c o n f i g u r a t i o n o n l y , t h e h a l f peak-to-peak flatwise b e n d i n g - moment a m p l i t u d e s a r e p r e s e n t e d i n f i g u r e 34 f o r t h e l i f t sweep a n d for t h e s p e e d sweep. I n t h e s p e e d sweep, t h e s h a r p d e c r e a s e i n m a g n i t u d e f o r V / Q R g r e a t e r t h a n i n t e r a c - 0.1 may b e t h e r e s u l t of d e p a r t i n g t h e s p e e d domain of s e v e r e b l a d e - v o r t e x t i o n . I n g e n e r a l , the flatwise b e n d i n g moments are more s e n s i t i v e t o s p e e d v a r i t i o n t h a n t o l i f t v a r i a t i o n .

C o n t r o l S y s t e m O s c i l l a t o r y Loads Comparison The free t i p r e d u c e s t h e o s c i l l a t o r y loads g o i n g i n t o t h e c o n t r o l s y s t e m v i a t h e p i t c h l i n k . T h i s is shown i n f i g u r e 35 where p e a k - t o - p e a k o s c i l l a t o r y p i t c h - l i n k l o a d s are p r e s e n t e d for t h e a d v a n c e - r a t i o sweep a n d f o r a l i f t c o e f f i c i e n t sweep a t 0.305 advance r a t i o . A s shown i n f i g u r e 35, as e i t h e r l i f t or s p e e d i n c r e a s e s , t h e free t i p c a u s e s l a r g e r e d u c t i o n s i n o s c i l l a t o r y l o a d s . The h i g h o s c i l l a t o r y l o a d s a s s o c i a t e d w i t h t h e f i x e d t i p may b e t h e r e s u l t of t h e t i p ' s a f t sweep. With a f t sweep, t h e f i x e d t i p ' s a e r o d y n a m i c c e n t e r is a f t o f t h e e l a s t i c a x i s , a n d , t h e r e f o r e , a n y a i r - l o a d p e r t u r b a t i o n i n t h e v e r t i c a l d i r e c t i o n f e e d s d i r e c t l y i n t o t h e p i t c h l i n k , r e s u l t i n g i n a n o s c i l l a t o r y l o a d g o i n g i n t o t h e con- t r o l s y s t e m . The swept t a p e r e d t i p would therefore make t h e c o n t r o l s y s t e m more s e n s i t i v e t o flow s t a t e s t h a t c o n t a i n c o n s i d e r a b l e v e l o c i t y p e r t u r b a t i o n s , s u c h a s those e n c o u n t e r e d when o p e r a t i n g a t h i g h s p e e d o r a t h i g h t h r u s t l e v e l s . High o s c i l l a t o r y l o a d s from a f t sweep are s u b s t a n t i a t e d by a w i n d - t u n n e l t e s t of f u l l - scale rotors w i t h v a r i o u s t i p s h a p e s , a r e c t a n g u l a r and a s w e p t t a p e r e d t i p b e i n g two of t h e t i p p l a n f o r m s t e s t e d ( r e f . 9 ) . Those t e s t r e s u l t s show t h e c o n t r o l - t o b e more s e n s i t i v e t o l i f t l e v e l w i t h t h e s w e p t t a p e r e d s y s t e m o s c i l l a t o r y l o a d s t i p t h a n w i t h t h e r e c t a n g u l a r t i p , i n t h e a b s e n c e of s i g n i f i c a n t c o m p r e s s i b i l i t y e f f e c t s . T h e r e f o r e , h i g h e r o s c i l l a t o r y l o a d s i n t o t h e c o n t r o l s y s t e m c a n b e e x p e c t e d w i t h a f i x e d - s w e p t - t i p c o n f i g u r a t i o n . C o n v e r s e l y , a free pitching-moment b a l a n c i n g , s w e p t t i p s u p p r e s s e s o s c i l l a t o r y l o a d s g o i n g i n t o c o n t r o l s y s t e m .

O v e r a l l O s c i l l a t o r y Loads P i c t u r e The l o a d s d a t a p r e s e n t e d h e r e i n are l i m i t e d , b u t s t i l l t h e y p r o v i d e i n s i g h t i n t o t h e e f f e c t s of t h i s f r e e - t i p c o n f i g u r a t i o n . With t h e free t i p , i n b o a r d b l a d e s t a t i o n s e x p e r i e n c e d lower o s c i l l a t o r y flatwise b e n d i n g moments when t h e a d v a n c e r a t i o was g r e a t e r than 0 . 2 . Harmonic a n a l y s i s of t h e bending-moment d a t a showed t h a t t h e improvement came l a r g e l y from s u p p r e s s i o n o f t h e f i r s t h a r m o n i c l o a d i n g .

Below a n a d v a n c e r a t i o of 0 . 2 , t h e o s c i l l a t o r y l o a d s rose f o r t h e f r e e - t i p c o n f i g - u r a t i o n , b u t no comparison was p o s s i b l e s i n c e t h e f i x e d - t i p c o n f i g u r a t i o n was n o t tested a t t h e lower a d v a n c e r a t i o s . The o s c i l l a t o r y load r i s e was a t t r i b u t e d t o b l a d e - v o r t e x i n t e r a c t i o n s c h a r a c t e r i s t i c of t h a t a d v a n c e - r a t i o r e g i m e . The f r e e - t i p t o i n c r e a s e a t r o t o r l i f t l e v e l s c o n f i g u r a t i o n g e n e r a l l y c a u s e d c h o r d w i s e l o a d s a b o v e C / a = 0.0708 and a t most s p e e d s t e s t e d . C o n c e r n i n g l o a d s g o i n g i n t o t h e L 2 2 c o n t r o l s y s t e m , t h e free t i p c a u s e d l a r g e decreases i n p i t c h - l i n k l o a d s a t a l l l i f t l e v e l s and a d v a n c e r a t i o s .

CONCLUSIONS An e x t e n s i v e research program was carried o u t t o a n a l y z e a n d e v a l u a t e a free- t i p rotor s y s t e m . The a e r o d y n a m i c c o n f i g u r a t i o n of t h e free t i p was i n v e s t i g a t e d , and there was a s u c c e s s f u l wind-tunnel d e m o n s t r a t i o n of t h e f r e e - t i p d e s i g n .

Based on t h e r e s u l t s of t h i s t e s t a n d on s u b s e q u e n t data a n a l y s i s , t h e follow- i n g c o n c l u s i o n s are drawn. F i r s t , t h e f r e e - t i p a s s e m b l y p i t c h e d f r e e l y i n r e s p o n s e t o air-flow p e r t u r b a t i o n . S e c o n d , t h e c o n t r o l l e r mechanism o p e r a t e d s u c c e s s f u l l y t h r o u g h o u t t h e t e s t program w i t h o u t f a i l u r e . T h i r d , t h e free t i p r e d u c e d power r e q u i r e m e n t s w i t h i n c r e a s i n g r o t o r l i f t c o e f f i c i e n t ; a t t h e same power c o e f f i c i e n t associated w i t h t h e f i x e d t i p a t CL/a = 0.0708, t h e f r e e - t i p CL/a was 15% g r e a t e r . F o u r t h , compared w i t h t h e f i x e d - t i p c o n f i g u r a t i o n , t h e free t i p r e d u c e d power r e q u i r e m e n t s by a b o u t 8%a t an a d v a n c e r a t i o of 0.3; h i g h - s p e e d power r e q u i r e - m e n t s were r e d u c e d more. F i f t h , with t h e free t i p , b l a d e flatwise b e n d i n g moments were r e d u c e d o v e r t h e i n b o a r d p o r t i o n of t h e b l a d e ; chordwise b e n d i n g moments were n o t r e d u c e d . And s i x t h , t h e free t i p r e s u l t e d i n fewer o s c i l l a t o r y loads b e i n g t r a n s m i t t e d i n t o t h e c o n t r o l system.

The free t i p w i l l be f u r t h e r d e v e l o p e d t o e x p l o i t its u n i q u e c a p a b i l i t i e s for i m p r o v i n g p e r f o r m a n c e a n d r e d u c i n g a l t e r n a t i n g loads.

REFERENCES Stroub, Robert H.: A Constant-Lift Rotor for a Heavier-Than-Air Craft. U.S.

Patent 4,137,010, Jan. 30, 1979.

Stroub, Robert H.: Performance Improvements with the Free-Tip Rotor. Presented at AHS 1-4 National Specialists' Meeting, Rotor System Design, Philadelphia, PA, Oct. 1980.

Silcox, H.; and Rosenstein, H.: Feasibility Study of a Constant-Lift Rotor Tip. Report D 210-11704-1, Boeing Vertol Co., Philadelphia, PA, July 30, 1980.

McVeigh, M. A. et al.: Investigation of a Rotor System Incorporating a Constant-Lift Tip. NASA CR-166361, 1981.

Stroub, Robert H.: An Experimental Investigation of a Free-Tip Rotor Configura- tion in a Forward Flight Wind-Tunnel Test. NASA TM-84409, 1983.

Stroub, Robert H.; and Young, Larry A . : The Results of a Wind-Tunnel Investiga- tion of a Model Rotor with a Free Tip. NASA TM-86758, to be published Aug. 1985.

Kumagai, Hiroyuki: A Feasibility Study of Free-Tip Rotor Application as a Passive Cyclic Control Device. NASA CR-166608, 1984.

Yates, L.; and Kumagai, H.: Application of Two-Dimensional Unsteady Aerodynam- NASA CR-166348, May 1982.

ics to a Free-Tip Rotor Response Analysis.

Stroub, Robert H.; Rabbott, John; and Niebank, Charles F.: Rotor Blade Tip Shape Effects on Performance and Control Loads from Full-scale Wind-Tunnel Testing. J. American Helicopter SOC., vol. 24, no. 5, Oct. 1979, p. 28.

TABLE 1 . - ROTOR GEOMETRIC DESCRIPTION Rotor r a d i u s , m 2.285 Blade c h o r d , m .1709 Blade twist, deg -9.45 T i p r e f e r e n c e chord, m .1709 T i p area, m .0322 T i p s p a n , m .2285 .0807 Rotor r e f e r e n c e s o l i d i t y Blade f l a p p i n g i n e r t i a , k g - m 2 9.175

I '

i

TABLE 2 . - T I P DRAG REDUCTION WITH TIP INCIDENCE ANGLE 6.0 0.40 0.0300 7.1 .25 .0125 12.0 .82 .0670 13.2 .66 .0345

M C 4

PITCH AXIS A N D CENTER O F G R A V I T Y

%

CONTROL J

MOMENT, Mc SELF ADJUSTING BLADE PITCH F i g u r e 1.- Schematic of the free tip.

Figure 2.- Free-tip rotor in Boeing Vertol wind tunnel.

Figure 3.- Close-up view o f free tip on rotor blade.

\TRAILING EDGE Figure 4.- Free-tip assembly.

ORIGINAL PAGZ rs

O F POOR QUALITY

- tan 4

T Figure 5.- Free-body diagram of controller tension-torsion strap.

8 70 '0

- 60

a 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 MOMENT, Nm Figure 6 . - Torque calibration of controller.

2 9 1052 9 5 2 852 Q) + .- E

z l

P 3 5 2 g 3000

-

E

2 5 2 1 ooc 0 5 2 C ROTOR REVOLUTIONS, rpm Figure 7 . - Rotor-blade natural frequency diagram.

SPANWISE B L A D E WEIGHT DISTRIBUTION

-5 2 8 O r

E . l o - 2- X CHORDWISE CENTER OF GRAVITY a - I .08 t n

-

.06 n

-

m .04 u .

-

t .02

a

W Figure 8.- Mass and center of gravity location o f free-tip assembly.

- 1.2 B 1 .o El El .8 - El .6 El .4 C Lt .2 -.2 -.4 ..

El 1 I I I .08 El .04 El

'a

-.04 El

2 -*08

E - -.12 El -.16 a El -.20 El I 1 I I I -.24 -6 -4 -2 0 2 4 6 8 10 12 14 a Figure 9.- Aerodynamic characteristics of free-tip planform at Mach 0.17.

Figure 10.- Free-tip rotor in test cell for test of tip response to a vertical air jet.

Figure 11.- Free-body diagram of free t i p .

N b to (D (D d en Q w- (3 Z O

a % I

I-

E 8

KJC., a d N to W to N to 03 I

2 7 I I

I I 7

I

6ap ' ev

A0 = AO,e-Xt sin (wt + 7r/2) he.

t = 1IX \ I 0.368 A0.

h-->

t A e

V

w = 1 L 2(T/2) TI2 Figure 13.- Graphical technique of determining system frequency and damping from response time-histories.

AZIMUTH POSITION, deg 0 60 120 180 240 300 360 420 480 540 600 660 720 I 1 1 1 1 1 1 I 1 1 1 1 -2 -4 C L / O 0.038 -6 0) a l -0 Q Q -a 0.0605 0.0707 -10 0.0798 -12 0.092 -14 F i g u r e 14.- V a r i a t i o n of f r e e - t i p p i t c h a n g l e d i f f e r e n t i a l w i t h r o t o r lift c o e f f i c i e n t : V/QR = 0.3 and x = 0.05.

Bls = 3.1" Alc = -2.9"

-

4.5 - 4.0 - 3.5 Bls = 3.0" Alc = 3.2" - 3.0 - 2.5 'CI

2 2.0 -

- 1.5 - 1.0 - .5 HARMONIC NUMBER ( a ) CL/a = 0.038 and 0.056.

for various r o t o r l i f t coefficients.

Figure 15.- Harmonic content of 8 0 - 4.0 - 3.5 CL/O = 0.0605

-

Bls = 3.2" 3.0 A l c = -2.4"

-

2.5 cn

-

4. 2.0 - 1.5 - 1.0 - .5 0 - - 5.0 - 4.5 CL/O = 0.0708 - Bls = 4.4" 4.0 A l c = -3.4"

-

3.5 - 3.0 0) - 2.5 - 2.0 - 1.5 - 1.0

-

- .5

I I I 1 1 1 1 I I I I I I I I I 1 I

-

( b ) CL/a = 0.0605 and 0.0708.

Figure 15.- Continued.

CL/a = 0.0798 91s = 4.3" A l c = -3.6" 0- 5.5 I- CL/O = 0.0915 - 5.0 Bls = 5.2" - 4.5 Alc = -3.5" - 4.0 - 3.5 - k 3.0 m m - d 2.5

-

2.0 - 1.5 - 1.0 - .5

I I l I l ~ l ~ 1 J ~ J ~ ' ' I

I I I 0- Figure 15.- Concluded.

AZIMUTH POSITION, deg 60 120 180 240 300 360 480 0 420 540 600 660 720 1 I I I 1 I I I 1 1 I 1 -2 -4 -6 0, 0) -0 -a -8 -10 -12 -14 (a) V/nR = 0.10.

AZIMUTH POSITION, deg 60 120 180 240 300 360 420 480 540 600 660 720 -2 -4 cn Q '0

- -6

a d -8 -10 -1 2 ( b ) V/QR = 0.15.

Figure 16.- Variation of free-tip AI3 with advance ratio: CL/a = 0.0708, 2 = 0.05.

AZIMUTH POSITION, deg 0 60 120 180 240 300 360 420 480 540 600 660 720 1 1 1 i i i 1 I I 1 I I

-12 L

( c ) V / a R = 0.2.

AZIMUTH POSITION, deg 0 60 120 180 240 300 360 420 480 540 600 660 720 I 1 1 1 1 I I 1 I I I I Figure 16.- Continued.

AZIMUTH POSITION, deg 0 60 120 180 240 300 360 420 480 540 600 660 720 I I I I I I I 1 I I I I -2 -4 UJ 0) 'D

. -6

m Q -8 -10 -12 ( e ) V/nR = 0.305.

AZIMUTH POSITION, deg 60 120 180 240 300 360 420 480 540 600 660 720 -2 -4 -6 UJ 0) 'D a -8 -10 -12 -14 ( f ) V/DR = 0.357.

Figure 16.- Continued.

( g ) V/nR = 0.391.

Figure 16.- Concluded.

4 4 AZIMUTH POSITION, deg 60 120 180 240 300 360 0 I I I I I , , - \ I -2 -4 -6 0) Q D rn Q -8 -10 -12 -14 Figure 17.- Compilation of free-tip A0 with advance ratio: CL/a = 0.0708, = 0.05.

2.5

-- & - 0.10

n Bls = 1.3" 1.5 Alc = -3.8"

In

Q 1.0

1 I I n

n

I I I l l I I - 1

I 3.5 - v 3.0 - R R = 0.205 - 2.5 Bls = 2.5" A I c = -3.2" - 2.0 m - 1.5 - 1.0

-

- .5

I 1 I I I I J m m I

I

-

HARMONIC NUMBER (a) V/QR = 0.10, 0.15, and 0.205.

Figure 18.- Harmonic content of A6 at various advance ratios: CL/a = 0.0708, = 0.05.

4 6 __ ~~ - 4.0

-

- 3 . 5 - 3.0 Bls = 3 . 2 " Alc = -3.4" - 2 . 5 Is) al '13

-

. 2 . 0 a

-

1 . 5 - 1 . 0 - .5 I O L

-

5.0

-

-

4.5 - 4 . 0 Bls = 3 . 8 " AIc = -3.4" - 3.5 - 3 . 0 cs, al '0 -

. 2.5

m Q - 2 . 0 - 1 . 5 - 1 . 0 - .5 I I n - 1 I 2 3 4 5 6 7 8 9 10 1 1 0 1 HARMONIC NUMBER (b) V / a R = 0.254 and 0.305.

Figure 18.- Continued.

- 5.5 - 5.0 v - f i R = 0.357 - 4.5 Bls = 5.3" - A I c = -3.2" 4.0 - 3.5

-

3.0 - 2.5 - 2.0 - 1.5 - 1.0

n

- .5

t L

0 I

6.0 6.5 I

v - = 0.392 RR 5.5 Bls = 6.7" Alc = -3.2" 5.0 4.5 4.0 B 3.5 U Q d 3.0 2.5

2 .o

1.5

1 .o

r i .5

I l l r l i l l ~ ~ l l J

I l l I I 1

-I- lr[ 2

- Figure 18.- Concluded.

t

-6 4 - 0.15 - 2 - - 0) m -0

. 0 -

rn d - -2

-4 t

0.205 cn m -0 rn d

'

I I I I I I 1 I .2 I 40 80 120 160 200 240 280 320 360 AZIMUTH ANGLE, deg Figure 19.- Recomposition of A€) waveform from harmonics 3 through 10: V/aR = 0.1 to 0.2.

Vial3 = 0.305 - X = 0.05

/ -\ -_ \

- 10,000 N E z d 1-20,000 E a a a n Q Z -30,000 a a \ \

s

t

-

-40,OOC I I I I I I I 1 I 1 1 I -50,OOC 0 30 60 90 120 150 180 210 240 270 300 330 360 Figure 20.- Azimuthal variation of tip aerodynamic loading parameters utilizing all harmonics: = 0.05, V / Q R = 0 . 3 0 5 .

i u E O a K a L (3 -2000 n

a

s

t

CL/U = 0.0708 1 -4000

--

CL/U = 0.0915 I 1 I I 1 I 1 I 1 - ~ - l 1 I -6000 0 30 60 90 120 1 5 0 180 210 240 270 300 330 360 AZIMUTH ANGLE, deg F i g u r e 21.- Aerodynamic l o a d i n g p a r a m e t e r u t i l i z i n g h a r m o n i c s 3 t h r o u g h 10: Y = 0.05, V/QR = 0 . 3 0 5 .

CLJU = 0.07 - X = 0.05 - 10,000 N E e r ' w

5 -20,000

Q: d c 2 E -30,000 Q:

s

t

-

- VJS1R = 0.305

-40,ooa

- - V J f i R = 0.392

I 1 I I I 1 I 1 I I I I -50,00( 0 30 60 90 120 150 180 210 240 270 300 330 360 Figure 22.- Azimuthal variation of tip aerodynamic loading parameter with all harmonics: f = 0 . 0 5 , CL/u = 0.0708.

I 52 4000 r CL/U = 0.07 - X = 0.05 Figure 23.- Aerodynamic loading parameter using only harmonics 3 through 10: x = 0.05, CL/a = 0.0708.

X = 0.05

\ I

V I a R = 0.305 u I I I 1 1 I I I I I 1 I R = 0 . 0 5 , CL/a = 0.0708, Figure 24.- Comparison of aerodynamic loading parameter: V / a R = 0.305.

-2 m a

- -4

c n Q -6 -8 -10 -12 -14 -16 -18 120 180 240 300 0 60 360 420 AZIMUTH POSITION, deg , Figure 25.- Comparison of A 8 from wind-tunnel test and from mathematical math model: CL/a = 0.0708, = 0 . 0 5 , V / Q R = 0.305.

.008 -

x = 0.05

= 0.305 !2R FIXED TIP .006 - .004 - .002 I I I I 1 0 .02 .04 .06 .08 .10 CLIO Figure 26.-Comparison of power required by the free-tip rotor and by the fixed-tip rotor at various rotor lift coefficients: = 0.05, V / Q R = 0.305.

it = 0 lm2F A = 3 0 0 i i 0 .02 .04 .06 .08 .10 .12 .oa 't it = u .06

/ /

'Dt .04 .02 0 .2 .4 .6 .8 1 .o (CLt)2 Figure 27.- Aerodynamic drag characteristics of the t i p region of a semispan wing at Mach 0.17.

CL/U = 0.07 X = 0.05

*oo81

- .006 b \ n - \ .004 '\ Figure 28.- Speed-power polars for the free- and fixed-tip rotor configurations at C / a = 0.0708 and x = 0.05.

L

- FIXED TIP

--

FREE TIP --\

$ 20

\

+-

0 ---

= 10

z

-

n z w a rb/R = 0.53 L Y a w n Y n

? I 30

a I . I .2 .3 .4 . I .2 .3 .4 j/- S1R Figure 29.- Half peak-to-peak magnitude of the flatwise bending moments at various blade locations for the free- and fixed-tip configurations: CL/a = 0 . 0 7 0 8 , 2 = 0 . 0 5 .

0 FREE TIP 0 FIXED TIP E z I-- z w c3 z 10

-

n z w m w

z 5

L

s

E z I-- z w

5 15

c3 z

-

n z w m 10 w I- a -I L 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 HARMONIC NUMBER HARMONIC NUMBER flatwise b e n d i n g moments between F i g u r e 30.- Comparison o f t h e h a r m o n i c c o n t e n t o = 0 . 0 5 , V/aR = 0 . 3 0 5 .

C / U = 0.0708, t h e free- a n d f i x e d - t i p c o n f i g u r a t i o n s : L 6 0 ORIGINAL PAGE' 1 8 3 F POCR QUALITY rb/R = 0.13 rb/R = 0.18 / / E z /

+-

fj 20

f r -

E

/

/

E z 10

-

/' n 0 z W m W I I I 1

E

- a 50 J LL rb/R = 0.38 rb/R = 0.53 Y a W CL 40 Y a J a I / /

- I /'

FIXED TIP

--

FREE TIP .02 .04 .06 .08 .I .02 .04 .06 .08 .1 CLIU c ,/a Figure 31.- Variation of the half peak-to-peak magnitudes with rotor lift level: x = 0.05, V/QR = 0.305.

CLIO = 0.07 - E 120 0 X = 0.05

v E

d

S I n

w 5 20 .60

Q : O .IO .20 .30 .40 .50 VIR R F i g u r e 32.- Comparison of c h o r d w i s e b e n d i n g moments between t h e f i x e d - and f r e e - t i p c o n f i g u r a t i o n s w i t h a d v a n c e r a t i o : if = 0 . 0 5 , C /a = 0.0708.

L 100 r VIRR = 0.305 - X = 0.05

20 1 1 I 1 I 1 I

0 .02 .04 .06 .08 .IO .I2 c LIO F i g u r e 33.- Comparison o f c h o r d w i s e b e n d i n g moments a t v a r i o u s r o t o r - l i f t c o e f f i c i e n t s : f = 0 . 0 5 , V/aR = 0.305.

d 4a V I a R = 0.305

x = 0.05

Y 3c 2c

/’

/ F LATW ISE / - / / - A M /-

---

E a CHORDWISE z I I I I I CLIO

-

a CLIa = 0.0708 - \ Lu X = 0.05 rn \ 0 .1 .2 .3 .4 .5 V I a R F i g u r e 34.- Half p e a k - t o - p e a k a m p l i t u d e o f b e n d i n g moments on t h e p i t c h s h a f t of t h e f r e e - t i p c o n f i g u r a t i o n .

X = 0.05

- FIXED TIP

-- FREE TIP

z a- Q o 250 d d K I I I I 1 I I -03 .04 .05 .06 .07 .08 .09 .I 2 0 o CLlO Y Q w - X = 0.05 Y CLIU = 0.07 n LL

2 750

I 2 5 a 0 .I .2 .3 .4 .5 .6 R R Figure 35.- Comparison of oscillatory l o a d s going into the control system for the fixed- and free-tip configurations.

2. Govmmcmt Accession No.

1. Report No. 3. Recipient's Catalog No.

NASA TM-86751 5. Report Date 4. Title and Subtitle May 1985 ANALYSIS OF THE FREE-TIP ROTOR WIND-TUNNEL TEST RESULTS 6. Performing Organization Code 8. Performing Organization Report No.

7. Author(s1 85236 R o b e r t H . S t r o u b 10. Work Unit No.

9. Performing Organization Name and Address NASA Ames R e s e a r c h C e n t e r 11. Contract or Grant No.

M o f f e t t F i e l d , CA 94035

I

13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address T e c h n i c a l Memorandum N a t i o n a l A e r o n a u t i c s a n d Space A d m i n i s t r a t i o n 14. Sponsoring Agency Code Washington, D . C . 20546 505-42-11 15. Supplementary Notes p o i n t of C o n t a c t : Robert H . S t r o u b , Ames Research C e n t e r , M S 247-1, M o f f e t t F i e l d , CA 94035 ( 4 1 5 ) 694-6653 o r FTS 464-6653 16. Abstract The r e s u l t s from a wind-tunnel test of a small-scale f r e e - t i p r o t o r are a n a l y z e d . The f r e e - t i p r o t o r h a s b l a d e t i p s t h a t a r e f r e e t o weathervane i n t o t h e t i p ' s r e l a t i v e wind, t h u s p r o d u c i n g a more u n i f o r m l i f t around t h e a z i m u t h . The f r e e t i p e x t e n d e d o v e r t h e o u t e r 10% of t h e r o t o r b l a d e a n d i n c l u d e d a s i m p l e , p a s s i v e c o n t r o l l e r mechanism. The f r e e - t i p assembly, which i n c l u d e s t h e c o n t r o l l e r , f u n c t i o n e d f l a w l e s s l y throughout t h e t e s t . I n a test of t h e f r e e - t i p ' s r e s p o n s e a f t e r p a s s i n g through a v e r t i c a l a i r j e t , t h e t i p p i t c h e d f r e e l y a n d i n a c o n t r o l l e d manner.

A n a l y s i s o f t h e t i p ' s r e s p o n s e c h a r a c t e r i s t i c s showed t h e f r e e - t i p s y s t e m ' s damped n a t u r a l f r e - quency t o b e 5.2 p e r rev. T i p p i t c h - a n g l e r e s p o n s e s t o t h e l o c a l airstream are p r e s e n t e d f o r a n a d v a n c e - r a t i o r a n g e of 0.1 t o 0.397 a n d f o r a s o l i d i t y w e i g h t e d r o t o r l i f t - c o e f f i c i e n t r a n g e of 0.038 t o 0 . 0 9 2 . Harmonic a n a l y s i s o f t h e r e s p o n s e s showed a dominance by t h e f i r s t harmonic.

Only a t low advance r a t i o s were t h e r e s i g n i f i c a n t c o n t r i b u t i o n s from t h e h i g h e r harmonics. A s a r e s u l t of t h e t i p b e i n g f r e e , f o r w a r d f l i g h t power r e q u i r e m e n t s were reduced by 8% o r more.

C o n s i d e r a b l y more power r e d u c t i o n w a s recorded f o r h i g h - t h r u s t c o n d i t i o n s . The r e d u c t i o n i n power r e q u i r e m e n t s w a s a t t r i b u t e d t o a f a v o r a b l e i n f l u e n c e of t h e t i p ' s n e g a t i v e p i t c h a n g l e rela- t i v e t o t h e i n b o a r d p o r t i o n of t h e b l a d e ; a h y p o t h e s i s is p r e s e n t e d t o a c c o u n t f o r t h a t f a v o r a b l e e f f e c t . The l e s s e n i n g of t i p d r a g b e c a u s e of its n e g a t i v e r e l a t i v e p i t c h a n g l e w a s a l s o s u p p o r t e d by fixed-wing wind-tunnel test o f t h e same t i p s h a p e . I n a d d i t i o n t o t h e power r e d u c t i o n , f l a t w i s e b l a d e b e n d i n g moments w e r e r e d u c e d by as much as 30% a t t h e i n b o a r d b l a d e s t a t i o n s . Chordwise l o a d s , however, were n o t reduced by t h e free t i p . Loads going i n t o t h e c o n t r o l system were reduced a t a l l s p e e d s and r o t o r l i f t l e v e l s . D e t a i l s o f t i p and c o n t r o l l e r d e s i g n and c o n s t r u c - t i o n are i n c l u d e d .

7. Key Words (Suggested by Author(s)I 118. Distribution Statement F r e e t i p C o n s t a n t l i f t t i p Blade t i p H e l i c o p t e r r o t o r F r e e - t i p r o t o r R o t o r t i p s h a p e S u b j e c t Category: 05 22. Rice' 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. NO. of Pages Unc 1 ass i f i e d U n c l a s s i f i e d 69