Analytical investigation of a helicopter rotor driven and controlled by a jet flap

NASA TECHNICAL NOTE

NASA TN D-3028

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ANALYTICAL INVESTIGATION OF

A HELICOPTER ROTOR DRIVEN

A N D CONTROLLED BY A JET FLAP

by WiZZium T. Evuns und John L, McCZozcd III

Ames Reseurch Center

Moffett Field CuZ$

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 W A S H I N G T O N , D. C. SEPTEMBER 1 9 6 5 TECH LIBRARY KAFB, N M

I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l l l l l 1 1 1 1 1 l l l l l 1 1 1 1 1 1 1 1 1 1 1 1 1

0079847 Z I L I U L I **. LI " Y U " ANALYTICAL INVESTIGATION O F A HELICOPTER ROTOR DRIVEN AND CONTROLLED BY A J E T F L A P By William T. Evans and John L. McCloud 1 1 1 Ames R e s e a r c h Center Moffett Field, Calif.

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ANALYTICAL INVESTIGATION OF A HELICOPTER ROTOR DRIVEN AND CONTROLLED BY A JET FLAP By W i l l i a m T. Evans and John L. McCloud I11 Ames Research Center Results of a t h e o r e t i c a l study of t h e c h a r a c t e r i s t i c s of a p a r t i c u l a r The study made extensive use of j e t - f l a t r o t o r a r e presented and analyzed.

It w a s found t h a t t h e momentum and power high-speed d i g i t a l computations.

c o e f f i c i e n t s varied s i g n i f i c a n t l y with s h a f t angle f o r many f l i g h t conditions.

This finding i s rationalized, and i t s significance explored. It w a s a l s o found t h a t higher harmonic control of t h e f l a p reduced higher harmonics of blade flapping, t h r u s t , and torque.

The study indicated t h a t higher speeds can be a t t a i n e d i n pure helicopter f l i g h t than w i t h any conventional r o t o r . It f u r t h e r indicated t h a t t h e maxi- mum a t t a i n a b l e speed i n such f l i g h t i s l i k e l y t o be higher if t h e o r e t i c a l supercirculatory t h r u s t recovery on t h e blade i s r e a l i z e d i n practice.

INTRODUCTION The concept of driving and controlling a helicopter r o t o r by a variably deflectable j e t f l a p has been proposed ( r e f s . 1 and 2 ) . Such a design o f f e r s at l e a s t t h r e e p o t e n t i a l advantages: (1) mechanical simplification due t o t h e s u b s t i t u t i o n of j e t - f l a p control f o r conventional blade-pitch control, ( 2 ) increased l i f t and propulsive force due t o jet-induced llsupercirculationJ1l and ( 3 ) reduced vibrations due t o higher harmonic control of t h e j e t f l a p . Appli- cations t o t h r e e types of pure helicopter have been suggested: (1) a high- speed, low-drag vehicle ( V > 200 knots), ( 2 ) an e f f i c i e n t medium-speed vehicle, and ( 3 ) a crane helicopter.

The present investigation w a s undertaken t o study t h e t h e o r e t i c a l c h a r a c t e r i s t i c s of a j e t - f l a p rotor. Because of t h e complexity of t h e problem, t h e study w a s based primarily on t h e r e s u l t s of high-speed d i g i t a l computa- t i o n s . Three versions of a computer program were w r i t t e n and a r e described herein. The programs a r e general, t h e f i r s t two being applicable t o j e t - driven o r jet-augmented r o t o r s of almost any design, and t h e t h i r d being appli- cable t o shaft-driven r o t o r s only. The t h i r d program w a s used t o permit comparisons of j e t - f l a p and conventional rotors.

It should be emphasized t h a t t h i s concept of t h e j e t - f l a p r o t o r includes t h e notion of complete control by j e t d e f l e c t i o n alone, t h a t is, t h e blade p i t c h i s fixed. I n a manner e n t i r e l y analogous t o conventional c o l l e c t i v e and c y c l i c p i t c h control, "collective" and "cyclic" j e t deflections can be defined and given analogous notation. Thus, i n t h i s report, t h e j e t - d e f l e c t i o n angle 6 i s given as

-

- - -

8 = A , - A, cos $ - B, s i n $ - A2 cos 2$ - . . .

-

-

where A .

i s termed t h e ''collective'' j e t deflection, A 1 t h e " l a t e r a l cyclic" - j e t deflection, B 1 t h e "longitudinal c y c l i c " j e t deflection, and t h e higher order coefficients "higher harmonic controlt1 parameters.

O f importance i n t h e study i s an o v e r - a l l j e t momentum coefficient Cj,.

Although it i s a f o r c e c o e f f i c i e n t , it can be expected t o c o r r e l a t e well with t h e r o t o r power c o e f f i c i e n t , Cp, since t h e r o t o r i s e n t i r e l y j e t propelled.

The jet-momentum c o e f f i c i e n t i s therefore emphasized i n t h i s report.

Problems of i n t e r n a l flow, however, a r e not examined.

NOTAT I O N average or "collective" j e t deflection, deg harmonic c o e f f i c i e n t s - of j e t deflection, deg, 6 = KO - A 1 cos $ - B1 s i n $ - A2 cos 2$ - . . .

nozzle a r e a of j e t f l a p ( a l l blades), f t 2 l a t e r a l and longitudinal c y c l i c pitch, respectively, deg harmonic c o e f f i c i e n t s of blade flapping, deg, p = a. - a1 cos $ - b l s i n $ - a2 cos 2$ - . .

t i p l o s s f a c t o r , 0.99 f o r j e t - f l a p rotor, 0.98 f o r shaft-driven r o t o r number of blades H r o t o r longitudinal force c o e f f i c i e n t , p( s ~ R ) ~ ~ R ~ M j V j r o t o r jet-momentum Coefficient , p( S2R)'flR2 L r o t o r l i f t c o e f f i c i e n t , p( m)25cR2 Mj r o t o r mass-flow c o e f f i c i e n t , ~ S ~ R S R ~

+ c

summation of component power c o e f f i c i e n t s , C PC7R + 'pi + 'Po

C o r i o l i s power c o e f f i c i e n t , computed as C %OR induced power c o e f f i c i e n t , CPi 2 ( V / W

C p r o f i l e power c o e f f i c i e n t , - f 1 G ~ l ' I 'do dx

n P O xc $ C propulsive power coefficient,

cxR TE)

%

Q s h a f t torque coefficient, CQ p( . Q R ) ~ S R ' R 2 ( m ) R l ' + a d 0 dX C Coriolis torque c o e f f i c i e n t , %OR p( . Q R ) ~ S R ' R X

propulsive force c o e f f i c i e n t , -

CX qSR2 X r o t o r propulsive force c o e f f i c i e n t , cXR p( m)2SR2 C l o c a l blade chord, f t d

t o t a l l o c a l section drag c o e f f i c i e n t , -

lC C drag c o e f f i c i e n t due t o section shape (no j e t e f f e c t s ) d0 l c B R c r 2 equivalent blade chord (on t h r u s t b a s i s ) , 9 ft Ce BR

f r2 d r

r C LeBRcr3 dr equivalent blade chord (on thrust-moment b a s i s ) , 9 ft JBRr3 rC m j V j C l o c a l section momentum c o e f f i c i e n t

' c y

j t o t a l l o c a l s e c t i o n l i f t c o e f f i c i e n t - c 2

' 92c

C l i f t c o e f f i c i e n t due t o section shape (no j e t e f f e c t s ) 2 0 d t o t a l l o c a l s e c t i o n drag per u n i t span, l b / f t e o f f s e t of flapping hinge, f t acceleration of gravity, ft/sec2 H downwind for.ce perpendicular t o s h a f t , l b mass moment of i n e r t i a about flapping hinge, slug-ft2 ' h L l i f t , l b t o t a l l o c a l section l i f t per u n i t span, l b / f t M Mach number t o t a l mass flow per second through a l l blades, slugs/sec f t - l b t h r u s t moment of blade about flapping hinge, weight moment of blade about flapping hinge a t P = 0, f t - l b m j e t mass f l u x per u n i t span, a l l blades, slugs/ft/sec r a d i a l m a s s f l u x at a given r a d i a l s t a t i o n , a l l blades, slugs/sec mrad number of azimuth positions used i n computation n s h a f t torque, f t - l b

Q

free-stream dynamic pressure pV2, l b / f t 2 ' 2 l o c a l dynamic pressure pv', l b / f t 2 ' 2 9 2 R r o t o r radius, f t r r a d i a l distance along blade from hub, f t supercirculation t h r u s t parameter, see equation ( 7 ) supercirculation l i f t parameter, see equation ( 6 ) s Z T t h r u s t along s h a f t a x i s , l b i n t e r n a l temperature of blowing duct, ? F TDUCT U l o c a l v e l o c i t y perpendicular t o blade span, f t / s e c

U dimensionless l o c a l velocity, U/m

V free-stream velocity, f t / s e c

j e t v e l o c i t y , f t / s e c

advance r a t i o induced v e l o c i t y i n T-direction, f t / s e c VT V induced v e l o c i t y i n H-direction, f t / s e c H X propulsive f o r c e , p o s i t i v e upstream, l b X dimensionless r a d i a l s t a t i o n , r/R U l o c a l s e c t i o n angle of a t t a c k , deg s h a f t angle, p o s i t i v e rearward f r o m t h e v e r t i c a l , deg U S P blade flapping angle with respect t o s h a f t p o s i t i v e upward, deg I R4

mass constant of blade, pce -

7' I h j e t - r e a c t i o n increment t o s e c t i o n drag c o e f f i c i e n t Ac supercirculation increment t o s e c t i o n drag c o e f f i c i e n t d S Ac j e t - r e a c t i o n increment t o section l i f t c o e f f i c i e n t supercirculation increment t o s e c t i o n l i f t c o e f f i c i e n t A c 2, Ax spanwise extent of s l o t i n terms of x j j e t d e f l e c t i o n , p o s i t i v e downward from chordline, deg e %

o f f s e t parameter, - -

I h c o l l e c t i v e p i t c h of blade a t x = 0.7, deg 80.7

v s h % - V T

inflow r a t i o , h m

v cos a , - VH

tip-speed r a t i o , CL

m

free-stream air density, s l u g s / f t 3 D bce r o t o r s o l i d i t y , - d 3 t . R bc l o c a l s o l i d i t y

'X

9 azimuth s t a t i o n , from r e a r i n d i r e c t i o n of r o t a t i o n , deg R r o t a t i o n a l v e l o c i t y of r o t o r , r a d s l s e c Subscripts C cut out ( a t 0. ULR) maX maximum 9 a t azimuth p o s i t i o n IJI DESCRIPTION O F COMPUTER P R O G R A M S Flow c h a r t s f o r t h e j e t - f l a p r o t o r programs a r e shown i n f i g u r e 1.

The b a s i c computational approach i s t h a t of reference 3, wherein a blade flapping p a t t e r n i s assumed, t h e r e s u l t i n g t h r u s t moment i s calculated and harmonically analyzed, t h e flapping i s then revised and t h e t h r u s t moment recalculated, and s o on, u n t i l t h e i t e r a t i o n repeats within t h e meaningful accuracy of t h e computations. Simultaneously with t h e flapping revisions, t h e momentum c o e f f i c i e n t i s a l s o revised u n t i l t h e s h a f t torque i s essen- j R

t i a l l y zero ( t h e required equilibrium condition) . (This simultaneous i t e r a -

t i o n on flapping p a t t e r n and C has proven q u i t e f e a s i b l e . ) The well-known j R a l t e r n a t e approach of i n t e g r a t i n g t h e d i f f e r e n t i a l equation of flapping motion ( r e f . 4) would a l s o have been a n e n t i r e l y reasonable point of departure f o r developing t h e s e programs.

After steady flapping and zero CQ a r e a t t a i n e d , additional i t e r a t i o n s a r e performed t o a t t a i n e i t h e r ( a ) a specified s h a f t angle and advance r a t i o

by adjustment of inflow r a t i o A and tip-speed r a t i o p (program A),, or

( b ) a specified r e s u l t a n t force at one or more s h a f t angles by adjustment of t h e j e t - d e f l e c t i o n controls (program X ) . When r e s u l t s a t several angles a r e computed, program X proceeds i n such a manner as t o f i n d t h e angle a t which C i s minimized. Both programs assume s u p e r c r i t i c a l pressure r a t i o s and j R a d j u s t j e t velocity, which a f f e c t s mass flow and C with each change of

C . Both programs permit suppression of a r b i t r a r y harmonics of blade flap-

j R ping, s o t h a t t e e t e r i n g and gimbal-mounted r o t o r s may be simulated as well as free-to-cone r o t o r s .

A t h i r d program f o r shaft-driven r o t o r s p a r a l l e l s program X , adjusting conventional controls t o obtain a specified r e s u l t a n t force.

A l l programs include t h e standard assumptions of r i g i d blades, uniform small inflow, t h e a p p l i c a b i l i t y of two-dimensional data t o blade elements, flapping angles, no lagging motion, e t c . O n t h e other hand, e f f e c t s of s t a l l , compressibility, and spanwise section v a r i a t i o n can be included i n t h e two- dimensional data used.l Two-dimensional j e t e f f e c t s a r e accounted f o r i n terms of t h e l o c a l momentum coefficient c j ( o f t e n designated c p ) , defined as mjVj/qzc. The t o t a l section l i f t and drag a r e assumed t o consist of t h r e e components each; ( b a s i c force) + ( j e t - r e a c t i o n increment) + (supercirculation increment): The f i r s t component of each equation i s determined by t a b l e lookup and i n t e r - polation as a t r i v a r i a t e function of l o c a l angle of attack, Mach number, and radial s t a t i o n ( i . e . , section shape). The j e t - r e a c t i o n increments a r e obtained by geometric considerations as i s calculated as Based on references 5 and 6, & 2 , with sz = 3.18 f o r a l l computations of t h i s study ( r e f . 6 ) . Finally,

&ds = -sdc*[1 - c o s ( a + & ) I

(7) J w i t h For t h e o r e t i c a l f u l l t h r u s t recovery, Sd = 1 ( i . e . , 0 5 Sd 5 1.

& + b d s = -e for a l l a, 6 ) . If no t h r u s t recovery i s assumed, Sd = 0 .

dj 3 I n t h i s study, t h e value Sd = 1 / 2 has been used i n most computations. (For a recent discussion of j e t - f l a p t h r u s t recovery, and a review of t h e l i t e r a - t u r e , see reference 7, wherein it i s argued t h a t both theory and experiment indicate t h a t f u l l t h r u s t recovery can be expected i n steady-state flow. How- ever, t h e most reasonable assumption t o apply t o a j e t - f l a p r o t o r i s not clear, and t h e e f f e c t of varying t h e parameter i s examined in t h e present study.)

Sd - The uniform inflow i s assumed t o be opposite t o t h e d i r e c t i o n of the r e s u l t a n t force r a t h e r than t h e t h r u s t , r e s u l t i n g i n an induced component vH i n t h e d e f i n i t i o n of p. While t h e j u s t i f i c a t i o n f o r t h i s minor refinement of a gross assumption i s open t o question, it w a s found t h a t t h e inclusion of vH did not materially a f f e c t computed r e s u l t s .

The formulas above a r e applied throughout t h e range of angle of a t t a c k and Mach number. This approach means, among other t h i n g s , t h a t p a t t e r n s of stall a r e not much a f f e c t e d by t h e s e formulas, as i l l u s t r a t e d in sketch ( a ) . The omis- s i o n of any s t a l l - a l l e v i a t i n g e f f e c t may be an unduly p e s s i m i s t i c assumption.

The spanwise d i s t r i b u t i o n s of both mass flow and j e t v e l o c i t y have been

I

assumed constant, which permits t h e def- i n i t i o n of t h e r o t o r momentum c o e f f i c i e n t as MjV j

c =

jR P ( S L R ) ~ I I R ~ where M j i s t h e t o t a l mass flow per second through a l l blades of t h e r o t o r .

The r e l a t i o n s h i p between l o c a l c and j C can be shown as j R - 2 9 , - AXjOXU2 Relationships among C and pressure j R r a t i o , nozzle a r e a , j e t v e l o c i t y and mass a flow a r e based on standard thermodynamic equations with t h e assumption of isen- Sketch (a) t r o p i c expansion.

DESCRIPTION O F ROTORS The j e t - f l a p r o t o r analyzed i n t h i s study i s two-bladed, with o f f s e t flapping hinges. The blade plan form, s e c t i o n v a r i a t i o n , and t w i s t a r e shown i n f i g u r e 2 ( a ) . The j e t f l a p extends fram 0.7R t o t h e t i p . Note t h e r a p i d t a p e r i n t h i s region from a t h i c k s e c t i o n ( 2 1 percent) a t t h e inboard end t o a t h i n section (about 8 percent) at t h e t i p . The t h i c k s e c t i o n i s required t o accommodate t h e i n t e r n a l duct. Other physical parameters a r e : R = 19.685 f t , y ' = 0.509, q = 0.0837, cr = 0.0488, and nozzle height = 0.0006R. Sign conven- t i o n s f o r p r i n c i p a l parameters a r e indicated i n f i g u r e 2 ( b ) .

Figure 3 shows p l o t s of t h e b a s i c a i r f o i l d a t a assumed. Data f o r t h e t i p s e c t i o n a r e based on curves f o r t h e NACA 64-008 s e c t i o n as reported i n reference 8. D a t a f o r t h e inboard region a r e based on t h e "Summary of A i r f o i l Data" ( r e f . 9) f o r NACA 6-series t h i c k sections and on t h e Mach number trends suggested by comparisons of t h e data f o r t h e NACA 0015 and 0012 sections, as reported in references 10 and 11, respectively. D a t a f o r extreme angles of a t t a c k a r e based on reference 12.

A few calculations were made f o r a shaft-driven r o t o r with t h e same physical c h a r a c t e r i s t i c s as t h e j e t - f l a p r o t o r , except t h a t a i r f o i l data t y p i - c a l of t h e NACA 0012 s e c t i o n were assumed f o r t h e e n t i r e r o t o r blade.

RFSULTS AND DISCUSSION The material presented here i s organized i n t h r e e main sections. The f i r s t two sections examine t h e inherent c h a r a c t e r i s t i c s of the j e t - f l a p rotor, first a t moderate speeds, and then a t high speeds. The discussion i n these sections i s f a i r l y lengthy because of t h e unfamiliar and untested nature of t h i s type of r o t o r . The f i n a l section b r i e f l y compares t h e j e t - f l a p r o t o r with conventional r o t o r s , from t h e standpoint of performance c a p a b i l i t i e s and power requirements.

C h a r a c t e r i s t i c s of t h e Jet-Flap Rotor a t Moderate Speeds I n t h i s section, r e s u l t s f o r advance r a t i o s from 0.3 t o 0.5, corresponding t o forward speeds from lo5 t o 175 knots, a r e examined. A l l r e s u l t s a r e f o r constant t i p speed of 591 ft/sec, corresponding t o i l = 30 rads/sec.

Dependence of momentum and power c o e f f i c i e n t s on s h a f t angle .- I n

f i g u r e 4(a) a r e shown t y p i c a l curves of C j , and Cp vs as f o r a fixed f l i g h t condition. The corresponding control s e t t i n g s and blade flapping harmonics a r e shown i n f i g u r e 4 ( b ) . (It should be remembered t h a t control of t h i s r o t o r i s accomplished exclusively by variable j e t - f l a p deflection, the blade p i t c h being f i x e d . ) For comparison, similar curves a r e shown in figure 5 f o r t h e

shaft-driven r o t o r ( control being conventional blade-pitch control) . For t h e

j e t - f l a p r o t o r , t h e v a r i a t i o n of power with s h a f t angle i s i n marked contrast i t s invariance f o r t h e conventional r o t o r . For t h e l a t t e r , t h e c l a s s i c a l t o expectation of "f lapping-f eathering equivalence" i s c l e a r l y indicated by t h e r e s u l t s ; t h a t i s , equal changes of s h a f t angle and longitudinal p i t c h control (feathering) r e s u l t i n an equal and opposite change of longitudinal flapping, such t h a t t h e r e s u l t a n t force, power, and torque a r e unchanged. Collective p i t c h i s e s s e n t i a l l y invariant - also, whereas, f o r t h e j e t - f l a p r o t o r , "collec- t i v e " j e t d e f l e c t i o n A . v a r i e s s i g n i f i c a n t l y .

This finding may be r a t i o n a l i z e d i n t h e following way. The r e s u l t a n t force on t h e j e t - f l a p r o t o r may be thought of (although it i s not so calcu- l a t e d ) as the sum of a basic r o t o r force and a j e t - f l a p increment. Although t h e b a s i c r o t o r f o r c e may be conceived of in various ways, it w a s calculated f o r purposes of i l l u s t r a t i o n as t h e force developed by t h e r o t o r when driven e n t i r e l y by an undeflected t i p j e t . Presented i n f i g u r e 6 i s t h e v a r i a t i o n of t h e basic r o t o r f o r c e with s h a f t angle f o r a p a r t i c u l a r advance r a t i o , as well as t h e incremental vectors needed t o produce a s p e c i f i e d r e s u l t a n t f o r c e f o r t h e j e t - f l a p r o t o r . It can be seen t h a t t h e incremental vector a t t h e s h a f t angle f o r minimum C j R i s a compromise between minimum extension and minimum t i l t i n g of t h e basic f o r c e vector.

Figure 7 shows curves of f o r advance r a t i o s of 0.3 t o 0.5 f o r C j , v s as two vehicles. (Specifically, t h e comparison i s made f o r two p a i r s of f i x e d values of CLR and CX at constant r o t a t i o n a l v e l o c i t y . This corresponds t o two p a i r s of f i x e d values of l i f t and "drag area" X/q.)

Also shown i n t h e f i g u r e i s t h e locus of optimum s h a f t angles f o r each vehicle.

Effects of blade -pitch.- While a constant blade p i t c h i s envisioned f o r t h e j e t - f l a p r o t o r , it i s important t o examine t h e e f f e c t s of blade p i t c h f o r an indication of t h e most appropriate value t o be incorporated i n a p r a c t i c a l

design. Figure 8 shows the e f f e c t s of various p i t c h angles (e,.,) between 8 '

and 1 2 ' . It can be seen t h a t t h e l e a s t power i s required a t 8 , and t h a t l e s s power would probably - be required at s t i l l lower p i t c h angles. The c o l l e c t i v e j e t d e f l e c t i o n A, increases rapidly as blade p i t c h i s decreased from 1 2 ' ( f i g . 4 ( b ) ) t o 8 ' - ( f i g . 8 ( b ) ) , as might be expected. "Longitudinal cyclic" j e t d e f l e c t i o n B1 decreases somewhat. I n a l l cases, coning i s v i r t u a l l y invariant, while a l l harmonics of blade flapping decrease, as t h e s h a f t angle becomes more nearly v e r t i c a l .

Note t h a t t h e minimum C j , does not occur a t t h e s h a f t angle f o r minimum i s flapping. Note a l s o ( f i g . 8 ( c ) ) t h a t t h e p r o f i l e power c o e f f i c i e n t C P O very s e n s i t i v e t o blade pitch, whereas t h e power component due t o C o r i o l i s i s almost invariant i n t h e range of t h e r e s u l t s presented. The forces, C 'COR' r e f l e c t s marked v a r i a t i o n i n l o c a l angle of a t t a c k marked v a r i a t i o n i n cpO on t h e r e t r e a t i n g blade (c(max = l3O f o r Clearly, t h e f l i g h t con- = 1 2 ' ) .

d i t i o n f o r t h e s e calculations i s not well matched t o a fLxed p i t c h of 12O.

E f f e c t s of Cx.- I n f i g u r e 9(a) a r e shown curves of f o r C j , vs as s e v e r a l values of Cx. The locus of optimum values of as i s a l s o indicated.

The power v a r i a t i o n along t h i s locus i s shown i n p a r t ( b ) of t h e f i g u r e .

I n t h e regime of steady forward f l i g h t f o r r e a l i s t i c machines ( i . e . , s u b s t a n t i a l Cx) , t h e power increases r a p i d l y with Cx, t h e p r i n c i p a l component being t h e propulsive power required. C b r i o l i s power a l s o increases, and i t s importance should be noted, since it amounts t o as much as one-third of t h e t o t a l a t low CX, and t o roughly one-fourth a t high Cx.

The power and momentum c o e f f i c i e n t s r i s e as drops t o zero because of Cx a rapid r i s e i n p r o f i l e power, r e f l e c t i n g a r a p i d r i s e i n section drag over much of t h e r o t o r . This drag r i s e must i n t u r n be due t o excessive l o c a l angles of a t t a c k . The process can be a t t r i b u t e d t o t h e high f i x e d p i t c h of t h e r o t o r blades, and t h e progressive rearward t i l t i n g of t h e t i p - p a t h plane; i n a conventional r o t o r , t h e r e s u l t would be increasing l i f t and t h e onset of 1 0 s t a l l .

I n t h e j e t - f l a p rotor, t h e same phenomenon occurs, s o far as t h e "basic r o t o r l i f t " (discussed e a r l i e r ) i s concerned; however, t h e over-all l i f t i s d e l i b e r a t e l y held constant by adjustments of t h e j e t - f l a p controls.

Attainable forces.- I n f i g u r e 9, r e s u l t s were presented f o r t h e j e t - f l a p r o t o r f o r propulsive force c o e f f i c i e n t s up t o CX = 0.015 a t an advance r a t i o For the same conditions, it i s shown i n f i g u r e 10 t h a t , a t t h e high- of 0.5.

e s t C x , t h e maximum j e t deflection (Eo + 1'B.I) exceeds TO0 f o r t h e shaft

angles computed. A t t h i s highest Cx, t h e e f f e c t of varying CL (choosing 19 can be seen t h e optimum s h a f t angle f o r each case) i s shown i n f i g u r e 11.

t h a t both C j , and b x a r e minimized a t CLR 0.006 (CLR/CJ = 0.123). The value of 6 , ~ a t t h i s condition i s about 72'. The values CLR = 0.006, Cx = 0.015, and V / f B = 0.5 correspond, respectively, t o L = 6060 l b , X/q = 18.25 f t 2 , and V = 175 knots, and suggest t h e order of magnitude of a t t a i n a b l e forces a t t h i s moderately high forward speed. Similar data f o r one- half t h e propulsive force a r e a l s o shown i n t h e figure, where it can be seen t h a t C j, and Emax a r e minimized a t CLR 2 0.005 ( C L ~ / C J = 0.102).

Effects of nozzle area.- A given value of C may be the r e s u l t of j R varying combinations of mass flow and j e t v e l o c i t y ( C = CmSs x ( V j / s L s ) ) .

j R While t h i s does not a f f e c t l o c a l section forces, which a r e dependent only on l o c a l without regard t o i t s component f a c t o r s , it does a f f e c t Coriolis c j might be forces, which a r e dependent on r a d i a l mass flow. Therefore, C 'COR s e n s i t i v e t o the parameter a f f e c t i n g mass flow in these computations, namely, t h e area of t h e nozzle. However, t h e r e s u l t s of a comparison of two nozzle areas, shown i n f i g u r e 12, indicate only a s l i g h t e f f e c t . (The comparison i s made f o r t h e same f l i g h t condition, not t h e same The l a r g e r nozzle area Cj,.

i s some 1 4 percent g r e a t e r than t h e smaller, which w a s t h e value used f o r a l l other computations of t h i s study. ) i s p a r t l y a t t r i b u t a b l e t o t h e f a c t T h i s minor e f f e c t of AN on "COR can be shown t o be roughly proportional t o r a t h e r than t o t h a t C

&

'COR AN i t s e l f , f o r constant C j R o However, because of differences i n j e t density, t h e a c t u a l e f f e c t i n t h e r e s u l t s of f i g u r e 12 i s even l e s s than would be indi- cated by t h i s approximate relationship.

Effects of higher harmonic control.- Possible b e n e f i t s of higher harmonic control of t h e j e t f l a p were b r i e f l y investigated. It w a s found t h a t t h e cosine and sine components of t h e second harmonic of blade flapping could be almost independently suppressed by-the corresponding components of second har- monic j e t - f l a p d e f l e c t i o n (2 and A2, respectively), at l e a s t f o r t h e a r b i - - - t r a r y f l i g h t condition chosen ( V / f B = 0.3, as = -18.46O, xo = -20.566', A 1 = 0 , The e f f e c t s of B1 = 12.57T0, r e s u l t i n g i n CLR = 0.0048 and CX = 0.0112).

such second harmonic control on t h e d i s t r i b u t i o n s of p, CT, and CQ a r e shown i n f i g u r e 13. The p r i n c i p a l e f f e c t i s a d r a s t i c reduction i n t h e second CT, but some reduction i s a l s o e f f e c t e d i n t h e t h i r d harmonic, harmonic of and i n both t h e second and t h i r d harmonics of The first harmonics of CQ.

both CT and CQ a r e s l i g h t l y increased. To t h e extent t h a t shake and vibra- t i o n s a r e due t o higher harmonics of f o r c e and moment v a r i a t i o n s , t h e s e r e s u l t s strongly suggest t h e p o t e n t i a l reduction of such undesirable e f f e c t s through appropriate use of higher harmonic control.

C h a r a c t e r i s t i c s of t h e Jet-Flap Rotor a t High Speeds I n t h i s section, r e s u l t s : f o r advance r a t i o s from 0.50 t o 0.86, corre- sponding t o forward speeds frbm 175 t o 301 knots, a r e examined.

Results a t constant ! J . R . - Results obtained a t high advance r a t i o s a r e shown i n f i g u r e 14. The l i f t and propulsive f o r c e c o e f f i c i e n t s a r e t h e same ~- as f o r c e r t a i n d a t a of f i g u r e 4, and correspond t o f i x e d values of vehicle weight and drag a r e a of 4920 l b and 6.09 s q ft, respectively. The highest advance r a t i o shown, 0.86, corrqsponds t o a f l i g h t v e l o c i t y of 301 knots, a speed at which pure h e l i c o p t e r f v i g h t would not be computable under any reason- able assumptions, f o r any conventional r o t o r . A t t h i s extreme condition, t h e advancing t i p Mach number i s 0.98, which, though high, i s not n e c e s s a r i l y impractical, i n view of t h e t h i n t i p s e c t i o n . A t both t h i s advance r a t i o and t h e advance r a t i o of 0.8, a portion of t h e j e t f l a p encounters t h e region of reverse flow on t h e r e t r e a t i n g blade.

Other than t h e high f l i g h t v e l o c i t y of 301 k n o t s , t h e r e s u l t s presented involve no p a r t i c u l a r s u r p r i s e s . The v a r i a t i o n s of C j R with as a r e e n t i r e l y s i m i l a r t o those at lower advance r a t i o s . The j e t - d e f l e c t i o n require- ments increase with advance r a t i o , but at a decreasing r a t e . Power require- ments b u i l d up rapidly, p a r t i c u l a r l y t h e propulsive power required, which Compressibility increases as t h e cube of advance r a t i o ( f o r constant Cx).

e f f e c t s a r e r e f l e c t e d i n increasing Cpo and momentum requirements i n cpcoR* Again, t h e s i g n i f i c a n t finding would seem t o be t h e mere f a c t t h a t it w a s possible t o compute a 3OO-knot case f o r p o s i t i v e propulsive force and s i g n i f i - cant l i f t .

Results at l i m i t e d t i p Mach number.- If advancing t i p Mach number i s t o be r e s t r i c t e d t o avoid severe compressibility e f f e c t s , it i s necessary t o reduce r o t a t i o n a l v e l o c i t y as advance r a t i o i s increased beyond some p a r t i c u l a r value.

To examine t h i s mode of high-speed f l i g h t , r s u l t s were obtained a t an advance r a t i o of 0.7 and an advancing t i p Mach numb r of 0.8, t h e same as t h a t which

prevailed a t an advance r a t i o of 0.5 in t h ! r e s u l t s previously discussed. The

forward speed corresponding t o t h e s e conditions w a s 220 knots, and t h e t i p speed, Q R , w a s 531 f t / s e c , corresponding t o R = 27 rads/sec.

Results a r e presented i n f i g u r e 15 f o r two values of C x , corresponding i n t h e e a r l i e r high-speed r e s u l t s , t o drag areas of 6.09 and 9.13 s q f t . A s t h e l i f t w a s 4920 l b , but t h e c o e f f i c i e n t C L ~ w a s n e c e s s a r i l y higher because of t h e reduction i n R.

Some power saving w a s r e a l i z e d , i n both t h e C o r i o l i s and p r o f i l e power components. These savings ( n o t i l l u s t r a t e d ) amounted t o about 20 percent and

17 percent, respectively, f o r t h e lower Cx. The l a r g e s t component, propulsive

(The power components were compared on a power, w a s necessarily t h e s a m e .

dimensional b a s i s a t t h e same forward speed.)

A n adverse e f f e c t can be seen i n t h e increase in required j e t deflection.

A s a s p e c i f i c example, at t h e optimum s h a f t angles, 6 - f o r Cx = 0.005 a t Cx a t V = 245 knots V = 220 knots ( f i g . 15) w a s g r e a t e r than f o r t h e same ( f i g . 14). Primarily because of t h i s e f f e c t of rapidly increasing &X w i t h forward speed, no attempt w a s made t o compute higher speed cases f o r an advanc- ing t i p Mach number of 0.8. It may be worth noting t h a t such f l i g h t a t 300 knots would require an advance r a t i o of 1.3, and an increase of 53 percent i n CLR Effects-of t h e t h r u s t recovery parameter.- One-half of t h e t h e o r e t i c a l f u l l t h r u s t recovery due t o supercirculation has been assumed in t h e calcula- t i o n s discussed s o far; t h a t is, t h e parameter sd has been s e t equal t o one- half i n equation ( 7 ) . In view of t h e large j e t deflections i n t h e high-speed r e s u l t s j u s t discussed, it w a s f e l t t h a t t h e e f f e c t s of varying Sd f o r one of these cases would be p a r t i c u l a r l y illuminating. This has been done f o r t h e f u l l range of sd, from 0 t o 1, for t h e least-propulsive-force f l i g h t condi- t i o n of f i g u r e 15 ( C X = O.OO5), and r e s u l t s a r e shown in f i g u r e 16. Although C j , decreases with increasing sd, as would be expected, t h e v a r i a t i o n i s not large. More importantly, t h e required maximum f l a p deflections increase rap- as = -16O, 6 - increases from 6g0 without t h r u s t idly; f o r example, a t recovery t o log0 with f u l l t h r u s t recovery. Cross p l o t s of 6 , , against S d suggest t h a t t h e r e probably e x i s t conditions (of g r e a t e r speed, or g r e a t e r propulsive f o r c e ) for which a solution could be computed f o r sa = 0, but could not be computed f o r S d = 1. In short, the r e s u l t s seem almost paradox- i c a l i n t h a t they suggest t h a t high-speed f l i g h t i s more r e a d i l y a t t a i n a b l e i f l e s s t h r u s t recovery a c t u a l l y occurs in a r e a l machine.

Another approach t o examining t h e e f f e c t s of assumed t h r u s t recovery i s t o consider t h e v a r i a t i o n of r o t o r forces with S d f o r f i x e d control s e t t i n g s and s h a f t angle. This has been done and r e s u l t s a r e shown i n f i g u r e 17. It can be seen t h a t , r e l a t i v e t o t h e usual value of = 1/2, t h e value of

cx

i s doubled f o r S d = 0, and cut i n half f o r Sd = 1. The corresponding range of d i s k tilt ( a s + a=) i s about 5'. Again, t h e r e s u l t seems paradoxical u n t i l t h e v a r i a t i o n of Cj, i s considered; t h e g r e a t e r force without t h r u s t recov- ery i s simply due t o much g r e a t e r momentum f l u x required t o turn t h e rotor, and the l e s s e r force with f u l l t h r u s t recovery i s due t o t h e f a c t t h a t t h e r o t o r t u r n s w i t h much lower momentum f l u x by v i r t u e of the t h r u s t recovery assumed.

The general conclusion may be *awn a t t h i s point t h a t speeds well in excess of 200 h o t s may be a t t a i n a b l e f o r p r a c t i c a l pure h e l i c o p t e r s with j e t - f l a p rotors, p a r t i c u l a r l y i f l i t t l e or no supercirculatory t h r u s t recovery occurs on t h e r o t o r blades in p r a c t i c e .

Comparisons With Conventional Rotors The comparisons i n t h i s section a r e concerned with performance c a p a b i l i t i e s and power requirements.

High performance c h a r a c t e r i s t i c s . - From t h e generalized charts of reference 13, one may draw c e r t a i n conclusions as t o t h e a t t a i n a b l e f l i g h t con- d i t i o n s f o r conventional shaft-driven r o t o r s .

(The charts a r e based on d i g i - t a l computations which a r e considered comparable t o those of t h e present study.)

For example, a s o l i d i t y of about 0.11 f o r rectangular blades with -8' of t w i s t would be required t o a t t a i n t h e f l i g h t condition of CLR = 0.00488, Cx = 0.0113, and V/QR = 0.5 (corresponding t o t h e r e s u l t s presented on f i g u r e s 7 and 9 f o r t h e j e t f l a p r o t o r ) . This s o l i d i t y i s g r e a t e r than t h a t of t h e j e t - f l a p r o t o r by a f a c t o r of about 2.2, and t h e required machine can be visualized as a 4- bladed r o t o r with blades of about 10 percent g r e a t e r e f f e c t i v e chord. To CLR = 0.0065, Cx = 0.015 ( f i g . 7) would a t t a i n t h e g r e a t e r r e s u l t a n t force of require an approximate t h r e e f o l d increase i n s o l i d i t y t o about 0 ,l5.

O n t h e basis of t h e charts, t h e maximum a t t a i n a b l e design speed of a conventional pure helicopter can be estimated t o be about 200 h o t s or s l i g h t l y more. The s o l i d i t y required f o r such speeds would be more than t h r e e times t h a t of t h e j e t - f l a p r o t o r . A few current design studies, such as r e f e r - ences 1 4 and 15, likewise indicate a speed l i m i t of t h i s order, regardless of s o l i d i t y or any other design parameter. I n contrast, as has already been shown, computational r e s u l t s can be obtained f o r t h e j e t - f l a p r o t o r f o r speeds as high as 300 h o t s .

Specific power comparison.- A few computations were c a r r i e d out f o r a shaft-driven r o t o r having t h e same physical c h a r a c t e r i s t i c s as t h e j e t - f l a p rotor, except t h a t a i r f o i l data based on t h e c h a r a c t e r i s t i c s of the NACA 0012 section were applied t o t h e e n t i r e blade. It may be i n s t r u c t i v e t o compare t h i s r o t o r with t h e j e t - f l a p r o t o r f o r t h e same s p e c i f i c f l i g h t condition.

C L ~ = 0.00488, This has been done i n f i g u r e 18 f o r t h e condition of Cx = 0.0113, and V/QR = 0.3, f o r which j e t - f l a p r e s u l t s were presented i n f i g - The j e t - ure 7 ( b ) , and f o r which t h e conventional r o t o r i s close t o s t a l l .

f l a p r o t o r c l e a r l y requires more power. While t h e data of f i g u r e 8 ( c ) suggest might be obtained through an optimum t h a t s u b s t a n t i a l reductions i n Cpo choice of blade p i t c h 8 , they a l s o indicate t h a t s i g n i f i c a n t reductions i n a r e probably not a t t a i n a b l e . Since C f o r t h e j e t - f l a p r o t o r i s "COR 'COR f o r t h e shaft-driven rotor, it appears t h a t s i g n i f i c a n t l y higher than c ' O t o t a l power required f o r t h e former would generally, and perhaps always, be higher than t h a t required f o r t h e l a t t e r , f o r t h e same f l i g h t condition. How- ever, while t h e conventional r o t o r i s close t o s t a l l at t h i s condition, t h e j e t - f l a p r o t o r can generate far g r e a t e r forces, and f a r g r e a t e r speeds, as has already been shown.

CONCLUSIONS Under t h e assumptions made, t h i s study has l e d t o t h e following conclusions : 1 . A j e t - f l a p r o t o r appears capable of higher self-propelled speed than any conventional r o t o r .

2. A j e t - f l a p r o t o r can generate f a r g r e a t e r forces than a conven- t i o n a l r o t o r of t h e same radius and s o l i d i t y .

3. For u m t a l l e d f l i g h t conditions, a j e t - f l a p r o t o r requires more power than a conventional r o t o r of b a s i c a l l y s i m i l a r design.

The maximum a t t a i n a b l e speed of a j e t - f l a p r o t o r i s l i k e l y t o be 4.

higher

i f t h e o r e t i c a l supercirculatory t h r u s t recovery on the blade i s not

r e a l i z e d i n practice.

5. The momentum and power c o e f f i c i e n t s required f o r a given f l i g h t condition vary s i g n i f i c a n t l y with s h a f t angle.

6. Higher harmonic control of t h e j e t f l a p i s l i k e l y t o reduce vibrations.

7. The nozzle height does not appear t o be a s e n s i t i v e parameter i n j e t - f l a p r o t o r design.

Ames Research Center National Aeronautics and Space Administration

Moffett Field, C a l i f . , J u l y 21, 1965

REFERENCES Dorand, Re&; and Boehler, Gabriel D . : Application of t h e Jet-Flap 1.

Principle t o Helicopters. J. Am. Helicopter S O C . , v. 4, no. 3, J u l y 1959, PP. 26-36.

2. Greeman, R . N.; and Gaffney, M. G . : Application of Circulation Control t o Helicopter Rotors. Rep. ARD 158, H i l l e r Helicopter Co., 1957.

3. Gessow, Alfred: Equations and Procedures f o r Numerically Calculating t h e Aerodynamic C h a r a c t e r i s t i c s of L i f t i n g Rotors. NACA TN 3747, 1956.

4. Gessow, Alfred; and C r i m , Almer D.: A Method f o r Studying t h e Transient Blade-Flapping Behavior of L i f t i n g Rotors a t Extreme Operating Condi- t i o n s . NACA TN 3366, 1955.

5. Malavard, L.; Jousserandot, P.; and Poisson-Quinton, Ph. : Jet-Induced Aero Digest, v O l = 73, nos. 3-5, 19%: sept., Circulation Control.

pp. 21-27; Oct., pp. 46-59; NOV, pp. 34-46.

A Study of Dike, D . J.; Dunn, H. S.; Hazen, D. C.; and Lehnert, R. F.: 6 .

Low Speed Aerodynamic C h a r a c t e r i s t i c s of High-Lift Flow Controlled t h e P r o f i l e s and Wings. Aeron. Engr. Rep. 349, Princeton Univ., 1958.

7. Garland, D. B.: Jet-Flap Thrust Recovery: I t s History and Experimental Realisation. A I M Paper 64-797, 1964.

8. Wilson, Homer B., Jr.; and Horton, Elmer A.: Aerodynamic C h a r a c t e r i s t i c s A i r f o i l Sec- at High and Low Subsonic Mach Numbers of Four NACA 6-Series NACA RM L53C20, 1953.

t i o n s at Angles of Attack From -2O t o 31'.

9. Abbott, Ira H.; von Doenhoff, Albert E.; and S t i v e r s , Louis S., Jr.: Suwnary of A i r f o i l Data. NACA TR 824, 1945.

10. Shivers, James P.; and Carpenter, Paul J.: E f f e c t s of Compressibility on Rotor Hovering Performance and Synthesized Blade-Section Characteristics Derived From Measured Rotor Performance of Blades Having NACA 0015 A i r - f o i l Tip Sections. NACA TN 4356, 1958.

11. Carpenter, Paul J.: L i f t and Profile-Drag C h a r a c t e r i s t i c s of an NACA O O l 2 A i r f o i l Section as Derived From Measured Helicopter-Rotor Hovering Per- formance. NACA TN 4357, 1938.

12. Critzos, Chris C.; Heyson, Harry H.; and Boswinkle, Robert W . , Jr.: Aerodynamic C h a r a c t e r i s t i c s of NACA 0012 A i r f o i l Section at Angles of Attack From 0 ' t o 1 8 0 ' . NACA TN 3361, 1955.

13. Tanner, Watson H . : Charts f o r Estimating Rotary Wing Performance i n Hover and a t High Forward Speeds. N A S A C R - 1 1 4 , 1964.

14. Tanner, Watson H.; and Bergquist, Russell R.: Some Problems of Design J. A i r c r a f t , and Operation of a 25O-Knot Compound He1.icopter Rotor.

v o l . 1, no. 5 , Sept.-Oct. 1964, pp. 252-259.

15. Wachs, Miller A.; and Rabbott, John P., Jr.: Rotary Wing A i r c r a f t Design Paper presented a t Vehicle Design and Propulsion Meeting, Trends.

Wright-Patterson AFB, Ohio, Sikorsky A i r c r a f t , 1963.

DESIGN PARAMETERS AIRFOIL SECTION DATA Planform, twist, mass, cutout, C Z , C d vs a , M, x offset, no.

I COMPUTING PARAMETERS

I_

I No. stations, suppressed harmonics, ,-

I assumed

._ .- ..- I FLIGHT CONDITIONS I Next case No . - ._

- Adjust X and p

Calc. final output with I

detail i f requested (a) Flow chart for program A.

Figure 1.- Flow charts for the computirsg programs for the jet-flap rotor.

DESIGN PARAMETERS AIRFOIL SECTION DATA 4 Planform, twist, mass, cutout, c2, Cd vs a , M, x offset, no. blades, nozzle area, ...

.

COMPUT I N G PARAM E TER S No. stations, suppressed harmonics, assumed flapping, tolerances, ...

.

1 OPERATING CONDITIONS

51, TDUCT, control settings, ...

Calc. CT, CH, A , p implied C L ~ , Cx, V/51R, as , supercirculation by flight conditions

lshaft torque cQ, other quantitiesry

Next case Calc. pressure ratio, and correct CQ for Coriolis effects flapping harmonics Analyze MT harmonically; and momentum coeff Cj, Calc. new flapping harmonics

t

Adjust controls (collective and/or cyclic jet - flap deflection)

t

4 Yes

No t

- Yes Adjust a, by arbitrary increment or to minimum of parabolic f i t Output summary answers detail if requested No ~ ~~ ( b ) Flow c h a r t f o r program X.

Figure 1.- Concluded.

1 8

Twist distribution 1) (00)

I r

(- 2O)

(-I 1 . 5 O )

.64 R

I

I I

, I

I

t

% 4 - w

C

J

L

I - J e t flap

t 0

a I

*I

Taper to - NACA

I

-Airfoil fairings-- NACA 632 A 0 2 I 4-

64AQQ8 at t i p

,0525 R

(a) Plan form, section variation, and t w i s t of blade.

Figure 2.- Rotor d e t a i l s .

Iu (b) Sign conventions for principal parameters.

Figure 2. - Concluded.

I .2 - 2.4

' I .

I

Tip section

--

Cutout to 0.7R

.8

- 2.0

.4 - 1.6

c z O

- 1.2

C d0

-.4 .8

-.8

.4

-1.2

20 40 60 80 IO0 120 I 4 0 I 6 0 I 8 0

U (a) Data through 1 8 0 ' at zero Mach number.

Figure 3 . - Basic blade-section data.

Iu 1 0

I .2

.a

C

.4

L

-

I .2

Tip section

--

Cutout to 0.7R

.a

C 1 0

.4

20 40 0 20 40 0 20 40 0 20 40

a ( b ) L i f t data.

Figure 3.- Continued.

.6

.4

c d O

,2

-

.6

Tip section

-- Cutout to 0.7R

.4

C d O

e 2

IO 20 0 I O 20 0 IO 20 0 IO 20

a ( c ) Drag data.

Figure 3.- Concluded.

Iu W

12 -

Cj,x 1 0 4

C ~ X lo4

us f o r CH = O L I I I I II I ! I 6 -14 -12 -I 0 -0 -6 - 4 U S ( a ) Effects on C and C p .

j R Figure 4.- Effects of s h a f t angle at a fixed f l i g h t condition f o r t h e j e t - f l a p r o t o r ; C L ~ = 0.0065, Cx = 0.015, V/m = 0 . 3 , e O a 7 = 12O, Q F i = 591 f t / s e c .

40 -

0 a, &,E, 0 B I

20 -

I

I ,-

I I I I .4 .2 h

n

+

I

-.2 -I

-I

optimum a s

I I I I J I -.4

-20 -16 -I 4 -I 2 -10 -0 -6 Q S ( b ) E f f e c t s on c o n t r o l requirements and blade flapping.

Figure 4. - Concluded.

I

I I J

I I .0001 4 -

/

‘0.7, E l l a O l I I a I ’ b l

I I I I -

-12 L -I 2 -0 -4 0 - 20 -I 6 ft ngle t a f i x e d f l i g h t condition f o r t h e s h a f t - Figure 5.- E f f e c t s of s h driven rotor; CQ = 0.003, Cx = 0.005, V/QR = 0.3, QR = 591 f t / s e c .

I

6 6 " J e t - \ \ \ \ \ C , X I O ~ R \ 5E

'i

" Basic

I '7

rotor force

I

I

b \

I

0 Specified resultant force

\

I

-+Vectors for minimum C j \

I

R \ (Fig 4 ( a ) 1

I

I

i

I

\ \

I

\

I

5c \

I

I

I

I

4 E -14' . as=-IOo 1-12" -I I \

I I I \ I I

0 2 4 6 8 I O 1 2

c X I O ~

X R Figure 6.- Basic and incremental forces f o r t h e j e t - f l a p r o t o r at various

shaft angles; v/m = 0.3, ! d R = 591 f t / s e c -

22 -

. - -

e - . 5 Y S1R

I

I

I

20 -

I

I

I

\/Locus of optimum as

I8 -

I

\

+ - - 0 " 5

I6 -

\

c j x1o4

R

\

\

1 4 -

\

\ \

\

12 -

\

1 0 -

I I I I I I g L -20 - I 8 -I 6 -I 4 -I 2 -10 -8 QS ( a ) CQ = 0.0065, Cx = 0.015 Figure 7.- Variation of optimum s h a f t angle with advance r a t i o f o r t h e j e t - f l a p r o t o r ; = 12O, I ; 1 R = 591 f t / s e c .

1 8 -

1 6 -

A .50 0 .45

-IA -

0 .40

0 .30

1 4 -

Locus of optimum Q~

v

1 2 -

IO - c j X I O ~ R 8 - 6 - 4 - 2 - I

0 I-- - - I __ - I I I I

-22 -20 -I 8 -16 - 1 4 -I 2 -10 Q S ( b ) C L ~ = 0.00488, CX = 0.0113 Figure 7.- Concluded.

I 1 -

' 0 . 7

IO -

0 1 2 O 0 I t 0 A IOo c j x104 R

o a0

9-

a -

I I I 7L . .

9- a - C , x lo4 7- 6 - I I I I I I 5L -16 4 -14 -12 -10 -a -6 a, ( a ) E f f e c t s on C and C p .

jR Figure 8.- Effects of blade p i t c h f o r t h e j e t - f l a p r o t o r ; C L ~ = 0.0065, Cx = 0.013, V/I;zR = 0.3, QR = 591 f t / s e c .

I I I 1 1 1 1 I 40 - - I I I I I 1

0 81

L I I I - 2 0 2 0 - Solid symbols denote optimum Q~ IO - .2

01 I

//+e n

-10 -

-.2

n

I I L I J -20 -.4 -I 4 -I 2 -I 0 -I 2 -I 0 -0 O S OS Effects on control requirements and blade flapping (see also fig. 4 ( b ) ) .

Figure 8 . - Continued.

22 -

20 -

18- 16- cpx I05 14- 12-

I O -

I I I I I I g L 8 9 IO I I 1 2 1 3 ' 0 . 7 ( e ) E f f e c t s on power components a t optimum s h a f t angles.

Figure 8.- Concluded.

I

\

\

1 8 -

CX

0 0

1 6 -

n .0020

& . . .

n .005o

0 ,0075

\

0 ,0113

0 .0150

\

14 -

\

Locus of optimum a s c j X I O ~

Y

R

\

1 2 -

\

1 0 -

8 - G L I I I I I I

-22 -20 -18 -16 - I4 -12 -10

Q S (a) E f f e c t s on t h e v a r i a t i o n of C vs as.

j R Figure 9.- E f f e c t s of propulsive force f o r t h e j e t - f l a p rotor; C L ~ = 0.00488, v/flR = 0.5, 00.7. = 120, flR = 591 ft/sec.

1 6 1 0

cpx I04

/

I -1- - - -1- - - I - I

4 8 12 1 6 20 0 24

cXx 103

( b ) Power components f o r optimum data of f i g u r e g ( a ) .

Figure 9. - Concluded.

80 -

I -18 -22 Figure 10.- J e t d e f l e c t i o n s f o r t h e d a t a a t highest shown i n f i g u r e 9 Cx (cx = 0.015); cLR = 0.00488, v/m = 0.5, e O a 7 = 120, QE = 591 f t / s e c .

I I I I I .OO 4 .006 . O 08 .002 c L R 11.- E f f e c t s of C L ~ f o r t h e j e t - f l a p r o t o r a t optimum s h a f t angles Figure = 12O, i2R = 591 f t / s e c .

f o r two values of CX; V/QR = 0.5,

-001 I - I I -

.0010 -

d R

-

X a .-

9 - .0009 -

8- 7 - .0007 - 6 - .0006 - * N 0 .136ft2 CP 0 .155ft2 5 - U .0004 - 0 4 - X ln ln E .0003 -

-- CK

c: \ > - .0002 - 2 - .ooo I - I -

------

O 1 I I I -16 -14 -12 -10 -16 -14 -12 -10 O S OS Figure 12.- E f f e c t s of nozzle a r e a f o r t h e j e t - f l a p rotor; C L ~ = 0.0065, cx = 0.015, v/m = 0 . 3 , eo.7 = 12O, s);R = 591 f t / s e c .

-

x2 B2

O0

0"

--

8.6O -8.9"

- 4

-8 - I I I I I I I I I

0 40 80 I20 I60 200 240 280 320 360

\cI

( a ) E f f e c t s on blade flapping.

Figure 13.- E f f e c t s of second harmonic control.

.o I O

- -

A2 B2

.008

0" 0"

-- 8.6" -8.9"

.006

CT

.004

,002 l-

I I I 1 I I I I I

0 40 80 I20 I60 200 240 280 320 360

+

( b ) Effects on t h r u s t distribution.

Figure 13. - Continued .

.3

Q, .2

T1 t

.-

E . I

-

E

A2 82

a O

0" 0"

--

Harmonic

8.6" -8.9O

-

/--

C ~ X io4

I I I I

- 2

- I I I I I I I I I

-4

I20 I60 200 240 280 320

0 40 80

J/

( e ) E f f e c t s on torque d i s t r i b u t i o n .

Figure 13. - Concluded.

.0040 -

,0036 - V - V, knots !2R

0 .86 301

,0032 - A .8 280 0 .7 245 A h / 0 ' .5 I 7 5

.0028 -

.0024 -

.0020 -

.OO I 6 -

.oo I 2 -

I I ,0008 -16 -14 -I 2 -I 0 -18 Q S ( a ) E f f e c t s on momentum c o e f f i c i e n t .

Figure 14.- E f f e c t s of high advance r a t i o ; C L ~ = 0.00488, CX = 0.005, 00.7 = 120, QR = 591 ft/sec.

c

120 - 120 - 120 -

- V, knots

r C Z R

0 .86 301

A .8 280

8 0 - e 80 - 80 -

0 . 7 245

-

0 . 5 I75

smax

B I

40 -

40 - 40 -

L

0 0 ’ 0 -

-18

-I 6 -I 4 -I 6 -14 -I 8

-18 -I 6 -I 4

Q S Q S Q S ( b ) Effects on jet-deflection control requirements.

Figure 14. - Continued.

.0016 -

a CP0

.0012 -

0 'pi

.0008 - .0004

c c A " A I

0 - .5 . 6 . 7 .0 . 9

v/n R

I I I I I I75 210 245 280 315 V, knots (c) Effects on power components at optimum shaft angles.

Figure 1 4 . - Concluded.

.0032 -

C X 0 .0050 0 .0075 C i R

.0024 -

.0020 -

I I I I I .0016L I - I ~ I- I 0 - -20 -I 8 -16 -14 - I 2 - I 0 Q S Figure 13.- Selected characteristics of the jet-flap rotor at a forward speed of 220 knots and an advancing tip Mach number of 0 . 8 ; V/m = 0 . 7 , I;~R = 531 ft/sec, eo.7 = 12O, C L ~ = 0.006025.

.0024 -

'd c l R 0 0

,0020 -

0 . 5

0 1.0

I I I I I .OO I 6 I-

120 -

80 -

40 -

~ 80 -

40 - e /

0' I I I I 1

- 20 -18 -16 -14 -12 - 1 0

Q S sa for the least- Figure 16.- Effects of the thrust recovery parameter propulsive-force condition of figure 15; C L ~ = 0.006025, Cx = 0.005, = 120, s2R = 531 ft/sec, V/QR = 0 . 7 . .

' 0 . 7

I

.o I 0 C L R C X .005 Cj R 1 - 1 . 5 I .o S d ( a ) E f f e c t s on force c o e f f i c i e n t s .

- 4"

Q s+a I

- 8"

I I -12"

I .o

0 . 5 'd 'd ( b ) Effect on tilt of t h e r o t o r d i s k .

a t f i x e d s h a f t angle and c o n t r o l s e t t i n g s ; Figure 17.- E f f e c t s of sd = 12O, S ? R = 531 f t / s e c .

as = -14.2, Eo = 33.0, B1 = 53.4, V/QR = 0.7, 4 6 .0012 -

.0010 -

.0008 -

C *

IR .0006 -

CP Open symbols : jet-flap rotor Solid symbols : shaft-driven rotor

.0004 -

,0002 -

A I I 0 ‘ I I I I -16 - 1 4 -12 -10 -8 -6 -4 Q S Figure 18.- Comparison of t h e j e t - f l a p and shaft-driven r o t o r s f o r t h e same f l i g h t condition; = 0.00488, CX = O.Oll3, V1Al.R = 0 . 3 , A l . R = 591 f t / s e c .

cLR NASA-Langley, 1965 A-2°21 I " T h e aeronazitical and space activities o f t h e United States shall be conducted so as t o contribute . . . t o the expansion of him" knowl- edge of p h e n o m e m in the atmosphere and space. T h e Administration &all provide f o r the widest practicable aird appropriate dissemination of information concerning its activities and the resul/s tbereo f .'I -NATIONAL AERONAUTICS AND SPACE ACT OF 1958

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