flight measurements

7/25/2019 Flight measurements

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R . M . N o . 3 4 8 5

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M I N I S T R Y O F T E H N O L O G Y

A E R O N A U T I C A L R E S E A R C H C O U N C IL

R E PO R T S A N D M E M O R A N D A

F l i g h t M e a s u r e m e n t s o f th e E l ev a to r a n d A i le r o n

H i n g e - M o m e n t D e r i v a ti v es o f th e F a ir e y D e l t a 2

A i rc ra ft u p t o a M a c h N u m b e r o f 1 6 a n d C o m -

p a f i s o n s w i t h W i n d - t u n n e l R e s u l t s

By R . Rose , M.Sc . , O . P . N icho las , B .Sc . ( Eng . ) and

G l y n i s V o r l e y

L O N D O N : H E R M A J ES T Y S S T A T I O N E R Y O F F I C E

1967

P R I E 1 5 S . 6 d . N E T


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F l ig h t M e a s u r e m e n t s o f t h e E le v a to r a n d A i le r o n

H i n g e - M o m e n t D e r i v at iv e s o f th e F a ir e y D e l t a 2

A i r cr a ft u p to a M a c h N u m b e r o f 1 6 a n d C o m -

p a r i s o n s w i t h W i n d - t u n n e l R e s u l t s

B y R . R o s e , M . S c . , O . P . N i c h o l a s , B . S c . E n g . ) a n d

Glynis Vorley

Re p o r t s a n d M e mo r a n d a No . 3485

Ju ly 1965

S u m m a r y

Aileron and elevator hinge-moment derivatives have been extracted from flight tests on the Fairey

Delta 2 in which the dynamic aircraft response, to control pulses was recorded. As this method is not

widely used, and has proved very successful, it is described in detail. Corrections had to be made for aero-

elastic distortion of the control surfaces, for inertia loads acting on the controls and for the dynamic

response of the instrumentation.

Where possible the results are compared with wind-tunnel data. There is good agreement for the

hinge moment due to control derivatives, b2, and the elevator, bl, whereas the results for aileron, bl, show

differences from the tunnel values at supersonic speeds.

bo could not be measured because of strain gauge drift; however consistent results were obtained for

the aileron hinge moment induced by the elevator deflection and

v ic e v e r s a

At transonic speeds these

terms are of similar magnitude to the conventional hinge moment derivatives b 1 and b 2, and must therefore

be considered by designers.

LIST OF CONTENTS

1. Introduction

2. Description of Aircraft and Instrumentation

2.1. Aircraft

2.2. Instrumentation

3. Flight Tests

4. Method of Analysis

4.1 . Elevator pulses

4.2 . Aileron pulses

4.3 . Steady turns

5. Results and Discussion

Replaces R.A.E. Tech. Report No. 65143 --A.R.C. 27 376.


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L I S T O F

C O N T E N T S c o n t i n u e d

6 . C o n c l u s i o n s

A p p e n d i x A T h e h i n g e m o m e n t s a c t in g o n e le v a t o r a n d a i l e r o n c o n t r o ls

A p p e n d i x B Ev a l u a t i o n o f b 2 a n d c ro s s - c o n t ro l d e r i v a ti v e s f ro m c o n t ro l p u l s e s

A p p e n d i x C D e t e rm i n a t i o n o f b 1 f ro m s t i c k f i x ed l o n g i t u d i n a l s h o r t -p e r i o d o s c i l l a t i o n s

A p p e n d i x D E v a l u a t i o n o f e l ev a t o r a n d a i l e r o n h in g e m o m e n t d e r i v a ti v e s d u e t o i n c id e n c e b l

f ro m f l i g h t a t d i f f e r e n t v a l u e s o f n o rm a l a c c e l e r a t i o n

S y m b o l s

R e fe r e n c e s

Ta b l e 1

Ta b l e 2

L e a d i n g a i r c ra f t d i m e n s i o n s

C o n t ro l s u r f a c e d e t a i l s

I l l u s t r a t i o n s

D e t a c h a b l e A b s t r a c t C a r d s

1. Introduction.

Th e re i s c o n s i d e ra b l e i n t e r e s t in p r e d i c t i n g v a l u e s o f t h e h i n g e m o m e n t s fo r c o n t ro l s . A t p r e s e n t t h e r e

a r e n o r e l i a b l e t h e o r i e s 1 fo r e s t i m a t i n g h i n g e m o m e n t s a t t r a n s o n i c a n d s u p e r s o n i c s p e e d s a n d p r e d i c -

t i o n s fo r th e s e c a se s a r e u s u a l l y b a s e d o n w i n d - t u n n e l re s u l ts . To g i v e c o n f i d e n c e i n t h e s e p r e d i c t i o n s i t

i s i m p o r t a n t t h a t s o m e c h e c k s a r e m a d e b e t w e e n t u n n e l a n d f l i g h t m e a s u r e m e n t s . T h i s r e p o r t p r e s e n ts

t h e r e s u lt s o f f li g h t m e a s u r e m e n t s m a d e a t R . A . E . B e d f or d o f tr a i li n g e d g e c o n t ro l h i n g e m o m e n t s o n

t h e F a i r e y D e l t a 2 w h i c h i s a r e s e a r c h a i r c r a f t w i t h a c o n t ro l c o n f i g u ra t i o n o f c u r r e n t i n t e r e s t a n d a

p e r fo rm a n c e w e l l i n t o t h e s u p e r s o n i c s p e e d r a n g e . Th e f l i g h t r e s u l ts a r e c o m p a re d w i t h t u n n e l s r e s u l t s z 5

m a d e a t t r a n s o n i c a n d s u p e r s o n i c s p e e d s .

A d y n a m i c f l i gh t t e st t e c h n i q u e h a s b e e n u s e d w h i c h a l l ow s t h e e l e v a t o r a n d a i l e r o n h i n g e - m o m e n t

. C

d e r i v a ti v e s w i t h t h e e x c e p t i o n o fb o t h e h i n g e m o m e n t a t z e ro m c l d e n c e a n d c o n t ro l a n g l e t o b e e x tr a c t e d .

2. Description o f Airc raft and Instrumentation.

2.1.

Aircraft.

Th e F a i r e y D e l t a 2 i s a 6 0 d e g d e l t a w i n g t a i ll e s s r e s e a r c h a i r c r a f t c a p a b l e o f s p e e d s u p t o a t l e a s t

M - - 1 . 7. F i g . 1 s h o w s a g e n e ra l a r r a n g e m e n t a n d F i g . 2 a p h o t o g ra p h o f t h e a i r c r a f t. Ta b l e 1 g i v es t h e

p r i n c i p a l d i m e n s i o n s o f t h e a i r c r a f t a n d T a b l e 2 d e t a i l s o f t h e c o n t ro l s u r f a c es .

Th e a i r c r a f t h a s fu l l - s p a n t r a i l in g -e d g e c o n t ro l s w h i c h a r e s p l i t i n t o s e p a ra t e e l e v a t o r s a n d a i l e ro n s ;

t h e e l e v a t o r s a r e a e ro d y n a m i c a l l y u n b a l a n c e d t h e a i l e ro n s a re r i g g e d u p 3 d e g a n d h a v e a s m a l l h o r n

b a l a n c e . Th e c o n t ro l s u r f a c es a r e o p e ra t e d b y i r r e v e r s ib l e h y d ra u l i c j a c k s . Th e e l e v a t o r j a c k s a r e p o s i -

t i o n e d i n t h e r e a r f u s e l a ge a n d o p e ra t e t h e e l e v a t o r s

via

t o rq u e t u b e s . Th e a i l e ro n j a c k s a r e s i t u a t e d b e -

n e a t h t h e o u t e r w i n g fo rw a rd o f t h e m i d p o r t i o n o f t h e a i l e ro n a n d o p e ra t e t h e a i le ro n s d i re c t l y .

C o n t ro l - f e e l fo r c e s a r e s u p p l i e d t o t h e p i l o t b y s i m p l e s p ri n g s t h e d a t u m o f e a c h s p r i n g b e i n g v a ri e d

w i t h i n a l i m i t e d r a n g e b y a n e l e c t r i c t r i m m o t o r . T o c a t e r f o r t h e l a rg e v a r i a t i o n s o f a i r c r a f t r e s p o n s e

a n d c o n t ro l e f f e c t iv e n e s s o v e r t h e f l i gh t e n v e l o p e t h e g e a r r a t i o s b e t w e e n t h e e l e v a t o r s a n d a i l e ro n s a n d

t h e c o r r e s p o n d i n g s t i c k m o v e m e n t c a n b e v a r i e d i n fl i g h t b y t h e p i lo t .

2


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2.2. I n s t r u m e n t a t i o n

T h e f o l l o w i n g p a r a m e t e r s , r e l e v a n t t o t h e te s ts , w e r e r e c o r d e d o n H u s s e n o t A . 2 2 p h o t o g r a p h i c t r a c e

r e c o r d e r s :

S p e e d

A l t i t u d e

E l e v a t o r a n g l e p o r t a n d s t a r b o a r d )

A i l e r o n a n g l e p o r t a n d s t a r b o a r d )

E l e v a t o r h i n ge m o m e n t p o r t a n d s t a r b o a rd )

A i l e ro n h i n ge m o m e n t p o r t a n d s t a r b o a r d )

S t r a i n -g a u g e b r i d g e v o l t a g e

I n c i d e n c e

N o r m a l a c c e l e r a t i o n

R a t e o f r o l l

S i d e s l ip a n g l e

T h e h i n g e m o m e n t s w e r e m e a s u r e d w i t h f o u r - a c t i v e - a r m s t ra i n - g a u g e b r i d g e s e n e r g i s e d b y a s t a b i li s e d

v o l t a g e f r o m V e n n e r a c c u m u l a t o r s . I n t h e c a s e o f t h e e l e v a t o r s t h e s t r a i n g a u g e s w e r e a t t a c h e d t o t h e i n n e r

s u r fa c e o f t h e t o r q u e t u b e s ; f o r t h e a i l e ro n s t h e g a t ig e s w e r e a t t a c h e d t o o n e e n d o f t h e j a c k b o d y . A t y p i c a l

s t r a i n i n c r e m e n t i n t h e t e s ts w a s 0 . 0 2 p e r cen t T h e s t r a i n g a u g e s w e r e c a re f u l ly m a t c h e d a n d d u r i n g g r o u n d

t e st s w e r e f o u n d t o h a v e n e g l ig i b le d r if t o v e r a t e m p e r a t u r e r a n g e - 4 0 d e g C t o + 4 0 d e g C . T h e b r i d g e s

h a v e b e e n c a l i b r a t e d b y a p p l y i n g k n o w n l o a d s t o t h e c o n t r o l s u r fa c e s . C o n t r o l - s u r f a c e a n g l e s w e r e m e a s -

u r e d b y p o t e n t i o m e t e r s a t t a c h e d t o t h e c o n t r o ls .

I n c i d en c e w a s m e a s u r e d b y o n e o f f ou r w i n d v a n e s m o u n t e d o n t h e n o s e b o o m o f t h e a i rc r a ft b e h i n d

t h e p i t o t -s t a t i c h e a d . T h e v a n e s w e r e a r r a n g e d i n a c r u c i f o r m c o n f i g u r a t i o n s o a s t o p r e s e r v e th e s y m -

m e t r i c a l a r r a n g e m e n t r e q u i r e d t o r e d u c e p o s i t i o n e r r o r s i n t h e t r a n s o n i c a n d s u p e r s o n i c s p e e d r a n g e .

3 Fl i gh t Tests

T h e m a i n f li g h t t e s ts c o n s i s t e d o f r e c o r d i n g t h e c o n t r o l h i n g e m o m e n t s a n d t h e r e s p o n s e o f t h e a i r c r a f t

d u r i n g a n d a f t e r e i t h e r a n e l e v a t o r o r a i l e r o n p u ls e . D u e t o t h e l a c k o f c o n t r o l o f t h r u s t w i t h r e h e a t o n

a n d t h e l i m i te d f u e l a v a i la b l e , it w a s n o t p o s s i b l e i n th i s a i r c ra f t a t t r a n s o n i c a n d s u p e r s o n i c M a c h n u m b e r s

t o s t a b i li s e s p e e d . T h i s c a u s e d s o m e d i f f ic u l t y i n t r i m m i n g t h e a i r c r a f t , p a r t i c u l a r l y a t t r a n s o n i c s p e e d s

w h e r e s i g n i fi c a n t t r i m c h a n g e s o c c u r r e d r a p i d ly . N e v e r t h e l e s s , p i l o t s f o u n d i t p o s s ib l e , a f t e r s o m e p r a c t i c e ,

t o t r i m t h e a i r c r a f t s a t i s f a c t o r i l y d u r i n g t h e s e n o n - s t a b i l i s e d c o n d i t i o n s . W i t h t h e a i r c r a f t i n t ri m , t h e p i l o t

t a p p e d t h e c o n t r o l c o l u m n i n e i th e r a la t e r a l o r r e a r w a r d s d i r e c t i o n a n d a l l o w e d i t t o r e t u r n t o i t s t r i m

p o s i t i o n u n d e r t h e a c t i o n o f th e f e e l s p r in g , r e s u l ti n g in a c o n t r o l p u l s e o f a b o u t o n e q u a r t e r s e c o n d

d u r a t i o n * . T h i s w a s t h e s h o r t e s t p u l s e po s s ib l e , a n d g a v e a g o o d c o m p r o m i s e b e t w e e n t h e r e q u i r e m e n t s

t h a t t h e a i r c r a f t s h o u l d n o t h a v e r e s p o n d e d s i g n i fi c a n tl y b y t h e t i m e t h e p e a k o f t h e p u l s e h a d b e e n r e a c h e d ,

a n d t h a t u n s t e a d y a e r o d y n a m i c e f f ec t s s h o u l d b e n e g li g ib l e A p p e n d i x A ). In s o m e c a s e s a c o m b i n a t i o n

o f e l e v a t o r a n d a i l e r o n m o v e m e n t o c c u r r e d d u e t o t h e d i f fi c u lt y o f m o v i n g t h e c o n t r o l c o l u m n p r e c i s e l y

i n t h e d e s i r e d d i r e c ti o n . F o r t h e e l e v a t o r t es ts , b o t h t h e i n it i al r e s p o n s e d u r i n g t h e p u l s e a n d t h e e n s u i n g

l o n g i t u d i n a l s h o r t - p e r i o d o s c i l la t i o n o f th e a i r c r a f t w e r e u s e d i n t h e a n a l y si s . H o w e v e r , f o r t h e a i l e r o n

p u l s e s , o n l y t h e i n i t i a l r e s p o n s e h a s b e e n a n a l y s e d , a s t h e h i n g e m o m e n t s i n d u c e d b y t h e d u t c h r o l l

o s c i l l a t i o n w e r e t o o s m a l l t o m e a s u r e a c c u r a t e l y . A t 4 0 0 0 0 ft , c o n t r o l p u l s e s w e r e r e c o r d e d i n le v e l f l ig h t

a t M a c h n u m b e r s f r o m 0 - 8 6 t o 1 - 6, f u r t h e r t e st s w e r e m a d e i n l ev e l f li g h t a t 1 0 0 0 0 ft , a t M a c h n u m b e r s f r o m

0.6 to 1 .2.

S o m e s u p p l e m e n t a r y t e s t s w e r e m a d e , in w h i c h r e c o r d s w e r e t a k e n d u r i n g l e v el f li g h t a n d t u r n s a t

c o n s t a n t n o r m a l a c c e l e r a t i o n . T h e s e t e s ts c o v e r e d a r a n g e o f M a c h n u m b e r s f r o m 0 . 85 t o 1 - 07 a t 4 0 0 0 0 ft

an d f r om 0 .55 t o 0 -97 a t 10 000 f t.

* F o r a f u l ly i r re v e r s ib l e s y st e m n o f u r t h e r m o v e m e n t s h o u l d o c c u r . H o w e v e r , t h e h y d r a u l i c j a c k s d i d

a l l o w s o m e s m a l l re s i d u a l m o v e m e n t o f t h e c o n t r o l s u r f a c e.


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4 M etho d of Analysis

The incidence vane readings have been corrected for the effects of boom interference evaluated by wind-

tunnel calibrations 4, and, in addition at subsonic speeds, for estimated wing and body upwash. Calculation

showed that the effect of pitching velocity on the vane readings was negligible, and this was therefore

ignored.

The control surfaces are subject to aeroelastic distortion, especially at high speed. Flight pressure-

plotting tests made earlier have shown tha t the aerodynamic loading is reasonably uniform, and making

this assumption, the mean angular distortion of the control is directly related to the jack load. In ground

tests s the distortion of the controls was measured under uniform loading conditions. This distortion was

measured relative to the jack output point since the control surface transmitters were attached at this

position. The effective stiffnesses of the elevator and aileron are respectively two thousand lb ft/degree

and about forty thousand lb ft/degree. Two factors contribute to this large difference in stiffness. Firstly,

the jack load is applied near the aileron mid-span, whereas it is applied at the root-end of the elevator.

Secondly, in the case of the elevator, flexibility of the linkage between the jack output and elevator roo t

accounts for abou t two-thirds of the measured distortion. In the present flight tests, it has been calculated

that significant elevator distortion occurred and this has been allowed for, but that the aileron distortions

were negligible.

Appendix A derives the relations between the measured control jack loads and the aerodynamic and

inertia loadings on the controls. The jack loads were measured by strain gauges, and although these were

carefully matched some drift occurred due to differential-temperatureeffects. Thus it has not been possible

to determine absolute values of jack loads very accurately, but as the rate of drift was sufficiently slow in

relation to the duration of most of the manoeuvres executed during the tests, incremental values of the jack

moments could be measured with confidence.

The dynamic response of the recording galvanometers and ratiometers has been allowed for in the

analysis. Simple laboratory checks showed that amplitude ratio effects were just significant in some cases.

A number of assumptions have been made in the analysis of the flight results and these are listed below.

a) All hinge-moment derivatives are linear within the range covered during each individual test, but

they are not necessarily linear over the full range of control angles and incidences covered in the flight

tests.

b) The shape of a control pulse may be represented by the first ha lf of a sine wave.

c) The change in aircraft incidence, up to the instant where an elevator pulse has its maximum, is

small.

d) The changes in sideslip and rate of roll, up to the instant where an aileron pulse has its maximum, are

small.

e) Movement of the controls is small, but possibly significant, during the aircraft oscillations following

an elevator pulse.

f) The distorted elevator can be represented by an undistorted control at an appropriate mean angle.

g) In applying the distortion corrections the aerodynamic and inertia loadings are assumed uniform

over the control surface.

h) Calibrations of the control jack load and the surface distortions may be extrapolated linearly to

the considerably higher flight loading conditions.

4.1. Elevator Pulses

Fig. 3a illustrates an idealised elevator pulse test, showing time histories of the elevator and aileron

jack moments, and incidence, during and following the pulse. A corresponding actual flight record is

shown for comparison, Fig. 3b. The essential differences between the actual and idealised records are that,

in practice, a small, but negligible, change of incidence occurs before the peak of the pulse, and also the

elevator does no t returri precisely to its trimmed value at the cessation of the pulse. However, these effects

are quite small and thus it is possible to use simple methods of analysis. This analysis is conveniently split

into two parts, treating first the response during the pulse and then the ensuing aircraft oscillation.


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From the increments in the control jack loads and the elevator angle between the trimmed conditions

and values at the peak of the elevator pulse according to equat ions B.7 and B.8 of Appendix B the hinge

moment derivatives b2~ and OCm /Otlmay be derived b2E is the elevator hinge moment due to elevator

angle derivative and OCHA/Orl s the aileron hinge moment due to elevator angle derivative. This latter

derivative is not normally considered but it was found in these tests to be of a very considerable magnitude.

The inertia term in equations B.7 and B.8 amounts typically to 5 per cent of the total measured hinge

moment.

The elevator pulse excites the longitudinal short period osci llation of the aircraft. Appendix C equat ions

C.4 and C.5 shows how measurements made during the oscillation allow bl~ and b~ to be determined.

bl~ is the elevator hinge moment due to incidence derivative and b~. is the aileron hinge moment due

to incidence derivative. In this case the inertia term amounts typically to 15 per cent of the measured total

hinge moment. The analysis uses values of the recorded quantities only at the peaks of the oscillation.

In practice it was found that reliable results could be obta ined at supersonic speeds; however at subsonic

speeds due to increased residual control motion following the pulse and increased damping of the air-

craft oscillation the method could only be applied in some cases. In this regime an alternative technique

was required to ob tain measurements of b~ and bt~ and this is discussed in Section 4.3.

4.2. Aileron pulses.

Figs. 4a and b show idealised and actual flight records of an aileron pulse. The initial response of the

aircraft is a rapid accelerat ion in roll with practically no change in sideslip and rate of roll. The aileron and

elevator hinge moments closely follow the aileron angle input.

Equations B.10 and B.11 of Appendix B show how b2~ and

OC~J O~

can be obtained from measure-

ments of incremental control loads and the aileron angle between the trimmed conditions and the peak of

the pulse b2~ is the aileron hinge momen t due to aileron-angle derivative and

OCn~JO~

s the elevator hinge

moment due to aileron-angle derivative. The lat ter derivative represents the effect on the elevator hinge

moment of aileron angle deflection which was found to be considerable in the present tests. The inertia

terms in these cases amoun t typically to15 per cent of the total hinge moment.

4.3.

Steady Turns.

At subsonic speeds the damping of the longitudinal short period oscillation of the aircraft is high and

as mentioned earlier under these conditions it is not possible to extract bl~ and b~A from elevator pulse

tests. However by measuring the elevator and aileron jack loads in steady flight at the same Mach number

but at two different values of normal acceleration it is possible to evaluate b~ and b~A as shown in

Appendix D. The required tests were made by accelerating the aircraft in level flight through the desired

range of Mach number and then decelerating the aircraft in a steady turn. By comparing values recorded

at the same Mach number during the two parts of such a flight test the dat a required for analysis are

obtained. It should be noted that in this case absolute rather than incremental jack loads are required

and as an appreciable time interval is involved between the recording of corresponding test points

strain gauge drift may become significant and as a consequence the accuracy is reduced. Also any two flight

points used in this analysis differ not only in incidence but also in the elevator and aileron angles required

to trim. The cont ributions due to control movement terms are generally larger than those due to bl~ and

b~. which are to be extracted from the tests. As a consequence the accuracy of the final result is further

reduced.

5. Results and Discussion.

Fig. 5 6 and 7 show the ranges of aileron angle elevator angle and incidence explored during the tests.

These envelopes are presented because tunnel tests show that in some cases hinge moments vary non-

linearly with incidence and control angle; thus values of derivatives depend on the range of control angle

and incidence used in a particular test. As an example Fig. 8 shows some tunnel measurements of aileron

hinge moment at M = 1-02 and the range of elevator angle and incidence covered in the flight tests at

10 000 ft and 40 000 ft. It can be seen that bl~ and 8Cm /~tl would be expected to differ at the two

altitudes.

5


7/29

F i g s. 9 to 1 4 s h o w t h e v a r i a t i o n w i t h M a c h n u m b e r o f t h e m e a s u r e d v a l u es o f bl~ b2~ aCHJO~ b l~

b2~ and

OCm /Or .

Th e f l i g h t r e s u l ts i n c l u d e d a t a f ro m t e s t s a t 1 0 0 0 0 f t a n d 4 0 0 0 0 f t u s i n g b o t h p u l s e a n d

s t e a d y t u rn t e c h n i q u e s . W h e re p o s s i b l e c o m p a ra b l e w i n d t u n n e l d a t a 2 3 a r e a l s o s h o w n . In t h e c a s e s

w h e re t h e t u n n e l t e s t s s h o w e d n o n - l i n e a r v a r i a t i o n s w i t h i n c i d e n c e a n d c o n t ro l a n g l e , t h e d e r i v a t i v e s

w e re e x t r a c t e d b y c o n s i d e r i n g t h e i n c i d e n c e a n d c o n t ro l a n g l e a p p ro p r i a t e t o t h e c o r r e s p o n d i n g f l i g h t

con d i t ion s (F ig . 8 ).

Th e f l i g h t v a l u e s o f t h e e l e v a t o r h i n g e m o m e n t d u e t o i n c i d e n c e d e r i v a t i v e b ~ , F i g . 9 , s h o w s o m e

s c a t te r , p a r t i c u l a r l y a t t r a n s o n i c s p e e d s w h e re a s n o t e d i n S e c t i o n 4 .3 t h e a c c u ra c y o f t h e a n a l y s i s i s p a r t i -

c u l a r ly p o o r , b u t t h e v a r i a t i o n w i t h M a c h n u m b e r i s w e l l d e f in e d , b ~ s h o w s a r a p i d i n c r e a se a t t r a n s o n i c

s p e e d s a n d a g r a d u a l d e c r e a s e a t s u p e r s o n i c s p e e d s. Th e r e i s n o d e t e c t a b l e d i f fe r e n c e b e t w e e n t h e r e s u l t s a t

1 0 0 0 0 f t a n d 4 0 0 0 0 f t, a n d t h i s s u g g e s ts t h a t t h e f a i r l y s i m p l e m e t h o d u s e d t o c o r r e c t t h e r e s u l t s f o r t h e

a e ro e l a s t i c d i s t o r t i o n o f t h e e l e v a t o r h a s b e e n a d e q u a t e , a n d c o n f i rm s t h e t u n n e l r e s u l ts w h i c h s h o w n o

n o n - l i n e a r i t i e s o v e r t h e r a n g e o f e l e v a t o r a n g l e a n d i n c i d e n c e e x p l o re d . Th e c o m p a r i s o n w i t h w i n d -

t u n n e l r e s u l ts i s g o o d .

F o r t h e e l e v a t o r h i n g e m o m e n t d u e t o e l e v a t o r - a n g l e d e r i v a t iv e b 2~ , F i g . 1 0, t h e s a m e g e n e ra l r e m a rk s

a s m a d e fo r b l ~ a p p l y , b E i s r o u g h l y t w i c e a s l a rg e a s b l ~ .

F i g . 1 1 s h o w s t h e v a r i a t i o n o f t h e e l e v a t o r h i n g e m o m e n t d u e t o a i l e ro n -a n g l e d e r i v a t iv e , OC n JO~ w i t h

M a c h n u m b e r . Th e r e s u l t s s h o w v e ry li t t le s c a t te r , a n d t h e d e r i v a t i v e is w e l l d e f i n e d . OCH~/c3 i s smal l a t

s u b s o n i c a n d s u p e r s o n i c s p e e d s , b u t i n c r e a s e s r a p i d l y a t t r a n s o n i c s p e e d s . Th i s d e r i v a t i v e h a s n o rm a l l y

b e e n i g n o re d b y d e s i g n e r s , b u t c l e a r l y i t s ef f e ct o n t h e c o n t ro l h i n g e m o m e n t s o f t h i s c o n f i g u ra t i o n a t

t r a n s o n i c s p e e d s i s v e ry s i g n if i c a n t. Th e w i n d - t u n n e l te s t s d o n o t p ro v i d e d a t a o n t h i s d e r i v a t i v e .

Th e f l i g h t r e s u l t s f o r th e a i l e ro n h i n g e m o m e n t d u e t o i n c i d e n c e d e r i v a t i v e b ~a a r e s h o w n i n F i g . 1 2.

In t h e s u b s o n i c r a n g e r e s u l t s f r o m t h e t w o a l t e rn a t e t e s t p ro c e d u re s a r e s h o w n . Th e y d i f fe r q u i t e s i g ni f ic -

a n t l y . F r o m t h e p r e v i o u s d i s c u s s i o n s o n t h e s t e a d y t u rn t e s ts , i t w o u l d a p p e a r t h a t t h e s e a r e g e n e ra l l y le s s

r e l i a b l e , a n d a s a c o n s e q u e n c e m o re w e i g h t h a s b e e n g i v e n w h e n d ra w i n g a m e a n l i n e t h ro u g h t h e t e s t

p o i n t s t o t h e r e s u l t s o f t h e p u l s e t e s t s. Th e r e i s a r a p i d i n c r e a s e i n b tA a t t r a n s o n i c s p e e d s fo l l o w e d b y a

r a p i d d e c re a s e a t s u p e r s o n i c s p e e d s . N o a e ro e l a s t i c c o r r e c t i o n s h a v e b e e n a p p l i e d s i n c e t h e c a l c u l a t e d

d i s t o r t i o n o f t h e a i l e ro n s w a s n e g l i g ib l e . H o w e v e r , t h e r e a r e q u i t e s i g n i f i c a n t d i f fe r e n c e s b e t w e e n t h e r e s u l t s

o b t a i n e d a t 1 0 0 00 f t a n d 4 0 0 0 0 f t . Th e s e d i f fe r e n c e s c o u l d b e d u e t o e i t h e r a n a e ro e l a s t i c d i s t o r t i o n o f t h e

w i n g , o r a n o n - l i n e a r v a r i a t i o n o f h i n g e m o m e n t o v e r t h e d i f f e r e n t r a n g e s o f e l e v a t o r a n g l e a n d i n c i d e n c e

a p p ro p r i a t e t o t h e t w o t e s t h e i gh t s . A t t r a n s o n i c s p e e d s w i n d - t u n n e l r e s u l ts 2 ,a s h o w m a rk e d n o n - l i n e a r

v a r i a t i o n s o f h i n g e m o m e n t w i t h i n c i d e n c e a n d e l e v a t o r a n g l e , f o r e x a m p l e a s s h o w n i n F i g . 8. A t s u p e r s o n i c

s p e e d s w i n d - t u n n e l v a l u e s o f t h e d e r i v a t i v e e x t r a c t e d fo r t h e 4 0 0 0 0 f t f l i g h t c o n d i t i o n s a r e c o n s i d e ra b l y

h i g h e r t h a n t h e c o r r e s p o n d i n g f l i g h t m e a s u re m e n t s . N o c o r r e s p o n d i n g w i n d - t u n n e l d a t a a r e a v a i l a b le fo r

t h e 1 0 0 0 0 ft f l i g h t c o n d i t i o n s a s t h e a p p ro p r i a t e r a n g e s o f a i r c r a f t p a r a m e t e r s w e re n o t c o v e re d i n t h e

t u n n e l p ro g r a m m e . H o w e v e r , e x t r a p o l a t i o n o f t u n n e l d a t a i n t h e r a n g e M = 1 .1 t o 1 . 2 , s u g g e s t s t h a t b t a

a t c o n d i t i o n s a p p r o p r i a t e t o f l i g h t a t 1 0 0 0 0 f t i s a p p ro x i m a t e l y 0 -6 l e ss t h a n a t 4 0 0 0 0 f t. Th i s d i f f e re n c e

i s a l m o s t i d e n t i c a l t o t h a t b e t w e e n f l i g h t r e s u l ts a t t h e t w o t e s t a l t it u d e s . Th i s s u g g e s ts t h a t t h e a p p a re n t

e f f ec t s o f a l t i tu d e i n t h e f l i g h t r e s u l t s s h o w n i n F i g . 1 2 a r e m a i n l y d u e t o n o n - l i n e a r i t i e s i n t h e h i n g e

m o m e n t c h a ra c t e r i s t i c s .

Th e r e s u l ts f o r t h e a i l e ro n h i n g e m o m e n t d u e t o a i l e ro n -a n g l e d e r i v a t i v e b z, ,, F i g . 1 3 , s h o w v e ry l i tt l e

s c a t t e r. Th e r e s u l t s a t 1 0 0 0 0 f t a n d 4 0 0 0 0 ft a r e d i f f e re n t . A g a i n i t i s t h o u g h t t h a t t h i s i s p ro b a b l y c a u s e d

b y n o n - l i n e a r e f f ec t s, b u t n o w i n d - t u n n e l r e s u l ts a r e a v a i l a b l e fo r c o m p a r i s o n .

F i g . 1 4 s h o w s t h e v a r i a t i o n o f t h e a i l e ro n h i n g e m o m e n t d u e t o e l e v a t o r d e r i v a ti v e ,

aCnJarl

w i t h M a c h

n u m b e r . Th i s d e r i v a t i v e h a s b e e n g e n e ra l l y i g n o re d i n t h e p a s t ; h o w e v e r , i n t h is c o n f i g u ra t i o n , a l t h o u g h

i t i s s m a l l a t s u b s o n i c a n d s u p e r s o n i c s p e e d s , i t i s s i g n i f i c a n t a t t r a n s o n i c s p e e d s a n d i s i n d e e d t h e n o f

t h e s a m e m a g n i t u d e a s b 2~ . W i n d - t u n n e l r e s u l ts s h o w a t r a n s o n i c p e a k i n g o o d a g r e e m e n t w i t h t h e f l ig h t

m e a s u re m e n t s , b u t a t s u p e r s o n i c s p e e d s , w h e re a s t h e v a r i a t i o n i s s i m i l a r , t h e a g re e m e n t i s n o t s o g o o d .

Th e e f f ec t o f t h e i n t e r - c o n t ro l g a p o n

3CnA/~?r

m u s t b e c o n s i d e ra b l e , h e n c e i t i s p o s s i b l e t h a t R e y n o l d s

n u m b e r e f fe c ts m a y b e c a u s i n g t h i s d i s c r e p a n c y . Th e p r e s e n t t e st s h a v e s h o w n t h a t a t t r a n s o n i c s p e e d s t h e

i n f l u e n c e o f o n e t r a i li n g e d g e c o n t ro l o n t h e h i n g e m o m e n t o f a n a d j a c e n t c o n t ro l i s c o n s i d e ra b l e .


8/29

6 Conclusions

The elevator and aileron hinge-moment derivatives of the Fairey Delta 2 have been determined, using

dynamic techniques, up to Mach numbers of 1.2 and 1.6 at 10 000 ft and 40 000 ft respectively. Where

possible, comparison has been made with wind-tunnel results 2 a obtained with a 1/9th scale model.

The results are summarised in Figs. 8 to 13.

All the derivatives show a charadteristic rapid increase at transonic speeds followed by a reduction at

supersonic speeds. For the elevator, it has been necessary to correct for the aeroelastic distortion of the

cont rol; a relatively simple method of analysis has been used with success, and the results of tests at 10 000

ft and 40 000 ft agree well with one another. On the basis of ground tests, it was calculated that no signi-

ficant aeroelastic distortion of the ailerons occurred. In this case, the 10 000 ft and 40 000 ft results show

considerable differences; wind-tunnel tests suggest this is probably due to non-linearity of the hinge-

moment characteristics over the range of elevator angle and incidence appropriate to the two test heights.

The results show that at transonic speeds the influence of one trailing-edge control on the hinge moment

of an adjacent control can be considerable. The influence of this derivative on control hinge moments has

normally been ignored by designers in the past; it would appear that this effect should be taken into

account in appropriate cases.

Although some of the flight results show considerable scatter, the derivatives are reasonably well

defined an dt he agreement with wind-tunnel results is reasonable in view of the difficulties involved in the

test techniques and the non-linear variation of some of the derivatives.


9/29

L I S T O F S Y M B O L S

A

OCL

a -~- - - -

Oa

B

boE

OCn

b 1 -

Oa

OCu~

b2~ aC~

c

HA

C ~ o V~ SA cA

H E

CH = Po V?SgcE

CL

0 = 32 18

H

Hj

Hk

A

iA -~ m s 2

B

in

= m ~

I

J

I

mA

mE

m

n

P

A i r c r a f t ro l l in g m o m e n t o f i n e rt i a

L i f t - c u rv e s l o p e

A i r c r a f t p i t c h i n g - m o m e n t i n e r t ia

C o n s t a n t i n e q u a t i o n (A .2 )

M e a n c h o rd o f c o n t ro l , a f t o f t h e h i n g e l in e

W i n g m e a n a e r o d y n a m i c c h o r d

A i l e ro n h i n g e -m o m e n t c o e f f i c i e n t

E l e v a t o r h i n g e - m o m e n t c o e f f ic i e nt

Li f t coef f ic ien t

A e r o d y n a m i c h in g e m o m e n t o f a c o n t r o l , n o se u p p o s it i ve

E l e v a t o r j a c k m o m e n t , n o s e u p p o s i t i ve

A i l e r o n j a c k m o m e n t , n o s e u p p o s it iv e

M o m e n t o f in e r t i a o f a c o n t r o l a b o u t t h e h i n g e l i n e

C i r c u l a r f r e q u e n c y o f t h e a i r c r a f t l o n g i t u d i n a l s h o r t -p e r i o d

o s c i l l a t i o n

A i l e r o n r o l l in g p o w e r

A i l e r o n m a s s

E l e v a t o r m a s s

A i r c r a f t m a s s

N o r m a l a c c e l e r a t i o n

A i r c r a f t r a t e o f r o l l, p o s i ti v e t o s t a rb o a rd

s lugs / f t2

s lugs / f t2

ft

f t s e c 2

l b f t

lb / f t

lb / f t

s lugs / f t2

se c - ~

s lugs

s lugs

s lugs

' a ' u n i t s

r a d / s e c


10/29

r~/~)

1 A

l g

S A

S

S

s

T

V

i

X A

X E

Ya

YE

~ d ~ n

o

N O T E :

Suff ices

A

E

2

= 0.002378

A d o t a b o v e a n y

L I S T O F S YMBOLS - - - c o n t i n u e d

A ir c r af t r a t e o f p i t ch p o s i t i v e n o se u p r a d / s e c

A m p l i t u d e r a t i o o f r a t e o f p i t c h t o n o r m a l a c c e l e r a t i o n i n th e l o n g i tu d in a l

sh o r t p e r io d o sc i l la t i o n

See Fig. 15 f t

See

Fig. 15 f t

Ai le ron a rea a f t o f h inge f t 2

Elev a tor a rea a f t o f h inge f t2

W in g a r e a f t 2

W in g s e misp a n f t

D u r a t i o n o f c o n t r o l p u l s e s e c

t rue a i r speed f t / sec

E q u iv a l e n t a i r sp e e d f t /s e c

See Fig. 15 f t

See

Fig . 15 f t

See

Fig. 15 f t

See

Fig. 15 f t

Airc ra f t inc idence rad ians

E le v a to r p i t c h in g p o w e r

I n c r e me n ta l v a lu e s o f p a r a m e te r s

S w e e p o f c o n t r o l h in g e l in e d e g r e e s

E le v a to r a n g le t r a il i n g e d g e d o w n p o s i ti v e me a s u r e d i n a p l a n e p a r a ll e l t o

the a i rc ra f t cen t re l ine rad ians

A i l e r o n an g l e t r ai l in g e d g e o f e i t h e r su rf a c e d o w n p o s i t iv e me a s u r e d i n a

p l a n e p a r a l le l t o t h e a i r c r a f t c e n t r e l i n e r a d i a n s

Air dens i ty a t sea leve l s lugs / f t 3

o f t h e a b o v e q u a n t i t i es d e n o te s d i f f er e n t ia t i o n w i th r e sp e c t t o t ime .

A i l e r o n

E le v a to r

C o n d i t i o n s i n s t e a d y t u r n s a t d i f fe r en t n o r ma l a c c e l e ra t i o n s


11/29

R E F E R E N C E S

N o . A u t h o r s )

1 W . E . A . A c u m . .

2 P . G . H u t t o n a n d D . M o r t o n

3 G . F . M o s s a n d R . W . H a y w a r d

4 F . W . D e e a n d D . G . M a b e y

R . R o s e , A . A . W o o d f i e l d a n d

C. S . Barnes

6 M . S h i n b r o t . . . . . .

7 W . E . A . A c u m . . . .

8 F . W . D e e . . . . . .

9 M . D . D o b s o n . . . . . .

10 D . J . K e t t l e . . . . . .

11 S. N e u m a r k . . . . . .

12 D . R . A n d r e w s . . . . . .

Ti t le, etc.

T h e c o m p a r i s o n o f t h e o r y a n d e x p e r i m e n t f o r o s c i ll a t in g w in g s .

A . R . C . C . P . 6 8 1 . M a r c h 1 9 6 2 .

R e s u l t s o f p r e s s u r e p l o t t in g a n d c o n t r o l h i n g e m o m e n t t e st s o n a

1 / 9 sc a l e m o d e l o f F a i r e y D e l t a 2 i n t h e A . R .A . t r a n s o n i c t u n n e l.

A . R . A . M o d e l t e s t n o t e J 1 2 / 1 .

U n p u b l i s h e d M . O . A . R e p o r t .

W i n d t u n n e l c a l i b r a t i o n s o f i n c i d e n c e v a n e s f o r u s e o n t h e F a i r e y

ER 103 .

J l . R . aeronau t . Soc . Vol . 67 , No . 628 , p . 267 . Apr i l 1963 .

F l i g h t m e a s u r e m e n t s o f t h e l if t, l o n g i t u d i n a l t r i m a n d d r a g o f th e

F a i r e y D e l t a 2 a t M a c h n u m b e r s u p t o 1 . 6 5 a n d c o m p a r i s o n s

w i t h w i n d - t u n n e l r e s u lt s .

R . A . E . T . R . 6 7 0 3 6 . J u n e 1 9 6 7 .

O n t h e a n a l y s is o f l i n e a r a n d n o n - l i n e a r d y n a m i c a l s y s te m s f r o m

t r a n s i e n t - r e s p o n s e d a t a .

N A C A T N 3 2 8 8 . D e c e m b e r 1 9 5 4 .

A e r o d y n a m i c f o r c e s o n a r e c t a n g u l a r w i n g o s c i ll a ti n g in a s u p e r -

s o n i c a i r s t r e a m .

R . M. 2763 , A .R .C . Au gus t 1950 .

F l i g h t m e a s u r e m e n t s a t s u b s o n i c s p e e d s o f t h e a i l e r o n r o ll i n g

p o w e r a n d l a t e r a l s t a b i l i t y d e r i v a t i v e s lv a n d y v o n a 6 0 d e g

d e l t a w i n g a i r c r a f t ( F a i r e y D e l t a 2 ) .

A . R . C . C . P . 7 3 9 . J u n e 1 96 3.

W i n d t u n n e l t e s ts a t s u p e r s o n i c s p e e d s o f t h e F a i r e y D e l t a 2 .

A . R . C . C . P . 6 7 2 . O c t o b e r 1 9 6 2 .

8 f t x 6 f t t r a n s o n i c w i n d t u n n e l t e s t s o n a 1 / 2 4 s c a le m o d e l o f t h e

F a i r e y D e l t a 2 ( E R 1 03 ).

A . R . C . C . P . 6 5 6 . M a y 1 9 6 2 .

A n a l y s is o f s h o r t - p e r i o d l o n g i t u d i n a l o s c i l la t i o ns o f a n a i r c r a f t:

i n t e r p r e t a t i o n o f fl i g h t te s t s.

A .R~C. R . M . 2940 . Se p t e m be r 1952 .

M e a s u r e m e n t s i n fl i g h t o f t h e l o n g i t u d i n a l s t a b i l i t y d e r i v a t i v e s

o f a 6 0 d e g d e l t a w i n g a i r c r a f t ( F a i r e y D e l t a 2 ) .

A . R . C . C . P . 6 3 9 . A p r i l 1 95 9.

10


12/29

APPENDIX A

The Hinge Moments Actin9 on Elevator and Aileron Controls.

Fig. 15 shows the relevant geometric data for the control configuration under discussion. The hinge

line of both surfaces is swept, and this introduces certain difficulties in the definition of the various quan-

tities involved. Unfortunately there is no clearly established rule to guide us here, and it is therefore

proposed to use the following definitions which have also been adopted for the Royal Aeronautical

Society aerodynamic data sheets. Control angles and chords are measured in a plane parallel to the plane

of symmetry of the aircraft, whilst the hinge moments are measured about the swept contro l hinge line.

A further difficulty arises as the conventional definition for positive aileron deflection is trailing edge

down for the starboard aileron and t railing edge up for the port surface, whereas trailing edge down is

normally considered positive in hinge moment nota tion ; the latter definition is used here.

At any instant in flight the sum of the control jack moment, the aerodynamic hinge moment and the

inertia reactions is zero. Using the definit ions shown in Fig. 15, it can be shown for the starboard elevator

that the control jack moment is given by:

- H s = H Z + r E me g n - ( x e r~ m t + I z cos )~)g1-Ie sec 2 - ( Y e re m e - I e sin )~)p

(A.1)

where the small term due to the aircraft acceleration along the flight path has been ignored. Hj is the jack

moment, H E is the aerodynamic hinge moment, both measured trailing edge down positive, and IE the

control inertia about the hinge axis. Similar equations may be written for the other three control surfaces.

The aerodynamic hinge moment is a function of control deflection and the aerodynamic quantities

describing the aircraft motion, these relationships not always being linear. In theory such a situation

can be dealt with by an equations of motion technique such as that proposed for the extraction of

aircraft stability derivatives by Shinbrot 6, but this would require a resolution of the test data well beyond

the accuracy available from the present flight tests. As the control pulses and consequent aircraft responses

used during the flight tests were generally rather small, it was assumed that the hinge-moment character-

istics could be linearised for the range of parameters covered in each test, and the formal analysis has

been made using linearised equations.

Consequent ly for the elevator, H e is expanded as

H e = Po V ~ S ece b o ~ + b ~ c~ + b 2 ~ t l + - - ~ - ~ qCeV +

0

+ O Cn ~ OcE O C~ &c~ ]

(A.2)

The term

OCn~/O~

represents the elevator hinge moment induced by aileron deflection; in the present

tests this term was found to be comparable in magnitude with primary control derivatives bl~ and bat.

As the strain gauges used to measure the jack moments were unable to give reliable absolute values,

almost all the analysis was made using incremental values. As a consequence b o could not be determined.

The frequency and amplitude of the control movements used were considerably larger than those of

the resulting aircraft motion and thus one would expect any unsteady aerodynamic effects to be more

important for the former. Estimates based on Acum 1 v suggest that at supersonic speeds unsteady con-

tributions are ver~small compared with those from the steady aerodynamic effects ; while at the subsonic

speeds tested they might produce up to 2 per cent change in the peak hinge moment , and a phase displace-

ment of 12 deg between the peaks of the control input and resulting hinge moment. In fact, the flight

11


13/29

r e c o r d s s h o w e d t h a t t h e p e a k o f t h e h in g e mo me n t d id n o t l a g b y mo r e t h a n 1 0 d e g b e h in d t h e p e a k o f

the cont ro l input . S ince th is i s equiva len t to le ss than 2 pe r cen t in ampl i tude , i t has been assumed tha t

uns teady e f fec ts have a negl ig ib le in f luence on the leve l o f the h inge m om ent peaks .

T h u s e q u a t i o n A . 2 ) i s r e d u c e d t o

. aCH ~ \

A H E = Po V~ SE cE bl~ Aa + b2E A t / + - - - ~ A ~ A.3)

w h e r e t h e s y mb o l A d e n o t e s i n c r e me n ta l v a lu e s .

F o r t h e s t a r b o a r d e l e v a to r e q u a t i o n s A . 1 ) a n d A . 3 ) g iv e

- A H j

= Po V SECE

bl~ Ac~+b2~ A

OC/tE

\

+ r E mE g A n - x E rE mE + I E c o s 4 ) A 0 -

- Ig sec 4 A/~ - YE re m E - Ig sin 4) A/~. A.4)

A s imi l ar e x p r e s s io n ma y b e w r i tt e n f o r th e s t a r b o a r d a i l er o n i n c r e me n ta l ja c k mo m e n t .

- - A H K = P o V : S A c A b l . 4 A c ~+ b 2 A

A~ + - - ~ -CHA At/) +

+ r A ma g A n - xA rA ma + Ia cos 4) A0 -

- 1 A sec 4 A~ - YA rA rnA --IA sin 4) Ai0. A.5)

12


14/29

APPENDIX B

Eva lua t ion o f b 2 and C ross -con tro l D er iva t ives f rom Con tro l Pu lses .

If a control pulse is of short duration , at the instan t of maximum control application the aircraft will

not have responded sufficiently to affect significantly the aerodynamic hinge moments. Consequently

at that instant , incremental values measured from the initial t rim condition, Aa, Ap and Aq are negligible,

but in the present tests their time derivatives are significant.

In the elevator pulses analysed no significant aileron movement occurred, and consequently A/~ was

zero. The incremental values of the elevator and aileron jack moments, for both the port and starboard

sides are given by:

- A H s = Po V 2 S ~ c E b 2 ~ A t / + r e m e g A n - ( x ~ r ~ m e + I ~ c o s 2 ) A g l - I E s e c 2 A i i

(B.1)

( 3 C H . 4

- A H r = P o V 2 S a c A -~ q A t / + r A mA g A n - ( x A r A m A + IA

cos 2) A~. (B.2)

These equations can be solved for b2~ and

OCHA/Ot/,

the remaining terms being either known aircraft

parameters or variables of motion. In fact, only At/was measured, A/] and A ~ were not measured and An

was measured by an instrument too coarse to give the required resolution. As we are dealing here with the

initial response to a control pulse before rate of pitch and incidence have had time to build up to any

extent, the effects of aircraft damping ma y be ignored, giving:

2 g O C , ,

A~ = - - A t / (B.3)

CL iB ~ at/

An - OCL

At/ (B.4)

Ot/ C L

Values of

OCm/Ot/and OCL/Otl

have been obtained from earlier tests made on the aircraft and reported

in Ref. 5.

The most plausible procedure for estimating the value of A is to assume that the elevator movement

can be approximated to a sine wave in this region, say

A t / ( t) = A t/m a X s in l I T )

where T is the duration of the control pulse.

(B.5)

The value coinciding with the maximum t/is,

A = -A t/ . (B.6)

Having thus conveniently defined all the variables in terms of At/, the peak value of elevator, equations

(B.1) and (B.2) can now be solved for b2~ and aCHA/0t for both port and starboard controls

- A H s S F r E m E O CL 2 ( x ~ r E m E + I ~ c o s 2 ) O C m

b 2 E = l p o V 2 S E c E A r l S t C E L m O r r t l i B ~ O t

/ s e o ) 2 1 B T ,

13


15/29

rt 1 2 L m : : B . 8 )

Po V~ SA CA Art SA ca art m tB c Ort ]

Con side r ing the a i le ron pulse , the acce le ra t ion in ro l l i s de te rm ined as for ~ in equ a t ion (B .3).

2g

P - CL iA~S ~ A~ . (B.9)

F l igh t s and tunne l 9'10 va lues of l~ sho w reaso nable agreemen t , and wh ere poss ib le fl igh t va lues hav e been

used . Apply ing a pro ced ure ident ica l to the e leva tor case , equa t ions fo r the eva lua t ion of b2. and the c ross

de r iva t ive

O C m J a ~

c a n t h e n b e o b t a in e d , g iv in g

r s e c 1

b~ = po v ~ s ~ ~ s~ ~ L ~ o ~ k T 2 y A r A l~ B .1 0 )

mZ S

O C~_._ - A H , b 2 E A ~ + S 2 y E r ~ m e - I ~ s i n 2 t ~ (B.10)

4 P V i S E c ~ A ~ a c SE cE m i S

where the a l te rna te s igns apply to s ta rboa rd and por t r e spec t ive ly . In the present te s ts , a sma l l cor rec t ion

for At /ha s bee n re ta ine d in equ atio n (B.11) as this term is signif icant, a l th ou gh A is negligible .

14


16/29

A P P E N D I X C

Determination o f b 1 rom the Stick Fixe d Longitudinal Short Period Oscil lations.

F o r t h is m o t io n i n c r e me n ta l v a lu e s a r e me a s u r e d b e tw e e n s u c c e s s iv e p e a k s o f t h e a i r c r a ft o s c i l la t io n .

In th e pres ent te s t s , Ap, AiO, A# and A~ a re negl ig ible. Fol lo win g s im i la r r easonin g to tha t o f Append ix B ,

i t can be shown f rom Ref . 11 tha t the a i r c ra f t mot ions in normal acce le ra t ion and p i tch ing a re g iven by ,

a Aa

An - (C.1)

CL

A 4

= - ~

~ A < ~

o 2 )

This r e la t ion has .been de r ived ignor ing the e ffec t o f the da mp ing de r iva t ives , s ince the dam ping was sma l l

in the f ligh t te s t s . J i s the f r equen cy of the longi tud ina l sho r t pe r io d osc i l la t ion an d (77/~) s the am pl i tud e

r a t i o o f p i t c h in g v e lo c i t y t o n o r ma l a c c e l e r a ti o n i n t h i s o s c i l l a ti o n . B o th t h e s e p a r a me te r s , a n d t h e u n -

t r imm ed l if t curve s lope , were m easu red in p rev iou s f l igh t te s t s 1z .

T h e i n c r e me n ta l j a c k mo m e n t f o r t h e e l e v a to r is , f r o m e q u a t i o n ( A .4 ),

b OCH~ \

- A H a = P o V g S E C~

1 E A c ~ + b 2 EA i ? + ~ - A ~ )

I D I

r e m ~ g + ( x ~ r e m e + I e c o s 2 ) < ~

~-~LAa. (C.3)

F r o m th is e q u a t i o n b l e m a y b e d e r iv e d , a s b2 E a n d

OCHE/O~

a r e k n o w n f r o m A p p e n d ix B . I n t h e p r e s e n t

tests , the term invo lving A~ is negligible . Th us

= A H s A~? a S [ r J ~ m m ~ + ( x ~ r e m E + i ~ c o s 2 ) Z _ ( 7 ~

(C.4)

b l~ = Po V ~ S E c~ A c~ b z ~ - ~ S e c e r a g \ n i l

In the case of the a i le ron , the te rm s in bo th A q and A~ a re negl ig ib le in the pres ent te s t s . Thus ,

m g \ n ) J

c . 5 )

i5


17/29

A P P E N D I X D

Evaluation of Elevator and Aileron Hinge M om ent D erivat ives due to incidence bl fro m f l ight at dif ferent

values o f normal acceleration.

I n f li g h t a t c o n s t a n t n o r m a l a c c e l e r a t i o n , t h e a n g u l a r a c c e l e r a t i o n te r m s c a n b e i g n o r e d a n d e q u a t i o n s

A.1) an d A.2) r ed uce t o ,

c ~ C ~

- H j = Po V ~ S E c ~ b o ~ + b ~ + b B ~ q + - U - j + rE m ~ gn

D . I )

a s i m i l a r e q u a t i o n m a y b e w r i t t e n f o r t h e a i le r o n s .

T a k i n g t e s ts a t t h e s a m e M a c h n u m b e r , b u t d i f f e re n t n o r m a l a c c e l e r a ti o n s , sa y , n l a n d n 2, w e g e t ,

l E k O o SE cE A b 2E

w h e r e s u f fi c e s 1 a n d 2 r e f e r t o t h e d i f f e r e n t t e s t c o n d i t i o n s a n d A s ig n i fi e s t h e i n c r e m e n t b e t w e e n t e s t c o n -

d i t i ons , b2E an d a C n J O ~ h a v e b e e n d e r i v e d i n A p p e n d i x B .

A s i m i l a r e x p r e s s i o n c a n b e d e r i v e d f o r t h e a i l e r o n s .

16


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T A B L E 1

Leading Aircraft Dimensions

G r o s s w i n g a r ea

S e m i - s p a n

N o m i n a l c e n t r e li n e c h o r d

T i p c h o r d

M e a n a e r o d y n a m i c c h o rd

W i n g s e c t i o n

T r a i l i n g -e d g e a n g l e

L e a d i n g - e d g e s w e e p b a c k

T r a i l i n g - e d g e s w e e p b a c k

T w i s t

D i h e d r a l

I n c i d e n c e w i t h r e s p e c t t o f u s e l ag e d a t u m

M e a n w e i g h t a t t e s t c o n d i t i o n

P i t c h i n g m o m e n t o f i n e r t i a c o e f f ic i e n t , iB

R o l l i n g m o m e n t o f i n e r t i a c o e f f i c ie n t , i a

S = 360 f t 2

s = 13-42 ft

2 5 f t

1 83 ft

= 16 75 ft

4 ~ S y m m e t r i c a l , m a x

t ic

a t 2 9. 5 ~ c h o r d

5.2

59.9

0

0

0

+ 1 5

12800 Ib

0 .269

0 .0558

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19/29

T A B L E 2

Control Surface Details

A i l e r o n

r n A , m a s s

I A, m o m e n t o f i n e r ti a a b o u t t h e h in g e

S A, a r e a a f t o f h i n g e

CA , m e a n c h o r d a f t o f h i n g e

rA

A ~ F i g . 1 5

YA

2 , s w e e p o f h i n g e

H o r n - b a l a n c e a r e a

R i g g e d u p a n g l e

Elevator

rg /E ass

I ~ , m o m e n t o f i n e r t i a a b o u t t h e h i n g e

S E, a r e a a f t o f h i n g e

c ~, m e a n c h o r d a f t o f h i n g e

x e F i g . 1 5

Y~

2 , s w e e p o f h i n g e

2 3 8 s l u g s

2 7 7 s l u g s f t z

1 6 0 4 f t 2

2 7 0 f t

0 6 5 f t

8 - 5 2 f t

1 0 - 0 1 f t

9 . 7

0 - 5 7 f t 2

3

3 1 5 s l u g s

6 1 7 s l u g s f t 2

2 0 - 1 8 f t z

3 6 9 f t

0 7 5 f t

7 5 7 f t

4 53 f t

9 . 7

18


20/29

O O

L 2 ~ J ~ j I

S CA L~ ~

L L v_

F I G . 1 . G e n e r a l a r r a n g e m e n t o f t h e F a i r e y D e l t a 2.


21/29

. . . . - ' ' ; -

~:: :~

. , ~ f

. ~ . 4

r - - ~

? ' ~ r ( t ~ . ' ~ * :

\

F l o 2 T h e F a i r e y D e l t a 2


22/29

bO

(3111

I - . a

Iij

Z

Qw

< \ \

I I

1 2 1 4

M A C H N U M B E R

1 6

El

F IG . 9 . E l e v a t o r h i n g e m o m e n t d u e t o i n c i d e n c e

d e r i v a t i v e v r s u s M a c h n u m b e r .


26/29

-2- 2

+ I 0 ~ 0 0 0 ~ P U L S E

1 5

-I .6

-I ,4

- 1 2

~2E ~

- I 0

+ 4 * . - I - / /

- 0 - g + f I

t

4 I

- 0 6 I

+

+

1-

+

X

+.

i l

y .

^

X

\

\

T U N N E L R E S U L T ~ FO R

4-070 OO,,Ct CON DITIO NS

- 0 4

- 0 . 2

O - A .

0 .4 - 0 .6 0 .8 1 .0 I - P I - 4-

M A C . . . H N U M B E R

FIG. 10. Ele vat or hing e mom ent due to elevator

angle derivative

v r s u s

Mach number.

1 . 6

- 0 8

- 0 - 6 .

c3CH~

- 0 2

[ : o o o o I

0 - 4 - 0 - 6 0 .8 I 'O I -P . . I - 4- I - 6

M A C N N U M B E R

FIG. 11. Elevator hinge moment due to aileron

angle derivative versus Mach number.


27/29

Ix.)

- ~ - 4 ,

- 2 0

- I - i

- - I - I

-I-4-

~ A

- I - 0

-0-

- -0 ,

- 0 " 2

4o,0o 0 c~, PULSE

+ i 0 , 0 0 0 ~ P U L S E

e 4 0 .0 0 0 Ft TU RN e

I 0 0 0 0 ~ - ~

T U R N

o

0

A T U N N E L R E ~ U I - S F O F t

~q ~ ~, 4 0 .~ 0 ~]0 F+. CONOITI0~S

I \ 1 \ / ~

~

I

I \ I ' ' , 1

o / 1 1 7 c . z

- -t , l ~ . . I ~

= I , ' ~ + + I " ' T

I

Jr

'\ I

4 0 , O O O F t

l l , l ~ 1

~I I +

'ti o o o o

m . ~ + ~ r

+ ~ l

AA

0 . 4 -

FIG. 12.

0 - 6 0 -~ I - 0 1 2 1 4 - 1 5

M A E H N U M B E R

Aileron hinge moment due to incidence

Derivative ver sus Mach number.

- I - 8

- I 6

- I

-beA

- I - 0

-0 g

- 0 6

- 0 - 4

- 0 2

l m

+ 1 0 ,0 0 0 f' k PUL SE

IO,OOOfl:

l

f

O i - A

0 - 4 - 0 6 0 - 8 1 . 0 I - P - 1 . 4- I - 6

M A C H N U M B E R

FIG. 13. Aileron hinge moment due to aileron

angle derivative

ver sus

Mach number.

40 ,000~


28/29

Fo

r~

R

2 0

-1 6

1.4

-1 2

I .0

- 0 . 8

- 0 6

: R

S

A I R C R A F T

C E I t T R E O F _

G R A V I T Y

~ A

~ E

- 0 - 4

0 2

0

I ~ - ~ ; ~ v ~ : :P I ' U I r I ' ~ 1

M A C H H U M B E R

F I G . 1 4. A i l e r o n h i n g e m o m e n t ' d u e t o e l e v a t o r -

a n g l e d e r i v a t i v e

v r su s

M a e h n u m b e r .

I ' C { : )

E L E V A T O R C E N T R E

O F G R A V I T Y

A I L E R O N C E N T R E

O F G R A V I T Y

F I G . 1 5. C o n t r o l g e o m e t r i c d a t a .


29/29

R . M . N o . 3 4 8 5

rown copyright 1 9 6 7

P u b l i s h e d b y

HER MAJESTY S STATIONERY OFFICE

T o b e p u r c h a s e d f r o m

4 9 H ig h H o l b o r n , L o n d o n w . c . l

4 2 3 O x f o r d S t r e e t . L o n d o n w . 1

1 3A C a s t l e S t r e e t , E d i n b u r g h 2

1 0 9 S t . M a r y S t r e e t , C a r d i f f

B r a z e n n o s e S t re e t , M a n c h e s t e r 2

5 0 F a i r f a x S t r e e t , B r i s t o l 1

3 5 S m a l l b r o o k , R i n g w a y , B i r m i n g h a m 5

7 - I 1 L i n e n h a l l S t r e e t , B e l f a s t 2

o 1 th r o u g h a n y b o o k s e l l e r

flight measurements

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