On the longitudinal dynamic stability of a ground effect wing

CoA R E P O R T AERO No. 2(

^358

THE COLLEGE OF AERONAUTICS

CRANFIELD

ON THE LONGITUDINAL DYNAMIC STABILITY O F A

GROUND E F F E C T WING

by

THE COLLEGE OF AERONAUTICS

CRANFIELD

On the Longitudinal Dynamic Stability of a Ground Effect Wing

by

P. E. Kumar, B. Sc. (Eng), A. C, G. I.

SUMMARY

An investigation into the longitudinal dynamic stability of a wing in ground effect has been made using a free-flight radio-controlled model and results from quasi-steady wind-tunnel tests. The full equations of motion of a ground effect wing have been determined but their application to stability analysis has so far been restricted to the treatment of the linearised problem using instantaneous derivatives. Analogue simulation of this simplified

analysis has proved promising. It is concluded that the GEW model in its latest form was still unstable in pitch and needed further development. It is hoped to do a fuller analogue simulation using the non-linear and heave derivatives, the latter to be obtained from tests using the Whirling Arm.

Acknowledgement This work was conducted imder contract number PD/28/016 of the Ministry of Technology, to whom the author is extremely grateful.

Thanks also go to Mr. Wayne Osborne, of the Aerodynamics Department, for invaluable help in the development of the G. E. W. model, and to Mr. David Hyndman of the Electrical Department for his help in the analogue simulation of the simplified equations of motion of the model.

LIST OF SYMBOLS b wing span

c mean wing chord

h height oi' wing above ground measured relative to some datum point on wing e. g. quarter chord.

X, Y, Z Aerodynamic forces relative to wind axes u, w perturbation velocities along x and z wind axes ü.w " accelerations " R rate of change of height (associated with ground shape) M pitching moment on wing

q perturbed rate of pitch ^ 6

q " pitching acceleration ^^ 6

u, w, h etc. non-dimensional perturbations u/V , w/V , h/c etc, V free stream velocity

q qt t m/pSV

' '^ o m mass of craft

S, S wing plan a r e a s of fore and r e a r wing respectively T aerodynamic time t / t

H relative density parameter m/ p SI

A'2 " " " WpS8 1 mioment arm of tandem wing

x^,x ,x , z etc, non-dimensional aerodynamic derivatives 1„ non-dimensional pitching inertia

A, B, C.D, E, F coefficients of stability quintic abilit

d/dj

1. o Introduction

Current trends in Ground Effect Machine Technology towards achieving higher speeds have indicated the need to develop a vehicle which might utilise aerodynamic lift, instead of a ground cushion, to achieve better efficiency of operation. As already mentioned in ref. 1 such a craft may take the form of a tandem wing configuration flying within ground effect and will, in all probability, invoke the use of endplates. These endplates will provide higher lift/drag ratios, than those achieved by a craft without them. and will also result in larger structural clearance heights.

Theory and experiment have both indicated a rearward shift of the centre of p r e s s u r e of a wing as it approaches the ground, and it is the associated changes in pitching moments and their effect on the dynamic stability of a GEW that will be investigated in this report. Towards this end results from quasi-steady wind-tunnel tests, and from free-flight trials of a tandem-wing model, will be used,

2. 0 Development of a Free-Flight GEW Model

The initial version of the GEW was essentially a wing with endplates and can be seen in Fig. 1. Details of construction and basic dimensions are to be found in section 5. 0 of ref. 1.

This version was, as expected, completely unstable in free-flight, and when tested tethered in a wind-tunnel. However, it adequately demonstrated the severity of the pitching instability. In free-flight the model perform^ed a coraplete loop in a fraction of a second within its chordlength off the ground. Modification of the model to a tandem-wing configuration, as shown in Fig. 2, was completed with the installation of radio-control and a 3.21 c. c. glow plug engine with throttle control. The all up weight was now 7 lbs.

This version was tethered over a groundboard in the Aerodynamics Department's open jet subsonic wind-tunnel and tested power off and power on as follows :-(a) Power-off tests - The speed of the wind-tunnel was slowly increased until the r e a r wing which acted as the all-flying tailplane and was set at the fully down position, lifted off the ground-board. The tailplane angle was then decreased until the whole craft took off. After a brief vertical oscil-lation the craft steadied itself at a certain height above the ground. Further height control was achieved by means of the tailplane angle. Extensions to the endplates by means of stiff paper increased the effective height at which the model operated and, consequently, gave better structural clearance than that obtained without the use of extensions.

(b) Power-on tests - With the engine idling the model required more down elevator, as compared to the power-off case, to mainlain a level

flying attitude. With controls fixed the height could be controlled by changing the throttle setting v i z . , opening the throttle increased the height and vice versa. More throttle, however, required more down elevator to maintain a

6

-and m g Sin (® + 6) - m g Sin & = 6 m g Cos O

2

Multiplying (2) by 1/pV S and using the s t a n d a r d n o n - d i m e n s i o n a l d i s t u r b a n c e s [ i . e . u = u / V , w = w / V . q = qt, t = m / p S V = V C ^ / 2 g Cos 0 , G O G O LJ T = t / t . /u^ = m / p S L = V t/lrr, and X = X / p S V e t c . ] ' 1 ' f x o ' T u u ' ^ ^ o ^ ,-v X. X ,„ dw X. hX, h X ' d u , , u , q d f l / * ^ w h h -r— ( 1 - ) - —^ -r- - UX - W X - " T " " o o " dT m M^ dT u w dT m ^ ^ ^ 2 ^ ^ ^ 2 o o dq X. C_ e

- T- -^ +

- 1 ^

= 0

(3)

d r m 2 ' A s s u m i n g x - . x * . x - = 0 we have " u w q -T- ^ - 3 - - u x - W X - (hX, + hX • ) + —-— = 0 d r M. dT u w ' h h ' 2 2 o

A s u i t a b l e way of n o n - d i m e n s i o n a l i s i n g the height dependent t e r m s i s a s follows 2 x^ = X , / p V b w h e r e b = wing s p a n and S = be and x^ = X - / p V S h h ' o „ „ 2 ^ h h ' c h ^ V ' h pSV o o h ^ and — = n o n - d i m e n s i o n a l height p a r a m e t e r s = h say

( — ) i s a s o r t of n o n - d i m e n s i o n a l v e l o c i t y and depends on the ground o s h a p e , = g s a y ^-^ X ^^, C^ 0 du q de ^ ^ C '^ • L „ . . . . . ^7- -^ -r~ - ux - w x - hx^ - gx^ + —r— - 0 (4) d r /u d r u w n ° n 2 (b) C o n s i d e r i n g the Z - e q u a t i o n : Z = u Z + wZ + l i z . + w Z . + hZ, + h Z • + qZ + qZ • + m g Cos O a u w u w h h q q

Z = m g Cos (© + e) Hence

w(m - Z . ) - m V - u Z - w Z - Ü Z . - hZ. - hZ^- - q Z - q Z . + m g Cos 0

w q o u w u h h ^ q ^ q ^

- mg Cos (© + e) = O (5) and for s m a l l 6. Cos (0 + ©) = Cos © - 6 Sin ©

and m g Cos © - m g Cos (© + 6) = + 6 m g Sin © Ignoring Z • , Z • and Z . we get

" " w u q ^a z hZ, +hZ^. C^ A , d w ^ d e , , , q . h h . L ^ , ^ _ . . -UZ + - J - - W Z - - ^ ( 1 + - ^ ) T + -—• 0 tan e = 0 u dT w dT ^^^ 2g 2 o .-. -Gz + ^ - ^ z - ^ ( 1 + ^ ) - hz - | z . + ^ 0 tan 0 = 0 (6) u dT w dT p h " h 2 ^ ' (c) C o n s i d e r i n g t h e M - e q u a t i o n : M ^ uM + wM + uM . + wM . + hM, + hM^ + qM + qM . a u w u w h h ^ q ^ q B q - uM - wM - ÜM. - w M . - hM, - hM- - qM - q M . = 0 u w u w h h ^ q ^ q 2 Ignoring M . . M - we g e t . on multiplying by n /pSV 1 , •^ ^ dw 1 ,,^„ , ^ , . . d0 , - um^^^ - w m ^ p ^ - M^m^ ^ - - — - (hM^^ + hM^^) - m ^ + P S V ^ I ^ dT o w h e r e m and n , r e f e r to the e l e v a t o r and i „ = B / m l _

r7 1 rJ ' i

dw ' ^ 1 ^ , h . ^ d0 ^ . d^e 1 u ' ^ l ' w ^1 w dT Im h ' V ' h q dT B , 2

T o ^ dT = M^m^r,^ (7)

10 -E m, c h = m u „ ( x z, - z X, ) - ju^ — ; Ï - t a n © (x m - m x + - ; LI„ + 0*^2^ u h u T i ' ' ^ 1 2 * u w u w 1_ ^2 X m, c u h + m Xv; - X m^.) + M , M o ( l + - ^ ) ( i ï i X, - -^ ) + u h u h 1 2 M.| u h 1 ' + Li^ -—r- (z m + m z - z m.' - m z,.) 1 2 u w u w u h u n C-T n \ . c C_ m, c F = P,Po ~ T " t a n ® (x -:; - X, m ) - /U,jU„ —;r— (z ^j + m z, ) 1 2 2 u i n u l'^2 2 u 1 u h 4. O C r i t e r i a for Stability C o n s i d e r the equation AX^ + BX'* + CX^ + DX^ + EX + F = 0

Routh h a s shown t h a t if A > 0, then a n e c e s s a r y but not sufficient condition for s t a b i l i t y i s that B, C, D. E. F > 0. Hurwitz and E r a s e r ( r e f s . 6 & 7) h a v e , h o w e v e r , developed s t a b i l i t y c r i t e r i a equivalent to t h o s e of Routh but e x p r e s s e d in d e t e r m i n a n t a l f o r m . If A > 0, then the c o m p l e t e s e t of n e c e s s a r y and sufficient conditions for s t a b i l i t y i s that a l l the t e s t functions T . . . . T s h a l l be p o s i t i v e , w h e r e ^ 2 = ^ 3 = ^ 4 = B D B D F B D F O A C A C E A C E O O B D O B D F O A C E

B A o o o D C B A O F E D C B O O F E D O O O O F It c a n be s e e n t h a t T^ = F T . , o r m o r e g e n e r a l l y T = F T , , so F 5 4 ° •' n n - 1

must be +ve for s t a b i l i t y ,

4, 1 The Coefficients of the Stability Quintic

T h e s e have b e e n defined in e q u a t i o n s (13) and in o r d e r to check for s t a b i l i t y t h e i r v a l u e s will have to b e d e t e r m i n e d . T h i s i m p l i e s d e t e r m i n i n g the v a l u e s of the a e r o d y n a m i c d e r i v a t i v e s involved. At t h i s s t a g e only a few of the q u a s i - s t a t i c d e r i v a t i v e s in ground effect a r e known from wind-tunnel t e s t s but it i s hoped that the h dependent ones will be obtained from t e s t s on the College of A e r o n a u t i c s Whirling A r m ,

The coefficient A i ^ i s c e r t a i n l y p o s i t i v e .

In s t a n d a r d a i r c r a f t s t a b i l i t y p r a c t i c e the d e r i v a t i v e m is dependent p r i m a r i l y on the c o n t r i b u t i o n from the t a i l p l a n e . A s s u m i n g t h i s holds n e a r the ground then the m a i n c o n t r i b u t i o n to m c o m e s from the t a n d e m wing

(m ) = - - — (a ) q h 2 S 2 h q h w h e r e S = tandena wing a r e a "2>K m a i n wing a r e a lift c u r v e slope of t a n d e m wing at a given height ' h ' , the not (x ) = u ' h (x ) = W h ation of ref. 5 -(C + ° ^ \ \ ^ ^^D 2 SU V p V S h ^ o 2 ^"^L 8o \ d T dU w h e r e (dT/dU) i s the r a t e of change of t h r u s t with f o r w a r d speed. V 8C

K\

= -

(^L

^ T

-^

\

12

-V c ac

/ \ _ o , m .

ac

ac^

/ \ _ c , m . , L ^ h 21,j. a C ^ ^ da )^ 1 a^

( m . ) = — (m ) (—) Near the ground {8e/da) is very nearly w h Mj q h a ^ h _{zero due to reduction in downwash} Hence (m. ) ~ 0

w'h

The heave t e r m s XJ-, Z • and m^ , for flight over level ground, are defined by

"^

= re

"^=r^/h

Terms such as a C ^ / a a ; = x . , a C ^ / 8 a ^ z . . 8C /8ff^ m^, D' 0 L' 6 m' 0

aC^/aU, aC^ /aU. ac /aU and aC /aC^ are obtainable from wind-tunnel D' L' m' m ' L

tests and apart from the velocity dependent terms can be found frona the results given in ref. 4.

The signs of the derivatives are as follows (m ) and (z ) are negative.

q h q h

(x ) is negative if 8C /aU is positive and dT/dU = 0.

(x ) is positive since (aC^/8o), >. 0 at large C^ but may tend to w h D' h • L

zero for low C . Lj

(z ) is negative if (aC /8U) is positive. u h •L' (z ) is negative.

w'h ^

(aC / a c ) depends on the height and the configuration being considered (i. e. wing with or without endplates) and. as can be seen from ref. 4, can be +ve or -ve,

(m ) is positive if (8C /aU) is +ve. u h m '

F o r m o s t c a s e s m > 0 and z < 0. x^ may. h o w e v e r , be s m a l l (+ve o r -ve) o r z e r o depending on t h e height.

Hence for p o s i t i v e B. with m . ~ 0. z,• > 0 o r x + z > z,-w h u z,-w ' h X m c z ni c

F o r positive F . t a n © (—:; - x, m ) > (—; + m z, ).

l,j. n VL l^ u h '

It i s difficult to obtain the conditions for T to be positive without 2. o. 4

a c t u a l l y s u b s t i t u t i n g the v a l u e s for the v a r i o u s l o c a l l i n e a r i s e d d e r i v a t i v e s into the coefficients of the quintic. If we d i s r e g a r d the velocity dependent t e r m s aC / a U . 8C / a U . a c / a U t h e n a we c a n apply t h e s e l i n e a r i s e d d e r i v a t i v e s ,

13 LJ i n

obtained f r o m the w i n d - t u n n e l t e s t s , to the e x a m i n a t i o n of the s t a b i l i t y of the quintic at c e r t a i n specific h e i g h t s above ground.

4. 2 C a s e of a Single Wing with E n d p l a t e s (ref. 4) ' ^ = 2 and c. g. a t q u a r t e r c h o r d .

a = 5°

h = 2 . 0 2 5 " P

C l a r k Y e n d p l a t e s

F o r a single wing m = z = 0 . I g n o r e Tci t e r m s for the p r e s e n t .

1 ^s

(x ) = -^ (C^ - -—^) = + 0 . 5 2 5 - . 0 2 8 6 = +.4964 ^ w ' h 2 ^ L da (z ) = - C^ = - 1 . 0 4 9 u ' h L 1 ^ ^ L 1

( V h = - 2 ( S - * - - a ^ ) = - 2 ( - o i i ^ ^ « - ^ ) = - 4-31

(m ) = 0 ^ h 8C AT ^7 ÖZ , _ h Now Z, = 7 and z, -Z . c -Z ^ h 8h h ^-2, ^.2_ p V b p V S ^ o ^ o

14 -c 8Z _ -c ^ ^h " „ 2 ^ 8h 2 ah C V ö ^ o 1 ^ ^ L - ^ - - 1 . 5 6 2 a(h/c) a x , ^ h ''^h 1 ^^D A l s o X, = -rr and o o «^ " "h "" p v \ '~ pV^S ^ 2 ^ ^ ) \ + . 0 0 5 9 5 M ar* „ , .. .^. . , „ , h . 8M/8h 1 ' ' m By definition from (7) m = 1—- = - ::jr-j-pV'^S p V ^ S '^ ''^^/''^ o m^ = +0. 56 h A^l = A<2 = _pSc m

F o r the m o d e l of F i g . 1 /u = 59. 5m = 7. 45 (for m g = 4 Ib). The coefficients of the quintic a r e , t h e r e f o r e :

^ = ^B B = 4, 32 i g C = 4, 21 - 11,03 i ^ D = 31 - 0.182 i ^ 13 E = 1. 25 F = 17, 1

H e n c e for i „ = 1, the equation of motion b e c o m e s X'' + 4, 32X^ - 6, 82X^ + 30, 8X^ + 1. 25X + 17. 1 = O

The application of R o u t h ' s t e s t functions to t h i s equation d e t e r m i n e s the e x i s t e n c e of two r o o t s with p o s i t i v e r e a l p a r t s and h e n c e the m o t i o n of the wing i s u n s t a b l e and d i v e r g e n t . The s a m e holds for l a r g e v a l u e s of i and we m a y , t h e r e f o r e , deduce that a single wing in ground effect i s vmstable u n d e r a l l c o n d i t i o n s .

4. 3 C a s e of a Tandena Wing Configuration

C o n s i d e r two t a n d e m wings of equal a r e a and a s p e c t r a t i o but with the l e a d i n g wing having e n d p l a t e s . T h i s a r r a n g e n a e n t i s t y p i c a l of that r e p r e s e n t e d

by F i g . 3.

Taking the c e n t r e of g r a v i t y of t h e whole c r a f t a s being at 0. 5c of the leading wing, and u s i n g the r e s u l t s given in ref. 4, we have for s t a t i c s t a b i l i t y :

a^ = 8 ° , Og = 0° and g = 1. 13, .*. 1,^, ~ 1.94c

^2

The o v e r a l l lift coefficient C + ^ - C = 1 . 49 L b^ Lg and C = , 0 1 5 5 g (m ) = - i - ^ (a ) = - i (5. 69) = - 2. 845 = (z ) q h 2 S 2 h 2 q ] ^

'Vh = - s

0155

ac,

(x ) = -^ (C - — 2 ) = i ( 1 . 4 9 - . 2 6 2 ) = 0 . 6 1 4 w h ^ L 8 a Z (z ) = -C^ = - 1 . 4 9 U h L 1 ^ ^ L 1 ( O . = - 9 (<^n + - T ^ ) = - ? (-0155 + 11.34) = - 5.678 _{w h ^ U da z} Assunae m and m . = 0 u w

ac

w h 2irp aa Y\ 3» 8o -2.68

16

-(^J

_{h ' 2 a ( h / c ) 2} 1 ^ ^ L 4 ( - 1 . 5 ) -0. 75 1 ^ ^ D h 2 8 (h/c) 2 4 (.032) = 0. 016 1 öC 1 m h 2 8(h/c) ^ ( - . 3 5 ) = - 0 , 1 7 5 1 8 . 5 , n = 9. 54

The coefficients of the quintic a r e A B C D E F = = = = = = ^B 5. 684 i 33. 23. 26. 25 -07 = 53 - 1 7 . 7 2 + 12 0. 2. 845 . 8 7 i 66 _^B It c a n be s e e n s t r a i g h t away t h a t the m o t i o n is u n s t a b l e , s i n c e F < 0. for a l l v a l u e s of i . Hence for s t a b i l i t y (if m ~ 0) we m u s t have m > 0.

4. 3. 1 Pitchirig i n e r t i a of GEW m o d e l

. The pitching i n e r t i a B (not to be confused with the coefficient of the X t e r m in the quintic) of the m o d e l shown in F i g , 4 w a s obtained using the b i f i l a r s u s p e n s i o n method. T h e m o d e l w a s s u s p e n d e d a s shown in the

d i a g r a m below and t i m e s for a s i n g l e o s c i l l a t i o n w e r e m e a s u r e d for different v a l u e s of ' d ' . / 1 1 J / r / / / f / < \ \ / /

d = J

> / B m g d ^ T ^

16 A

, T = p e r i o d of o s c i l l a t i o n 15. 25 lb ft na B ml„ ~ 5.77

Hence for the G E W , the quintic b e c o m e s

X^ + 6. 176 X^ - 7. 12 X^ + 3. 34 X^ + 4, 6 - 3. 07 = 0

which i n d i c a t e s t h r e e r o o t s with p o s i t i v e r e a l p a r t s . F o r p o s i t i v e C we m u s t , t h e r e f o r e , have i „ < 2. 6.

D

4. 4 R e s u l t s from Analogue Simulation

The s t a b i l i t y q u i n t i c s p r e v i o u s l y d e t e r m i n e d in s e c t i o n s 4, 2 and 4, 3 w e r e put on the AD 256 Analogue Conaputer of the E l e c t r i c a l D e p a r t m e n t . T h e s e equations w e r e :

X^ + 4. 32 X"* - 6. 8? X^ + 30. 8 X^ + 1. 25 X + 17. 1 = 0 (a) X^ + 8. 529 X'* + 20. 38 X^ + 22. 37 X^ + 26. 53 - 17. 72 = 0 (b) with i „ = 1 .

B

T h e t i m e - h i s t o r i e s of the m o t i o n s following a d i s t u r b a n c e a r e shown in F i g . 7.

It m u s t be s t r e s s e d that the p r e s e n t a n a l y s i s w a s simplified c o n s i d e r a b l y , in t h a t no h t e r m s w e r e included in the equations of motion. F u r t h e r no n o n l i n e a r i t i e s w e r e r e p r e s e n t e d in the equations and only l i n e a r i s e d d e r i v a -t i v e s a-t a fixed heigh-t w e r e u s e d . Hence -the c u r v e s of F i g . 7 a r e useful m e r e l y in indicating the r a t e at which the G E W ' s s t a r t to d e p a r t f r o m the ground on being d i s t u r b e d . It can be s e e n that the t a n d e m wing a s r e p r e s -ented by equation (b) above, i s l e s s u n s t a b l e than the single wing. P o i n t s frona F i g . 5. although s t r i c t l y inapplicable on account of the GEW m o d e l having different fore and r e a r - w i n g a r e a s and a different i „ f r o m that s i m u l a t e d , have been included in F i g . 7 for c o m p a r i s o n .

It i s hoped to conduct a fuller analogue s i m u l a t i o n p r o g r a m m e in the n e a r future including a s m a n y of the n o n - l i n e a r t e r m s a s p o s s i b l e a s well a s t e r m s in h (and li* if significant).

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

A g r e a t d e a l of information h a s been gained about the s t a t i c and d y n a m i c longitudinal s t a b i l i t y of a t a n d e m wing in ground effect, frona both t e t h e r e d t e s t s in the w i n d - t u n n e l and c o n s t r a i n e d " f r e e " flight o b s e r v a t i o n s . The t a n d e m wing m o d e l developed w a s s t i l l found to be u n s t a b l e in pitch and f u r t h e r d e v e l o p m e n t will be n e c e s s a r y to m a k e the c r a f t c o n t r o l l a b l e . The u s e of split flaps and flexible e x t e n s i o n s to the e n d p l a t e s w e r e found to be useful t o w a r d s obtaining s u i t a b l e pitch c h a r a c t e r i s t i c s and ground c l e a r a n c e .

18

-but t h e i r application to s t a b i l i t y a n a l y s i s h a s been l i m i t e d on account of the lack of infornaation on c e r t a i n heave " d e r i v a t i v e s " and the n o n - l i n e a r v a r i a t i o n s of the o t h e r s . An analogue s i m u l a t i o n of the simplified equations of motion h a s p r o v e d e x t r e m e l y p r o m i s i n g and w a r r a n t s f u r t h e r development in the future to include the full n o n - l i n e a r a e r o d y n a m i c c h a r a c t e r i s t i c s of a wing in ground effect,

R e f e r e n c e s

1. Stability of Ground Effect Wings - P . E. K i u n a r , CoA R e p o r t A e r o No. 196, (1967).

2. Low Speed Wind-Timnel T e s t s on a T w o - D i m e n s i o n a l Aerofoil with

Split F l a p n e a r the Ground - J. Bagley, C. P , No. 568, (1961). 3. Unpublished P h . D . t h e s i s - P . R. AshiU.

4. An E x p e r i m e n t a l Investigation into the A e r o d y n a m i c C h a r a c t e r i s t i c s of a Wing with and without E n d p l a t e s in Ground Effect

P . E . K u m a r , CoA R e p o r t A e r o No. 201, (1968).

5. A i r c r a f t Stability and C o n t r o l - A. W. B a r i s t e r , P e r g a m o n P r e s s , (1961). 6. M a t h e m a t i s c h e Annalen, VoL 46, p. 273, (1895) - A. Hurwitz.

7. On the C r i t e r i a for Stability of S m a l l Motions - R. A. E r a s e r , P r o c . Roy. S o c . , Vol. 124. p . 642, (1929).

F I G U R E 2 TANDEM WING CONFIGURATION

FIGURE 4 CINE-RECORD OF RESPONSE OF G . E . W. MODEL TO FLYING OVER A RAMP. (Camera Speed 24 f. p, s. )

- 1 0 MODEL LEAVES RAMP - 2 -•o IMPACT WITH GROUND

FIG.5. TIME HISTORY OF INCIDENCE AND HEIGHT OF G.E.W. MODEL.

loo

HORIZONTAL DISTANCE d TRAVELLED HORIZONTAL VELOCITY V OF MODEL

FIG.6. TIME HISTORY OF VELOCITY AND DISTANCE TRAVELLED BY G.E.W. MODEL.

6 0

4 0

2 0

TIME («cc»)

FIG.7. RESPONSE OF A G.E.W. TO A DISTURBANCE IN GROUND EFFECT ( A N A L O G U E SIMULATION OF EQUATIONS (q)» (b) OF SECTION 4 - 4 )