Stability of ground effect wings

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

C R A N F I E L D

STABILITY OF GROUND EFFECT WINGS

by

THE COLLEGE OF AERONAUTICS

CRANFIELD

Stability of Ground Effect Wings A preliminary survey of theoretical

and experimental techniques.

by

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

SUMMARY

A survey of existing experitnental and theoretical work associated with wings in ground effect has indicated a lack of information concerning the unsteady, or quasi-steady, aspects of the problem. This report states some of the problems encountered in the stability and control of a ground effect wing and attempts at obtaining some feel for the longitudinal and lateral stability derivatives. An outline of possible future theoretical work is given, as a r e also some preliminary quasi-steady wind-tunnel r e s u l t s .

ACKNOWLEDGEMENT

This work was carried out under Ministry of Technology (formerly Ministry of Aviation) contract number PD/28/016.

1.0 Introduction 1 2.0 Wings in steady motion near the ground 1

2.1 Longitudinal motion 3 2.2 L a t e r a l motion 8 3.0 Future theoretical work 9

4.0 Review of experimental work 11 4.1 Preliminary quasi-steady t e s t s of a wing in ground effect 13

4.2 Preliminary results 13 4 . 3 Future wind tunnel t e s t s 13 5.0 F r e e flight model of a GEW 13

6.0 Conclusions 14 References 15

1

-1. o Introduction

The rapid advances made in the sphere of Hovercraft technology during the past few y e a r s has fostered considerable interest in the possibility of developing an even faster ground effect machine (GEM). Such a vehicle would necessarily have to be aerodynamic in shape, from the standpoint of drag at the higher speeds envisaged, and consequently the utilisation of the aerodyn-amic lift acting on a wing flying in ground effect would be a more efficient means of support than the ground a i r cushions used by present day GEM's. However, before the ground effect wing (GEW) can become a commercial proposition a complete understanding of the aerodynamic forces and moments acting on such a wing will have to be gained in o r d e r to provide adequate stability and control of the craft. The sort of GEW envisaged at present is primarily for over water operation, although overland operation is possible where the t e r r a i n is substantially flat. In practice, therefore, the operational environment of such a craft is seldom likely to be steady. Waves over

water, uneven ground and atmospheric turbulence within the wind shear layer near the ground a r e all factors which will affect the motion of a GEW.

As early a s 1921, Wieselsberger published his classic report on a wing flying n e a r the ground and since then many authors have contributed towards a fuller understanding of the phenomenon. Theoretical work has mainly concerned itself with the solution of the problem of a two-dimensional wing in ground effect under steady flow conditions, and as yet no analysis has yielded an exact solution for the case of a finite wing near the ground. Numerical solutions to the linearised problem, however, do give a fair agreement with experimental results obtained.

As far as the author is aware no theoretical work has as yet been published for the case of a wing in unsteady motion near the ground, nor that for the quasi-steady c a s e s of yawed or banked wings in ground effect. Wind tunnel t e s t s have, however, been conducted in America to measure the roll and yaw derivatives of a wing investigating in the process the effect of ground on tandem wing a r r a n g e m e n t s .

It is the purpose of this report to state some of the problems associated with ground effect which have so far remained unsolved or not been investigated, and to review the existing experimental techniques involved.

2,0 Wings in steady motion near the ground

A survey of the work c a r r i e d out in this field has been made by Ashill (Refs. 1 & 2) who has further considered the design of a GEW for the case of minimum induced drag. This has, for the practical case of a rectangular wing, invoked the use of endplates and a suitable choice of incidence and camber. The effect of the gap between the endplate and the ground was also investigated.

Ando (Ref. 3) considered the case of a semicircular lifting line in ground effect with special consideration once again to the case of minimum induced drag. Saunders (Ref. 4) considered the main p a r a m e t e r s affecting a

GEW by means of two-dimensional linearised theory and adapted the Kernel function method of Watkins, Woolston & Cunningham (Ref. 5) to numerical solution by means of a digital computer. He obtained good agreement between his theoretical results and those obtained experimentally by C a r t e r (Ref. 6) and Fink & Lastinger (Ref. 7).

The results of Saunders theoretical analysis in the presence of the ground were as

follows:-(i) decreased lift due to wing thickness, (ii) increased lift due to wing incidence,

(iii) decreased lift due to reduction in relative forward velocity due to image wing,

(iv) aft shift of the wing centre of p r e s s u r e , (v) changes in pitching moments due to (iv).

As has been previously mentioned the configuration of a GEW is likely to take the form of a wing with endplates and since the vorticity distribution on the wing is carried over onto the endplates and n e a r e r the ground, the theo-retical problem can be simplified into the solution for a two-dimensional wing in ground effect. This would be for zero sideslip cases only since the effect of the endplates on the lateral stability of the craft is appreciable.

The responses of the GEW result from either

(a) a change of attitude of the GEW whilst flying over a plane ground, or

(b) a change of ground shape, whilst the GEW is flying steady, straight and level above it.

Accordingly, we may summarise the longitudinal and lateral stability derivatives a s

follows:-w

y

J

J

J

J

J

J

y

y

y

y

y

y

y

y

y

y

y

y

y

y

y

J

y

y

y

e

y

y

y

y

y

y

y

y

y

y

y

y

y

y

y

ii

y

y

y

y

y

y

The last four sets of derivatives in the above table a r e due to ground effect and although some of the derivatives due to rate of roll, rate of yaw,

3

-not, they have been included above for the sake of completeness. The <j) G and h derivatives are based on the rates of change of ground shape.

As to which of the derivatives is the most dominant, necessitating some form of control for the craft, is uncertain, but (see section 2 later in this report) it appears that the m and m-' derivatives require investigation.

2.1 Longitudinal motion

The main difficulty in the analysis of the motion of a GEW after a disturbance, whether due to gusts or ground shape, is the lack of information as to the variation of the longitudinal (or lateral) derivatives with height above ground. We know from aircraft stability that there is an increase in the static margin (stick fixed) near the ground leading to larger elevator angles being required for flaring during landing. If we consider the case of a typical GEW with endplates, fin and tailplane, as in the diagram below, then we may expect very coarse elevator movements in order to keep the craft trimmed in ground effect.

Apart from the increase in the stick fixed static margin due to the reduction of downwash on the wing and tail surface, the rearward shift of the wing aerodynamic centre in ground effect also results in t r i m changes. With a GEW having its e . g . eift of the aerodynamic centre the rapid forward move-ment of the a . c . as the craft increases its height above the ground results in an increasing nose-up pitching moment. This leads to an increase in

incidence resulting in a further departure from the ground, and so on. This pitching instability was clearly shown up in the early tests of the free-flight model (see later section) during which the model executed a very violent loop within its own chord-length off the ground, having been initially disturbed by a bump in the ground. The provision of a tailplane and elevator may not suffice to react against the sudden nose up pitch and consequently one of two arrangements may be necessary to provide adequate stability. The first arrangement is to move the e . g . ahead of the a . c . thereby reducing the nose-up pitch on departure from the ground and also the amount of elevator

necessary to r e t r i m ;

//////A/yy////////////

and the second arrangement is to use a tandem wing configuration, such as Lockheeds (1964), the r e a r wing acting as a tailplane in ground effect. This r e a r wing could also have endplates

/////////A////////////////

We have, for the sake of simplicity, ignored the thrust of some propulsive device and its line of action, on the effective overall t r i m of the GEW, but it will have to be borne in mind for actual c a s e s .

To summarise the foregoing review of the longitudinal stability and response of a GEW, the main aerodynamic derivatives affecting the craft motion a r e :

-(i) the change of jpitching moment with change of height above ground i . e . d C m _ / d ( h / c ) .

G

(ii) the change of a . c . position with change of height above ground i . e .

dho/ - r , d<Wc)

where Cm = pitching moment coeff. about e.g.

G

c h

height of some wing datum point above the ground ( e . g . e . g . )

wing mean chord

position of a . c . as fraction of mean chord

Theoretical investigations to determine the pitching moment of two-dimensional flat plate aerofoils in ground effect have been done by de Haller

(Ref. 8) and D a t w y l e r (Ref. 9), whilst S a u n d e r s (Ref. 4) h a s d e t e r m i n e d the v a r i a t i o n of (dCm/da) with a s p e c t r a t i o and height f o r flat r e c t a n g u l a r w i n g s . L o c k h e e d s (Ref. 10) conducted a c o m p l e t e s e r i e s of t e s t s in the wind tunnel to d e t e r m i n e t h e longitudinal (and l a t e r a l ) s t a b i l i t y c h a r a c t e r i s t i c s of wings with both e n d p l a t e s , f l a p s and t a n d e m c o n f i g u r a t i o n s . F i g s . 1 & 2 h a v e b e e n

o b t a i n e d f r o m F i g . 41 of t h e i r r e p o r t f o r a wing of a s p e c t r a t i o 2 , C l a r k Y s e c t i o n , 12% t h i c k with f l a t - p l a t e e n d p l a t e s of d e p t h / c h o r d r a t i o 0 . 1 5 . Now at t h e a e r o d y n a m i c c e n t r e t h e pitching m o m e n t i s c o n s t a n t i . e . ( d C m / d C ^ ) = 0. ^ L .'. C = - - 4 ^ (x - X ) (1) m c op ac & C , = - ^ (x - X , ) m c / c cp c / 4 .'. X = - ^ : r - C + X c = 0 . 2 5 c - C m c / , c (2) cp C^ m c / ^ ci ' 4 L / 4 / 4 — ^ L

H e n c e we can find t h e c e n t r e of p r e s s u r e shift due to height above ground f r o m F i g s . 1 & 2 . A l s o f r o m t h e s a m e d a t a s o u r c e we c a n obtain t h e v a l u e s of Cjj^ for v a r y i n g h / c and t h e s e a r e shown in F i g , 2 . F i n a l l y we can get t h e a e r o d y n a m i c c e n t r e shift due to ground p r o x i m i t y f r o m equation ( 1 ) . T h i s

i s plotted in F i g . 3 ( a ) .

C o n s i d e r t h e c a s e of a GEW with a t a n d e m wing a c t i n g a s t a i l p l a n e ( s e c o n d a r r a n g e m e n t m e n t i o n e d a b o v e ) . T a k i n g m o m e n t s about t h e C . G . of t h e c o m p l e t e craift f o r flight out of ground effect.

Cm = C + C + (h - h-)C^ - V C^ (3) ™G mo^ m o ^ 0 L w j Lwg w h e r e (h - h ) = d i s t a n c e b e t w e e n GEW a . c . and e . g . -^r = ^2^2 S^c S = r e a r wing a r e a S = GEW a r e a ( i . e . m a i n wing a r e a )

1 = d i s t . b e t w e e n GEW e . g . and r e a r wing a . c . c = GEW c h o r d

In ground effect (3) b e c o m e s

C = (C + AC ) + (C + AC ) + [(h - h„) + A(h - h^)]

m ^ van ni„ mn m „ •- 0 0 -* % IliQ^ UIQ^ " ^ 0 2

(C^ + AC_ ) - V ( C , + AC, ) (4) Lw^ Lw^ LWg L ^ ^

w h e r e t h e A i n d i c a t e s t h e c o n t r i b u t i o n s due to ground effect.

F o r longitudinal s t a t i c s t a b i l i t y we a r e p r i m a r i l y i n t e r e s t e d in t h e c h a n g e in C with v a r i a t i o n in height above t h e g r o u n d . U s i n g ( h / c ) a s t h e height

mQ p a r a m e t e r we c a n r e w r i t e (4) a s 8 C ' ^ G 8 9 V 8

dïÏÏ/T) ^ a(fi/c) ^^mo "^ ^m^ ^G ^ 8(1/7) ^^ ' V G ^ L ^ ' 'd(hM ^ L ^

t h e G suffix r e f e r r i n g to ground effect i . e . C = ( C + AC )

L L i-'iu Wi w^ w ^

G

A s s u m e , f o r t h e s a k e of s i m p l i f i c a t i o n

(i) C d o e s not v a r y with h / c ( t r u e only f o r h / c > 0.2) "^0

(ii) T w o - d i m e n s i o n a l flow o v e r t h e GEW with e n d p l a t e s

(iii) I g n o r e t h e effect of the wake v o r t i c i t y on t h e downwash on t h e wing. (iv) Z e r o shift in t a i l p l a n e a . c , position and C v e r y s m a l l

t h e n 8C

i ( ^ = <^ - ^O^G MÏÏT^ < ^ L , ^ ) ' <^L^ . A C ^ ^ ^ , ^ h - h^)

7

-F r o m S e r e b r i s k y & B i a c h u e v (ref. 13) we h a v e

AC = A (effect of i m a g e bound v o r t i c e s and effect of wing t h i c k n e s s ) ^ 1

3 5

= (—=— - 1) C + X w h e r e a = 2 - D lift s l o p e of wing out of ^0 Wj " l ground effect.

f o r h / c ") . 0 4 and X i s defined below Now X = effect of t h i c k n e s s a s e s t i m a t e d by T a n i et a l If we f u r t h e r a s s u m e a f l a t p l a t e a e r o f o i l t h e n X = 0 and a c c o r d i n g l y (5) b e c o m e s 8C ™G a a -rFT-r = (C^ + AC^ ) -rrrr—,^ (h - h ) - V °, • (AC^ ) a(fi/c) L L 3(fi/c) 0 8(fi/c) ' ' - L ^

" i 1 ^2

= C- ( ^ - 7 - f - r (Ah^) 0 L a^ 8 ( h / c ) 0

wi 0

N O T E : With i n c r e a s e in h / c and with a.Q = 2IT A(h - h ) i n c r e a s e s

but Ah d e c r e a s e s . 8 ( Ï Ï 7 ^ = 0 . 5 5 7 C g^j-^^j 1 F r o m F i g . 3(a) a s s u m e a h y p e r b o l i c v a r i a t i o n of Ah with h / c of t h e f o r m Ah = . 0 0 4 5 / h / c 8C C "^G _ . _ 3 „ (..0015 . . . 0 0 2 5 / - W 1 ^^^

^^/^) • S (h/c)' (h/c)2

This variation of the rate of change of pitching moment with height is plotted in F i g . 3(b).

It can be seen from both Figs 3(a) and 3(b) that for heights below

h / c = 0.1 the change of pitching moment is appreciable for only small changes of height. The simplified theory stated above obviously breaks down for low heights and consequently a theory valid for this region will have to be devel-oped. However, in spite of not being valid at very low heights, the simple theory does indicate the violent pitching instabilities that can occur on a GEW being disturbed from the t r i m state near the ground. This low height oper-ation of GEW's warrants further investigoper-ation in the future.

2.2 Lateral Motion

The lateral and directional motion of a GEW will depend primarily on the endplate configuration. Although endplates will provide some directional stability a fin will probably be needed for the same purpose, particularly in the banked cases where the influence of the endplates on the wing is not s y m m e t r i c .

Consider the case of a GEW under steady sideslip conditions. The loads on the craft a

in linearised theory).

acting on the craft a r e as in the diagram below (F. being the local circulation

F o r a sideslip ^, F > F

• <^l ^ ^2^ > <^1 ^ ^ 3 ' and hence

the lift on the trailing wing tip region is greater than that on the leading region. Consequently a + ve rolling moment (as defined in R & M 1801) r e s u l t s .

Sideforce Y > | Y | and (Y + Y ) > 1Y | , and hence in general, for small sideslip angles, the sideforce derivative due to sideslip is - ve. Depending on the e.g. position the yawing moment due to sideslip may be +ve or - ve on a GEW without a fin and accordingly an aft located fin is to be

9

-preferred to maintain +ve directional stability.

Summarising the sideslip derivatives for a GEW with endplates: 1 is +ve

V

n is +ve with a fwd. e . g . and aft fin y is -ve

V

Taking the case of the GEW in a banked attitude the loads a r e as in the following diagram:

VIEW FROM REAR

/ / / / / / / / / / / / / / / / / /

The lower wing tip region has the greatei' local lift force and consequ-ently the rolling moment due to positive bank (as defined in B & M1801) is -ve. F o r the same reason the lift on the lower endplate is greater than that on the other endplate and hence the sideforce due to bank is +ve. The induced drag on the wing tip region further from the ground is greater on account of a wake being shed from the base of the endplate and so the yawing moment due to bank will probably be -ve. Hence the bank deriv-a t i v e s for deriv-a GEW with endplderiv-ate deriv-a r e of the following signs: 1 is -ve

y is + ve

0

n, is - ve However, strong crossflows may exist on the wing undersurfaces for both the sideslip and bank cases and these may well influence the above-mentioned derivatives markedly, A further factor influencing the derivatives i s the gap between the endplates and the ground. Theoretically, for infinite-simal gaps the outflow velocity is infinite and in a practical case can result in an alteration of the wing undersurface p r e s s u r e distribution.

3.0 Future Theroetical Work

From the previous section it is c l e a r that some form of theory, whether linearised two-dimensional or lifting surface, will have to be investigated for

a wing at low height/chord r a t i o s . Datwyler has already considered the case of a two dimensional flat plate wing with its trailing edge touching the ground and some modifications could well be made to his theory to apply for small gaps at the trailing edge. De Hallers analysis has, however, already taken account of small height/chord r a t i o s , for both the two-dimensional flat plate and circular a r c aerofoils, in that the limiting cases of his method, involving Jacobian elliptic functions and Theta functions, correspond to those considered by Datwyler. We may assume, therefore, that de Hallers' method is valid for all heights above the ground. The quasi-steady roll and yaw cases may yield some revealing results on a simple lifting line theory approximating to the lifting surface problem.

However, the simplified longitudinal theory previously mentioned h a s . In fact, highlighted the unsteady problem of a wing pitching or oscillating, near the ground and once again a lifting line approximation miay prove useful. The formulation of the lifting surface problem of a wing in steady and unsteady motion near the ground has already been undertaken, but the integro-differential equation resulting is too cumbersome to be solved either analytically or

numerically. Solution using a digital computer may be possible but is thought, at present, to be too time consuming. As an initial approximation Datwylers theory could again be extended to cater for the case of a two-dimensional

wing (flat plate) oscillating with its trailing edge touching the ground.

One of the main assumptions of two-dimensional theories is that of the wake lying in the plane of the wing. This may not, in fact be a valid assumption since, for the case of a wing at small, but noticeable incidence the trailing vortex sheet will initially leave the t r a i l i n g edge parallel to the wing, as is shown in the diagram below.

Lifting surface theories have so far not considered the case of wings with endplates, and in the ground effect cases the effect of sidewash due to the image wake system, for large gaps between the endplates and the ground, will naost certainly have to be taken into account.

However, it is not the intention to develope theories for all the afore-mentioned cases but to concentrate mainly on producing a valid finite wine theory for low heights above ground, and for the quasi-steady cases of r o l ^ and yaw,

11

-4 . 0 Review of experimental work

Almost all experimental work on GEW's has been for steady flow conditions utilising one of the following techniques for simulating the

ground:-(1) In the wind-tunnel: (a) image wing method (b) ground board (c) moving belt (2) Towing the model over water or ground

(3) Tethered flight in a circular path of a self propelled model. An appraisal of the advantages and disadvantages of the various techniques for ground simulation appear elsewhere ( e . g . Saunders Ref. 4 , Ashill Ref 1). The best representation of any real situation i s , of course, to reproduce it in an experimental facility and consequently the methods employing either a towed model or a self-propelled one should yield results directly applicable after a scale correction. Tonnies (Ref. 12) was amongst the first to use a towed model which was supported in front of a carriage running on a t r a c k . The track was on a ramp and the carriage was

propelled by a falling weight. One of the main difficulties in such a method is the recording of the forces and moments acting on the wing and as a result this method was not used again until C a r t e r (Ref. 6) towed a model wing over water, using a ship tank, and Lockheeds (Ref. 10) mounted their wing on a boom in front of a truck and ran it over salt flats. The results from the latter t e s t s a r e very unsatisfactory and Incomplete,

The image wing method h a s , however, yielded good results but the models require very careful alignment for t r u e geometric imaging in the wind-tunnel. This method has been used by Serebrisky and Biachuev (Ref. 13), Fink and Lastinger (Ref, 17), Lockheeds (Ref, 10) and AshiU (Ref. 2) for wings of finite span and Fink, Lastinger and Ashill also

investigated the effects of endplates and tip-bodies on lift and drag. Lockheeds investigated the quasi-steady derivatives in roll and yaw in addition to the

effects of trailing edge flaps and tandem wing configurations, Werle (Ref. 14) used a water tunnel to compare the various methods of ground sinaulation i . e . ground board, inaage wing, wake splitter plate and moving belt, for two-dimensional flow using a wing profile with and without edge blowing,

The advantage of using a small water tuimel to visualise the flow due to a given ground simulation technique lies in its ease of operation and economy, It is interesting to note that although C a r t e r , Fink and Lastinger used the sanae aerofoil section (Glenn Martin 22% thick) their results for the variation in lift coefficient with height above ground differed. This difference may be attributed to the t e s t s being done at different Reynolds numbers; the tunnel models having wing tip fairings; interference from the wind tunnel model struts and distortion of the water surface below the wing in the towed t e s t s ,

Full scale flight investigations into the effect of ground on aircraft

take-off and landing performance have been conducted since the early twenties. Reid (Ref. 15), Tonnies (Ref. 12), Wetmore & Turner (Ref. 16) and more recently Rolls' and Koenig (Ref. 17) have carried out t e s t s using full scale aircraft, the latter comparing their flight results with those obtained from a

wind tunnel model and from theory (Gersten Ref. 18). However, all these reports refer only to particular aircraft and apart from the general charact -e r i s t i c s of ground -eff-ect, th-e r-esults a r -e not univ-ersal.

The tethered model technique is a fairly recent one and so far has

only been applied to models of air cushion vehicles. Liiva (Ref. 19) describes the circular track built at the University of Toronto to investigate the dyn-amic responses of air cushion models by using a cine camera for flight path recording. Kurylowich (Ref. 20) used the same technique to obtain the aerodynamic derivatives of an air cushion vehicle. This method is the most attractive one for studying the stability of ground effect vehicles, once the effects of the retraining cable have been determined in that it allows the determination of model response to flying over a varying ground plane e . g . over a r a m p , step or wavy floor. Tinajero and F r e s h (Ref. 21) did in fact use such a method to study the response of a 7 foot air cushion vehicle weighing about 235 lbs, which was supplied with compressed a i r from an outside source and, was tethered so as to fly around a circular track of 40' mean diameter, with complete freedom to pitch and heave. Once again a cine-camera was used for recording the motion of the vehicle.

A few full scale tests on GEW's have been carried out in the past few y e a r s with a view to studying the stability of such a craft prior to manufacture. The Kawasalsi Aircraft Company of Japan and the Vehicle Research Corporation of America both built ram wings, the former company's machine known as the KAG-3 and the l a t t e r ' s the MARAD VRC-1. The KAG-3 was essentially a wing borne in the water by two floats which served as endplates. Wind tunnel t e s t s using a ground board, and over-water towing tests were conducted on a tenth full scale model to evaluate the performance and stability of such a craft. A summary of the results was presented by Ando in 1964 at the

Swansea Symposium. The full scale craft ran into both porpoising and rolling instabilities and it appears that not enough emphasis was put on the design of the endplate floats which were giving r i s e to large cross -flows and separated flows over the wing-float junctions. The VRC-1 was similar in basic configuration to the KAG-3 but was designed for overland operation initially. At the low Speed end it was essentially a hovercraft with edge blowing but at speed these jets were shut off and the craft became a GEW with endplates. Unfortunately no information regarding the flight t r i a l s of the VRC-1 a r e available and shortly after they began the project was cancelled.

Little experimental work appears to have been done for oscillating wings near the ground although the derivative % has been measured for a wing

oscillating between two parallel walls, for different distances between the walls, by Milne and Willox (Ref. 22). It should be noted that the wing was only

subjected to heaving oscillations.

The whirling a r m yields another method of ground simulation by allowing the model, attached at one end of the a r m , to move over a ground plane. This technique will be discussed m o r e fully in another r e p o r t .

13

4 . 1 Preliminary quasi-steady t e s t s of a wing in ground effect.

Tests were conducted in the No. 2 wind tunnel of the aerodynamic department using the image wing method to determine the bank and yaw derivatives of a wing in ground effect. Two identical wings of aspect ratio 2 . 5 , 30" span and symmetric RAE 101 section were used. This wing section although not ideally suited for a GEW was used in view of the preliminary nature of the t e s t s . Tunnel speed for all cases was 130 ft/sec corresponding to a Reynolds number, based on wing chord, of 0.825 x 10 . Corrections due to support strut interference were included in the final analysis of the r e s u l t s . Endplate configurations were not investigated.

4.2 Preliminary results

F i g s . 4(a), (b) and (c) show the variation of 1 , n and y with height

° V V V

above ground for three different angles of attack. The results for 1 and n from Lockheeds (1964) report have been included for a Clark Y aerofoil with flat endplates and aspect ratio 2 with endplate depth/chord ratio of 0 . 1 ,

Figs 5(a), (b) and (c) show the variation of 1,, n and y. with height Q 9 0 9

above ground for zero yaw and 2 incidence. The results obtained apply only to small angles of sideslip and bank (upto about 3°), In both the yaw and bank configurations strong c r o s s flows on the underwing surfaces were noticed by means of flow visualisation using paraffin and chalk and it is thought that these flows would affect the yawing moment and sideforce derivatives. In view of the symmetric aerofoil section used the results cannot be applied to a practical GEW, However, the effect of endplates in making 1 +ve is seen

in F i g 3(a). ^

4 . 3 Future wind turmel t e s t s

The image wing method using the Clark Y wings of Ashill (1966) will once again be used to determine the quasi-steady l a t e r a l derivates. The contributions to these derivatives from endplates and tip half-bodies will be investigated, A set of s t r u t s which allow the lower wing to be banked and moved along horizontally, in o r d e r to maintain a t r u e ground plane, have been manufactured. In the yaw cases the strut fairings remain at zero incidence to the flow thereby reducing interference on the wings. Tests a r e to commence shortly.

5.0 F r e e flight model of a GEW

A free flight model of a GEW has been constructed and can be seen in F i g s . 6(a), (b), (c) and (d). The aerofoil section is a d a r k Y 11% t / c and the wing is of R = 2, S = 4 i ft^ and c = 18". The endplates a r e of the same section as the main wing and a r e canted out at 2° relative to the line of flight. They a r e 2 " deep and have thin I 5 " diameter rubber wheels embedded in their bases so as to allow the model to run along the ground before lifting

off. The initial version of the model (Figs. 6(a) and (b)) weighed 4 lbs and was powered by a l ^ c c . F r o g diesel engine. The lightness of the model was achieved by using a novel form of manufacture. The main wing was made from expanded polystyrene foam, the aerofoil section being cut with a hot

1 "

wire, covered with — mahogany veneer bonded to it with a special adhesive. The endplates were made from solid balsa wood and covered with veneer. The engine pylon was made from plywood and balsa and the entire model was painted with polyurethane paint ensuring a water-fuel-proof and smooth surface. A rudder and flatplate tailplane and elevator were included for control

purposes.

Early flight t r i a l s indicated a severe nose up pitching instability as the model lifted off the ground. This was due to the rapid forward movement of the wing aerodynamic centre, as the wing height above ground increased, and also the rather aft e . g . position of the model, with the elevator being fixed.

Modifications to the model have included the installation of radio control equipment, tp operate the rudder and elevator, which has been embedded in a cut-out in the wing. The e . g . has been moved forward to about 0.4c from the wing leading edge and the all up weight is now nearing 6 lbs. It was anticipated that with adequate elevator control the model could be trimmed to fly at height/chord ratios between 0.14 to 0 . 3 .

F i g . 7 is an estimated plot for the quarter-chord pitching moments on the GEW model based on test results in Lockheeds (1964) wind-tunnel report. The model is expected to operate at lift coefficients between 0.6 and 0 . 8 .

However, tethered t e s t s in the wind-tunnel again showed up the pitching instability mentioned e a r l i e r , in spite of the use of the elevator, and it appeared that a tandem wing configuration may be the best solution. The model was modified accordingly and can be seen in F i g s . 6(c) and (d). A 3.21 c . c . glow plug engine with throttle control was fitted and tethered t e s t s in the wind-tunnel were repeated power on and power off. The configuration was found to be statically and dynamically stable except during the initial take-off period.

6.0 Conclusions

Although some of the physical principles involved in ground effect a r e fairly well understood there is still a large gap in the knowledge of this phenomenon particularly on the unsteady flow side. In addition the lifting surface equations in ground effect have as yet yielded no analytical solutions. Linearisation of the problem has resulted in numerical approaches which have yielded results fairly consistent with those obtained from wind-tunnel t e s t s . Ways for compensating for the limitations of linearisation have been suggested, such as allowing for wing thickness, and non-planer wakes, but have so far only been applied to specific wing planforms and steady flow. Existing experimental techniques need further development to cover the unsteady and quasi-steady flow cases before a practical realisation ( e . g . a GEW) m a t e r i a l i s e s .

15 REFERENCES 1. 2. 3. 1 0 . 1 1 , 12. 1 3 . 1 4 . 1 5 . ASHILL, P . R . ASHILL, P . R , ANDO, S. ANDO, MIGASHITA & TERAI SAUNDERS, G.H. WATKINS, WOOLSTON & CUNNINGHAM CARTER, A.

FINK & LASTINGER

de HALLER DATWYLER LOCKHEED BRYANT, L.W. & GATES, S . B . TONNIES, E . SEREBRISKY & BIACHUEV WERLE, H. REID, E . G . 1965 CoA Note 152. 196 7 Unpublished Ph.D t h e s i s .

An idealised ground effect wing - Ae, Qrtly F e b . 1966.

Summary of the model t e s t s for the simple ram wing KAG-3 - Swansea Sympos. July 1964. Aerodynamic characteristics of wings in ground proximity, MIT MSc Thesis, June 1963.

A systematic kernel function method for d e t e r -mining the aerodynamic forces on oscillating o r steady-finite wings at subsonic speeds,

NASA, TR R-48, 1959.

Effect of ground proximity on aerodynamic characteristics of Aspect Ratio 1 aerofoils with and without endplates - NASA TN D-970, Oct 1961. Aerodynamic c h a r a c t e r i s t i c s of low aspect ratio wings in close proximity to the ground

-NASA TN D-926, July 1961.

"La portance et la trainee induite minimum d'une aile au voisinage du sol" - ETH Zurich No. 4, 1936.

See NACA TM 828 "Ground effect - theory and practice" - E. Pistolesi.

Report 16906, Wind tunnel investigation of single and

tandem low aspect ratio wings in ground effect.March 1964. Nomenclature for stability coefficients - ARC

R & M 1801, 1937.

Effect of the ground on an airplane flying close to it, NACA TM 674, 1932.

Wind tunnel investigation of the horizontal motion of a wing near the ground - NACA TM-1095, Sept. 1946.

Simulation de 1'effect de sol au tunnel hydro-dynamique - La Recherche Aerospatial No. 95, July-Aug. 1963.

A full scale investigation of ground effect, NACA TR 265, 1927.

16, WETMORE & TURNER Determination of ground effect from tests of a glider in towed flight - NACA Report 645, 1940. 17. _{ROLLS & KOENIG} Flight measured ground effect on a low aspect

ratio Ogee wing including a comparison with wind-tunnel r e s u l t s , NASA TN D-3431, June 1966.

18. GERSTEN, K. Calculation of the aerodynamic characteristics of wings of finite span near the ground - RAE t r a n s . 1054, Dec. 1963.

19. LIIVA, J . A facility for dynamic testing of models of airborne vehicles with ground effect, UTIA TN 53, Oct, 1961,

20, KURYLOWICH, G, The lightline tethering technique for d e t e r m -ining the aerodynamic derivatives of an a i r cushion vehicle - UTIA Report 110, Sept. 1965. 2 1 . TINAJERO & FRESH Aerodynamic response of a 7 foot ground effect

machine flying over uneven surfaces

-DTMB Report 1436, Aero Report 982, June 1960. 22. MILNE & WILLOX Measurement of the derivative Zw for oscillating

lO

\

3

'"Ie

FIG.I. VARIATION OF Q . WITH ^c AND o< CLARK Y, ASPECT RATIO = 2 , V c = l 2 % FLAT ENDPLATES '*/c»^5(FROM LOCKHEED RPT I6906 FIG. 41.)

o ..< - 0 6 - 0 7 • " - 0 8 - 0 9 - l O \ \ / ,

7

>5

_{y /}

r

f

RG.2. VARIATION OF Cmc/ WITH *^/c AND «>*. CLARK Y, ASPECT RATIO » 2 , Vc =12%, FLAT END PLATES «'/c - 1 5 ( F R O M LOCKHEED RPT I6906 FIG. 4 l )

FIG.3(a) VARIATION OF GEW a.c. WITH ^Ic

I 2 O

FIG3(b) VARIATION OF •> CMG /^ (j^/c) WITH HEIGHT ABOVE

GROUND FOR A 2-DIMENSIONAL FLAT PLATE AEROFOIL. ^ o - O 4 0 5 r c o - • 0 2 5 + O S r \< FIG. 4 ( b ) . " . FROM LOCKHEEDS (1964) > ^ \ ^ / w i T H FLAT ENDPLATES 7^ SI-FIG. 4(c) . 6 ° / / / / f / A gt , -'° i 1

SIDESLIP DERIVATIVES FOR AN RAE lOI AEROFOIL ASPECT RATIO = 2-5 IN GROUND EFFECT (MOMENTS & FORCES

0 2 — I —

O*

—r—

(S

ho = HEIGHT ABOVE GROUND AT LX5WEST WINGTIP + 2 + I

'V A

BANK DERIVATIVES FOR AN RAE lOI AEROFOIL, ASPECT RATIO = 2-5, IN GROUND EFFECT ( M O M E N T S

& FORCES MEASURED ABOUT MID -SPAN TRAILING E D G E )

- O S •06 • 07 E O - 0 8 - 0 9 - lO - II s — . " ' ^ ^ ^ ^ W. 45 5

^<t^'

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FIG.7. PITCHING MOMENTS FOR A CLARK Y, ASPECT RATIO = 2, WING WITH FLAT-PLATE ENDPLATES

^

FIG. 6(b)

FIG.6 (c) MODIFIED TANDEM WING GEW MODEL.

1^

^ 1 ^

f

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