College of Aeronautics Report 8325 January 1984
A Technique for Optimising the Aerodynamic Design of a Generalised Combat Aircraft with Forward Swept Wings for
the purposes of Stability and Control Investigation by
M. V. Cook and
S. J. P. O'Riordan
TECHfJISC'- - OOL DELFT
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BIBLIOTHEEK
Kluyverweg 1 - DELFÏ
College of Aeronautics Cranfield Institute of Technology Cranfield, Bedford MK43 OAL, UK
Cranfield
College of Aeronautics Report 8325January 1984
A Technique for Optimising the Aerodynamic Design of a Generalised Combat Aircraft with Forward Swept Wings for
the purposes of Stability and Control Investigation by
M. V. Cook and
S. J. P. O'Riordan
College of Aeronautics Cranfield Institute of Technology Cranfield, Bedford MK43 OAL, UK
ISBN 0 902937 98 7 £7.50
"The views expressed herein are those of the authors alone and do not necessarily represent those of the Institute. "
List of Symbols
Summary PAGE 1. Introduction 1
2. Literature review 3 3. Design Philosophy 5 4. Airframe Optimization Technique 8
4.1. The airframe optimization program 8
4.2. Optimized airframe models 16 4.3. The derivative program 20
5. Stability Analysis 28 5.1. Solution of the equations of motion 28
5.2. Analogue simulation 32 5.3. Sunmary 33 6. Conclusions 34 7. Recommendations 34 8. References 35 APPENDICES
1. The longitudinal trim equations 37 2. The longitudinal stability derivatives 40
3. The lateral stability derivatives 51
4. The equations of motion 56 5. The analogue simulation
ACKNOWLEDGEMENTS
The study which is the subject of this report was initiated by MOD(PE) FS(F)3 RAE, Farnborough in response to a proposal by the College of Aeronautics under the terms of contract No. A81A/2078. This report is an interim statement on the f i r s t 12 months study in the research program.
The support and encouragement of the technical monitor, formerly Mr. G.F.Butler and currently Dr. A.J.Ross both of RAE Farnborough, is gratefully acknowledged.
ac
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ASW
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^Di
^Lc
^Lw
CR^T
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I XX^yy
^zx
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L
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Lr
Lv
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Wing section lift-surve slope Wing Aspect Ratio
Wing lift-curve slope Aft Swept Wing
Wing span
Mean aerodynamic chord of the wing Induced drag coefficient
Canard lift coefficient Wing lift coefficient Wing root chord
Thrust coefficient Weight Coefficient
Wing Chord as a function of semi-span Drag force of the aircraft
Aft datum/mass centre distance Aft datum/wing root distance Forward swept wing
Gravitational acceleration Rolling moment of inertia Pitching moment of inertia Roll/Yaw inertia cross coupling Yawing moment of inertia
Induced drag factor Rolling moment
Lift force of aircraft
rolling moment due to roll rate rolling moment due to yaw rate rolling moment due to sideslip
Non-dimensionless wing/canard separation Non-dimensionless canard/centroid separation Non-dimensionless wing/centroid separation Mach number
Aerodynamic Pitching moment Aircraft mass
M n N n
P Roll Rate (^®/9t) q Pitch Rate (^^at) q^ Dynamic Pressure r Yaw rate (^^/at)
'W3( gf)
^W3(%)
'Wa,
Yawing moment Normal load factor
S^ Canard area c S Wing area T Thrust t Time u x-velocity u u/V u x-acceleration UQ Initial x-velocity
V Aircraft mass centre velocity V y-velocity (sideslip velocity) V 'Never exceed' velocity of aircraft W Weight of the aircraft
w z velocity
w Initial z velocity
X x-Force x Centreline axis (longitudinal) AX Change in x-force
A C „ Change in x-force coefficient with a Xa
V Y-force y Spanwise axis through mass centre
r Dihedral angle
C Rudder angle
n Canard angle
e Pitch angle
A Sweep angle
Taper ratio
i^^^^)
5 Aileron angle
p Air density
o Wing/canard interference drag factor
a« canard induced drag factor
(j) Roll Angle
i|) Yaw angle
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SUMMARY
A technique has been developed for optimising the airframe for
aerodynamic performance of a generalised combat aircraft having a forward swept wing with close coupled canard. A computer program has been written for this purpose the output from which includes geometric and other parameters as required for stability and control studies. A second computer program has also been written to estimate the aerodynamic stability and control
derivatives of an optimised airframe. Two airframes have been investigated, one having a single engine the other having two engines.
An initial study has been made of the flying qualities problems arising from the configurations. An analogue simulation has been carried out which has highlighted some interesting problems resulting from the longitudinal static instability inherent in both configurations. (Preliminary interpret-ation of the lateral flying qualities indicates considerable instability but the sources and nature of the instability has yet to be satisfactorily determined. A trade-off between the requirement for minimum weight and the stability characteristics has also been undertaken.
INTRODUCTION
In high performance aircraft design the use of wing sweep has
long been recognised as a means for reducing drag at high speeds. Certainly, in terms of general aerodynamic performance there is little to choose between the use of a forward swept wing (F.S.W.) as opposed to an aft swept wing
(A.S.W.) However, as the F.S.W. is torsionally divergent the weight of such a wing with adequate torsional stiffness has been prohibitive so, the
A.S.W. has been preferred with its torsional stability and lighter structure. Recent advances in aircraft structures employing composite materials have made possible the use of a F.S.W. with an acceptably light weight structure of sufficient torsional stiffness. It is therefore not surprising that a great deal of interest is now being shown in the secondary aerodynamic advantages arising from the use of a F.S.W., particularly for combat aircraft where the relatively small benefits can far outweigh the cost of achieving them.
In general at high angles of attack the A.S.W. stalls progressively from the wing tip inboard whereas, the F.S.W. stalls progressively from the wing root outboard. Consequently, the F.S.W. remains aerodynamically effective at angles of attack beyond that of stall onset, particularly with respect to lateral control. This means that the F.S.W. can be simpler, it needs no wing fences or fixed leading edge droop and is thus generally more efficient than the A.S.W. Furthermore, a canard close coupled with the F.S.W. can be used to produce a flow field over the wing that will suppress the onset of stall hence, higher useable angles of attack and greater lift are available for manoeuvre performance enhancement.
It is therefore considered that if a F.S.W. with close coupled canard is integrated into the design of a combat aircraft then for a given design performance a lighter more manoeuvrable aircraft will result. It is
anticipated that such an aircraft would capitalise on the advantages
provided by the use of advanced flight control techniques to further enhance the aerodynamic performance. It is also suspected that the flying and
handling qualities of such an aircraft might differ from those of a more conventional aircraft, particularly the lateral flying qualities at high angles of attack.
2
-The study reported herein represents the first stage of a continuing research programme in which it is hoped to obtain an improved understanding of the flying and handling qualities of a generalised combat aircraft with a F.S.W; the proposed research programme is the subject of ref.l. By far the greater part of the work to date has been concerned with the definition of a realisable aircraft model against a notional performance specification. This has necessitated the acquisition of large amounts of information from
various sources which have been used in the design of a computer program for optimising the aerodynamic design of the airframe. The program iterates
the large number of design variables until the parameters defining the per-formance fall within specified limits. The program has led to the
geometric design of two reasonably practicable airframes, one with a single engine the other with two engines. As further information becomes
available so the fidelity of the aerodynamic modelling incorporated in the program is improved.
A start has been made on the analysis of the stability and control characteristics of the two airframes and much of the effort has been
directed towards the estimation of aerodynamic stability and control derivatives. In view of the relative complexity of the mathematical description of some
derivatives and the need to obtain precise values for many flight conditions, a program has been written for the purpose. Also, an analogue simulation of a simplified small perturbation model of the aircraft has been used for
preliminary investigations prior to the setting up of a digital simulation of the full non-linear aircraft model.
2. LITERATURE REVIEW
Before attempting any kind of investigation into the flying qualities of a combat aircraft with a F.S.W. it was obviously essential to define
a sensibly realisable airframe model in sufficient detail. Such a formidable task could not be contemplated in the context of the present study without reference to relevant source material. Having defined a notional performance criterion the information required included weight and volume distribution, engine performance data and substantial aerodynamic models for the
configurations adopted. To expedite the search for relevant information a computerised literature search was carried out at an early stage in the study.
Fortunately, a reasonably detailed design study of a combat aircraft with F.S.W. and a STOL capability had already been completed in the College of Aeronautics, ref.2. Although some important differences exist between the present airframe design, which is CTOL,and that of ref.2. sufficient
similarity has been retained by choosing the canard to be in line with the high wing so the numerical data was assumed to be a reasonable approximation for use in the present study. Generally, the basic aircraft layout was de-signed to comply with the most well researched areas of F.S.W. aerodynamics. Some of the more important sources of information used in formulating an airframe design concept are discussed below.
A thin supercritical wing having 45° of forward sweep was selected as its use was supported in sufficient detail by ref.3. Further information on the high angle of attack properties of a wing with 45° of forward sweep was obtained from ref.4. and information concerning the effect of aspect ratio variation from ref.5. Information on wing-canard interaction was obtained from ref.6. Unfortunately, many very useful sources contained in ref.7 were not available until sometime later in the study. Two particularly useful sources of material on the drag characteristics of canard-wing combinations were found in ref.8 and ref.9. The form of the data in ref.8 was particularly easy to assimilate in representing the canard-wing interference, both for airframe optimisation and derivative estimation.
4
-Structural information was taken almost exclusively from the College of Aeronautics Aircraft Design course notes, "Initial Project Design", ref.10. This source provided an empirical structural analysis of over one hundred recent aircraft types. Each aircraft is represented by a number of major sub-assemblies and the mass of each is expressed as a function of a number of variables. In some cases mathematical expressions of increasing complexity are available to suit the degree of accuracy required. In such cases, for example for the wing, the most complex expression was used bearing in mind the capabilities of the computer used and the limit on development time. Typical sub-assemblies included the wing, canard, forward fuselage and so on.
3. DESIGN PHILOSOPHY 3.1. General
The application of a F.S.W. to a generalised combat aircraft is not
in itself particularly beneficial unless the design emphasis is concentrated on the relatively limited advantages offered by such an airframe configuration. The most obvious advantages would appear to be the facility for post-stall manoeuvring, the increased lift to drag ratio and the increase in sustained turn rate, all of which could provide an aircraft with a decisive
advantage in an air combat situation. The improved aerodynamic efficiency of the aircraft with a F.S.W. implies a reduction in weight and a
corresponding reduction in required thrust which leads to an improved normal acceleration capability and consequently an improved sustained
turn rate performance. Continued roll control after the onset of stall permits manoeuvring in very high angle of attack regions of the flight envelope
without the drag penalty associated with more conventional aircraft. The design philosophy has therefore been to try to capitalise on these advantages by producing an airframe in which the above mentioned performance advantages are optimised.
3.2. Airframe and Engine
As mentioned elsewhere, the detail shape, size and aerodynamic performance of the airframe has been optimized with the aid of a computer program
developed for the purpose. The initial assumptions concerning the airframe layout follow current trends and were,
(i) high wing
(ii) close coupled canard (iii) single or twin fin
(iv) a notional engine based on the Rolls Royce RB199
In view of the variety of roles that such an aircraft might undertake it was difficult to decide whether the aircraft should be a small single engined
6
-model or a larger twin engined layout favouring the multi-role application. Consequently, in the interests of producing a broadly based study both airframes have been investigated in parallel. Also, the most demanding per-formance critera favoured the additional power of a twin engined layout.
It was considered reasonable to base the engine on the RB199 as any future U.K. combat aircraft would probably include that engine or a derivative of it.
In keeping with current trends, a thin super critical wing was chosen which would be expected to produce a good transonic acceleration
performance and a high cruise efficiency. The canard foreplane was des-igned such that the trim liftforce is positive for all flight conditions
in the interests of aerodynamic efficiency. Further, it was assumed that the aircraft would carry a realistic quantity of fuel internally and that the nose would house some sort of radar, space provision was thus designed in accordingly.
It was anticipated that the aircraft would carry external stores: fuel tanks. weapons, specialised equipment pods, etc. External .stores have not been
considered in this work other than to acknowledge the need for suitable hard mounting points, the effects of aerodynamic interference and the required ground clearance.
3.3. Performance
The research programme limits the present study to subsonic flight only with a view to extending the work into the supersonic flight envelope at a later date. It was discovered that of the aerodynamic data obtained from the references none was available for Mach numbers higher than 0.93 which, coincidently, was sufficient for the present study. However, it would have
been particularly short sighted to ignore the requirements for supersonic flight entirely in a study of an advanced aircraft of this type so, where relevant, consideration has been given to the requirements for high speed flight.
and is reasonably representative of present day performance expectations. Two design flight conditions DESl and DES2 are identified and the corresponding parametric design criteria have been used in the optimisation programme. The design point DESl calls for a 6g sustained turn at 0.6M at sea level and was chosen as the resulting aircraft would be directly comparable with the College of Aeronautics S-81 design project aircraft. Design point DES2
calls for a more ambitious performance, a 9g sustained turn at a speed determined by the use of the same gross wing area as produced by DESl. Most of the work to date has concentrated on the design flight condition DESl.
8
-4. AIRFRAME OPTIMIZATION TECHNIQUE
For the purposes of obtaining realistic and relevant stability and control data for a generalised combat aircraft with a F.S.W. a computer based technique has been devised which enables the airframe geometry to be optimized for aerodynamic performance. Having defined
an airframe in this way further analysis produces the required stability and control data. Clearly, as combat aircraft with a F.S.W. are a relatively recent departure in aircraft design so, the essential information is in short supply. Consequently, aerodynamic information in particular has been obtained from numerous sources and many assumptions have been made in its application in an attempt to define adequate models for the computer programs. Further, as new information has become available the programs
have been, and indeed continue to be developed in the search for improved accuracy and realism. Computational techniques have been used to implement the
optimization procedure as they facilitate rapid evaluation of the many possible design constraints and assumptions whilst permitting rapid modification
of the algorithms as new information becomes available. A more detailed discussion of the program can be found in Ref.18.
4.1. The Airframe Optimization Program 4.1.1. General Description
The program seeks to optimize the aerodynamic performance of the wing-canard combination whilst simultaneously optimizing the airframe geometry to meet a specified performance requirement. The structure of the program is such that various constraints and assumptions can be applied to define the optimization criteria.
The airframe is assumed to comprise a number of major sub-assemblies, shown for the single engined variant on Fig.4.1. The mass and C.G.location of each sub-assembly is determined by the program using the formulae of ref .10. The longitudinal moments of each sub-assembly about an aft datum are summed and the total moment sum is divided by the total mass to determine the mass centre of the aircraft. In its present form the program is not designed to
to produce a geometry with its C.G. at a pre-determined location or with defined static margins. However, sensible choice of initial design parameters can steer the outcome to a certain extent.
For the purpose of building up the aircraft geometry, the airframe is diivided into three modules, the rear fuselage and wing, the mid fuselage and canard and the forward fuselage. A description of the optimization procedure follows in the order in which it is executed.
4.1.1.1. Rear Fuselage and Wing
The mass optimization process starts by assuming that the engine which is a fixed component, occupies the aft most two metres of the fuselage. This defines the aft fuselage module of the aircraft. The point of intersection of the wing quarter chord line and fuselage longitudinal axis is determined by the operator as a design parameter.This point can be selected to facilitate the inclusion of some other feature for example, a specified canard size, the penalty being non-optimum mass. This facility is useful as a means for influencing the static margins which would otherwise be an arbitrary output of the program. The aerodynamic design of the wing closely follows that described in ref.3. and has 45° of forward sweep with a taper ratio of 0.4.
4.1.1.2. Mid Fuselage and Canard
The main role of the mid fuselage in the design process is to locate the canard at the correct distance ahead of the wing, it also provides the engine intake ducting and some internal volume for fuel. Its length, therefore is the main output variable in its design. The fuel mass and payload mass centroids are both assumed to be located 1.5 metres ahead of the engine
compressor intake face and are considered as part of the mid fuselage for the purposes of mass computation. However, the payload may comprise underwing stores and the fuel is assumed to be stored in internal wing tanks as well as in a centre fuselage tank.
The canard is fixed in position at the forward end of the mid fuselage
section the length of which, and hence the canard location, is defined initially such that its forward edge aligns with the wing tip quarter chord point to
aero 10 aero
-dynamic model based on that described in ref.6 is used to optimize the canard and wing mutual interference. The engine air intake ducting is also considered and the requirement to keep the intakes clear of the canard wake contributes to the
design of the mid fuselage. When the mid fuselage is adequately defined it is integrated with the rear fuselage and the whole is described by a rectangular tube having a cross section measuring 1 metre by 1 metre for the single engined variant and 1 metre by 2 metres for the twin engined variant.
4.1.1.3. Forward Fuselage
The forward fuselage is assumed to have an aerodynamically clean outline of relatively invariable shape and size being similar to that of contemporary combat aircraft, for example the F-14 or F-20. The length is fixed at 7.5 metres and it is attached to the mid fuselage section such that the pilot head rest position coincides with the forward edge of the mid fuselage. This leads to a split air intake geometry the detail design of which is beyond the scope of the present work.
4.1.1.4. Undercarriage
The nose wheel occupies a fixed location in the forward fuselage whilst the location of the main wheels in the aft fuselage is determined as being 1 metre aft of the final position of the aircraft C.G. This is intended to follow
conventional practice and to ensure adequate stability during the ground run. 4.1.2. Program - Structure
The program has been designed to obtain the minimum mass by seeking to optimize the geometry and aerodyhamic performance of the canard-wing combination simultaneously. This it continues to do iteratively until the output parameters fall within specified limits. The overall objective is to combine the advantages of forward sweep, wing section, wing location, canard location, engine thrust, aircraft mass and so on in the best possible way whilst producing a consistent aircraft design.
The program is structured in modular form and makes full use of a limited number of subroutines as shown by the flow chart on Fig.4.2. Each run of the
program commences with the input of the design point data comprising, flight condition information and initial guesses for the main design variables. The first iteration then proceeds to estimate the mass and mass distribution for this data and calculates an aircraft geometry to meet the design point
flight condition requirements. This produces a new mass estimate together with centroid and trim condition data which is then used as input data for the second iteration, this process is thus repeated until the design criteria are met. The subroutine modules used in the programme are described as follows.
(i) Subroutine "Wing"
This subroutine calculates the wing area necessary to produce sufficient lift at a specified value of C. to turn the aircraft mass at the design flight condition, for example 200m/sec at 6g. The effective aircraft mass is determined after allowing for canard lift. The subroutine then goes on to calculate
aspect ratio by taking into account the available engine thrust and the requirement to sustain the turn.
(ii) Subroutine "Centroid"
Having defined a wing geometry, this subroutine proceeds to calculate the mass of every aircraft sub-assembly based on the current geometric estimate. The moment of every sub assembly is calculated about an aft datum and the sum total moment is divided by the total mass to obtain a mass centroid location.
The dimensionless lengths referring the canard and wing to the centroid,! and 1 respectively are defined at this stage.
(iii) Subroutine "Canard"
Subroutine "centroid" then refers to subroutine "canard" which calculates the necessary canard area to trim the aircraft at four specified critical flight conditions whilst ensuring that the total lift coefficient never exceeds 0.35. The four critical flight conditions are:
1 1 2 3 4 Airspeed
1 Normal load factor Airspeed
Normal load factor Airspeed
Normal load factor Airspeed
Normal load factor
= 300m/sec = 0 = 300m/sec = 9 = V stall = 1 = 200 m/sec = 9
12
-(iv) Subroutine "Max"
This subroutine simply selects the maximum canard area as determined by the subroutine "canard". This canard area is then used in the subsequent computations.
On returning to the main program the wing area and aircraft mass are
compared with the specified values and if they do not agree to within 0.1% and 1 Kg respectively then the process is repeated until they do. When agreement is
reached the program outputs the current values of the design variables. 4.1.3. Input and Output Data
4.1.3.1. Input Data
Prior to running the program the operator must define the design flight condition which determines the limiting manoeuvre performance of the aircraft. Also, the operator must have a notional outline geometry to provide initial values of the critical design variables. These values together with a small number of critical aerodynamic parameters constrain the program to a
realisable airframe. Thus in order to evaluate the influence of the critical design variables on aircraft configuration, parameter sweeps can be carried out by running the program repeatedly for small changes in the parameters of
interest. The input data to the program can be divided into three groups as follows:
(i) Fixed parameters defining the design flight condition, these are shown in table 4.1 below;
TABLE 4.1 Parameter
Normal load factor Airspeed Payload mass Engine thrust Symbol
n
Vm
MJ
T
The payload mass would obviously be chosen to correspond with the notional airframe size. These parameters remain unchanged throughout the execution of the program.
(ii) Fixed parameters defining the baseline airframe configuration of interest, these are shown together with the values assumed in the present study in table 4.2 below;
Table 4.2 Parameter
Aft datum to wing root Jc distance Wing Sweep Angle
Maximum lift coefficient - Wing Maximum lift coefficient - Canard Zero lift pitching moment coefficient Zero lift drag coefficient
Induced drag factor
Pilot + associated systems mass
Symbol
Dw
'K
^L^max ^LciTiax^m
%K
MP • 1 Typical Value 1 Chosen to suit45° 1
0.9
0.9 1 ! -0.0375 0.0232 K/iT = 0.38 600 kgThese parameters have been determined from a consideration of the type of aircraft under investigation and within the limits of the
aerodynamic information available. Their values remain fixed throughout execution of the program. Of particular interest is the parameter D^^, this is included here rather than as a design variable in order to constrain the program to a realisable configuration.
(iii) The initial values of the principle design variables. These variables are adjusted during the course of running the program and their final values define the aircraft configuration. By defining the initial values the operator is able to steer the design process in the desired direction. The design variables together with some typical initial
14
-values used in the study are shown in table 4.3 below; Table 4.3
Design variable Canard mass
Wing Jc to centroid distance (dimensionless) Canard Jc to centroid distance (dimensionless) Rear fuselage mass
Wing area Canard area Wing span
Mean aerodynamic chord
Symbol Typical initial
value 1 175 kg 1 w 1 c 0.8 '• 3.05 ;
i
690 kg Sw 1 25 m^ 1 ' 7 i b 1 10 m 1 1 c 2 m 1 . 1 4.1.3.2. Output DataThe output data comprises the parameters shown in table 4.4 below;
Table 4.4 Output Design Parameter
* Wing area Canard area Over-all length
Canard L.E. to aft datum distance C.G. to aft datum distance
Total aircraft mass Aspect ratio
Wing span
Mean aerodynamic chord
Symbol \
h
DC
m
A
b
c
Additionally some sub-assembly mass data can be extracted from the program.
4.1.3.3. Design Example
Using the values of the fixed design parameters shown in table 4.2 and the values of the design variables shown in table 4.3 the program was run to produce design data for a single engine aircraft. Values assigned to the flight condition parameters for this example were as follows;
Normal load factor Airspeed
Payload mass Thrust
Wing root to aft datum distance
6 g 200 m/sec 4320 kg
48 KN 3.15 m
The output data obtained from the program defines what is considered to be a reasonably realistic aircraft configuration as follows;
Wing area Canard area Over-all length
Canard L.E. to aft datum distance C.G. to aft datum distance
Total aircraft mass Aspect ratio
Wing span
Mean aerodynamic chord
20.18 m^ 1.67 m^ I 13.11 m ; 8.11 m '. t 4.85 m j 8090 kg j
4.88 1
9.92 m 2.034 m1
16
-4.2. Optimized Airframe Models
The optimization program has been used to refine the design of two airframe models, one having a single engine the other having two. Both have been designed to meet DES 1 shown on the flight envelope, fig. 3.1. Referring to fig. 3.1. it will be seen that the design point conditions are;
altitude - sea level normal load factor - 6 g
airspeed - 200 m/sec
The absolute limits assumed were a normal load factor of 7 g and a never exceed speed (Vne) corresponding to a Mach number of 0.9. Choosing to work at 6 g normal load factor allows for a 15% structural safety factor which was assumed to be implicit in the structure data base. The chosen Vne corresponds with the available aerodynamic data, particularly for the wing.
In order to produce an airframe layout from the program output data, refer to table 4.4. in section 4.1.32, it is necessary to take into
consideration the outline design objectives in the interpretation of a design. 4.2.1. Single Engine Variant
A summary of the optimized design data and weight analysis data is shown on table 4.5 This design data has been interpreted to produce a 3-view drawing of the aircraft shown on fig. 4.3. and the result would appear to be reasonably credible.
4.2.2. Twin Engine Variant
A summary of the optimized design data and weight analysis data is shown on table 4.6. The 3-view layout drawing of the aircraft interpreted from this data summary is shown on fig. 4.4. and again, the result would appear to be reasonably credible.
To illustrate the capability of the design optimization program and its relative usefulness an analysis has been made of the output from a number of runs of the program in which the critical design parameter Dw was varied. In the first instance its influence on the minimum total mass
Table 4.5 Single Engined Aircraft GEOMETRIC DESIGN DATA
Quantity Wing Area
Canard Area Overall length
Centroid - Aft Datum Length Aspect Ratio
Span
Mean Aerodynamic Chord Taper Ratio (Wing)
Value 20.18m 1.67m^ 13.11m 4. 84m 4.88 9.92m 2.03m 0.4 T (213.15 ft ) (17.64 ft^) (42.61 ft) (15.73 ft) (32.24 ft) (6.60 ft)
1
Powerplant Description:A single developed RB199 - 22000 lbs (10000 kg) thrust with full reheat - estimated 11000 lbs (5000 kg)military power.
Design Flight Condition
At full dry thrust. Mach No. 0.6 at sea level, the aircraft must be capable of a 6g turn with 3850kg (8470 lbs) of fuel/payload.
Combat ThrustAeight ratio (max) = 1 . 2 4
Weight Analysis: Component Wing Fuselage Fin Canard Main Undercarriage Mass (Kg) 889 1130 26 26 192 Total Structure 2263 Engine 1100 Total Powerplant 1100 Total Systems 878 Basic Equipped Mass 4230
All Up Mass 8090 % A.U.M. 10.99 13.97 0.32 0.32 2.37 27.97 13.60 13.60 10.85 52.29 100.00
- 18
-^ ^-^
Table 4.6 Twin Engined Aircraft GEOMETRIC DESIGN DATA
Quantity Wing Area
Canard Area Overall length
Centroid - Aft Datum Length Aspect Ratio
Span
Mean Aerodynamic Chord Taper Ratio (wing)
Value 25.95m^ 5.56m^ 12.78m 4 . 46m 4.21 10.46m 2.48m 0.4 (274.010 ft^) (58.73 ft^) (41.54 ft) (14.50 ft) (34.00 ft) (8.06 ft) Powerplant Description:
2 X Standard RB199 engines. 16000 lbs (7273 kg) thrust with full reheat - 8000 lbs (3637 kg) thrust military_power. Design Flight Condition
With 5% reheat at Mach = 0 . 6 , sea-level, the aircraft must be capable of a 6g turn with 5555 kg (12221 lbs) of fuel/payload
Combat Thrust/Weight ratio (max) = 1.32 Weight Analysis: Component Wing Fuselage Fins Canard Main Undercarriage Total Structure Engines Total Powerplant Total Systems Basic Equipped All Up Mass Mass (Kg) 1186 1104 79 79 216 2664 1820 1820 940 5424 10979 % A.U.M. 10.80 10.06 0. 72 0.72 1.9 7 24.26 16.58 16.58 8.56 49.40 100.00
of the airframe was investigated and is summarised on fig. 4.5. It is quite clear that this particular geometric parameter has a significant influence and one may conclude that care in the longitudinal positioning of the wing can lead to considerable advantages. Further, the influence of the same parameter on airframe longitudinal stability was investigated and the findings are shown on fig. 4.6. Here the variation in the moment arm of the wing lift referred to the C.G., reduced to a dimensionless parameter, is shown as a function of D . And again it is quite clear that the distance of the wing quarter chord point to the aft datum is an
important parameter in the design optimization process.
4.2.3. Comments on the design
With reference to the stall boundary on fig. 3.1. this defines the flight condition for onset of wing stall. As the aircraft is capable of being flown and controlled at angles of attack well beyond that at which stall commences the boundary may be regarded as separating linear aerodynamic flight conditions from the non-linear. It is interesting to note that the difference between the normal load factor at DES 1 and the
implied maximum value as determined by the wing stall curve can be accounted for by the canard lift. As the canard serves to unload the wing a little so the effective region of linear aerodynamics of the flight envelope is enlarged or, alternatively, the speed at which stall commences is reduced.
In order to produce an airframe more in keeping with current military requirements an airframe optimization will be carried out for design point DES 2 on fig. 3.1. This point calls for a 9 g sustained turn and initial investigations indicate that the 9 g airframe will be of similar dimensions to the present designs. It has already been established that the present 6 g airframe designs both have sufficient thrust to maintain a 9 g sustained turn. A further tendency is that the higher normal load factor design will have an aspect ratio of around 3.5 rather than the present value of 4.5 which agrees well with the findings of ref. 5 .
20
-4.3. The Derivative Program
4.3.1. General Description
The input information for the derivative program is obtained from the output of the airframe optimization program from which it proceeds to compute values for the longitudinal static trim condition, the longitudinal aerodynamic stability and control derivatives and the lateral aerodynamic stability derivatives. The program was initially developed to provide
longitudinal stability data only and more recently the algorithms to produce lateral stability data have been added. Although the program is running satisfactorily it is still yery much subject to further development.
In general terms the estimation of aerodynamic stability derivatives and, in particular the lateral derivatives is difficult. In this instance the problems are further compounded as little existing information applies to aircraft with F.S.W. and extension or interpretation of existing data to meet this case is notoriously risky. Consequently, until very much more experience has been gained of the stability characteristics of aircraft with a F.S.W. then the output should be accepted with some caution. 4.3.2. Program Structure
The program structure is particularly simple as shown by the flow chart on fig. 4.7. The program is modular in structure making use of subroutines throughout.
Input to the program is the geometric data output by the optimization program and airspeed and total mass to define the flight condition, sea level flight being assumed throughout. The values of trim angle of attack, elevator angle and thrust to trim are then calculated iteratively using the algorithm described in Appendix 1. Two substantial subroutines are then called in turn, the first to calculate the longitudinal derivatives and the second to calculate the lateral derivatives.
(i) Longitudinal Derivatives Subroutine
Expressions for the longitudinal stability derivatives were derived from first principles and are fully described in Appendix 1. This was thought essential in view of the drag characteristic due to the canard-wing
mutual interference, not normally encountered with a conventional aircraft layout. At present the computations apply to the linear aerodynamic flight regime only. Also, the subroutine computes the
"elevator" control derivatives and the coefficients of the longitudinal characteristic quartic applicable to a linearised small perturbation model.
(ii) Lateral Derivatives Subroutine
This subroutine has not been developed to the same extent as that for computing the longitudinal derivatives and could undoubtedly benefit from a more detailed evaluation of the derivative expressions. The expressions for the lateral stability derivatives were derived from the ESDU data sheets with amendments to make allowances for the F.S.W.; the expressions are fully described in Appendix 3. Again the present
derivative expressions are applicable to the linear flight regime only. This subroutine does not, as yet, calculate the lateral control derivatives although it does compute the coefficients of the lateral stability
quintic as applicable to a linearised small perturbation model.
4.3.3. Computational Algorithms 4.3.3.1. Longitudinal
As stated above the expressions for the longitudinal derivatives, described in Appendix 2, were developed from first principles. This was done as no flight or wind tunnel test data was to hand for a complete F.S.W. aircraft. This approach ensured that the aerodynamic differences arising from a wing-canard configuration were accounted for and
that the sign convention was consistent throughout.
In the computation of the longitudinal force derivatives the parameter 3Cjj/9oi, the drag variation with incidence, is important. However, for a conventional aircraft it is usually approximated by the variation of the wing induced drag with incidence only. Clearly, this would be inadequate for the present application and a more comprehensive expression has been developed to take into account the changes in total aircraft induced drag and the changes in mutual wing-canard interference effects with incidence. As can be seen by reference to Appendix 2, the
22
-expressions for the force derivatives are more complex than usual but are still, yery much, functions of aircraft geometry,
Estimation of the force-rotary and moment-rotary derivatives was made more difficult by a total lack of any reference applicable to aircraft with forward sweep wings in which some of the wing area is ahead of the pitch axis and some aft of the same axis. Therefore, a simple strip analysis was used to produce integrable expressions of a single variable. The results are considered to be valid for the linear flight regime and do account for the tapering wing and its flow
separation characteristics. Obviously, more relevant information will be applied to the aerodynamic models should it become available at a later date.
4.3.3.2. Lateral
Whilst the effect of a F.S.W. on aircraft shape is quite dramatic its influence on lateral flying qualities will probably be less so. However, the stability characteristics of an aircraft with F.S.W. will undoubtedly be different especially in the longitudinal context. One might be tempted to assume that the effects on lateral stability
characteristics will be less different in order to justify a relatively simple approach to lateral derivative estimation. Indeed, this approach was adopted in the first instance simply because of the need to obtain
some derivative data and the total lack of relevant information. The estimation procedure of the ESDU data sheets was used throughout with the appropriate assumptions and amendments applied as necessary. Some of the more necessary deviations are detailed in Appendix 3 along with
expressions for all the lateral derivatives, brief explanations of the more significant observations follow.
It was considered that roll and yaw rate effects would give rise to force and moment damping derivatives in much the same way as in a
conventional aircraft. Thus, the case for amending the ESDU data was not very well founded. However, a brief comparative consideration of the pressure distributions on an A.S.W. and a F.S.W, were made for both the rolling situation, fig. 4,8 and the yawing situation, fig, 4.9. This leads one to suspect that N might be smaller for a F.S.W. as the tip forces tend to oppose the leading edge forces whereas, the values of L , L and N
possible area of inaccuracy concerns the calculation of L where the sweep angle of the quarter chord line of the wing ( A j is reduced to Ag, the effective sweep angle. To apply this to the F.S.W. it has been assumed that this adjustment is an isobaric effect which changes the sweep angle from -45° to -33°. However, in the ESDU data sheets example calculation the sweep angle for an A.S.W. is increased rather than
decreased. Some uncertainty thus exists in the validity of this derivative.
The sideslip dependent derivatives were calculated by assuming the effects of wing sweep to be simply reversed. This would appear to
apply reasonably to the derivatives L and N only as the derivative Y is very largely dependent on body-fin considerations only; Y was therefore calculated as determined by the data sheet without substantial amendments.
It is quite clear that the lateral stability derivatives produced by the program should therefore be considered very carefully as their validity must be suspect until such time as more appropriate data becomes available.
4,3.4. Input and Output Data 4.3.4.1. Input Data
The input data for the derivative program comprises, quite simply, the design data output by the optimization program, which is contained in table 4.4, and the airspeed and total mass appropriate to the flight
condition of interest. It should be noted that information for calculating the various moments of inertia of the aircraft as required by the program for computing the coefficients of the characteristic equations are not
input. At present inertia values are written into the program and are approximations based on the values for similar contemporary aircraft whose inertias are known. This is a temporary expedient until such time as a more satisfactory method for predicting inertia values can be written into the program.
24
-4.3.4.2. Output Data
The output data comprises the numerical values for the parameters shown in table 4.5 below;
TABLE 4.5. Output Parameter
Trim incidence angle Trim elevator angle Thrust coefficient Trim thrust
Dry power setting
Longitudinal stability quartic
Longitudinal stability derivatives
Longitudinal elevator control derivatives
Lateral stability quintic normalised coefficients Symbol a
n
C T
j
T
% A B C D E \ \ \ a b c d e ContinuedContinued
Lateral stability derivatives
•
Lateral aileron and rudder control derivatives
Y
r,
\
Note that at present the program outputs zero for the lateral control derivatives as the relevant algorithms have not yet been implemented,
4.3,5, Design Example
The derivative program was run for the same single engined aircraft design example as described in section 4,1,3.3, at the same flight condition. The input data used comprised the output data of the optimization program example with the addition of the parameters tabulated below.
Total Aircraft Mass Flight Speed C.G, to Canard ^c, 1 C.G. to Wing lc, 1^ 8090 kg 200 m/sec .1,605 -0,02
26
-It should be noted that dimensionless lengths 1^ and 1,^ were obtained from the optimization program although they are not specified in its output data at the present time. These parameters will be included in the direct output of the optimization program at the next coding review.
The data output by the derivative program for the above input data was as follows,
._
Trim incidence Trim elevator angle Thrust coefficient Trim Thrust
Dry power setting
3,57 deg 5,01 deg 0,025 12478,5 N 25,44% ' Longitudinal Stability Quartic coefficients A = 1, B = -1,015, c -0,194, D = 8.541, E = -0,144 ^u = ^w = ^q = X = n •0.051 -0.264 -2,41 x 10' 0,725 IZ. w -0,377 -2.792 3.870 x 10"^ -11,832 M^ = 0,031 \ = 0.382 M = -0,0104 M =19,027 Lateral Stability Quintic coefficients a = 1, b = 13,509, c -196,207, d = -752,824, e = -232,832 \ -II I I \
-
h--0.488 -0.041 0,134 0 0 ^y-Lo = Lr = ' ,-
h--6.091 x 10"^ -0.091 0.028 0 0 \ \-
h--0,020 -0.016 -0.058 0 0Note that the stability derivatives are dimensionless and are defined in accordance with the notation of Appendix 4. Also, as the program is still in development a satisfactory method for computing some of the derivatives still has to be found. Thus, there is no guarantee that the computed derivative values are reasonable.
As a further example of the relative usefulness of the program, it was run for the same aircraft example at a variety of flight speeds. The canard 'elevator' trim angle as a function of aircraft incidence is shown on fig. 4.10 and the derived canard angle of attack as a function of indicated airspeed is plotted on fig. 4.11. Information for the latter graph was obviously obtained after some manipulation of the basic trim data output by the derivative program.
28 -5. STABILITY AND ANALYSIS
A preliminary analysis of the stability and control characteristics of the single engine aircraft variant has been undertaken. The analysis has
obviously been limited to small perturbation studies only which have produced some interesting observations from which some significant lessons have been learned. The analysis has been limited to running the airframe optimization program and the derivative program on a Commodore micro-computer for various flight conditions. The small perturbation equations of motion have been solved and the interpretation of the characteristic modes of motion has been aided by a simulation using the VIDAC 1224 analogue hybrid computer.
5.1. Solution of the Equations of Motion.
Using the optimized single engine aircraft variant data described in section 4.2 the derivative program was run for a range of flight conditions covering the speed envelope from stall to just below sonic velocity at sea level con-ditions. For this exercise a notional total airframe mass of 8500Kg was assumed. Output data from the program for the flight conditions selected is contained in table 5.1. and includes trim data as well as the dimensionless stability derivatives which are referred to wind axes throughout.
The steady state trim values for body incidence a^ and canard angle n are plotted as functions of airspeed on Fig.5.1 and Fig.5.2. respectively. The curve shapes are probably not too unconventional although the range of trim
values in both cases is tending to become quite large. The proper interpretation of a trim curve for a very unstable airframe as in this case is probably
questionable in any event, the significant quantity would more likely be the control power necessary to maintain trim in an active system context.
5.1.1. Longitudinal Stability.
Solution of the longitudinal characteristic equation produces a pair of complex roots in each case which fairly obviously define a phugoid mode. The short period pitching mode is non-oscillatory and is represented by two real roots, both of short time constant one of which is unstable. This is not entirely surprising as the static stability of the aircraft is considerably relaxed such that the static and manoeuvre margins are negative. A summary of the mode characteristics is contained in table 5.2.
TABLE 5.1.
FLIGHT CONDITION
SUMMARY OF STABILITY AND CONTROL DATA ENGINE VARIANT AT SEA LEVEL.
1 1
TRIM DATA (A.U.M. . V (m/s) «0 (deg) \ r i m C L LONGITUDINAL Xu Xw Xq Zu Zw Zq Mu Mw Mq LONGITUDINAL X ri Z n M n 1 = 8500Kg) 85 20.41 -12.04 0.93 2 100 14.78 -6.34 0.68 AERODYNAMIC DERIVATIVES -0.8210 0.0715 -0.0053 -1.8414 -3.1174 0.3321 0 0.3821 -1.6155 -0.4344 0.2044 -0.0039 -1.3506 -2.9241 0.3321 ' 0 0.3821 ; -1.3732 CONTROL DERIVATIVES -0.0643 -0.2069 0.3321 -0.-469 -0.2069 0.3321 LATERAL AERODYNAMIC DERIVATIVES
Yv Yp Yr
Lv
Lp Lr Nv Np Nr i J -0.4880 -0.2315 0.1374 0.1605 -0.0751 0.0827 -0.0163 -0.0891 -0.0993 -0.4880 -0.1676 0.1375 0.1041 -0.0761 0.0647 -0.0162 -0.0645 -0.0805 3 150 6.34 ' 2.2 0.30 ;—,_ -0.0835 0.1749 -0.0017 -0.6150 -2.7486 , 0.3321 ' 0 0.3821 -0.9154 1 ; -0.0207 ; -0.2069 '[ 0.3321 ' -0.4880 • -0.0719 0.1352 0.0210 -0.0815 0.0368 -0.0186 -0.0277 !-0.0616 FOR SINGLE 1 1 1 4 200 3.34 5.24 0.17 -0.0247 0.0982 -0.0009 -0.3533 -2.7193 0.3321 0 0.3821 -0.6866 . -0.0113 -0.2-69 0.3321 -0.4880 -0.0379 0.1336 -0.0083 -0.0912 0.0267 -0.0201 -0;0146 -0.0577 1 5 250 1.94 6.65 0.11 -0.0092 0.0508 -0.0006 -0.2317 -2.7115 , 0.3321 : 0 0.3821 -0.5493 , -0.0070 -0.2069 0.3321 -0.4880 ' -0.0221 -0.1328 -0.0219 -0.1112 ' 0.0220 -0.0210 -0.0085 -0.0563 6 300 1.19 7.42 0.08 -0.0040 0.0219 -0.0004 -0.1657 j -2.7089 0.3321 0 0.3821 -0.4577 -0.0047 -0.2069 0.3321 -0.4880 -0.0135 0.1323 -0.0292 -0.1742 0.0195 -0.0214 -0.0052 -0.055730
-TABLE 5.2.
r
SUMMARY OF LONGITUDINAL STABILITY MODE CHARACTERISTICS FOR SINGLE ENGINE VARIANT.
i FLIGHT i CASE Speed (m/sec) Phugoid Oscillatory mode (rad/sec) Non osc-illatory mode T,(sec) '2(sec) 85 0.17 0.32 0.47 -0.70 100 0.14 0.24 0.41 •0.58 150 0.10 0.10 0.28 -0.37 200 0.07 0.05 -•- + • 0.21 , -0.28 250 0.06 0.03 0.17 -0.22 300 0.05 0.02 0.14 -0.18 .,-. -L. -5.1.2. Lateral Stability.
The solution of the lateral characteristic equation produces roots the
interpretation of which is somewhat more difficult. A summary of the stability mode characteristics is contained in Table 5.3. below.
TABLE 5.3.
SUMMARY OF LATERAL STABILITY MODE CHARACTERISTICS FOR SINGLE ENGINE VARIANT.
FLIGHT CASE 1 Speed m/sec) 85 Oscillatory Mode (Ü (rad/sec) 1.86 C 0.51 Unstable ^1 ' Mode (sec) -2 100 1.72 ; 1.39 I 0.56 : 0.89 ! f. i '• J — : ; i—:— Stable '2 Mode (sec) -Unstable 3 ^ , i Mode (sec) -0.90 -0.95 -0.86 -30.30' -30.86 i -51.71 Stable '4 . : mode (sec) 12.35 ' 14.35 '; 55.55 1.096 i 0.87 0.84
The oscillatory mode would appear to be a well damped low frequency
dutch roll which collapses to two real roots with time constants T. and Tp for the higher speed flight cases. Given that Nv is negative it is difficult to see how a stable mode could develop in any event. Also, the change from oscillatory to non-oscillatory characteristics occurs when the sign of Lv changes from positive to negative, which further confounds the observation. In reality one might expect the reverse situation to be more appropriate as, at higher speeds when the incidence is lower, the fin would be more effective as the immersion in wing root wake would be reduced. However, the ESDU data sheets are unlikely to allow for this rather specialised effect.
Similarly, observation of the remaining time constants, T^ and T^, indicates the presence of a lightly damped mode and a heavily damped mode which
would normally be the spiral and roll modes respectively. For the three higher speed cases the signs and magnitude would appear to be reasonable bearing tn mind that Lv is negative. However, for the lower speed
cases the situation is puzzling, Lv is positive indicating that even more so than usual the spiral mode time constant should be negative. Also, the time constant of the roll mode is given approximately by (-Lp/Ix) which suggests the roll mode to be always stable with a time constant around one second. Clearly, when Lv is positive the stability analysis results are difficult to interpret.
32 -5.2. Analogue Simulation
An attempt was made to gain a better insight into the nature of the stability characteristics of the aircraft by simulating the small
perturbation equation of motion on a VIDAC 1224 analogue-hybrid computer. Owing to the very unstable airframe and the preliminary nature of this
investigation results of very limited general use only were obtained. The simulation model used is described in appendix 5.
5.2.1. Longitudinal Characteristics
Reference to Table 5.2. confirms the aircraft to be very unstable for all flight cases. Consequently, meaningful observations of the stability characteristics were very difficult to obtain. By choosing suitably enlarged scaling factors the observation time was extended but, even so the divergent characteristics could only be observed for about a second which was
sufficient only to confirm the divergent mode time constant.
In order to establish that the oscillatory mode was in fact a phugoid a feedback loop was added to the model to stabilize the unstable
mode. Vertical velocity feedback (incidence) to elevator was used and the loop gain was increased arbitrarily until the model became stable. This was easily achieved,the model then demonstrating the classical short period and phugoid modes. A recording of the response to elevator is shown on fig.5.3. for flight case 4. The damped short period oscillation is evident when the elevator displacement is applied and removed. It is interesting to note that the feedback gain required to achieve minimum short period mode stability is of the order of 35 deg/deg in terms of incidence feedback to elevator.
It was therefore concluded that the longitudinal stability characteristics of the basic airframe demonstrate a normal phugoid mode and two exponential modes one of which is divergent. The latter characteristic is consistent with an airframe with a negative static margin.
5.2.2. Lateral Characteristics
It was not possible to reach a satisfactory conclusion on the nature of the lateral modes in the limited time available. This was largely due to the high level of instability of the airframe and the uncertainty associated with the lateral derivative estimates. Attempts to identify the modes
indicated by the roots of the lateral characteristic equation shown in table 5.3. were not very successful. Reasonable correlation between the
divergent response time constant and the time constant of the most unstable mode was obtained. However, attempts at a reduced response with one or more degrees of freedom suppressed were inconclusive. A
proper understanding of the lateral characteristics therefore requires a more searching investigation starting with the stability derivatives. 5.3. Summary
The airframe investigated conforms to a configuration having 45° of forward sweep and a close coupled canard,these two constraints corresponding well with the available sources of information. Particular advantages are
that such a configuration is reasonably well supported with existing aero-dynamic data and a wing has been constructed using composite material technology and is thus proven feasible. The airframe optimisation program does allow for a S% wing weight penalty, the estimated increase for a
composite material wing. With this kind of approach to the airframe design a reasonably acceptable configuration has been produced.
Estimation of the stability derivatives has been a difficult problem and will certainly require a lot more attention in any continuing studies.
Hovjever, the longitudinal stability derivative estimates would appear to be reasonable although more detailed estimates should make allowance for
thrust effects. The lateral stability derivatives, on the other hand, have proven very difficult to estimate with any confidence. A great deal of further work is required to achieve an acceptable set of lateral stability derivatives. It is fairly evident that adaptation of the ESDU data sheets to provide derivative estimates!for a FSW aircraft is not a satisfactory direction in which to proceed.
Solution of the small perturbation longitudinal equations of motion produces stability modes which are readily explained and conform with the static instability of the basic airframe. Further, artifical stabilisation of the airframe would appear to pose few problems. Unfortunately, solution of the lateral small perturbation equations of motion produces stability modes which are distinctly non-standard and hence difficult to explain. The problem
undoubtedly lies with the estimation of the lateral stability derivatives which must be improved before further progress may be made.
34
-6. CONCLUSIONS
(i) By means of the computer based design technique described it is possible to produce a realistic FSW combat aircraft configuration optimised for
aerodynamic performance over a subsonic flight envelope.
(ii) In all cases the optimum configuration possesses longitudinal static instab-ility but of a degree which is compatible with current technology.
(iii) Airframe configurations possessing relaxed longitudinal static stability inevitably lead to significant reduction in airframe weight.
(iv) The use of a FSW can lead to aerodynamical ly efficient airframe con-figurations without compromising on performance or weight.
(v) Relatively low canard loads to trim are required thereby ensuring a good margin for the demands of the automatic flight control system.
(vi) The longitudinal stability derivatives can be estimated with a fair degree of confidence and the stability characteristics of the airframe are normal and consistent with the degree of static instability.
(viii) The lateral stability derivatives cannot be satisfactorily estimated by the means described and consequently the lateral stability analysis of the airframe was inconclusive.
7. RECOMMENDATIONS
(i) The airframe optimization program should be modified to include
longitudinal static margin computations which may be used as a design constraint. The program might also usefully include dihedral and fin size computations
leading to optimized values of the derivatives Lv and Nv.
(ii) Longitudinal stability derivative computations should continue to be developed and should include the effects of thrust.
(iii) Lateral stability derivative estimation procedures need reviewing completely before any real progress can be made on lateral stability analysis. Of
necessity, this work must depend on the increasing availability of published material.
8. REFERENCES
1. Cook, M.V. "A proposal for a study of the dynamics, stability and control of combat aircraft with forward swept wings." College of Aeronautics Proposal, Cranfield, February, 1982.
2. Jayakoda, D. "Design of a supersonic forward swept wing combat aircraft using a Pegasus type engine." College of Aeronautics, Cranfield.
M.Sc thesis, Vol.1 September, 1982.
3. Sims, K.L. "An aerodynamic investigation of a forward swept wing." M.Sc Thesis, Air Force Inst, of Tech., Wright-Patterson AFB., Ohio, December, 1977.
4. McCormack, G.M. and Cook, W.L. "A study of stall phenomena on a 45° swept forward wing." NACA TN 1797.
5. Savage, P.W. Experimental analysis of the effects of sweep and aspect ratio, on incompressible flow about forward swept wings." MSc Thesis, Air Force Inst, of Techu, Wright-Patterson AFB, Ohio, December, 1981. 6. Marshall, S.B. and Knott, M.J. "An investigation into wing-canard
interaction for a model with forward swept wings." University of Bristol, B.Sc thesis, 1981.
7. "International Conference on forward swept wing aircraft". Bristol University, March, 1982.
8. Kroo, I.M. "Minimum induced drag of canard configurations" AIAA paper 82-4217, Vol.19, No.9, May, 1982.
9. Butler, G.F. "Effect of downwash on the induced drag of canard-wing combinations." AIAA paper 82-4111.
10. Howe, D. and Fielding, J.P. "Initial Project Design." Course notes, College of Aeronautics, Cranfield.
36
-11. Spacht, 6. "The forward swept wing - a unique design challenge." AIAA paper, 80-1885, 1980.
12. Sherrer, V.C. Hertz, T.J. and Shirk, M.H. "Wind tunnel demonstration of aeroelastic tailoring applied to forward swept wings." AIAA 80-0796 800000 in: Structures, Structural Dynamics and Materials Conf. Seattle, Washington. May, 1980.
13. Boyden, R.P. "Subsonic roll damping of a model with swept back and swept forward wings." NASA TM-78677. March, 1978.
14. Huffman, J.K. and Fox, C.H. "Subsonic longitudinal and lateral-directional static aerodynamic characteristics for a model with swept back and swept forward wings." NASA TM-74093, February, 1978.
15. Weeks, T.M. Uhuad, G.C., and Large, R. "A wing tunnel investigation of the aerodynamic characteristics of forward swept wings."
Air Force Wright Aeronautical Labs., Flight Dyn.Lab. Wright-Patterson AFB., Ohio, 45433.
16. Data Sheets. Aerodynamics Vols. 1 - 5 Engineering Sciences Data Unit,London. 17. Babister, A.W. "Aircraft dynamic stability and response." Pergamon, 1980.
18. O'Riordan, S.J.P. "The automated design optimisation of a forward swept wing fighter for stability studies." Cranfield Report CoA 8402 January, 1984.
