Development of a Flight Dynamics Model of a Flying Wing Configuration

Master thesis in Aeronautical Engineering

Development of a Flight Dynamics Model of a Flying Wing Conﬁguration

Candidate Supervisor Jacopo Tonti Prof. Guido De Matteis

External supervisor Prof. Arthur Rizzi (Kungliga Tekniska högskolan)

Academic Year 2013/2014

cbn 2014 by Jacopo Tonti

Some rights reserved. This thesis is available under a Creative Commons CC BY-NC-3.0 IT License. (creativecommons.org/licenses/by-nc/3.0/it/)

Alla mia musa , a Vale

«As ailerons, these damn spoilers make great rudders!»

Bruce Miller, after flying the Marske Pioneer 1A

Abstract

The subject of UCAV design is an important topic nowadays and many countries have their own programmes. An international group, under the initiative of the NATO RTO AVT-201 Task group, titled “Extended Assessment of Reliable Stability & Control Pre- diction Methods for NATO Air Vehicles”, is currently performing intensive analysis on a generic UCAV configuration, named SACCON. In this thesis the stability and control characteristics of the SACCON are investigated, with the purpose of carrying out a comprehensive assessment of the flying qualities of the design. The study included the generation of the complete aerodynamic database of the aircraft, on the basis of the experimental data measured during TN2514 and TN2540 campaigns at DNW-NWB low speed wind tunnel. Moreover, system identification techniques were adopted for the extraction of dynamic derivatives from the time histories of forced oscillation runs. The trim of the aircraft was evaluated across the points of a reasonable test envelope, so as to define a set of plausible operative conditions, representing the reference conditions for subsequent linearization of the dynamic model. The study provided a thorough description of the stability and control characteristics and flying qualities of the unaugmented SACCON, laying the groundwork for future improvement and validation of the configuration in the next design stages.

Keywords: Aerodynamic Modelization, System Identiﬁcation, Stability & Control, Linear Dynamics, Flying Qualities, Flying Wing, UCAV, SACCON.

Table of Contents

Contents i

List of Figuresv

List of Tables ix

Nomenclature and Symbols xi Frames of reference...... xi Notations ...... xii

1 Introduction1 1.1 Background of the NATO RTO program...... 2 1.2 Problem description ...... 4 1.3 Objective and methodology ...... 5 1.4 Thesis outline...... 7

2 Literature review9 2.1 Historical perspective...... 9 2.1.1 Modern stealth UCAVs...... 14 2.2 An overview on ﬂight mechanics analysis...... 15 2.2.1 Static stability ...... 15 2.2.2 Dynamic stability...... 18 2.2.3 Flying and handling qualities...... 20 2.2.3.1 Cooper-Harper rating scale...... 20 2.2.3.2 MIL-HDBK-1797A...... 22 2.2.3.3 CAP criterion ...... 27 2.3 Flying wing design issues ...... 28 2.3.1 Longitudinal issues...... 29 2.3.2 Lateral-directional issues...... 30

3 Aerodynamic database 33 3.1 Foreword ...... 33 3.2 Wind tunnel campaigns ...... 35

i TABLE OF CONTENTS

3.2.1 Wind tunnel model...... 35 3.2.2 Experimental setup...... 37 3.2.3 Tests and results...... 38 3.3 Database generation ...... 42 3.3.1 Database format ...... 45 3.3.2 Static data processing ...... 47 3.3.3 Dynamic data processing ...... 49 3.4 Aerodynamic analysis ...... 50 3.4.1 Baseline...... 51 3.4.2 Dynamic behavior ...... 53 3.4.3 Control authority...... 56

4 Static analysis 63 4.1 Flight envelope deﬁnition ...... 64 4.1.1 Airspeed limitations ...... 65 4.1.2 Altitude limitations ...... 66 4.1.3 CG limitations ...... 66 4.2 Longitudinal static stability...... 68 4.3 Trim assessment ...... 70 4.4 Limitations ...... 79

5 Dynamic analysis 81 5.1 Aerodynamic identification...... 81 5.2 Dynamic modes...... 87 5.2.1 Longitudinal dynamics...... 88 5.2.2 Lateral-directional dynamics...... 95 5.3 Flying qualities assessment ...... 106 5.3.1 Longitudinal flying qualities...... 108 5.3.1.1 Short period ...... 108 5.3.1.2 Phugoid...... 110 5.3.2 Lateral-directional flying qualities...... 112 5.3.2.1 Roll subsidence...... 112 5.3.2.2 Dutch roll...... 113 5.3.2.3 Spiral...... 114 5.3.3 Control dynamics...... 115 5.3.3.1 Response to step elevator...... 115 5.3.3.2 Response to step aileron...... 116 5.3.3.3 Response to step rudder...... 118 5.4 Chapter summary ...... 120 ii TABLE OF CONTENTS

6 Concluding remarks 123 6.1 Conclusions...... 123 6.2 Further research ...... 127

Appendices 131

A SACCON conﬁguration 131 A.1 General description...... 131 A.2 Mass and inertia properties ...... 132 A.3 Geometric properties...... 133

B Theoretical basis and deﬁnitions 135 B.1 Physical model ...... 135 B.1.1 Assumptions ...... 135 B.1.2 Coordinate systems and transformations ...... 136 B.1.3 Mathematical relations...... 138 B.2 Conventions and customs ...... 140 B.2.1 Control sign convention and deﬁnitions ...... 140 B.2.2 Aerodynamic parameters convention ...... 142 B.2.3 Propulsion system customs ...... 143 B.2.4 Mass and geometry...... 143

C Linearized Model 145

D XML database structure 151 D.1 Overview ...... 151 D.1.1 Fundamental table structure...... 151 D.2 Database structure...... 152 D.2.1 Aerodynamics...... 153 D.2.2 Geometry and mass ...... 157 D.2.3 Propulsion...... 158 D.2.4 Flight control system...... 159

Bibliography 163

iii

List of Figures

2.1 Nature’s noteworthy flying wing designs...... 9 2.2 The Penaud and Gauchot “Amphibian” - 1876 [46]...... 10 2.3 Dunne’s D.8 flying wing biplane - 1912 [52]...... 11 2.4 Chyeranovskii BICh-17 experimental fighter - 1934...... 12 2.5 The Horten Vc - 1941...... 12 2.6 The Northrop-Grumman B-2 “Spirit” - 1989...... 13 2.7 Modern stealth flying wing UCAV designs...... 14 2.8 Pitching moment curves (fixed elevator) [2]...... 16 2.9 Conventional wing-tail arrangement [2]...... 17 2.10 Dynamic response of a statically stable aircraft [52]...... 18 2.11 Cooper-Harper rating scale [52]...... 21 2.12 MCH-UVD diagnosis tool [33]...... 22 2.13 CAP requirements for Category B flight phase [35]...... 28 2.14 Northrop N-1M...... 31 2.15 The drag rudder deployed on the wing tip of the Northrop N-9M...... 32

3.1 Planform and geometric parameters of the DLR-F17SACCON [16]...... 36 3.2 The DLR-F17/SACCON in the DLR-NWB with yaw link support [47]. . . . 37 3.3 Lateral coefficients of the DLR-F17 versus α at different β [15]...... 41 3.4 Influence of sting mounting on longitudinal coefficients (Body axes) [38]. . . 42 3.5 The frame of reference convention adopted in TN 2514 and TN 2540 [20]. . . 43 3.6 Baseline drag and lift coefficients versus α, varying β...... 51 3.7 Baseline pitching moment coefficient versus α, varying β...... 52 3.8 Baseline lateral-directional coefficients (Body frame) versus β, varying α. . . 53 3.9 1-cycle average of lift driven by pitch oscillations [20]...... 54 3.10 1-cycle average of pitching moment driven by pitch oscillations [20]...... 54 3.11 1-cycle average of lateral coefficients driven by 1 Hz roll oscillations [20]. . . 55 3.12 1-cycle average of lateral coefficients driven by yaw oscillations...... 55 3.13 Elevator contribution to lift...... 57 3.14 Elevator contribution to pitching moment...... 58 3.15 Total lift and pitching moment with elevator...... 58 3.16 Rolling and yawing moments induced by the ailerons...... 59

v LIST OF FIGURES

3.17 Rolling and yawing moments induced by the drag rudders...... 60 3.18 LCDP...... 62

3.19 Cnβ DYN...... 62

4.1 The analysis envelope of the SACCON...... 67 4.2 Limit locations of the CG of the SACCON (in red the ARP)...... 67 4.3 Variation in static margin with CG position and angle of attack...... 69 4.4 Variation of static margin with CG position and velocity...... 70 4.5 Flow chart diagram of the double variable iteration procedure...... 72 4.6 Variation of angle of attack to trim with CG location...... 74 4.7 Variation of elevator to trim with CG location...... 75 4.8 Map of angle of attack to trim versus altitude and CG location...... 76 4.9 Map of elevator to trim versus altitude and CG location...... 76 4.10 Sketch of forces acting on an airplane in horizontal level ﬂight...... 77 4.11 Variation of required thrust with CG location...... 78 4.12 Variation of aerodynamic eﬃciency with CG location...... 79

5.1 Comparison of the longitudinal combined dynamic derivatives calculated with the two linear methods for 1 Hz oscillations...... 85 5.2 Roll motion combined dynamic derivatives...... 86 5.3 Yaw motion combined dynamic derivatives...... 86 5.4 Short period root locus varying airspeed and static margin at sea level. . . . 89 5.5 Phugoid root locus varying airspeed and static margin at sea level...... 90

5.6 Phugoid normalized shape at U8 “ 150 m/s and h “ 0 m for K » ´5%. . . 91 5.7 Third mode root locus varying airspeed at h “ 0 m (K » 0%)...... 92

5.8 Third mode normalized shape at U8 “ 70 m/s and h “ 0 m for K » 0%. . . 92 5.9 Short period root locus at h “ 12 000 m...... 93 5.10 Phugoid root locus at h “ 12 000 m...... 94

5.11 Tumbling normalized shape at U8 “ 100 m/s and h “ 0 m for K » ´5%. . . 95 5.12 Dutch roll root locus varying airspeed and static margin at sea level. . . . . 96 5.13 Dutch roll normalized shape in diﬀerent ﬂight phases for K » ´5%. . . . . 97

5.14 Dutch roll shape approaching coalescence at U8 “ 200 m/s for K » ´5%. . 98 5.15 Variation of lateral-directional derivatives with airspeed at sea level. . . . . 99 1 5.16 Variation of yaw damping derivative Nr with airspeed at sea level...... 100 5.17 Variation of dutch roll and spiral poles with airspeed at sea level (K » ´5%).100 5.18 Variation of spiral pole location with airspeed and SM at sea level...... 101 5.19 Variation of spiral pole location with airspeed and SM at h “ 12, 000 m. . . 102 5.20 Variation of dynamic stability parameters with airspeed at sea level. . . . . 104

5.21 Dutch roll root locus varying altitude and static margin at U8 “ 200 m/s. . 105 5.22 Analysis envelope with prescribed ﬂight phases...... 107 vi LIST OF FIGURES

5.23 Short period degree assessment...... 108 5.24 Short period frequency variation with airspeed and CG position...... 109 5.25 CAP assessment for short period characteristics...... 110 5.26 Phugoid degree assessment...... 111 5.27 Phugoid frequency variation with airspeed and CG position...... 111 5.28 Roll subsidence degree assessment...... 112 5.29 Dutch roll level assessment at sea level (Category A)...... 113 5.30 Spiral divergence degree assessment...... 114 5.31 Longitudinal response to step elevator at sea level...... 115 5.32 Longitudinal response to step elevator at 12 000 m...... 116 5.33 Variation of roll rate response to step aileron with airspeed (K » ´5%). . . 117 5.34 Variation of roll angle response to step aileron with airspeed (K » ´5%). . 118 5.35 Variation of sideslip angle response to step aileron with airspeed (K » ´5%).118 5.36 Lateral-directional response to step rudder in diﬀerent ﬂight conditions. . . 119

A.1 Designed arrangement of the control surfaces of the SACCON [37]...... 131 A.2 Wing airfoils of the SACCON UCAV conﬁguration [16]...... 133 A.3 Radius distribution and relative thickness of the SACCON conﬁguration. [16].134

B.1 Attitude angles and positive direction of velocities...... 136 B.2 Wind axes arrangement and positive signs of α and β...... 137 B.3 Positive deﬂection of fundamental control surfaces...... 140 B.4 Relative arrangement of Geometry (blue) and Body (black) frames...... 143

D.1 Comprehensive view of the structure of the input ﬁle...... 153

vii

List of Tables

2.1 Definition of handling quality levels in MIL-HDBK-1797A [35]...... 23 2.2 Definition of flight phase categories in MIL-HDBK-1797A [35]...... 24 2.3 Short period requirements in MIL-HDBK-1797A [35]...... 24 2.4 Phugoid requirements in MIL-HDBK-1797A [35]...... 25 2.5 Roll subsidence requirements in MIL-HDBK-1797A [35]...... 25 2.6 Spiral requirements in MIL-HDBK-1797A [35]...... 26 2.7 Dutch roll requirements in MIL-HDBK-1797A [35]...... 26

3.1 Prospect of control deﬂection combinations tested during TN 2514 and TN 2540 at DNW-NWB (OB and SP are mutually exclusive)...... 39 3.2 Prospect of forced oscillation tests of TN 2514 and TN 2540 at DNW-NWB. 40 3.3 Template of a generic spreadsheet with three states...... 46 3.4 Control authority of the SACCON at α “ 50 and β “ 00 (in 1/rad)...... 60

4.1 Summary of SACCON stability and trim issues...... 80

5.1 Spiral eigenvector variation due to dutch roll collapse at sea level (K » ´5%).103

5.2 Lateral departure eigenvector at sea level and U8 “ 250 m/s for K » ´5%. 104 5.3 MIL-HDBK-1797A aileron response requirements for Class II aircrafts. . . . 117

A.1 Mass and inertia properties of the SACCON...... 132 A.2 Geometric properties of the SACCON...... 133

Nomenclature and Symbols

Frames of reference

NOTE Body frame is chosen as default frame of reference. Thus, for the sake of clarity, the superscript for all quantities expressed in that coordinate system will be omitted.

Frame Tag Deﬁnition [1,5] O: at sea level on the vertical of the aircraft initial position x: pointing North, tangent to meridians Fixed Vertical E y: pointing East, tangent to parallels z: pointing to the center of the Earth

O: aircraft center of gravity x: pointing North, tangent to meridians Local Vertical V y: pointing East, tangent to parallels z: pointing to the center of the Earth

O: aircraft center of gravity x: in the direction of velocity relative to air Wind W z: in the aircraft plane of symmetry, pointing toward its belly y: consequently, on the right

O: aircraft center of gravity x: in the direction of the projection of velocity relative to air on Stability S the plane of symmetry z: in the aircraft plane of symmetry, pointing toward its belly y: consequently, on the right

O: aircraft center of gravity x: along fuselage reference line, pointing toward the nose Body B z: in the aircraft plane of symmetry, pointing toward its belly y: consequently, on the right

O: foremost point of the aircraft fuselage x: parallel to fuselage reference line, pointing toward the tail Geometry G z: in the aircraft plane of symmetry, pointing towards its topside y: consequently, on the right

xi NOMENCLATURE AND SYMBOLS

Notations

NOTE Vectors are denoted by an under line; matrices by bold symbols; tensors by a double arrow; time derivatives by a dot pq9 ; space derivatives by a prime pq1, dimensionless quantities by a hat pqˆ . Names of variables and parameters used in the present document and within the simulator are, in general, the combination of a symbol and a subscript. The frame of reference to which a variable is referred is speciﬁed (if applicable) as superscript tag. Some symbols and acronyms may be used as subscripts.

Symbol Tag Description Unit A “ b2{S - Aspect ratio - B B Engine gyroscopic moment N ¨ m C C Aerodynamic coeﬃcient - D D Drag N

E “ CL{CD E Aerodynamic eﬃciency - F F Force vector N F - Aerodynamic force vector N G - Linear momentum kg ¨ m{s H - Angular momentum kg ¨ m2{s I I Element of the inertia tensor kg ¨ m2

K “ kn ´ k - Longitudinal static margin (Body frame) - L L Lift N L - Rolling moment (never used as subscript) N ¨ m

M8 Mach Free stream Mach number - M M Moment vector N ¨ m M - Pitching moment (never used as subscript) N ¨ m M - Aerodynamic moment vector N ¨ m N - Yawing moment (never used as subscript) N ¨ m P P Power W Q Q Engine torque kg ¨ m S S Surface m2 T T Thrust N T BA T_BA Rotation matrix from frame A to frame B -

U8 TAS Free stream velocity (true airspeed) m/s W W Weight N X, Y , Z X, Y, Z Aerodynamic force components N

a A Acceleration m{s2

a8 a Free stream speed of sound m/s b b Span m xii NOMENCLATURE AND SYMBOLS

c c Chord m f - Frequency Hz g g Gravitational acceleration m{s2 h alt Altitude m k - Distance in ratio of reference chord - m m Mass kg n n Load factor -

p8 pres Free stream air pressure Pa p, q, r p, q, r Roll, pitch, yaw rates rad/s 1 2 q8 “ 2 ρ8U8 qd Free stream dynamic pressure Pa t t Time s v v Velocity vector m/s u, v, w u, v, w Velocity components m/s x x Position vector m x, y, z x, y, z Position components m/s

Θ8 temp Free stream temperature K Λ - Sweep angle deg Ξ euler Attitude angles vector deg Ω Omega Engine nominal rpm 1/s

α alpha Angle of attack deg β beta Angle of sideslip deg γ gamma Flight path angle deg δ d Control surface deﬂection angle deg

ζv zeta_v Engine vertical incidence deg ζh zeta_h Engine horizontal incidence deg ϑ theta Pitch angle deg

κ “ πfx{U8 - Reduced frequency (x is a reference length) - λ “ ctip{croot - Taper ratio - 2 ρ8 rho Free stream air density kg{m ϕ phi Roll angle deg ψ psi Yaw angle deg ω omega Angular velocity vector rad/s

Subscript Tag Description 0 0 Initial or equilibrium condition a a Aileron air air Airbrake asym asym Asymmetric deﬂection

xiii NOMENCLATURE AND SYMBOLS

c c Canard eng eng Engine e e Elevator glob glob Global in in Inboard l l Rolling moment ldg ldg Landing gear lef lef Leading edge flap m m Pitching moment n n Yawing moment out out Outboard port (LX) port (LX) Port (left side) r r Rudder ref ref Reference root root Root of the aerodynamic surface spl spl Deceleron (split surface) spo spo Spoiler star (RX) star (RX) Starboard (right side) sym sym Symmetric deflection t t Throttle tef tef Trailing edge flap tip tip Tip of the aerodynamic surface x, y, z x, y, z x, y, z axis

Acronym Tag Description AC AC Aerodynamic center (1/4 root chord in general) ARP ARP Aerodynamic reference point CG CG Center of gravity CP CP Center of pressure DoF - Degrees of freedom ERP ERP Engine reference point FCS FCS Flight Control System LE - Leading edge mac - Mean aerodynamic chord NP - Neutral point SM - Static margin SPO - Short period oscillation S&C - Stability and Control TAS TAS True airspeed TE - Trailing edge

xiv

Chapter 1

Introduction

The flying wing design is a very attractive configuration due to the aerodynamic performance advantages it offers over its conventional counterpart, primarily higher aerodynamic and structural efficiency. However, the omission of horizontal and vertical stabilizers leads to even severe stability and control authority issues. Further difficulties arise from the problem of fitting the pilot, engines, flight equipment, and payload all within the depth of the wing section. Moreover, due to the practical need for a thick wing, the flying wing concept is relegated in the slow-to-medium speed range. These compromises are difficult to reconcile and efforts to do so can reduce or even negate the expected advantages of the flying wing design, such as reductions in weight and drag. These reasons contributed to tie to tailless designs the reputation of being impracticable and notoriously difficult to control. As a consequence, no flying wing aircraft has ever been designed and flown successfully for the civil aerospace sector, where the technical advantages associated with such a configuration are easily outweighed by the requirements on safety and degradation in handling qualities. Not even the military sector, with its relaxed aviation regulation requirements, along with the advent of fly-by-wire control systems, ever considered the flying wing configuration appealing and feasible at first glance, since its flaws seem to easily match or overcome its strengths. However the flying wing, despite the disadvantages inherent in its design, gained re- newed interest, due to its potentially low radar reflection cross-section. In fact, stealth technology relies, among other features, on the presence of flat surfaces that coherently reflect radar waves only in certain directions, thus making the aircraft hard to detect unless the radar receiver is at a specific position relative to the aircraft. Hence, the flying wing proves to be a successful design whenever stealth requirements become a prominent con- cern, especially since the introduction of modern fly-by-wire flight control system (FCS) allowed to mitigate the stability and control deficiencies affecting the design. Nevertheless, of the few attempts made to build a military flying wing aircraft (especially by the Horten Brothers and Northrop Corporation [45]), only one survived premature cancellation and entered mass production: the Northrop B-2.

1 1. Introduction 1.1: Background of the NATO RTO program

During the last decade, the ever more widespread development of increasingly advanced unmanned combat air vehicles (UCAV) has definitely boosted the interest of the aerospace community on flying wind design. The massive use of state-of-the-art flight control systems, along with the lack of issues related to the presence of crew onboard, has allowed for less conventional configuration to be adopted with much more confidence, by exploiting their full potential, while alleviating their flaws.

1.1 Background of the NATO RTO program

The ability to accurately predict both static and dynamic stability characteristics of air vehicles using computational fluid dynamics (CFD) methods could revolutionize the vehicle design process for air vehicles. A validated CFD capability would significantly reduce the number of ground tests required to verify vehicle concepts and, in general, could eliminate costly vehicle “repair” campaigns required to fix performance anomalies that were not adequately predicted prior to full-scale vehicle development. As a result, significant reductions in acquisition cost, schedule, and risk could be realized. Historically, many military aircraft development programs have encountered critical stability and control (S&C) deficiencies during early stages of flight test or worse still in service, despite thousands of hours of wind tunnel testing. These surprises have occurred across the speed range from takeoff and landing to cruise flight, and particularly at the fringes of the operating envelope, where separated and vortical flows dominate [14]. The dramatic increase in computing power and the affordability of PC clusters now make it feasible to undertake time-accurate high-fidelity CFD simulations. Current capabilities of CFD to predict static and dynamic stability of aircrafts were assigned an overall Technology Readiness Level (TRL) of 4. For such a reason, it has been widely believed within the research community that the next significant improvement in the state-of-the-art for predicting the S&C characteristics of a new vehicle might be through the application of CFD tools. In particular, the application of high-end CFD codes with a Reynolds- avereged Navier-Stokes (RANS) or a better level of technology to specific areas of S&C interest before first flight can help focus the wind tunnel program and provide improved understanding of the underlying flow physics. When S&C parameters are determined by wind tunnel or CFD methods, the basic principle is to determine forces and moments on an aircraft when it is undergoing oscillations in pitch, roll or yaw. While S&C problems most commonly occur near the margins of the flight envelope, the computational solution of S&C for even steady flight conditions can be demanding. Fortunately, a critical mass of international researches has been assembled to address this challenge through the North Atlantic Treaty Organization (NATO) Research and Technology Organization (RTO).

2 1.1: Background of the NATO RTO program 1. Introduction

In 2007, a 3-year international collaboration was initiated through the NATO1 RTO Applied Vehicle Technology AVT-161 titled “Assessment of Stability and Control Predic- tion Methods for NATO Air and Sea Vehicles”. The aim of the task group was to investigate the applicability of current CFD tools for predicting S&C characteristics of air and sea vehicles. The specific objectives were to 1) assess the state-of-the-art in computational fluid dynamics methods for the prediction of static and dynamic stability and control characteristics of military vehicles in the air and sea domains; 2) identify shortcomings of current methods and identify areas requiring further development, including aspects of computational uncertainty [17]. Improvements to the prediction capability (specifically in the ability of turbulence models to predict flow separation around blunt surfaces) were suggested by AVT-161 and are being carried forward by AVT-183 (2010-2014). In addition, AVT-161 has led to a specialists meeting task group, namely AVT-189, where the results and progress of AVT-161 will be evaluated by experts external to AVT-161. The success of AVT-161, and the input and identification of potential new partners from AVT-189, has motivated the establishment of the AVT-201 task group in 2012 (scheduled to end in 2015), with the desire to pursue and extend the efforts of AVT-161 in using CFD methods to predict S&C characteristics of aircrafts [14]. The target configuration conceived and intensively studied by the RTO team is a generic UCAV geometry called “Stability And Control CONfiguration”, or simply SACCON. The design consists of a highly swept lambda wing with a planform primarily devised to meet marked stealth requirements and later adjusted to improve its aerodynamic performances. The detailed description of the aircraft is presented in AppendixA. The main objective of the ongoing AVT-201 is to determine an overall strategy for cre- ating S&C databases for vehicle simulation at full-scale conditions, including the deflection of control surfaces, throughout the operational envelope of the vehicle. The investigations carried out have the purpose to assess the usefulness of engineering methods not only as an analysis tool during the early aircraft design, but also as a design tool to improve the shape definition of the vehicle, in order to achieve better performance [21]. The topics to be covered in the pursue of the main objective are summarized below [14].

• Perform additional in-depth correlation studies, using the detailed ﬂow ﬁeld measurements obtained by AVT-161 to enhance understanding of discrepancies between predicted and experimental dynamic derivatives.

• Carry out further wind tunnel testing to extend the dynamic data set to include multiple frequency and amplitude maneuvers, in order to obtain, where possible, full-scale test data for a maneuvering vehicle, that can be used for validation of the

1In addition to the participating NATO members, Sweden (FOI) and Australia (DSTO) were also invited to join the task group.

3 1. Introduction 1.2: Problem description

methods and capabilities that are being developed.

• Design, build and test modified S&C wind tunnel model with trailing-edge control surfaces, to evaluate the ability to predict control effectiveness, stability characteristics, and other flight dynamics characteristics of the configuration with controls deflected.

• Investigate techniques for generating ﬂight simulation models from CFD predictions, that is build S&C databases from experimental and CFD data to determine level of accuracy and sensitivity of ﬂight simulation using CFD when compared with experimental data model.

• International collaboration, speciﬁcally the concept of “virtual laboratory”, as pio- neered by AVT-113, and used to great eﬀect in AVT-161.

The key benefits expected from the research are the reduction of project risk and design cycle time and, hence, of sub-scale testing, manpower and financial resources; as well as an enhanced understanding and prediction capabilities of aircraft characteristics before fabrication, leading to an early identification and explanation of unexpected behavior, through the medium of reliable flight simulation [14].

1.2 Problem description

The challenges faced by the task group of the RTO program when designing and testing the SACCON conﬁguration are manifold, but they can be roughly summarized as follows.

1) Optimization of the planform for attainment of both stealth requirements and adequate aerodynamic performance.

2) Execution of two parallel campaigns of wind tunnel experiments and computational studies carried out with several CFD tools.

3) Understanding of the extensive non-linear behavior of the vortical ﬂow ﬁeld generated by the highly swept wing at a wide range of angles of attack and sideslip, in order to improve the accuracy of numerical modelization.

4) Understanding of the particular nuances of each distinct CFD grid and ﬂow solver, before broad application of the tools in this class of problems.

5) Generation of two complete aerodynamic databases, one with experimental (wind tunnel) data and the other with CFD data, to be used to “ﬂy” the aircraft in a simulator.

6) Evaluation and analysis of S&C characteristics, based on both databases, in order to assess the reliability of CFD predictions as a design tool since early design stages.

4 1.3: Objective and methodology 1. Introduction

Points 1), 3) and 4) have been extensively treated as part of the research of AVT-161. Wind tunnel tests and CFD computations, point 2), were carried out in several rounds during both AVT-161, where several leading edge and surface treatments were tested, and AVT-201, where control deflection and engine flow effects were measured. This thesis work focused on the issues represented by points 5) and 6), that is the generation of a complete aerodynamic database of SACCON and the subsequent evaluation of its S&C characteristics, limited to the data provided by wind tunnel campaigns of AVT-201.

1.3 Objective and methodology

The main objective of the thesis work was to use the experimental data provided by wind tunnel tests, carried out at DNW-NWB facility as part of the AVT-201 research schedule, to perform a complete analysis of the stability and control characteristics and flying qualities of the SACCON aircraft, a lambda wing flying wing design, whose detailed description is provided in AppendixA. The results thus obtained will serve as reference for future validation of S&C characteristics prediction based on CFD estimations, ultimately, to assess the reliability of CFD methods as design, as well as analysis, tools. In the context of providing exhaustive results about S&C characteristics of the SACCON aircraft, the underlying principles were to develop a robust and general algorithm to perform the calculations and to define a convenient format for the aerodynamic database to be processed. The latter to be adopted when generating the database from the CFD data, so as to facilitate data correlation and validation. The work methodology adopted to achieve the target set was analytical and can be broken down into the following aspects.

• As a first step, it was defined a structure for the aircraft database suitable for fast S&C analysis. This includes, (i) the choice of the file format and of (ii) the structure of the tables (multidimensional or spreadsheet), (iii) the identification and implementation of all parameters necessary for the S&C algorithm. Particular regard was used in the setup of the aerodynamic portion of the database, in order to facilitate processing without comprising data readability.

• Then all available wind tunnel results were aggregated into a single complete aerodynamic database of the SACCON. This database was then consolidated with geometry and mass, propulsion and ﬂight control system data, which were integrated in a fashion similar to that of the aerodynamic portion. Without any information about mass distribution of the SACCON (neither wind tunnel model, nor full-scale), these parameters were deducted by comparison to a comparable aircraft [29].

• The next phase involved the analysis of the aerodynamic data collected in the database of the aircraft, with the purpose of (i) identifying the range of linear aerody-

5 1. Introduction 1.3: Objective and methodology

namic behavior, expected to prevail at least during the cruise and loiter segments of the mission profile of the UCAV [21]; (ii) examining the aerodynamic characteristics beyond the condition of departure of the linear behavior, dominated by nonlinear flow effects. Moreover, during this stage the data were manipulated in order to isolate the contributions of control surfaces for a preliminary assessment of their effectiveness on the aircraft forces and moments.

• Next logical step was to shape an analysis envelope for the SACCON, in order to define a set of plausible operative conditions, each defined by a combination of airspeed, altitude and CG location. The scope of the analysis envelope is to investigate the sensitiveness of the S&C characteristics and flying qualities of the aircrafts to velocity, altitude and centering. Again, no information regarding aircraft performances nor mass distribution were available, so those of comparable aircrafts were adopted and, if necessary, scaled. In particular, the same performance figures and powerplant of the Dassault nEUROn were considered.

• Static analysis and trim evaluation were then carried out over the full flight envelope, with the purpose of (i) exploring the influence of altitude and CG location on the equilibrium characteristics of the SACCON, especially elevator deflection and aerodynamic efficiency, and (ii) provide a first estimation of required thrust in straight leveled flight. Moreover, the results were used to adjust the limits of the flight envelope, taking into account stall and control surface saturation.

• Finally a comprehensive linear dynamic analysis was conducted over the revised flight envelope. The outcomes of the analysis were then used to (i) evaluate the dynamic behavior of the SACCON, quantifying the sensitiveness of its dynamic response to velocity, altitude and CG location, to (ii) verify the compliance of the design’s handling qualities with MIL-HDBK-1797A aviation regulations throughout the flight envelope and to (iii) highlight the control and handling problems of the configuration and outline a feasible strategy to make it a practical design.

The work described in this dissertation was initiated at the Department of Aeronautical and Vehicle Engineering (Farkost och Flyg) at the KTH - Royal Institute of Technology in Stockholm. There a research team, led by Prof. Arthur Rizzi, was conducting intensive CFD research on the SACCON, in close collaboration with other teams worldwide, as active Swedish member of the AVT-201 and former participant in the foregoing AVT task groups. The work was eventually concluded at “Sapienza” - Università di Roma under the supervision of Prof. Guido De Matteis. The aerodynamic model and subsequent analyses presented in this dissertation are based on the data provided by DLR (Deutsches Zentrum für Luft- und Raumfahrt e.V.) and were obtained at DNW (German-Dutch wind Tunnel) NWB low speed wind tunnel.

6 1.4: Thesis outline 1. Introduction

1.4 Thesis outline

Following this introduction, the subject matter of the dissertation is organized in subsequent chapters summarized below.

Chapter 2 presents a detailed literature review. It introduce a brief history of the development of ﬂying wing aircrafts, together with a review of modern UCAV designs. Then a concise review of the basic aspects of aircraft stability and control analysis is reported. Finally, the advantages and drawbacks, especially stability issues, associated to this category of air vehicles are covered, along with the attempts made to improve the design.

Chapter 3 describes the generation of the database of the SACCON. First the background of wind tunnel test is introduced, followed by the review of the procedure adopted to merge all data into a single database. The results of the aerodynamic and control authority analyses are then discussed.

Chapter 4 covers the deﬁnition of the ﬂight envelope and the execution of stability and trim analyses. The outcomes are then discussed and applied to update the prototype envelope.

Chapter 5 presents the details of the linearization process of the model and the results of subsequent analysis (both longitudinal and lateral aspects are covered). It also discusses the control and handling qualities aspects of the considered airframe and identiﬁes the critical areas and drawbacks.

Chapter 6 concludes this dissertation. It summarizes ﬁndings, identiﬁes limitations and sets directions for further research work on the subject.

Chapter 2

Literature review

By virtue of the aim of the research and of the nature of its target configuration, the literature review first presents a brief history of the flying wing design, followed by a review of the latest stealth UCAV development projects. It then describes the distinctive characteristics of the flying wing concept and their issues, especially regarding stability and control. An overview of the main aspects of flight mechanics and handling qualities analyses concludes the chapter.

2.1 Historical perspective

Tailless aircrafts have been experimented with since the earliest attempts to fly. By merely looking at birds circling in the sky, the flying wing possibly represents the simplest and most immediate configuration imaginable when venturing the design of a flying machine. Nature itself seems to reinforce the idea that a flying machine consisting of a single wing is, in fact, a practicable design, as successfully adopted by soaring/gliding birds, bats, plant seeds and, in prehistoric times, pterosaurs (see Fig. 2.1). It is no coincidence that the later journals of Leonardo da Vinci contain a detailed study of the flight of birds and several different designs for wings based, in structure, upon those of bats. However, at a closer look, bird-like and aircraft flight mechanics differ radically, essentially

(a) Albatross. (b) Fruit bat. (c) Zanonia seed.

Figure 2.1: Nature’s noteworthy ﬂying wing designs.

9 2. Literature review 2.1: Historical perspective because of the capability of living creatures to move their bodies, thus benefiting from wing flapping and dynamic shifting of the center of gravity. The movable surfaces of aircrafts, necessary for their flyability, somehow mimic the first feature, by locally changing the shape of the machine, but only at an incredibly lower scale, with effects not even nearly comparable to those achieved by the wings of animals. In the early days of the aeronautical era the preeminent challenge dwelled in the design of stable and controllable configurations, prior to focus on the improvement of pure performance. However, despite all the amazing progresses and technological leaps made by the aerospace industry in the past century, the appearance of the conventional aircraft, i.e. a main wing paired to set of tail surfaces, all attached to a more or less cylindrical fuselage, has not changed significantly since the beginning of the flight era. This is mainly due to the extreme level of confidence reached in the aforesaid configuration, herein referred to as conventional configuration, regarding stability and control issues, as well as structural reliability and on-board system integration. Many unconventional configurations have been explored over the last century, some of which even proved (at least theoretically) better characteristics for certain aspects than the standard one, but none has yet been able to replace it, nor become comparably widespread. The reason dwells in the fact that unconventional configurations exhibit, in general, poorer S&C characteristics and/or necessitate more complex structural designs. Moreover, considering that, until a few decades ago, the technical knowledge was not mature enough to provide the tools and expertise to adequately support the development of unconventional aircrafts, it is clear why such configurations invariably failed when compared to the standard design.

Figure 2.2: The Penaud and Gauchot “Amphibian” - 1876 [46].

Nevertheless, for more than a century, there have been countless patents, projects, and concepts relating to tailless airplanes. Many models and prototypes were constructed; most enjoyed only a brief period of development and public interest, and then quickly

10 2.1: Historical perspective 2. Literature review disappeared. The lack of adequate financial backing, lack of government or public interest, and politics often contributed to the premature end of a worthwhile project. Whatever the source of inspiration, most designers persevered with their experiments and research despite the lack of experimental facilities and financial backing. The critical period was when experiments passed from the model and glider stages to powered flight. For the reasons previously cited, projects were often terminated altogether at this stage. In other cases, the problems of stability and control associated with the absence of the tail proved insurmountable, so a conventional tail was added [45]. The pioneering age of aviation is replete with frustrated, brilliant men, to whom the description “neglected genius” could have applied. The greater contributions of the period came from European engineers, inventors or simple enthusiasts, who studied the flight characteristics of every conceivable type of flying creature. They all attempted the trial of sustained and controlled flight, often by means of flying wings, and, although they met scarce success, their efforts laid the foundations for the development of aviation. Some of the earliest contributions to flying wings came from English Lt. John William Dunne, between 1907 and 1914. He started his work from a tailless glider and followed it up by a series of powered bi-planes. Even at this early stage of development, he had realized the advantage of wing sweep to increase the effective tail length. He also incorporated wash out or twist at the wing tips to counteract the premature tip stall characteristics. His D.5 flying wing biplane, depicted in Fig. 2.3, was perhaps the first tailless aircraft to display inherent longitudinal stability.

Figure 2.3: Dunne’s D.8 ﬂying wing biplane - 1912 [52].

It was not until the deep-chord monoplane wing became less experimental, after World War I, that the opportunity to discard any form of fuselage arose and extensive studies concerning the true ﬂying wing took place between the 1930s and the 1940s. Soviet designers such as Boris Ivanovich Chyeranovskii started research independently

11 2. Literature review 2.1: Historical perspective and in secret under Stalin after the 1920s. With signiﬁcant breakthrough in materials and construction methods, aircraft such as the BICh-17 (Fig. 2.4) became possible [45].

Figure 2.4: Chyeranovskii BICh-17 experimental ﬁghter - 1934.

Several late-war German military designs were based on the flying wing concept, as a proposed solution to extend the range of the otherwise very short-range jet engined aircraft. Most famous contributors were Reimar and Walter Horten, often credited as the Horten brothers, who served in the army during the World War II. They were aircraft pilots and enthusiasts and, although they had little formal training in aeronautics, they designed some of the most advanced aircraft of the 1940s [52]. Their extensive work on tailless airplanes finally culminated in the design of the world’s first jet-powered flying wing, the Horten IX Ho-229, which had its maiden flight in the year 1945.

Figure 2.5: The Horten Vc - 1941.

In the U.S., the most signiﬁcant contribution toward the development of tailless aircraft came from Jack Northrop, who became involved in the development of the cleanest possible airplane early in his career as an aircraft designer in the late 1920s. One of his earlier designs, the Northrop N-1M, ﬂew in 1940, followed by the N-9M in 1942. Northrop’s interest persisted after the war, when he proposed the concept as a design solution for

12 2.1: Historical perspective 2. Literature review long-range bombers. Such trend culminated in the piston-powered YB-35 in 1946 and its jet-powered conversion YB-49 a year later. Unfortunately a series of technical problems and a fatal crash during landing of the YB-49 doomed the future of that design, which was eventually discarded in favor of more conventional solutions like the Convair B-36 and the Boeing B-52 and never entered production.

Figure 2.6: The Northrop-Grumman B-2 “Spirit” - 1989.

In the mid-1970s, the search for a new U.S. strategic bomber to replace the Stratofortress was underway, to no avail. Besides it was becoming clear that the best way to avoid missiles and intercepts was the adoption of low detection measures, today known as stealth technology. The increasing importance of stealth design features, together with the advent of fly-by-wire technology, eligible for alleviating the stability and control flaws of all-wing aircrafts, boosted again the interest in flying wing configuration in the 1980s. The approach eventually led the most famous, as well as the only successful, flying wing of all times, the Northrop B-2, shown in Fig. 2.6. By virtue of its advanced flight controls systems the B-2 shows Level 1 flying qualities throughout its flight envelope [9]. Since the 1990s, a peculiar type of tailless aircraft has emerged. Defined as the blended wing body, or simply BWB, it features a flattened and airfoil-shaped body, which produces most of the lift, the wings contributing the balance. The body form is composed of distinct and separate wing structures, though the wings are smoothly blended into the body. With the marked increase of composite materials use in airframe structures such non-cylindrical shapes are nowadays considered feasible. Currently, due to the excellent performance in the slow-to-medium speed range and its stealth capabilities, the flying wing configuration is still regarded as a practical concept for aircraft designers and there has been continuous interest in applying it both to military and commercial aircraft design.

13 2. Literature review 2.1: Historical perspective

2.1.1 Modern stealth UCAVs

Since the early years of the 1990s, thanks to the development of ever more reliable communications links and to the wider use of automated systems, the military acquired much more confidence with the concept of using uninhabited aircrafts for performing actual combat missions. The idea was revived in the form of various designs generally designated as Unmanned Combat Air Vehicles (UCAV). The continuous pursue of the best achievable performance, supported by a robust competence in the aforesaid technologies, has produced a series of remarkable aircrafts, result of the inevitable synthesis of flying wing, stealth and UCAV technologies. UCAVs missions would be conducted by an operator in a ground vehicle, warship, or control aircraft over a high speed digital data link. Even so, the operator would fly the UCAV

(a) Boeing X-47 “Pegasus”. (b) Lockheed-Martin RQ-170 “Sentinel”.

(e) AVIC 601-s “Lijan”. (f) Dassault nEUROn.

Figure 2.7: Modern stealth ﬂying wing UCAV designs.

14 2.2: An overview on flight mechanics analysis 2. Literature review with a merely supervisory role, rather than as an actual pilot. The robot would, in fact, be able to handle the details of flight operations and complete its mission autonomously, if communications were cut. So far the U.S. have played a worldwide leading role in the development of UCAV platforms of the first generation and they are, to all effects, laying the foundations for the second one, which will likely correspond to the sixth of fighter aircrafts altogether [34]. However Europe and other countries are actively endeavoring to bridging the gap and their efforts are finally paying off, even though most of the configurations are just technology demonstrators and research prototypes. The best representatives of this new breed of flying machines are depicted in Fig. 2.7.

2.2 An overview on ﬂight mechanics analysis

A discussion on the underlying principles and equations that govern both static and dynamic stability of an aircraft, as well as the estimation of its ﬂying qualities is addressed [9]. An appreciation of these aspects is doubly important. At the early design stages, they lead the engineer to shape a design capable to generate adequate lift and control forces and inherently stable. At more advanced design stages, they are considered when the compliance of the aircraft with regulation requirements is tested. It is important to point out that all the concepts exposed in this section are the result of linear analysis and, as such, based on the assumption of linearity of the aerodynamic coeﬃcients and, ultimately, of the aircraft model. The latter, along with the linearization procedure used to derive it, is described in AppendixC.

2.2.1 Static stability

The motion of an airplane can usually be broken into two parts: the first is the longitudinal or symmetric portion, which consists of motions inside the xz plane, with the wings always leveled; the second is the lateral-directional portion, which consists of rolling, yawing and sideslipping, at constant elevation angle. Such separation can be applied to both static and dynamic analyses. However the results of greater importance in the context of static analysis are those associated with the longitudinal portion of the aircraft motion [2]. Hence the principles reviewed in the present section will be limited to longitudinal stability, it being understood that the same approach is applicable in a similar fashion to directional stability analysis. The stability of a generic system is defined as its tendency to recover to the initial condition after a disturbance without any external input. In aeronautical terms, longitudinal static stability involves the generation of a restoring (nose-down) pitching moment in response of an increase in the angle of attack, without any control action from the pilot. Moreover, a steady flight condition is defined balanced, if the resultant force and moment

15 2. Literature review 2.2: An overview on ﬂight mechanics analysis about the center of gravity are both zero, that is the aircraft is in equilibrium. In particular, this requires the pitching moment to be zero.

(a) Balanced aircraft. (b) Unbalanced aircraft.

Figure 2.8: Pitching moment curves (ﬁxed elevator) [2].

Thus, static analysis suggests that, for an aircraft to be statically stable in pitch, the variation in pitching moment with angle of attack must be negative; then, for an equilibrium condition to exist, the pitching moment at zero angle of attack must be positive [1].

Cmα ă 0 (2.1a)

Cm0 ą 0 (2.1b)

The derivative Cmα is occasionally called pitch stiffness, as it models a spring-like behavior of the aircraft in the pitch axis. i.e. Figure 2.8 shows all the possible graphs of the pitching moment coefficient Cm versus the angle of attack α, measured from the zero-lift line of the aircraft. It is clear that a design can be considered practical only if its pitching moment curve can be traced back to one those of Fig. 2.8a, i.e. if the signs of Cmα and Cm0 are opposite, otherwise a trim condition is not guaranteed. In fact, an unstable aircraft can be equipped with an appropriate FCS to stabilize its response, while it is never possible to fly an aircraft that cannot be balanced. In other words, it is not the stability requirement, taken by itself, that restricts the possible configurations, but rather the requirement that the airplane must be simultaneously balanced and stable [2]. i.e. A positively cambered airfoil exhibits a moment about its aerodynamic center always negative within the normal range of angle of attack. Thus, in a conventional configuration, the value of Cm0 is made positive by the contribution of an auxiliary surface, conveniently set with a slight negative incidence.

The same surface also provides most of the negative component of Cmα , given that the lift it generates, despite being modest in comparison to that of the wing, possesses a much longer lever arm. A sketch of the standard arrangement is oﬀered in Fig. 2.9.

16 2.2: An overview on ﬂight mechanics analysis 2. Literature review

Figure 2.9: Conventional wing-tail arrangement [2].

The identical argument, applied to the case of a canard, i.e. tail-ﬁrst, arrangement, leads to the conclusion that the auxiliary surface (the canard) must be set at a slightly positive incidence. It is worth to point out that canards has the virtue of producing lift directed consistently with that of the wing, thus alleviating its load, as opposite to the stabilizer. A mathematical analysis of the longitudinal static stability of a complete standard aircraft yields the position of the point at which the resultant lift is applied, called neutral point. Since the pitching moment of an isolated surface about its AC can be safely considered invariant with α, it follows that the resultant aerodynamic moment of the aircraft about the that very point is constant with α. On this basis, it is possible to express the variation in pitching moment due to changes in α, as:

Cmα “ ĆLα pkn ´ kq (2.2) where the term in brackets denotes the dimensionless distance of the NP from the CG, positive for CG fore of the NP. It follows that the neutral point corresponds to the AC of the complete aircraft, that is to the position of CG at which Cmα is zero and static stability is neutral. Thence the name. The larger the surface and the moment arm of the tail, the further aft moves the neutral point. For example, the neutral point of the configuration depicted in Fig. 2.9 would lie somewhere aft of the wing AC. The term in brackets in (2.2) is called static margin K, usually quoted in percentage of the mean aerodynamic chord, and it quantifies the margin of movement of the CG prior to reach the stability limit. At first analysis, the SM is a measure of the static stability of the airplane with respect to α disturbances [21]. It can be stated, the proof given in plenty of literature, that the pitch stiffness can be made negative for virtually any combination of lifting surfaces and bodies by placing the center of gravity far enough forward of the neutral point [2]. If the CG is behind the neutral point, the aircraft is longitudinally unstable (K ă 0), and active inputs to the control surfaces are required to maintain steady flight. Though, the trade-off of reduced stability is an increase in responsiveness to commands, i.e. an improvement in maneuverability, a concept antithetical to stability. Indeed, an aircraft with a large static margin is very stable, but also sluggish to respond to commands and more prone to saturate the controls, due to their reduced effectiveness.

17 2. Literature review 2.2: An overview on ﬂight mechanics analysis

The value of the SM is of critical importance in the design of an aircraft, not only because it represents the main indicator of the stability of the design, but also because, ultimately, it determines the controllability and handling qualities of the vehicle.

2.2.2 Dynamic stability

The evaluation of static stability only provides a description of the reaction of the aircraft immediately following a disturbance. This result, as crucial as it is, is not sufficient to ascertain how the airplane will actually behave in time after a perturbation in steady flight. The study of the dynamic response of the aircraft is of great relevance, especially in the evaluation of flying qualities, as it defines its handling characteristics and measures the level of ease and comfort with which it can be flown.

Figure 2.10: Dynamic response of a statically stable aircraft [52].

In general, static stability is a necessary, but not sufficient condition for the dynamic stability of a system. The dynamic response of a system, as the static one, can be either stable, neutral or unstable, depending on the evolution of the amplitude of its response. Static stability analysis provides some useful, but rather crude measure of the airplane dynamics, in the sense that neutral or negative static stability always implies dynamic stability of the same type; while positive static stability admits any type of dynamic behavior. This last case is clearly outlined in Fig. 2.10. The response to a disturbance can be derived from the linearized six degrees of freedom equations of motion of the aircraft. The approach is based on the method of representing the aerodynamic forces and moments by means of stability coefficients, first introduced by George H. Bryan in 1911. The technique assumes that the aerodynamic actions can be expressed as a function of the instantaneous values of the perturbation variables [4]. Using a first order Taylor series expansion, the approach finally leads to a set of linear differential equations with constant coefficients, which in normal form reduces to:

x9 “ A x (2.3) By virtue of the already-mentioned decoupling between symmetric and asymmetric motions, the problem can be broken into two distinct, easier to solve sets of diﬀerential

18 2.2: An overview on ﬂight mechanics analysis 2. Literature review equations, namely longitudinal and lateral-directional dynamics. Moreover, a useful facilitation is represented by the fact that, when applying eigenanalysis to linear models in the form (2.3), the solution comes in the form of natural modes, which decouple the response of the aircraft into a set of simpler motions, each dominated by a limited number of states. In particular, the solution comes in the form:

λ t xptq “ x0 e (2.4)

where λ is one of the eigenvalues or poles of the system and x0 is the eigenvector that describes the associated natural mode. Natural modes can be fully characterized by their frequency and damping ratio, which, in turn, are determined by the value of the associated eigenvalue, in general a couple of complex conjugate poles. In addition, information about relative amplitude and phase shifting between the state variables associated to each mode, i.e. their dynamic behavior, are incorporated in the eigenvectors. Since damping ratio quantifies the time trend of the amplitude of the response, it is the definitive parameter to assess the dynamic stability of an aircraft, or, more precisely, of each distinct mode. Moreover, by applying the analysis to different flight conditions, the tool provides a reliable prediction of the modification of dynamic stability properties over the whole flight envelope. The typical modes of motion of a conventional aircraft are listed below.

• Longitudinal modes

1) Phugoid: it can be described as a lazy interchange of kinetic energy and potential energy about the equilibrium ﬂight condition. The motion has low damping and very long period. It is usually easily manageable by the pilot. 2) Short period: it is a heavily damped pitch oscillation, with a very short period and a time to half of the order of 1 s. Speed does not have time to change signiﬁcantly, hence it involves essentially an angle of attack variation.

• Lateral-directional modes

1) Roll subsidence: it consists of almost pure rolling motion and it is generally non-oscillatory. It expresses the damping of rolling motion. 2) Spiral: it is a non-oscillatory motion, consisting of a slow turn with sideslip. It is unstable in conditions of reduced dihedral eﬀect and high directional stability.

3) Dutch roll: is a coupled roll and yaw motion, with a period of 3˜15 s, often not suﬃciently damped for good handling, especially in aircrafts with high dihedral.

19 2. Literature review 2.2: An overview on ﬂight mechanics analysis

2.2.3 Flying and handling qualities

Handling qualities are those characteristics of a flight vehicle that govern the ease and precision with which a pilot is able to perform a flying task. They have a critical bearing on the safety of flight and on the ease of controlling an airplane in steady flight and in maneuvers. The way in which particular vehicle factors affect handling qualities has been a matter of study in aviation for decades. The problem of a preliminary and trustworthy estimation of the flying characteristics and ease of operation of an aircraft arose since the first flights. Due to the increasing frequency of aircraft crashes in the early twentieth century, aeronautical engineers became aware of the primary importance of a design aimed at achieving specific handling qualities, as well as adequate stability characteristics (two often antithetical concepts) [13]. Today, flying and handling qualities play a significant and necessary role in the design of both civil and military, piloted and autonomous airplanes. In order to ensure the accomplishment of the desired mission safely and successfully with the minimum amount of workload for the pilot, the aircraft, whether it is augmented or not, must satisfy the corresponding regulation. Yet, what constitutes acceptable characteristics is often not obvious, and several attempts have been made to quantify pilot opinion on acceptable handling qualities. Refer- ence standards for the handling qualities of any category of air vehicle have been developed and are now in common use [27]. Subjective flying qualities evaluations such as Cooper-Harper ratings are used to distinguish between “good-flying” and “difficult-to-fly” aircraft. Moreover, quite useful and reliable flying qualities estimates may be provided on the basis of various dynamic characteristics, by correlating pilot ratings to the frequencies and damping ratios of the aircraft’s modes of motion, as in done in the U.S. military specifications. These standards essentially define a subset of the dynamics and control design space that provides good handling qualities for a given combination of aircraft type and flying task [6]. Nowadays new aircraft designs can be simulated way before actual flight testing to assess their airworthiness. Nevertheless, such real-time, pilot-in-the-loop simulations are expen- sive and require a great deal of information about the aircraft, which are not likely to be available at early stages of design.

2.2.3.1 Cooper-Harper rating scale

The Cooper-Harper rating scale is a set of criteria formalized in the late 1960s and ever since used by test pilots and engineers to evaluate the handling qualities of aircraft during ﬂight test. The scale ranges from 1 to 10, with 1 indicating the most desirable handling characteristics and 10 the worst. The criteria are evaluative and, thus, the scale is considered subjective. It is important to note that a Handling Qualities Rating (HQR) can only be assigned

20 2.2: An overview on flight mechanics analysis 2. Literature review to a well defined combination of a repeatable task, a well trained pilot, that is actively engaged in accomplishing that task, and a specific aircraft.

Figure 2.11: Cooper-Harper rating scale [52].

The scale cannot be applied straightforwardly for the purpose of evaluating the flying qualities of an unmanned aircraft, for the very reason that it is based on the “sensations” of a pilot physically located onboard the vehicle. Even though, it is arguable that it might be adopted in the case of remotely piloted UAV. In that scenario a pilot is actually present and his perceptions, however limited compared to those of a conventional pilot, could be, with due caution, taken into account. Recently an alternative version of the Cooper-Harper scale has been proposed by Cum- mings, et al. [33]. Since in UAV operations displays are often the only information link between operators and vehicles, a quasi-subjective display evaluation tool called the Modi- fied Cooper-Harper for Unmanned Vehicle Displays (MCH-UVD) has been developed. The tool, adapted from the Cooper-Harper aircraft handling scale, allows operators to evaluate a display, rather than the dynamic behavior of the aircraft directly, by translating their judgments on potential display shortcomings into a number corresponding to a particular deficiency in operator support.

21 2. Literature review 2.2: An overview on ﬂight mechanics analysis

Figure 2.12: MCH-UVD diagnosis tool [33].

The intent of the redesign was to represent a severity scale that deﬁnes the ability to complete the mission. Like the original Cooper-Harper scale that rated aircraft controllability on a scale of severity, the intent was to scale severity that reﬂected the UVD’s ability to support safe mission completion. At the same time, the intent was to maintain the concepts of the human information processing model within this new scale, as this is a critical component to UV display designs [33].

2.2.3.2 MIL-HDBK-1797A

The first comprehensive military handling qualities specifications were issued in the early 1940s by the Navy Bureau of Aeronautics and the U.S. Army Air Force (AAF-C- 1815), in acknowledgement of the demand of the military services of a unified standard, less subjective than the Cooper-Harper scale and based on quantifiable parameters. More importantly, the subsequent version MIL-F-8785B of 1954, began the precedence within the handling qualities community that the true value in a specification document was an elaborate Background Information and Users Guide (BIUG), wherein the data which form the specification are contained, rather than the detailed requirements per se. The BIUG forms the historical lessons-learned for handling qualities which provide a continual improvement process for air vehicle handling qualities. The use of military specifications fell out of favor in the 1980s. The last in this series

22 2.2: An overview on flight mechanics analysis 2. Literature review was MIL-F-8785C issued in 1980. MIL-F-8785C was then re-worked and updated into a military standard (MIL-STD-1797A) in 1995, which was further re-designated in 1997 as a handbook, the MIL-HDBK-1797A. This latter specification is intended to assure flying qualities that provide adequate mission performance and flight safety regardless of design implementation or flight control system mechanization (although it primarily focuses on unaugmented piloted aircrafts). The structure of the specification allows its use to guide these aspects in design, construction, testing and acceptance of the subject aircraft [35]. Under MIL-HDBK-1797A three levels of acceptability of the flight characteristics, related to the ability to complete the operational missions for which the airplane is designed, are defined. These levels are presented in Tab. 2.1.

Level Degree Deﬁnition HQR

Flying qualities clearly adequate for the mission 1 Satisfactory flight phase. Desired performance is achievable ě 3.5 with no more than minimal pilot compensation Flying qualities adequate to accomplish the mission flight phase, but some increase in pilot work- 2 Adequate ě 6.5 load or degradation in mission effectiveness, or both, exists Flying qualities such that the aircraft can be controlled in the context of the mission flight phase, 3 Controllable ě 9.5 even though pilot workload is excessive or mission effectiveness is inadequate, or both

Table 2.1: Deﬁnition of handling quality levels in MIL-HDBK-1797A [35].

For the purpose of handling qualities evaluation an aircraft is placed in one of the following classes:

Class I small light aircraft;

Class II medium weight, low-to-medium maneuverability aircraft;

Class III large, heavy, low-to-medium maneuverability aircraft;

Class IV high-maneuverability aircraft.

The specification introduces a further subdivision of the analysis depending on the flight phase, based on the experience with aircraft operations that certain flight phases

23 2. Literature review 2.2: An overview on flight mechanics analysis require more stringent values of flying qualities parameters than others do. A description of the different flight phases defined within MIL-HDBK-1797A is summarized in Tab. 2.2.

Type Category Deﬁnition

Phases that require rapid maneuvering, precision A tracking, or precise ﬂight–path control

Nonterminal Phases that are normally accomplished using gradual maneuvers and without precision track- B ing, although accurate light–path control may be required

Phases normally accomplished using gradual ma- Terminal C neuvers and usually require accurate ﬂight–path control

Table 2.2: Deﬁnition of ﬂight phase categories in MIL-HDBK-1797A [35].

The specification provides a comprehensive assortment of requirements, spanning all modes of motion of a conventional airplane, that specify the limits of acceptability to be met by the aircraft under study, according on the flight phase. In terms of longitudinal modes, acceptable limits on the stability of the short period, which defines the longitudinal control dynamic, are quantified by the range of damping ratio for each flight phase categories and quality levels, as Tab. 2.3 shows.

Category Level A, C B

1 0.35 ď ζ ď 1.30 0.30 ď ζ ď 2.00

2 0.25 ď ζ ď 2.00 0.20 ď ζ ď 2.00

3 ζ ě 0.15 ζ ě 0.15

Table 2.3: Short period requirements in MIL-HDBK-1797A [35].

One can observe that the range constraints summarized in Tab. 2.3 identify a relatively wide region of acceptability, relaxing the work of aircraft designers. Cook demonstrated that the ideal damping ratio of SPO mode is 0.7, a value that ensure satisfactory margin of stability, while minimizing the settling time after a disturbance [3]. Indeed, a value bigger

24 2.2: An overview on ﬂight mechanics analysis 2. Literature review than 1.0, indicating an overdamped system, would imply a generally longer settling time. The quality level of phugoid mode for all phases is characterized by its damping ratio, as shown in Tab. 2.4[35]. Note that such requirement applies with both free and ﬁxed pitch control.

Level All categories

1 ζ ě 0.04

2 ζ ě 0 unstable, 3 T2 ě 55 s

Table 2.4: Phugoid requirements in MIL-HDBK-1797A [35].

The requirements for the phugoid mode, compared to those of the SPO, are clearly relaxed, because of the longer period, which leaves the pilot plenty of time to act. Furthermore, it can be stated that a phugoid frequency approximately one tenth of that of the SPO represent an ideal value [10]. The performance of the roll subsidence mode is evaluated by means of its time constant

τR, expressed in seconds, according to Tab. 2.5.

Level (τR min) Category Class 1 2 3

I, IV 1.0 s 1.4 s A II, III 1.4 s 3.0 s

B all 1.4 s 3.0 s 10 s

I, II-C, IV 1.0 s 1.4 s C II-L, III 1.4 s 3.0 s

Table 2.5: Roll subsidence requirements in MIL-HDBK-1797A [35].

The requirements on spiral stability are aimed primarily at insuring that the aircraft will not diverge too rapidly in bank from a wings level condition during periods of pilot inattention. The criterion is formulated according to the requirement that, following a disturbance in bank of up to 20 degrees, the time for the bank angle to double amplitude

25 2. Literature review 2.2: An overview on ﬂight mechanics analysis shall be greater than the values reported in Tab. 2.6. This requirement must be met with the aircraft trimmed in symmetric leveled ﬂight and with free cockpit controls [35].

Level (T2 min) Category 1 2 3

A, C 12 s 8 s 4 s B 20 s

Table 2.6: Spiral requirements in MIL-HDBK-1797A [35].

Finally, the requirement speciﬁed for the dutch roll are aimed at attaining a suﬃciently stable and well damped lateral-directional oscillatory dynamic.

Requirements (minimum value) Level Category Class ζ [-] ζ ω [rad/s] ω [rad/s]

A (CO, GA, RR, TF, RC, all 0.4 0.4 1.0 FF, AS)2

I, IV 0.19 0.35 1.0 1 A II, III 0.19 0.35 0.4

B all 0.08 0.15 0.4

I, II-C, IV 0.08 0.15 1.0 C II-L, III 0.08 0.10 0.4

2 all all 0.02 0.05 0.4

3 all all 0 - 0.4

Table 2.7: Dutch roll requirements in MIL-HDBK-1797A [35].

The requirements are a bit more complex than those seen so far, due to the strong coupling

2Indicating respectively: air-to-air COmbat, Ground Attack, in-ﬂight Refueling (Receiver), Terrain Following, ReConnaissance, close Formation Flying, Antisubmarine Search

26 2.2: An overview on ﬂight mechanics analysis 2. Literature review of the mode and the key importance of its adequate controllability. It is worth to point out that longitudinal requirements were empirically derived from pilot comment. Speciﬁcally, they were established using criteria based on a human operator’s ability to act as the aircraft’s augmentation and control system. Moreover, given that the primary guide to determine these values was pilot input on unaugmented aircraft, their applicability to autonomous UAVs is limited to those that are designed to match piloted aircraft dynamics for landing purposes or gust rejection, irrespective of the UAV’s control system [13].

2.2.3.3 CAP criterion

The Control Anticipation Parameter (CAP), introduced by Bihrle in 1965, is one of the earliest and most diffused flying qualities criteria, especially for unaugmented piloted aircrafts. The CAP is defined as the ratio of the aircraft’s pitch acceleration to change in steady state load factor. and it is used to correlate the sensitivity of the human vestibular organ to pitch acceleration to a sensed g-loading of an aircraft.

CAP can be expressed as ratio of short period natural frequency ωSP and normal acceleration derivative w.r.t. angle of attack Nα (see AppendixC), or equivalently as ratio of instantaneous pitch acceleration and steady state normal acceleration [3]:

θ: q9p0q ω 2 CAP “ “ « SP (2.5) ∆ss Nzp8q Nα where

Zw u0 N “ ´ ω “ M Z ´ M Z ` u α g SP q w w q 0 b ` ˘ This expression gave rise to the short period frequency requirements found in the military speciﬁcation handbook, which are summarized graphically in charts such as the one found in Fig. 2.13 (relative to Category B ﬂight phase). CAP can then be evaluated graphically using the parameters in (2.5), which, in turn, can be derived from the reduced second order model for the short period mode.

In conclusion, it is important to notice that the application of flying qualities analysis to UAVs presents a unique problem: the absence of a human pilot. Since flying qualities analysis traditionally focuses on pilot opinion, a major component of flying qualities analysis must be rethought. There is however, a large body of work of piloted criteria that does provide guidance for the application of flying qualities analysis to UAVs. Any application of a criterion to UAVs must follow some of the basic tenants used in piloted analysis. In general, it must be simple enough to use, effective enough to make worth using, and familiar enough so that there is a feeling of intuitive comfort in using it [13].

27 2. Literature review 2.3: Flying wing design issues

Figure 2.13: CAP requirements for Category B ﬂight phase [35].

2.3 Flying wing design issues

A flying wing is a tailless fixed-wing aircraft that has no definite fuselage, with most of the crew, payload, and equipment being housed inside the main wing structure. It is often regarded as, theoretically, the most aerodynamically efficient configuration for a fixed wing aircraft. It also would offer high structural efficiency for a given wing thickness, leading to light weight and high fuel efficiency. Because the airframe lacks conventional stabilizing and/or associated control surfaces, in its purest form the flying wing can easily suffer from the inherent disadvantages of being unstable and difficult to control.

28 2.3: Flying wing design issues 2. Literature review

2.3.1 Longitudinal issues

The first challenge in the design of a tailless aircraft consists in obtaining a configuration, if not stable, at least balanced, that is ending up with a pitching moment curve of the type of Fig. 2.8a. For straight winged tailless airplanes, the lack of horizontal tail makes the compliance with the requirement expressed by (2.1b) only possible with the adoption of a reflex airfoil, as done by the Horten brothers. Effectively, the same result is attained if a flap, deflected upward, is incorporated at the trailing edge of a symmetrical airfoil [2]. However, this solution, in both of its forms, comes with a reduction in maximum achievable lift, along with a sensible increase in drag, together with the limited CG range, hence straight wing flying wing configuration is seldom adopted. The only feasible alternative for all-wing airplanes is the swept-back wing with twisted tips (washout): when the net lift is zero, the forward part of the wing produces a positive contribution and the rear part a negative one for a resulting positive couple [2]. However, swept wings, especially if untapered (like that of the SACCON), tend to be subject to tip stall, due to the high suction peaks on the leading edge in the proximity of the outer wing sections, caused to trailing vorticity in the wake of the inboard wing sections [21]. If, on the one hand, the advantage of such a behavior is a more progressive stall, its drawbacks are represented by a de-stabilizing nose-up pitching moment, caused by the forward movement of the center of pressure, the loss of aileron effectiveness and the risk of asymmetric stall, leading to undesirable roll tendency. The use of tip slats was advocated by Donlan [28] as being the most effective method for delaying the tip stall, as they may increase the angle of stall as much as 10˝, if judiciously located. In addition, slats can also be employed to adjust the Cm0 of the configuration, although at the price of increased drag. Besides that, another typical phenomenon of highly swept wings is the development of complex vortical flows on the upper surface of the wing. Such flow topology guarantees lift up to higher angle of attack than straight wings, at a price of a reduced lift slope, but it is responsible for undesirable behavior of the pitching moment as well, including sudden dips and non-linearities concurrently with vortex breakdown dynamics [12].

Referring to the value of Cmα , as given by (2.2), it is clear that the position of the NP of a tailless aircraft coincides with that of the AC of the wing. Thus the only possible way to achieve negative pitch stiffness, i.e. positive static stability, is to locate the CG ahead of the wing AC. Jones reports that an extreme reduction of thickness toward the trailing edge may cause a backward displacement of the AC of 2 or 3 percent [26]. In any case, this severely restricts the allowable CG range in comparison to a conventional configuration. In particular, Donlan [28] suggests an optimal static margin range from 2% to 8%, mainly due to limitations in control power for such aircrafts. Often the only feasible way to provide stability to a tailless design is artificially, by means of suitable stability augmentation systems based on modern fly-by-wire technology. In this regard, already

29 2. Literature review 2.3: Flying wing design issues in 1941 Northrop [25] advised that an intentionally unstable configuration augmented by reliable and sophisticated fly-by-wire control system represents the best solution for a flying wing, especially if sizable.

A second preeminent issue is represented by pitch damping, denoted by Cmq . For conventional airplanes most of the contribution to pitch damping (actually nearly 90% of it) comes from the horizontal stabilizer, the effect of the fuselage being negligible. Nevertheless Jones [26] points out that, if the airplane is statically stable (AC aft the CG), the free rotation in pitch couples with motions normal to the chord and the damping of such motions is effective in contrasting the pitching. In fact, the lack of direct damping appears to alter the sequence of the motions in such a way as to make this coupling more effective in the case of tailless configurations. Remarkably, despite a rotary damping coefficient Cmq just one tenth that of conventional aircrafts, the actual capability of tailless aircrafts to damp pitch oscillations in flight is nearly as great. Northrop [25] further asserts that, despite the low pitch damping, SPO results well damped due to the plunge damping parameter CZw , that absorbs most of the energy of oscillation. Furthermore, as explained by Donlan [28], a relaxed or negative static margin may lead to the development of an uncontrolled dynamic, called tumbling. It is a divergence motion consisting of a continuous pitching rotation, capable of rendering conventional control surfaces almost useless, once it is initiated. Indeed, tumbling was deemed responsible for the accident that claimed the lives of Captain Glen Edwards and other four crew members, during a low altitude stall test on board of the Northrop YB-49. According to Donlan, to avoid tumbling dynamic, the static margin should never be permitted under any condition to become negative. Nevertheless, it has been argued that a non-negative static stability, might not be a guarantee against this phenomenon [9]. To exert the necessary control action, a tailless aircraft can only rely on large elevons fitted at the trailing edge of the wing. Then, with the exception of delta wing designs, the longitudinal distance between the control surface and the CG will be considerably smaller than in a conventional aircraft. As a consequence, for the same static margin, the elevator of a tailless aircraft will prove much less effective than that of a conventional configuration, also implying larger deflections. Poor longitudinal control authority may become critical during take-off, as the aircraft may not be able to generate a strong enough rotation moment to overcome the combined action of the nose-down moment of its own weight about the point of ground contact and that created by friction on wheels.

2.3.2 Lateral-directional issues

Despite possessing no direct stiffness in roll (Clϕ = 0), stable airplanes exhibit an inherent tendency to fly with leveled wings, called dihedral effect or, less frequently, roll stiffness. The phenomenon is the consequence of the interaction of gravity with the derivative Clβ and arises whenever a lateral velocity, thus sideslip β, is established due to an

30 2.3: Flying wing design issues 2. Literature review

unbalanced lateral weight component. The value of Clβ , whether positive or negative, is generally kept small, to avoid excessive roll-yaw coupling (primary cause of undesirable dutch roll characteristics, if negative) and lateral oscillations in rough air [26]. Since dihedral effects originates from the configuration of the wing alone, the lateral static stability for flying wing aircrafts is not much different from that of a conventional configuration and satisfactory roll stiffness can be achieved using standard design practice.

The same principle applies to roll damping Clp , which is determined by the wing. Lateral control is the only aspect that presents no apparent difficulty. It is achieved by means of conventional ailerons or spoilers controls, placed at an appropriate span location. The main difficulty in the design of a flying wing lies undoubtedly in the provision of sufficient weathercock stability and yaw damping. Owing to the absence of any form of vertical stabilizer, a flying wing shows poor directional stability, despite the beneficial effect of the lack of fuselage. Wind tunnel tests showed that attainable values of Cnβ for a flying wing never exceed the 33% of those of a tailed design. Jones [26] states that the fin surface necessary to realize the required degree of weathercock stability can be greatly reduced by fitting lateral controls with zero or even favorable yaw coupling. Nevertheless, Rahman [9] asserts that small fins fitted at the wing tips do not provide a valid solution, especially for large configurations, and should in any case be avoided, on penalty of an increase in drag and weight (potentially negating the advantage of the flying wing). Jones [26] further suggests that the use of sweepback planform combined with downward cranked (anhedral) wing tips could secure adequate directional stability, particularly at high speed and angle of attack. The solution was actually implemented by Norhrop in its N-1M, as it is clearly visible in Fig. 2.14, although he later abandoned it.

Figure 2.14: Northrop N-1M.

Another practical solution to increase directional stability of tailless aircrafts, advised by Prandtl and later the Horten brothers, is represented by the proper use of wing twist and airfoil sections, in order to establish a bell-shaped lift distribution, together with a sweepback planform. Apparently this induces the wing tips to generate a forward-oriented lift vector, that will eﬀectively pull the trailing wing forward. As in the case of pitching motion, the elimination of the tail has a negative impact on yaw damping capability of the vehicle. In fact the damping action of the wing, caused by

31 2. Literature review 2.3: Flying wing design issues the distribution of drag along the span, has a marginal effect and it is subordinate to the value of the local lift coefficient. In this case the adoption of fin-like surfaces at the tip of the wing [26] produces marginal effects, quantified in Reference [26] in a Cnr derivative roughly 10% of that of a conventional design. The type of surface usually employed to control yaw is the rudder, which cannot be fitted in a flying design. Northrop tested several rudder-like controls designs, the most successful of which was the split aileron, or drag rudder, sometimes also referred to as deceleron. The functioning is based on differential drag produced by the surface and by virtue of their long moment arm from the CG (approximately half span). With the implementation of a flight control system, integrated with adequate sensors, it is possible to obtain an aircraft with directional flying and handling qualities as good as those of a standard configuration.

Figure 2.15: The drag rudder deployed on the wing tip of the Northrop N-9M.

Moreover, if mounted far enough from the CG, the drag required to exert sufficient yawing moment will be tolerable, making split aileron the most effective and ingenious method for providing both directional stiffness and damping to a flying wing. Still, the use of drag as a mean of control makes the design more suited for steady cruising in still air, while it becomes less efficient when maneuvering or in turbulent air. Finally, Donlan [28] infers that the thrust line should be kept as close as possible to the centerline, so as to minimize the control power, i.e. additional drag, required in asymmetric thrust conditions (engine failure).

32 Chapter 3

Aerodynamic database

The first subject that had to be addressed was the generation of the aerodynamic database of the SACCON concept. The database constitutes the actual aerodynamic model of the configuration under study as it will be used to estimate the S&C characteristics of the final aircraft. The main aspects covered in the chapter are the collection of the wind tunnel measurements, their processing and some remarks following their analysis. Finally the evaluation of control effectiveness is discussed, along with some remarks concerning the limitations of the configuration.

3.1 Foreword

In modeling an aircraft’s aerodynamic database the choice of the more suitable mathematical structure is often a crucial challenge. This is mainly due to the complex, non-linear functional dependencies of forces and moments on both present and past values of several flow and control parameters. Addressing the problem remains difficult even after the decoupling of symmetric (longitudinal) and asymmetric (lateral) dynamics, motivated by the symmetry characteristics of (most of) aircrafts, greatly reduced the intricacy of the former issue. A reasonable simplification is that the airplane mass and inertia are significantly larger than those of the surrounding fluid. Also the flow is often considered quasi-steady, which implies that steady-state aerodynamic conditions are reached instantaneously after a disturbance, de facto neglecting the memory effect of the flow field. In general, the static dependencies of the aerodynamic coefficients upon steady parameters, chiefly incidence angles and Mach number, constitute the so-called baseline database of the model, which provides a fundamental overview of the aerodynamic loads throughout the flight envelope of interest. Furthermore, it has the potential to represent non-linear phenomena such as static stall, compressibility effects and the onset and breakdown of vortical flows [11]. Inte- grating the baseline database with the portion accounting for the effects of control surfaces deflections, yields the complete static model of the aircraft. Moreover, the data contained in such a model can be directly measured from static wind tunnel tests.

33 3. Aerodynamic database 3.1: Foreword

A quasi-steady model can be effectively employed to investigate the S&C characteristics of the aircraft through simulation of flight maneuvers. On this regard, the results obtained by Da Ronch et al. [29] indicate a fairly good agreement between time-accurate and quasi- steady solutions, as long as the maneuver involves moderate angular rates and low angle of attack (lazy eight). Da Ronch et al. [29] further report that such correspondence is lost as the maneuver gets more rapid and involves higher angles of attack. In that case the onset of non-linearities in the flow, such as vortices and separation, occurs and relevant time history effects are triggered. Therefore the discrepancies observed between time-accurate and quasi-steady solution were entirely ascribed to the lack of an accurate description of lead/lag effects in vortex development. As a matter of facts, a constantly increasing number of common interest application, such as the SACCON, are dominated by non-linear, vortical flows, sometimes in the transonic regime and/or at high angle of attack, so much so that the assumption of quasi-steady flows becomes narrow. In these cases the inclusion of dynamic behavior modelization, especially concerning reduced frequency effects, becomes mandatory for the attainment of adequate correlation with time-accurate reference solutions. With the introduction of the assumption that the influence of control surfaces deflection on dynamic effects is negligible, the characterization of full functional dependencies of the aerodynamic coefficients for a complete model can be broken down as:

0 δ ω Ci “ Ci α, β, M8 ` ∆Ci α, β, M8, δe, δa, δr ` ∆Ci α, β, M8, p, q, r `

´baseline ¯ ´ control ¯ ´ rotational ¯ (3.1) looooooomooooooon looooooooooooooomooooooooooooooon loooooooooooooomoooooooooooooon t 9 ` ∆Ci α, β, M8, α,9 β

´ unsteady ¯ loooooooooooomoooooooooooon valid for i “ X, Z (or D, L), m, Y , l, n and where the contributions of dynamic effects and controls are introduced as increments to the baseline values. The above decomposition fits well with the common practice of wind tunnel experiments: forced oscillation and control deflection data measurements are preceded by the determination of the baseline database, ω δ t which can be subtracted from the firsts, yielding the increments ∆Ci , ∆Ci and ∆Ci with all available dependencies. It is worth to note that rotational increments correspond to quasi-steady contributions, since transients are not taken into account. Usually, forces and moment coefficients are then tabulated as functions of the flight states and control settings, covering the designed or expected flight envelope. The database is formulated in a fashion that overcomes the general assumption of uncoupled longitudinal and lateral dynamics, since every dependency and cross-effect is preserved within its data. Da Ronch [11] points out that, if five values were to be used to provide a coarse resolution for each state and control setting appearing in (3.1), the total number of table entries, i.e.

34 3.2: Wind tunnel campaigns 3. Aerodynamic database the number of possible combinations, would be 511, which is of magnitude 107. Indeed, the adequate modelization of an aircraft aerodynamics does not require such amount of data; although a reasonable aerodynamic database to cover the expected ﬂight envelope could easily require one hundred-thousand entries.

3.2 Wind tunnel campaigns

The SACCON tests, part of the NATO RTO AVT-201, were conducted in two separate phases. The first took place at Low Speed Wind Tunnel of the German-Dutch Wind Tun- nel Association (DNW-NWB) in Braunschweig, Germany. The second part was performed at NASA Langley Research Center (LaRC) in the 141 ˆ 221 low speed wind tunnel facility located in Hampton, Virginia. In addition, the Defense Science and Technology Organi- zation (DSTO) in Australia performed some basic research using a smaller scale model in their water tunnel. The shared goals of these test campaigns were the generation of a complete aerodynamic dataset of both stability and control characteristics of the SACCON, to be used for the construction of an initial S&C model, and the capturing of the complex vortical flow topology over the configuration during dynamic trajectories. The data taken into account within this study are the ones obtained at the DNW-NWB. The facility is a continuous, closed-circuit, low speed wind tunnel of the atmospheric type, with capabilities for aeroacustic and dynamic testing [48]. It can be operated with open, slotted or closed test section, with maximum flow velocity varying from 70 m/s to 80 m/s. The test section measures 3.25 m by 2.8 m. Model supports include basic α-β support, half-model support, support for 2-D-models, a rotary motion support for rolling and spinning tests, and the Model Positioning Mechanism (MPM). The latter is a six DoF parallel kinematics system, designed for static and dynamic model support. Characteristic features of this unique test rig are the six constant length struts of ultra-high modulus carbon fiber and the six electric linear motors, which move along two parallel rails. The first eigenfrequency of the MPR is greater than 20 Hz. The MPM is located above the test section and can be operated in the open test section as well as in the closed one. The location of oscillation axes can be chosen arbitrarily and, in addition to classic sinusoidal oscillations, multi-DoF maneuvers can be replicated [16].

3.2.1 Wind tunnel model

Several wind tunnel models have been built for testing in diﬀerent laboratories. Diﬀer- ent scalings and solutions have been adopted, depending on the aspects to be investigated. The low speed tests, subject of this study, were carried out using the DLR-F17/SACCON model. It is a 1:8 scale model designed to be tested in low speed wind tunnel experiments and can be mounted either by a belly or a back sting. The geometric data of the model are

35 3. Aerodynamic database 3.2: Wind tunnel campaigns

given in Fig. 3.1. Note that cref indicates the mean aerodynamic chord (mac) and MRP the moment reference point, henceforth called aerodynamics reference point or ARP. DLR-F17/SACCON features variable radius round leading edges (RLE) prepared with a carborundum grit trip, used to achieve fixed transition (FT) and, hence, fully turbulent flow, so as to better compare results with CFD predictions. Thus the designation RLE-FT. Moreover, PIV measurement requirements motivated the finishing of the surface with a layer of shiny black paint containing particles of Rhodamine B. The compound reflects laser light at a different wavelength, which can be filtered, resulting in highly accurate PIV measurement extremely close to the surface [16].

Figure 3.1: Planform and geometric parameters of the DLR-F17SACCON [16].

The model was manufactured at NASA Langley Research Center using Carbon Fiber- Reinforced Polymer (CFRP) and it weighs less than 10 kg. Light weight models are, in fact, required in case of unsteady aerodynamics tests, in order to obtain accurate estimates of the aerodynamic forces, which are easily dwarfed by inertial eﬀects (of both the model and the supporting structure). Moreover, the light model allowed the use of a smaller and more sensitive balance, that provided better force and moment resolution. The pre-design geometry was adjusted by DLR by increasing the overall thickness at the root chord, in order to provide enough space for the internal strain gauge balance. The model was equipped with control surfaces on the left wing, produced with rapid prototyping. The controls included an inboard elevon (IB or δe) and an outboard surface

36 3.2: Wind tunnel campaigns 3. Aerodynamic database

which could be deflected as an elevon (OB or δa) or split as drag rudder (SP or δr), for a total of three distinct controls. The elevon hinge lines are located at 80% chord, w.r.t. the airfoil parallel to the wing tip [37]. A complete description of the full-scale SACCON configuration can be found in Appendix A, along with the final arrangement of the control surfaces (Fig. A.1).

3.2.2 Experimental setup

The DNW-NWB tests took place in the closed test section using the MPM. Different connection links between the belly sting support and the internal balance were provided by two different rigid cranked yaw links or by using an internal pitch link driven by a seventh axis. The solutions allowed an angle of attack range from 0˝ to 30˝. The position of the belly sting connection was chosen to minimize the influence of the sting on the overall flow topology. In particular, the connection between the sting support and internal balance was completely covered by the model fuselage for the configurations with yaw link. For the pitch link, this was impossible and only a cover could be used to smooth the geometry in that area. A picture of the MPM carrying the DLR-F17/SACCON model is given in Fig. 3.2. Forces and moments were measured using a Emmen 196-6 strain gauge balance, mounted inside the fuselage of the model. Previous investigations with the X-31 configuration showed that the accurate prediction of forces and moments requires the effect of the support system to be taken into account [16], especially for pitching moment measurements. Flow quantities, such as the Mach number, were derived from pressure and temperature measurements in the settling chamber, the test section and in the plenum.

Figure 3.2: The DLR-F17/SACCON in the DLR-NWB with yaw link support [47].

37 3. Aerodynamic database 3.2: Wind tunnel campaigns

For the measurement of the instantaneous attitude and position of the model, the laboratory employed an optical system mounted below the test section featuring two high- speed video cameras. The cameras acquired SXGA (1280ˆ1024) images at 300 frames per second. The position of the model was calculated in real time from the pixel coordinates of three markers applied to the model surface. Additionally, a conventional inclinometer was installed for static angle of attack measurements. The model was equipped with more than 200 pressure taps on its upper and lower sides. The taps were connected with pressure tubes to electronically scanned pressure (ESP) modules within the model. At nine additional positions, unsteady pressure sensors were mounted, with the purpose of synchronizing the unsteady measurements. Their locations resulted from previous preliminary CFD computations, based on best practice procedures resulting from CFD prediction of conﬁgurations with round leading edges, such as the results from AVT-113 [30]. Particular care was used in the preparation of the connections between the pressure taps and the PSI modules, so as to obtain tubes of the same length, in order to guarantee the same time-dependent behavior for each pressure tap during the unsteady pressure measurements. The resulting big bundles of ﬂexible tubing were then carefully installed to prevent kinks. DNW-NWB’s standard Hottinger-Baldwin MGC+ data acquisition system were employed for data acquisition of force and pressure measurements. The sampling frequency was 600 Hz for the balance and 300 Hz for the video cameras and the ESP modules. The integration time was 2 s.

3.2.3 Tests and results

The data used in this study refer to the measurements obtained during test campaigns TN 2514 in December 2011 and TN 2540 in May 2012. The first focused on the determination of the effects of the deflection of a single control surface at a time; while in the second combined deflection of the control surfaces was investigated. The prospect of all deflection combinations tested is presented in Tab. 3.1, along with a picture illustrating the location of the controls. Of course, outboard elevon and outboard split aileron deflections are mutually exclusive, since they are realized by the same surface. All experimental data were obtained at sea level atmospheric conditions, at a free stream 6 velocity U8 “ 50 m/s, corresponding to M8 » 0.149 and Reynolds number Re » 1.6 ¨ 10 . A preliminary phase of exploratory runs was conducted in both campaigns for calibra- tion purposes and also for obtaining a first overview of the aerodynamics of the DLR-F17 model. They involved a series of α and β sweeps performed at zero deflection. The first phase of each campaign addressed static measurements of the aerodynamic forces and moments, performing α sweeps for different angle of sideslip and viceversa at fixed control (or combined controls) deflection. An additional α sweep at zero sideslip run was performed when changing control deflection for tare purposes.

38 3.2: Wind tunnel campaigns 3. Aerodynamic database

Each static measurement was conducted statically, i.e. the model was ﬁrst positioned at a ﬁxed incidence and then the forces and moments were determined. Conversely, a quasi- statical approach involves the continuous acquisition of data as the incidence is slowly varied and the calculation of values at breakpoints as moving averages [23]. As mentioned, static runs involved angle of attack and angle of sideslip sweeps, in particular, with α spanning from 00 to 300 and β spanning from ´100 to 100.

IB OB SP

-20 -10 0 -5 10 20 -20 -10 0 0 0 10 20 -20 0 10 10 20 0 0 5 0 0 10 -20 -10 0 20 0 10

Table 3.1: Prospect of control deﬂection combinations tested during TN 2514 and TN 2540 at DNW-NWB (OB and SP are mutually exclusive).

The fact that several runs were dedicated to the same control led to partial overlapping of swept parameters, which can be exploited to corroborate the reliability of the estimates, by providing mean values along with uncertainty bounds, in order to be statistically more accurate. Although it is not common practice for wind tunnel researchers to present results with associated error bounds, ground-based experiments are, indeed, aﬀected by uncertainty that include a variety of systematic and random errors, such as direct measurement uncertainty, similitude errors, and modeling errors [22]. During dynamic runs the model underwent forced multi-cycle oscillations, each around a single axis at a time, of the duration of approximately 30 s. Dynamic data was measured

39 3. Aerodynamic database 3.2: Wind tunnel campaigns for sinusoidal roll, pitch and yaw oscillations with amplitude of 50 and frequencies f from 0.25 to 3 Hz, corresponding to reduced frequencies κ from 0.015 to 0.06 in pitch and 0.024 to 0.29 in roll and yaw, see Tab. 3.2 for full prospect. The point of rotation was located 0.855414 m aft the nose of the model on its plane of symmetry, as shown in Fig. 3.1. All dynamic tests were performed at zero sideslip, only changing the reference angle of attack. Three repetitive runs in wind-off conditions were followed by six repetitive runs in wind- on conditions. Some dynamic measurements were conducted using two repetitive runs in wind-off conditions followed by four repetitive runs in wind-on conditions. For elimination of mass and inertial forces the first wind-off run was processed with the first wind-on, the second wind-off with the second wind-on and so on [47].

f α0 [Hz] [deg] 1 5 f α0 2 f α0 [Hz] [deg] 0.25 [Hz] [deg] 1 0.5 5 1 2 0.75 10 2 5 0.5 1 3 1 10 2 1 2 0.25 2 10 0.5 0.5 3 1 15 0.75 15 1 2 1 2 15 0.5 2 3 1 20 0.25 2 0.5 (a) Roll oscillation. 0.75 20 (b) Pitch oscillation. 1 2

Table 3.2: Prospect of forced oscillation tests of TN 2514 and TN 2540 at DNW-NWB.

The incidence of the model w.r.t. free stream velocity as well as its attitude were set up according to the convention shown in Fig. 3.5. In particular, to realize a sideslip β at a given angle of attack for static runs, the model was first turned around its z-axis at α “ 0 so as to obtain ψ “ β, then the angle of attack was adjusted around the turned y-axis. On the other hand, for dynamic runs the pitch angle of the model was adjusted so as to realize ϑ “ α0, then the oscillation occurred around the rotated axis. The first remark that emerged from a first analysis of the outcomes of the campaign

40 3.2: Wind tunnel campaigns 3. Aerodynamic database

Figure 3.3: Lateral coefficients of the DLR-F17 versus α at different β [15]. involves the lack of symmetry of lateral coefficients with respect to β. The issue is present at zero sideslip, with the values of non-symmetric coefficients are significantly different from zero, and tends to exacerbate as the angle of attack increases, as it is evident in Fig. 3.3. With reference to the zero sideslip curve, the discrepancies at low angle of attack are presumably induced by asymmetric vortex bursting location, due to subtle asymmetries in the model geometry or wind tunnel flow. Instead, the magnitude of the behavior at higher angles of attack suggests that it is likely attributable to the tendency of high swept wings at high α to develop vertically asymmetric vortices [8]. In either case, further investigations, aimed at assessing the primary causes of the issue, are mandatory [15]. In second instance, the initial analysis of the data allowed a better estimation of the effect of the belly sting support on longitudinal coefficients. Indeed, the intent was to make the rear sting support as baseline for the S&C model of the SACCON, since (a) it is closer to a “flight case” and (b) it was adopted in all high speed campaigns. In this regard, the effects of the belly sting mounting on longitudinal coefficients were thoroughly examined by Irving [38]. The influence of the belly support was quantified into an increment, derived comparing DNW-NWB belly sting data with the rear sting ones, collected at NASA LaRC, with the assumptions that (1) the effect of the sting is invariant with M8 and β, (2) the spread of the data obtained with the two supports is statistically similar and (3) the increment is constant outside the range of angles tested. The first two hypotheses were dictated by the nature of the available data, which did not allowed a straightforward comparison.

41 3. Aerodynamic database 3.3: Database generation

Figure 3.4: Inﬂuence of sting mounting on longitudinal coeﬃcients (Body axes) [38].

The results of the modelization of belly sting influence derived by Irving are summarized in Fig. 3.4 expressed in Body reference frame. The effect on horizontal and vertical force (and likewise on drag and lift) are limited and the larger discrepancies tend to appear at both ends of the α range investigated in the experiments. Conversely, the influence on pitching moment is definitely significant, as the presence of the support alters the flow and hence the pressure distribution on the lower surface of the model. As a matter of facts, the Cm measured using the belly sting is substantially larger than that obtained with a rear sting and the two curves never overlap. This step, normally not required for an S&C model, was included to facilitate comparison with CFD results, in the background of the task of AVT-201 [38]. Finally, it is important to note that some of the measurements were obtained at the margin of the accuracy of the balance, because of insufficient size and deflection of the controls fitted on the model. This drawback eventually motivated the design and construction of a second model, called DLR-F19, to replace the original one for the assessment of low speed control effectiveness, since, ultimately, no significant flap effect could be measured using the DLR-F17 model [47].

3.3 Database generation

The experiments provided a comprehensive low speed S&C database of the SACCON configuration. The data were processed by DLR before being released. Statistical fluctuations were smoothed with the application of a 0 ˜ 10 Hz low-pass filter and wall and

42 3.3: Database generation 3. Aerodynamic database blockage correction algorithm was used on static data, aﬀected by an error of 4.0% at α “ 300. No sting bending correction was required, since model position and attitude were measured optically (unlike at NASA LaRC) [20]. Moreover, the point of application of forces and moments, correspondent to the location of the balance, was moved at a position 0.6 m aft the nose of the model, henceforth called Aerodynamic Reference Point (ARP), denoted in Fig. 3.1 as MRP. Finally the data were expressed in both model ﬁxed (Body) and aerodynamic (Wind) frames, according to the convention represented in Fig. 3.5 (Luftfahrtnorm LN 9300 [23]). The process eventually yielded four separate versions of the results, listed below:

1. Body frame with corrections (B2MmK) and without corrections (B2MoK);

2. Wind frame with corrections (B3AmK) and without corrections (B3AoK). where the suﬃxes “mK” and “oK” stand for mit Korrectur (with correction) and ohne Kor- rectur (without correction) respectively. Data were stored in the DLR ftp server [47].

Figure 3.5: The frame of reference convention adopted in TN 2514 and TN 2540 [20].

The results were provided as non-dimensional coeﬃcients, scaled in the usual manner. In particular, forces were normalized with the product of the free stream dynamic pressure q8 of the test section and the reference area, which is deﬁned as the projected area of the DLR-F17 model without considering the cutout needed for the sting and balance and it corresponds to S “ 0.77 m2. Reference length used for the scaling of pitching moment was the mean aerodynamic cord (mac) c, while rolling and yawing moments were scaled by the

43 3. Aerodynamic database 3.3: Database generation wing half-span b{2. Dimensional values of forces and moments can thus be obtained by multiplying the coeﬃcients for the following values:

‚ forces X, Y , Z, D, L Ñ q8 S

‚ pitching moment M Ñ q8 S c

‚ non-symmetric moments L, N Ñ q8 S b{2

The mean aerodynamic chord was determined according to the geometry of the planform of the model and was used as reference length for the deﬁnition of the Reynolds number:

ρ U c Re “ 8 8 » 1.6 ¨ 106 (3.2) µ

The results from steady state and dynamic tests are provided by DLR as ZIPped ASCII ﬁles, suitable for the visualization program Tecplot. Each ﬁle contains the data from a single run of TN 2514 and TN 2540 campaigns, organized in tables with a separate format for static and dynamic tests. Tables relative to static tests have a number of rows equal to the number of angles swept during the run and a total of twelve columns, namely:

• measurement number MP;

• angle of attack ALm in deg;

• angle of sideslip BEm in deg;

• free stream velocity VU in m/s;

• forces and moments coeﬃcients

– CL, CD, CY_AE, CMY_AE, CMX_AE, CMZ_AE for aerodynamic frame, – CZ_MF, CX_MF, CMY_MF, CY_MF, CMX_MF, CMZ_MF for model ﬁxed frame;

• angle of attack (from video) ALv in deg;

• angle of sideslip (from video) BEv in deg.

Tables relative to dynamic tests have a number of data rows equal to the total duration of the oscillation run (in seconds) multiplied by the rate of data acquisition (600 Hz), corresponding to roughly 18 000 rows. The columns are more than those of static run tables, since in this case a larger number of parameters is collected and in the same table both model ﬁxed and aerodynamic frame results are collected. This yields a total of twenty-nine columns, namely:

44 3.3: Database generation 3. Aerodynamic database

• time T in s;

• model attitude Psi, Phi, Theta in deg;

• model position X, Y, Z in mm;

• free stream velocity VU in m/s;

• coeﬃcients in model ﬁxed frame CX_MF, CY_MF, CZ_MF, CMX_MF, CMY_MF, CMZ_MF;

• coeﬃcients in aerodynamic frame CD, CY_AE, CL, CMX_AE, CMY_AE, CMZ_AE;

• pressure coeﬃcient from Kulities 1 to 10 K#.

All auxiliary information about test campaign, run number, flow conditions and control deflection configuration are reported in the heading of the table.

3.3.1 Database format

A common denominator that facilitates comparisons of wind tunnel and CFD results is to consider aircraft stability and control characteristics in the form of a comprehensive aerodynamic model identified from those results. In this context, this was accomplished by collecting the results of all runs of TN 2514 and TN 2540 DNW-NWB campaigns and arranging them in a single database, the aim being to generate a tabular model to assess the characteristics of the design. The same database, with minor adjustments, can also be used to fly the aircraft in real-time simulation. The data were retrieved from the DLR ftp server and processed, in order to obtain a practical and manageable stability and control database. With this in mind, a spreadsheet structure, i.e. a two-dimensional table, was preferred to a multi-dimensional lookup tables. The reason of such choice was twofold: first the data did not possess adequate symmetry characteristics, namely the number of breakpoints were not the same for all runs; secondly the processing of multi-dimensional arrays is usually computationally less efficient, especially when it comes to simulation. Not to mention that a spreadsheet is undoubtedly much more practical to handle, given the fact that each row reports the values of the states along with an indefinite number of associated data, facilitating data reading and troubleshooting. Among others, the solution was adopted by SAAB AB in conjunction with the Royal In- stitute of Technology (KTH) in the development of the Generic Aerodata Model (GAM). The database was then successfully implemented by the Swedish Defense Research Agency (FOI) in the ADMIRE simulator [50]. In that instance, the use of tabular arrays combined with the exploitation of pre-compiled S-functions, to embed the interpolation routines, allowed for a dramatical drop in computational time of the simulations. In a nutshell, the aim of this step of the study was to setup a series of stability and control aerodynamic tables and populate them with a combination of states and associated

45 3. Aerodynamic database 3.3: Database generation dimensionless coefficients, expressed in the fashion suitable for linear analysis. This means that the generic table should contain a number of columns equal to the number of the flight parameters (or states) swept in the available data, e.g. α, β, angular rates, control deflections, etc. . . , plus the six aerodynamic coefficients, whether they were expressed in Body or Wind frame of reference. On the other hand, the number of rows should be equal to the sum of all the unique combinations of the aforesaid states that were actually tested. A template of the structure of the generic spreadsheet (with three state columns) is presented in Tab. 3.3. Each highlighted block corresponds to a distinct value of the state specified in the header, in this case two δ conditions were tested, the first for two and the second for three different β values, each, in turn, tested for several values of α. It is clear how the table format allows a more flexible dissemination of the data, that is of the combination of tested conditions, since it does not require a constant distribution of breakpoints for each column. Obviously there cannot be less than two distinct values of a state within each block, otherwise interpolation would not be possible and the validity of the model would be severely limited. The different structure and nature of static and dynamic experimental results imposed to follow two different approaches, in order to achieve the desired format just described.

Table 3.3: Template of a generic spreadsheet with three states.

46 3.3: Database generation 3. Aerodynamic database

3.3.2 Static data processing

Static data provided by DLR were already in a format very close to the desired one, except that they were fragmented in multiple files, which had to be incorporated in a small number of complete spreadsheets. Runs at zero control surface deflection were taken as baseline configuration and were stored in a separate table. The initial intention was to group all control deflection data into a single spreadsheet, so as to limit the number of tables to process. However, the set of control deflections tested during the experiments produced a combination of states that could not be exploited for interpolation. The reason for this, as clarified in Tab. 3.1, lies in the fact that there are not enough breakpoints to compute interpolation for combined inboard elevon and split aileron deflection. Consequently data relative to each single control were grouped in a dedicated table, while combined effect data were not used for the purpose of this study. The solution eventually facilitated the isolation of controls contributions, which was necessary for the replication of controls on the right wing, given that the wind tunnel model accommodated controls on the left wing only. The procedure followed to merge static data into a comprehensive spreadsheet database is described below, broke down in its fundamental steps. Specific MATLAB routines were developed to address each step of the process.

1) Aggregation The data relative to each specified subset, i.e. zero-control, inboard elevon, outboard elevon and split aileron, were appended into a dedicated table. Resulting spreadsheets had a number of rows equal to the sum of the measurements for a given control and nine columns: three for the states, namely α, β and the deflection δ, and six for the aerodynamic coefficients. Apparently the zero-control table lacks the column for deflection and only has eight columns.

2) Sorting Rows were rearranged so as to put the values of the rightmost state (the third or second column, depending on the table) in ascending order. This identiﬁed a series of blocks within the column that share the same state value. The procedure was then applied on cascade to all the columns on the left, yet limited to the rows that bound each block on the right.

3) Uniformation Multiple rows relative to the same combinations of states, due to the mentioned overlapping of run conditions, were identiﬁed and replaced with their average. Then the spreadsheets, now containing only unique state combinations, were uniformed. Essentially a regular distribution of breakpoints was determined, according to the number of data available, so as to reduce numerical errors. So, the irregularly dis-

47 3. Aerodynamic database 3.3: Database generation

tributed data were interpolated at the new evenly-distributed breakpoints, obtaining more convenient monospaced spreadsheets.

4) Symmetrization As premised in Section 3.2.3, static data showed a pronounced asymmetry with respect to sideslip condition (see Fig. 3.3). Such behavior, expectable in unsteady transients, especially following dynamic stall, has no reason to occur on a symmetric airplane in steady conditions (to which static measurements are referred), thus it was decided to corrected it. This was attained by substituting the absolute values of the

coeﬃcients at each ˘β with their average and by zeroing CY , Cl and Cn for β “ 0 in the zero-control spreadsheet.

5) Isolation The control deflection spreadsheets processed so far were referred to a control applied only on the left half-wing. In order to determine the contribution of the right wing counterpart, it was necessary to isolate the effect of the deflection. This was accomplished by subtracting the baseline (zero-control) spreadsheet from each control deflection spreadsheet, obtaining the third term of the r.h.s. of (3.1).

6) Mirroring The isolated contributions of the elevons were mirrored on the right one, first symmetrically, yielding an elevator effect, then asymmetrically, returning an aileron effect. The split surface was mirrored symmetrically to obtain an air-brake effect and asymmetrically to yield a drag rudder effect. The following rule was applied to perform the mirroring procedure, so as to comply with the sign convention adopted:

RX LX Ci pα, β, δq “ Ci pα, ´β, ˘δq i “ X, Z, m (or D, L, m) (3.3a)

RX LX Cj pα, β, δq “ ´Cj pα, ´β, ˘δq j “ Y , l, n (3.3b)

where the same δ (“`” sign) applies to symmetric commands, while the opposite δ (“´” sign) applies to asymmetric commands. Once calculated the counterparts

contributions, the sign of the aileron commands δa was adjusted according to the usual convention (see AppendixB).

7) Combination The contributions of the surfaces on both sides were combined, so as to generate symmetric as well as asymmetric commands. In particular, the functions of elevator and ailerons were assigned to the inboard and outboard elevons, respectively; while the role of rudder was addressed to the split deﬂection of the outboard elevons. In addition, a version of the spreadsheets with isolated surface deﬂections contributions was saved to be used for simulation.

48 3.3: Database generation 3. Aerodynamic database

3.3.3 Dynamic data processing

The estimation of the dynamic portion of the database was obtained by imposing forced sinusoidal motions around the aircraft centre of gravity. As previously noted, dynamic runs performed on the DLR-F17/SACCON at DNW-NWB consisted of a 30 s record of the forces, moments, model position, and pressures measured as the scale model underwent 1 DoF forced oscillation about one of its Body axes. Nominally multiple data runs were taken at each test condition and used to eliminate inertial forces. The general practice for forced oscillation wind tunnel data consists in the processing of each multi-cycle run to obtain a condensed one-cycle average of the original data, together with the standard deviation, indicating the spread of the response across the cycles. The results are then plotted, often together with the correspondent static curve, and analyzed, in order to assess the properties of the dynamic response of the design and the characteristics of unsteady aerodynamic phenomena. Particular emphasis is used on the investigation of non-linear behaviors, in the evaluation of their extent and characteristics and, especially, in the identification of their dependence on the frequency of the oscillation. Exhaustive analyses of forced oscillation data were performed as part of the AVT-161. In order to comply with the mathematical modelization enunciated by (3.1), the data recorded during forced oscillations had to be processed and the increments due to the angular rates extracted. Generally speaking, forced oscillation tests can only measure combinations of both linear and angular rates, e.g. pitch oscillation motions include pitch rate as well as angle of attack rate, inevitably leading to highly correlated signals of α and q for pitch rotations and β and p or r for roll or yaw rotations, practically undistinguishable. Linear oscillations, namely plunge and sideway motion, are required to estimate the isolated influence of α9 or β9. However, no test of this type was performed during TN 2514 and TN 2540, hence no direct evaluation of unsteady aerodynamics effects could be derived from the wind tunnel results. Eventually, only angular rates were used as input signals (as common for flight test evaluations), well knowing that α9 and β9 effects are included in the resulting coefficients [18]. Hence, considering that neither sideslip angle nor Mach number sweeps were performed during forced oscillation tests and that no combined rotations maneuvers were simulated, the last two terms on the r.h.s. of (3.1) were reformulated as:

ω t 9 p q r ∆Ci α, β, M8, p, q, r ` ∆Ci α, β, M8, α,9 β Ñ ∆Ci α, p¯ ` ∆Ci α, q¯ ` ∆Ci α, r¯ ´ ¯ ´ ¯ ´ ¯ ´ ¯ ´ ¯ according to the common practice [18, 20] of putting p¯ “ p ‘ β9, q¯ “ q ‘ α9 and r¯ “ r ‘ β9, where the symbol ‘ indicates an undeﬁned combination, not a sum. The procedure followed to extract dynamic data from forced oscillation time-histories and merge them into a suitable spreadsheet database is described below, broken down in its fundamental steps. Again, each step of the process was implemented in a speciﬁc

49 3. Aerodynamic database 3.4: Aerodynamic analysis

MATLAB routine, so as to hasten the process. Apart from the ﬁrst three, the processing traced the same steps described in Section 3.3.2, which, ergo, are not described in detail.

1) Averaging The angular rates were obtained by direct diﬀerentiation of the φ, ϑ and ψ signals

and then normalized, taking U8 as reference velocity and either the reference chord or the wing span as reference lengths. Then a 1-cycle average of all time response data was calculated. The procedure was applied to the attitude angle concerning the forced oscillation and to the aerodynamic coefficients, while other data, listed in 3.3, were omitted. The first second of the time response was ignored, so as to consider only the data relative to fully developed dynamic by cutting off the initial transient, in order to achieve more accurate result.

2) Sampling The data of each 1-cycle average were sampled at eight distinct values of the measured rates. This provided an adequate description of the aerodynamic response of the SACCON to angular disturbances, both positive and negative in sign, at several values of nominal angle of attack, i.e. 5˝, 10˝, 15˝, 20˝. The sampled data were stored in speciﬁc tables complying with the format deﬁned by Tab. 3.3.

3) Aggregation Each tables collecting the sampled 1-cycle average of each run were progressively appended to its speciﬁc spreadsheet, depending on the rate tested. The generated spreadsheets had a number of rows equal to the number of dynamic runs carried out for the DoF multiplied by eight and eight columns: two for the states, namely α and the normalized rate, and six for the aerodynamic coeﬃcients.

4) Sorting

5) Uniformation

6) Isolation The contributions of the angular rates were isolated from the results by subtracting the baseline data to the dynamic eﬀects spreadsheets.

This concludes the generation of the database of the SACCON. The procedure yielded a complete database representing a thorough aerodynamic model of the conﬁguration under study and, above all, suitable for rapid implementation in a ﬂight simulator.

3.4 Aerodynamic analysis

Extensive aerodynamic analysis has been carried out within the AVT-161 task group on the ground of the results provided by the successful joint eﬀorts of experimental and

50 3.4: Aerodynamic analysis 3. Aerodynamic database

CFD methods. The investigations addressed several aerodynamic aspects of the configuration, such as the prediction of turbulent transition, aerodynamic optimization of the design, the evaluation of vortical structures, assessment of the influence of different leading edge configurations, with the aim to correctly interpret the flow physics of the design. The results of AVT-161 provided a substantial understanding of the aerodynamic performance and peculiarities of the SACCON, as exhaustively documented by [15, 16, 18, 23]. The section presents an overview of the main aspects concerning the aerodynamic characteristics of the SACCON, based on those outcomes.

3.4.1 Baseline

The overall longitudinal coefficients of the configuration at different sideslip angles are shown in Fig. 3.6 and Fig. 3.7. The curves indicate the strong influence of vortical structures in the topology of the flow around the aircraft. It can be seen that drag rapidly increases its slope for α ą 100, in a divergence-like fashion, signifying the onset of a tip vortex, which strengthen as the angle of attack increases. The reduced slope of the curve and the deferral of stall to higher angle of attack, in this case for α ą 280 and rather smoothly, display the influence of non-linear vortical flow on the lift generated by the SACCON. The graph also shows a beneficial effect of sideslip in delaying the stall. The non-linear lift contribution, generated by the vortex systems on the upper surface of the configuration and predominant for α ą 150, continuously increases as the strength of the apex vortex does and due to the large region of attached flow.

(a) Drag. (b) Lift.

Figure 3.6: Baseline drag and lift coeﬃcients versus α, varying β.

51 3. Aerodynamic database 3.4: Aerodynamic analysis

(a) Pitching moment. (b) Interpretation of the ﬂow topology [24].

Figure 3.7: Baseline pitching moment coeﬃcient versus α, varying β.

The curve of the pitching moment coefficient is shown in Fig. 3.7a. Its positive slope and positive Cm0 are indicative of an unstable aircraft and, worse, not inherently balanceable, i.e. whose trim is not guaranteed and, in any case, not trivially achieved. In addition, the pitching moment shows an even stronger sensitivity to the non-linear flow components, as can be appreciated in the graph. In fact, it was found that the pitching moment curve gains its characteristic appearance due to the vortex systems behavior on the upper surface of the configuration. With increasing angles of attack a tip vortex is created, which becomes stronger as its onset point, initially fixed, starts moving upstream beyond a certain α. An interpretation of the behavior of the pitching moment, provided by [24, 21], is reported in

Fig. 3.7b, showing the characteristic Cm discontinuity (dip), caused by the different vortex locations and interactions. A detailed explanation of the vortical structure of the flow of the SACCON was suggested by Huber at al. [24]. Moreover, during AVT-161 it was found a significant susceptibility of the pitching moment to different leading edge configurations and turbulent transition location [15]. Rolling and yawing coefficients are grouped in Fig. 3.8. The sideforce coefficient shows a rather conventional trend, characterized by decent values and a negative slope (CYβ ă 0), except that for α » 150, in correspondence to the pitching moment dip. As a general remark, it can be stated that the SACCON displays decent roll stiffness up to 15˝ angle of attack and poor directional stability up to 10˝ angle of attack. As the angle of attack increases, the vortical flow effects fortify and the asymmetrical bursting of the vortices of the upper side due to sideslip activates unstable tendencies in both roll and yaw. In particular, the loss of lift, due to premature vortex breakdown, on the windward half-wing

52 3.4: Aerodynamic analysis 3. Aerodynamic database

(a) Rolling moment. (b) Yawing moment.

Figure 3.8: Baseline lateral-directional coefficients (Body frame) versus β, varying α. induces a destabilizing rolling moment, which tends to increase β and lateral stability is lost permanently On the other hand, sideslip has a variable effect on yawing moment, depending on the values of α and β. In fact, for α » 150, the behavior is unstable, but, as the angle of attack is further increased, some directional stability is recovered for β ą 50. This could be caused by the drag increment on the windward half-wing, which is exposed to the turbulent flow downstream the bursting point. However, the overall directional stability characteristics of the configuration appear irremediably insufficient. These results prove that the SACCON actually exhibits decent lateral characteristics, at least at moderate angles of attack, but poor directional stability, owing to the drawbacks inherent to the flying wing design.

3.4.2 Dynamic behavior

The solid database of dynamic results, constituted by the time histories of the aerodynamic coeﬃcients measured during the forced oscillation runs, provides a valuable instru- ment to investigate the unsteady aerodynamic characteristics of the SACCON. However, a detailed aerodynamic analysis of the ﬂow topology is beyond the scope of this study, not to mention that the breadth of dynamic data collected during the two wind tunnel campaigns exceeds what can be fully examined in a single section. For this reason, the discussion is limited to the most meaningful results that were derived from the experimental measurements of AVT-161. In this perspective, the graphs reported in this section depict the 1-cycle average of the oscillation response together with standard deviation bars, modeling the spread of the data across all cycles of the reference run.

53 3. Aerodynamic database 3.4: Aerodynamic analysis

(a) Lift loops at 1 Hz. (b) Pitching moment loops at 1 Hz.

Figure 3.9: 1-cycle average of lift driven by pitch oscillations [20].

The data plotted in Figs. 3.9 and 3.10 show the results of the 50 amplitude sinusoidal pitch oscillations about nominal angles of attack of α “ 50, 100, 150, 200 (cf. Tab. 3.2) and clearly demonstrate the non-linear characteristics of the flow field generated by the aircraft. Static data are plotted in the background to facilitate the comparison. The difference between the static and dynamic curves is interpreted as the dynamic damping effect. In general, the damping effect produced by sinusoidal oscillations forms elliptical loops about the static data, which widen with frequency, as can be appreciated in the figures. The pitching moment experiences a more pronounced dynamic effect than the lift, whose loops are barely identifiable below α “ 150. In the higher α range, near flow separation, the lower frequency 1 Hz oscillation results in a more non-linear behavior than

(a) Lift loops at 3 Hz. (b) Pitching moment loops at 3 Hz.

Figure 3.10: 1-cycle average of pitching moment driven by pitch oscillations [20].

54 3.4: Aerodynamic analysis 3. Aerodynamic database the higher 3 Hz one. Presumably this is due to the flow dynamics having sufficient time to transition between the different states at the lower frequencies. Conversely, at higher frequencies the flow does not have enough time to transition, yielding smoother trends [18].

(a) Sideforce loops. (b) Rolling moment loops. (c) Yawing moment loops.

Figure 3.11: 1-cycle average of lateral coeﬃcients driven by 1 Hz roll oscillations [20].

The 1-cycle average of the dynamic effects of 1 Hz roll oscillation on lateral-directional 0 0 0 0 0 coefficients are shown in Fig. 3.11 for α “ 0 , 5 , 10 , 15 , 20 . Only the increments ∆Ci attributable to dynamic effects are shown. The loops remain fairly elliptical up to α “ 100, exhibiting minimal deviation; then they become increasingly irregular and asymmetric with large standard deviation, sign of significant flow unsteadiness originated by vortical flows. Moreover, qualitative information about roll derivatives can be derived from the shape of loop. In particular, the slope of the ellipse major axis is proportional to the Clβ term, while the direction of the oscillation loop indicates the sign of the damping derivative

Clp , that is to say positive (propelling) for clockwise loops and negative (damping) for counter-clockwise loops.

(a) Sideforce loops. (b) Rolling moment loops. (c) Yawing moment loops.

Figure 3.12: 1-cycle average of lateral coeﬃcients driven by yaw oscillations.

55 3. Aerodynamic database 3.4: Aerodynamic analysis

Finally, Fig. 3.12 shows the results of the 50 amplitude sinusoidal yaw oscillations about nominal angles of attack of α “ 50, 100, 150, 200. The lack of any vertical surface on the SACCON configuration results in rather small yaw effects. As with the previously discussed oscillation data, the amplitude of the loops around the static curve increases as the frequency does, while the shape becomes more regular. One can observe that the lateral asymmetry and the vertical offset found in centroids of the ellipse of roll and yaw motions are emblematic of small asymmetries in the model geometry as well as potential flow angularity [20]. In conclusion, a common factor to all graphs is the significant growth of standard deviation at the highest angles of attack, indicative of considerable flow unsteadiness during the cycles.

3.4.3 Control authority

As already mentioned, the controls designed for the SACCON comprehend two elevons per side, the latter of which can split to operate as drag rudder. In this scenario, the elevator control was appointed to the inboard elevons; the outboard elevons explicated the ailerons command; while the rudder command was assigned to the split deflection of the outboard elevons. Due to the overlap of two fundamental commands to the same surface, the feasibility of such control surface configuration must be further investigated through complete simulation, in order to assess its actual capability to provide acceptable control characteristics. The initial design of the SACCON envisaged the accommodation of two additional split aileron located on the wing tips, which, however, were never prototyped and tested in any of the wind tunnel campaigns conducted so far. The effects of the elevator, that is the contribution of the inboard elevons, on lift and pitching moment are shown in the next figures, first as isolated contributions, then summed to the baseline values, to put their effects in perspective. The contribution of the elevator to lift is illustrated in Fig. 3.13. It presents a rather 0 odd behavior for δe “ 5 , as, apparently, the command induces an overall downforce w.r.t. the baseline configuration at low angle of attack, with a sudden inversion for α ě 200. The conventional behavior is restored for δ ą 50, with lift increasing as the deflection does. The anomaly could be due to the disruption of the precarious vortex structures induced by the deployment of the surface, supposedly leading to premature vortex breakdown with consequent drop of vortex lift. The effectiveness of the elevator is severely compromised at the highest angles of attack, that is to say for α ą 200, up to almost complete loss of efficacy for α ą 250. On the other hand, the trend of the curves for negative deflection is much more desirable, at least within low to medium α, then the ill-effects of non-linearities and separation reduce the efficacy of the surface, although not as much as for positive deflection. From Fig. ?? the worst condition is found to be a medium negative deflection at high α, which involves an elevator efficacy close to zero, if not slightly inverted.

56 3.4: Aerodynamic analysis 3. Aerodynamic database

Figure 3.13: Elevator contribution to lift.

The much more critical influence of the elevator effector on the pitching moment is presented in Fig. 3.14. It can be seen that it globally shows a more desirable trend than lift, at least at low to medium angle of attacks, with a well definite negative slope throughout all deflections. Some effectiveness is lost for negative (upward) deflection at α » 100. For α ě 200 the influence of non-linear flow induces an inversion in the sign of the pitching moment increment and a general reduction of the effectiveness of positive deflection of the control, while the effect of negative deflection remain acceptable up to α “ 250. At 0 high angles of attack around δe “ 5 the slope is inverted and the elevator produces an undesirable nose-up moment, which jeopardize the controllability of the aircraft at high α. Fortunately, the correct behavior is restored as the deflection is incremented. The total effect of the elevator on lift and pitching moment are shown in Fig. 3.15, allowing a direct visual quantification of the increments, compared to the baseline values of the coefficients. It is observed that the lift is not significantly changed by the deflection of the elevator, regardless of the angle of attack; while the pitching moment shows a significant sensitivity to the control up to medium α. Nevertheless, whatever effect is exerted, it practically disappears at the highest angles of attack. More importantly, the control results inadequate to provide enough moment to counter-act the nose-up tendency

57 3. Aerodynamic database 3.4: Aerodynamic analysis

Figure 3.14: Elevator contribution to pitching moment.

(a) Total lift. (b) Total pitching moment.

Figure 3.15: Total lift and pitching moment with elevator.

58 3.4: Aerodynamic analysis 3. Aerodynamic database of the SACCON, given that, at maximum deflection, negative moment is achieved only for α ă 100. Hence, the issue of elevator effectiveness is not relegated to high α range, as advisable at least to guarantee the trimmability within a plausible flight envelope.

(a) Rolling moment. (b) Yawing moment.

Figure 3.16: Rolling and yawing moments induced by the ailerons.

The aileron effect, shown in Fig. 3.16, is denoted by a perfectly linear trend, in both rolling and coupled yawing contributions. It is worth to note that only two, rather limited deflections of the outboard elevons were tested and chances are that the investigation of broader range of deflection will reveal more intricate patterns in the dependency of lateral coefficients upon lateral control. The data of yawing moment are indicative of an adverse yaw effect, which intensify as the α increases becoming quite prominent. Just the condition of α “ 00 features a preferable proverse yaw effect. Finally, the effects of the application of rudder control, realized by the differential deployment of split outboard ailerons, are plotted in Fig. 3.17. The direct effect on yawing moment coefficient presents a qualitatively satisfactory behavior, despite minor discontinuities, yet within a reasonably linear trend. It can although be argued that the peak effect on yaw exerted by the drag rudders at their maximum deflection is matched, in 0 magnitude, by the adverse yaw effect of ailerons at just δa “ 10 , making the effectiveness of such control effector at least questionable. Hopefully the designed tip split ailerons will prove capable of providing better directional control. The change in rolling moment due to drag rudders is characterized by a rather discontinuous behavior, caused by the less unpre- dictable outcome of the interaction of the split surface with the complex airflow around the configuration. The plot in Fig. 3.17a shows how the various curves do not share a common

59 3. Aerodynamic database 3.4: Aerodynamic analysis

(a) Rolling moment. (b) Yawing moment.

Figure 3.17: Rolling and yawing moments induced by the drag rudders. pattern, even though the overall roll response is positive. The strong non-linear flow physics that dominate the aerodynamics of the SACCON, especially the large separation regions, greatly influence the capacity of the designed control surfaces to provide satisfactory control actions. The values reported in Tab. 3.4 clearly quantify how control power represents a main issue for the SACCON, delineating a scenario in which not even the exploitation of control allocation to multiple surfaces is likely to be sufficient to generate suitable control authority. If this was to be the case, it would potentially require major redesign of the configuration.

Elevator Ailerons Rudder

C 0.148 C 0.0463 C 0.0153 Lδe lδa ´ lδr C 0.0326 C 0.00707 C 0.00229 mδe ´ nδa nδr ´

Table 3.4: Control authority of the SACCON at α “ 50 and β “ 00 (in 1/rad).

The highly non-linear dependence of control actions exerted by the SACCON on angle of attack, especially in the high α range, dreads the possibility of undesirable reversal phenomena. In this regard, Fig. 3.16a shows how the already poor lateral control authority of the SACCON is substantially reduced for α ą 150; in addition the aileron deﬂection at high angles of attack produces signiﬁcant adverse yaw, as depicted in Fig. 3.16b. The com-

60 3.4: Aerodynamic analysis 3. Aerodynamic database bination of reduced aileron effectiveness and large adverse yaw may lead to the so-called roll reversal phenomenon, which involves a roll in a direction opposite to that commanded. Reference [8] (p. 732) reports that a valid method to verify the susceptibility of an aircraft to roll reversal is the Lateral Control Departure Parameter (LCDP) criterion. The expression of the LCDP is derived from the simplified equations of rolling and yawing motions and is defined as follows:

Cn ` kARI Cn LCDP “ C ´ C δa δr (3.4) nβ lβ C k C lδa ` ARI lδr where kARI (Aileron to Rudder Interconnect) is the ratio of rudder to aileron deflection for coupled lateral-directional control effectors. In the case of the SACCON kARI “ 0 and the figure takes the name Aileron Alone Departure Parameter (AADP). For regular response, LCDP must be strictly positive. If negative with a large magnitude, chances are that the aircraft will also be prone to depart in yaw and spin entry is likely [8].

Reference [8] also suggests the use of the so-called Cnβ DYN criterion for predicting yaw departure at high angle of attack. The expression, commonly used in ﬂight dynamics analysis, is derived from the open loop lateral-directional quartic equation:

Izz Cnβ DYN “ Cnβ cospαq ´ Clβ sinpαq (3.5) Ixx

The criterion can be regarded as the extension of the condition Cnβ ą 0 valid at low angles of attack: for directional stability at high angles of attack Cnβ DYN must be positive. If the parameter is negative, the aircraft may experience yaw departure and the dutch roll mode may be unstable. Resistance to yaw departure tendency can be improved by an increment in dihedral effect, even though a large Clβ rises the roll sensitivity of the vehicle to lateral gusts and command inputs. The first criterion (Fig. 3.18) predicts that the SACCON experiences aileron reversal in the neighborhood of α » 150; then regular response is recovered and maintained up to α “ 250. Beyond that incidence the aileron command is strongly reversed. On the other hand, Fig. 3.19 indicates that the aircraft experiences directional divergence for α ą 170 and the severity of this diverge increases with the angle of attack, up to α “ 250; then it improves slightly. It is worth to note that no prediction was derived for α “ 00, since no β-sweep data was available in the wind tunnel data considered. The results of these criteria proved to correlate well with experimental and flight test measurements and are widely used with good degree of confidence [8]. Still, they represent mere indicators of complex and, often, unsteady behaviors, which require complete non- linear analysis to be fully understood.

61 3. Aerodynamic database 3.4: Aerodynamic analysis

Figure 3.18: LCDP.

Figure 3.19: Cnβ DYN.

62 Chapter 4

Static analysis

This chapter presents a discussion of the results of static analysis of the SACCON applied to the aerodynamic model delivered by the database generated according to the procedure described in Chapter3. The static analysis of the SACCON provided quantitative evaluation of the static characteristics of the design, which was important to assess control authority as well as to identify critical areas of operation. Some qualitative com- ments were already forwarded in the context of the analysis of the aerodynamic data in Section 3.4. The first step was the definition of a reasonable flight envelope, across which perform the assessment of longitudinal static stability and trim. The investigation of the influence of CG position throughout the whole envelope was also considered, in order to provide a better understanding of both stability and controllability issues of the SACCON and to derive first attempt CG location limits. As discussed in Section 3.4, the aerodynamic design of the aircraft yields a pitching moment with positive slope, indicating negative longitudinal stability for CG located at the ARP, i.e. 4.8 m aft the nose, and positive valued for α “ 00, a combination that makes the balancing of the aircraft extremely demanding for the elevator, which tends to saturate quickly. As if that was not enough, the aerodynamic analysis of the model delineated a configuration with extremely poor control authority, making the balancing of the aircraft even more elusive, and to all appearances inadequate to guarantee acceptable control characteristics. In view of a forthcoming development of a wind tunnel model with improved control effectiveness, it was decided to artificially boost the effectiveness of the controls by multiplying the available data, specifically the increments due to control effectors, by a factor of 2. By virtue of the mathematical formulation adopted for the aerodynamic model (3.1), this was accomplished by simply putting:

˜δ δ ∆Ci α, β, δe, δa, δr “ 2 ¨ ∆Ci α, β, δe, δa, δr (4.1) ´ ¯ ´ ¯

63 4. Static analysis 4.1: Flight envelope deﬁnition

This allowed to extend the analysis, especially the evaluation of trim, to a reasonably broad range of ﬂight conditions, otherwise restricted to a much narrower envelope, due to the quick saturation of the elevator, which would have provided uninteresting results.

4.1 Flight envelope deﬁnition

The term flight envelope or service envelope is used to refer to the range of flight conditions that bounds the satisfactory operation of the aircraft and beyond which some aspect becomes unacceptable. In general, a flight envelope summarizes a set of restrictions to airspeed, altitude, Mach number, load factor, angle of attack, angle of sideslip, etc. . . arising from a matrix of interrelated aspects, ranging from structural loads to handling qualities, from engine performance to aeroelastics, that have to remain within acceptable limits for the aircraft to operate safely and carry out its mission effectively. Since the boundaries of a complete flight envelope depend on several areas of technical expertise, they are usually defined after numerous reviews of the design and review of results from ground tests and predictions of flight characteristics in such areas as structures, aerodynamics, stability and control, flight controls. Usually an initial, limited, low-risk, flight envelope is established, typically lying in the middle of the projected final flight envelope. Subsequent flight tests are then devoted to expanding the initial envelope by pushing the airplane at increasing ranges, both low and high, of engine operation, airspeeds, altitude, load factor, centers of gravity and with system/subsystem failures. Indeed, opening the envelope is a task that demands caution and must be approached systematically, in coordination and cooperation of the many disciplines involved in the design and test of an airplane [31]. In the case of the SACCON, no prototypes of the final configuration have yet been build and the experimental and numerical investigations only covered aspects related to aerodynamics and control. Moreover, no specific information regarding the mission profile of the aircraft, nor about its power system and internal structure are available. For these reasons, at such a early design phase a rather crude flight envelope was defined with the sole purpose to investigate the dynamic behavior of the SACCON, test the effectiveness of its controls and, ultimately, assess its handling qualities in the actual context of plausible flight conditions. The limitations taken into account for the definition of the boundaries of the flight envelope of the SACCON regarded:

• airspeed;

• altitude;

• CG location.

Only steady, level ﬂight conditions were considered, hence the edges outlined by the envelope represent “1g” ﬂight conditions. Due to the lack of whatsoever information concerning

64 4.1: Flight envelope definition 4. Static analysis weight, mass distribution and propulsive system of the SACCON, specifications and data of comparable aircrafts were appropriately scaled, if necessary, and used, for the individuation of suitable ranges for the aforementioned parameters. In particular, the performance of the SACCON in terms of service ceiling and maximum airspeed mimic those of the Dassault nEUROn, similar in design and mission specification; while mass and inertia properties were scaled down and adapted from those of the Northrop B-2. The considerations that led to the definition of the edges of the envelope are described in the following paragraphs.

4.1.1 Airspeed limitations

The restrictions in the range of velocity, within which an aircraft can operate safely and achieve steady level flight, are related to the aerodynamic performance, propulsion system and structural capabilities of the airframe and varies with altitude. The lower limit of the speed envelope is determined by the ability of the airframe to generate enough lift to maintain steady level flight and corresponds to the stall speed. This lower speed boundary changes with altitude: as the density of air decreases, a greater velocity is necessary in order for the wing to produce the lift required to sustain the airplane. Neglecting the dependence of aerodynamic coefficients upon air density (which is congruent with assuming their invariance w.r.t. Reynolds number), the value of stall speed can be derived from the following relation:

2 m g Vst “ (4.2) dρ8 SCLmax

where CLmax is the maximum lift coefficient of the baseline configuration. The equation shows that, as the altitude increases, the density drops in a exponential fashion and the stall speed rises inversely and it defines a curve that continues up to the maximum altitude. The upper limit for flight speed is attributable, in first instance, to the engine power available to overcome drag, thus corresponding to the velocity at which drag equals the maximum thrust and no increment in velocity can be achieved, unless exploiting the weight of the aircraft itself (nosedive). Hence, the lower portion of the boundary is sloped in the same manner as the stall curve, due to increase in drag at lower altitude. However, the aspect of power requirement is not the only restricting the maximum allowable speed. In fact, the maximum speed can be limited either to avoid flying in flow regimes the aircraft is not suited for (notably transonic, which trigger buffet phenomena) or to prevent aeroelastic flutter phenomena, which activate as the dynamic pressure rises. Usually the requirements on structural integrity are more restrictive than the aerodynamics or propulsive ones and maximum speed is constrained by the requirement of avoiding damage or, worse, failure of the airframe. No specific performance figures of the SACCON are yet available, except that it is designed

65 4. Static analysis 4.1: Flight envelope deﬁnition to cruise in the high subsonic regime. Taking the nEUROn as reference, the maximum velocity of the SACCON was set to 270 m/s („ 980 km/h) [49].

4.1.2 Altitude limitations

An aircraft can fly from sea level up to the maximum operating altitude, which, in case of a UAV, is normally limited by the performance capability of the airplane/engine combination alone, since pressure differential limitations do not apply, as the cabin is not pressurized. In certain configurations, e.g., flaps down or “dirty” configuration, the maximum allowed altitude may be lower than in the “clean” configuration. In this study, though, only flaps-up configuration was considered. The power needed varies almost linearly with altitude, but the nature of drag means that it varies with the square of speed, making easier to go higher than faster. This is true up to the altitude where lack of oxygen for the engines starts to play a significant role. It was supposed that the same powerplant of the nEUROn powered the SACCON, namely one SNECMA M88 40 kN of (dry) thrust afterburning turbofan engine [49]. Then, the absolute or maximum ceiling for the SACCON was supposed to be equal to the service ceiling of the nEUROn, corresponding to 14 000 m. Considering the speed limitations, prescribed in the previous paragraph, the maximum speed of the SACCON corresponds to

M8 » 0.92 at cruise altitude.

4.1.3 CG limitations

Prescribed limits for the location of the CG are crucial, for the longitudinal stability and maneuverability characteristics of the aircraft depend closely on its position relative to the NP. With no knowledge concerning mass distribution or simply the centering of the aircraft, it is impossible to ascertain a reasonable range for the CG location. Nevertheless, being the aim of the investigation the assessment of acceptable bounds for the CG range, with no constraints other than the realization of adequate S&C characteristics, the analysis allowed for a crude approach. Then a rather wide stretch of CG positions was set arbitrarily, regardless of any consideration about the actual mass distribution of the ﬁnal aircraft. In this context the ARP, shown in Fig. 3.1 and located 4.8 m aft the nose, was taken as intermediate location for the CG, as it appeared close to its most plausible location. The location of the CG was then varied between 4.0 m and 5.0 m, in order to cover the broader possible range of displacement and provide results with extensive validity.

The envelope resulting from the application of the aforementioned constraints is shown in Fig. 4.1 with superimposed calculation breakpoint grid. It can be seen that the upper limit for velocity is a vertical line, indicating that the power requirement is always met, as excess thrust is available from the engine in any ﬂight condition within the envelope. The stall velocity varies from around 43 m/s at sea level to about 100 m/s at the maximum

66 4.1: Flight envelope deﬁnition 4. Static analysis

Figure 4.1: The analysis envelope of the SACCON altitude. The displacement of the center of gravity cannot be represented in such diagram, but the prescribed limits are reported in Fig. 4.2, highlighted by green dots for the sake of clarity, along with the location of the ARP, marked by a red bar. The low-speed flight represent the most critical condition for stability and trim, due to the intensification of nose-up pitching moment at high angle of attack, which require large elevator deflection with consequent risk of saturation. On the other hand CG locations too far from the NP, that is a too high static margin, either positive or negative, compel excessive elevator deflection at a wide range of flight conditions, not limited to near-stall

Figure 4.2: Limit locations of the CG of the SACCON (in red the ARP).

67 4. Static analysis 4.2: Longitudinal static stability

ﬂight, and should be avoided in any case.

4.2 Longitudinal static stability

Prior to enter the discussion of the trim of the SACCON, it is important to address the issue of its static stability, with the purpose to quantify the static characteristics of the configuration across the analysis envelope defined in Section 4.1. In particular, the value of the static margin is of primary importance for the determination of the aircraft’s longitudinal handling qualities, which primarily regulate the airworthiness of the airplane. The aerodynamic center of an airplane corresponds, similarly to that of an airfoil, to the longitudinal positions for which the aerodynamic moment is constant with respect to the variation of angle of attack, and thus lift (at least within a certain range). For this reason, the AC of a complete configuration is usually referred to as the neutral point NP. Reference [1] gives the following definition for the NP in ratio of the reference chord:

Cmα pARP q kn ” kNP “ kARP ´ (4.3) CLα

The static margin SM is a measure of the static stability of the airplane with respect to angle of attack disturbances. It corresponds to the distance from the CG to the NP in ratio of the reference chord, but can also be directly expressed rearranging (2.2) as ratio of the slope of the pitching moment (w.r.t. the CG) and lift coeﬃcient with angle of attack.

Cmα pARP q Cmα pCGq K “ kn ´ k “ kARP ´ ´ k “ ´ (4.4) CLα CLα

Whereas the lift curve slope CLα is positive within normal limits of angle of attack, the pitch stiffness Cmα , which is a strong function of CG position, can take both negative and positive values, greatly influencing the overall behavior of the aircraft. A concept not to be confused with the aerodynamic center is the center of pressure CP, defined as the point of the aircraft where the resultant of the pressure field acts, thus the point about which the aerodynamic moment is zero. From simple classical mechanics considerations, it is derived as:

CmpARP q kCP “ kARP ´ (4.5) CL

The center of pressure becomes crucial in the trimming of the conﬁguration, for it inﬂuences the global pitching moment at the CG that has to be balanced by the elevator: a CP close to the center of mass implies a resultant with a short lever arm and thus a small moment to compensate, for a given resultant, and viceversa.

68 4.2: Longitudinal static stability 4. Static analysis

Figure 4.3: Variation in static margin with CG position and angle of attack.

Fig. 4.3 shows the variation in static margin with CG position at several values of α for the baseline SACCON. As expected, at low angle of attack the SM decreases as the CG moves aft and the influence of α is nearly unnoticeable, indicating a rather linear behavior. Then, from α “ 100 up, the curve of the static margin becomes sensitive to the angle of attack and starts shifting upward, that is the static margin increases at given CG location. This is significant of the departure from linear behavior, due to the set off of non-linearities induced by vortical flow structures and separation. The curves for α ą 150 have been omitted, since the SM values they reported were way outside a meaningful range of values, making them scarcely interesting. Within the conventional angle of attack range for steady level flight, the SM is seen to go negative for xCG ą 4.6 m, which roughly coincides with the neutral point. To attain a desirable positive static stability of 5% (highlighted in Fig. 4.3 by a dashed line), the mass distribution of the SACCON must yield a CG located fore of 4.4 m, which is unlikely to be attainable outside a narrow range of operative conditions, as it calls for a rather forward shifted weight distribution. Due to the limitations of available aerodynamic data, the neutral point and also the static margin plot result relatively insensitive to variations in airspeed, as well as altitude, as illustrated in Fig. 4.4. Again the sole diversions from the linear trend of the plot are registered at the lowest speeds, where the increase in angle of attack, necessary to sustain the vehicle, forces the aircraft to operate in the region beyond the pitching moment dip, dominated by non-linear behavior. In practice though, it is a known fact that the neutral point does shift aft at higher Mach numbers [32], inducing an increase in the static stability.

69 4. Static analysis 4.3: Trim assessment

(a) h “ 0 m. (b) h “ 14 000 m.

Figure 4.4: Variation of static margin with CG position and velocity.

The results of the analysis outline an overall unstable conﬁguration, capable of achieving positive stability only for extremely forward shifted CG. For intermediate CG locations 0 (4.4 m ă xCG ă 5.0 m) and in cruise conditions (α ă 10 ), the SM ranges from 5% to ´10%. This suggests that some sort of relaxed stability could be attained, at least in a limited number of operative conditions, with a appropriate weight distribution and suited payload management during the mission. On the other hand, reduced longitudinal stability, or better still instability, translates in a greater reactivity of the aircraft to command inputs, that is to better maneuverability. Yet, it is important to keep in mind that the eﬀectiveness of the controls has been raised to the double of the actual value, due to the scarce control authority exhibited by the design. This implies that, no matter how sharp the reactiveness to controls might be, the magnitude of the response of the SACCON will likely be inadequate.

4.3 Trim assessment

The scopes of the calculation of equilibrium conditions of the SACCON in steady, i.e. non-maneuvering, level flight (γ “ 0) are the validation of the proposed analysis envelope, through the identification of critical areas, and the investigation of control authority, which provide a good estimate of pitch axis control powers, especially for low speed flight conditions. The aerodynamic data are those of the database obtained according to the procedure described in Chapter3. The analysis was done solely for the longitudinal axis, for both theoretical and practical reasons. The first is related to the absence of asym-

70 4.3: Trim assessment 4. Static analysis metric thrust conditions as the SACCON is single-engined; the second is due to the fact that the available database made it impossible to assign ailerons and rudder commands to distinct surfaces, as both are expressed by the outboard elevons. At first it was considered to bypass this shortcoming by allocating both lateral and directional commands to the same surface, that is superposing their deflections. However the proposed solution was not deemed satisfactory, as it would cause an inadmissible deterioration of the already scarce effectiveness of the ailerons. Moreover no data (neither experimental nor numerical) was available regarding blended deflection of the elevons, making it impossible to reliably modelize such unconventional aerodynamic configuration, particularly within the already adverse aerodynamics background of the design. Indeed, the testing of tip drag rudders, envisaged in the original design of the SACCON (cf. Fig. A.1), as surfaces dedicated to directional control is mandatory for the completion of the database of the aircraft, as the integration of directional control is necessary to extend the validity of the controls model to all three fundamental axes. As pointed out by Etkin [2] and illustrated in Fig. 2.8, an airplane with fixed controls can be balanced only if flying at the α or CL at which Cm “ 0. Thus, in order to fly at different speed, some form of longitudinal control is necessary, so as to achieve equilibrium at different values of α. A variable pitching moment is generated by deflections of the elevator, which may be all (in this case referred to as stabilator) or part of the tailplane, or a trailing edge flap for tailless designs. The elevator is a symmetric command, thus its actuation induces increments in all longitudinal coefficients, without affecting the lateral ones. The predominant effect of the elevator regards pitching moment. Usually the ∆CL for aircrafts with tails is small enough to be neglected, whereas it is not so for tailless aircrafts as the elevator is accommodated on the main wing and its influence on lift is significant. The contribution ∆CD can safely be neglected in any case. Textbook practice is to assume linear aerodynamics and address the trim problem via a set of algebraic linear equations, that can be solved using standard methods. The linearized aerodynamic model for lift and pitching moment with explicit elevator contribution in trim conditions is given by:

C C α C δ C L “ Lα ` Lδe e “ Ltrim $ (4.6) ’ C C C α C δ 0 & m “ m0 ` mα ` mδe e “

%’ where CLtrim is the lift necessary to sustain the weight of the airplane. The system yields:

CLtrim Cm ` Cm0 CL C Cm ` Cm C α “ δe δe (4.7a) δ “ ´ Lα 0 α Ltrim (4.7b) trim C C C C etrim C C C C Lα mδe ´ mα Lδe Lα mδe ´ mα Lδe

71 4. Static analysis 4.3: Trim assessment

In the case of tailless airplanes, not just the increment to lift of the elevator is significant, but also the variation in Cm0 induced by the deflection of the trailing edge flap, which locally alters the camber of the wing airfoil. In addition, the strong non-linear flow phenomena dominating the aerodynamics of the SACCON made the range of applicability of whatsoever linear model too narrow for any practical purpose. In this scenario the linear approach was evidently inadequate to evaluate trim, being it unable to account for the complexity of the aerodynamics of the configuration under study. The linear method, expressed by (4.7), was then discarded in favor of a more general approach, based on the direct identification of the values of the pair angle of attack/elevator deflection, yielding trim at each individual point of the analysis envelope. The procedure was set as a double variable iteration on α and δe with CL and Cm the target parameters to be adjusted, to CLtrim and 0 respectively. Basically, the angle of attack was used to regulate lift and achieve vertical balance; while the deflection of the elevator was adjusted to cancel the pitching moment and achieve rotational equilibrium. The procedure is summarized by the diagram in Fig. 4.5. The longitudinal data of the SACCON were pre-processed in order to generate a special trim spreadsheet, with the purpose of speeding up the trim search algorithm, by explicitly

Figure 4.5: Flow chart diagram of the double variable iteration procedure.

72 4.3: Trim assessment 4. Static analysis

integrating convergence conditions within the data. For all combinations of α and δe tested, the lift coefficient was replaced by the difference CL ´ CLtrim (equal to the weight coefficient and derived according to (4.8)) and the actual CG was taken as reduction point for the pitching moment, i.e. it was incremented with the transport moment of lift (from the ARP to the actual CG). The calculation was repeated for each distinct point of the analysis envelope, as CLtrim changes with altitude and velocity and Cm is influenced by the centering of the aircraft, yielding a new trim condition each time.

2 W CLtrim “ CW “ 2 (4.8) ρ U8 S

For the convergence of the iterative procedure, successive values of α and δe resulted from linear interpolation of the past values. For this reason the initialization of the process required two separate values for each variable: the elevator was set to 00 for the ﬁrst iteration and to 50 for the second; the angle of attack was ﬁrst set equal to the value necessary to balance the weight and then incremented by 10 for the second step. The formula used for linearly interpolate the n-th value of the variable is:

xn´1 ´ xn´2 xn “ xn´1 ´ n´1 ¨ (4.9) n´1 ´ n´2 where indicates the error, that is, by virtue of the aforementioned pre-processing, either the value of the difference CL ´ CW or the value of Cm, depending on the variable to update. In this sense, a negative value of CL ´ CW indicated that the lift was not enough to sustain the weight, thus the angle of attack α had to be increased; whereas a negative value of Cm induced a decrement of the elevator deflection δe. The flow chart in Fig. 4.5 shows how the main iteration loop was subdivided into secondary loops, which carried out α and δe iterations separately, so as to better govern the convergence of the procedure. For errors on both lift and moment smaller than 10´7, convergence was met, as the solution was accurate enough, and the algorithm progressed to the next point of the envelope. The described method for the evaluation of trim angles had the merit of being able to catch up with the complex aerodynamic behavior of the SACCON, in the sense that, since it involved a very localized linearization, it allowed to keep track of the complex trend of the data with the best possible precision, minimizing the loss of detail. The outcomes of trim evaluation, presented in the following figures, are discussed in terms of the values that α and δe assume, so as to cancel the resultant force and moment acting on the airframe and allow steady level flight. The four plots in Figs. 4.6 and 4.7 illustrate the influence of CG location on the trim of the SACCON. The angle of attack solution is reported for h “ 0 m in Fig. 4.6a and

73 4. Static analysis 4.3: Trim assessment

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 4.6: Variation of angle of attack to trim with CG location. h “ 12 000 m in Fig. 4.6b. At the lower velocities, the first plot is indicative of a terminal flight condition (take-off or landing). It shows how, as the velocity decreases below 60 m/s (or 216 km/h), the angle of attack exceeds 150, forcing the aircraft to operate within the region beyond the pitching moment dip, where its aerodynamic behavior becomes extremely discontinuous and susceptible to α variations. To fly in such condition is highly undesirable, especially when close to the ground. During take off, the issue can be avoided by simply carrying out the maneuver at a slightly higher speed, by delaying the rotation phase, provided long enough runways. On the contrary, the issue potentially represents a risk during landing, as the maneuver cannot be performed at too high speed. It is then advisable to perform the maneuver so as to defer the final deceleration when in close proximity of the ground. Nevertheless, the model did not account for ground effect, which could induce unpredicted modifications in the aerodynamic loads on the SACCON, considerably altering the accuracy of such prediction. At high altitude the angle of attack to trim is larger, due to the thinner air, and the curves are slightly less smooth than those of low altitude, presenting some discontinuities at low velocity. Moreover the angle of attack drops less rapidly, meaning that cruise flight of the SACCON is performed at moderate attitude, thus generating considerable drag. In both plots of Fig. 4.6, a forward shifting of the CG, i.e. an increase in SM, causes an increase in the value of angle of attack to trim, more consistent the lower the velocity. This dependency, in disagreement with the “classical theory” for conventional aircrafts (expressed by (4.6)), is instead expected for tailless aircrafts. The reason is the necessity to account for the contribution to lift exerted by the elevator, which decreases, eventually

74 4.3: Trim assessment 4. Static analysis

becoming negative, as the SM rises. However, in Fig. 4.6a it can be seen that, for U8 ă 60 m/s, the lesser angle of attack to trim is attained for xCG “ 4.6 m, roughly corresponding to neutral stability. A possible explanation is the fact that the disturbance introduced by the deflection of the elevons deteriorates the flow, especially at high incidence, to such an extent as to compromise the effectiveness of the wing to generate lift. Indeed this issue is one of the major drawbacks of tailless designs.

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 4.7: Variation of elevator to trim with CG location.

The elevator to trim presents the typical trend predicted by theory, as found in Fig. 4.7a. The deflection required to compensate the pitching moment of the aircraft increases at the lower speeds, due to the rise of pitching moment as α increases. The entity of the elevator deflection at low speed tightly depends on the SM: the more stable is the aircraft, the more negative elevator is required to trim it a low speed; while unstable configurations require positive deflection of the elevator. As a matter of facts, the elevator curves in both plots of

Fig. 4.7a flatten out for xCG “ 4.6 m, which approximately corresponds to neutral stability for the SACCON. It can be observed that the effect of altitude on the elevator to trim is mainly quantitative, rather than qualitative, as the trend of the curves at 12 000 m is much alike that at sea level. The curves are less sharp and the deflections cover a wider range than in the low altitude case, due to the reduced aerodynamic support of thinner air. Also, the figure shows a slightly discontinuous behavior of the curves at low speed, in a fashion similar to the angle of attack. The outcomes of the analysis, specifically the values assumed by the elevator to trim, suggest that the SM of the SACCON should never be permitted to exceed the range

75 4. Static analysis 4.3: Trim assessment

´10% ă K ă 10%, that is a CG located between 4.2 m ă xCG ă 5.0 m. In fact, a CG too far from the NP, whether fore or aft, leads to saturation of the elevator at the lower velocities, making the configuration not flyable. In addition, a too high SM forces large negative deflections of the elevator at the lowest airspeeds, requiring high values of α to trim. This brings the aircraft to operate in the non-linear flow region, inducing a severe

(b) U8 “ 250 m/s. (a) U8 “ 130 m/s.

Figure 4.8: Map of angle of attack to trim versus altitude and CG location.

(b) U “ 250 m/s. (a) U8 “ 130 m/s. 8

Figure 4.9: Map of elevator to trim versus altitude and CG location.

76 4.3: Trim assessment 4. Static analysis degradation of handling qualities and, ultimately, of the airworthiness of the airplane, precisely in ﬂight phases (low velocity) that require greater precision.

The plots in Figs. 4.8 and 4.9 illustrate the variation of trim parameters, α and δe respectively, with altitude and CG location first at low and high speed. To preserve readability, the scales of figures (a) and (b) are not the same, given that at low velocity both α and δe span a considerably wider range of values than at high velocity. It can be seen that altitude has an influence on trim qualitatively similar to that of velocity, even though inverse, as an increase in altitude induces an increase in angle of attack and a variation in elevator to trim with the same characteristics illustrated in Fig. 4.7. The thrust required to trim the aircraft was calculated considering that it had to completely neutralize the drag generated by the aircraft. Hence, assuming a thrust axis parallel to the fuselage waterline, thrust was expressed as:

1 T “ ρ U 2 SC (4.10) 2 8 8 D

Note that thrust orientation changes with the angle of attack, that is it follows the pitch attitude of the aircraft, as opposed to lift and drag, whose orientation is fixed in steady level flight. In particular, lift is always perpendicular to the undisturbed flow and, thus, aligned to the weight; while drag always acts in the same direction of the flow. Strictly speaking, then, only the projection of thrust along the flow direction effectively counteracts drag; while the component perpendicular to the flight path contributes in sustaining the weight of the airplane, as illustrated in Fig. 4.10. Generally speaking, thrust should be taken into account in the evaluation of trim, given that it evidently takes over part of the lifting task, thus reducing the trim angle of attack. Nonetheless, the vertical component

Figure 4.10: Sketch of forces acting on an airplane in horizontal level ﬂight.

77 4. Static analysis 4.3: Trim assessment of thrust never exceeds the 5% of the weight of the SACCON (estimated at α “ 200 and E “ 10), inducing a change in angle of attack |∆α| ă 10. Consequently thrust evaluation was decoupled from trim and its eﬀect on the balancing of the SACCON was neglected without appreciable loss of approximation.

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 4.11: Variation of required thrust with CG location.

By virtue of its ﬂying wing design, the SACCON requires relatively limited thrust to maintain trimmed ﬂight at all altitudes, as it appears from Fig. 4.11. Still, thrust appears to be rather sensitive to CG location, owing to the fact that trimming α, thus induced drag, varies with the SM, as illustrated in Fig. 4.6. In particular, the velocity of minimum required thrust ranges from approximately 70 m/s for xCG “ 5 m (K »

´10 %) to about 170 m/s for xCG “ 4 m (K » 15 %). The trim thrust plot relative to high altitude of Fig. 4.11b shows that, due to its flying wing configuration, the SACCON operates on the back side of the power required curve even for significantly high values of airspeeds. More unusual is the fact that, at high altitude, the drag produced by the more stable configurations progressively decreases as velocity increases. The reason for such odd behavior is the fact that the balancing of the aircraft in such condition requires a very small deflection of the elevator, as shown Fig. 4.7b, which allows for an aerodynamically cleaner configuration. This, together with the reduction of angle of attack at high speed, induces an overall increase in aerodynamic efficiency. The validity of this explanation is corroborated by the values of aerodynamic efficiency, whose trends are reported in Fig. 4.12. Specifically

Fig. 4.12b shows that the lift to drag ratio for xCG ă 4.4 m actually increases with airspeed (at least past a certain velocity), as opposite to all other CG conﬁgurations. In addition,

78 4.4: Limitations 4. Static analysis

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 4.12: Variation of aerodynamic efficiency with CG location. almost each curve of both figures shows a distinct peak of efficiency concurrently to the zeroing of the elevator deflection. Globally, stable configurations achieve higher efficiency than unstable ones, at low as well as at high altitude. In particular, the best overall performance is attained for xCG “ 4.4 m, corresponding to a relaxed static margin of about 5%, being it a condition that allows the SACCON to preserve high efficiency both during terminal flight phases (low altitude and velocity) and during cruise flight (high altitude and velocity). To conclude, it is important to notice that a performance analysis based on an aerodynamics model not accounting for compressibility effects is likely to yield an underestimated prediction of drag, which worsen as the Mach number rises beyond the critical value. Therefore required thrust would be equally underestimated. In light of that, there is the concrete chance that the actual drag generated by the aircraft during high velocity, low altitude flight will exceed the thrust available from the engine.

4.4 Limitations

The results of trim analysis revealed some fundamental problems and shortcomings of the configuration. The issues identified by the analysis, by its own very nature, do not just involve a deterioration of the flying qualities of the aircraft, but actually represent forbidden flight conditions, in which not even steady level flight can be achieved. Ultimately, the process entailed a tailoring of the boundaries of the proposed flight envelope, especially regarding the CG range, with the aim of prevent operation in unsafe conditions.

79 4. Static analysis 4.4: Limitations

A summary of stability and trim problems of the SACCON is presented in Tab. 4.1.

Parameter Remarks

The balancing of the aircraft becomes extremely inconstant for CG located further back. Moreover the deflection of the elevator to trim the aircraft at high altitude saturates the control at most velocities. At the same time, a too forward CG induces a too stable configuration, which, despite CG yielding smoothly varying trim parameters and globally requiring reduced thrust, involves excessive (negative) deflections of the elevator al low speed. In light of that, the CG location should range from 4.2 m to 5.0 m, corresponding to a SM comprised between 10% and ´10%. The calculated stall velocity appears to be a rather optimistic prediction, since it does not account for the detrimental effect of the elevator on the lift generated by the wing, which calls for higher angle of attack to trim. Then, in order to avoid flying within the undesirable region dominated by non-linear aerodynamics, it is advisable to shift rightward the left edge of the envelope, i.e. increase U 8 the minimum velocity, of around 10 m/s (or 36 km/h). On the other hand, compressibility effects would likely make the drag generated by the SACCON at low altitude, high speed flight exceed the capability of the engine. This, together with aeroelastic considerations, would probably require to modify the right edge of the envelope, so as to restrict the maximum velocity edge. The study did not account for the variatin of engine thrust with altitude. Thus a complete evaluation of the h performance of the engine would likely imply a modification of the upper bound of the envelope, especially in the high airspeed region.

Table 4.1: Summary of SACCON stability and trim issues.

80 Chapter 5

Dynamic analysis

The purpose of this section is to estimate the effect of airspeed and static margin on the longitudinal and lateral-directional dynamics of the SACCON, with the ultimate goal of assess the flying qualities of the aircraft across the analysis envelope. Stability analysis provided useful results regarding control authority and allowed to determine the complete set of trim flight conditions to be taken as reference for the subsequent study of the dynamic characteristics of the design. Dynamic analysis comprised the investigation of the following aspects:

• dynamic analysis of the linear airframe model;

• evaluation of longitudinal and lateral-directional handling qualities.

The study is based on classical eigenanalysis of the state space linear aircraft motion model, as defined by Bryan. The derivation of linear dynamics equations is considered in AppendixC. The design of a stability/command augmentation system was not within the scope of the thesis, but it would be a priori requirement to carry out complete simulation of the flight of the SACCON, particularly in conditions of relaxed or negative longitudinal stability. At the end, this exercise clearly identified the most critical areas of the envelope, where the integration of SAS and automatic controls could be useful or even mandatory.

5.1 Aerodynamic identiﬁcation

The modelization of the aerodynamic behavior of an aircraft, with the purpose of the assessment of its handling qualities, is based on the classic aerodynamic derivatives, which have to be provided in the form of a coefficient, indicating the slope of the generic parameter with respect to the state in question. The static and control portions of the aerodynamic database developed so far, comply with this definition and the corresponding derivatives can readily be extracted by direct finite differentiation. This is not valid for dynamic derivatives, as they come in the form of the time histories measured during forced

81 5. Dynamic analysis 5.1: Aerodynamic identification oscillation tests in the wind tunnel. In this case, the derivation of adequate coefficients gives rise to an identification problem, as the procedure involves the extraction of a single-valued parameter from each experimental time history, considering both states and coefficients.

The difference between the static and dynamic values, that is the increments ∆Ci measured during the forced oscillation runs, are usually regarded as aerodynamic damping effects. The modelization of these phenomena, by means of the identification of single dynamic derivatives, was the very target of this phase of the study. The problem is successfully addressed by means of the application of system identification techniques. In particular, a variety of different methods exist to address the issue, spanning from more elementary and “crude” ones, to more general and accurate non-linear methods, often implemented in specific software applications. All of these procedures yield reduced-order models of the unsteady aerodynamic behavior of the reference configuration, which constitute the set of conventional coefficients useful for flying quality evaluation, as well as flight mechanics simulation. Several system identification procedures for the derivation of dynamic derivatives are extensively accounted by Da Ronch in [11] and by Irving et al. in [18]; other are briefly presented in [20, 22]. All discussions focus on the model identification problem and describe appropriate estimation techniques for analysis of dynamic data, with the purpose of the generation of a general aerodynamic model structure. Only two of all the system identification methodologies discussed in the cited references were considered when modeling the dynamic behavior of the SACCON, specifically the single point method and a more refined, but still linear, method. The single point method for deriving the dynamic derivatives from the sinusoidal cycle data is presented in reference [22]. It is an immediate procedure, that involves the computation of the difference between the values assumed by the coefficient at the maximum and minimum rates divided by the difference between the maximum and minimum rates. In the most general form, the calculation of the derivative of the coefficient Ci with respect to the rate j can be expressed as:

∆C ∆C i|jmax ´ i|jmin ∆Cij “ (5.1) lref pjmax ´ jminq 2 U8 where ∆ indicates that increment of the coefficient from the baseline value, j represents either an angular rate (p, q, r) or a linear rate (α9 , β9) and lref corresponds to c for longitudinal motions or b for lateral ones. Equation (5.1) provides a rapid, even though rather crude, estimation of the required derivative. Reference [18] discusses three separate techniques. The first two assume linear model for the prediction of forces and moments, whereas the third adopts a more general non- linear model structure. Each approach also uses different parameter estimation procedures. Within this study it was decided to consider the second linear method, henceforth referred

82 5.1: Aerodynamic identiﬁcation 5. Dynamic analysis to as the II linear method, as it represents a ﬁner linear alternative to the single point method. The procedure involved the following steps.

1) The baseline force/moment data were subtracted from dynamic run data for a given dynamic run, leaving an incremental term, which was assumed to be attributable to the dynamic terms.

2) Angular rates were derived from the ϕ, ϑ, ψ time histories, through simple diﬀer- entiation of the corresponding signals. After that they were non-dimensionalised in the conventional fashion with either wing reference chord (longitudinal) or semi-span (lateral-directional) and the free stream velocity.

3) The force/moment increments were tabulated against the normalized rates and a curve ﬁt technique was employed to obtain a match to the resulting trends, in order to determine the dynamic derivative. Of course, ﬁrst order match returns a “linear” derivative.

The sinusoidal roll, pitch and yaw oscillations performed at DNW-NWB combined both body and velocity vector rotation rates, that is the motions were not purely oscillatory, but each inevitably included a translational component. For example, the pitch oscillation motion involved a significant plunge, i.e. vertical displacement, component, mainly responsible for the value of α9 ; similarly, yaw and roll oscillations included significant components of lateral translation, responsible for β9. For this type of motions, incidence rate (α9 , β9) and angular rate (p, q, r) derivatives are not separable and only their combined effect can be determined. This introduced an identifiability problem when estimating the dynamic derivatives. The only way to work around the problem is to lump together the terms into an equivalent derivative. In particular, the inevitable inclusion of the α9 and β9 effects within the angular rates allows to express the dynamic derivatives as:

Ciq “ Ciq ` Ciα9 (5.2a)

C “ C ` C sinpαq (5.2b) ip ip iβ9

C “ C ´ C cospαq (5.2c) ir ir iβ9 where i indicates the generic force/moment coefficient and α is the instantaneous angle of attack. Then, to split the combined derivative into the individual terms requires motions triggering only the translational degree of freedom, such as pure plunging or lateral oscillation. For instance, to obtain α9 , z position time history from the plunge runs is first differentiated to obtain a z9; then the inverse tangent of z9 divided by the tunnel speed

83 5. Dynamic analysis 5.1: Aerodynamic identiﬁcation

(assumed constant) returns the ∆α, which can be differentiated again to yield α9 . The same steps apply for the calculation of β9, taking y position signal in lieu of z. It should be noted that multiple differentiation of the same signal usually leads to very noisy results, which may considerably affect the reliability of the predicted derivatives. Therefore it is advisable to apply filtering to both position and actual incidence terms, prior to the differentiation step [18]. Of course the filtering introduces a phase shift in the data and an acceptable compromise between smoothness and phase lag must be reached. In spite of that, Irving et al. [18] further assert that the derivation of α9 from the 1-cycle averages of both rate and coefficients produces a rather clean α rate, without need of additional filtering.

The aforesaid linear approaches were proven to yield good reliable results for the low α regime, where the flow is relatively linear; while requiring more caution when used to model the dynamic behavior of the SACCON in the high angle of attack region. Indeed, their derivation makes them likely unsuitable for catching the complex effects of the non-linear flow at higher α, due to the decrease in the accuracy of linear predictions when dealing with complex vortical flows. Moreover, it was reported a marked increase in the scattering of the results at the high α, almost absent at low angle of attack [18]. In particular, the results of the described linear approaches show that, up to α “ 100, the test results are relatively consistent, with little spread in the maximum and minimum derivatives estimates and with reduced influence of frequency. Up to such angle of attack the traditional linear derivative is sufficient to accurately evaluate the dynamic derivatives of the SACCON. Beyond that point, the standard deviation makes the maximum and minimum estimates diverge and the effect of frequency becomes significant. In addition, the time histories of the data contained multiple hysteresis loops, which cannot be covered by the traditional model [18].

Nevertheless the linear approach was deemed adequate in the frame of this study, given that the configuration was to be tested only in trim conditions, which involved limited values of angle of attack throughout all the envelope, except in the narrow band near stall. Hence, it was just a matter of choosing one of the linear methods previously described, ideally the one capable of providing the most accurate estimation at the lower computational cost. Indeed the single point is undoubtedly straightforward, but rather crude; whence the II linear method is potentially more accurate and refined, at the price of a higher computational cost. The longitudinal pitch derivatives were extracted using both techniques and the results compared, in order to bring out, at least qualitatively, the difference between the two linear methods and provide a practical criterion to select the more suitable one. The plots in Fig. 5.1 illustrate the pitch rate derivatives extracted from 1 Hz oscillation data, which was taken as test case for the comparison, as at that frequency the non-linear behavior, exhibited by the aerodynamics of the SACCON, was the most pronounced. The data were

84 5.1: Aerodynamic identiﬁcation 5. Dynamic analysis

Figure 5.1: Comparison of the longitudinal combined dynamic derivatives calculated with the two linear methods for 1 Hz oscillations. calculated at α “ 50, 100, 150, 200, generating the curves depicted in the figure. They show a fairly good agreement in the low α range, which is then lost for α ą 100. Altogether, the predictions of the single point method are characterized by a larger “overshoot” and seem to be more influenced by non-linear effects at high α, especially regarding the drag coefficient. In light of the comparison shown in Fig. 5.1, the single point method was preferred, as it yielded adequately accurate estimates of the parameters with the minimum computational cost, allowing for fast application to the large database of dynamic data. The longitudinal derivatives show very limited values up to 100 of angle of attack, with a considerable change at higher α. Interestingly, the dynamic effect of pitch motion on drag is inverted at α “ 150, indicating a reduction in drag for positive pitch rotation; while 0 lift damping results inverted up to α “ 10 . The pitch damping ∆Cmq remains negative, indicative of a stable behavior. Moreover, the limited values of the lift damping (at least at low α) and pitch damping are typical features of tailless aircrafts. In fact, in such designs, the sole contribution to these derivatives comes from the wing, whose AC lever arm is far more small than that of a horizontal stabilizer, reducing the global sensitivity of the aircraft to pitch rate (limited ∆CLq ) and the magnitude of the moment of the lift increment (limited ∆Cmq ). The combined roll derivative, shown in Fig. 5.2, were evaluated at α “ 50, 100, 150. Roll damping is overall satisfactory and never changes sign, even though it reduces around α “ 100, indicating strong damping of roll motion; the coupled effect on yawing moment is moderate; while effect in sideforce is more pronounced, with a peak around α “ 100.

85 5. Dynamic analysis 5.1: Aerodynamic identiﬁcation

Figure 5.2: Roll motion combined dynamic derivatives.

The combined yaw derivative, shown in Fig. 5.3, were evaluated at α “ 50, 100, 150, 200. The dynamic derivatives exhibit stronger fluctuations, indicating a more marked influence of the angle of attack. Moreover, all three derivatives change their sign, which is highly undesirable for the yaw damping derivative, especially considering that the reversal occurs between 100 and 150, thus at angle of attacks easily reached during maneuver or terminal flight phases. Anyway, the SACCON presents a very poor yaw damping effect, 10 to 30

Figure 5.3: Yaw motion combined dynamic derivatives.

86 5.2: Dynamic modes 5. Dynamic analysis times smaller than that of a conventional configuration. Again, the drastic and sudden variations in the aerodynamic characteristics of the SACCON, especially at high angles of attack, are caused by the complex vortex flow field existing on the lee side of the aircraft, induced by the combination of a high swept, low aspect ratio wing with a thin airfoil with sharp leading edge. It is worth to note that, in such conditions, i.e. high angle of attack, the usage of traditional stability derivative concept yields, at best, a narrowly accurate description of the aerodynamic forces and moments. Accurate estimations necessarily require advanced non-linear mathematical modeling [8].

5.2 Dynamic modes

The quantitative evaluation of the dynamic behavior of the SACCON was carried out on the basis of the results derived from the eigenanalysis of its state space dynamic model. This, in turn, was the product of the application of Bryan’s linearization method to the standard 6 DoF equations of motion, that is the application of small perturbation theory together with the decoupling of longitudinal and lateral dynamics, around the trim condition of each point of the analysis envelope. In order to use matrix method for solving the equations of motion, the resulting Linear-Time-Invariant (LTI) multi-variable system was manipulated so as to yield a normal form dynamic formulation. The linearization procedure is outlined in detail in AppendixC. The scope of the linearization process is to reduce the full order, non-linear aircraft model to a set of linear differential equations that can be manipulated to yield a state space linear dynamic system in normal form (cf. Paragraph 2.2.2), in which longitudinal and lateral dynamics are completely decoupled. The procedure was looped over all the flight conditions defined by the analysis envelope and involved the steps described below.

1) At each prescribed ﬂight condition, trim parameters, namely α0 and δe0 , were extracted from the trim results calculated in the previous step and some auxiliary parameters, such as Mach number and dynamic pressure, were calculated.

2) Static and control derivatives were estimated from the aerodynamic database using linear interpolation on the corresponding data in the neighborhood of the trim values

of α0 and δe0 (all other states were identically zero at equilibrium). Instead, rotational derivatives were interpolated from the values determined via system identiﬁcation.

3) The non-dimensional derivatives database was used, together with mass and inertia data of the aircraft, to calculate the dimensional derivatives relative to the actual ﬂight condition, according to the procedure described in AppendixC.

4) The values of the dimensional derivatives were substituted in the state matrices of the generic aircraft linearized dynamics model, allowing to calculate its eigenvalues and (right) eigenvectors.

87 5. Dynamic analysis 5.2: Dynamic modes

The procedure was coded into a MATLAB algorithm and implemented to be fully automated. The results of the eigenanalysis, i.e. the eigenvalues and eigenvectors, were stored in a dedicated spreadsheet, conveniently joined by the primary ﬂight parameters.

5.2.1 Longitudinal dynamics

The longitudinal dynamics model of the generic aircraft resulting from Bryan’s linearization, expressed in Stability axes system (C.2), has the following normal form:

˜ ˜ ˜ ˜ ˜ ∆u9 Xu Xw u0 Xq Xϑ 0 ∆u Xδe ˜ ˜ ˜ ˜ ˜ »∆α9 fi »Zu{u0 Zw Zq{u0 Zϑ{u0 0fi »∆αfi »Zδe {u0fi ˜ ˜ ˜ ˜ ˜ ∆δ (5.3) —∆q9ffi “ — Mu Mw u0 Mq Mϑ 0ffi ¨ —∆qffi ` — Mδe ffi e — ffi — ffi — ffi — ffi —∆ϑ9ffi — 0 0 1 0 0ffi —∆ϑffi — 0 ffi — ffi — ffi — ffi — ffi — 9 ffi — ffi — ffi — ffi —∆hffi — hu hw u0 0 hϑ 0ffi —∆hffi — 0 ffi — ffi — ffi — ffi — ffi – fl – fl – fl – fl where the engine control, namely ∆δt, was omitted and vertical velocity increment ∆w was replaced by the corresponding angle of attack variation ∆α, according to the definition:

∆w ∆α » tanp∆αq “ (5.4) u0

State matrix was denoted by Along and input matrix by Blong. Output equations were not derived, since complete observability of the system was also supposed. The plot in Fig. 5.4 shows the root locus of longitudinal dynamics for several CG locations, corresponding to K » 10%, 5%, 2.5%, 0%, ´5%. The figure provides a visual representation of the influence of the SM on longitudinal dynamic motions of the SACCON. The short period and the phugoid poles are marked. The phugoid poles, being it a rather slow motion, are clustered near the origin; while the short period poles are more spread. Of course, to distinguish between phugoid and short period makes sense only when the poles comes in two complex conjugate couples, that is, in general, for strictly positive stability. Indeed, the root locus clearly illustrate that the longitudinal modes become unspecific for xCG ą 4.5 m, at least in the classical sense. The root locus of Fig. 5.4 allows to forward the following remarks regarding the SPO.

• The dynamic is present at all airspeeds for xCG ă 4.5 m and it promptly disappears in neutral or negative stability conditions, giving way to a couple of non-oscillatory

dynamics, of which the unstable one is tumbling. For xCG “ 4.6 m (marginal stability,

K » 0) the mode exists only for U8 ă 61 m/s.

• The SPO poles move away from the origin with increased airspeed and tend to get farther from the real axis with forward CG positions. Thus, at higher velocities and

88 5.2: Dynamic modes 5. Dynamic analysis

stable CG positions, the short period dynamics will be fast, which is desirable from handling qualities point of view.

• The angular position of the SPO poles, upon which damping is tightly dependent, decreases for forward CG, while being almost insensitive to airspeed. This indicates a reduction of damping for stable conﬁgurations.

Figure 5.4: Short period root locus varying airspeed and static margin at sea level.

The phugoid poles can be seen in Fig. 5.4, but they are clustered so close to the origin, to be impossible to discern, when represented together with the SPO poles. Therefore, the root locus of the phugoid is shown in Fig. 5.5, where the region near the origin is magniﬁed. By analyzing the root locus, the following observations can be made.

• The dynamic is always present, except at low airspeed for K » 0%.

• The dynamic appears to be stable for all SM, except in conditions of neutral stability. The behavior, although in contrast with conventional textbook results, suggests that the angle of attack undergoes negligible variations during the oscillations and it is

89 5. Dynamic analysis 5.2: Dynamic modes

indicative of the weak dependency of the motion upon Cmα , from which the instability arises. In addition, it is seen that the degree of stability of the mode increases with the absolute value, rather than on the relative one of the SM.

• Velocity exerts a stabilizing effect on phugoid dynamic, at least for positive stability, as phugoid branches move towards the stable half-plane as airspeed increases, crossing the imaginary axis at around 90 ˜ 100 m/s. On the other hand, for negative SM the velocity first decreases the stability of the motion, by lowering its damping ratio, then returns to increase it. For neutral stability the influence of velocity is fickle, all the more so that a phugoid dynamic establishes at high speed exclusively.

• The damping rises with velocity, even if not monotonically, for all CG locations. This is caused by the severe reduction in aerodynamic eﬃciency with airspeed, as illustrated in Fig. 4.12. The frequency drops rapidly with velocity in the low-to- medium speed range, tending almost asymptotically to the same value for all SM. The behavior is in perfect accordance with the simpliﬁed model.

Traditional analysis [1,2] suggests that the longitudinal root locus of an unstable con-

Figure 5.5: Phugoid root locus varying airspeed and static margin at sea level.

90 5.2: Dynamic modes 5. Dynamic analysis

figuration, that is with negative SM, should yield four aperiodic motions, or, at most, two aperiodic motions plus a third mode branch. Nevertheless the root locus in Fig. 5.5 shows a well established phugoid branch for K » ´5%. The explanation for such atypical outcome in statically unstable conditions may lie in the tiny scale of angle of attack variation induced by the phugoid oscillations. In fact, despite triggering a divergent dynamic, the α disturbance is not strong enough to manifest an appreciable effect within the period of the phugoid, hence the effects of ∆ϑ and ∆û steadily prevail.

Magn. Phase ∆ˆu 0.636 ´95.7˝ ∆α 0.00570 ´104˝ ∆ˆq 0.00132 ´97.0˝ ∆ϑ 1 0˝

Figure 5.6: Phugoid normalized shape at U8 “ 150 m/s and h “ 0 m for K » ´5%.

It is worth to note that a third mode branch appears in the root locus at airspeeds comprised between 61 m/s and 145 m/s for xCG “ 4.6 m, as illustrated in the enlargement provided in Fig. 5.7. The arrangement of the root locus in such condition is somewhat unusual. The root locus originates at 60 m/s with no deﬁned short period nor phugoid, replaced by two couples of real-valued poles, one of which on the positive half-plane. As velocity increases, the leftmost and rightmost poles get farther from each other, while the middle ones interact with each other, evolving in the third mode dynamic, at about 61 m/s. The third mode branch develops in a arc shape and the poles return to coalesce at around 145 m/s, closer to the imaginary axis, and then move away from each other on the real axis. At this point the real pole, hitherto located on the positive half-plane, stops and reverses its drift, starting to move back towards the negative half-plane. Further increasing velocity, it eventually coalesce, in close proximity of the imaginary axis, with the rightward moving pole of the former third mode branch, giving rise to the phugoid mode, at around 210 m/s. Finally, the root locus “terminates” with a couple of complex conjugate stable phugoid poles, joined by a couple of subsidence poles, for an overall stable behavior. To better understand the properties of the third mode, developed by the SACCON, the

91 5. Dynamic analysis 5.2: Dynamic modes

Figure 5.7: Third mode root locus varying airspeed at h “ 0 m (K » 0%).

Magn. Phase ∆ˆu 0.599 44.8˝ ∆α 0.394 152˝ ∆ˆq 0.00769 134˝ ∆ϑ 1 0˝

Figure 5.8: Third mode normalized shape at U8 “ 70 m/s and h “ 0 m for K » 0%.

92 5.2: Dynamic modes 5. Dynamic analysis

eigenvector associated to the mode at U8 “ 70 m/s is plotted in polar coordinates in Fig. 5.8. The normalized eigenvector expresses the shape of the motion, which is entirely different from the short period and phugoid modes. It defines a dynamic dominated by pitch attitude variation, with a strong contribution of airspeed and angle of attack disturbance, while pitch rate perturbation is negligible. The motion can be described as a very slow rotation of the aircraft around the CG, that generates wide oscillations of pitch attitude, inducing variations in angle of attack, which, in turn, translate in significant variations of airspeed. Flight altitude is marginally influenced by the dynamic, for instance, in reference the condition, the predicted altitude variation was less than 60 m. The mode is seen to be entirely different from both the SPO and the phugoid, mainly because it excites all three degrees of freedom. Therefore, there is no straightforward approximation to it based on a two DoF approach [2]. It should be noted that the third mode maintains such peculiar characteristics for velocities up to about 85 m/s. At higher airspeeds the specific features of the third mode fade away: the ∆α variation reduces, becoming negligible, and the motion assumes a shape analogous to a conventional phugoid.

Figure 5.9: Short period root locus at h “ 12 000 m.

93 5. Dynamic analysis 5.2: Dynamic modes

Figure 5.10: Phugoid root locus at h “ 12 000 m.

The longitudinal dynamics of the SACCON do not undergo substantial modification at high altitude. The main difference is the fact that the third mode does not emerge. According to the root locus shown in Fig. 5.9, the SPO is present for strictly positive SM and, overall, the motion is less damped and slower. The phugoid, shown in Fig. 5.10, is still unstable at low airspeeds for positive SM and stabilizes around 170 ˜ 180 m/s, depending on the CG location. In neutral stability conditions the dynamic readily stabilizes at low speed; while being always stable for negative SM. As the SPO, the motion is less damped, as the aerodynamic efficiency remains high (cf. Fig. 4.12), and much slower. To conclude, the vector diagram of tumbling divergence is presented in Fig. 5.11. The motion arises from the collapsing of the short period oscillation into a couple of aperiodic motions, one stable and the other, tumbling indeed, unstable. The motion develops as a continuous, uncontrolled pitching rotation and, in fact, it mainly involves longitudinal attitude variation, together with substantial angle of attack increment. Pitch rate contribution is small, compared to ∆ϑ or ∆α and of the same order of magnitude of the change in velocity. The properties of the dynamic, specifically the relative participation of the states, remains almost unchanged throughout the whole envelope.

94 5.2: Dynamic modes 5. Dynamic analysis

Magn. Phase ∆ˆu ´0.0371 - ∆α 0.555 - ∆ˆq 0.0325 - ∆ϑ 1 -

Figure 5.11: Tumbling normalized shape at U8 “ 100 m/s and h “ 0 m for K » ´5%.

As mentioned, the aircraft tendency to enter tumbling must be regarded with particular care, as it represent a hazardous behavior, easily capable of rendering conventional control surfaces almost useless, once fully developed. However it must be pointed out that the impact in impairing the aircraft’s handling qualities is related to the rapidity of the motion. As for the phugoid, tumbling departure dynamic can be tolerated, provided it is slow enough to allow correction, if promptly detected.

5.2.2 Lateral-directional dynamics

The lateral-directional dynamics model of the generic aircraft resulting from Bryan’s linearization, expressed in Stability axes system (C.4), has the following normal form:

∆β9 Y 1 Y 1 u Y 1 u Y 1 u 0 ∆β Y 1 u Y 1 u v p{ 0 r { 0 ϕ{ 0 δa { 0 δr { 0 ∆p L1 u L1 L1 0 0 ∆p L1 L1 » 9fi » v 0 p r fi » fi » δa δr fi ∆δa ∆r9 “ N 1 u N 1 N 1 0 0 ¨ ∆r ` N 1 N 1 ¨ — ffi — v 0 p r ffi — ffi — δa δr ffi — ffi — ffi — ffi — ffi «∆δrff —∆ϕ9ffi — 0 1 tanpϑ q 0 0ffi —∆ϕffi — 0 0 ffi — ffi — 0 ffi — ffi — ffi — 9ffi — ffi — ffi — ffi —∆ψffi — 0 0 secpϑ0q 0 0ffi —∆ψffi — 0 0 ffi — ffi — ffi — ffi — ffi – fl – fl – fl – fl (5.5) where lateral velocity increment ∆v was replaced by the corresponding angle of sideslip variation ∆β, according to the definition:

∆v ∆β » tanp∆βq “ (5.6) u0

95 5. Dynamic analysis 5.2: Dynamic modes

State matrix was denoted by Alat and input matrix by Blat. Once again, output equations were not derived, since complete observability of the system was also supposed. For the sake of clarity, roll subsidence poles are not shown and only the portion of the root locus close to the imaginary axis is depicted. Otherwise dutch roll and spiral poles would have been extremely clustered near the origin, making the root locus hardly legible. The roll subsidence pole is fast and strongly inﬂuenced by airspeed. It determines the speed of response for the roll motion to aileron controls. As the ﬂight velocity increases, 1 the dimensional derivative Lp increases, indicating an ever faster response. On the other hand, the sensitivity of roll subsidence to CG position greatly reduces with airspeed.

Figure 5.12: Dutch roll root locus varying airspeed and static margin at sea level.

The plot in Fig. 5.12 shows the portion of the lateral root locus close to the imaginary axis, thus depicting dutch roll and spiral dynamics. The ﬁgure provides a visual representation of the inﬂuence of the SM on lateral-directional dynamic motions of the SACCON. The dutch roll and the spiral poles are marked. The spiral poles, being it a rather slow non-oscillatory motion, are clustered on the origin; while the dutch roll poles are more spread. The root locus allows to forward the following remarks regarding the dutch roll.

• The dynamic is predominantly unstable and exhibits a rather weak dependency upon

96 5.2: Dynamic modes 5. Dynamic analysis

the CG location (as expectable), related to the variation of the aerodynamic derivatives with the angle of attack (cf. Fig. 5.2 and Fig. 5.3). The poles cross the imaginary axis at around 200 m/s to 250 m/s, from positive to negative SM.

• The motion disappears for high enough dynamic pressure, i.e. high airspeed and/or low altitude. In particular, shortly after becoming stable, the poles coalesce on the real axis, giving rise to a couple of non-oscillatory modes, one of which, eventually, moves to the unstable half-plane.

• As long as it is unstable, the motion gets slower with airspeed; then, once the poles cross the imaginary axis, the frequency almost freezes.

• Once become stable, the damping ratio increases rapidly with velocity. At the lower airspeeds, aside the fact that the dynamic is unstable, the damping exhibits less sensitivity to the airspeed.

The shape of the dutch roll eigenvector in a terminal ﬂight phase, namely a low speed ﬂight at sea level, and a generic cruise condition, is illustrated in Fig. 5.13. The low speed vector diagram of Fig. 5.13a illustrates a quite conventional dutch roll dynamic, regarding both states participation and phase lags. The vector diagram relative to cruise condition in Fig. 5.13b maintains the same phase lags, but states participation results considerably altered, arguably due to the rarefaction of air, which slows down the response and decreases its damping. This explanation is corroborated by the fact that angular rates are minimal,

(a) U8 “ 60 m/s, h “ 0 m. (b) U8 “ 250 m/s, h “ 12 000 m.

Figure 5.13: Dutch roll normalized shape in diﬀerent ﬂight phases for K » ´5%.

97 5. Dynamic analysis 5.2: Dynamic modes

Magn. Phase ∆β 0.0389 35.5˝ ∆ˆp 0.00812 147˝ ∆ˆr 0.00171 ´11.2˝ ∆ϕ 1 0˝ ∆ψ 0.211 ´158˝

Figure 5.14: Dutch roll shape approaching coalescence at U8 “ 200 m/s for K » ´5%. inducing little ∆β and ∆ψ responses and, ultimately, outlining a motion dominated by roll rotation. Little or negligible dependency on SM, especially at high altitude, is manifested. The shape of the dutch roll, as its poles approach coalescence, was also investigated, in order to understand the alteration originated by such transition. The diagram in Fig. 5.14 represents the eigenvector of the lateral oscillation in sea level flight at U8 “ 200 m/s. It is seen that the phase shift of the states is altered, primarily the ∆ψ disturbance, and also the magnitudes, especially that of ∆β. The shape is almost invariant w.r.t. both altitude and CG location, as long as the flight condition, that is the dynamic pressure, is equally near to the collapse of the mode. The degeneration and later collapse of the dutch roll oscillation is likely attributable to a detrimental combination of strong roll-yaw coupling, especially via dihedral effect, and trifling, if not reversed, yaw stiffness and damping. Unfortunately, the strong roll-yaw coupling of the SACCON, made the employment of simplified models of the lateral oscillation of little use, due to the complete unreliability of the results. However, the scenario is eloquently depicted in Fig. 5.15. Note that sideforce derivatives were not reported, their influence being marginal and their dependency on CG location almost null. The pictures show that each roll derivative is around two orders of magnitude bigger than 1 the corresponding yaw one and, except for Lr at low speed, roll derivatives keep their sign unaltered, as opposed to yaw ones. In addition, the former group exhibits much less sensitivity to CG location, i.e. angle of attack, than the latter. Regarding Fig. 5.15a, one can observed that lateral stability derivative increases up to extremely large values at high 1 velocity, with a severe impact on the stability of the dutch roll. On the other hand Lr coupling derivative assumes negative values, contrary to the custom. 1 On the right, Fig. 5.15b illustrates how yaw stiffness Nβ progressively decreases with ve-

98 5.2: Dynamic modes 5. Dynamic analysis

(a) Roll. (b) Yaw.

Figure 5.15: Variation of lateral-directional derivatives with airspeed at sea level.

locity, changing sign between 110 m/s and 140 m/s, thus revealing the loss of weathercock stability, due to the inversion of the derivative Cnβ at low angle of attack (as envisaged by 1 Fig. 3.8b). Coupled derivative Np is fairly regular, both in value and in trend. In order to emphasize the details of the yaw damping parameter, the result is enlarged 1 in Fig. 5.16. The derivative Nr assumes decent values at low airspeed, but it gets incon- veniently small as the velocity is increased, eventually becoming slightly positive. This reversal, prone to occur in configurations with highly swept wings [7], signals the inver- 3 sion of the Cnr coefficient . On this regard, it is interesting to observe that the velocity at 1 which the sign of Nr inverts is the same at which the coalescence of dutch roll poles occurs. Hence, the canceling of yaw damping appears to be key to the lateral-directional behavior of the SACCON, since it dictates the definitive disappearance of dutch roll oscillation. In general, it was found that the aforementioned characteristics contribute to the intensification of the roll components of the dutch roll motion with airspeed, at the expense of yaw ones, which decrease progressively (as illustrated in Fig. 5.14). This ultimately leads to the collapse of lateral oscillation, supplanted by a couple of aperiodic motions, of which one is a subsidence, the other a fast roll-dominated divergence. The movement of the dutch roll poles on the real axis, subsequent to their coalescence, complicates the correct identification of the spiral mode’s pole, due to the overlapping

3 1 1 Indeed the relationship between Nr and Cnr is direct, given that Nr ” Nr with Ixz “ 0; the same 1 holds for Nβ (cf. AppendixC)

99 5. Dynamic analysis 5.2: Dynamic modes

1 Figure 5.16: Variation of yaw damping derivative Nr with airspeed at sea level. of former dutch roll poles on the already clustered set of spiral poles near the origin. Therefore, in order to facilitate the study of the root locus, the real and imaginary parts of the dutch roll and spiral poles for a single SM are plotted against airspeed in Fig. 5.17, so as to improve their identiﬁability. The graph allows to fully appreciate the inﬂuence of velocity on the dutch roll and spiral poles, especially during the fading and subsequent collapsing of the lateral oscillation (roll convergence pole was not included for the sake of

Figure 5.17: Variation of dutch roll and spiral poles with airspeed at sea level (K » ´5%).

100 5.2: Dynamic modes 5. Dynamic analysis clarity). It is worth to note that the values assumed by the former spiral pole in the vicinity of dutch roll coalescence are all but conventional, so much so that the pole identifies a mode that has nothing of a conventional spiral (the shape is analyzed in detail hereinafter). Still, the identification of the pole was unequivocal, since, apart from the “large” roll subsidence pole, it was the only real pole; after dutch roll collapse, the spiral pole was identified as the one closer to the origin. With the purpose of providing a useful benchmark to compare to, the spiral pole was also estimated using two approximate models of the dynamic. In particular, the values in Fig. 5.18b derive from:

1 1 1 1 a4 LβNr ´ LrNβ λspi » ´ (5.7a) λ » (5.7b) a spi 1 3 Lβ where the first approximation is based on the consideration that a typical spiral’s pole is very small, thus chiefly defined by the last two coefficients of the characteristic polynomial of lateral-directional dynamics, namely a3 and a4; whence the second expression is obtained manipulating (5.5) with the assumptions of ∆p9 “ ∆p “ 0 and ∆β » const (∆β9 “ 0). The results at sea level are plotted in Fig. 5.18, next to the accurate solution, derived from the complete quartic equation of lateral-directional dynamic. The accurate solution shows a forward peak in the location of the spiral pole, in correspondence with the collapse of the dutch roll mode. As depicted in Fig. 5.18a, the closer the dutch roll complex conjugate poles get to the real axis, the further the spiral pole moves on the positive half-plane, reaching a values just less than 1. The peaks are reached at the coalescence of the dutch

(a) Accurate. (b) Approximate.

Figure 5.18: Variation of spiral pole location with airspeed and SM at sea level.

101 5. Dynamic analysis 5.2: Dynamic modes roll poles; then the spiral pole suddenly drops back to slightly negative values. Arguably, such inconstancy of the spiral pole location can be attributed to the same unconventional interactions that lead to the fading of the dutch roll oscillation. Approximation (5.7a) provides a particularly accurate estimation of the spiral’s pole; whereas (5.7b) is found to be disastrously unreliable. In addition to that, the ﬁrst approximation provides a simple explanation for the discontinuous trend depicted in Fig. 5.18a, which is undoubtedly due to the zeroing of the a3 coeﬃcient of the characteristic polynomial. Now, considering the expression of a3 relative to the model (5.5):

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a3 “ Lr Np Yβ ´ Nβ Yp ` Lp Nβ Yr ´ Nr Yβ ` Lβ Nr Yp ´ Np Yr ´ Yϕ (5.8) ´ ¯ ´ ¯ ´ ¯ becomes clear that the cause for the zeroing of a3 cannot be attributed to a single derivative, but rather it originates from the peculiar combination of the values taken by the whole set of lateral-directional derivatives in conditions of high dynamic pressure. Going back to Fig. 5.18a, it can be seen that the phenomenon is anticipated for low or negative SM and the peak occurs at lower airspeeds, as the disruption of the lateral oscillation does. In this sense, a larger SM is seen to possess a stabilizing effects on spiral divergence. Being caused by the coalescence of the dutch roll poles, this behavior occurs in the same conditions. In particular, it requires high values of dynamic pressure, achievable only at high speed, low altitude flight. In fact, increasing the altitude, the peaks gradually shift towards highest velocities, eventually disappearing completely for h ě 6 000 m. In the low to medium velocity range, the spiral mode fluctuates between stable and unstable,

Figure 5.19: Variation of spiral pole location with airspeed and SM at h “ 12, 000 m.

102 5.2: Dynamic modes 5. Dynamic analysis prior to the departure due to the dutch roll collapse. This fact is emphasized in Fig. 5.19, which shows the location of the spiral’s pole at high altitude, conveniently far from the conditions of departure. The oscillating behavior of the spiral pole is clearly appreciable. In addition, the effect of the SM is mutable and a positive SM can be either beneficial or detrimental, depending on the flight speed. The comparison of the eigenvector of the altered spiral mode with that of conventional one, provides immediate understanding of the mutation the mode undergoes as dutch roll mode fades away. The eigenvectors presented in Tab. 5.1 refer to sea level flight of a configuration with slightly negative SM (K » ´5%). At 150 m/s, the dynamic presents rather conventional characteristics. It is dominated by heading disturbance with an important contribution of roll; follow yaw and roll rates; while the variation in sideslip angle is minimal. At 200 m/s, the lateral oscillation is about to collapse and the spiral pole has moved far on the positive half-plane. This gives rise to a deeply mutated motion, dominated by roll angle a comparable contribution of roll rate; ∆ψ and ∆r follow, in the same mutual ratio as ∆ϕ and ∆p; ∆β disturbance is of the same magnitude as ∆r, but with opposite sign. Moreover, the overall ratio between the dominant and smallest disturbance shifts from around 200 to less than 7, indicating a significant contribution of all states in the “altered” form of the spiral mode. Hence, in correspondence to the coalescence of dutch roll poles, the spiral mode undergoes a radical mutation, losing the characteristics of a spiral divergence and resembling more to a self-sustained roll, somewhat like an autorotation. Also, the motion dangerously reduces its time constant, thus acquiring a considerable rapidity, especially for largely positive or neutral SM, which is highly undesirable from a handling qualities perspective.

U8 “ 150 m/s U8 “ 200 m/s ∆β ´0.0049228 ´0.15170 ∆ˆp 0.0078527 0.75870 ∆ˆr 0.022993 0.15314 ∆ϕ 0.35214 1 ∆ψ 1 0.20733

Table 5.1: Spiral eigenvector variation due to dutch roll collapse at sea level (K » ´5%).

It is interesting to analyze the characteristics of the aperiodic departure mode that originates from the collapsing of dutch roll at high velocity. The eigenvector reported in Tab. 5.2 summarizes the nature of the motion, as predicted by linear analysis at a velocity

U8 “ 250 m/s at sea level, for K » ´5%. Roll rate and attitude are the predominant components of the dynamic, followed by yaw rate and attitude; sideslip is the lesser component, with a magnitude of less than 17% of ∆p. The favorable contribution of roll rate suggests

103 5. Dynamic analysis 5.2: Dynamic modes that the dynamic develops as a self-sustained rolling rotation, to all extents comparable to an autorotation involving primarily the x-axis and secondarily the z-axis. Indeed, the dynamic is similar to that generated by the spiral pole just before the coalescence of the dutch roll, given that the respective poles are very closely located on the real axis. The fact that the departure occurs in conditions of high dynamic pressure (low altitude and high airspeed) makes low altitude missions excessively hazardous without the implementation of suitable lateral stability augmentation system.

U8 “ 250 m/s ∆β ´0.16960 ∆ˆp 1 ∆ˆr 0.25819 ∆ϕ 0.69874 ∆ψ 0.18067

Table 5.2: Lateral departure eigenvector at sea level and U8 “ 250 m/s for K » ´5%.

The coeﬃcient a4 and Routh discriminant ∆R represent the ﬁgures to quantify the global degree of stability of a dynamic system. In particular, a negative value of the former indicates static instability and the presence of a positive real pole; a negative value of the latter marks the presence of a couple of complex conjugate poles with positive real part. The values of a4 and ∆R at sea level are presented in Fig. 5.20: a4 becomes negative

(a) Stability parameter. (b) Routh discriminant.

Figure 5.20: Variation of dynamic stability parameters with airspeed at sea level.

104 5.2: Dynamic modes 5. Dynamic analysis when the spiral becomes unstable; ∆R becomes positive when the dutch roll stabilizes. In contrast to what observed on the longitudinal root locus, the effect of altitude on lateral-directional poles is quite considerable, as illustrated by the root locus in Fig. 5.21. Overall, the effect of density reduction with altitude is an alteration in the frequency of the dynamics of the SACCON. The roll subsidence mode (again omitted from the picture for the sake of clarity) experiences the most intense slowdown, in fact its poles move from around ´12 to less than ´2.5. It can be seen that the spiral becomes increasingly faster at high altitude, which has a detrimental effect on the flying qualities of the aircraft. Finally, the change in dutch roll with altitude is somewhat similar to that due to velocity, but reversed. In particular, the dynamic gets faster with altitude, but only when it is unstable; otherwise the frequency is almost insensitive to altitude.

Figure 5.21: Dutch roll root locus varying altitude and static margin at U8 “ 200 m/s.

105 5. Dynamic analysis 5.3: Flying qualities assessment

5.3 Flying qualities assessment

In this section, the handling qualities of the SACCON configuration are considered, the purpose being to identify control related handling qualities limitations. First of all it was necessary to situate the SACCON within the frame of handling qualities definitions, according to the formalization provided by MIL-HDBK-1797A. Within the scenario described in Section 2.2.3, the hypothesized weight of the SACCON, along with its mission requirements place the aircraft in Class II, that is medium weight, low-to- medium maneuverability. Indeed the SACCON was not intended as a high-maneuverability aircraft and Class IV requirements do not apply. In second instance, the operating points of the analysis envelope had to be associated to the correct flight phase, as defined in Tab. 2.2. Assuming the generic mission specifications of an all-altitude bomber, somewhat similar to those of the Northrop B-2, the flight envelope was divided into three portions, denoted by different colors.

• A low-altitude, medium-to-high speed corridor was prescribed for airspeed greater than 100 m/s and altitudes comprised from sea level to 3000 m, at low speed, and from sea level to 6000 m, at high velocity. The embraced flight conditions comprise low altitude precision delivery, as well as terrain following penetration missions, requiring compliance with Category A flight phase specifications. The portion is highlighted in red.

• Operative conditions involving airspeeds from stall velocity to 100 m/s up to 3000 m and 120 m/s from 3000 m to 14000 m are regarded as terminal flight conditions, hence liable to the requirements relative to Category C flight phases. The conditions comprise descent from high altitude cruise and loitering, as the maximum efficiency velocity is within this portion for all altitudes (cf. Fig. 4.12). The portion is highlighted in yellow.

• The remaining point of the envelope were considered generic cruise ﬂight, subject to Category B ﬂight phase requirements. The portion is highlighted in green.

The outcome of the above division of the envelope is illustrated in Fig. 5.22. The analysis proceeded for the longitudinal and lateral-directional dynamics separately. The criteria contained within the adopted regulation, among other requirements, constrain the values of the damping ratio and frequency of the various dynamics, then, the study involved the calculation of such parameters at each operative condition comprised by the analysis envelope. The values of frequency and damping of a mode are directly set by its pole, expressed as λ “ a ` b, and are expressed as:

|b| ωN “ (5.9) 1 ´ ζ2 a 106 5.3: Flying qualities assessment 5. Dynamic analysis

a ζ “ ´ (5.10) |λ|

Then the values of the period, damped frequency and time to half (or double) can be derived from the previous deﬁnitions:

2 π T “ (5.11) ωN

2 ω “ ωN 1 ´ ζ “ b (5.12) a lnp2q lnp2q t1{2 “ ´ “ ´ (5.13) ζ ωN a where the time to half turns into time to double t2 for unstable dynamics.

Figure 5.22: Analysis envelope with prescribed ﬂight phases.

The results were compared to the requirements outlined by the speciﬁcation, in order to quantitatively assess the handling qualities of the SACCON. The prescribed levels of airworthiness are marked, when applicable, by diﬀerent lines. In particular:

• a solid line ------denotes Level 1 limits;

• a dashed line --- indicates Level 2 limits;

• a dash-dot line - ¨ - marks Level 3 limits.

The responses of reduced order models to control inputs were also evaluated.

107 5. Dynamic analysis 5.3: Flying qualities assessment

5.3.1 Longitudinal ﬂying qualities

The eﬀect of airspeed, altitude and CG location on natural frequency and damping ratio of the longitudinal modes are presented in the following ﬁgures.

5.3.1.1 Short period

The damping ratio of the short period is shown in Fig. 5.23, at low and high altitude. The dependency of the damping ratio on airspeed is appreciable at low speed, but relaxes as the velocity is increased, especially at low altitude. At high altitude some variation with airspeed is preserved up to the edge of the envelope, with a peak in the medium velocity region, especially in the case of relaxed stability. The influence of mass distribution is somewhat inverse and tends to increase with airspeed, more sharply at high altitude. At low altitude, which represents a Category A/C flight phase, according to Fig. 5.22, the SPO meets Level 1 requirements for K ă 10%, while it reaches only Level 2 for xCG “ 4.2 m. The rather dramatic drop in damping with altitude causes a significant deterioration of the characteristics of the SPO. In this case Category B requirements apply, except for a narrow range at low speed, and Level 1 is attained only around marginal stability. As the SM increases, the degree of the SPO worsen progressively, to the point that only Level 3 requirements are met for xCG “ 4.2 m. Of course, the results do not explicitly emphasize the fact that the absence of the short period for non-positive stability, i.e. xCG ą 4.5 m, automatically ratifies the non-flyability of the SACCON, at least as it is. In this case, the sole solution is the implementation of a

(a) h “ 0 m (Category C/A). (b) h “ 12 000 m (Category C and B).

Figure 5.23: Short period degree assessment.

108 5.3: Flying qualities assessment 5. Dynamic analysis well designed SAS, capable of “electronically” restore a conventional SPO.

The plots in Fig. 5.24 show the variation of SPO frequency. At low altitude and except for low airspeeds, the responsiveness of the mode varies almost linearly with static margin. At high altitude the frequency shows a similar linear behavior only at high velocity. In general, airspeed and SM have a stimulating eﬀect on SPO dynamic; while altitude is seen to induce a relaxation of the response, which becomes fairly sluggish in high altitude ﬂight.

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 5.24: Short period frequency variation with airspeed and CG position.

CAP assessment results are illustrated in Fig. 5.25. Flying qualities levels are marked with bold lines according to the mentioned key. The plots show that the configuration qualifies for Level 1 CAP requirements for all positive SM, regardless of airspeed in all flight phases. It must be noted that, especially at low velocity, only marginal Level 1

flying qualities are achieved for the highest SM, i.e. xCG “ 4.2 m. The characteristics of the longitudinal control dynamic for neutral stability, at least in flight conditions in which the SPO is defined, are totally unsatisfactory at low altitude and only partially acceptable at high altitude. The cyan branch that appears in the Category A flight phase plot of Fig. 5.25b is the spurious product resulting from the use of a reduced order model. Indeed, the root locus of the full order model of Fig. 5.4 does not display short period poles for xCG “ 4.6 m. The SPO is not present for negative SM, thus no results were available. The outcomes of the analysis at intermediate altitudes did not show significant changes.

109 5. Dynamic analysis 5.3: Flying qualities assessment

(a) Sea level, low velocity (Category C) (b) Sea level, high velocity (Category A)

Figure 5.25: CAP assessment for short period characteristics.

5.3.1.2 Phugoid

The damping ratio of the phugoid is shown in Fig. 5.26, at low and high altitude. The requirements enunciated in the regulation are invariant on the flight phase. In fact, since the phugoid is a poorly damped trajectory dynamic, the scope of the regulation is merely to avoid it to become excessively rapid, regardless of the flight phase. In first instance, the damping ratio of the phugoid is inversely proportional to the aerodynamic efficiency of the aircraft, which is designed to be efficient. Hence the phugoid is generally weakly damped. Airspeed has a beneficial influence on the degree of the phugoid, due to the reduction in

110 5.3: Flying qualities assessment 5. Dynamic analysis

(a) h “ 0 m (Category C/A). (b) h “ 12 000 m (Category C/B).

Figure 5.26: Phugoid degree assessment.

E; conversely altitude tends to deteriorate the characteristics. Phugoid damping is almost insensitive to CG location. Overall, the SACCON exhibits a poorly damped phugoid. At low altitude non-positive static stability, i.e. K ě 0%, grants Level 1 phugoid degree at all airspeeds; while, for positive SM, Level 1 is attained only at medium-to-high velocity. Slowing down, the degree for stable conﬁgurations drops to Level 2, the higher the SM,

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 5.27: Phugoid frequency variation with airspeed and CG position.

111 5. Dynamic analysis 5.3: Flying qualities assessment the higher the velocity at which this happens. At high altitude, Level 1 is achieved for non-positive SM at all airspeeds; while stable conﬁgurations settle within Level 2. The same dependency pattern is shown by the frequency of the motion, depicted in Fig. 5.27. Indeed, the dependency on CG location is so weak that it almost vanishes as high speed. The phugoid becomes quite rapid at low altitude, low airspeed, with a period of just 20 ˜ 40 s, which reduces to 90 s at high speed. At high altitude the period remains bigger than 90 s. This behavior can be explained considering that dynamic pressure q8 acts as a gain for phugoid dynamic, in the sense that to an increment in its value corresponds a proportional increment in the frequency of the motion. In turn, a speed up of the motion, increases its dissipation, thus its damping.

5.3.2 Lateral-directional ﬂying qualities

The formulation of the requirements for lateral-directional dynamics is slightly less immediate than that for longitudinal ones. The assessment of lateral ﬂight qualities involves the estimation of more parameters, other than damping ratio and natural frequency, as well as the evaluation of combined ﬁgures, accounting for coupled dynamics.

5.3.2.1 Roll subsidence

The degree of the roll mode is determined by its time constant τR, which is closely 1 related to the value of the roll damping derivative Lp. The result at low altitude is reported in Fig. 5.28a. Roll time constant is extremely susceptible to airspeed and it reduces of more than 6 times across the velocity range. On the other hand, the inﬂuence of CG position

(a) h “ 0 m varying xCG. (b) xCG “ 4.8 m varying h.

Figure 5.28: Roll subsidence degree assessment.

112 5.3: Flying qualities assessment 5. Dynamic analysis

is so weak, that it was decided to emphasize the variation of τR with altitude, shown in Fig. 5.28b. The decrease in air density with altitude strongly reduces the responsiveness of the dynamic and its time constant gets closer to Level 1 limit (1 s) at the highest altitudes. Nevertheless, the roll mode is well within Level 1 requirements in all conditions.

5.3.2.2 Dutch roll

The dutch roll represents the major flaw of the flying wing design of the SACCON. As pointed out during the analysis of the root loci, the dynamic is unstable in the absolute majority of flight conditions and, when stable, its characteristics do not even meet Level 3 requirements, due to the extremely low frequency, attributable to poor directional stiffness

Cnβ . This is clearly proven in Fig. 5.29, which reports the assessment of dutch roll ﬂying qualities summarized in Tab. 2.7. Dutch roll quality assessment was carried out only at low altitude, since the instability of the mode placed it unconditionally below the limits imposed by the regulation.

Figure 5.29: Dutch roll level assessment at sea level (Category A).

The situation enforces the implementation of an adequate SAS, which is mandatory not merely to stabilize, but also to adjust the dutch roll performance of the SACCON.

113 5. Dynamic analysis 5.3: Flying qualities assessment

5.3.2.3 Spiral

The degree of the spiral mode is determined by the time taken by bank disturbance up to 200 to double its amplitude. The degree is, then, determined by the time to double of the spiral mode, which is shown in Fig. 5.30. The criterion can only be applied to unstable poles, since a stable spiral automatically satisﬁes the condition. Thus only positive values, relative to unstable poles, are reported in the logarithmic plot.

(a) h “ 0 m (Category A/C). (b) h “ 12 000 m (Category B).

Figure 5.30: Spiral divergence degree assessment.

At low altitude (Fig. 5.30a), Level 1 requirements are met at low speed, for all CG locations. At higher velocity, the rightward shifting of the pole, due to the dutch roll collapse, dramatically increases the rapidity of the divergence, which reaches a time to double as low as 1 s. This induces a signiﬁcant deterioration in the degree of the motion, which drops from Level 1 to below Level 3 in just 30 m/s of velocity variation. After that, a more conventional and stable spiral behavior is restored. As already mentioned, as altitude is increased, the alteration of the spiral mode shifts to ever larger velocities, until it completely disappears for h ą 6 000 m. For this reason, spiral’s degree assessment at intermediate altitudes is analogous to that depicted in Fig. 5.30a, except for the fact that the drop in quality level gradually shifts rightward, eventually moving outside the operative envelope. Finally, at high altitudes (Fig. 5.30b) the dynamic unconditionally attains full Level 1 degree. Note that in Fig. 5.30b Category B ﬂight phase requirements were extended also at the low velocity range, since the limit on Level 1 degree is more restrictive than that of Cat- egory C, yielding a more conservative quality level assessment.

114 5.3: Flying qualities assessment 5. Dynamic analysis

5.3.3 Control dynamics

MIL-HDBK-1797A [35] conveniently expresses the handling qualities requirements for the response to control inputs, in terms of the characteristics of the time-variation of speciﬁc states, critical to each maneuver. Hence, handling qualities assessment requires the evaluation of the response of the linear system to particular control input, usually a unitary step, in order to measure the evolution of the states involved in the maneuver.

5.3.3.1 Response to step elevator

The requirements for longitudinal control, i.e. elevator, are specified in terms of CAP requirements, discussed in Paragraph 5.3.1.1, and do not actually require the explicit evaluation of the response, which is nonetheless presented for the sake of completeness. The response to a step elevator input was obtained for nz, q9, q and ϑ using the reduced order model for the short period dynamic. This was done so as to avoid the interference of velocity reduction caused by having omitted thrust from the model. The results are shown in Fig. 5.31 and Fig. 5.32. The response to the elevator is regulated by the short period dynamic, thus it is influenced by flight parameters in a way similar to the SPO. The upper plots (Figs. 5.31a and 5.31b) illustrate the longitudinal response of the SAC- CON in a terminal flight phase at low altitude and low velocity. The reduction of the SM induces a stiffening of the response, which reduces its oscillation, inducing larger variations of the states, but takes more time to settle. The lower plots (Figs. 5.32a and 5.32b) illustrate the longitudinal response at a high altitude cruise flight condition. The lower air

(a) U8 “ 60 m/s and K » 10%. (b) U8 “ 60 m/s and K » 2.5%.

Figure 5.31: Longitudinal response to step elevator at sea level.

115 5. Dynamic analysis 5.3: Flying qualities assessment

(a) U8 “ 250 m/s and K » 10%. (b) U8 “ 250 m/s and K » 2.5%.

Figure 5.32: Longitudinal response to step elevator at 12 000 m. density boosts the oscillatory behavior of the response, while the higher value of dynamic pressure amplifies it (the amplitude of the response is increased of around 7 times). The same observations regarding the influence of the CG still apply. Overall, elevator effectiveness and, consequently, longitudinal maneuverability are considerably improved with reduced SM, in perfect accordance with theory.

5.3.3.2 Response to step aileron

The characteristics of lateral-directional dynamic response to aileron are stated in terms of the output roll rate, sideslip excursion, either proverse or adverse, time to reach a certain bank angle and the sign of the response. The aileron response requirements for Class II aircrafts are summarized in Tab. 5.3, where k is the ratio between the actual time taken to reach 45˝ bank angle and the Level 1 limit value specified by the regulation. The Level 1 requirement on roll rate imposes that the second roll rate peak should be of the same sign and not less than a certain percentage of the first peak. The plots in Fig. 5.33 show the roll rate response due to step aileron at various airspeeds and altitudes. Due to the unconditional instability of the dutch roll, lateral control dynamic results unstable, thus the second peak is always of the opposite sign from the initial or intended direction, if not even divergent. The open loop response in terms of roll rate is clearly below Level 3 regardless of the operative condition and flight phase. The plots in Fig. 5.34 show the corresponding roll angle, which is found to be coherent with the imposed command, albeit unstable. The dynamic is tremendously fast and Level 1 requirements on time to reach ϕr value of bank angle are thoroughly met at all conditions.

116 5.3: Flying qualities assessment 5. Dynamic analysis

Parameter Cat. A Cat. B Cat. C unit

Roll rate p at ﬁrst minimum

Level 1 60 25 60 % of pmax Level 2 25 0 25

Time to reach ϕr bank angle

0 Level 1 (ϕr “ 45 ) 1.4 1.9 1.0 0 Level 2 (ϕr “ 45 ) 1.9 2.8 1.5 s 0 Level 3 (ϕr “ 25 ) 2.8 3.8 2.0 Adverse/Proverse sideslip

Level 1 6 k{2 k 10 k{3 k 10 k{3 k deg or rad Level 2 15 k{4 k 15 k{4 k 15 k{4 k

Table 5.3: MIL-HDBK-1797A aileron response requirements for Class II aircrafts.

Finally, Fig. 5.35 illustrates the increment in sideslip angle ∆β due to a step aileron command. The aileron command is seen to always develop proverse sideslip; except in ﬂight conditions after the collapse of the dutch roll, in which the lateral divergence mode dom- inates the motion. Other than that, being the control dynamic unstable, it is impossible to assess its sideslip characteristics according to the speciﬁcation listed in Tab. 5.3.

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 5.33: Variation of roll rate response to step aileron with airspeed (K » ´5%).

117 5. Dynamic analysis 5.3: Flying qualities assessment

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 5.34: Variation of roll angle response to step aileron with airspeed (K » ´5%).

(a) h “ 0 m. (b) h “ 12 000 m.

Figure 5.35: Variation of sideslip angle response to step aileron with airspeed (K » ´5%).

5.3.3.3 Response to step rudder

The aircraft dynamic response to a step command on the rudder, that is split elevon, is presented in Fig. 5.36. No explicit requirements are speciﬁed by the regulation, so the results are presented with the aim to qualitatively visualize the response of the SACCON. The main remark regarding response to rudder command is the extremely strong coupling between lateral and directional dynamics triggered by the drag rudder displacement. Due to its very nature, the directional control generates as much roll as yaw and the re-

118 5.3: Flying qualities assessment 5. Dynamic analysis sponse is governed by the unstable dutch roll dynamic. The response in a terminal flight condition is shown in Fig. 5.36a and 5.36b. The location of the CG affects quite considerably the control effectiveness, in particular the ∆ψ variation for negative SM seems almost negligible, while being adequate for positive SM. In addition, the sign of the coupled roll tendency inverts from concordant for positive SM to discordant for negative SM. In both cases, the amplitude of roll oscillations is slightly larger than that of yaw oscillations, indicating a control more effective in roll than in yaw. The response in cruise flight (Fig. 5.36c and 5.36c) shows less sensitivity to CG location. It is dominated by a proverse coupled roll effect, yaw being just marginally influenced.

(a) U8 “ 60 m/s, h “ 0 m, K » 10%. (b) U8 “ 60 m/s, h “ 0 m, K » ´5%.

Figure 5.36: Lateral-directional response to step rudder in diﬀerent ﬂight conditions.

119 5. Dynamic analysis 5.4: Chapter summary

5.4 Chapter summary

A summary of handling and control problems and limitations for the SACCON detected during the analysis is presented below.

Longitudinal dynamics

• Short period

– For SM K ă 2.5%, regardless of velocity or altitude, the short period disappears into a couple of aperiodic motions, giving rise to a tumbling mode. – The short period mode fails to meet Level 1 requirements for K ą 5%, both at low and high altitude, for it is not adequately damped.

• Phugoid

– The dynamic is always present, except at low-to-medium airspeed and low altitude for K » 0, where it combines with the short period to generate a third mode branch. It is unconditionally stable for non-zero SM, at least for K ě ´5%. – The motion is poorly damped, especially at high altitude. Overall, conﬁgura- tions with neutral or negative stability were seen to attain improved phugoid quality, attaining Level 1 degree at all airspeeds and altitudes.

Lateral-directional dynamics

• Roll subsidence

– The mode is unconditionally stable and well responsive, allowing the aircraft to achieve Level 1 roll characteristics through the whole envelope.

• Dutch roll

– The mode is predominantly unstable and very slow at all combinations of airspeed and CG location. For these reasons the aircraft’s ﬂying quality settles below Level 3. – The dynamic collapses in conditions of high dynamic pressure, giving to a couple of aperiodic motions, one of which eventually develops into an unsafe self- sustained roll.

• Spiral

– Globally, the characteristics of the spiral satisfy Level 1 requirements, either because the motion is stable or because its time to double is long enough.

120 5.4: Chapter summary 5. Dynamic analysis

– The mode is greatly inﬂuenced by the behavior of the dutch roll and it is seen to undergo profound alteration in correspondence to the degeneration of the lateral oscillation, mutating into a sort of fast, self-supporting roll dynamic. During these transitions, the characteristics of the dynamic deteriorates and its degree drops below Level 3.

Control dynamics

• Elevator

– The predicted longitudinal control authority is too weak and the elevator power was artiﬁcially enhanced by a factor of two, in order to make this a practical design. Control allocation may be used at low airspeeds by assigning outboard elevons for additional pitch control, at the expense of a reduction in roll control authority. – The control dynamic, i.e. the SPO, unconditionally satisﬁes Level 1 CAP requirements, at least for conditions in which short period mode is present, that is for K ě 2.5%.

• Ailerons

– In terms of the time required to reach ϕr bank angle, the predicted performance of the aircraft in roll is adequate. By virtue of the planform shape, the roll axis inertia is moderate and the outboard ailerons suﬃce to allow the SACCON to meet Level 1 requirements in all conditions. – The direction of the response is in accordance with the intended command. Nevertheless, the control dynamic of the ailerons is dominated by the unstable dutch roll, thus it fails to meet the requirements regarding the second peak or roll rate and the limitations concerning the intensity of coupled yaw.

• Rudder

– The effectiveness of the rudder command is generally very poor, even though it exhibits significant sensitivity to the CG location. The usage of the already conceived wing tip split surfaces is deemed the only feasible solution to increase directional control authority as well as to provide the SACCON with control surfaces dedicated to directional control. – The coupled effect of the rudder on roll is seen to overcome the intended effect on yaw, with a sign that depends on the SM of the configuration. Moreover, the behavior exacerbates at high altitude, where the influence of the drag rudder on yaw becomes negligible compared to that on roll.

121

Chapter 6

Concluding remarks

This chapter concludes this research work and presents a summary of the main ﬁndings. In addition, it suggests some guidelines for further research on the subject.

6.1 Conclusions

The diverse work phases undertaken with the purpose of assessing the flying qualities of the SACCON were presented in this thesis report. The study involved several analysis aspects, namely (i) the aggregation of experimental data into a comprehensive, suitably formatted database; (ii) the static analysis and trimming of the airframe across a prescribed test envelope; (iii) the study of the dynamic characteristics of the model upon its linearization into a LTI multi-variable system; (iv) the assessment of the flying qualities of the SACCON on the basis of the outcomes of the dynamic analysis. The breadth of the data at such a early design stage was limited and the design itself still rather unrefined, with a number of unsolved issues, especially regarding control authority and allocation and some unexplained asymmetric aerodynamic behavior. Therefore the findings and remarks presented in the context of this study represent first attempt solutions to the issue of the quantitative assessment of the flying qualities of the SACCON aircraft, useful to provide a leap of understanding of the S&C characteristics of the design, in the broader perspective of the general validation of the airframe within the framework of the NATO RTO AVT-201. However, an effort was made in order to obtain a comprehensive set of valuable results and certain conclusions were drawn. These are summarized as follows.

• Aerodynamic database synthesization The experimental data provided by the DWN-NWB wind tunnel facility, were aggregated so as to obtain a comprehensive low speed aerodynamic database of the target configuration. The tests explored the dependency of the six aerodynamic coefficients upon α, β, control effectors deflection and angular rates. In order to obtain a more manageable dataset and facilitate the subsequent linearization of the model,

123 6. Concluding remarks 6.1: Conclusions

the wind tunnel data were conveniently divided into three groups, according to their functional dependencies:

– baseline, storing the static loads of the zero-control conﬁguration; – control, expressing the increments introduced by the control surfaces deﬂection; – rotational, introducing the quasi-steady increments due to angular rates.

As for data organization, a bi-dimensional spreadsheet format was preferred to multi- dimensional table, for the former proved to be more flexible and computationally more efficient. An XML superstructure database format was also defined, the aim being to specify a flexible and comprehensive format for the complete model of the aircraft (aerodynamics, mass distribution, propulsion, flight control system), suitable for fast, advanced S&C simulation (see AppendixD).

• Aerodynamic analysis A coarse investigation of the resulting database of the SACCON was carried out, with the backing of the outcomes of AVT-161, in order to point out the main aerodynamic peculiarities and issues of the design. The analysis revealed a rather smooth aerodynamic behavior for α up to 10˝, with almost linear trends in all coefficients. At higher angles of attack, with the strengthening of vortical flow structures, the linear behavior is permanently lost, inducing vigorous discontinuities in the pitching moment. Concurrently, the rapid increase in drag causes a heavy deterioration of the aerodynamic efficiency of the design. However, lift was seen to be unaffected by flow non-linearities, but rather to benefit from the contribution of vortex lift all the way until stall. The detrimental influence of non-linear low phenomena was seen to cause some peculiar inversions in the slopes of lateral-directional coefficients curves versus β at high α, not hazardous during cruise flight, but conceivably risky during terminal and maneuvering flight. The same divergence from linear behavior was exhibited by the time histories of forced oscillation data. In fact, the results showed significant 0 non-linear behavior and considerable statistical spread for α ą 10 , except for Cm, which presented strong variations since low angle of attack.

• Control authority The most severe flaw of the SACCON was found to be the dramatically poor control authority of the surfaces fitted in the model. The increments induced by the deflection of the effectors were at best marginal, if not negligible. Moreover, the roll/yaw cross coupling of both ailerons and drag rudders was found to be very strong, inducing coupled effects of the same magnitude of direct ones, but opposite in sign. Even worse, within the non-linear flow regime, the effect of the elevator becomes discontinuous up to the point to invert its sign. For this reason, the effectiveness of the controls was artificially boosted by a factor of 2.

124 6.1: Conclusions 6. Concluding remarks

• Static stability and trim A test envelope was deﬁned, in order to identify a set of operative conditions through which evaluate the inﬂuence of airspeed, altitude and CG location. The upper limits of the envelope were assigned a priori and set equal to the performance of the Dassault nEUROn (the same powerplant of the nEUROn was also assumed). Limit positions for the CG were appointed so as to yield a SM range of about ´10% ď K ď 15%, corresponding to a CG shift of 1.2 m. On the other hand, inertia properties were derived from those of the Northrop B-2. The evaluation SM variation with CG location suggested that the aircraft would, at best, operate in condition of relaxed stability, more likely of complete instability. In fact it was seen that positive SM could only be achieved for extremely forward shifted centerings, unlikely attainable under practical operative conditions. Longitudinal trim analysis revealed that for static

margins |K| ą 10% and low airspeeds (U8 ă 80 m/s), large elevator deflections were required to maintain trim, leading to saturation of the control. Moreover, in case of too positive SM, the consequence of large negative deflection of the elevator was a considerable loss in lift generation capability. This is in contrast to what is desired at take off and landing speeds, when the highest possible lift coefficient is required to sustain the weight of the aircraft. Hence, unless fitting the aircraft with additional high-lift devices, it was apparent from longitudinal trim analysis alone that the only feasible way for the SACCON to fly is with a SM comprised between ˘10%. Necessary thrust prediction indicated that stable configurations tend to require less thrust to trim than unstable, due to better aerodynamic efficiency. In particular, required thrust in cruise flight was seen to diminish with velocity, arguably due to near-zero of the elevator deflection, with corresponding increase in aerodynamic efficiency. Nevertheless, the model did not account for compressibility effects and drag prediction at high speed, especially at low altitude, is likely to be underestimated.

• Linear dynamics Longitudinal dynamic analysis showed that, as soon as the static margin gets below 2.5%, the short period mode deteriorates rapidly. This is in agreement with the longitudinal trim requirement, which calls for relaxed static stability, but poses a problem when considering that the practical CG locations of the SACCON will likely yield negative SM. The analysis outlined a scarcely damped, but always stable phugoid dynamic, which disappears only in conditions of relaxed stability. In particular, in a narrow range of airspeed at low altitude for K » 0, it combines with the SPO, identifying a third mode branch. The lateral-directional dynamics were severely aﬀected by the absence of vertical tail. The dutch roll oscillation is unconditionally unstable, besides sluggish. In addition, in conditions of high dynamic pressure, the mode collapses generating a couple of

125 6. Concluding remarks 6.1: Conclusions

aperiodic motions, one of which rapidly turns into a roll divergence-like motion. The collapse of the dutch roll strongly alters the spiral motion, whose pole rapidly moves to the right, developing a fast roll divergence motion. However, past the correspondence of the lateral oscillation poles, a more conventional spiral is restored. Other than that, the spiral was overall acceptable, either stable or slowly divergent.

• Flying qualities The airworthiness of the SACCON was assessed according to the guideline principles specified by MIL-HDBK-1797A. The unaugmented aircraft struggles to maintain a desirable longitudinal dynamic behavior. The SPO unconditionally met Level 1 characteristics just for K » 2.5% and its quality could not be assessed for negative or neutral stability, since it was replaced by aperiodic motions. On the other hand, the phugoid is (almost) always present, but fails to attain Level 1 degree, due to poor damping and instability. The study showed that CG location requirements for short period and phugoid are generally antithetical, as the second mode behaved better in conditions of negative SM and viceversa. The CAP assessment placed the longitudinal control dynamic of configurations with positive SM within Level 1 boundaries. Of course, the absence of a short period mode in case of non-positive SM automatically implies inadequate control dynamics. The roll axis was found to be satisfactorily responsive, also thanks to a reduces moment of inertia, and Level 1 requirement on roll subsidence was comfortably met. The dutch roll characteristics unconditionally settled below Level 3, mainly because of the instability of the motion, but also of its slowness. The spiral was globally decent and, except during the interaction with the coalescent dutch roll poles, it achieved Level 1 flying quality. Lateral-directional control dynamics were dominated by the unstable dutch roll, a fact that thoroughly undermined the control characteristics of the unaugmented SACCON. In particular, a meaningful assessment of the response to step aileron and rudder commands was impossible, due to the divergence of the responses. Nevertheless, the aileron proved to be effective and the roll control power adequate, also by virtue of the small roll inertia of the aircraft. Conversely, the split outboard elevons were found to be inadequate as rudder command effectors, as the cross coupling roll effect induced by their deployment was predominant, to the extent to dwarf the direct effect on yaw, especially at high altitude.

126 6.2: Further research 6. Concluding remarks

6.2 Further research

In light of the outcome of the study, with regards to future work on the subject, the following suggestions are forwarded.

• Aircraft model The enlargement of the aerodynamic model of the SACCON, with the inclusion of the effects of compressibility (Mach dependency) is deemed mandatory, in order to extend the validity of the model and improve the accuracy of its predictions in the high velocity range of the envelope. Moreover, it is also necessary to test the tip drag rudders and introduce them in the model. The directional control exerted by the split deflection of the outboard elevons was found to be extremely deficient, with too strong cross coupling effects. Not to mention the fact that it is necessary to properly allocate the rudder command to dedicated effectors, as it is surely not practical to have it to share the same control surface devoted to the aileron command. Furthermore, the aerodynamic data collected so far consider the aircraft as a rigid structure. The assumption is tolerable, given the full scale size of the aircraft, which, with its 12,3 m span by 10,5 m length, is a medium-sized vehicle. Still, methods like the strip element approach would allow easy integration of any structural deforma- tion under variable aerodynamic loading. This may include wing bending, torsion and even flutter. Structural/aerodynamic interaction aspects may therefore be also considered for further research.

• Flight control system The design of a complete inner loop flight control system, for both longitudinal and lateral dynamics, is certainly required, as the flying and handling qualities of the unaugmented aircraft turned out to be poor and surely not adequate for the mission of the aircraft. A longitudinal SAS with α and q feedback is necessary, in order to establish adequate longitudinal control dynamic even for relaxed or negative stability, as well as to avoid dangerous tumbling tendency. In fact, the degeneration of the SPO radically alters the longitudinal control dynamic, inducing inconsistent and/or inadequate response patterns, especially in mission segments that require rapid or precision maneuvering, such as terminal flight phases or low altitude, high velocity flight. On the other hand, the phugoid dynamic could be improved via the implementation of propulsion/control integration logics within the outer loop controller. Also lateral-directional dynamics must benefit the integration of stability augmentation, comprising aileron-rudder interconnect (ARI). The aim of such controller should be threefold: 1) to tame the undesirable dutch roll behavior, both by increasing its frequency and by avoiding its collapse; 2) to suppress the alteration of the spiral motion in conditions of high dynamic pressure; 3) to alleviate the adverse/proverse sideslip developed by the aileron controls, by means of a washed out β feedback loop.

127 6. Concluding remarks 6.2: Further research

• Advanced simulation The execution of full non-linear, dynamic simulations of maneuvers and gust response is necessary to quantitatively validate the airframe beyond the narrow figures of linear analysis, in favor of a farther-reaching and more detailed evaluation of the dynamic behavior of the SACCON. A first step in this direction was made with the definition of a XML database format (cf. AppendixD), in which store all data required for full dynamic simulation, i.e. aerodynamics, propulsion, mass and inertia, flight control systems, etc . . . . The structure was specifically conceived to allow accelerated simulation in Simulink, via the pre-compilation of the database and related interpolation routines into MATLAB mex-files. Arguably a simulation tool of such sort would provide a powerful and reliable mean for a complete and detailed verification of the design, allowing to overcome the limits of the linear analysis, so as to achieve superior prediction capabilities.

• Propulsion system It is reasonable that the configuration could derive enormous benefit from the implementation of thrust vectoring, both in terms of control authority, particularly considering directional controllability, and flying qualities enhancement, since thrust vector control (TVC) could be employed to improve the stability characteristics of the SACCON. However, the pros and cons of such a configuration, specifically its feasibility, need to be carefully examined, also considering that no information about the powerplant of the aircraft is yet available.

128

Appendix A

SACCON conﬁguration

This section describes the target aircraft and its mass, inertia and geometric properties. Due to the lack of data in such a early design phase, especially regarding mass distribution, missing parameters were derived from those of comparable aircrafts.

A.1 General description

The target conﬁguration of the AVT-201 Task Group is a generic UCAV geometry called SACCON, acronym for “Stability And Control CONﬁguration”, a generic UCAV

Figure A.1: Designed arrangement of the control surfaces of the SACCON [37].

131 A. SACCON configuration A.2: Mass and inertia properties configuration. The planform and section profiles were defined in cooperation with the European Aeronautic Defense and Space Company (EADS-Cassidian) to meet the S&C requirements in connection with the objectives of the research group. Fig. A.1 shows the general layout of the aircraft. Modifications with respect to airfoil sections and center section geometry have been introduced by DLR and DNW-NWB [19]. The aircraft has 6 control surfaces, highlighted in different colors in Fig. A.1: a couple of inboard elevons, operated as elevator; a couple of outboard elevons, operated as ailerons; a couple of tip split elevons, operated as drag rudders. The outboard elevons can also be split and act as drag rudders. All control surfaces are located on the trailing edge. A maximum flap deflection range of ˘300 is assumed on all flaps including split surfaces.

A.2 Mass and inertia properties

No information regarding mass and inertia properties of the SACCON was available during the conduct of the present study, forcing to retrieve the required data from those of comparable aircrafts. Therefore the reference mass was assumed similar to that of the Dassault nEUROn; while the moments of inertia were derived from those of the Northrop B-2. In particular, the relation adopted for the calculation of the moments of inertia is:

0.9 0 0 I I B2 SF m (A.1) SACCON “ ¨ » 0 1.0 0 fi ¨ SACCON mB2 — 0 0 0.95ffi — ffi – fl where SF » 4.237 indicates the scale factor between the span of the B-2 and that of the full scale SACCON and the factors matrix was introduced to adjust the distribution of the components of the tensor of inertia. In the expression Ixz is assumed equal to zero.

Mass and inertia properties are liste in Tab. A.1. It may be noted that the value of Izz is conveniently smaller than the sum Ixx ` Iyy. Higher Izz values would cause a slowdown of the lateral directional dynamics, making it harder to augment, especially in the absence of a conventional rudder.

Parameter Value Units

m 5 120 kg

4 2 Ixx 1.5879 ¨ 10 kg m 4 2 Iyy 2.2755 ¨ 10 kg m 4 2 Izz 2.2616 ¨ 10 kg m

Table A.1: Mass and inertia properties of the SACCON.

132 A.3: Geometric properties A. SACCON conﬁguration

A.3 Geometric properties

The SACCON geometry can be described as blended wing-body design with an untapered lambda planform and a leading edge sweep angle of 53˝. To mimic current UCAV stealth requirements, the wing’s leading edge is parallel to its trailing edge and the wing tip is parallel to the trailing edge of the fuselage section [16]. The wing section is defined by three different airfoils: at the root of the fuselage, including two sections with the same profile at the inner wing that form the transition from the fuselage to the wing and the outer wing section (see Fig. A.2). Moreover, the outer wing section profile is twisted by 5˝ around the leading edge to reduce the aerodynamic loads and to shift the onset of flow separation to higher angles of attack.

Figure A.2: Wing airfoils of the SACCON UCAV conﬁguration [16].

Geometric data were scaled up from the dimensions of the wind tunnel model used during DNW-NWB low speed wind tunnel campaigns, namely the DLR F-17/SACCON.

Parameter Value Units Parameter Value Units mac c 3.832 m Aspect ratio A 3.076 - Wing span b 12.30 m Taper ratio λ 1 - Wing area S 49.22 m2 Length l 10.50 m ˝ Sweep angle ΛLE 53 deg Root chord croot 8.486 m

Table A.2: Geometric properties of the SACCON.

133 A. SACCON conﬁguration A.3: Geometric properties

The key geometric properties of the SACCON are listed in Tab. A.2; while the original dimensions of the model are reported in Fig. 3.1 in Subsection 3.2.1. The leading edge starts sharp at the root chord, then the radius grows in the spanwise direction up to the intersection between the fuselage and the wing and ﬁnally decreases again. The radius distribution and relative thickness of the airfoil are illustrated in Fig. A.3.

Figure A.3: Radius distribution and relative thickness of the SACCON conﬁguration. [16].

134 Appendix B

Theoretical basis and deﬁnitions

B.1 Physical model

In this section the assumptions and the mathematical relations that together constitute the physical model of the motion of the aircraft are described. Also coordinate system transformations are deﬁned.

B.1.1 Assumptions

Considering the ﬁeld of aircraft ﬂight dynamics, the following assumptions were adopted:

• Earth is inertial and ﬂat, thus both centripetal and Coriolis accelerations due to terrestrial rotation are neglected;

• gravity acceleration is constant and equal to its value at sea level (g “ 9.81m{s2);

• atmosphere is stationary, undisturbed and complies with the standard model;

• control surfaces dynamics and engine response are instantaneous;

• aircraft sensors measure instantaneously the exact values of ﬂight parameters.

It is worth to point out that, despite the level of approximation of the data included in the aircraft database varies from case to case, precise calculations of the forces and moments experienced in ﬂight are unlikely to be available. Therefore the error introduced by ignoring centripetal and Coriolis accelerations and the variation of gravity acceleration will be dwarfed by the errors inherent in the database. Indeed it is unnecessary and overcomplicating to relate the aircraft motion to an inertial frame. The deﬁnition of the aircraft aerodynamics is completely ascribed to the inputted database and it is any way restricted by the rest of the simulator. Hence no assumption regarding the characteristics of the aerodynamic model can be made in advance.

135 B. Theoretical basis and deﬁnitions B.1: Physical model

B.1.2 Coordinate systems and transformations

All of the axes systems used to define the motion of the aircraft are body carried frames, i.e. frames whose origin is fixed with respect to the moving body, with the only exception of Fixed Vertical frame, which is fixed at sea level on the vertical of the initial position of the aircraft. Among these, Body and Geometry frames are also body-fixed frames, meaning that their axes follow the motion of the body in which are embedded.

Figure B.1: Attitude angles and positive direction of velocities.

Relative orientation between two coordinate systems is expressed by means of Tait- Bryan (rotating axes) angles, according to the ZYX (intrinsic) convention. The order is crucial and must always be complied with. A complete rotation involves the following steps:

1. rotation around z axis of angle Ψ;

2. rotation around the new y axis of an angle Θ;

3. rotation around the new x axis of an angle Φ; and the generic rotation matrix has the form:

cospΦq sinpΘq cospΨq` cospΘq cospΨq sinpΦq sinpΘq cospΨq » ` sinpΦq sinpΨq fi BA T “ — sinpΦq sinpΘq sinpΨq` cospΦq sinpΘq sinpΨq` ffi (B.1) —cospΘq sinpΨq ffi — ` cospΦq cospΨq ´ cospΦq cospΨq ffi — ffi — ffi — ´ sinpΘq sinpΦq cospΘq cospΦq cospΘq ffi — ffi – fl

136 B.1: Physical model B. Theoretical basis and deﬁnitions

The rotation matrix from Body to Local vertical frame T VB is obtained simply substituting the attitude angles ϕ, ϑ, ψ (see Fig. B.1) to the generic angles in (B.1).

Figure B.2: Wind axes arrangement and positive signs of α and β.

Considering that Fixed Vertical and Local Vertical frames share the same orientation and the transformation from Geometry to Body coordinates is achieved simply by inverting x and z axes, the remaining fundamental rotation matrices are:

cospαq cospβq sinpβq sinpαq cospβq Body to Wind T WB “ »´ cospαq sinpβq cospβq ´ sinpαq sinpβqfi (B.2a) — ´ sinpαq 0 cospαq ffi — ffi – fl cospαq 0 ´ sinpαq Body to Stabilty T SB “ » 0 1 0 fi (B.2b) —sinpαq 0 cospαq ffi — ffi – fl Furthermore there is a couple of notable transformation matrices, which allow to project resultant force and moment of the propulsive system from its local axes to Body frame. They account for the effects of incidence and thrust vectoring, the first influencing both thrust and torque, the second just thrust. The general form of such matrices is:

cospξhq cospξvq ´ cospξhq sinpξvq sinpξvq Beng Engine to Body T “ » sinpξhq cospξhq 0 fi (B.2c) —´ cospξhq sinpξvq sinpξhq sinpξvq cospξvqffi — ffi – fl

137 B. Theoretical basis and deﬁnitions B.1: Physical model

Depending on whether the rotation is applied to thrust or torque, the angles rξv, ξhs will, in general, assume the values ζv ` δtvv , ζh ` δtvh T or rζv, ζhsQ respectively. The matrix defining the inverse“ rotation corresponds‰ to the transpose of the former one. Combined rotations are obtained multiplying the matrices. It is worth to observe that, in case the configuration does not have a plane of symmetry, the arrangement of the axes of body-fixed frames could be ambiguous.

B.1.3 Mathematical relations

For the purpose of ﬂight dynamics simulation and analysis, the aircraft motion can be reduced to that of a rigid body with 6 degrees of freedom, 3 translations and 3 rotations about the coordinate axes. The aircraft motion is governed by Euler’s equations of motion, which derive from fundamental principles of classical mechanics (Newton’s laws). These relations are then specialized to comply with the assumptions adopted and applied to a 6 degrees of freedom variable-mass rigid body, giving:

BG ` ω ˆ G “ v m9 ` m v9 ` m ω ˆ v “ F (B.3) Bt

BH ` ω ˆ H “ I9 ω ` I ω9 ` ω ˆ I ω “ M (B.4) Bt

Resultant force and moment on the right-hand side of (B.3) and (B.4) respectively can be expressed as the sum of different contributions, such as gravitational, aerodynamics (which includes control system loads), propulsion and gyroscopic (for moment only). Such differentiation is present within the simulator: in particular total force and moment result from the summation of weight, aerodynamic loads, thrust and propulsion system gyroscopic effect. The terms on the right-hand assume then the following expressions:

F “ W ` F ` T (B.5) M “ M ` Q ´ F ˆ xARP ´ T ˆ xERP ` B where the gyroscopic eﬀect introduced by the engine is given by:

T Beng eng Beng B “ ω ˆ Heng “ ω ˆ T Heng “ ω ˆ T 2π Ω Iengxx 0 0 (B.6) ´ ¯ ˆ ” ı ˙ and the contributions to force and moment of the propulsion system have already been projected in Body frame, that is right multiplied by the appropriate T Beng rotation matrix. Positive directions of forces and moments acting on the aircraft comply with axes direction deﬁned in Fig. B.1.

138 B.1: Physical model B. Theoretical basis and deﬁnitions

The x vectors in the second equation represent the location in Body axes of two important points of the aircraft:

• the aerodynamic reference point ARP, i.e. the point in which aerodynamic loads are applied, taken as reference for the aerodynamic database of the aircraft;

• the engine reference point ERP, i.e. the point in which the thrust or propulsive force of the engine is applied.

Reformulating equations (B.3) and (B.4) in scalar form and expanding the terms on the right-hand side according to (B.5) (neglecting for the gyroscopic contribution from the engine), yields the following six dynamic equilibrium equations, the ﬁrst three for translation, the second three for rotation.

m9 u ` m u9 ` m pq w ´ r vq “ Wx ` X ` Tx

m9 v ` m v9 ` m pr u ´ p wq “ Wy ` Y ` Ty (B.7)

m9 w ` m w9 ` m pp v ´ q uq “ Wz ` Z ` Tz

2 2 I9xx p ` I9xy q ` I9xz r ` Ixx p9 ` Izz ´ Iyy q r ` Ixy pq9 ´ p rq ` Ixz pr9 ` p qq ` Iyz q ´ r “ ´ ¯ “ L ` Qx ` Bx ´ Y pzARP ´ zCG` q ` Z py˘ARP ´ yCGq ´ Ty pzERP ´ zCGq ` Tz pyERP ´ zCGq

2 2 I9yy q ` I9xy p ` I9yz r ` Iyy q9 ` pIxx ´ Izzq p r ` Ixy pp9 ` q rq ` Iyz pr9 ´ p qq ` Ixz r ´ p “ ´ ¯ “ M ` Qy ` By ` X pzARP ´ zCGq ´ Z pxARP ´ xCGq ` Tx pzERP ´ zCGq ´ Tz pxERP ´ xCGq

2 2 I9zz r ` I9xz p ` I9yz q ` Izz r9 ` Iyy ´ Ixx p q ` Ixz pp9 ´ q rq ` Iyz pq9 ´ p rq ` Ixy p ´ q “ ´ ¯ “ N ` Qz ` Bz ´ X pyARP ´ yCG` q ` Y px˘ARP ´ xCGq ´ Tx pyERP ´ yCGq ` Ty pxERP ´ xCGq (B.8)

Equations (B.7) and (B.8) represent the most general expression of the equation of motion implemented in the simulator. Depending on the individual conﬁgurations analyzed with the simulator, some of the terms may cancel, but the equations will always be valid. The relation between the rate of change of the attitude angles and the angular velocity of the aircraft in Body frame is:

ϕ9 1 sinpϕq tanpϑq cospϕq tanpϑq p »ϑ9fi “ »0 cospϕq ´ sinpϕq fi »qfi (B.9) 9 —ψffi —0 sinpϕq secpϑq cospϕq secpϑqffi —rffi — ffi — ffi — ffi – fl – fl – fl This concludes the description of the relations that govern the motion of the aircraft implemented in the simulator.

139 B. Theoretical basis and deﬁnitions B.2: Conventions and customs

B.2 Conventions and customs

In this section are defined the conventional signs of control surfaces deflection and aerodynamic angles together with the convention followed to calculate aerodynamic forces and moment from the interpolated dimensionless coefficients. Finally custom conventions regarding propulsion system parameters are described.

B.2.1 Control sign convention and deﬁnitions

The SACCON Flight Simulator control signs convention complies with that deﬁned by Cook [3], which is based upon the principle that a positive control action by the pilot gives rise to a positive aircraft response; whereas a positive control surface deﬂection gives rise to a negative aircraft response (in terms of resulting moment). Thus:

roll positive right push force on the stick ñ positive right stick displacement ñ starboard aileron upward and port aileron downward (negative mean) ñ starboard wing downward roll response (positive moment); pitch positive pull force on the stick ñ positive aft stick displacement ñ elevator trailing edge upward (negative) ñ nose upward pitch response (positive moment);

yaw positive push force on the right rudder pedal ñ positive rudder bar displacement ñ rudder trailing edge displaced to starboard (negative) ñ nose to starboard yaw response (positive moment).

Positive deﬂection for the fundamental control surfaces are shown in Fig. B.3 and can be compared with the positive direction of external moments.

Figure B.3: Positive deﬂection of fundamental control surfaces.

140 B.2: Conventions and customs B. Theoretical basis and deﬁnitions

Control surfaces whose deflection is defined only in one direction, do not stick to this convention and the deflection is always positive. Examples of such controls are flaps, slats, airbrakes, symmetric spoilers, symmetric decelerons, etc. . . . On the other hand, for ordinary designs, the sign of deflections of the other surfaces (except canards) complies with the right-hand rule: a positive deflection corresponds to a positive rotation around the hinge, assuming hinge lines parallel to the respective Body frame axis. The model can handle up to 38 separate control states. Whenever multiple controls converge to the same surface, like in the case of elevons, ruddervators or decelerons configurations, it is necessary to distinguish the contribution of each control to the resultant deflection of the surface. Starting from the definition of the equivalent control deflections:

Elevator with elevons or ruddervators δe “ 1{2 pδRX ` δLX q (B.10a)

Ailerons with elevons δa “ 1{2 δelvnRX ´ δelvnLX (B.10b) ` ˘ Ailerons with asymmetric spoilers δa “ δspoLX ´ δspoRX (B.10c)

Rudder with twin tail δr “ 1{2 δrRX ` δrLX (B.10d) ` ˘ Rudder with ruddervators δr “ 1{2 ´δrudvRX ` δrudvLX (B.10e) ` ˘ Rudder with asymmetric decelerons δr “ δsplLX ´ δsplRX (B.10f)

Airbrakes with symmetric decelerons δair “ δsplRX ´ δsplLX (B.10g) ˇ ˇ Airbrakes with symmetric spoilers δair “ ˇδspoRX ´ δspoLXˇ (B.10h) ˇ ˇ ˇ ˇ actual deﬂections of each surface result:

Elevons (RX, LX) δ “ δe ˘ δa (B.11a)

Ruddervator (RX, LX) δ “ δe ¯ δr (B.11b)

Decelerons (RX, LX) δspl “ δair ¯ 1{2 sgnpδrq ¯ 1 ¨ δr (B.11c) “ ‰ Spoilers (RX, LX) δspo “ δair ¯ 1{2 sgnpδaq ¯ 1 ¨ δa (B.11d) “ ‰ where sgn indicates signum function. The above deﬁnitions are valid for inboard, outboard or tip (if applicable) portion separately, subscripts have been omitted for clarity. Elevon and ruddervator deﬂection is positive for trailing edge rotated downward, i.e. toward the belly of the aircraft.

141 B. Theoretical basis and deﬁnitions B.2: Conventions and customs

B.2.2 Aerodynamic parameters convention

The simulator evaluates the aircraft dynamics in Body coordinate system therefore the dimensionless aerodynamic coeﬃcients are derived from the aerodynamic database in the same reference frame respecting the positive direction of the axes. The reference area is S; reference length is c for longitudinal loads and b from lateral loads. Values are provided by the user with the database. The equations used to derive aerodynamic forces and moments are then:

1 1 X “ ρ U 2 SC (B.12a) L “ ρ U 2 S b C (B.12d) 2 8 8 X 2 8 8 l

1 1 Y “ ρ U 2 SC (B.12b) M “ ρ U 2 S c C (B.12e) 2 8 8 Y 2 8 8 m

1 1 Z “ ρ U 2 SC (B.12c) N “ ρ U 2 S b C (B.12f) 2 8 8 Z 2 8 8 n

An exception is represented by lift CL and drag CD coeﬃcients, which are deﬁned exclusively in Wind coordinate system and their signs are inverted with respect to the direction of the corresponding axes.

1 1 L “ ρ U 2 SC (B.13a) D “ ρ U 2 SC (B.13b) 2 8 8 L 2 8 8 D

However these values are uniquely used to calculate aerodynamic eﬃciency of the aircraft and their role is not prominent. Finally dimensionless angular rates are deﬁned as:

p b pˆ “ (B.14c) α9 c 2U8 αˆ9 “ (B.14a) 2U 8 q c qˆ “ (B.14d) 2U8 ˆ β9 b β9 “ (B.14b) 2U8 r b rˆ “ (B.14e) 2U8

142 B.2: Conventions and customs B. Theoretical basis and deﬁnitions

B.2.3 Propulsion system customs

Incidence angles of the engine express its orientation referred to Body frame and hence the orientation of resultant thrust and torque (for zero thrust vectoring), of course assuming that they are both applied on the engine axial direction. The signs of the angles are consistent with Body axes convention: in particular vertical incidence is positive for engine intake side rotated upward; horizontal incidence is positive for intake side rotated to starboard. The signs of thrust vectoring angles follows the same convention as incidence angles: vertical angle is positive for thrust rotated upward, while horizontal angle is positive for thrust rotated to starboard. As mentioned in paragraph B.1.2, it is assumed that thrust vectoring only affect the orientation of thrust, leaving torque vector positioning unaltered. This is due to the fact that torque is related to the engine rotating parts, which are not influenced by thrust vectoring. Moreover it is assumed that the location of the point of application of engine loads, namely ERP, does not change with vectoring deflections. Lastly the positive sign of the angular velocity of the engine is concordant with the direction of Body x axis or equally counter-clockwise seen from the intake side.

B.2.4 Mass and geometry

The simulator reads mass distribution properties from the data provided in the input database. In case ﬁnal conﬁguration is the assemble of multiple components, its global mass and center of gravity location are evaluated by the initialization routines as the solution of a multi-body problem. The location of the center of gravity of each component is expressed in Geometry

Figure B.4: Relative arrangement of Geometry (blue) and Body (black) frames.

143 B. Theoretical basis and deﬁnitions B.2: Conventions and customs frame, so that it is independent from global center of gravity location; while its inertia tensor elements are in Body frame. CG location of the components are stored within the database in Geometry coordinate system, although the simulator works in Body frame. To switch frame for the generic vector it is suﬃcient to put:

T xB “ ´xG yG ´ zG ” ı Then the procedure to calculate global mass distribution involves the following steps (frame superscripts have been omitted, since Body frame is implied).

1) Total mass is simply the sum of the masses of all the components:

mglob “ mi (B.15) i ÿ 2) The location of the center of gravity results from:

1 x “ mi x (B.16) CGglob m CGi glob i ÿ 3) Finally global tensor of inertia is obtained as:

I I m T ∆x (B.17) glob “ i ` i HS p iq i ÿ where ∆x x x and T is Huygens-Steiner inertia transport matrix, whose i “ CGi ´ CGglob HS general expression is given by:

∆y2 ` ∆z2 ´∆x∆y ´∆x∆z 2 2 THS p∆xq “ » ´∆x∆y ∆x ` ∆z ´∆y∆z fi 2 2 — ´∆x∆z ´∆y∆z ∆x ` ∆y ffi — ffi – fl Geometry and mass section of the simulator is currently under development and could be extended and/or changed. In particular, the implementation of mass and inertia variation with dedicated states is under consideration.

144 Appendix C

Linearized Model

The relations derived in Subsection B.1.3 represent the most general formulation of the 6 DoF motion for a rigid aircraft. The mathematical model is constituted by six dynamic equilibrium equations, specifically (B.7) for translation and (B.8) for rotation, expressed in Body frame, completed by the equation of the rate of change of the attitude angles (B.9). In order to solve the problem of flight dynamics analysis, that is to determine the stability characteristics of the aircraft as well as its response to control inputs and external disturbances, the equations of motion can be conveniently linearized by means of the small disturbances technique and simplified with the introduction of the following assumptions:

• the disturbances around the equilibrium condition are small compared to the stationary terms and such that the products between perturbation quantities is negligible w.r.t. the stationary terms;

• the dependency of asymmetric aerodynamic coeﬃcients (CD, CL, Cm) upon symmetric quantities is always negligible.

• the maneuvers considered are short enough not to cause appreciable variation in mass and inertia.

Basically, the technique assumes that the motion of the vehicle can be decomposed into a stationary term, representative of the selected equilibrium condition, and an unsteady contribution, indicating the time-evolution of the disturbance. Moreover, the second assumption decouples the longitudinal and lateral-directional dynamics. The introduction of these simplifying hypotheses considerably reduces the complexity of the model, allowing for a straightforward closed solution. The equations can be further simplified if a straight leveled flight condition is chosen as initial equilibrium condition, that is if v0 “ p0 “ q0 “ r0 “ ϕ0 “ ψ0 “ δa0 “ δr0 “ 0. Then, the equations are transformed into Stability frame, which implies by definition w0 “ 0. Therefore, the expressions of the states to substitute in the equations, in order to derive the small disturbance version of the model are:

145 C. Linearized Model

u “ u0 ` ∆u p “ ∆p ϕ “ ∆ϕ δe “ δe0 ` ∆δe v “ ∆u q “ ∆q ϑ “ ϑ0 ` ∆ϑ δa “ ∆δa (C.1)

w “ ∆w r “ ∆r ψ “ ∆ψ δr “ ∆δr

In 1911 George H. Bryan proved that the perturbations of aerodynamic loads can be expressed as linear functions, in the form of ﬁrst order truncations of the Taylor series expansion, of the motion and control states. The set of equations resulting from the application of such assumption together with small disturbance approach is:

m ∆u9 “ Xu∆u ` Xw∆w ` Xq∆q ` Xw9 ∆w9 ` Xδe ∆δe ` Xδt ∆δt ´ mg cospϑ0q ∆ϑ $ ’ m ∆w9 “ Z ∆u ` Z ∆w ` Z ∆q ` Z ∆w9 ` Z ∆δ ` Z ∆δ ` m u ∆q ´ mg sinpϑ q ∆ϑ ’ u w q w9 δe e δt t 0 0 ’ ’ ’ ’ Iyy ∆q9 “ Mu∆u ` Mw∆w ` Mq∆q ` Mw9 ∆w9 ` Mδe ∆δe ` Mδt ∆δt ’ &’ ∆ϑ9 “ ∆q ’ ’ ’ ’ ∆h9 “ sinpϑ q∆u ´ cospϑ q∆w ` u cospϑ q ` w sinpϑ q ∆ϑ ’ 0 0 0 0 0 0 ’ ’ “ ‰ %’

m ∆v9 “ Yv∆v ` Yp∆p ` Yr∆r ` Yδa ∆δa ` Yδr ∆δr ´ m u0 ∆r ` mg cospϑ0q ∆ϕ $ ’ I ∆p9 “ I ∆r9 ` L ∆v ` L ∆p ` L ∆r ` L ∆δ ` L ∆δ ’ xx xz v p r δa a δr r ’ ’ ’ ’ Izz ∆r9 “ Ixz ∆p9 ` Nv∆v ` Np∆p ` Nr∆r ` Nδa ∆δa ` Nδr ∆δr ’ &’ ∆ϕ9 “ ∆p ` tanpϑ0q∆r ’ ’ ’ ’ ∆ψ9 “ secpϑ q∆r ’ 0 ’ ’ %’ where the equation of altitude evolution was added to the longitudinal dynamic. Finally, putting the system in normal form yields for the longitudinal dynamics:

˜ ˜ ˜ ˜ ˜ ˜ ∆u9 “ Xu∆u ` Xw∆w ` Xq∆q ` Xϑ∆ϑ ` Xδe ∆δe ` Xδt ∆δt $ ’ ∆w9 “ Z˜ ∆u ` Z˜ ∆w ` Z˜ ∆q ` Z˜ ∆ϑ ` Z˜ ∆δ ` Z˜ ∆δ ’ u w q ϑ δe e δt t ’ ’ ’ ˜ ˜ ˜ ˜ ˜ (C.2) ’ ∆q9 “ Mu∆u ` Mw∆w ` Mq∆q ` Mϑ∆ϑ ` Mδe ∆δe ` Mδt ∆δt ’ &’ ∆ϑ9 “ ∆q ’ ’ ’ ’ ∆h9 “ h ∆u ´ h ∆w ` h ∆ϑ ’ u w ϑ ’ ’ %’ 146 C. Linearized Model

The terms that appear in the equations result from the following combinations:

ZuXw9 Zu ZuMw9 X˜u “ Xu ` Z˜u “ M˜ u “ Mu ` 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9

ZwXw9 Zw ZwMw9 X˜w “ Xw ` Z˜w “ M˜ w “ Mw ` 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9

u0Xw9 u0 u0Mw9 X˜q “ Xq ` Z˜q “ M˜ q “ Mq ` 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9

g sinpϑ0qXw9 g sinpϑ0q g sinpϑ0qMw9 X˜ϑ “ ´g cospϑ0q ´ Z˜ϑ “ M˜ ϑ “ ´ 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9

Z X Z Z M ˜ δe w9 ˜ δe ˜ δe w9 Xδe “ Xδe ` Zδe “ Mδe “ Mδe ` 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9

Z X Z Z M ˜ δt w9 ˜ δt ˜ δt w9 Xδt “ Xδt ` Zδt “ Mδt “ Mδt ` 1 ´ Zw9 1 ´ Zw9 1 ´ Zw9 where, for jet powered aircrafts:

S ρ U S ρ U X “ ´ 8 C ` 2C X “ 8 C ´ C u 2 m Du D0 w 2 m L0 Dα ` ˘ ` ˘ S ρ U c S ρ c X “ ´ 8 C X “ ´ C q 4 m Dq w9 4 m Dα9

2 2 S ρ U8 S ρ U8 Xδ “ ´ CD Xδ “ CX e 2 m δe t 2 m δt

S ρ U S ρ U Z “ ´ 8 C ` 2C Z “ ´ 8 C ` C u 2 m Lu L0 w 2 m D0 Lα ` ˘ ` ˘ S ρ U c S ρ c Z “ ´ 8 C Z “ ´ C q 4 m Lq w9 4 m Lα9 (C.3)

2 2 S ρ U8 S ρ U8 Zδ “ ´ CL Zδ “ CZ e 2 m δe t 2 m δt

S ρ U8 c S ρ U8 c Mu “ Cmu Mw “ Cmα 2 Iyy 2 Iyy

2 2 S ρ U8 c S ρ c Mq “ Cmq Mw9 “ Cmα9 4 Iyy 4 Iyy

S ρ U 2 c S ρ U 2 c M 8 C M 8 C δe “ mδe δt “ mδ 2 Iyy 2 Iyy t

147 C. Linearized Model

On the other hand, for the lateral-directional dynamics (neglecting β9 terms):

1 1 ∆v9 “ Yv∆v ` Yp∆p ` Yr ∆r ` Yϕ∆ϕ ` Yδa ∆δa ` Yδr ∆δr $ 1 1 1 1 1 ’ ∆p9 “ Lv∆v ` Lp∆p ` Lr∆r ` Lδ ∆δa ` Lδ ∆δr ’ a r ’ ’ ’ ∆r N 1 ∆v N 1 ∆p N 1 ∆r N 1 ∆δ N 1 ∆δ (C.4) ’ 9 “ v ` p ` r ` δa a ` δr r ’ &’ ∆ϕ9 “ ∆p ` tanpϑ0q∆r ’ ’ ’ ’ ∆ψ9 “ secpϑ q∆r ’ 0 ’ ’ The terms that%’ appear in the equations result from the following combinations:

1 1 Ixz 1 Ixz Yr “ Yr ´ u0 Lv “ Lv ` Nv Nv “ Nv ` Lv Ixx Izz

1 Ixz 1 Ixz Lp “ Lp ` Np Np “ Np ` Lp Ixx Izz

1 Ixz 1 Ixz Lr “ Lr ` Nr Nr “ Nr ` Lr Ixx Izz

I I L1 L N xz N 1 N L xz δa “ δa ` δa δa “ δa ` δa Ixx Izz

I I L1 L N xz N 1 N L xz δr “ δr ` δr δr “ δr ` δr Ixx Izz where

S ρ U8 S ρ U8 b S ρ U8 b Yv “ CYβ Lv “ CLβ Nv “ CNβ 2 m 2 Ixx 2 Izz

2 2 S ρ U8 b S ρ U8 b S ρ U8 b Yp “ CYp Lp “ CLp Np “ CNp 4 m 4 Ixx 4 Izz

2 2 S ρ U8 b S ρ U8 b S ρ U8 b Yr “ CYr Lr “ CLr Nr “ CNr 4 m 4 Ixx 4 Izz (C.5)

Yϕ “ g cospϑ0q

S ρ U 2 S ρ U 2 b S ρ U 2 b Y 8 C L 8 C N 8 C δa “ Yδa δa “ Lδa δa “ Nδa 2 m 2 Ixx 2 Ixx

S ρ U 2 S ρ U 2 b S ρ U 2 b Y 8 C L 8 C N 8 C δr “ Yδr δr “ Lδr δr “ Nδr 2 m 2 Ixx 2 Ixx

148 C. Linearized Model

It is worth to point out that, for the sake of notation, the angle between xS and xE has been indicated with the Euler angle ϑ0, even though, as a matter of facts, it has the physical meaning of the path angle, usually denoted with γ0. Hence, for a level flight, ϑ0 “ 0. Non-dimensional derivatives were estimated at each flight condition comprised within the analysis envelope, as part of the localized linearization procedure described at point 2) of Section 5.2. In particular, the required values were extracted using linear interpolation on the available data by means of a central finite difference:

Ci pj0, k0 ` ∆k, l0,... q ´ Ci pj0, k0 ´ ∆k, l0,... q C “ (C.6) ik 2 ∆k where i “ X, Z (or D, L), m, Y , l, n and j, k, l, . . . express the functional dependency ˝ of the generic coeﬃcient Ci and the increment ∆k was set to 1 so as to localize the linearization as much as possible. Of course, unsteady derivatives C and C were put to zero, for their contributions iα9 iβ9 are combined with those of the associated rotational derivatives, as motivated in Section 5.1 and expressed by (5.2). Throttle derivatives were also put to zero, due to the lack of whatsoever data regarding the propulsive system. Finally, owing to the lack of data modeling compressibility eﬀects, velocity (or Mach) derivatives were approximated empirically as follows:

CDu “ 0 (C.7a)

2 M80 CLu “ 2 CL0 (C.7b) 1 ´ M80

Cmu “ 0 (C.7c)

149

Appendix D

XML database structure

The section describes the XML superstructure database format, conceived to be inter- faced with the SACCON Flight Simulator.

D.1 Overview

The SACCON Flight Simulator accepts a single XML file, which contains all the data necessary to run simulations. Such file is read by the initialization routine in MATLAB using XML toolbox and the data contained in it rearranged in a format more suitable to be processed by the simulator. The input data XML file is generated by single user. All the contents described hereinafter must be provided in the right order using the same syntax. To ensure correct initialization of the simulator, default file and folder names and locations must be kept. In addition to that, the user must remember that:

• all aerodynamic, geometric and mass data are deﬁned according to the deﬁnitions set out in AppendixB;

• data tables must be in spreadsheet format;

• all quantities are expressed in SI units and degrees, except where otherwise speciﬁed.

D.1.1 Fundamental table structure

A database suitable for flight simulation of an aircraft is nothing but a collection of data assembled and organized in different formats depending on the simulation software that will read it. The fundamental units of a database are the tables (or spreadsheets) that summarize the actual value of each parameter for different combinations of the states. For this reason a fundamental table structure has been defined and, hence, applied throughout the database for increased consistency and readability.

151 D. XML database structure D.2: Database structure

... STATE_1_TAG STATE_2_TAG . . . STATE_N_TAG N n1 n2 ... nN ... ... . . . ...

...

desc string with short description of the table;

states cell array containing the tags of the states upon which the table depends;

dimen the number of the aforesaid states;

sizes array with the number of breakpoints of each state, in the same order as above;

STATE array of breakpoints for each state;

table database spreadsheet, that is a matrix with a column for each state (once again in the same order as they are listed in states ﬁeld) plus a columns of variable values and a number of rows equal to the product of all the elements of array sizes.

D.2 Database structure

The aircraft database stored in the XML file is arranged in a structure, divided into a series of substructures, according to the category of the data, as shown in Fig. D.1. The format of the data collected in each substructure will be described in more detail in the next sections. A file named "template.xml" represents a sample of input data XML file used and read by the simulation program. The values presented hereinafter are just an example. The preamble of the XML is presented below. The very first field of the structure is a string containing the name of the aircraft/database.

152 D.2: Database structure D. XML database structure

SACCON

Figure D.1: Comprehensive view of the structure of the input ﬁle.

D.2.1 Aerodynamics

The ﬁrst portion of the ﬁle contains the aerodynamic part of the database.

153 D. XML database structure D.2: Database structure

Zero control low speed alpha beta 2 315 012345678 etc... -10 -505 10

012345678 etc...

. . . . . . . . . . . . . . . . . .

The first six structures correspond to the block “coefficient tables” of Fig. D.1. Each one collects all the tables of one aerodynamic coefficient, first longitudinal (fields CX, CZ, Cm), then lateral (fields CY, Cl, Cn). Each coefficient structure can hold as many fundamental table structures as needed to fully describe the characteristics of the design configuration to be simulated. In this example only the first table of CX coefficient is shown, since the same format is repeated for every table of every coefficient.

0.600 B -1 -11111

154 D.2: Database structure D. XML database structure

Next three fields correspond to the “frame of reference” block in Fig. D.1. ARP is a vector representing the position of the aerodynamic reference point, i.e. the point of the aircraft which aerodynamic coefficients are referred to, expressed in Geometry frame of reference. frame is a character flag indicating whether aerodynamic coefficients are expressed in Body “B”, Stability “S” or Wind “W ” frame of reference. signs is a six elements array, whose components indicates if the sign of each coefficient complies with convention: 1 if yes; ´1 if the sign is inverted.

Mach altitude 0.20

Field const is used to store names and values of parameters that keep a constant value throughout the aerodynamic database. It is composed by:

states cell array collecting the names of the constant states;

values array storing constant values of the states in the same order as they are listed above.

If no constant states are present, the ﬁeld must be kept empty. Substructure uncer collects uncertainty parameters tables, such as standard deviation of experimental data, analytical uncertainties for robust analysis, etc..., for each coeﬃcient.

Standard deviation alpha 1 31 012345 etc...

012345 etc...

. . . .

155 D. XML database structure D.2: Database structure

. . . . . . . . . . . . . .

Finally in substructure correc are stored correction parameters, such as increments related to diﬀerent wind tunnel mounting systems, for each coeﬃcient.

Sting increment alpha 1 31 012345 etc...

012345 etc...

. . . . . . . . .

156 D.2: Database structure D. XML database structure

. . . . . . . . .

These last two portions reproduce inside the layout of the ﬁrst section of the aerodynamic database, collecting a series of tables, divided according to the coeﬃcient which refer to.

D.2.2 Geometry and mass

The second portion of the ﬁle contains reference geometry and mass data of the aircraft.

0.479 1.538 0.769 10 0.600111000

georef 3 elements array containing reference chord, span and surface; masses 10 elements array, of which element number:

1 represents the mass of the component; 2 3 4 represent the location of the component center of gravity in Geometry frame;

5 to 10 are the elements of the tensor of inertia Ixx, Iyy, Izz, Ixy, Ixz, Iyz in Body frame.

In case only global mass and inertia of the configuration are known, field masses will be a single row array. On the other hand, if final configuration is the assemble of multiple components, the mass properties of each one must be stored in a separate row.

157 D. XML database structure D.2: Database structure

Later versions of the simulator will introduce the possibility to input mass properties and center of gravity location in function of dedicated states in form of spreadsheet tables, so that the simulator will be able to treat them as it now does with aerodynamic data.

D.2.3 Propulsion

This structure collects the data of the propulsion system of the aircraft, namely the conﬁguration of the engines, some of their dynamic characteristics and thrust and torque information. Thrust and torque data of each engine are organized in the same fundamental structure used so far. In this case though, these structures are not isolated, but collected in an array. In fact it is supposed that the available data will be equal for all the engines and this solution allows for a simpler form of the structure. In this example a conﬁguration with two engines is presented.

0.6 0.61 -100 -5 -500 4500 4500 ...... 1000 100011 Thrust and torque of engine 1. Mach alt 2 00

Thrust and torque of engine 2. Mach alt 200

In the first field engpar engine configuration and working parameters are stored. It is a 8 columns array with one row per engine. In particular, column number:

1 2 3 represent the position of the engine reference point in Geometry frame;

4 5 represent incidence angles (in degrees) of the engine, that is the orientation of the engine referred to Body frame and hence the orientation of resultant thrust and

158 D.2: Database structure D. XML database structure

torque (at zero thrust vectoring), assuming that they are both applied on the engine axial direction. The signs of the angles are consistent with Body axes convention: in particular vertical incidence is positive for engine intake side rotated upward; horizontal incidence is positive for intake side rotated to starboard;

6 is the nominal working rotation velocity of the engine in rpm, positive if concordant with Body x axis, i.e. counter-clockwise if seen from the intake side;

7 is the axial moment of inertia of the engine;

8 is a ﬂag indicating whether it is a turbine or propeller system.

In this case the spreadsheet tables collect data both for thrust and torque, so they are slightly different from the ones used in the aerodynamic part, having one extra column. If torque information is not available, the corresponding column must be filled with 0. If a propulsive system is not present (like in gliders) or it is necessary to exclude it from the analysis, it is sufficient to leave the engpar field empty. Similarly, if gyroscopic effects are not relevant or must be excluded, it is sufficient to assign 0 to the values of nominal rpm and axial moment of inertia (engpar elements 6 and 7 respectively).

D.2.4 Flight control system

The fourth and last portion of the ﬁle contains ﬂight control system data.

00 00 00 00 00 00 00 00 00 00 00 00 . . .

At the present stage of development of the simulator, this structure only stores the limit deflections of the control surfaces installed on the aircraft. Each field is a 2 elements array, containing minimum and maximum deflection of the surface in degrees.

159

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