FEDERAL UNIVERSITY of MINAS GERAIS MECHANICAL ENGINEERING DEPARTMENT Aerospace Engineering Undergraduation Program

FEDERAL UNIVERSITY OF MINAS GERAIS MECHANICAL ENGINEERING DEPARTMENT Aerospace Engineering Undergraduation Program

GEOVANA NEVES FELIX SILVA

OPTIMIZATION AND COMPARISON OF TURBOPROP AND TURBOFAN AIRCRAFT

UNDERGRADUATION SENIOR THESIS

BELO HORIZONTE 2018 GEOVANA NEVES FELIX SILVA

OPTIMIZATION AND COMPARISON OF TURBOPROP AND TURBOFAN AIRCRAFT

Undergraduation Senior Thesis presented to the Aerospace Engineering Undergraduation Program of the Federal University of Minas Gerais, as a partial requirement for obtaining the title of Bachelor in Aerospace Engineering.

Advisor Ricardo Luiz Utsch de Freitas Pinto DEMEC - UFMG

Co-Advisor Tarik Hadura Orra EMBRAER S.A.

BELO HORIZONTE 2018

I dedicate this work to my parents and sisters. ACKNOWLEDGMENT

First, I would like to thank my parents, Baldonato and Jaquelina, and sisters, Fernanda, Luana and Daniela, that always supported and encouraged me. I am also grateful for my best friend Humberto Lemos, who helped to revise my text since the first written page. Moreover, I would like to thank my friend Fernanda Fenelon, who also revised my text and now is looking forward to continue the studies I started in my undergraduation senior thesis. And I am grateful for Chiara Titton, she supported me with her friendship even though I was kilometers away from her. I would like to acknowledge the excellent support I received from my co-advisor from Embraer S.A., Tarik Orra. He taught me during months and I am grateful for his patience and interest in my work. Also, I would like to thank the engineers from Embraer S.A., Ana Cuco and Alexandre Antunes, who revised my work and provided essential feedback. In fact, I received an important support at Embraer S.A. that was crucial for the success of this academic work, and for that I am thankful. I also would like to thank my advisor from UFMG, Ricardo Luiz Utsch de Freitas Pinto, who guided me during the year. The UFMG provided all the support necessary for my education as aerospace engineer and I am grateful for all professors who were part of my academic experience. In special, I would like to thank the Centro de Estudo Aeronáuticos (CEA) at UFMG since all the people there, professors and students, contributed for my learning during the undergraduation program. I also want to acknowledge the SAE Aerodesign Brazil Competition which was a fundamental part of my academic life and formation as aerospace engineer. The interest for aircraft design and optimization was encouraged during my years as part of the UFMG team, Uai, Sô!Fly!!!, in the Aerodesign Competition and I am grateful for all the learning experience provided by the technical committee. Finally, I would like to thank the Funda¸cãoUniversitáriaMendes Pimentel (FUMP) for the financial assistance provided since my first year at UFMG. The scholarship I received allowed me to focus on my studies and I admire the projects done at FUMP in order to fund students. A problem well-stated is a problem half-solved. (Albert Einstein) ABSTRACT

NEVES, Geovana. Optimization and Comparison of Turboprop and Turbofan Aircraft. 2018. 98 pages. Undergraduation Senior Thesis – Aerospace Engineering Undergraduation Program, Federal University of Minas Gerais. Belo Horizonte, 2018.

According to the International Air Transport Association (IATA), it is expected a regional growth in the aviation market for the next years. In North America, the increase in number of passengers will be 452 million by 2036 compared to 2016 considering only the regional aviation, representing 37% of the total number of passengers expected. Several aircraft were designed to accomplish a typical mission in this specific market and the current airplanes are mainly turbofan and turboprop powered. Given this scenario, a discussion has emerged for the next generation of aircraft and the question to be answered is: “Turboprop or Turbofan?”. The present work aims at comparing optimized geometries for a turboprop and a turbofan in order to evaluate what configuration best suits the regional aviation market considering as criteria fuel consumption, specific range and block time. The motivation of this study is to understand the differences between the aircraft that lead one to stand out over the other given a technical criterion. The discussion and conclusion of the analysis are based on the optimal results. Although the number of passengers considered is the same, the flight qualities differs considerably and the critical performance requirements for each aircraft may also be different. The open-source software SUAVE is used for modeling and optimization. The reference airplanes are the E170 Jet, designed by the brazilian manufacturer EMBRAER S.A., and the ATR-72 600 turboprop aircraft, designed by the ATR Company. Both airplanes are used to calibrate the aircraft model as well as a baseline geometry.

Keywords: aircraft design, regional aviation, optimization, turboprop, turbofan RESUMO

NEVES, Geovana. Otimiza¸cãoe Avalia¸cão Comparativa de Aeronaves Turboélice e Turbo- fan. 2018. 98 f. Trabalho de Conclusão de Curso – Gradua¸cãoem Engenharia Aeroespacial, Universidade Federal de Minas Gerais. Belo Horizonte, 2018.

De acordo com a Associa¸cãoInternacional de Transporte (IATA), éesperado um cresci- mento na avia¸cãocomercial nos próximos anos. Na América do Norte, o aumento no número de passageiros seráde 452 milhões no ano de 2036 em rela¸cãoa 2016 considerando apenas a avia¸cão regional, o que representa 37% do total de passageiros previsto. Diversas aeronaves foram projetadas para cumprir com a missãot´ıpica nesse mercado espec´ıfico e as atuais aeronaves são principalmente turboélice e turbofan. Dado este cenário, uma discussão surgiu a respeito da nova gera¸cão de aeronaves e a principal dúvida a ser respon- dida é: “Turboélice ou Turbofan?”. Este trabalho acadêmico tem como objetivo comparar aeronaves otimizadas turboélice e turbofan para 70 passageiros em termos de consumo de combust´ıvel, alcance espec´ıfico e tempo de bloco. A motiva¸cão desta investiga¸cão é entender as diferen¸casentre as aeronave que levam uma a se sobressair em rela¸cão a outra dado um critério técnico. A discussão e resultados da análise são baseados nos resultados otimizados para cada aeronave. Apesar de o número de passageiros ser o mesmo, as carac- ter´ısticas de voo de cada aeronave diferem consideravelmente e os requisitos dimensionantes relacionados a desempenho tambémpodem ser distintos. O software de código aberto SUAVE foi utilizado para modelagem e otimiza¸cão. Os aviões de referência são o jato E170 da fabricante brasileira EMBRAER S.A. e o turboélice ATR 72-600 da fabricante ATR. Ambas as aeronaves são utilizadas para calibra¸cão do software bem como geometrias de referência.

Palavras-chave: projeto de aeronaves. avia¸cão regional, otimiza¸cão, turboélice, turbofan LIST OF FIGURES

Figure 1 – Typical Mission...... 8 Figure 2 – Important segments of the Take-off run...... 10 Figure 3 – Important airspeed during the Take-off run...... 11 Figure 4 – General Free Body Diagram for ground roll...... 11 Figure 5 – Second Segment Climb...... 14 Figure 6 – Free Body Diagram considering Climb Segment...... 14 Figure 7 – Free Body Diagram considering Cruise Segment...... 16 Figure 8 – Payload Range Diagram...... 18 Figure 9 – Free Body Diagram - Descent Segment...... 19 Figure 10 – Import segments of the landing run...... 20 Figure 11 – Turbofan components...... 25 Figure 12 – Turboprop components...... 27 Figure 13 – Efficiency Comparison...... 29 Figure 14 – Velocity and Altitude Comparison...... 30 Figure 15 – Turbofan Network...... 30 Figure 16 – Example of public data containing weight information, E170 jet.... 35

Figure 17 – Example of the impact in the Payload Range Diagram due to errors in CD 37 Figure 18 – Example of Pareto Plot - BOW vs Block fuel ...... 43 Figure 19 – E170 AR Payload Range Diagram, FL350, ISA +0°C...... 47 Figure 20 – E170 TOFL, ISA +0°C...... 48 Figure 21 – E170 TOFL, ISA +15°C...... 49 Figure 22 – E170 LFL, ISA +0°C...... 50 Figure 23 – Design Mission ...... 53 Figure 24 – DoE results for turbofan aircraft ...... 55 Figure 25 – Carpet plot: Aspect ratio vs. Wing Area...... 56 Figure 26 – Carpet plot: Aspect ratio vs. Sweep Angle...... 57 Figure 27 – Carpet plot: Thickness to chord ratio vs. Sweep Angle ...... 57 Figure 28 – Pareto Chart ...... 59 Figure 29 – Optimized geometries for β equal 1, 0.5 and 0...... 60 Figure 30 – ATR 72-600 Payload Range Diagram, FL210, ISA +0°C ...... 64 Figure 31 – ATR 72-600 (SUAVE) vs ATR 72-500 - TOFL, ISA +0°C ...... 65 Figure 32 – Design Mission ...... 68 Figure 33 – DoE results for turboprop aircraft...... 70 Figure 34 – Carpet plot: Aspect Ratio vs. Wing Area...... 71 Figure 35 – Carpet plot: Aspect Ratio vs. Thickness to Chord Ratio ...... 71 Figure 36 – Carpet plot: Thickness to Chord Ratio vs. Wing Area...... 72 Figure 37 – Pareto Chart ...... 74 Figure 38 – Optimized geometries for β equal 1, 0.5 and 0...... 75 Figure 39 – Payload Range Diagram Comparison...... 82 Figure 40 – Block Fuel Comparison...... 87 Figure 41 – Embraer E170...... 92 Figure 42 – Blueprint of Embraer E170...... 93 Figure 43 – ATR 72-600...... 94 Figure 44 – Blueprint of ATR 72...... 95 LIST OF TABLES

Table 1 – Major Competitors in the US Market ...... 1 Table 2 – Typical Mission Segments...... 8 Table 3 – Coefficient of Equation 2.23 ...... 13 Table 4 – Cruise Profiles...... 17 Table 5 – Coefficient of Equation 2.52 ...... 21 Table 6 – Methodology structure based on a MDO process ...... 33 Table 7 – Aerodynamic parameters and the most impacted performance results.. 36 Table 8 – Constraints considered for the aircraft optimization...... 40 Table 9 – Matrix of Experiments - Parameter variation...... 41 Table 10 – E170 - Empty Weight Breakdown ...... 46 Table 11 – E170 AR Payload Range Diagram, FL350, ISA +0°C...... 47 Table 12 – E170 - WAT estimation...... 49 Table 13 – E170 - TOFL estimation ...... 50 Table 14 – E170 - LFL estimation ...... 51

Table 15 – E170 - CLmax values...... 51 Table 16 – E170 - Aerodynamic estimations for drag coeﬃcients ...... 51 Table 17 – Design Mission...... 53 Table 18 – DoE results for turbofan aircraft...... 54 Table 19 – Turbofan design variable bounds...... 59 Table 20 – Optimized geometries for β equal 1, 0.5 and 0...... 61 Table 21 – ATR 72-600 - Empty Weight Breakdown ...... 63 Table 22 – ATR 72-600 Payload Range Diagram, FL210, ISA +0°C...... 64 Table 23 – ATR 72-600 - TOFL estimation ...... 65 Table 24 – ATR 72-600 - Second Segment Climb Gradient γ estimation...... 66 Table 25 – ATR 72-600 - LFL estimation ...... 66

Table 26 – ATR 72-600 - CLmax values...... 66 Table 27 – ATR 72-600 - Aerodynamic estimations for drag coeﬃcients ...... 66 Table 28 – Design Mission...... 68 Table 29 – DoE results for turboprop aircraft ...... 69 Table 30 – Turboprop design variable bounds...... 73 Table 31 – Optimized geometries for β equal 1, 0.5 and 0...... 76 Table 32 – Mission parameters comparison...... 79 Table 33 – Time to climb to cruise altitude, MTOW - Comparison ...... 80 Table 34 – BOW comparison ...... 81 Table 35 – MTOW comparison...... 81 Table 36 – TSFC comparison...... 83 Table 37 – True airspeed and TSFC ratio comparison...... 84 Table 38 – L/D comparison...... 84 Table 39 – Speciﬁc range comparison - E170 versus ATR 72-600...... 85 Table 40 – Block fuel for turbofan airplanes...... 86 Table 41 – Block fuel for turboprop airplanes ...... 86 Table 42 – Block fuel comparison...... 87 Table 43 – Block time comparison ...... 88 Table 44 – E170 AR - Weights ...... 92 Table 45 – E170 AR - Performance...... 92 Table 46 – ATR 72-600 - Weights (Basic Version)...... 94 Table 47 – ATR 72-600 - Performance ...... 94 LIST OF ABBREVIATIONS AND ACRONYMS

ATR Avions de Transport R´egional

BOW Basic Operating Weight

CAD Computer-Aided Design

CFD Computational Fluid Dynamics

DoE Design of Experiments

FL Flight Level

HH Hot and High

IATA International Air Transport Association

ISA International Standard Atmosphere

LFL Landing Field Length

MDO Multidisciplinary Design Optimization

MZFW Maximum Zero Fuel Weight

MTOW Maximum Take-oﬀ Weight

PAX Passengers

ROC Rate of Climb

ROD Rate of Descent

SL Sea Level

SLSQP Sequential Least Squares Programming

SSCG Second Segment Climb Gradient

TO Take-oﬀ

TOFL Take-oﬀ Field Length

TOW Take-oﬀ Weight

TSFC Thrust Speciﬁc Fuel Consumption

US United States of America

WAT Weight Altitude and Temperature LIST OF SYMBOLS

AR Wing Aspect Ratio a Speed of Sound b Wing span

CD Drag coeﬃcient

CDP Parasite drag coeﬃcient

CD0 Drag coeﬃcient term independent of the lift coeﬃcient

CD Lift Induced drag coeﬃcient Induced

CDCompres- Compressibility drag coeﬃcient sibility

Cf Skin friction coeﬃcient

Cfac Wing calibration form factor set to 1.1 as default

Cfus Factor normally set to 2.3 used for fuselage form factor computation

CL Lift Coeﬃcient

CLmax Maximum Lift Coefficient ct Thrust specific fuel consumption in SI units cBHP Specific fuel consumption in SI units

D Drag

dmaxref Increment in CLmax for landing ﬂap position. einviscid Span-eﬃciency factor g Acceleration due to gravity hf Fuselage Height

K Scaling Factor used in the induced drag computation determined from ﬂight test data kf Form Factor kfuselage Form Factor for fuselage kwing Form Factor for wing

Kc Flap chord correction factor

Km Flap motion correction factor

Ksw Sweep correction factor

L Lift

L/D Aerodynamic Eﬃciency

L/D second Aerodynamic Efficiency at the second segment in the take-off path segment lf,e Effective fuselage length - fuselage length minus the wing chord root divided by two.

M Mach Number m engine constant which depends on the engine design and it is usually near 1

Nult Ultimate design load factor for the aircraft

Nseat Number of Seats

P Power

Pavailable Power Available

Prequired Power Required sa Slat Angle

Sref Wing Reference Area

S, Sw Wing Platform Area

SHT Horizontal tail area

SVT Vertical Tail area

SFC Speciﬁc Fuel Consumption

T Thrust

TSLS Sea-level static thrust t/c Thickness-to-chord ratio of the wing

(t/c)avg Average wing thickness to chord ratio V Airspeed

VS Stall speed

VMC Minimum Control Speed with the critical engine inoperative

V1 Decision Speed on the take-oﬀ run

VR Rotation speed on take-oﬀ condition

VMU Minimum unstick speed

VLOF Lift-oﬀ speed

V2 Take-oﬀ safety speed

VEF Speed at which the engine failure occurs

Vapp Approach speed

W Weight

Wwing Wing structural weight

WHT Horizontal Tail structural weight

WvT Vertical Tail and Elevator structural weight

Ww,p Weight of the wing-mounted engines, nacelles and pylons

Wf Fuselage structural weight

Wfurn Furnishings Weight

WLG Landing Gear Weight

Wpropulsion Propulsion system Weight

Wp,dry Dry weight of the engine

Λ Wing Sweep Angle

Λc/4 Wing sweep angle at 1/4 chord line

ΛHTc/4 Horizontal Tail sweep angle at 1/4 chord line

ΛVTc/4 Vertical Tail sweep angle at 1/4 chord line

λ Wing taper ratio

δumax Used in the fuselage parasite drag calculation - maximum velocity increase on an ellipsoid of revolution µ Ground friction coeﬃcient

γ Climb gradient

ω˙ fuel Fuel Weight Flow

ηP Propeller Eﬃciency

∆Pf Maximum diﬀerential pressure of the fuselage

ρ - Air density for a condition of interest

ρ0 - Air density for sea level condition CONTENTS

1 – Introduction...... 1

2 – Literature Review...... 3 2.1 Aircraft Design Process...... 3 2.2 Conceptual Design Analyses...... 5 2.2.1 Aerodynamics...... 5 2.2.1.1 Lift ...... 6 2.2.1.2 Drag...... 6 2.2.2 Performance...... 8 2.2.2.1 Take-off...... 9 2.2.2.2 Climb...... 13 2.2.2.3 Cruise...... 16 2.2.2.4 Range...... 17 2.2.2.5 Descent...... 19 2.2.2.6 Landing...... 20 2.2.2.7 Fuel Consumption ...... 21 2.2.3 Weight Estimation ...... 21 2.2.4 Propulsion...... 24 2.2.4.1 The Tradeoff between Thrust and Efficiency...... 24 2.2.4.2 Turbofan Engine...... 25 2.2.4.2.1 Thrust...... 26 2.2.4.2.2 Thrust Specific Fuel Consumption ...... 26 2.2.4.3 Turboprop Engine ...... 27 2.2.4.3.1 Power...... 28 2.2.4.3.2 Specific Fuel Consumption...... 28 2.2.4.4 Turbofan and Turboprop Comparison ...... 29 2.2.4.5 SUAVE Model: Energy Network Method...... 30 2.3 Optimization ...... 31 2.3.1 Multidisciplinary Optimization in the Aircraft Design - MDO.. 32

3 – Methodology...... 33 3.1 Aircraft Model ...... 34 3.1.1 Weight Model...... 35 3.1.2 Aerodynamic Model ...... 36 3.1.2.1 Drag Model Evaluation ...... 36

3.1.2.2 CLmax Model Evaluation...... 38 3.1.2.3 L/D Model Evaluation...... 38 3.1.3 Engine Model...... 39 3.2 Optimization ...... 39 3.2.1 Constraints ...... 40 3.2.2 Design Variables ...... 41 3.2.3 Pareto Analysis...... 42 3.3 Comparison...... 44

4 – Results and Discussion...... 46 4.1 Turbofan Aircraft Results ...... 46 4.1.1 Aircraft Model and Calibration ...... 46 4.1.2 DoE Analysis...... 52 4.1.3 Pareto Analysis...... 56 4.1.4 Optimized Geometries ...... 60 4.2 Turboprop Aircraft Results ...... 63 4.2.1 Aircraft Model and Calibration ...... 63 4.2.2 DoE Analysis...... 67 4.2.3 Pareto Analysis...... 71 4.2.4 Optimized Geometries ...... 75 4.3 Turbofan and Turboprop Comparison...... 78 4.3.1 Mission Parameters...... 78 4.3.2 Payload Range Diagram...... 81 4.3.3 Speciﬁc Range...... 83 4.3.4 Block Fuel and Block time...... 85

5 – Conclusion...... 89

6 – Future Works ...... 90

A–Reference Airplanes...... 91 A.1 Turbofan Aircraft: E170 AR...... 92 A.2 Turboprop Aircraft: ATR-72 600 ...... 94

Bibliography...... 96 1

1 Introduction

According to IATA [1], the increase in number of passengers in North America will be 452 million by 2036 compared to 2016 considering only the regional aviation, representing 37% of the total number expected. In fact, the regional aviation has an important role in an airline’s business planning since it offers a balance between capacity and demand in order to increase the possible profit. This is linked to the expected growth in the regional aviation market, which has further increased the competition among airlines interested in capturing more potential passengers. In this context, aircraft manufactures have the opportunity to offer a product capable of satisfying the segment needs, such as reduced costs and aircraft availability. Several airplanes were designed to accomplish a typical mission in this specific market and the current aircraft are mainly turbofan and turboprop powered. Table 1 presents some of the major competitors in the US regional aviation regarding aircraft manufactures.

Table 1 – Major Competitors in the US Market

Manufacturer Aircraft Engine PAX Fleet Bombardier CRJ200 Turbofan 50 385 Embraer ERJ145 Turbofan 48 233 Embraer E170 Turbofan 72 179 Bombadier Dash 8 Q400 Turboprop 82 53 ATR ATR 72 Turboprop 50 26 ATR ATR 42 Turboprop 70 26

Source: AEROWEB, 2016[2]

These aircraft perform missions of short and medium range, which varies according to the powerplant used. Given this scenario, a discussion has emerged for the next generation of aircraft and the main question to be answered is: “Turboprop or Turbofan?” The present work aims at comparing optimized geometries for turboprop and turbofan airplanes in order to evaluate what configuration best suits the regional aviation market considering as criteria fuel consumption, specific range and block time. The goal is to provide the technical information necessary to answer the previous question quantitatively. The study involves the application of fundamental aircraft design concepts and optimization techniques in order to provide an impartial and reliable conclusion. The motivation of this analysis is to understand the differences between the aircraft that lead one to stand out over the other given a technical criterion. Although the number of passengers is the same, the flight qualities differs considerably and the critical performance requirements for each aircraft may also be different. The open-source Chapter 1. Introduction 2 software SUAVE [3] is adopted to model and optimize the two concepts here addressed to be studied. The reference airplanes are the E170 jet and the ATR 72-600 turboprop. They are used to calibrate the aircraft model as well as a baseline geometry. The discussion and conclusion of the analysis are based in the optimal results. With the analysis rigor defined, the next steps are to clearly describe the purpose of the present work, its scope and how it will be accomplished.

Goal

The present work aims at comparing optimized geometries for turbofan and turboprop aircraft in order to evaluate what configuration best suits the regional aviation market considering as criteria fuel consumption, specific range and block time. For specific range, the comparison also extends to the physical parameters involved in its estimation such as TOW, cruise speed, SFC, and aerodynamic efficiency.

Scope

The modeling and optimization of the aircraft are consistent with the conceptual design phase introduced in Section 2.1. The models used are mainly based on semi-empirical relations and only geometric parameters that deﬁne the wing shape are optimized.

Methodology

First, the modeling, calibration and validation are accomplished using the SUAVE software [4] and public data of the baseline aircraft [5, 6]. Then the most critical geometric parameters in terms of fuel consumption and BOW are determined in order to define the design variables. The optimization is performed using a gradient algorithm for both fuel burn and MTOW as terms of the aggregating objective function. The best result for each aircraft given a defined criterion is set as the reference to be compared. The comparison is conducted considering fuel consumption, specific range and block time.

Chapter 2 establishes the fundamental concepts of aircraft design applied in this analysis and it also presents the models used in the SUAVE software. The main aeronautical disciplines are discussed such as aerodynamics, performance, weight and propulsion. An overview about MDO is also provided in the aircraft design context. Chapter 3 describes the methodology developed and its steps in order to accomplish an impartial and reliable comparison. Chapter 4 presents the model validation, optimization and comparison results. Chapter 5 highlights the important results and provides the conclusion of the present study. Chapter 6 introduces suggested complementary analysis for future work. 3

2 Literature Review

2.1 Aircraft Design Process

The aircraft design process starts with the specification of the mission requirements. In the aerospace industry, market studies are continuously being made in order to provide a forecast about opportunities and airlines demand. In parallel, several researches aim at developing new technologies to make the design of improved aircraft possible. In general, the main requirements to be set are related to the number of passengers, maximum payload capacity, maximum cruise speed, take-off field length for sea level and hot and high condition as well as short take-off field performance, range, time to climb, target block fuel, etc. Then the conceptual design phase starts followed by preliminary design, detail design, manufacturing, flight test and certification considering the case of commercial aircraft [7]. Many authors [7, 8, 9, 10, 11, 12] suggest the appropriate scope for each step in the design process which is summarized below:

1. Requirements Phase List of expectations that the new design must meet. For example, number of passenger, short and conventional take-off field length considering different atmospheric conditions, landing field length, rate of climb or time to climb to a given altitude, noise, range considering all the possible take-off runs including maximum range and hot and high condition, cruise altitude, payload, etc. The requirements usually are the result of a market study including the analysis of competitors. The new aircraft must be competitive and in order to evaluate the design, a historical study should be made and all existing airplanes should be classified according to a competitiveness criterion. In the aerospace industry, other requirements are necessary about the financial risk. For instance, a maximum price for the new airplane can be set as a target as well as the cost per block hour and manufacturing expenses. All the information usually are estimated considering the competitors and the aircraft manufacturer experience. Therefore, a financial risk exists and it should be mitigated during the design process.

2. Conceptual Design The conceptual design phase is responsible for the initial idea of the new aircraft. In other words, the aircraft conﬁguration is determined and it is possible to ﬁrst estimate its performance using mainly historical and competitors data, semi-empirical Chapter 2. Literature Review 4

relations and low-fidelity models since the information available about the new design is superficial. The following characteristics are defined in the conceptual phase according to Gudmundsson [7]: 2.1. Type of the aircraft (Piston, Turboprop, Turbofan, Turbojet, etc) 2.2. External Geometry 2.3. Mission 2.4. Technology (Avionics, Fly-by-wire, Materials, Engines) 2.5. Aesthetics 2.6. Ergonomics 2.7. Certification basis (LSA, Part 23, Part 25, Military) 2.8. Ease of Manufacturing 2.9. Maintainability 2.10. Initial Cost Estimation 2.11. Evaluation of Marketability The conclusion of the conceptual design is an initial loft (blueprint) and an initial performance evaluation.

3. Preliminary Design The preliminary design phase has as a first goal to answer if the new design is viable in technological and financial terms. To accomplish this task, more technical analysis are made in order to expose potential problems and possible solutions as well as opportunities to increase the aircraft performance. The scope of the analysis is listed below [7]: 3.1. Detailed Geometry Development 3.2. Layout of major load paths in the main structures 3.3. Weight Estimation 3.4. Details of the Mission 3.5. Performance 3.6. Stability and Control 3.7. Evaluation of special Aerodynamic Features 3.8. Evaluation of Certifiability 3.9. Evaluation of Mission Capability 3.10. Preliminary Production Cost Estimation The fidelity of the models used can range from semi-empirical relations (lower fidelity) to CFD analysis (higher fidelity) and wind tunnel data. The expected result for the preliminary phase is a drawing package and a preliminary design evaluation in order to determine if the new design is feasible in both technical and financial terms. Chapter 2. Literature Review 5

4. Detail Design From the preliminary design loft, the detail design phase is responsible for detailing the new design in order to build and ﬂight it. A brief list of the necessary analysis is given below [7]: 4.1. Structural Detail Design 4.2. System Detail Design 4.3. Aerodynamic Detail Analysis 4.4. Performance Detail Analysis 4.5. Stability and Control Detail Analysis 4.6. Maintenance Procedures Planning 4.7. Material and equipment Logistics 4.8. Subcontractor and Vendor Negotiations

As observed above, the main aeronautical disciplines involved in the aircraft design process are aerodynamics, performance, stability and control, propulsion and weight. In addition, optimization techniques can be applied to deﬁne the geometry. The next sections present the theoretical formulation used for each analysis available on SUAVE software [4] considering only conceptual design scope in order to optimize an aircraft in terms of fuel consumption and MTOW.

2.2 Conceptual Design Analyses

2.2.1 Aerodynamics

The aerodynamic characteristics of an aircraft has a considerable impact on its performance. The aerodynamic coefficients of the new design at different flight conditions yield the aerodynamic databank, which is an output from the aerodynamic discipline to the other technologies. Therefore, it is mandatory to compute the aerodynamics of the new airplane as it becomes a necessary input for further analyses. First, the flow conditions considered are introduced below regarding the local Mach Number.

Subsonic, M < 1 everywhere

Transonic, mixed regions where M < 1 and M > 1. If M∞ is near unity, the ﬂow can become locally supersonic, weak shock waves on both the top and bottom surfaces of the airfoil are generated behind which the ﬂow becomes subsonic again.

For the inviscid flow prediction, it is assumed that no friction is involved as well as thermal conduction or diffusion. In addition, compressibility effects are considered for flight Mach Number greater than 0.3. The methods used for computing the lift and drag are the ones available on SUAVE [4]. In the following paragraphs, the theoretical formulation for calculating lift and drag considering subsonic and transonic flow is presented. Chapter 2. Literature Review 6

2.2.1.1 Lift

The available method for estimating the inviscid lift is given by a vortex lattice theory [13] and it is considered the zero fidelity method for lift calculation [4]. Semi- empirical relations are applied to account for fuselage, compressibility and viscous effects in order to obtain the coefficient of lift CL for the aircraft from the inviscid wing CL. The vortex lattice method is based on the Weissinger’s lifting-line method [14] where discrete horseshoe vortices are positioned along the 1/4 chord line of a swept wing. The flow tangency condition is satisfied at the control points at 3/4 chord line which allows the determination of the bound vortex strength.

The computation of CL increment due to high lift devices such as ﬂaps and slats on the CLmax is carried out considering semi-empirical correlations [15, 16] as presented in equations 2.1, 2.2 and 2.3.

sa ∆C = cos(Λ)1.4cos(sa)2 (2.1) Lslat 23 sa - Slat Angle Λ - Wing Sweep Angle

∆CLflap = KcKmKswdmaxref (2.2)

Kc - Flap chord correction factor

Km - Flap motion correction factor

Ksw - Sweep correction factor dmaxref - Increment in CLmax for 25% chord ﬂaps at the 50° landing ﬂap angle.

CLmax = CLmax,wing + ∆CLslat + ∆CLflap (2.3)

2.2.1.2 Drag

The total drag is calculated by adding diﬀerent contributions such as parasite drag, induced drag, compressibility drag and miscellaneous drag. The list below present the method used for estimating each drag contribution. Chapter 2. Literature Review 7

Parasite Drag The parasite drag is due to skin friction and pressure drag and its estimation is calculated for wing, horizontal and vertical tail, fuselages, pylon and nacelles [16]. The skin friction coeﬃcient assumes compressible ﬂat plate formulation for all aircraft components.

CDF = kf Cf Sref (2.4)

kf - Form Factor

Cf - Skin friction coeﬃcient

Sref - Wing Reference Area

2 kfuselage = (1 + Cfusδumax) (2.5)

kfuselage - Form Factor for fuselage [16]

Cfus - User deﬁned factor normally set to 2.3

δumax - Maximum Velocity increase on an ellipsoid of revolution

2 2 2 2 2Cfac((t/c)cos(Λ) ) Cfaccos(λ)(t/c) (1 + 5cos(Λ) ) kwing = 1 + + (2.6) p1 − M 2cos(Λ)2 2(1 − M 2cos(Λ)2)

kwing - Form Factor for wing [16]

Cfac - Wing form factor calibration set to 1.1 as default t/c - thickness-to-chord ratio of the wing

Lift Induced Drag The inviscid oswald coeﬃcient is calculated using vortex lattice method [4]. Then, the induced drag is calculated considering a viscous and an inviscid components as described below.

1 e = 1 (2.7) + π · AR · K · CD einviscid P C2 C = L (2.8) Di πARe

einviscid - Span-eﬃciency factor AR - Wing Aspect Ratio K - Scaling Factor determined from ﬂight test data

CDP - Parasite drag coeﬃcient Chapter 2. Literature Review 8

Compressibility Drag The compressibility drag is computed by correcting the drag considering the crest

critical Mach number (Mcc) as given by the equations below [16].

t/c t/c = (2.9) corrected cos(Λ) C C = L (2.10) Lcorrected cos(Λ)2 14.641 M 3 CDc = 0.0019 cos(Λ) (2.11) Mcc

Miscellaneous Drag The miscellaneous drag is taken into account considering the contributions of control surface gaps, air conditioning system, fuselage upsweep, etc. The semi-empirical data is based on references [15, 16].

2.2.2 Performance

The ﬂight of an aircraft can be divided in distinct segments which can be discussed and formulated separately. Their composition represent the mission designed for the new aircraft and each segment is presented in Table 2 and Figure 1 considering a regional airplane. The segments accounted for in the fuel consumption computation using SUAVE are also indicated in Figure 1. Table 2 – Typical Mission Segments

0-1 Taxi 4-5 Descent 1-2 Take-oﬀ 5-6 Loiter 2-3 Climb 6-7 Landing 3-4 Cruise 7-0 Taxi

Source: Gudmundsson, 2013[7]

Figure 1 – Typical Mission

Source: The Author Chapter 2. Literature Review 9

The next paragraphs develop the formulation for take-oﬀ (tricycle landing gear), climb, cruise, descent and landing considering both turboprop and turbofan engine.

2.2.2.1 Take-oﬀ

The take-off (TO) performance usually refers to the distance required for an aircraft to accelerate and lift-off. The aeronautical regulations (e.g. 14 CFR Part 25, items 25.103 through 25.121 [17]) require the analysis of four take-off conditions given a TOW for commercial aircraft which are described below: 1. Take-off with all engine operating considering an obstacle of 35 ft. The total distance calculated must be multiplied by a factor of 1.15 and must not exceed the take-off distance available.

2. Take-oﬀ with an engine failure (for multi-engine aircraft) at VEF , one second before

V1, considering an obstacle of 35 ft. The total distance calculated must not exceed the take-oﬀ distance available. 3. Aborted take-oﬀ with all engine operating, where the total distance must account

for the acceleration up to the V1 and the deceleration until full stop of the aircraft. The brakes are considered to be applied two seconds after reaching V1. The total distance calculated must not exceed the accelerated-stop distance available.

4. Aborted take-oﬀ with an engine failure at VEF , where the total distance must account

for the acceleration up to the VEF and the deceleration until full stop of the aircraft. The brakes are considered to be applied two seconds after reaching V1. The total distance calculated must not exceed the accelerated-stop distance available.

VEF - Speed at which the engine failure occurs

The take-off analysis for each listed condition is essential in order to determined the allowable takeoff weight for a given altitude, atmosphere condition and available distance for take-off. The allowable weight will be the smallest given a fixed distance considering the four take-off conditions required by aeronautical regulations and it will be a function of the parameters listed below according to the reference [18]:

1. Pressure altitude 2. Temperature 3. Wind velocity and direction 4. Clearway and stopway 5. Runway slope 6. Runway condition 7. Pavement strength 8. Obstacle heights and distances 9. The use of requirement for an engine-inoperative turn procedure after takeoﬀ Chapter 2. Literature Review 10

10. Engine bleed conﬁguration 11. Flap setting 12. Speed limit of the tires of the airplane 13. Type of wheel brakes on the airplane 14. Specialized takeoﬀ techniques such as improved climb

In addition to the take-off limitations, the allowable weight can also be restricted due to climb gradient requirements as discussed in Section 2.2.2.2. The analysis considering all the factor and restrictions introduced here require detailed information that does not necessarily are available in the first stages of an aircraft design. In order to develop an understating of the take-off segment, a simplified physical model is discussed in this section, however, further simplifications are necessary in order to compute the take-off field length and allowable weights considering the scope of conceptual design phase. The TO run is split in important segments as shown in Figure 2 in order to simplify the formulation for each one.

Figure 2 – Important segments of the Take-oﬀ run.

Source: Gudmundsson, 2013[7]

During ground roll, the aircraft is considered to be in a constant accelerated movement in which the nose landing gear is in contact with the runaway. Then after the rotation speed VR is reached, the aircraft starts to rotate and the nose landing gear leaves the ground. The next TO segment takes into account a transition maneuver which leads the aircraft to the climb phase. The TO distance is considered until the aircraft overcome an obstacle required by aeronautical regulations which diﬀers according to the class of the airplane. The important airspeeds during the TO run are presented in Figure 3. Chapter 2. Literature Review 11

Figure 3 – Important airspeed during the Take-oﬀ run.

Source: Gudmundsson, 2013[7]

Gudmunsson [7] gives the following description for each important airspeed:

VS - Stalling speed or minimum steady ﬂight speed for which the aircraft is still control- lable.

VMC - Minimum Control Speed with the critical engine inoperative

V1 - Maximum speed during the take-oﬀ at which the pilot can either safely stop the

aircraft without leaving the runaway or safely continue to V2 take-oﬀ even if a critical

engine fails (between V1 and V2)

VR - Rotation speed. The speed at which the airplane’s nosewheel leaves the ground. It is

high enough to ensure the aircraft can reach V2 at 35 ft (commercial) in the case of an engine failure on a multiengine aircraft.

VMU - Minimum unstick speed. The airspeed at which the airplane is no longer “sticks” to the ground. It is a function of the ground attitude of the airplane. The minimum is

achieved when the ground attitude is at CLmax or at the maximum possible due to geometric restrictions. Deﬁned for commercial aircraft in 14 CFR Part 25.

VLOF - Lift-oﬀ speed

V2 - Take-oﬀ safety speed. Airspeed in which the airplane must be capable of reaching in a given altitude above the ground according to aeronautical regulations.

The equation of motion for a ground run is derived considering the general free-body diagram presented in Figure 4. In this condition, L < W .

Figure 4 – General Free Body Diagram for ground roll.

Source: Gudmundsson, 2013[7] Chapter 2. Literature Review 12

dV g = (T − D − µ(W − L)) (2.12) dt W

1 L = ρV 2SC (2.13) 2 L

1 D = ρV 2SC (2.14) 2 D

P = T · V (2.15)

D - Drag as a function of V P - Power g - acceleration due to gravity W - Weight, assumed constant L - Lift as a function of V µ - ground friction coeﬃcient T - Thrust

The solution of the equation of motion can be computed using numerical integration method. The diﬀerence between turboprop and turbofan aircraft is mainly on how the thrust is calculated. The distance traveled is determined by integrating the velocity during the ground roll as expressed by Equation 2.17.

Z Z dV Z g V = a · dt = · dt = (T − D − µ(W − L)) · dt (2.16) dt W Z S = V · dt (2.17)

For rotation, a typical time of 2 to 5 seconds is expected for large airplanes to reach climb phase. The Equation 2.16 can also be applied if the drag and lift forces are updated considering the change in the aircraft attitude. The distance during transition and climb can be computed considering the climb angle and that the obstacle is cleared after the transition segment is completed. The equations below gives the total distance for transition and climb phase. Climb Angle: T − D T 1 sin θ = = − (2.18) climb W W L/D Transition distance: T 1 S = R · sin θ ≈ 0.2156 · V 2 · − (2.19) TR climb S W L/D Transition height:

hTR = R(1 − cos θclimb) (2.20) Climb distance over an obstacle:

SC · tan θclimb = hobstacle − hTR (2.21) Chapter 2. Literature Review 13

The total distance of the take-oﬀ run is given by summing each segment:

Stotal = SGround−Roll + SRotation + ST ransition + SClimb−obstacle (2.22) Although the formulation derived above seems to be simple, the information required in order to solve the equation of motion can be very challenging considering the fact that in conceptual design just a few geometric parameters of the new aircraft are known. The attempt to predict some parameters in advance in the conceptual design phase as the ones listed in the beginning of the section can introduce uncertainties in the results that may be not traceable and lead to unreliable estimations. Therefore, the SUAVE software [4] offers a semi-empirical formulation for estimating take-off field length which is based on historical data from certified aircraft. The advantage in using the semi-empirical model lies on the fact that it covers all four take-off conditions estimation. In addition, the model gives information about the physical trends and trade-offs of the take-off field length allowing decision making about the new design. For tube-wing aircraft, the results are satisfactory as shown in the Chapter 4 for the E170 jet and ATR 72-600 aircraft. The semi-empirical model is based on the most critical parameters for take-off field length such as wing area, maximum lift coefficient, take-off weight and engine thrust as discussed in the reference [4]. The equation of the semi-empirical model and its coefficients are presented below where V2 is typically 1.2 of the stall speed for a given flap setting.

2 i X V 2 TOFL = k · 2 (2.23) i T/W i=0

Table 3 – Coeﬃcient of Equation 2.23

Engine k0 k1 k2 2 857.4 2.476 1.40e-4 3 667.9 2.343 9.30e-5 4 486.7 2.282 7.05e-5

Source: Lukaczyk et al., 2015[4]

2.2.2.2 Climb

The climb performance of an aircraft dictates how quickly the airplane reaches a desired cruised altitude and thus how its noise footprint is perceived. Also, as introduced before, the climb gradient in the second segment shown in Figure 5 may impose restrictions in the allowable weight due to aeronautical regulations demand. The climb gradient in the second segment can be calculated using Equation 2.32 and must be equal or greater than 2.4%. Although other requirements related to climb gradient in diﬀerent conditions must be met, the minimum climb gradient in the second segment is the most restrictive Chapter 2. Literature Review 14 for civil transport aircraft according to reference [18]. Therefore, it is essential to evaluate this parameter in the conceptual design in order to provide more realistic estimations for the allowable take-oﬀ weight.

Figure 5 – Second Segment Climb

Source: The Author

Now, considering ﬁrst a general climb segment, the performance is primarily measured in terms of rate of climb and climb gradient. To determine its parameters, the climb formulation is derived from the free body diagram presented in Figure 6.

Figure 6 – Free Body Diagram considering Climb Segment.

Source: Gudmundsson, 2013[7]

The general planar equations of motion for an airplane is presented below considering the Figure 6.

W dV L − W cos θ + T sin ε = z (2.24) g dt

W dV D − W sin θ + T cos ε = x (2.25) g dt Chapter 2. Literature Review 15

The following assumptions are applied in order to consider a steady ﬂight during climb.

1. Steady motion implies dV/dt = 0 2. The climb angle θ is a non-zero quantity 3. The angle of attack α is small 4. The thrust angle ε is 0 °

Then the Equations 2.24 and 2.25 can be rewritten as

L = W cos θ (2.26)

T − D = W sin θ (2.27)

The climb angle, horizontal and vertical airspeed can be determined using equations

T 1 sin θ = − (2.28) W L/D

VH = V cos θ (2.29) For jets: TV − DV ROC = V = V sin θ ≡ (2.30) V W For propellers: P − P ROC = V = V sin θ ≡ available required (2.31) V W

ROC - Rate of climb

Pavailable - Power Available

Prequired - Power Required

In the SUAVE software [4], the estimation of the climb gradient in the second segment discussed previously is given by the approximation in Equation 2.32. In this condition, the drag must account for an increase due to engine failure and therefore asymmetric ﬂight.

T 1 γ = − (2.32) W L/D γ - Climb gradient Chapter 2. Literature Review 16

The equations 2.24 and 2.25 can also be solved numerically considering diﬀerent proﬁles for the climb phase which are available in the SUAVE software [4]:

1. Constant-Airspeed Constant-Climb-Rate 2. Constant-Mach Constant-Climb-Rate 3. Constant-Mach Constant-Climb-Angle 4. Constant-Throttle Constant-Airspeed

The Constant-Throttle Constant-Airspeed climb profile is the most representative profile available on SUAVE considering commercial aircraft since it is more convenient for the pilot to leave the throttle in a set position. However, the airspeed set to be constant in the software is the true airspeed while in the operation, the speed schedule during climb is composed by a segment in which the calibrated airspeed is constant and then the mach is set to be constant since it must not exceed the maximum operating mach number. Moreover, SUAVE may present convergence problems on the mission solver when considering the Constant-Throttle Constant-Airspeed climb profile which is unacceptable in an optimization environment using gradient based algorithms.

2.2.2.3 Cruise

The cruise segment is considered as a straight and level ﬂight which the aircraft is designed for in order to perform eﬃciently. In other words, the goal is to have the highest possible airspeed for a given fuel consumption. The Figure 7 shows the free body diagram for the cruise phase.

Figure 7 – Free Body Diagram considering Cruise Segment.

Source: Gudmundsson, 2013[7] Chapter 2. Literature Review 17

The planar equations of motion is derived below considering the Figure 7 and steady motion.

L = W (2.33)

D = T (2.34)

The solution of the above equations bring to light important characteristics of the aircraft such as maximum airspeed, stall airspeed in level ﬂight and best range airspeed. In the context of the present work, the stall airspeed is one of the most important parameters since it is a function of CLmax as expressed in Equation 2.35. s 2W VS = (2.35) ρSCLmax

2.2.2.4 Range

The range of the aircraft can be determined considering the cruise proﬁles described in Table 4.

Table 4 – Cruise Proﬁles

Proﬁle V ρ CL/CD SUAVE 1 Constant airspeed/altitude Constant Constant Available [4] 2 Constant attitude/altitude Constant Constant Not Available 3 Constant airspeed/attitude Constant Constant Not Available

Source: Lukaczyk et al., 2015[4]

The formulation for range can be done considering the following expressions.

dR Rate of change of distance V = = (2.36) dW Rate of change of weight −ctT

ω˙ c ≡ fuel (2.37) t T

cBHP V ct = (2.38) ηP

ω˙ c ≡ fuel (2.39) BHP P

ct - Thrust speciﬁc fuel consumption ω˙ fuel - Fuel Weight Flow

cBHP - Speciﬁc fuel consumption ηP - Propeller Eﬃciency Chapter 2. Literature Review 18

Then the equation can be rewritten considering Equations 2.33 and 2.34.

dR V (L/D) = (2.40) dW −ctW

Z Wini−Wf V C 1 R = L dW (2.41) Wini −ct CD W

In order to solve the equation, the cruise proﬁles presented in4 has to be considered. The simplest formulation is given by proﬁle 3 - constant airspeed/attitude since V and

CL/CD are constant.

V C Z Wini 1 V C W R = L dW = L ln ini (2.42) ct CD Wini−Wf W ct CD Wf

The range can be computed for diﬀerent TOW and fuel weight which covers the possible missions performed by the aircraft operators as well as highlights the trade-oﬀs between range and payload. The results can be displayed in a chart named Payload Range Diagram as explained in Figure 8.

Figure 8 – Payload Range Diagram

Source: Lukaczyk et al., 2015[4] Chapter 2. Literature Review 19

2.2.2.5 Descent

The formulation for descent segment is derived considering the free body diagram presented in Figure 9.

Figure 9 – Free Body Diagram - Descent Segment.

Source: Gudmundsson, 2013[7]

The planar equations of motion is given below

W dV L − W cos θ + T sin ε = z (2.43) g dt

W dV −D + W sin θ + T cos ε = x (2.44) g dt 1. Steady motion implies dV/dt = 0 2. The climb angle θ is a non-zero quantity 3. The angle of attack α is small 4. The thrust angle ε is 0 ° Then the equations of motion can be rewritten considering steady unpowered descent.

L = W · cos θ (2.45)

D = W · sin θ (2.46)

The angle of descent is derived by the ratio between Equations 2.45 and 2.46.

1 tan θ = (2.47) L/D Chapter 2. Literature Review 20

The rate of descent is expressed in terms of the airspeed V

s 2 cos θ W V = (2.48) ρCL S s C 2 W V = D (2.49) V 3/2 ρ S CL D V VV = V · sin θ = V = (2.50) W CL/CD

2.2.2.6 Landing

Similar to the take-oﬀ analysis, the landing performance refers to the distance required for an aircraft to approach and decelerate. The landing run is split in important segment as shown in Figure 10 in order to simplify the formulation for each one.

Figure 10 – Import segments of the landing run.

Source: Gudmundsson, 2013[7]

The approach phase starts from a steady descent. Then the pilot performs a flare maneuver in order to raise the nose of the aircraft and touch the runway smoothly. The landing segment finishes with the deceleration from the touch-down until the complete stop of the aircraft. The pilot only actuates the brakes after a free roll distance. The free-body diagram to be considered in the landing analysis is the same as the one used for take-off run (Figure 4). The difference is the order of each phase as discussed above. For this reason, the theoretical formulations are the same of those derived for take-off run (Equations 2.16, 2.17). The total distance required for landing the aircraft is then given by summing each phase contribution as expressed in the Equation 2.51.

Stotal = Sapproach + Sflare + Sfree roll + Sbreaks on (2.51) Chapter 2. Literature Review 21

Analogous to the take-off field length estimation, the SUAVE software [4] also offers a semi-empirical model to compute the landing field length based in the formulation proposed by Torenbeek [10]. The semi-empirical relation is given by the Equation 2.52.

2 X 2 i LF L = ki · Vapp (2.52) i=0

Vapp - Approach speed

Table 5 – Coeﬃcient of Equation 2.52

Wheel Trucks k0 k1 k2 2 250 0 0.2533 4 250 0 0.3030

Source: Lukaczyk et al., 2015[4]

2.2.2.7 Fuel Consumption

It is important to determined the fuel required for a mission which can be accomplished considering the Equation 2.37 rewritten below.

dW ω˙ = fuel = c · T (2.53) fuel dt t Z Wfuel = ct · T · dt (2.54) The Equation 2.54 can be applied for all segments presented in Figure 1 using numerical integration. The sum of all segments gives the required fuel weight to accomplish the design mission.

2.2.3 Weight Estimation

The weight estimated during the design process is an important input for the performance analyses as observed in the theoretical development in section 2.2.2. The methods available in the literature range from simpliﬁed methods which requires only some geometric parameters to more sophisticated methods that require detailed information about the aircraft [7]. Considering the scope of conceptual design, the SUAVE software uses semi-empirical relations for a tube-and-wing aircraft based in data from references [15, 16]. The methodology developed by Shevell [16] at Douglas Aircraft and Kroo [15] calculates a portion of the empty weight of the aircraft which takes into account the wing, tail, fuselage, furnishings and landing gear weight. The equations uses English engineering units in pounds and feet, unless otherwise speciﬁed and they are presented below for each component listed. Chapter 2. Literature Review 22

1. Wing √ 3 −6 Nultb WMTOW WMZF (1 + 2 · λ) Wwing = 4.22Sw + 1.642 · 10 · 2 (2.55) (t/c)avg cos Λc/4 Sw(1 + λ)

Wwing - Wing structural weight

Sw - Wing area

Nult - Ultimate design load factor for the aircraft. Its value must comply with aeronautical regulations such as CFR 14 Part 25. b - Wing span λ - Wing taper ratio

(t/c)avg - Wing thickness to chord ratio

Λc/4 - Wing sweep angle at 1/4 chord line

2. Horizontal Tail + Elevator √ 3 −6 NultbHT WMTOW cw SHT WHT = 5.25SHT + 0.8 · 10 · 2 1.5 (2.56) (t/c)avg cos ΛHTc/4 lHT SHT

WHT - Horizontal Tail structural weight

SHT - Horizontal Tail area

bHT - Horizontal Tail span

lHT - Distance between wing aerodynamic center and horizontal tail aerodynamic center

(t/c)avg - Horizontal Tail thickness to chord ratio

ΛHTc/4 - Horizontal Tail sweep angle at 1/4 chord line

3. Vertical Tail

3 WMTOW NultbVT 8.0 + 0.44 · −5 Sw WVT = 2.62SVT + 1.5 · 10 · 2 (2.57) (t/c)avg cos ΛVTc/4

WvT - Vertical Tail and Elevator structural weight

SvT - Vertical Tail area

bvT - Vertical Tail span

(t/c)avg - Vertical Tail thickness to chord ratio

ΛVTc/4 - Vertical Tail sweep angle at 1/4 chord line

4. Fuselage

−3 Ip = 1.5 · 10 ∆Pf · wf (2.58)

−4 lf,e Ib = 1.91 · 10 · Nlim(WMZF − Ww − Ww,p) · 2 (2.59) hf Chapter 2. Literature Review 23

If the Ip > Ib, If = Ip. If not,

2 2 Ip + Ib If = (2.60) 2 · Ib

Wf = (1.051 + 1.020 · If )Sf,wetted (2.61)

Wf - Fuselage structural weight

∆Pf - Maximum diﬀerential pressure of the fuselage

Ww,p - Weight of the wing-mounted engines, nacelles and pylons

lf,e - Eﬀective fuselage length. Fuselage length minus the wing chord root divided by two.

hf - Fuselage Height

5. Furnishings For aircraft with 300 or fewer seats,

Wfurn = (43.7 − 0.037 · Nseat) + 46 · Nseat (2.62) For aircraft over 300 seats,

Wfurn = (43.7 − 0.037 · 300) + 46 · Nseat (2.63)

Wfurn - Furnishings Weight

Nseat - Number of Seats

6. Landing Gear

WLG = 0.04 · WMTOW (2.64)

WLG - Landing Gear Weight

7. Propulsion System including Engine

0.9255 Wpropulsion = 1.6 · Wp,dry = 1.6 · (0.4054 · TSLS ) (2.65)

Wpropulsion - Propulsion system Weight

Wp,dry - Dry weight of the engine

TSLS - Sea-level static thrust

An iterative process is needed in order to deﬁne the components weight and MTOW as observed in the equations above. The strategy adopted in the present work to deal with this issue will be discussed in Chapter 3. Chapter 2. Literature Review 24

2.2.4 Propulsion

This section describes the aspects of flight propulsion that are necessary for aircraft design. The two main characteristics discussed are thrust (or power) and fuel consumption since they directly dictates the airplane performance. Besides, the tradeoff between thrust and efficiency is introduced in order to give a first comparison considering a turbofan and a turboprop engine. Then each power plant is described in terms of its thrust and fuel consumption behavior due to changes in aircraft speed and altitude considering empirical relations [19]. Finally, the method for engine modeling used in the SUAVE software is presented.

2.2.4.1 The Tradeoﬀ between Thrust and Eﬃciency

A generic propulsion device [11] generates thrust by interacting with the ﬂow and this physical phenomena can be explained considering Newton’s second law which states that the force on an object is equal to the time rate of change of momentum (mass times velocity) of that object. In this case, the ﬂow is moving thought the generic

propulsion device and its initial momentum per unit time is m˙ · V∞ (m˙ is the mass flow). The time rate of change of momentum is simply the change of momentum of the air flowing through the propulsion device. This can be calculated considering the difference between the momentum of the air flowing in and out. The Equation 2.66 is the thrust equation considering a generic propulsion device as described above.

T =m ˙ · (Vout − Vin) =m ˙ · (Vout − V∞) (2.66) An equation for efficiency can also be derived considering it as a function of velocity. The definition of efficiency is given by Equation 2.67 and Equation 2.68 is developed by reference [11] considering a generic propulsion device.

useful power available η = (2.67) total power generated

2 η = (2.68) 1 + Vout/V∞ As observed above, the thrust can be generated considering two mechanisms. The ﬁrst one is by having a relatively large mass ﬂow m˙ with a small change in the velocity of

the air. The other one generates thrust by increasing the diﬀerence Vout − V∞ for a small m˙ . In case of a propeller, m˙ is large since the propeller diameter allows a bigger ﬂow mass. However, the change in the velocity is limited by the airspeed in the propeller tip in order to avoid wave drag. On the other hand, a turbofan engine takes a relatively small mass

flow and increases the difference Vout − V∞ without the severe limitation in airspeed in comparison with a propeller. This is the reason why propeller powered aircraft usually fly at low speeds whereas a turbofan aircraft can fly in transonic conditions. Chapter 2. Literature Review 25

Now, considering the efficiency Equation 2.68, it is clear that the efficiency of the power plant increases by decreasing the ratio Vout/V∞. This mean that a propeller is more efficient than a turbofan since it generates a small change in the velocity of the flow. However, a turbofan can generate more thrust since it does not have a severe limitation in airspeed. With this example, the tradeoff between efficiency and thrust is illustrated and the power plant should be selected according to the mission requirements. If the airplane must fly in transonic speeds then a turbofan is suitable for the design. On the other hand, if there is a compromise between speed and fuel consumption then both turbofan and turboprop engines should be compared.

2.2.4.2 Turbofan Engine

The turbofan is presented in Figure 11 with a longitudinal cut in order to show each engine component. The turbofan is similar to a pure jet, however the main diﬀerence is given by the fan and its contribution to the total thrust generated. The engine showed in Figure 11 is composed by a fan, compressor, combustion chamber, turbine and nozzle.

Figure 11 – Turbofan components.

Source: Maerkang, 2009[20]

As discussed previously, a generic propulsion device generates thrust by interacting with the flow and the simplified thrust equation [11] illustrates that the thrust generated is a function of the flight condition which includes speed and altitude (m˙ = ρ∞AV∞, ρ∞ is a function of altitude). In case of a turbofan engine, the bypass ratio, an important parameter, is defined as the mass flow passing through the fan, externally to the core divided by the mass flow through the core itself [11] considering the Figure 11. This parameter is one of those which dictates the engine behavior. For high bypass ratio (above Chapter 2. Literature Review 26

5), the eﬀects of speed and altitude in the turbofan thrust is closer to a propeller than it is closer to a pure jet.

2.2.4.2.1 Thrust

The variation of thrust with altitude can be approximated considering the empirical relation given in Equation 2.69 as suggest by Mattingly [19] in order to discuss the engine expected behavior.

T ρ m = (2.69) T0 ρ0 T - Thrust for a condition of interest ρ - Air density for a condition of interest

T0 - Thrust for sea level condition

ρ0 - Air density for sea level condition m - depends on the engine design and it is usually near 1 Equation 2.69 shows that as the altitude increases and thus the air density decreases, the thrust generated decreases. Considering the eﬀect of speed, the variation of thrust is given by the empirical relation expressed by Equation 2.70 as discussed by reference [11].

T −n = AM∞ (2.70) T0 A - Function of altitude, A > 0 n - Function of altitude, n > 0

M∞ - Mach number The Equation 2.70 includes the effect of altitude combined with the effect of speed. Although the parameters A and n must be defined for each engine and flight condition, it is possible to state that the thrust decreases by increasing the Mach number.

2.2.4.2.2 Thrust Speciﬁc Fuel Consumption

The thrust speciﬁc fuel consumption is deﬁned as [11]

ct = weight of fuel burned per unit thrust per unit time (2.71) or

weight of fuel for a given time increment c = (2.72) t (thrust output)(time increment) The units in SI (International System of Units) gives

N 1 [c ] = = (2.73) t N · s s Chapter 2. Literature Review 27

However, the thrust speciﬁc fuel consumption was also conventionally deﬁned using

lb 1 [TSFC] = = (2.74) lb · h h

The variation of ct with Mach Number for a given altitude follows the empirical relation expressed in Equation 2.75 for M∞ ranging from 0.7 to 0.85 [11].

ct = B · (1 + k · M∞) (2.75) B - Empirical constant found by correlating the engine data k - Empirical constant found by correlating the engine data

2.2.4.3 Turboprop Engine

The turboprop is a propeller driven by a gas-turbine engine as shown in Figure 12.

Its performance is expressed in terms of power, P = T · V∞.

Figure 12 – Turboprop components.

Source: Maerkang, 2009[20]

The propeller performance is measure in terms of propeller eﬃciency deﬁned by Equation 2.76 which is a function of the advance ratio J expressed in Equation 2.77.

P ηprop = (2.76) PA

V J = ∞ (2.77) N · D P - Shaft Power

PA - Available Power N - Number of rotations per second of the propeller D - Propeller Diameter Chapter 2. Literature Review 28

The advance ratio is a similarity parameter for the propeller performance in the same category as Reynolds Number and Mach Number. This parameter can be used to estimate the propeller eﬃciency using empirical data such as the Naca Report TR 640. The propeller eﬃciency is a necessary input for the calculation of available power. In the case of a turboprop engine, the available power is actually given by the sum of two contributions, the power generated by the shaft and the thrust due to the jet exhaust as described in Equation 2.78. Usually, the second contribution correspond to 5% of the total thrust generated.

PA = ηprop · P + Tjet · V∞ (2.78)

2.2.4.3.1 Power

Some engine manufactures present the turboprop performance in terms of equivalent shaft power which includes the eﬀect of jet exhaust and is deﬁned as

PA Pes = (2.79) ηprop

As a ﬁrst approximation, the PA can be considered constant with Mach Number as discussed by reference [11]. The eﬀect of altitude on the power available is given by the empirical relation in Equation 2.80.

P ρ n A = (2.80) PA0 ρ0 n - Empirical constant, n = 0.7

2.2.4.3.2 Speciﬁc Fuel Consumption

The speciﬁc fuel consumption is deﬁned as

c = weight of fuel burned per unit power per unit time (2.81) or

weight of fuel for a given time increment c = (2.82) (power output)(time increment) The units in SI (International System of Units) gives

N [c] = (2.83) W · s However, the speciﬁc fuel consumption was also conventionally deﬁned using

lb [SFC] = (2.84) hp · h Chapter 2. Literature Review 29

The variation of c with velocity and altitude is first considered constant [11]. Although the value of c remains constant by increasing the altitude, the power required defined as PR = D · V∞ decreases, where D is the aircraft drag. Therefore, c can be decreased by decreasing the power generated by the engine as the PR decreases. The power available varies with altitude, however, the cruise altitude can be defined in such a way that the fuel consumption is minimized.

2.2.4.4 Turbofan and Turboprop Comparison

The turboprop and turbofan engines can be compared in terms of propulsive eﬃciency, ﬂight Mach Number and cruise altitude as presented in Figures 13 and 14.

Figure 13 – Eﬃciency Comparison.

Source: Medium - Images, 2017[21] Chapter 2. Literature Review 30

Figure 14 – Velocity and Altitude Comparison

Source: Mattingly, 1996[19]

As observed above, the turboprop has a more restrict operation than a turbofan engine. However, the turboprop has a higher propulsive eﬃciency. The comparison between engines can only be realistically made considering two real engines and two similar aircraft in order to evaluate fuel consumption.

2.2.4.5 SUAVE Model: Energy Network Method

The SUAVE software uses an energy network method [4] in order to model diﬀerent propulsive systems. In the case of a gas-turbine, the energy network framework is composed by individually modeled components such as fan, compressor, turbine, combustor, etc, in order to compute thrust and fuel consumption rate. In the software, the one dimensional ﬂow equations are solved across each component according to references [22, 23]. The Figure 15 represents the turbofan network used to compute the engine thrust and fuel consumption. Figure 15 – Turbofan Network.

Source: Lukaczyk et al., 2015[4]

The engine used in the optimization will be modeled for E170 by composing an energy network framework for gas-turbine. For ATR 72 600, external data for a general turboprop engine provided by EMBRAER S.A. will be used. Chapter 2. Literature Review 31

2.3 Optimization

The use of optimization in engineering design is a common and efficient approach specially in complex problems that involves non-intuitive relations. A mathematical model is used in order to represent a real problem which must preserve the main characteristics necessary to simulate it. Simplification and restrictions are applied and the goal is usually to minimize or maximize a certain parameter which is represented as an objective function. In addition, the optimization can provide useful information about the design space that is valuable for the development of new solutions or for the understanding of the design limitations and tradeoffs. In order to briefly discuss about the optimization techniques, the general optimization problem is presented below considering it as a minimization problem and single-objective optimization.

minimize f0(x) x

subject to gk(x) ≤ ck, k = 1, . . . , n. (2.85)

hi(x) = bi, i = 1, . . . , m.

The basic elements of an optimization problem consist of the following list. x - Vector of design variables which represents the parameters that aﬀect the objective function value. The design variables are the unknown quantities to be deﬁned by the optimization solution. In addition, bounds can be set on these variables since they may represent physical measurements. In other words, inequalities constraints can be used to restrict the design variables possible values. f0(x) - Objective Function: it is a mathematical representation of the parameter being minimized which is function of the design variables. hi(x), gk(x) - Constraint Functions is a set of restrictions that the optimization solution must satisfy in order to be feasible. They are expressed as equality or inequality constraints respectively which may represent limitations on the design variables as well as criteria for other parameters or physical relations.

A variety of optimization algorithms is available and they are usually classified in groups. The main division between algorithms is related to the method used for computing the iterations until the solution is reached which divides them in gradient-based and gradient-free optimization algorithms [24]. The first category uses gradient information to decide where to move in the design space . The objective function can be nonlinear and must have continuous first derivatives and, in some cases, continuous second derivatives. Gradient-free algorithms use sampling and/or heuristics to decide where to move in the design space. Chapter 2. Literature Review 32

2.3.1 Multidisciplinary Optimization in the Aircraft Design - MDO

A methodology for designing complex engineering systems is essential to exploit the synergism and mutually interacting phenomenas in order to achieve the optimal solution. The previous discussion highlights the optimization general deﬁnition and algorithms. This section expands the discussion in terms of the disciplines involved in an optimization problem by presenting Multidisciplinary Design Optimization (MDO) methodology appli- cable to aircraft design. In fact, an airplane optimization contains more than one discipline as illustrated by the Breguet equation for computing the aircraft range.

V C W R = L · ln initial (2.86) ct CD Wfinal Where the airspeed V is given by market studies as a performance requirement,

CL the ratio is calculated by the aerodynamics discipline, the parameter ct is under the CD propulsion discipline and the ratio between the initial and ﬁnal weight involves structure discipline, due to empty weight estimation, and propulsion, due to the fuel weight estimation. Consequently, it is possible to state that aircraft design is inherently multidisciplinary. In MDO, there are two well-deﬁned components. One of them is the optimization algorithm, it can be one from the groups presented previously according to the nature of the optimization problem, and the other component is the simulation model necessary to evaluate the designs chosen by the optimizer. With this two main components described, a typical process in MDO can be listed below according to reference [25].

1. Define the overall system requirements. 2. Define the design vector, the objective function and the constraints. 3. System decomposition in modules. 4. Modeling of physics via governing equations in the module level. 5. Model integration into an overall system simulation. 6. Benchmarking of the model (calibration) with respect to a known system from past experience if available. 7. Design Space Exploration (DoE) to find sensitive values and important design variables 8. Formal optimization to find the solution that minimizes the objective function 9. Post-optimality analysis to explore sensitivity and tradeoffs: sensitivity analysis, approximation methods, etc.

The present work aims at applying the MDO methodology listed above in order to have a rational optimization process. However, the focus is not the MDO itself, some techniques are only used to guarantee the necessary organization due to the multidisciplinary nature of the problem. The SUAVE software represents the items 3 to 5. 33

3 Methodology

The turboprop and turbofan powered aircraft for approximately 70 PAX compete in the regional aviation market performing, in general, missions of medium and short range as presented in Chapter 1. Although they have the number of passengers in common, the comparison between the two types of airplane has to be carefully conducted since they present distinct characteristics that may be an advantage or disadvantage according to the criterion chosen. In addition, comparing designs from different sources may lead to skewed results since the hypothesis considered behind the performance estimations may also be different. To avoid skewing of the comparison, the analysis must be carried out considering both airplanes modeled and optimized with the same assumptions and models. Aiming at an organized and impartial approach, the methodology structure is based on the MDO process presented in Section 2.3.1 for aircraft design. Table 6 presents the correspondence between the methodology phases and the steps in the MDO process adopted for defining the final geometry for both turbofan and turboprop aircraft.

Table 6 – Methodology structure based on a MDO process

E170 and ATR72-600 data · Deﬁne the overall system requirements · Deﬁne the objective function and the constraints

SUAVE · System decomposition in modules · Modeling of physics via governing equations in the module level · Model integration into an overall system simulation

Aircraft model/calibration · Benchmarking of the model with respect to a known system from past experience, if available. · Multidisciplinary Design Analysis (MDA) in order to compute performance results for baseline geometry

Optimization Strategy · Design of Experiments (DoE) to ﬁnd sensitive values and important design variables · Formal multidisciplinary optimization (MDO) to ﬁnd the solution that minimizes the objective function

Source: The Author

The methodology is divided into three phases and each one of them is described in detail in the next sections. Section 3.1 presents the modeling and the calibration strategy of the aircraft model. Section 3.2 discusses how the design variables are deﬁned and how the optimization is conducted. Finally, Section 3.3 describes the approach applied in the comparison between the turboprop and the turbofan aircraft. Chapter 3. Methodology 34

3.1 Aircraft Model

The modeling is preceded by the search of public data related to the aircraft defined as baseline geometry. As presented in Section 2.2, the aircraft model is based on semi-empirical relations, therefore it is important to compare the results obtained using the SUAVE software with public data. Calibration of model’s constants may be necessary in order to best fit the references. In this work, the sources were the manufacturer’s information of each aircraft and literature results in order to ensure that the data is reliable. The specification sheet [5, 6], Airport Planning Manual (APM) [26], Flight Crew Operating Manual [27] and papers with aircraft information [4] are the best options to be used as reference. Even with the sources listed, the data is scarce, thus it is necessary to define what parameters available will be considered to calibrate or to validate the aircraft model. Since the goal is to optimize the aircraft in terms of fuel consumption and MTOW, the aerodynamic, engine and weight models must be validated through performance estimations that capture the influence of all disciplines while ensuring that the mission simulated is consistent with public data. The performance estimation suggested to be compared with official values from the aircraft manufactures are listed below.

1. Payload Range Diagram

1.1. Range for MTOW, Full Payload, Optimum Flight Level, ISA +0°C 1.2. Range for MTOW, Full Fuel, Optimum Flight Level, ISA +0°C 1.3. Range for TOW with Full Fuel, zero Payload, Optimum Flight Level, ISA +0°C

2. Takeoﬀ Field Length (TOFL)

2.1. TOFL - MTOW, SL, ISA +0°C 2.2. TOFL - TOW for 500nm or 300nm range, SL, ISA +0°C 2.3. TOFL - Maximum allowable weight for Denver International Airport (DIA), 5333 ft, ISA +23°C or similar condition

3. WAT (Weight for Altitude and Temperature) - limited by second segment climb gradient

3.1. SL, ISA 0°C 3.2. Denver International Airport (DIA), 5333 ft, ISA +23°C or similar condition

4. Landing Field Length (LFL)

4.1. LFL - MLW, SL, ISA +0°C

The error accepted for each estimation is 3.5% since the model must be capable of representing the performance expected for a turbofan and a turboprop aircraft. More Chapter 3. Methodology 35 parameters could be considered, however, the semi-empirical model is limited to some of the typical conditions that the aircraft will face on the operation. Therefore, the conditions listed above were chosen and they are part of the mission simulated during the optimization. The intention is to guarantee that the trade-oﬀs are reasonably represented as well as the sizing requirements that dictates the performance estimations such as MTOW. All the models formulation were previously detailed in Section 2.2 and the next sections describe the strategy applied to validate and calibrate them. Section 3.1.1 describes the control parameters used to approximate the BOW estimation to public data. Section 3.1.2 discuss what are the best conditions to use to evaluate parameters such as CLmax, drag estimations and L/D. Finally, Section 3.1.3 presents the suggested considerations to calibrate the engine model.

3.1.1 Weight Model

The weight model implemented in SUAVE for tube-and-wing aircraft were presented in Section 2.2.3. The inputs are mainly geometric dimensions and they can be measured using the blueprint of the reference aircraft. CAD software such as SOLID- WORKS® oﬀers an useful feature to measure dimensions using 2D drawings. With the geometric inputs, the empty weight breakdown is done considering the contributions of the horizontal tail, propulsion, rudder, furnishings, fuselage, landing gear, vertical tail and wing. Unfortunately, detailed weight data is generally not public, thus the reference value must be the basic operating weight given in the speciﬁcation sheet of the baseline aircraft. Figure 16 shows an example of public information about the E170 jet.

Figure 16 – Example of public data containing weight information, E170 jet

Source: EMBRAER S.A., 2015[26]

During the optimization, the geometric parameters for wing, horizontal and vertical tails are continuously changing. In addition, the weight of the landing gear varies during Chapter 3. Methodology 36 the optimization since it is proportional to the MTOW. In the case of the engine weight for each aircraft, it must be exclusively a function of the static thrust at sea level. Therefore, the contributions of these components will dictate the increase or decrease in the empty weight of each aircraft being analyzed during the optimization, while the weight of the other components such as fuselage and furnishings is considered to be fixed based on the reference aircraft geometry. The calibration of the weight model can be conducted, if necessary, considering the fuselage weight as the control parameter. As shown in Section 2.2.3, the fuselage weight is a function of the maximum differential pressure encountered by the aircraft, which is a consequence of the service ceiling and pressurization. The maximum differential pressure must range from 5.5 to 9.4 psi [28] where the absolute ceiling must be taken into account. The exactly value must be defined in order to approximate the empty weight estimation to the public data.

3.1.2 Aerodynamic Model

The aerodynamic models implemented in SUAVE for the estimation of drag,

CLmax and L/D considering the second segment climb gradient are based on semi-empirical relations previously introduced in Section 2.2.1. The inputs are mainly related to the aircraft geometry and high lift device deﬂections. The prediction of these aerodynamic parameters directly aﬀects the performance results in the conditions discussed in the beginning of Chapter 3. Therefore, the strategy is to assign the evaluation of a given aerodynamic parameter to a performance estimation. The list below shows the relations between aerodynamic prediction and the most impacted performance results.

Table 7 – Aerodynamic parameters and the most impacted performance results

Aerodynamic Parameter Performance Analysis

CD Payload Range Diagram

CLmax TOFL and LFL estimations L/Dsecond segment Second Segment Climb Gradient estimation

Source: The Author

3.1.2.1 Drag Model Evaluation

The drag model is evaluated by comparing the calculated payload range diagram with the public data. In order to isolate the aerodynamic inﬂuence, the empty weight is inputted equal to the one provided by the aircraft manufacturer. The engine also impacts the payload range diagram and the strategy is to ﬁrst calibrate the engine model SFC and design thrust with the engine manufacturer’s data as discussed in Section 3.1.3. Chapter 3. Methodology 37

The total drag can be estimated by the sum expressed in Equation 3.1. Each term of the equation was discussed in Section 2.2.1.

CD = CD0 + CDLift Induced + CDCompressibility (3.1) The payload range diagram provides useful information about the aerodynamic model since displacement or distorsion in the curves indicate where the errors may be coming from. In case of a displacement, the error may be caused by errors in the parasite drag since it does not depend on the value of the lift coefficient. In case of a distortion, the error may be generated due to limitations of the induced lift drag model or compressibility drag model. In order to illustrate the impact of each portion of the drag coefficient, a parametric analysis was carried out. Figure 17 presents an example of impact on the final payload range diagram. The data used in this example was based in the E170 jet.

Figure 17 – Example of the impact in the Payload Range Diagram due to errors in CD

Source: The Author

The explanation for the red curve behavior in Figure 17 lies on the fact that if the CD0 is increased, its increment will impact in a similar amount the three simulated points. However, if the CDlift induced is decreased, as in the situation given by the green curve, the most impacted condition will be when the aircraft is ﬂying at the MTOW since this portion of the drag is a function of the lift coeﬃcient, consequently it is also a function of the weight. This makes the curve rotates in relation to the reference one. Chapter 3. Methodology 38

3.1.2.2 CLmax Model Evaluation

The CLmax estimation is evaluated using TOFL and LFL results since the distance calculated for both takeoff and landing is directly affected by the CLmax as presented in Section 2.2.2. In addition, the public data for TOFL and LFL can be easily found for different flap settings which allow the verification of the CLmax for more than one flap and slat deflection.

Considering the V2 equal to 1.2 · VS for TOFL estimation, Equation 2.23 can be rewritten as

2 i X W 2 2.88 TOFL = k · · (3.2) i T ρC S i=0 Lmax Now, considering the Vapp equal to 1.23 · VS for LFL estimation, Equation 2.52 can be rewritten as

2 i X 3.0258 · W LF L = k · (3.3) i ρC S i=0 Lmax As illustrated by Equations 3.2 and 3.3, the TOFL and LFL are functions of the inverse of the CLmax . In addition, the LFL is affected only by the CLmax model. In the case of TOFL, the estimation is also affected by the engine model, however, the static thrust for sea level can be compared to the engine manufacturer data in order to isolate the CLmax influence. A calibration factor can be applied, if necessary, in the ki constants of the TOFL and LFL models in order to approximate the results to the official values.

3.1.2.3 L/D Model Evaluation

The L/D estimation for the second segment in the takeoﬀ path can be evaluated by comparing the WAT estimated and the oﬃcial value for a given altitude and temperature. As presented in Section 2.2.2, the second segment climb gradient can be calculated using Equation 2.32.

T 1 γ = − (2.32) W L/D The WAT is defined as the takeoff weight at a given altitude and temperature that is limited by the second segment climb gradient (γ) indicated in the requirement. For two engine airplanes, γ must be equal or greater than 2.4%. As Equation 2.32 shows, γ is a function of the thrust and L/D in the second segment. The static thrust for sea level can be compared to the engine manufacturer data in order to isolate the L/D influence. Since the γ estimation is very sensitive to variations in L/D, the evaluation of the L/D must be restricted to the conditions listed in the beginning of Section 3.1 due to the semi-empirical model limitation and a calibration factor can be applied in this parameter in order to match the WAT estimation with public data. Chapter 3. Methodology 39

3.1.3 Engine Model

As presented in Section 3.1.3, the engine can be modeled by using the network concept in the SUAVE software or with external data from a different software such as the GasTurb®. In the first case, the calibration of the engine modifies internal parameters of its components. In the second case, a calibration factor is applied in the final values of SFC and thrust or power. The approach to evaluate the different models is similar and the first step is to gather engine public data. Unfortunately, the engine official values are the most scarce information necessary to perform the model validation. It is common to only have access to the design thrust and SFC at a given atmospheric condition and the static thrust at sea level. The strategy is to evaluate the engine model described in Section 2.2.4 using the payload range diagram and the TOFL estimations. The SFC will directly affect the range calculation as illustrated by Equation 3.4 where ct stands for TSFC (Thrust Specific Fuel Consumption). Therefore, the public payload range must be used in order to evaluate the SFC estimations. In case of reasonable differences between official data and theoretical results, a calibration factor can be applied in the overall pressure ratio of the engine model or in the SFC final estimation itself.

Z Wini 1 V C R = L dW (3.4) Wini−Wf ct W CD For the thrust estimation, the public static thrust value must be used to evaluate the engine model and then the TOFL data must be compared in order to evaluate the variation of the engine thrust with speed, atmospheric condition and altitude. The reason why thrust estimation can be evaluated using the TOFL official values is due to the fact that takeoff distance is a function of the inverse of the thrust as expressed in Equation 3.2 in which public data is available for a range of altitudes and atmospheric conditions. In case of reasonable differences between official data and theoretical results, a calibration factor can be applied in the calculated static thrust for takeoff condition.

3.2 Optimization

The general optimization problem is deﬁned by Equation 3.5 as introduced in

Section 2.3, where f0(x) is the objective function, x is the design variables vector and gk(x) and hi(x) are the constraints.

minimize f0(x) x

subject to gk(x) ≤ ck, k = 1, . . . , n. (3.5)

hi(x) = bi, i = 1, . . . , m. The strategy to deal with the optimization problem in the scope of this work is to first define the constraints that must be satisfied by the new design. The geometric Chapter 3. Methodology 40 design variables are selected by applying a DoE study. Then the objective function is evaluated considering fuel burn and MTOW in a pareto analysis. The optimization is executed considering the engine fixed in order to analyze only geometric trade-offs. The final optimized geometries are defined considering three different objective functions as described in Section 3.2.3. The optimization algorithm used is the SLSQP available in the SciPy package for Python since this optimizer has shown great performance in similar problems using SUAVE as the modeling software [29]. In addition, this optimizer is open source and it is a gradient based algorithm capable of handling non-linear constraints.

3.2.1 Constraints

The constraints are based on physical restrictions and in the Top Level Aircraft Requirements (TLARs) for each aircraft type, and also disciplinary consistency constraints. Table 8 presents the constraints considered for the optimization problem where TLAR represents the corresponding performance requirements for the turboprop or the turbofan aircraft.

Table 8 – Constraints considered for the aircraft optimization

Constraint Bounds 1 Fuel Margin = 0 2 Minimum Throttle ≥ 0 3 Maximum Throttle ≤ 1 4 MZFW Consistency = 0 6 TOFL for MTOW, SL, ISA ≤ T LAR 7 Second Segment Climb Gradient for MTOW, SL, ISA ≥ T LAR 7 LFL for MLW, SL, ISA ≤ T LAR 8 Design Range = T LAR 9 Time to Climb to Cruise Altitude ≤ T LAR 10 Range for Hot and High TO condition ≥ T LAR 11 Maximum Fuel Available ≥ T LAR

Source: The Author

The first four constraints are considered in order to guarantee a physical result. The fuel margin is defined as the landing weight subtracted by the BOW and the maximum payload and it must be positive in order to ensure that the fuel burned in the design mission is equal to the available fuel for the harmonic mission. The upper bound in the throttle prevent the optimizer to select an aircraft that needs more thrust than the engine is capable of generating and the lower bound is applied to avoid numerical problems. The MZFW consistency is defined as the MZFW subtracted by the BOW and maximum payload which must be equal to zero. This strategy is applied since the BOW is a function Chapter 3. Methodology 41 of MZFW and an iterative process is needed in order to converge the values of BOW and MZFW. The constraints based on the TLARs represent the most critical conditions which size the aircraft. They were also applied in other similar aircraft optimization problems as presented by references [29, 30, 31].

3.2.2 Design Variables

The design variables are first selected as the geometric parameters which define the wing, such as aspect ratio, area, taper ratio, thickness to chord ratio and sweep angle. In addition, the tails are resized in order to maintain the same tail volume coefficient of the baseline geometry with the assumption that this strategy will lead to a stable aircraft. Aiming at evaluating the influence of the selected design variables, a DoE study is conducted where the fuel burn, MTOW and constraints variations are computed considering the engine fixed. The definition of DoE is related to a family of numerical methods and practical guidelines for selecting the trial points in the design space in order to explore possible tradeoffs. Often, a DoE is executed before setting up the formal optimization problem since it allows the identification of the key drivers among the potential design variables [25]. For the present work, the matrix of experiments is defined considering a parametric study in which only isolated factors are evaluated as shown in Table 9. The goal with this analysis is to properly define the design variables for each aircraft type.

Table 9 – Matrix of Experiments - Parameter variation

Experiment Wing Aspect Taper t/c Sweep Number Area Ratio Ratio Angle 1 1.05 1.00 1.00 1.00 1.00 2 1.00 1.05 1.00 1.00 1.00 3 1.00 1.00 1.05 1.00 1.00 4 1.00 1.00 1.00 1.05 1.00 5 1.00 1.00 1.00 1.00 1.05 6 0.95 1.00 1.00 1.00 1.00 7 1.00 0.95 1.00 1.00 1.00 8 1.00 1.00 0.95 1.00 1.00 9 1.00 1.00 1.00 0.95 1.00 10 1.00 1.00 1.00 1.00 0.95

Source: The Author

With the computed value for fuel burn, MTOW and the constraints for each experiment, the variation of the results with respect to the parameter alteration can be calculated as shown by Equation 3.6. This information is essential for deﬁning the most Chapter 3. Methodology 42 important design variables among the potential ones and allows to reduce the number of design variables if it is worthwhile. The strategy to deal with the variation sign in the equation is applied aiming at a more intuitive result interpretation where the sign of the variation in the performance indicator is maintained.

∆f(x ) x V ariation = i − 1 / abs i − 1 (3.6) f(xref ) xref

xref Reference values for the design variables

xi Design variables with variations f(x) Value computed for a performance indicator

In order to compute the correct variation in the performance indicators due to geometric alteration, some consistencies must be met such as the value of MTOW, MZFW, BOW and the design range, the distance traveled disregarding the reserve segments. As presented in Section 3.1.1, the BOW is a function of MTOW and MZFW, which end to be also functions of the BOW. Therefore, an iterative process is needed in order to ﬁnd the values for BOW, MTOW and MZFW. In addition, the distance traveled in the cruise segment in order to meet the design range is also unknown. The strategy to guarantee these consistencies is to run an iterative process similar to an optimization procedure for each element in the matrix of experiments with only constraint functions, which turns to be a feasilization problem. Applying this approach, the algorithm will try to satisfy the constraints and the process will ﬁnish when it has converged to a feasible solution without modifying the geometry, only the unknown parameters. In this case, the variables to be determine for each analyzed aircraft in the matrix of experiment are the MTOW, MZFW and cruise distance.

3.2.3 Pareto Analysis

For optimization problems with more than one objective in which a conflict is expected, a pareto strategy can be applied. This approach transforms a multiobjective problem into a single objective function optimization. In the present work, aggregating function is used in order to combine the objectives into a single scalar function [32]. Each objective is multiplied by a weight factor and different values are considered in order to compute the optimal solutions. In aircraft design, two main goals is to achieve a low fuel consumption and a light operating weight since these characteristics have a positive impact on the total costs. In fact, these two desirable attributes are widely known and are key drivers in the aircraft sizing as discussed by reference [33]. The challenge in pursuing both characteristics in the conceptual design phase relies on the fact that they are conflicting objectives. Therefore, Chapter 3. Methodology 43 it is expected distinct aircraft designs when considering fuel burn or BOW which can be compared considering a non-technical criteria such as the costs involved. As discussed by reference [33], the BOW impacts directly on the production costs and the fuel consumption is a key parameter for the operational costs. In the present work just technical criteria are used such as fuel consumption and MTOW. The costs estimations are purely statistical and outside the scope of this analysis. In addition, the maximum take-off weight objective can capture tradeoffs between BOW and fuel burn when it is being optimized, as shown by reference [33]. Therefore, in order to explore the design space, a pareto analysis is carried out considering as objectives the fuel consumption and MTOW. The objective function considering aggregating approach is set as,

∗ ∗ f0(x) = β · Wfuel burn + (1 − β) · MTOW (3.7)

∗ Where β is a constant which can range from 0 to 1, Wfuel burn is the fuel burn divided by the reference value and MTOW ∗ is the MTOW divided by the baseline value. An optimization is executed for each β value desired. Furthermore, for the same β value, more than one optimization is carried out considering diﬀerent initial guesses. The data resulting from the optimization can be used to construct a pareto plot as shown in Figure 18.

Figure 18 – Example of Pareto Plot - BOW vs Block fuel

Source: Bianchi, 2017[33]

The ﬁnal optimized geometries used for comparison are the solutions for β equal to 0, 0.5 and 1. In other words, it is considered the fuel burn and MTOW optimization cases as well as the case when each of these technical criteria contributes equally to the objective function. Chapter 3. Methodology 44

3.3 Comparison

The comparison between the turbofan and turboprop aircraft considers the reference airplanes as well as the optimized geometries for β equal to 0, 0.5 and 1, as previously stated. The results chosen to be compared are the mission parameters, payload range diagram, specific range, the block fuel and block time. The goal here is beyond just defining the best aircraft given a criterion but also understanding why a specific configuration is more competitive in a defined scenario and what are the opportunities for each aircraft type. The next paragraphs present a discussion on each topic being considered in the comparison. The typical mission performed by a turboprop aircraft differs considerably from the one performed by a turbofan mainly due to the cruise speed and service ceiling which are consequences of the propulsion type. Therefore, the first comparison must be between the main mission parameters which here is generally considered as the time to climb to cruise altitude, service ceiling and cruise speed. Moreover, the aircraft weights must be also compared since an expressive difference is observed between these two types of airplanes. In fact, the BOW is a function of the maximum loads which are related to the aircraft maximum cruise speed. In other words, the higher the cruise speed, the higher the loads and hence the BOW. Therefore, it is expected a higher BOW for the turbofan type than the one for turboprop aircraft. Summarizing, for the mission analysis, the following parameters must be compared and discussed in order to identify the explanation for the differences observed.

1. Time to climb to cruise altitude 5. Fuel Available 2. Cruise altitude 6. BOW 3. Cruise Speed 7. MTOW 4. Payload

The next step is to analyze the previous parameters using the payload range diagram and specific range equation. The first approach offers a visual comparison between the maximum range given a fixed payload. In addition, the impact of each objective function optimized can also be seen on the payload range diagram, which illustrates the consequence of the possible design decisions. An example of payload range diagram can be seen in Figure 17 presented in Section 3.1.2.1, where the impact of the polar drag variation was discussed. The instantaneous specific range illustrates the impact of each parameter discussed before in the aircraft flight performance as given by Equation 3.8 considering the cruise segment. In addition, the fuel weight flow relates to the TSFC as shown by Equation 3.9 and since the cruise segment is considered 1g trimmed flight, it is possible to write Equations 3.10 and 3.11. Chapter 3. Methodology 45

R dR/dt V SR = = = (3.8) fuel burn dmf /dt m˙

m˙ = TSFC · T (3.9)

T = D (3.10)

W = L (3.11)

SR - Specific Range D - Drag m˙ - fuel flow L - Lift TSFC - Thrust Specific Fuel Consumption W - Aircraft Weight T - Thrust V - Cruise True Speed

Equation 3.8 can be rewrite as Equation 3.12.

V · (L/D) V L 1 SR = = · · (3.12) TSFC · W TSFC D W

This equation summarizes the potential of an aircraft in terms of fuel consumption by linking all its critical parameters. The first term given by the speed and TSFC ratio relates the engine characteristics with the design speed. The second term is given by the aerodynamic efficiency and the last one is the inverse of the aircraft weight. By looking at each term, it is possible to understand the differences calculated in the specific range for the turbofan and turboprop aircraft. For the block fuel and block time, the calculation must be done for different ranges in order to compare the airplanes in distinct scenarios. Indeed, the differences between a turboprop and turbofan aircraft will vary according to the mission range and hence the best aircraft for a defined criterion may change with the desired range as well. The values considered in this analysis for range are 250, 500, 750, 1000, 1250 and 1500 nm in which the fuel burn in the climb, cruise and descent segment is considered as block fuel. The block time also takes into account only these segments. The block fuel directly relates to the operational costs since the fuel represents an expressive part of the total expenses of an airline [34]. In addition, it is widely known that the airlines management plan their operation in order to maximize profit which means to properly size their fleet according to the demand. Therefore, another critic parameter relating financial planning is the aircraft availability since an airplane that flies faster is able to do more flights in a day compared to a slower one. 46

4 Results and Discussion

4.1 Turbofan Aircraft Results

4.1.1 Aircraft Model and Calibration

The models described in Section 2.2 and the evaluation procedure presented in Section 3.1 were used in order to model the E170 aircraft performance. Differences in the reference values from distinct official sources, such as the documents [26, 5], were noted. Therefore, it was decided to set as the main reference the specification sheet [5] when the public information is conflicting for the conditions of interest listed in Section 3.1, and the document [26] for others conditions in which the public data is scarce since reference [26] presents detailed information about the E170 jet. The decision was based on the fact that the specification sheet [5] is the most updated information, however, it presents limited performance results. All the inputs used to model the E170 jet in SUAVE as well as the python scripts are indicated in Appendix A.1. A performance analysis was carried out in order to compute the Payload Range Diagram, TOFL and LFL. The empty weight breakdown was also computed and the results are presented in Table 10 as well as the reference value taken from reference [26]. The maximum differential pressure value used was 8.94 psi, which is consistent with the feasible range discussed in Section 3.1.1.

Table 10 – E170 - Empty Weight Breakdown

Component Weight (kg) Horizontal tail 646 Propulsion 4092 Rudder 116 Systems 6573 Fuselage 4087 Landing gear 1488 Vertical tail 291 Wing 3444 Empty Weight 20737 Reference 20736 Diﬀerence +1

Source: The Author

The weight model is considered to be satisfactory and validated to be used in the turbofan aircraft optimization. Chapter 4. Results and Discussion 47

The results for payload range diagram comparison are presented in Figure 19. Table 11 presents the diﬀerences between the SUAVE calculation and the reference [26] for E170 AR version. The fuel reserves considered take into account alternate airport and holding of 30 min.

Figure 19 – E170 AR Payload Range Diagram, FL350, ISA +0°C

Source: The Author

Table 11 – E170 AR Payload Range Diagram, FL350, ISA +0°C

TOW Fuel SUAVE Reference Diﬀerence Diﬀerence (-) Available (kg) Range (nm) Range (nm) (nm) (%) MTOW 7060 1381 1340 41 3.1% MTOW 9428 2039 2020 19 0.9% BOW + Fuel 9428 2320 2362 42 1.8%

Source: The Author

The maximum error calculated was 3.1% which is considered acceptable. The semi-empirical aerodynamic model for CD prediction was validated, however, modiﬁcations were necessary in the engine model inputs in order to calibrate the SFC values. The control parameter was the overall pressure ratio of the turbofan which was set to 21:1 in order to have a SFC of approximately 0.68 at Mach 0.8, FL350 [35]. The design thrust for the same condition was set to 27550N since this parameter is also an input. The resulting static thrust at SL was 129 kN, 2.3% bigger than the manufacturer data. Chapter 4. Results and Discussion 48

The impact of the engine model limitations can be observed in the take-off field length estimations. The document [26] presents TOFL charts for ISA +0°C and +15°C, however, as discussed previously, the TOFL results from source [26] are conflicting with the value presented by the reference [5] for TOFL at MTOW, SL and ISA +0°C. Therefore, the strategy applied was to evaluate the curves tendency and WAT with the document [26]. The reference [5] was used to evaluate the absolute errors only in the conditions of interest listed in Section 3.1. The comparison between SUAVE results and reference [26] is presented in Figures 20 and 21 . The discontinuities in the TOFL curves are due to the second segment climb gradient requirement. When γ is equal to 2.4%, the TOW is equal to the WAT. For the aircraft to be able of taking off in a higher TOW, the flap setting must be changed to a smaller deflection, thus at a lower CLmax . The E170 flap settings for take-off are the flap 4, 2 and 1 [26].

Figure 20 – E170 TOFL, ISA +0°C

Source: The Author Chapter 4. Results and Discussion 49

Figure 21 – E170 TOFL, ISA +15°C

Source: The Author

The WAT estimation is given in Table 12 for conditions that represents airports of interest such as Denver International Airport and Santos Dumont Airport.

Table 12 – E170 - WAT estimation

Condition Flap SUAVE Reference Diﬀerence Diﬀerence Setting WAT (kg) WAT (kg) (kg) (%) SL, ISA +0°C 4 38600 38600 0 0% 6000 ft, ISA +15°C 4 31205 31990 -785 -2.4 % 6000 ft, ISA +15°C 2 35850 36000 -150 -0.4 % 6000 ft, ISA +15°C 1 37000 37000 0 0%

Source: The Author

The error in the WAT estimation is considered acceptable for this academic analysis, however, improvements are desirable since 785kg may represent 8 less passengers in the maximum allowable weight. As observed, the TOFL curves reasonably captures the tendency presented by the reference values [26]. The total errors in the TOFL estimation are computed in Table 13 Chapter 4. Results and Discussion 50 against reference [5] for the conditions of interest. The TOW for 500nm, full PAX, ISA, SL was calculated using SUAVE considering 1600kg as fuel reserves. The TOFL at Denver International Airport was extrapolated from the reference values [26] in order to evaluate the SUAVE estimation at hot and high take-oﬀ conditions.

Table 13 – E170 - TOFL estimation

Condition TOW SUAVE Reference Diﬀerence Diﬀerence (kg) TOFL (m) TOFL (m) (m) (%) MTOW, SL, ISA +0°C 38600 1626.43 1644 -17.57 -1.1%

TOW for 500nm, full PAX 31406 1123.39 1151 -27.61 -2.4 % SL, ISA +0°C Denver, WAT 36681 3117.05 3094.44 22.61 0.7 % ISA +23°C, 5433 ft

Source: The Author

Using the same approach as in the TOFL calculation, the LFL was computed using the document [26] as reference to evaluate the tendencies as presented in Figure 22 for ISA +0°C and ﬂap setting 6. The LFL value for MLW, SL, ISA +0°C was compared to reference [5] as shown in Table 14.

Figure 22 – E170 LFL, ISA +0°C

Source: The Author Chapter 4. Results and Discussion 51

Table 14 – E170 - LFL estimation

Condition TOW SUAVE Reference Diﬀerence Diﬀerence (kg) LFL (m) LFL (m) (m) (%) MLW, SL, ISA +0°C 33300 1278.48 1241 37.48 3.02%

Source: The Author

The aerodynamic model for CLmax prediction was validated to be used in the turbofan optimization since the estimation for TOFL and LFL present errors considered acceptable for this academic analysis. Although the engine model at SL gives a higher static thrust, the values for TOFL and range estimations are consistent with public data and, therefore, the engine model is also validated to be used in the turbofan optimization. The final values for the parasite drag in which miscellaneous drag are included, the oswald coefficient and the CDcompressibility for cruise condition (Mach = 0.78) considering the whole aircraft are presented in Table 16. The CLmax estimations for each flap position is also presented in Table 15. The flap 4 and 5 have the same deflection, however, the first one is assigned to take-off and the other to landing where the landing gear is considered extended. The model used is not capable of differentiating the CLmax according to the landing gear position, hence the values of CLmax for flap 4 and 5 are equal.

Table 15 – E170 - CLmax values Table 16 – E170 - Aerodynamic estimations for drag coeﬃcients

Flap Position CLmax C 0.02317 6 2.733 Dp C 0.00242 5 2.624 Dcompressibility 4 2.624 e 0.79 2 2.130 1 1.989 Source: The Author 0 1.421

Source: The Author Chapter 4. Results and Discussion 52

4.1.2 DoE Analysis

A DoE was conducted using the turbofan aircraft model and the E170 aircraft as the baseline geometry in order to identify the most important geometric design variables in the aircraft design. In this analysis, the engine is considered ﬁxed. The key characteristics considered were selected from the performance parameters deﬁned as constraints in Section 3.2.1. The list below presents the performance indicators chosen to be analyzed in the DoE study.

Block Fuel Time to climb to cruise level Speciﬁc Range in the cruise segment Fuel Burn (block fuel + reserves) TOFL (MTOW, SL, ISA) Second Segment Climb Gradient (MTOW, SL, ISA)

The matrix of experiment is the one presented in Section 3.2.2 and the geometric parameters considered were the area, thickness to chord ratio, taper ratio, sweep angle and aspect ratio of the main wing. Furthermore, the design mission considers 1340 nm of range for the block fuel and reserves calculation, which is also known as the harmonic mission since it represents a mission at MTOW and Full Payload [31]. Table 17 details each segment modeled using SUAVE for the DoE analysis. For climb and descent segments, the values presented for airspeed are mean values since both segments are divided into more subsegments with slightly diﬀerences due to atmospheric changes. The proﬁle chosen for each segment was based on reference [4] and in the tutorials of SUAVE [3] in order to avoid convergence problem in the mission solver during the analysis and optimization. The design mission described in Table 17 is presented in Figure 23 in terms of altitude and distance traveled. Chapter 4. Results and Discussion 53

Table 17 – Design Mission

Segment Considerations Fundamental Parameters

Take-oﬀ MTOW V2 = 1.2 · VS, SL, ISA Maximum Throttle Flap conﬁguration 4

Climb Constant Throttle, δthrottle = 1. Constant Airspeed CAS = 265kts Cruise Constant Altitude, h = 35000ft Constant Airspeed T AS = 450kts Descent Constant Rate, ROD = 2000 ft/min Constant Airspeed CAS = 250kts Reserve Constant Rate, ROC = 2500 ft/min Climb Constant Airspeed T AS = 268kts Reserve 140 nm to alternative h = 15000ft Cruise airport and 30min loiter Mach = 0.5 Reserve Constant Rate, ROD = 590 ft/min Descent Linear Mach Mach0 = 0.3, Machf = 0.24

Landing MZFW Vref = 1.23 · VS, SL, ISA Flap conﬁguration 6

Source: The Author

Figure 23 – Design Mission

Source: The Author

ROD - Rate of descent CAS - Calibrated Airspeed ROC - Rate of Climb h - Altitude T AS - True Airspeed Chapter 4. Results and Discussion 54

The variations for each element in the matrix of experiments were computed as described in Section 3.2.2 for the selected performance characteristics and the normalized results are presented in Table 18 using Equation 3.6. In the table, SSCG stands for second segment climb gradient.

Table 18 – DoE results for turbofan aircraft

Performance S(m2) AR (-) Taper (%) t/c (%) Sweep Angle (°) Matrix Indicators 72.72 8.6 32.75 -11 -23 Variation Block Fuel -0.059% 0.152% -0.026% -0.163% 0.141% Time to Climb -0.348% 0.609% -0.174% -0.609% 0.435% Speciﬁc Range 0.05% -0.134% 0.032% 0.2% -0.139% -5% Fuel Burn -0.04% 0.163% -0.025% -0.126% 0.097% SSCG -0.553% -4.596% -0.825% 0.556% -1.085% TOFL 0.978% -0.025% 0.144% 0.733% 0.047% Block Fuel 0.063% -0.16% -0.007% 0.16 % -0.156% Time to Climb 0.348% -0.609% 0.00% 0.522% -0.609% Speciﬁc Range -0.023% 0.167% 0.014% -0.167% 0.191% 5% Fuel Burn 0.043% -0.171% -0.007% 0.111% -0.121% SSCG -1.182% 2.323% -0.895% -2.266% -0.631% TOFL -0.569% 0.351% 0.177% -0.337% 0.282%

Source: The Author

As observed, the block fuel, specific range and fuel burn are most affected by the aspect ratio, thickness to chord ratio and sweep angle. The block fuel, one of the most important parameters of the present analysis, vary at least ±0.141% if one of these critical parameters changes ±1%. This result is due to the strong dependency of the drag polar in relation to these geometric parameters. As expected, the fuel consumption, and therefore specific range, are mainly impacted by changes in the total drag. The time to climb is mainly affected by all parameters except by the taper ratio and this behavior is also explained by the dependency of the drag polar and total lift. The second segment climb gradient has a small absolute magnitude and hence it is very sensitive to all parameters since it is a function of the aerodynamic efficiency which varies considerably with both drag polar and weight in the second segment of the take-off path. While aspect ratio, thickness to chord ratio and sweep angle directly impact the total drag, the taper ratio main effect is on the empty weight of the wing which has a minor impact on the total drag as observed in the previous results. Finally, the TOFL is most affected by wing area and thickness to chord ratio because these parameters directly impacts on the total lift and

CLmax /BOW respectively. The previous results can also be interpreted using plots where the focus now is to identify the most important design variables in the overall variations. Figure 24 presents the absolute variations for all parameters of interest. Chapter 4. Results and Discussion 55

Figure 24 – DoE results for turbofan aircraft

(a) (b)

(e)

Source: The Author Chapter 4. Results and Discussion 56

As observed, the most impacting design variables are the aspect ratio, area, thickness to chord ratio and sweep angle of the wing. The taper ration presents only a minor eﬀect on the second segment climb gradient. Therefore, the geometric design variables chosen to be used in the formal optimization problem will be the aspect ratio, area, thickness to chord ratio and sweep angle of the main wing.

4.1.3 Pareto Analysis

As discussed in Section 3.2.3, fuel consumption and BOW are widely used as technical objective function in a formal optimization problem where they represent conflicting objectives in the aircraft design. For this reason, the MTOW is also an interesting technical objective function since it is able to integrate fuel consumption and BOW. For a turbofan airplane, the tradeoffs can be first seen by using a carpet plot which relates two geometric design variables with fuel burn and BOW. The figures below present the carper plot considering as parameters the wing area, aspect ratio, thickness to chord ratio and sweep angle. The data used to construct the plots were generated without considering the constraints discussed in Section 3.2.1 since the goal here is to just evaluate the possible tradeoffs in the design space where the conflict of BOW and fuel burn is highlighted for a turbofan aircraft.

Figure 25 – Carpet plot: Aspect ratio vs. Wing Area

Source: The Author Chapter 4. Results and Discussion 57

Figure 26 – Carpet plot: Aspect ratio vs. Sweep Angle

Source: The Author

Figure 27 – Carpet plot: Thickness to chord ratio vs. Sweep Angle

Source: The Author Chapter 4. Results and Discussion 58

As expected, better values of fuel consumption are achieved for higher values of aspect ratio and lower values of wing area. This is explained by the drag polar since an increase in AR means a decrease in the induced drag while lower wing area values allow the aircraft to fly at higher values of aerodynamic efficiency during cruise. The fuel consumption is also decreased for higher values of sweep angle and lower values of thickness to chord ratio due to a reduction in the compressibility drag. The impact on the BOW is almost the opposite since higher values of aspect ratio, sweep angle and lower values of thickness to chord ration tend to increase the empty weight of the wing. With this information, it is expected wings with higher aspect ratio and sweep angle when the objective function is fuel burn. On the other hand, higher values of thickness to chord ratio is expected as solution for MTOW as the objective function. The wing area will play an important role with the constraints since it directly impacts the TOFL and time to climb. The expected tradeoffs in the optimization problem can be confirmed using a pareto strategy as discussed in Section 3.2.3. The formal optimization problem is stated below for the turbofan aircraft. All the constraint values are based on the E170 performance estimations.

∗ ∗ minimize f0(x) = β · Wfuel burn + (1 − β) · MTOW x subject to: MTOW = BOW + F uel Burn + Maximum P ayload MZFW = BOW + Maximum P ayload Design Range = 1340 nm TOFL (MT OW,ISA,SL) ≤ 1520 m (4.1) SSCG (MT OW,ISA,SL) ≥ 0.03 Range H&HTO ≥ 1219.8 nm T ime to Climb ≤ 21.5 min LF L (MLW,ISA,SL) ≤ 1270 m Maximum T hrottle ≤ 1. Maximum F uel Available ≥ 9450 kg.

The optimization was carried out considering diﬀerent values of β and initial guesses. In the initial trials, the convergence of MTOW, BOW and MZFW were not implemented using the design variable strategy discussed in Section 3.2.2, in other words, the values of MTOW and MZFW used to compute the BOW of a given iteration were the values of the previous one in the optimization process. This scenario may lead to numerical diﬃculties since the optimizer is gradient based and the consistency of MTOW, MZFW and BOW is not guaranteed. Therefore, in order to avoid numerical problems, the MTOW Chapter 4. Results and Discussion 59 and MZFW were introduced as design variable which improved the optimizer performance. The bounds considered for each design variable are presented in Table 19.

Table 19 – Turbofan design variable bounds

Design Variable Lower Bound Upper Bound 2 2 Swing 65 m 80 m AR 7.6 9.8 t/c 0.09 0.15 Λ1/4c 15° 30°

Source: The Author

The results are presented in Figure 28, where the points that do not belong to the pareto front are the optimization solutions prior to the design variables modiﬁcation.

Figure 28 – Pareto Chart

Source: The Author

As expected, the fuel burn and MTOW minimization are conflicting as shown by the pareto front in Figure 28. Therefore, a tradeoff is confirmed between a high aerodynamic efficiency configuration versus a solution that also indirectly takes into account the BOW. The discussion regarding the optimized geometries is given in the next section. Chapter 4. Results and Discussion 60

4.1.4 Optimized Geometries

The geometries chosen to be discussed in more detail are the ones for β equals to 0, 0.5 and 1, as deﬁned previously in Section 3.2.3. Figure 29 presents a comparison between the optimal solutions and the reference wing.

Figure 29 – Optimized geometries for β equal 1, 0.5 and 0.

Source: The Author

As can be observed, for all cases the optimizer explore solutions with a high aspect ratio and sweep angle. In fact such characteristics beneﬁt the aerodynamic eﬃciency since both induced and compressibility drag are reduced. However, lower values of these parameters were expected for the MTOW optimization case. The interpretation for this behavior is that the wing weight model may underestimates its weight. For high aspect ratio and sweep angle wings, it is expected weight penalties due to aeroelastic restrictions. The reference [29] also discusses this possible limitation in the SUAVE weight model. Table 20 presents the detailed results for the optimal solutions in contrast to the E170 jet. The constraint values are also compared. Chapter 4. Results and Discussion 61

Table 20 – Optimized geometries for β equal 1, 0.5 and 0.

Design Baseline β = 1 β = 0.5 β = 0.0 Variables Aircraft Fuel Burn MTOW Wing Area [m2] 72.72 75.86 69.94 67.53 Aspect Ratio [-] 8.6 9.8 9.8 9.2 Wing t/c [-] 0.11 0.115 0.131 0.150

Wing Sweep [°] 23 30.0 30.0 30.0 Cruise Distance [nm] 1103.2 1118.3 1118.9 1107.5 MTOW [kg] 37200 37768 37042 36601 MZFW ratio [-] 0.8102 0.8211 0.8163 0.8079

Constraints Bounds TOFL (MTOW, ISA, SL) ≤ 1520 m 1520 m 1520 m 1517 m Second Segment Climb ≥ 0.03 0.0432 0.0410 0.0319 Gradient (MTOW, ISA, SL) Range for H&H TO Condition ≥ 1219.8 nm 1356.1 nm 1355.2 nm 1228.3 nm

(5433 ft, ISA + 23°C) Time to Climb to FL350 ≤ 21.5 min 19.2 min 19.1 min 20.8 min Maximum Fuel ≥ 9420 kg 9876.8 kg 9953 kg 11127.5 kg LFL (MLW, ISA, SL) ≤ 1270 m 1247.8 m 1267.5 m 1270 m Maximum Throttle ≤ 1 1 1 1 Design Range = 1340 nm 1340 nm 1340 nm 1340 nm

Objective Function Value 1.0044 0.9570 0.9799 0.9839 Fuel Burn (kg) 7091.9 6756.4 6805.9 7032.9 Fuel Burn Variation (%) - -4.73 -4.033 -0.832 MTOW (kg) 37200 37768 37042 36601 MTOW Variation (%) - 1.53 -0.425 -1.610

Source: The Author Chapter 4. Results and Discussion 62

For the fuel burn case, the optimal solution has both AR and sweep angle equal to the upper bound presented in Table 19. As discussed previously, higher AR and sweep angle lead to higher aerodynamic efficiency in a transonic aerodynamic regime. However, the drawback in this case is that the BOW is also increased, which causes the MTOW to increase as well. In order to meet the requirements of take-off performance, the optimizer increases the wing area proportionally. The thickness to chord ratio is not reasonably increased as the wing area because a higher thickness to chord increases considerably the compressibility drag which would penalize the fuel burn consumption. As can be observed from Table 20, in fact, the most critical constraint was the TOFL for the fuel burn case. Therefore, it is possible to state that when optimizing fuel burn, it is expected solutions of higher AR, sweep angle, wing area and MTOW. The maximum reduction in fuel burn considering the theoretical models used is 4.73% and the increase in MTOW is 1.53%. The main disadvantage with this approach is that the most efficient airplane in terms of performance is not the most profitable one as discussed by reference [33]. The optimized geometry is more complex and this leads to not just an increase in MTOW but also an increase in the production costs, which may be prohibitive. For the intermediary case where β is equal to 0.5, the objective function considers equally the influence of the fuel burn and MTOW. The AR and sweep angle are also equal to the their upper bound and the TOFL is again the demanding constraint. The main difference between the fuel burn case and the intermediary one is that the optimizer explore solutions of higher thickness to chord ratio in order to increase the CLmax instead of increasing the wing area which causes the BOW to decrease as well as the MTOW. In fact, a higher thickness to chord negatively impacts the compressibility drag, however, a lower MTOW is achieved in comparison to the reference aircraft. The fuel burn reduction was 4.03%, while the MTOW also decreased 0.425%. Finally, for the MTOW case, the sweep angle and thickness to chord ratio are equal to the upper bound and the AR is decreased in comparison to the previous optimal solutions discussed. Moreover, the demanding constraint was the LFL and not the TOFL. The interpretation for this characteristic is similar to the intermediary case where the optimizer explore solutions of higher thickness to chord and CLmax instead of increasing the wing area which causes the MTOW to decrease. The fuel burn reduction is 0.832% and the MTOW decrease is 1.61%. Again, the wing weight model may be non-conservative leading to solutions of higher AR ans sweep angle when compared to the reference aircraft. For the purposes of this academic work, this condition does not disqualify the analysis, but it is important to emphasize that the gains presented here may be overestimated. In addition, just technical objective functions were considered and it is not possible to affirm that the optimal solutions encountered here are in fact more competitive than the reference aircraft in terms of profit. Chapter 4. Results and Discussion 63

4.2 Turboprop Aircraft Results

4.2.1 Aircraft Model and Calibration

The same strategy applied to the E170 model was conducted for the ATR 72-600 aircraft. In this case, the main reference used in the calibration of the model was the speciﬁcation sheet provided by the manufacturer [6]. Furthermore, additional information available for the ATR 72-500 version was also used to evaluate if the SUAVE model properly represents the performance tendency of the ATR 72 aircraft [27]. All the inputs used to model the ATR 72-600 turboprop in SUAVE as well, as the python scripts, are indicated in Appendix A.2. The empty weight breakdown was computed and the results are presented in Table 21. The BOW considered was the one used by the reference [6]. The maximum diﬀerential pressure value used was 6.0 psi, which is consistent with the feasible range discussed in Section 3.1.1.

Table 21 – ATR 72-600 - Empty Weight Breakdown

Component Weight (kg) Horizontal tail 314 Propulsion 1760 Rudder 95 Systems 5602 Fuselage 2264 Landing gear 920 Vertical tail 236 Wing 2548 Empty Weight 13739 Reference 13500 Diﬀerence 239

Source: The Author

The computed diﬀerence was 1.77% for the empty weight and it was decided to apply a decrease of 239 kg in the system’s weight in order to equal the SUAVE estimation for the BOW with public data. The weight model is considered to be satisfactory and validated to be used in the turboprop aircraft optimization. The results for payload range diagram comparison are presented in Figure 30. Table 22 presents the diﬀerences between the SUAVE calculation and reference [6] for ATR 72-600 version. The fuel reserves for each point at the payload range diagram were determined considering the data available in [27], where the fuel reserves must account for alternate airport and holding. Chapter 4. Results and Discussion 64

Figure 30 – ATR 72-600 Payload Range Diagram, FL210, ISA +0°C

Source: The Author

Table 22 – ATR 72-600 Payload Range Diagram, FL210, ISA +0°C

TOW Fuel SUAVE Reference Diﬀerence Diﬀerence (-) Available (kg) Range (nm) Range (nm) (nm) (%) MTOW 2000 494 500 -6 -1.2% MTOW 5000 1660 1655 5 0.3% BOW + Fuel 5000 1885 1895 -10 -0.5%

Source: The Author

These results were achieved by applying an increase in the parasite drag estimated by SUAVE for a turboprop. The total increment was 21.4 drag counts in the parasite drag coefficient in order to approximate the calculation to more realistic values of miscellaneous drag. The final parasite drag coefficient is 280 drag counts and the oswald coefficient estimated for the ATR 72-600 is 0.716. The absolute maximum error calculated was 1.2% which is considered acceptable. The semi-empirical aerodynamic model for CD prediction was calibrated and the engine model was compared with the data available in [27] which validated the SFC estimation. The TOFL model was compared to ATR 72-600 specification sheet in order to compute the absolute differences. The model was also compared to the ATR 72-500 data which provided detailed information about TOFL values and thus it could be used to Chapter 4. Results and Discussion 65 evaluate the model tendency. The comparison with SUAVE results and reference [27] for ATR 72-500 is presented in Figure 31 for SL, ISA condition. The absolute differences are presented in Table 23 considering the ATR 72-600 public data [6].

Figure 31 – ATR 72-600 (SUAVE) vs ATR 72-500 - TOFL, ISA +0°C

Source: The Author

Table 23 – ATR 72-600 - TOFL estimation

Condition TOW SUAVE Reference Diﬀerence Diﬀerence (kg) TOFL (m) TOFL (m) (m) (%) MTOW, SL, ISA +0°C 23000 1389.67 1367 22.67 1.7%

TOW for 300nm, full PAX 21200 1192.98 1175 17.98 1.5 % SL, ISA +0°C TOW for 300nm, full PAX 21200 1438.36 1410 28.36 2.0 % 3000 ft, ISA +10°C

Source: The Author

As observed, the TOFL curves reasonably captures the tendency presented by the reference values [27]. Furthermore, the maximum error for the TOFL was 2.0% which is considered acceptable. For the WAT estimation, only data related to Denver International Airport was available. The table below presents the comparison for the second segment climb gradient estimation considering as TOW the WAT informed by the manufacturer [6]. Chapter 4. Results and Discussion 66

Table 24 – ATR 72-600 - Second Segment Climb Gradient γ estimation

Condition Flap SUAVE Reference Diﬀerence Deﬂection γ (%) γ (%) (%) TOW of 21000 kg 15° 2.37 2.40 -1.3 5333 ft, ISA +23°C

Source: The Author

The aerodynamic model for L/D prediction in the second segment regarding turboprop aircraft is considered validated due to the results above. The engine model was not modiﬁed since it was compared to the data available in [27]. For LFL, the model was compared and calibrated considering the data presented in [6]. The results are presented in Table 25.

Table 25 – ATR 72-600 - LFL estimation

Condition TOW SUAVE Reference Diﬀerence Diﬀerence (kg) LFL (m) LFL (m) (m) (%) MLW, SL, ISA +0°C 22350 916.55 915 1.55 0.17%

LW with full PAX + reserves 21000 864.96 862 2.96 0.34% SL, ISA +0°C

Source: The Author

The CLmax estimated by SUAVE for both take off and landing flap deflections (15° and 30°) was increased by a multiplication factor of 1.18 since it was underestimated by the SUAVE model when compared to data available in [27]. The final results for the

aerodynamic model are presented in Tables 26 and 27. The aerodynamic model for CLmax prediction was calibrated and validated to be used in the turboprop optimization since the estimation for TOFL and LFL present errors considered acceptable for this academic analysis. The engine model is also considered validated as well as the model for drag prediction.

Table 26 – ATR 72-600 - CLmax values Table 27 – ATR 72-600 - Aerodynamic estimations for drag coeﬃcients

Flap Deﬂection CLmax C 0.028 30° 2.63 Dp e 0.716 15° 2.18 0° 1.63 Source: The Author Source: The Author Chapter 4. Results and Discussion 67

4.2.2 DoE Analysis

A DoE was conducted using the turboprop aircraft model and the ATR 72-600 aircraft as the baseline geometry in order to identify the most important geometric design variables in the aircraft design. In this analysis, the engine is considered fixed. The key characteristics considered were selected from the performance parameters defined as constraints in Section 3.2.1. The list below presents the performance indicators chosen to be analyzed in the DoE study. Here the climb throttle was chosen instead of time to climb because the climb profile used in the turboprop mission is the ”Constant Rate Constant Equivalent Airspeed” due to convergence problems in the mission solver, hence, the time to climb is fixed and the throttle is variant with time.

Block Fuel Climb Throttle Available Fuel for Hot & High condition - Denver Airport (Fuel HH) Fuel Burn (block fuel + reserves) Second Segment Climb Gradient (MTOW, SL, ISA) TOFL (MTOW, SL, ISA) The same considerations for the turbofan aircraft were applied in the turboprop DoE study. The design mission considers 500 nm of range and Table 28 details each segment modeled using SUAVE. The rate of climb presented is a mean value since the climb segment is divided into more subsegments with diﬀerences due to atmosphere changes. The design mission described in Table 28 is presented in Figure 32 in terms of altitude and distance traveled. Chapter 4. Results and Discussion 68

Table 28 – Design Mission

Segment Considerations Fundamental Parameters

Take-oﬀ MTOW V2 = 1.143 · VS, SL, ISA Maximum Throttle Flap Deﬂection 15° Climb Constant Rate, ROC = 800 ft/min Constant Airspeed EAS = 170kts Cruise Constant Altitude, h = 21000ft Constant Airspeed T AS = 260kts Descent Constant Rate, ROD = 2000 ft/min Constant Airspeed CAS = 250kts Reserve Constant Rate, ROC = 900 ft/min Climb Constant Airspeed T AS = 180kts Reserve 35 nm to alternative h = 10000ft Cruise airport and 45min loiter Mach = 0.38 Reserve Constant Rate, ROD = 800 ft/min Descent Linear Mach Mach0 = 0.3, Machf = 0.2

Landing MZFW Vref = 1.23 · VS, SL, ISA Flap Deﬂection 30°

Source: The Author

Figure 32 – Design Mission

Source: The Author Chapter 4. Results and Discussion 69

The variations for each element in the matrix of experiment were computed as described in Section 3.2.2 for the selected performance characteristics and the normalized results are presented in Table 18 using Equation 3.6.

Table 29 – DoE results for turboprop aircraft

Performance S(m2) AR (-) Taper (%) t/c (%) Sweep Angle (°) Matrix Indicators 61 12 53 15 3 Variation Block Fuel -0.13% 0.16% -0.004% -0.028% 0.0004% Climb Throttle -0.05% 0.23% -0.008% -0.002% 0.0004% Fuel HH -3.50% -6.28% 0.185% -1.361% 0.0063% -5% Fuel Burn -0.16% 0.14% -0.004% -0.029% 0.0004% SSCG -0.63% -1.09% 0.033% -0.235% 0% TOFL 0.81% -0.20% -0.033% 0.224% -0.0003% Block Fuel 0.16% -0.14% 0.005% 0.037% 0.0001% Climb Throttle -0.09% 0.20% -0.009% -0.011% -0.0005% Fuel HH 3.09% 5.59% -0.182% 1.261% -0.0082% 5% Fuel Burn 0.18% -0.12% 0.005% 0.036% 0.0001% SSCG 0.52% 0.91% -0.036% 0.195% -0.0031% TOFL -0.70% 0.22% 0.040% 0.008% 0.0019%

Source: The Author

As observed, the block fuel, fuel burn and climb throttle are most affected by the AR and wing area. The block fuel vary at least ±0.13% if one of these critical parameters changes ±1%. The explanation for this result is similar to the one discussed in the turbofan DoE. There is a strong dependency of the total drag in relation to these geometric parameters in a subsonic aerodynamic regime. The SSCG has a small absolute magnitude and hence it is very sensitive to all parameters since it is a function of the aerodynamic efficiency which varies considerably with both drag polar and weight in the second segment of the take-off path. The fuel for hot & high (HH) condition is given by the TOW, which is a function of the SSCG, minus the payload and BOW. In consequence, the fuel HH is also a function of SSCG and it is very sensitive to all parameters as well. While aspect ratio impact the total drag, the taper ratio main effect is on the empty weight of the wing, which has a minor impact on the total drag as observed in the previous results. The sweep angle influence is negligible since the aerodynamic regime is subsonic and there is no compressibility drag. Finally, the TOFL is most affected by area and thickness to chord ratio because they directly impacts on the total lift, CLmax and BOW. The previous results can also be interpreted using plots, where the focus now is to identify the most important design variables in the overall variations. Figure 24 presents the absolute variations for all parameters of interest. As observed, the most impacting design variables are the aspect ratio, wing area and thickness to chord ratio and, therefore, they are chosen to be the design variables. Chapter 4. Results and Discussion 70

Figure 33 – DoE results for turboprop aircraft

(a) (b)

(e)

Source: The Author Chapter 4. Results and Discussion 71

4.2.3 Pareto Analysis

The approach used in the turbofan optimization was applied for turboprop optimization and carpet plots were generated in order to evaluate the possible tradeoﬀs in the design space, where the conﬂict of BOW and fuel burn is highlighted for a turboprop aircraft. Figures 34, 35 and 36 presents the results.

Figure 34 – Carpet plot: Aspect Ratio vs. Wing Area

Source: The Author

Figure 35 – Carpet plot: Aspect Ratio vs. Thickness to Chord Ratio

Source: The Author Chapter 4. Results and Discussion 72

Figure 36 – Carpet plot: Thickness to Chord Ratio vs. Wing Area

Source: The Author

Similar to the turbofan, better values of fuel consumption are achieved for higher values of aspect ratio and lower values of wing area. The fuel consumption is also decreased for lower values of thickness to chord ratio due to a reduction in the proﬁle drag. The impact on the BOW is almost the opposite since higher values of aspect ratio and lower values of thickness to chord ratio tend to increase the empty weight of the wing. With this information, it is expected wings with higher aspect ratio when the objective function is fuel burn for the turboprop optimization. On the other hand, lower values of AR are expected as solution for MTOW as the objective function. The wing area will play an important role considering the constraints since it directly impacts the TOFL and LFL. Chapter 4. Results and Discussion 73

The expected tradeoﬀs in the optimization problem can be conﬁrmed using a pareto strategy as discussed in Section 3.2.3. The formal optimization problem is stated in Equation 4.2 for the turboprop aircraft. All the constraint values are based on the ATR72-600 performance estimations.

∗ ∗ minimize f0(x) = β · Wfuel burn + (1 − β) · MTOW x subject to: MTOW = BOW + F uel Burn + Maximum P ayload MZFW = BOW + Maximum P ayload Design Range = 500 nm TOFL (MT OW,ISA,SL) ≤ 1391 m (4.2) SSCG (MT OW,ISA,SL) ≥ 0.037 Range H&HTO ≥ 335 nm T hrottle Climb ≤ 1. LF L (MLW,ISA,SL) ≤ 917 m Maximum T hrottle ≤ 1. Maximum F uel Available ≥ 5000 kg.

The optimization was carried out considering diﬀerent values of β and initial guesses. In the initial trials, the design variables were the wing area, thickness to chord ratio and aspect ratio and it was observed that the variations of fuel burn and MTOW were lower than the ones encountered for the turbofan aircraft. In order to allow more degrees of freedom in the design, the taper ratio was also included in the optimization as a design variable. The bounds considered for each design variable are presented in Table 30.

Table 30 – Turboprop design variable bounds

Design Variable Lower Bound Upper Bound 2 2 Swing 50 m 72 m AR 10 14 t/c 0.11 0.18 λ 0.3 0.7

Source: The Author

The results are presented in Figure 37, where the points that do not belong to the pareto front are the optimization solutions prior to the design variables modiﬁcation. Chapter 4. Results and Discussion 74

Figure 37 – Pareto Chart

Source: The Author

As expected, the fuel burn and MTOW minimization are conflicting, as shown by the pareto front in Figure 37 for the turboprop aircraft. The main difference between the turbofan and turboprop optimization was the achievable reduction in both fuel burn and MTOW since the turboprop based on the ATR 72-600 aircraft has shown to be closer to the optimal solutions than the E170 jet was considering only technical objective function. Moreover, a trade-off is also confirmed between a high aerodynamic efficiency configuration versus a solution that also indirectly takes into account the BOW for the turboprop airplane. The discussion regarding the optimized geometries is given in the next section. Chapter 4. Results and Discussion 75

4.2.4 Optimized Geometries

The geometries chosen to be discussed in more detail are the ones for β equals to 0, 0.5 and 1, as deﬁned previously in Section 3.2.3. Figure 38 presents a comparison between the optimal solutions and the reference wing.

Figure 38 – Optimized geometries for β equal 1, 0.5 and 0.

Source: The Author

As can be observed, for the fuel burn case, the optimizer explore geometries with a high aspect ratio while decreasing the taper ratio in order to decrease the BOW. In fact such characteristics benefit the aerodynamic efficiency since the induced drag is reduced due to two reasons. The first one is related to a reduction in the CL which is function of the MTOW, and the second reason is given by a decrease in the factor k, which is a function of the AR in the drag polar 2 terms equation. Other impacts are discussed in the next paragraphs considering the taper ratio influence. For the intermediary and MTOW cases, the aspect ratio value is lower than the one encountered for fuel burn case and the taper ratio is further decreased. Table 31 presents the detailed results for the optimal solutions in contrast to the ATR 72-600 aircraft. The constraint values are also compared. Chapter 4. Results and Discussion 76

Table 31 – Optimized geometries for β equal 1, 0.5 and 0.

Design Baseline β = 1 β = 0.5 β = 0.0 Variables Aircraft Fuel Burn MTOW Wing Area [m2] 61 62.18 60.56 60.69 Aspect Ratio [-] 12 14.00 12.05 11.81 Taper ratio [-] 0.53 0.385 0.335 0.3 Wing t/c [-] 0.15 0.157 0.153 0.160 MTOW [kg] 23000 23280 22875 22789 MZFW ratio [-] 0.9130 0.9149 0.9124 0.9117

Constraints Bounds TOFL (MTOW, ISA, SL) ≤ 1391 m 1327.51 m 1306.52 m 1303.13 m Second Segment Climb ≥ 0.037 0.0464 0.0401 0.0397 Gradient (MTOW, ISA, SL) Range for H&H TO Condition ≥ 335 nm 732.9 nm 393.3 nm 373.8 nm

(5433 ft, ISA + 23°C) Maximum Fuel ≥ 5000 kg 5000 kg 5053.7 kg 5524.6 kg LFL (MLW, ISA, SL) ≤ 917 m 917 m 917 m 917 m Maximum Throttle ≤ 1. 1 1 1 Design Range = 500 nm 500 nm 500 nm 500 nm

Objective Function Value 1.00453 0.99056 0.99825 0.99081 Fuel Burn (kg) 2009.05 1981.1 2003.9 2013.1 Fuel Burn Variation (%) - -1.39 -0.256 -0.202 MTOW (kg) 23000 23280 22875 22789 MTOW Variation (%) - 1.22 -0.543 -0.917

Source: The Author Chapter 4. Results and Discussion 77

For the fuel burn case, the optimal solution has the aspect ratio equal to the upper bound presented in Table 30. The drawback in this case is that the BOW is also increased which causes the MTOW to increase as well. On the other hand, the taper ratio was decreased in comparison to the reference aiming at reducing the BOW while the thickness to chord ratio had to be increased in order to satisfy the constraint of maximum fuel available on the wing tanks. The concern here is related to a possible tip stall in which the sections closer to the tip, where the aileron is usually located, stall first. A lower taper ratio decreases the chords closer to the tip which causes the local lift coefficient to increase in this region in comparison to a wing of higher taper ratio. Therefore, the sections closer to the tip are going to reach the maximum lift coefficient earlier than the others which causes a tip stall. Moreover, the taper ratio modifies the wing loading for a fixed CL which may decrease the oswald coefficient for loadings considerably different from the elliptical one. In consequence, an expressive decrease in the taper ratio may also cause an increase in the induced drag which is being considered in the aerodynamic model used in the SUAVE software. For the tip stall problem, there is no implemented constraint that prevents the optimizer to decrease the taper ratio in other to avoid the tip stall. A strategy to deal with this problem in future analysis could be the implementation of a constraint in which the section that reaches the maximum lift coefficient first is geometrically limited. Since this consideration was not made, the optimized results may be overestimated which is still acceptable in the scope of this academic analysis. For the requirement related to the landing performance, the optimizer increases the wing area proportionally to the increase in MTOW. Therefore, it is possible to state that when optimizing fuel burn, it is expected solutions of higher AR, wing area and MTOW. The maximum reduction in fuel burn considering the theoretical models used is 1.39% and the increase in MTOW is 1.22%. The main disadvantage with this approach is that the most efficient airplane in terms of performance is not the most profitable one as discussed by reference [33]. The optimized geometry is more complex and this lead to not just an increase in MTOW but also an increase in the production costs which may be prohibitive. For the intermediary case where β is equal 0.5, the AR is lower than value encountered in the fuel burn case and the LFL is again the demanding constraint. Another difference between the fuel burn case and the intermediary one is that the optimizer explore solutions of even lower taper ratio in order to decrease the BOW as well as the MTOW. The fuel burn reduction was 0.256% while the MTOW also decreased 0.543%. Finally, for the MTOW case, the thickness to chord ratio is the highest value of all optimization cases while AR is the lowest. Moreover, the demanding constraint was again the LFL. The interpretation for this characteristic is that the optimizer explore solutions of higher t/c and CLmax instead of increasing the wing area which causes the MTOW to decrease. The fuel burn reduction is 0.202% and the MTOW decrease is 0.917%. Chapter 4. Results and Discussion 78

In order to improve the results for all optimization cases, a more complex high lift device or a bigger flap deflection could be considered to increase the CLmax in the landing condition. This consideration was not applied in order to maintain the optimized geometries similar to the reference one where just wing geometric parameters were modified. Otherwise, the same improvement would have to be taken into account for the turbofan aircraft as well. Furthermore, similar to the turbofan optimization, it is important to emphasize that the results presented here may not represent real achievable gains since some considerations or models are non-conservative. In addition, just technical objective functions were considered and it is not possible to affirm that the optimal solutions encountered here are in fact more competitive than the reference aircraft in terms of profit.

4.3 Turbofan and Turboprop Comparison

The E170 jet and the ATR 72-600 compete in the regional aviation market where both aircraft offer a similar passenger capability while performing in general missions of medium and short range. This work aims at comparing the optimized geometries of each airplane in order to define which aircraft type best suits the aviation market given a defined criterion. As discussed in Chapter 3, the methodology was structured in three steps in order to avoid skewing of the comparison. The first one was the model calibration using the public data from the E170 jet and ATR 72-600 aircraft. The modeling environment used was the SUAVE software in which semi-empirical models were applied in order to properly represent each aircraft. An optimization was carried out for both E170 and ATR 72-600 as baseline geometries considering different objective functions. The purpose of this section is to evaluate the optimized geometries following the approach described in Section 3.3. The comparison first considers the mission parameters, then the payload load range is also analyzed followed by the specific range, block fuel and block time.

4.3.1 Mission Parameters

As previously introduced, the mission performed by a turboprop and turbofan differs considerably. Table 32 presents a comparison between the main parameters that define the mission performance. The values presented in Table 32 are equal for all geometries since they are performance requirements inputted in the optimization process. The only two values that change from one aircraft to another is the time to climb and fuel available. The first one varies for the turbofan airplanes modeled since the mission implemented considers the climb segment with throttle fixed hence the rate of climb is a variable for each geometry. For the turboprop aircraft, the mission implemented considers a climb segment with fixed rate of climb due to convergence problems as previously discussed. In consequence, the rate of climb is fixed for all geometries considering the design mission Chapter 4. Results and Discussion 79 implemented for the turboprop aircraft model. For the fuel available, the variation is due to geometric changes in the total volume available on the wing for fuel tanks. Although the maximum fuel constraint enforces a minimum value for the available fuel, some optimized geometries may present a higher value. In the following analysis, the maximum fuel available is considered equal to the baseline geometry in order to isolate the impact due to the empty weight and aerodynamic efficiency variation.

Table 32 – Mission parameters comparison

Parameter Turbofan Turboprop Diﬀerence (abs) Diﬀerence (%) Cruise Altitude (ft) 35000 21000 14000 -40.0 Time to Climb* (min) 21.5 32.8 11.3 52.6 Cruise Speed (KTAS) 450 260 190 -42.2 Maximum Payload (kg) 9404 7500 1904 -20.2 Fuel Available* (kg) 9428 5000 4428 -47.0

Source: The Author

(*) - Time to climb and maximum fuel available vary for each aircraft, the values presented in the table are based on the E170 and ATR 72-600 airplanes.

As can be observed from Table 32, the cruise altitude of the airplanes are expressively different. The turbofan cruise altitude is 35000 ft while the turboprop cruise is at 21000 ft. It is important to emphasize that the turboprop aircraft with the PW127 engine [36, 37] may reach higher altitudes if the TOW is less than the MTOW. Although some references [27] present cruise altitudes higher than 21000 ft, they perform the calculation for lower values of TOW. The cruise altitude is a direct consequence of the propulsion type since a turboprop engine presents a more limited flight envelope than the one encountered for the turbofan engine as discussed in Section 2.2.4. The main reason is related to the propeller limitation of mach on the blade tip in order to avoid shock waves and hence a decrease in the propulsive efficiency. In higher cruise altitudes, the aircraft mach increases for a fixed true airspeed due to variations on the speed of sound with the atmosphere. Therefore the blade tip reaches the mach 1 earlier in higher altitudes for a fixed true airspeed and propeller rotation which limits the turboprop altitude envelope. Moreover, the power generated by the gas turbine also decreases with altitude which contributes to the service ceiling definition. For the cruise speed, the same explanation applies since the turboprop is also limited in terms of aircraft speed in order to avoid a decrease in the propulsive efficiency. In addition, the gas turbine for the turboprop engine is not designed to generate the power required to fly at a higher cruise airspeed. Therefore, the cruise speed is 42.2% higher for the E170 jet which correspond to a mach 0.78 in the cruise altitude. Chapter 4. Results and Discussion 80

The maximum payload is also 20.2% bigger for the turbofan which, in this case, may be explained by market demands of increased payload capacity. The aircraft can transport passengers and their luggage as well as cargo which may be part of the airlines services. The fuel available in the regional aviation context is mainly a consequence of the available volume that can be used as fuel tanks in the wing. Since the turbofan wing volume is bigger, the E170 jet presents a fuel capacity 47% bigger than the one presented by the ATR 72-600 airplane. The fuel capacity may also be a market requirement since the airlines may plan to carry more fuel to one airport to another or due to desired routes of increased distance. In this case, the E170 shows to be a more ﬂexible aircraft since it is able to carry more fuel or travel longer distances if desired. Since the time to climb may vary between the turbofan aircraft, Table 33 presents a detailed information in which the time to climb is given for each optimized geometry in comparison to the turboprop airplanes.

Table 33 – Time to climb to cruise altitude, MTOW - Comparison

Time to Baseline β = 1 β = 0.5 β = 0.0 Climb (min) Aircraft Fuel Burn MTOW Turbofan, FL350 21.5 19.2 19.1 20.8 Turboprop, FL210 32.8 32.8 32.8 32.8 Diﬀerence (abs) 11.3 13.6 13.7 12.0 Diﬀerence (%) 52.6 70.8 71.7 57.7

Source: The Author

As can be observed, the optimized geometries for the turbofan airplane present an increased climb performance when compared to the E170 aircraft. This is mainly due to an increase in the aerodynamic eﬃciency since all the optimized geometries present at least a higher sweep angle than the reference aircraft. In comparison to the turboprop, the turbofan airplanes overcome its competitor by at least 52.6% in the time to climb to cruise altitude which is even higher for the turbofan. Therefore, it is possible to state that the turbofan aircraft is faster than the turboprop considering climb performance and cruise speed. This increased speed has a price which can be seen in the BOW and MTOW comparison in Tables 34 and 35 since the speed directly impacts the loads envelope and, hence, the empty weight as well. Chapter 4. Results and Discussion 81

Table 34 – BOW comparison

BOW Baseline β = 1 β = 0.5 β = 0.0 (kg) Aircraft Fuel Burn MTOW Turbofan 20737 21618 20839 20196 Turboprop 13500 13802 13371 13272 Diﬀerence (abs) -7237 -7816 -7468 -6924 Diﬀerence (%) -34.9 -36.2 -35.8 -34.3

Source: The Author

Table 35 – MTOW comparison

MTOW Baseline β = 1 β = 0.5 β = 0.0 (kg) Aircraft Fuel Burn MTOW Turbofan 37200 37768 37042 36601 Turboprop 23000 23280 22875 22789 Diﬀerence (abs) -14200 -14488 -14167 -13812 Diﬀerence (%) -38.2 -38.4 -38.2 -37.7

Source: The Author

Both MTOW and BOW present a similar diﬀerence between the turboprop and turbofan aircraft which is consistent with the cruise airspeed of each airplane. As stated previously, the loads envelope is a function of the aircraft maximum cruise speed which can be clearly represented by the V-n Diagram required by the aeronautical regulations. Therefore, an aircraft of higher speed must ﬁrst pay the price in the BOW since the empty weight will inherently increase. The aircraft speed also impacts in the engine performance which will be discussed in Section 4.3.3.

4.3.2 Payload Range Diagram

The payload range diagram offers a visual comparison between the airplanes in terms of maximum range given a fixed payload. In other words, it is possible to see the capability of each aircraft type in terms of range as well as what are the impacts of each optimized geometry on the range estimation considering that all optimized airplanes present the same maximum fuel available. The fuel reserves were determined considering reference [27] for the turboprop aircraft. For the turbofan, the reserve mission profile described in Section 4.1.2 was considered. In addition, the burned fuel during taxi, take-off and landing was also subtract from the total fuel in order to isolate the exactly fuel available for climb, cruise and descent. The payload range diagram considers the design range which takes into account the distance traveled during climb, cruise and descent. Figure 39 presents the results Chapter 4. Results and Discussion 82 for all optimized geometries and for the baseline aircraft. The dotted lines represents the turboprop airplanes while the others present the results for the turbofan aircraft.

Figure 39 – Payload Range Diagram Comparison

Source: The Author

All aircraft were designed to have the same range for the harmonic mission considering as performance requirement the values for E170 and ATR 72-600. Therefore, the points that correspond to MTOW and maximum payload coincide between the airplanes of same type. As expected, a more expressive variation on the other points can be observed for the turbofan aircraft since the optimization results showed a maximum gain on the fuel burn of 4.73% while the reduction for the turboprop was only 1.39%. This means that the optimized geometries considering a turbofan has a higher aerodynamic efficiency which allow them to fly further at MTOW and maximum fuel since they burn less fuel per unit of distance. The same variation on the curves can be observed for the turboprop but it is less expressive. Since the maximum fuel available presented in Table 32 is different for each aircraft, the maximum range is also different. The turbofan is capable of performing a mission of higher range given a fixed payload when compared to the turboprop aircraft due to the increased fuel capacity. Moreover, it is widely known that the range is a function of the aerodynamic efficiency, fuel available, TSFC, TOW and cruise speed. Therefore, it can be state that the payload range diagram shows the range difference where the fuel capacity impact is the most highlighted. The impact of the other parameters is discussed in the next section. Chapter 4. Results and Discussion 83

4.3.3 Speciﬁc Range

The specific range is considered in this comparison in order to remove the fuel capacity influence and only to consider the engine, weight and aerodynamic characteristics impact on the cruise performance. The instantaneous specific range is given by Equation 4.3 as introduced in Section 3.3.

V L 1 SR = · · (4.3) TSFC D W

The first comparison considers the term given by the ratio between the cruise true airspeed and the TSFC. For the turboprop aircraft, the TSFC computation was directly made by taking the thrust at the initial cruise and the fuel weight flow. The design mission simulated using SUAVE is the same presented in Section 4.2.2. For the turbofan aircraft, the engine model considers the TSFC as a function of the overall pressure ratio of the gas turbine, airspeed, altitude and ISA variations. Therefore, the TSFC for the turbofan airplanes is equal given the same flight condition. The values for each turboprop aircraft are presented in Table 36.

Table 36 – TSFC comparison

TSFC Baseline β = 1 β = 0.5 β = 0.0 (h−1) Aircraft Fuel Burn MTOW Turbofan 0.7001 0.7001 0.7001 0.7001 Turboprop 0.4037 0.4062 0.4041 0.4037 Diﬀerence (abs) -0.2964 -0.2939 -0.2960 -0.2968 Diﬀerence (%) -42.3 -42.0 -42.3 -42.4

Source: The Author

The TSFC increases with a decrease in throttle since a throttle less than one at cruise implies that the turboprop engine deviated from the design point. This does not mean that the absolute fuel consumption increased since the fuel weight ﬂow is proportional to the decrease in the thrust required. Therefore, it is observed an increase in the TSFC for the optimized geometries that presented a reduction in the fuel burn since these results are due to a decrease in the thrust required in comparison to the reference turboprop aircraft. Moreover, it can be observed from Table 36 that the TSFC for a turboprop is at least 42% less than the value computed for a turbofan airplane. This result is one of the reasons why the common sense believes that the turboprop aircraft consumes less fuel. In other words, the lower TSFC is usually related to the turboprop aircraft reduced fuel consumption as the only critical and decisive parameter. However, as previously shown, the turboprop aircraft is slower than the turbofan. Therefore, in order to evaluate each propulsion type, the airspeed must be taken into account. The TSFC and true airspeed Chapter 4. Results and Discussion 84 ratio can be compared in order to provide such perspective. Table 37 presents the values of the ratio for the E170 jet and ATR 72-600 aircraft. The TSFC considered for the turboprop is the one calculated for the ATR 72-600.

Table 37 – True airspeed and TSFC ratio comparison

Parameter Turbofan Turboprop Diﬀerence (abs) Diﬀerence (%) V [m/s] 231.5 133.76 -97.74 -42.2% TSFC [h−1] 0.7001 0.4037 -0.2964 -42.3% TSFC [s−1] 1.945 · 10−4 1.121 · 10−4 8.233 · 10−5 -42.3% V 6 6 3 TSFC [m] 1.1904 · 10 1.1928 · 10 2.4 · 10 0.2%

Source: The Author

Surprisingly, the ratio between the airspeed and TSFC are almost the same for the turbofan and turboprop aircraft which undermines the common belief that the turboprop airplane burns less fuel due to the engine exclusively without considering the airframe integration. Therefore, the explanation for why a turboprop aircraft consume less for a fixed range must be related to the aerodynamic efficiency or the MTOW. Table 38 presents the comparison between the aerodynamic efficiency for the turbofan and turboprop aircraft.

Table 38 – L/D comparison

L/D Baseline β = 1 β = 0.5 β = 0.0 (-) Aircraft Fuel Burn MTOW Turbofan 13.76 15.00 14.44 13.58 Turboprop 14.66 15.19 14.62 14.51 Diﬀerence (abs) 0.90 0.19 0.18 0.93 Diﬀerence (%) 6.54 1.27 1.25 6.85

Source: The Author

It was expected the turbofan L/D to be higher than the value presented by the turboprop aircraft. Since the missions here are for MTOW, the CL at which the turboprop flies is higher than it is usually observed in the operation. The cruise altitude also impacts the CL at cruise and different altitudes are also observed for the ATR72-600 aircraft. These discrepancies may increase the L/D estimated here for the turboprop airplane. In addition, since the model calibration considered the final performance estimations, it is possible to have errors in the engine and aerodynamic model that cancel each other. This does not compromises the comparison since the match of range captures the main trends, however, it is important to highlight possible limitations on the models used due to the lack of detailed and official information. Chapter 4. Results and Discussion 85

As expected, all geometries optimized for β equal to 1 and 0.5 presents a higher aerodynamic efficiency in comparison to the baseline geometry. For β equal to 0, the decrease in MTOW penalizes the aerodynamic efficiency for both turbofan and turboprop aircraft. Moreover, the variation in L/D is more expressive for the turbofan airplane which is consistent with the maximum fuel reduction encountered. For all β values including the reference aircraft, the turboprop airplane has shown to have a higher aerodynamic efficiency. However, this difference is small and still not explain the fuel consumption discrepancy between the turboprop and turbofan airplanes. Finally, the last term to be compared is the MTOW which was presented in Table 35. In fact, the discrepancy in the MTOW is expressive as previously discussed. In order to gather the previous information, Table 39 presents the values for each term in the specific range equation considering the optimized geometries for β equal to 1.

Table 39 – Speciﬁc range comparison - E170 versus ATR 72-600

Parameter Turbofan Turboprop Diﬀerence (abs) Diﬀerence (%) V 6 6 3 TSFC [m] 1.1904 · 10 1.1928 · 10 2.4 · 10 0.2% L D [-] 15.00 15.19 0.19 1.27 1 −1 −6 −6 −6 W [N ] 2.70 · 10 4.38 · 10 1.68 · 10 38.0 SR [m/N] 48.21 79.36 31.15 39.3

Source: The Author

As can be observed, the turboprop aircraft flies a higher distance per unit of fuel weight and the critical parameter in this result is the expressive difference between the turboprop and turbofan MTOW. The engine impacts the airspeed envelope of the aircraft which in consequence influences the loads magnitude and also the empty weight. Therefore, it is possible to state that the engine type choice in an aircraft design indirectly impacts its fuel burn by impacting first the BOW and MTOW. Of course other factors are of important influence in the fuel burn calculation, however, the results presented here show that one of the main reasons why the turboprop burn less fuel than a turbofan aircraft is due to its low MTOW value.

4.3.4 Block Fuel and Block time

The previous section discussed one of the main reasons why a turboprop aircraft burns less fuel per unit of distance in contrast to a turbofan airplane for the same passenger capability. The comparison now focus on the absolute values of block fuel and block time for different ranges in order to define what is the best aircraft when the criteria is fuel consumption or block time. Figure 40 and Tables 40, 41 and 41 present the block fuel for the turboprop and turbofan aircraft as well as the difference calculated in percentage. Chapter 4. Results and Discussion 86

The mission proﬁles considered for each aircraft are the ones presented in Section 4.1.2 and Section 4.2.2. Moreover, it is important to emphasize that the turboprop airplanes have a smaller payload capacity in comparison to the turbofan aircraft which forces the turboprop to perform a mission of higher range with less passengers. This is one of the reasons why the turboprop is not competitive for longer missions since the possible number of passengers is smaller in contrast to the turbofan airplanes. Although the turboprop presents this limitation, the block fuel and block time were computed for a maximum distance of 1500 nm in order to provide an analysis for diﬀerent scenarios.

Table 40 – Block fuel for turbofan airplanes

Block Baseline β = 1 β = 0.5 β = 0.0 Fuel (kg) Aircraft Fuel Burn MTOW 250 nm 1100.1 1063.0 1059.4 1085.7 500 nm 2115.1 2013.3 2025.2 2097.7 750 nm 3109.9 2948.1 2973.3 3088.7 1000 nm 4085.4 3867.9 3904.6 4059.8 1250 nm 5042.6 4773.4 4819.7 5011.7 1500 nm 5982.3 5665.3 5719.3 5945.5

Source: The Author

Table 41 – Block fuel for turboprop airplanes

Block Baseline β = 1 β = 0.5 β = 0.0 Fuel (kg) Aircraft Fuel Burn MTOW 250 nm 661.6 649.4 660.1 663.7 500 nm 1252.9 1231.7 1250.0 1256.5 750 nm 1836.3 1807.1 1832.1 1841.4 1000 nm 2412.2 2375.8 2406.7 2418.6 1250 nm 2980.6 2937.9 2973.8 2988.3 1500 nm 3541.8 3493.2 3533.6 3550.7

Source: The Author Chapter 4. Results and Discussion 87

Table 42 – Block fuel comparison

Diﬀerence in Baseline β = 1 β = 0.5 β = 0.0 Block Fuel (%) Aircraft Fuel Burn MTOW 250 nm -39.9 -38.9 -37.7 -38.9 500 nm -40.8 -38.8 -38.3 -40.1 750 nm -41 -38.7 -38.4 -40.4 1000 nm -41 -38.6 -38.4 -40.4 1250 nm -40.9 -38.5 -38.3 -40.4 1500 nm -40.8 -38.3 -38.2 -40.3

Source: The Author

Figure 40 – Block Fuel Comparison

Source: The Author

The differences computed for block fuel are consistent with the difference calculated in the specific range in Table 39. The turboprop airplanes burn at least 38.2% less than a turbofan aircraft for the same range. Moreover, it can be observed that the block fuel difference is lower for the optimized geometries considering β equal to 0 and 0.5 which is explained by the fact that the turbofan aircraft presented a higher achievable gain in fuel burn than the optimized turboprop airplanes. These results imply that it is possible to improve more the turbofan aircraft than the turboprop which may decrease the difference in fuel consumption and hence increase the competitiveness of the turbofan airplane in terms of fuel burn. Considering the second criterion, Table 43 presents the values computed for block time. Chapter 4. Results and Discussion 88

Table 43 – Block time comparison

Turbofan (min) Turboprop (min) Diﬀerence (abs) Diﬀerence (%) 250 nm 41 64 23 57.4% 500 nm 74 122 48 64.1% 750 nm 108 180 72 67.0% 1000 nm 141 237 96 67.9% 1250 nm 174 295 121 69.4% 1500 nm 208 353 145 70.0%

Source: The Author

As expected, the turbofan aircraft flies faster and therefore its block time is smaller for a fixed range when compared to a turboprop. The difference is expressive since the turboprop block time is in average 66% higher than the turbofan block time. The computed results proves that in fact a turboprop aircraft burns less fuel while flying slower than a turbofan airplane. Before defining the best aircraft for a given criterion, it is important to discuss the context of the regional aviation market. Different demands occur which can be exemplified by two scenarios. The first one consists of a route that presents a highly intense flux of passengers such as Belo Horizonte (CNF) to São Paulo (GRU). The other is related to a route of less flux of passengers during the day such as São Josédos Campos (SJK) to Rio de Janeiro (SDU) in Brazil. The airlines size their fleet in order to properly meet the demand of each route. This means that they will need a fleet capable of performing more flights in a day in the first scenario and, in the second scenario, they are able to prioritize only fuel consumption. In consequence, the block time is a critical parameter for the CNF to GRU route while for the SJK to SDU route, the main parameter is fuel consumption only. This interpretation relates the airline profit in each scenario with the technical figures of merit discussed which is acceptable for this academic analysis. However, the planning challenge for an airline is more complex and requires appropriate financial models in order to predict what are the critical parameters for each route in order to maximize profit. Considering the technical interpretation, it is possible to state that the turbofan is more competitive in highly intense flux of passengers routes while the turboprop can be used in the others. Therefore, considering the fuel burn as criterion, the turboprop aircraft are preferred while the turbofan is the most suitable option when the criterion is block time. 89

5 Conclusion

This academic work started by first describing the methods used in order to model an aircraft considering the conceptual design phase scope as presented in Chapter 2. The main aeronautical disciplines were taken into account aiming at representing the most important trade-offs faced in aircraft design regarding the regional aviation. The discussion also included an overview about MDO due to the multidisciplinary nature of the problem. Most of the models were based on semi-empirical relations available on SUAVE which inherently requires an appropriate validation using official data from existing aircraft. Moreover, the goal of the present work was to compare a turboprop and a turbofan optimized airplanes considering the regional aviation, which also requires model validation in order to properly represent each aircraft, allowing an impartial analysis. Therefore, the methodology was structured in order to ensure that the airplane model is reliable. It consisted of three steps in which the first one was the model calibration, followed by the optimization and then the comparison between the turbofan and turboprop airplanes. The baseline geometries were the E170 jet and ATR 72-600 turboprop, which have a similar passenger capacity. The model validation was conducted considering a maximum error of 3.5% for performance estimations. The optimization was carried out using the previous validated models as well as the performance results as constraints in order to establish the requirements for each aircraft type. Different objective functions were applied in order to verify the impact on the optimized geometries. It was demonstrated that the E170 turbofan aircraft has more potential to be improved considering technical objective functions than the turboprops based on the ATR 72-600. All the results captured the trends expected and the model accuracy is acceptable in the scope of this analysis. The comparison between the turboprop and turbofan aircraft lead to the conclusion that the MTOW discrepancy is the main factor on the fuel burn difference. Furthermore, the turboprop aircraft is the most preferred when considering as criterion fuel consumption, while the turbofan airplane is the most competitive in terms of block time. The optimized geometries presented gains in relation to the reference. Moreover, the block fuel difference is lower for the optimized airplanes considering the weight factor β in the aggregating objective function equals to 0 and 0.5, since the turbofan has shown to have more potential to be improved regarding fuel burn. In addition to the goals proposed, the development of the present academic work also allowed the technical improvement of the author which is the primarily objective of the undergraduation senior thesis. A well-structured knowledge was developed considering the fundamentals of aircraft design and optimization regarding turboprop and turbofan aircraft. Therefore, the academic analysis presented here is considered successful on both technical and educational terms. 90

6 Future Works

The academic analysis developed here has shown opportunities to be improved or complemented. A weight model verification is suggested for the turbofan considering wings of high sweep angle and aspect ratio since the model may underestimate the wing weight in this scenario. For the turboprop aircraft, it is suggested the implementation of an additional constraint aiming at taking into account the taper ratio impact on the wing stall propagation. A detailed study on drag prediction regarding turboprop powered aircraft is also recommended since it can increase the SUAVE model accuracy. As complementary analysis, it is suggested the optimization of a turbofan considering a reduced flight envelope similar to a turboprop airplane in order to understand the impact of airspeed in the MTOW. The turboprop airplane may also be optimized considering an extended flight envelope similar to a turbofan aircraft aiming at defining the airspeed ranges in which the turboprop is still more competitive than a turbofan in terms of fuel consumption. In other words, it is suggested a crossed optimization in which the turbofan must accomplished a turboprop alike mission and vice versa. It is also suggested the consideration of financial models in order to capture the airlines opportunities. Moreover, an optimization considering variable engine can also provide more information about important trade-offs in the aircraft design and it is also recommended for future work. 91

A Reference Airplanes

This appendix presents the basic information about the reference airplanes. Due to the amount of ﬁles and data, all the models, scripts and their output are available online on the author’s Github. The oﬃcial version of the SUAVE software is also available on the same website. The links are the following:

https://github.com/nevesgeovana/TCC https://github.com/nevesgeovana/SUAVE https://github.com/suavecode/SUAVE

For more detailed information about the implementation, the author’s contact is [email protected]. Appendix A. Reference Airplanes 92

A.1 Turbofan Aircraft: E170 AR

Figure 41 – Embraer E170

Source: EMBRAER S.A., 2015[26]

Table 44 – E170 AR - Weights

Weights Maximum Takeoﬀ Weight 37200 kg Maximum Landing Weight 33300 kg Basic Operating Weight 20736 kg Maximum Zero Fuel Weight 30900 kg Maximum Payload 9743 kg Maximum Usable Fuel* 9335 kg Maximum Usable Fuel 11625 l

Source: EMBRAER S.A., 2017[5]

Table 45 – E170 AR - Performance

Performance Max Cruise Speed M 0.82 Time to climb to FL350** 16 min Takeoﬀ Field Length** (ISA, SL) 1151 m Takeoﬀ Field Length (MTOW, ISA, SL) 1644 m Landing Field Length (MLW, ISA, SL) 1241 m Service Ceiling 41000 ft Range*** 2150 nm

Source: EMBRAER S.A., 2017[5]

(*) Fuel density: 0.803 kg/l (**) TOW for 500 nm, full PAX considering single-class seating and passengers at 100 kg (***) Full PAX, typical mission reserves Appendix A. Reference Airplanes 93 Blueprint of Embraer E170 Source: EMBRAER S.A., 2015 [ 26 ] Figure 42 – Appendix A. Reference Airplanes 94

A.2 Turboprop Aircraft: ATR-72 600

Figure 43 – ATR 72-600

Source: ATR Aircraft, 2017[6]

Table 46 – ATR 72-600 - Weights (Basic Version)

Weights Maximum Takeoﬀ Weight 22800 kg Maximum Landing Weight 22350 kg Basic Operating Weight 13500 kg Maximum Zero Fuel Weight 20800 kg Maximum Payload 7500 kg Maximum Usable Fuel 5000 kg

Source: ATR Aircraft, 2017[6]

Table 47 – ATR 72-600 - Performance

Performance Max Cruise Speed* M 0.45 Time to climb to FL250 18 min Takeoﬀ Field Length** (ISA, SL) 1175 m Takeoﬀ Field Length (MTOW, ISA, SL) 1333 m Landing Field Length (MLW, ISA, SL) 914 m Service Ceiling 25000 ft Range with max PAX 825 nm

Source: ATR Aircraft, 2017[6]

(*) 95% MTOW, ISA, Optimum FL - Estimated considering sound speed at Optimum FL (**) TOW for 300 nm, full PAX, SL, ISA Appendix A. Reference Airplanes 95

Figure 44 – Blueprint of ATR 72

Source: ATR Aircraft, 2017[6] 96

Bibliography

1 IATA. 2036 Forecast Reveals Air Passengers Will Nearly Double to 7.8 Bil- lion. 2017. . [Online: Accessed 15-April-2018]. Cited on page 1.

2 AEROWEB. Forecast International’s Aerospace Portal: U.S. Commercial Air- craft Fleet 2016. 2016. . [Online: Accessed 15-April-2018]. Cited on page 1.

3 BOTERO, E. M. et al. Suave: An open-source environment for conceptual vehicle design and optimization. In: 54th AIAA Aerospace Sciences Meeting. [S.l.: s.n.], 2016. p. 1275. Cited 2 times on pages 2 and 52.

4 LUKACZYK, T. W. et al. Suave: An open-source environment for multi-ﬁdelity conceptual vehicle design. In: 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. [S.l.: s.n.], 2015. p. 3087. Cited 13 times on pages 2, 5, 6, 7, 13, 15, 16, 17, 18, 21, 30, 34, and 52.

5 EMBRAER S.A. E170 AR Speciﬁcations. 2017. . [Online: Accessed 01-May-2018]. Cited 6 times on pages 2, 34, 46, 48, 50, and 92.

6 ATR Aircraft. ATR 72-600 Speciﬁcations. 2017. . [Online: Accessed 01-May-2018]. Cited 7 times on pages 2, 34, 63, 65, 66, 94, and 95.

7 GUDMUNDSSON, S. General Aviation Aircraft Design. [S.l.]: Butterworth- Heinemann, 2013. Cited 11 times on pages 3, 4, 5, 8, 10, 11, 14, 16, 19, 20, and 21.

8 TORENBEEK, E. Advanced aircraft design: Conceptual design, technology and optimization of subsonic civil airplanes. [S.l.]: John Wiley & Sons, 2013. Cited on page 3.

9 RAYMER, D. Aircraft Design: A Conceptual Approach. [S.l.]: American Institute of Aeronautics and Astronautics, Inc., 2012. Cited on page 3.

10 TORENBEEK, E. Synthesis of subsonic airplane design: an introduction to the preliminary design of subsonic general aviation and transport aircraft, with emphasis on layout, aerodynamic design, propulsion and performance. [S.l.]: Springer Science & Business Media, 1976. Cited 2 times on pages 3 and 21.

11 ANDERSON, J. D. Aircraft performance and design. [S.l.]: WCB/McGraw-Hill Boston, MA, 1999. v. 1. Cited 7 times on pages 3, 24, 25, 26, 27, 28, and 29.

12 ROSKAM, J. Airplane design. [S.l.]: DARcorporation, 1985. Cited on page 3.

13 OWENS, D. Weissinger’s model of the nonlinear lifting-line method for aircraft design. In: 36th AIAA Aerospace Sciences Meeting and Exhibit. [S.l.: s.n.], 1998. p. 597. Cited on page 6. Bibliography 97

14 WEISSINGER, J. The lift distribution of swept-back wings. 1947. Cited on page 6.

15 KROO, I. and Shevell, R., A241A˚ Course Notes: Aircraft Design, Synthesis and Analysis. . Acessed: June 16, 2018. Cited 3 times on pages 6, 8, and 21.

16 SHEVELL, R. S.; SHEVELL, R. S. Fundamentals of ﬂight. [S.l.]: Prentice Hall Englewood Cliﬀs, NJ, 1989. v. 2. Cited 4 times on pages 6, 7, 8, and 21.

17 ADMINISTRATION, F. F. A. 14 CFR Part 25 - AIRWORTHINESS STAN- DARDS: TRANSPORT CATEGORY AIRPLANES. [S.l.: s.n.], 2013. Cited on page 9.

18 AIRPLANES, W. B. B. C. Jet Transport Performance Methods. [S.l.]: Boeing Company, 2009. Cited 2 times on pages 9 and 14.

19 MATTINGLY, J. D. Elements of gas turbine propulsion. [S.l.]: McGraw-Hill, 1996. Cited 3 times on pages 24, 26, and 30.

20 Maerkang. Components of jet engines. 2009. . [Online: Accessed 24-June-2018]. Cited 2 times on pages 25 and 27.

21 Medium - Images. Stop Disrespecting the Turboprop. 2017. . [Online: Accessed 24-June-2018]. Cited on page 29.

22 Cantwell, B. J. AA210A Course Notes. . [Online: Accessed 24-June-2018]. Cited on page 30.

23 GREITZER, E. et al. N+ 3 aircraft concept designs and trade studies, ﬁnal report volumes 1 and 2. Rep. CR—2010-216794, NASA, Hampton, VA, 2010. Cited on page 30.

24 VANDERPLAATS, G. N. Numerical optimization techniques for engineering design. [S.l.]: Vanderplaats Research and Development, Incorporated, 2001. Cited on page 31.

25 Willcox, K. and Weck, O. MIT - Multidisciplinary System Design Optimization. . [Online: Accessed 01-April-2018]. Cited 2 times on pages 32 and 41.

26 EMBRAER S.A. Commercial Aviation - E170-E1 APM. 2015. . [Online: Accessed 01-May-2018]. Cited 9 times on pages 34, 35, 46, 47, 48, 49, 50, 92, and 93.

27 ATR Aircraft. ATR 72-600 - Flight Crew Operating Manual. 1997. Cited 7 times on pages 34, 63, 64, 65, 66, 79, and 81.

28 Chris Lomax. Cabin Pressurization. . [Online: Accessed 01-July-2018]. Cited on page 36. Bibliography 98

29 WENDORFF, A.; BOTERO, E.; ALONSO, J. J. Comparing diﬀerent oﬀ-the-shelf optimizers’ performance in conceptual aircraft design. In: 17th AIAA/ISSMO Multi- disciplinary Analysis and Optimization Conference. [S.l.: s.n.], 2016. p. 3362. Cited 3 times on pages 40, 41, and 60.

30 SILVA, C. R. Ilario da; ORRA, T. H.; ALONSO, J. J. Multi-objective aircraft design optimization for low external noise and fuel burn. In: 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. [S.l.: s.n.], 2017. p. 1755. Cited on page 41.

31 VOS, M. H. R. System-level assessment of tail-mounted propellers for regional aircraft. In: 31st Congress of the International Council of the Aeronautical Sciences. [S.l.: s.n.], 2018. Cited 2 times on pages 41 and 52.

32 COELLO, C. A. C. C. A short tutorial on evolutionary multiobjective optimization. In: SPRINGER. International Conference on Evolutionary Multi-Criterion Optimization. [S.l.], 2001. p. 21–40. Cited on page 42.

33 BIANCHI, D. H. D.; ORRA, T. H.; SILVESTRE, F. J. Evaluation of the impacts of objective function deﬁnition in aircraft conceptual design. Journal of Aircraft, American Institute of Aeronautics and Astronautics, v. 55, n. 3, p. 1231–1243, 2017. Cited 4 times on pages 42, 43, 62, and 77.

34 A4A. Passenger Airline Cost Index (PACI). . [Online: Accessed 20- October-2018]. Cited on page 45.

35 GE Aviation. CF34-8C Data Sheet. . [Online: Accessed 01-July-2018]. Cited on page 47.

36 A4A. EASA TYPE-CERTIFICATE DATA SHEET, PW 100-150 Series. . [Online: Accessed 10-August-2018]. Cited on page 79.

37 A4A. Pratt Whitney Canada, PW 100-150 Series. . [Online: Accessed 10-August-2018]. Cited on page 79.