team four critical design review - university of michiganriboch/publications/teamfourcdr.pdf ·...

TEAM Four Critical Design Review

Kai Jian CheongRichard B. Choroszucha*

Lynn LauMathew MarcucciJasmine Sadler

Sapan ShahChongyu ”Brian” Wang

03.XII.2008

0.1 Abstract

The purpose of this report is to present the final configuration and design of the cargo plane de-signed for use with the Federal Emergency Management Agency (FEMA) for relief and transoceanicmissions. In addition, we will quickly recall the preliminary configurations and explain the down-select process with key changes to our final design. FEMA is in need of a long range cargo jet totransport emergency relief supplies with the capability of short take off and landing (STOL). Theplane is required to fly at cruise speeds of about Mach 0.80 while carrying 60,000 pounds (lbs) ofcargo for a 500 nautical mile (nm) relief mission. It should fly without the cargo for a transoceanicmission of at least 3,200 nm. A very important constricting factor is the ability to take off andland within a 2,000 to 3,000 feet (ft) critical field length on wet surfaces which may or may not bepaved. The jet’s fuselage must be able to support and hold a cargo container that is 560 inches(in) long by 128 in wide by 114 in high.

0.2 Executive Summary

Spinning Cube Aviation designed three individual configurations for use with FEMA and USAFduring the preliminary design stage. The design chosen was configured for FEMA due to a higherprofit margin of 135 million dollars. The overall design of the aerocraft consists of a standardcircular cross-section fuselage, twin engine propulsion system, T-tail empennage design, rear cargobay door, and quadricycle landing gear system. The key design additions from the preliminarydesigns to the final included the use of a quadricycle landing gear, both fuel tanks contained insidethe fuselage, a longer and more slender nose, and an all moving T-tail system. Our final FEMAcargo jet fulfills and surpasses all requirements set by the Federal Aviation Administration (FAA):One Engine Inoperative (OEI), lateral and longitudinal tip over, and controllable static margin.Some of the key risk factors of the aerocraft include the all-moving tail and quadricycle landing gearsystem due to its complexity and maintenance issues. In addition to standard maintenance problemsthat could arise from the intricate system for both, there is also a higher cost and complexity in themanufacturing and production processes of the aerocraft. Spinning Cube Aviation has taken theseissues into consideration while designing our final configuration for FEMA and decided it is stillthe most beneficial and efficient design for the aerocraft even though it is slightly more expensive.The all-moving tail will drastically improve the aerocraft’s control and stability during flight, alongwith the increased ability to counteract high crosswinds. The added landing gear weight is alsojustified because this will help keep the aeroplane in full contact with the ground and increaselateral stability while on wet and uneven landing and takeoff surfaces.

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Contents

0.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1 Introduction and Mission 61.1 Mission Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Candidate Configurations 92.1 Design Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Down Selection 10

4 Design Comparison 11

5 Introduction to Final Design 125.1 Introduction to Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.2 Aeroplane Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6 Layout and Design 146.1 All-Moving Tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146.2 Cockpit Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.3 Cargo Bay Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.4 Cargo Bay Door . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Aerocraft Sizing and Sizing Trade Studies 197.1 Aerocraft Sizing Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197.2 Sizing Trade Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

8 Weight Estimates 228.1 Initial Weight Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228.2 Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238.3 Refined Mission Fuel Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238.4 Refined Weight Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

9 Center of Gravity Location and Excursion 259.1 CG Excursion During Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259.2 Loading CG Excursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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10 Wing Design and High Lift Systems 2810.1 Aerofoil Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2810.2 Wing Design Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2810.3 High Lift Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

11 Empennage and Control Surfaces 3111.1 Empennage Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3111.2 Control Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3211.3 One Engine Inoperative Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 33

12 Landing Gear Design 34

13 Propulsion 36

14 Performance Analysis 3814.1 Stall Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3814.2 Takeoff and Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3814.3 Cruise, Climb and Flight Ceiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3914.4 Trimmed Lift and Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3914.5 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

15 Aero Loads 4115.1 Maneuver and Gust Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4115.2 Lifting Surface Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

16 Load Path 44

17 Cost Analysis 46

18 Conclusions 47

Bibliography 48

A Configuration Comparison 49

B Mission Fuel Fraction 50

C Centers of Gravity 51

D Engineering Drawings 53

E One Engine Inoperative 59

F Distributed Aerodynamic, Inertia and Gravity Loading Plots 60

G Wing Aerofoil Trade Study 63

H MATLAB Code 80H.1 Powell’s Parasite Drag Coefficient Matlab Code . . . . . . . . . . . . . . . . . . . . . 80H.2 Weights Sensitivity Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80H.3 Preliminary Sizing Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83H.4 Preliminary Static Margin Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . 84H.5 Preliminary Weights Estimate Matlab Code . . . . . . . . . . . . . . . . . . . . . . . 85

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H.6 Powell’s Inviscid Flapped Wing Loading Code . . . . . . . . . . . . . . . . . . . . . . 86

I Calculations 92I.1 Calculations for Stall Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92I.2 Calculations for Climb Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

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List of Figures

1.1 Relief Mission Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Transoceanic Mission Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Isometric View of Final Design: FEMA Aerocraft . . . . . . . . . . . . . . . . . . . . 8

6.1 Isometric View of the All-Moving Tail . . . . . . . . . . . . . . . . . . . . . . . . . . 146.2 View of the All-Moving Tail Deflected . . . . . . . . . . . . . . . . . . . . . . . . . . 156.3 View of the General Layout of the Cockpit . . . . . . . . . . . . . . . . . . . . . . . 166.4 Isometric View of Cargo in Cargo Bay . . . . . . . . . . . . . . . . . . . . . . . . . . 166.5 Engineering Drawing of Cargo in Cargo Bay . . . . . . . . . . . . . . . . . . . . . . . 176.6 Example of Cargo Bay Doors Opened . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.1 Sizing Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207.2 Trade Studies Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207.3 Carpet Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9.1 CG Excursion During Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259.2 CG Excursion At Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

10.1 NLF0215F Aerofoil View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2810.2 Detailed View of Wing Full Span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2910.3 General View of High Lift Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3010.4 Sectional Lift Coefficient According to Normalized Wing Span Location . . . . . . . 30

11.1 Detailed CAD Top View of Control Surface Locations . . . . . . . . . . . . . . . . . 32

12.1 Position of Landing Gear with Respect to Fuselage . . . . . . . . . . . . . . . . . . . 3412.2 Landing Gear Retraction Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

13.1 General Electric (GE) CF6-80E1A3 Engine . . . . . . . . . . . . . . . . . . . . . . . 36

14.1 Trimmed Lift and Drag Data from AVL . . . . . . . . . . . . . . . . . . . . . . . . . 40

15.1 V-n Diagram for Minimum Cruise Weight . . . . . . . . . . . . . . . . . . . . . . . . 4115.2 V-n Diagram for Maximum Cruise Weight . . . . . . . . . . . . . . . . . . . . . . . . 4215.3 Aero Loads on Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

16.1 Torsion Moment About the y-Axis for Critical Points With Maximum Weight . . . . 44

D.1 Engineering Drawing of Assembled Plane . . . . . . . . . . . . . . . . . . . . . . . . 53D.2 Engineering Drawing of Fuselage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54D.3 Engineering Drawing of Nose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55D.4 Engineering Drawing of Tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56D.5 Engineering Drawing of Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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D.6 Engineering Drawing of Fuselage Tail . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

F.1 Normal Force Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60F.2 Chordwise Longitudinal Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . 61F.3 Spanwise Pitch Moment Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 61F.4 Inertia Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

G.1 Trefftz Plot for α = −10◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64G.2 Trefftz Plot for α = −09◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64G.3 Trefftz Plot for α = −08◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65G.4 Trefftz Plot for α = −07◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65G.5 Trefftz Plot for α = −06◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66G.6 Trefftz Plot for α = −05◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66G.7 Trefftz Plot for α = −04◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67G.8 Trefftz Plot for α = −03◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67G.9 Trefftz Plot for α = −02◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68G.10 Trefftz Plot for α = −01◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68G.11 Trefftz Plot for α = 00◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69G.12 Trefftz Plot for α = 01◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70G.13 Trefftz Plot for α = 02◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70G.14 Trefftz Plot for α = 03◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71G.15 Trefftz Plot for α = 04◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71G.16 Trefftz Plot for α = 05◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72G.17 Trefftz Plot for α = 06◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72G.18 Trefftz Plot for α = 07◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73G.19 Trefftz Plot for α = 08◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73G.20 Trefftz Plot for α = 09◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74G.21 Trefftz Plot for α = 10◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74G.22 Trefftz Plot for α = 11◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75G.23 Trefftz Plot for α = 12◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75G.24 Trefftz Plot for α = 13◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76G.25 Trefftz Plot for α = 14◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76G.26 Trefftz Plot for α = 15◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77G.27 Trefftz Plot for α = 16◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77G.28 Trefftz Plot for α = 17◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78G.29 Trefftz Plot for α = 18◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78G.30 Trefftz Plot for α = 19◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79G.31 Trefftz Plot for α = 20◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

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List of Tables

1 Table of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1 General Aerocraft Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Table of Candidate Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.1 Comparison Aeroplanes for Final Blue Configuration . . . . . . . . . . . . . . . . . . 11

5.1 Aeroplane Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8.1 Mission Fuel Fractions for a Transport Mission . . . . . . . . . . . . . . . . . . . . . 228.2 Mission Fuel Fractions for Diversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 228.3 Initial Weight Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228.4 Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238.5 Refined Mission Fuel Fraction (Segment I) . . . . . . . . . . . . . . . . . . . . . . . . 238.6 Refined Mission Fuel Fraction (Segment II) . . . . . . . . . . . . . . . . . . . . . . . 238.7 Refined Mission Fuel Fraction (Segment III) . . . . . . . . . . . . . . . . . . . . . . . 238.8 Refined Weights Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

10.1 Wing Geometry Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

11.1 Horizontal and Vertical Tail Characteristics . . . . . . . . . . . . . . . . . . . . . . . 3111.2 Control Surface Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

12.1 Tire Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

13.1 Engine Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

14.1 Takeoff and Landing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3814.2 Stability Derivatives due to Angle of Attack and Sideslip Angle . . . . . . . . . . . . 4014.3 Stability Derivatives due to Roll Rate, Pitch Rate and Yaw Rate . . . . . . . . . . . 40

15.1 Critical Loading Angles of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

17.1 Program Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4617.2 Market Pricing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

A.1 Comparison Aeroplanes for Red Configuration . . . . . . . . . . . . . . . . . . . . . 49A.2 Comparison Aeroplanes for White Configuration . . . . . . . . . . . . . . . . . . . . 49

B.1 Mission Fuel Fraction at Various Stages . . . . . . . . . . . . . . . . . . . . . . . . . 50

C.1 CG Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

E.1 One Engine Inoperative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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List of Symbols

◦F: Degrees FahrenheitAOA, α: Angle of Attack

AR: Aspect RatioAVL: Athena Vortex Lattice (computer program)CAD: Computer Aided DesignCD: Drag CoefficientCD0 : Parasite Drag CoefficientCG: Center of Gravity

CLmax : Maximum Lift CoefficientDAPCA IV: Development and Production Cost for Aircraft

FAA: Federal Aviation AdministrationFAR: Federal Aviation Regulation

FEMA: Federal Emergency Management Agencyft: Feet

GE: General ElectricL/D: Lift to Draglb: Pound-Mass

MAC: Mean Aerodynamic ChordMATLAB: Matrix Laboratory (computer program)

n: Load Factornm: Nautical MilesOEI: One Engine Inoperativepsf: pounds per square foot

RDT&E: Research, Development, Test and EvaluationSFC: Specific Fuel ConsumptionSL: Landing DistanceSTO: Takeoff Distance

STOL: Short Takeoff and LandingT/W: Thrust to Weight RatioTOP: Takeoff ParameterUSAF: United States Air ForceV-n: Velocity versus Load FactorW/S: Wing LoadingWE : Empty WeightWP : Payload WeightWTO: Takeoff Weight

Table 1: Table of Symbols

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Chapter 1

Introduction and Mission

1.1 Mission Requirements

The overall requirements for the cargo aerocraft given to us by FEMA for relief and transoceanicinclude the ability to fly at a Mach number of 0.80 or higher, the ability to takeoff on a balancedfield length of 2,500 ft on a 95◦ F day, and the capability to warm up and taxi for 8 minutes. Thecrew includes two pilots and one loadmaster. There are also various requirements that are specificto the transoceanic and relief type missions. Relief missions must have a flight range of at least500 nm, a descent to 1,000 ft for 100 nm at a Mach number of 0.6, landing distance of 3,000 ftwith the ability to handle 25 knot crosswinds, and enough reserve fuel to accommodate an extra350 nm missed approach along with a 30 minute hold at 5,000 ft. Transoceanic flights must havea flight range of 3,200 nm which can include an aerial refuel, a 2,500 ft landing distance or less,a descent to sea level, and enough reserve fuel to accommodate a missed approach of 150 nm anda 45 minute hold at 5,000 ft. In addition, the relief mission must be able to carry 60,000 lbs ofpayload including support equipment, and the transoceanic mission must be able to carry 10,000lbs of bulk cargo with density of 20 lb/ft3. The relief payload dimensions are 46.7 ft long by 10.7ft wide by 9.5 ft high with a 1 ft clearance around the top and both sides of the payload.

The relief and transoceanic mission profile can be seen below in Figure 1.1 and Figure 1.2.

Figure 1.1: Relief Mission Profile

A military version of this cargo plane was considered for the United States Air Force (USAF)that would have the capability to carry 120,000 lbs of payload with two pilots, a loadmaster, and25 paratroopers. The takeoff distance must not exceed 5,500 ft on a 95◦ F day, the range mustbe 5,000 ft at Mach 0.80 or above, a landing distance must be less than 3,500 ft, and must holdenough reserve fuel to accommodate a 200 nm diversion with a 30 minute hold at 5,000 ft. Thismission design was not carried out in final stage so no further information will be presented for this

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Figure 1.2: Transoceanic Mission Profile

aerocraft.

1.2 Introduction

Spinning Cube Aviation has developed a final design to be used for FEMA for its purposesof relief mission cargo transport. We have arrived at a final design after down selecting fromthree previous preliminary designs that included: a military version of an aerocraft meant to carryextra payload and paratroopers, a twin engine configuration with T-tail and high wing, and aconfiguration with one engine on the vertical fin of the T-tail. Our design was centered on themission requirements and profile provided by FEMA for transoceanic and relief mission flights.

After cost analysis for both the FEMA and USAF mission aerocrafts, Spinning Cube came tothe conclusion that it was beneficial for us to pursue the FEMA design for a higher profit margincompared to USAF aerocraft. Important characteristics of the FEMA aerocraft final design arepresented in Table 1.1 below. More detailed explanations of all parameters listed in Table 1.1 aswell as discussion of all aerocraft subsystems will be presented in the following chapters.

Takeoff Weight (lbs) 243,500Empty Weight (lbs) 131,557

Mach 0.85Cruise Ceiling (ft) 45,000Type of Engine General Electric CF6-80E1A3

Takeoff Thrust (lbs) 63,121Wing Span (ft) 143

Aspect Ratio (AR) 9Fuselage Length (ft) 123Fuselage width (ft) 17.5

Range (nm) 1,924Cost per plane (Millions) (2008 USD) 308

Table 1.1: General Aerocraft Characteristics

This report discusses the final configuration of the design used for the FEMA mission aerocraft.The cargo jet consists of a high wing structure with two General Electric (GE) CF6-80E1A3 turbojetengines and a T-tail empennage design. The layout and design of the plane was meant to take theeffective characteristics of historically successful planes while making more efficient changes to fulfillthe special Short Take Off and Landing (STOL) requirements set forth by FEMA. An isometricview of the final design of the aerocraft can be seen in Figure 1.3 below.

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Figure 1.3: Isometric View of Final Design: FEMA Aerocraft

11

Chapter 2

Candidate Configurations

2.1 Design Drivers

To meet FEMA’s need for a long range cargo jet to transport emergency relief supplies withSTOL capability, Spinning Cube Aviation developed three different designs (Blue, Red, and White),all of which met these basic mission requirements. All three designs used a high wing structureand T-tail.

The Blue design used a conventional design with two wing-mounted GE turbofan engines.This plane adopted the effective design characteristics from successful historical planes while stillmodifying details to fulfill the STOL requirements.

The Red design was unique because it had a single engine mounted on the vertical fin in apusher configuration. This design was to understand the effects from a high aspect ratio.

The White design considered the USAF’s need for a transport plane with STOL requirements.This design incorporated four wing-mounted engines and an expanded fuselage to carry additionalpayload weight from the combat vehicles and paratroopers. It was substantially larger, moreexpensive to produce, and the only one to be limited by the 200 ft wing span constraint.

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Chapter 3

Down Selection

The Blue plane was chosen as the final design for continued work and analysis based onconfiguration, cost, and feasibility. The White design did not fulfill the OEI requirement of thefeasibility study and thus, was not considered for the final design. Both the Blue and Red designsmet all of the criteria set by mission requirements and feasibility studies. The Red design wasdiscounted due to the higher risk associated with the single-engine design during the transoceanicmission. Also, preliminary cost estimations showed the Blue design was less expensive than theRed design. An overall comparison between the three designs is shown below in Table 3.1. Allmargins are fulfilled for all designs.

Blue Red White Final Config

Mission (FEMA or Military) FEMA FEMA Military FEMAWE (lbs) 88949 99160 249660 88949WTO (lbs) 198310 194462 550255 198310Cruise Mach number 0.85 0.85 0.85 0.85Price (Millions) (2008 USD) 197.5 223 330.9 197.5RDT&E + Flyaway Cost (Billions) (2008 USD) 8.9 7.8 33.1 8.9Takeoff Distance Margin (%) 4.5 7.2 6 4.5Landing Distance Margin (w/o / with thrust rev. %) 0/+32 +11/+46 0/+31 0/+32Static Margin (%) 8.8 7 0.7 8.8One-Engine Inoperative Test Passed Yes N/A No YesTipover Test Passed Yes Yes Yes Yes

Table 3.1: Table of Candidate Comparisons

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Chapter 4

Design Comparison

This downselected design compares closely with three other aerocrafts: Lockheed Martin C-130J, Tupolev Tu-330, and the BAE Nimrod. The values that vary dramatically are primarily dueto the effects of having a shorter takeoff and landing distance. However, from the comparison chartin Table 4.1 below, the historical assumptions were somewhat poor, but were a good beginningstep.

Our design has changed dramatically from the preliminary stage to this design review. Itremains to be fairly consistent with performance parameters of existing aerocrafts. The weighthas increased about 50,000 lbs. The takeoff and landing constraints were optimized resulting inincreased wing loading and thrust to weight ratio. Also, with this improved design, we are able toincrease the landing distance and decrease the takeoff distance so the aerocraft effectively uses theallotted runway.

Downselected Final Blue Lockheed Martin Tupolev BAE NimrodBlue Config Config C-130 J Tu-330

WTO (lbs) 198,310 243,500 164,000 228,175 234,165WE (lbs) 88,949 131,557 75,562 151,013 112,765

T/W 0.369 0.56 0.09 - 0.59W/S (psf) 72 108 94 108.4 92.26

SL (ft) 2,250 3,200 2,550 7,220 -STO (ft) 2,613 2,280 4,700 7,220 -

AR 6.633 9 10.1 9.7 6.4Wing Span (ft) 135 143 133 143 127

Table 4.1: Comparison Aeroplanes for Final Blue Configuration

Comparison data for the Red and White design can be found in Appendix A.

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Chapter 5

Introduction to Final Design

5.1 Introduction to Final Design

The downselected blue configuration was refined and further analyzed in order to produce anoptimized design for the mission requirements. The primary modifications were made in the areasof tail configuration, nose geometry, aspect ratio, and landing gear arrangement. These changes,along with the other subsystem designs are discussed in detail in the following chapters. An overallsummary of the aeroplane’s specifications is first presented in the following section.

5.2 Aeroplane Specifications

This aeroplane is designed to fulfill FEMA’s need for a disaster relief cargo aerocraft capableof long range transport with austere STOL field capability. It has a gross takeoff weight of 243,500lbs., with an empty weight of 131,557 lbs. and payload weight of 60,000 lbs. The aeroplane requiresa thrust-to-weight of 0.56 and a wing loading of 108. It cruises at Mach 0.85 at a ceiling of 45,000ft. with a range of 1,924 nm. Its high lift system, consisting of slats and triple slotted flaps, helpsproduce a max coefficient of lift of 3.2. Two General Electric CF6-80E1A3’s produce a max thrustof 72,000 lbs. each with a specific fuel consumption of 0.344.

The aeroplane has a wingspan of 143 ft with an AR of 9 (nine). It is a high wing configurationwith a supercritical aerofoil and an all moving T-tail. The total length of the fuselage is 123 ft,while its maximum height is 17.5 ft. The landing gear is quadricycle with independent steering tomake taxiing and ground operations feasible. It is capable of landing within 3,200 ft without theuse of thrust reversers and can takeoff in 2,800 ft. The total number of aeroplanes to be producedis 35, each with a planned price of $308 million. A summary of these specifications is given belowin Table 5.1.

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WE (lbs) 131,557WTO (lbs) 243,500WP (lbs) 60,000T/W 0.56W/S (psf) 108Cruise Speed (Mach) 0.85Cruise Altitude (ft) 45,000Range (max payload) (nm) 1,924CLmax 3.2Thrust Required at T/O (lbs) 136,000SFC (lb/lbf-hr) 0.33Static Margin (%) 7.9SL (ft) 3,200STO (ft) 2,280Wingspan (ft) 143Aspect Ratio 9Fuselage length (ft) 123Fuselage height (ft) 17.5Landing Gear quadricycleTail Configuration T-tailQuantity Produced 35Price (2008 USD) 285 million

Table 5.1: Aeroplane Specifications

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Chapter 6

Layout and Design

The Blue Design is a conservative design with the exception of the all-moving tail and quadricyclelanding gear. All engineering drawings can be found in Appendix D. All engineering drawings aredone in inches.

6.1 All-Moving Tail

To reduce the size of the tail empennage, we have chosen to use an all-moving tail. Upon furtherresearch, this has proven very effective for aeroplanes that fly in the transonic and supersonic regime.

The all-moving tail provides an interesting challenge from a controls perspective, but has beensuccessfully implemented on a number of planes in different fashions first with the North Amer-ican F-100 Super Sabre to the Russian MIG-21, with varying type of purposes; from fighters totransports. [2, p.78] The all-moving tail will be operated by three independent hydraulic actuatingsystem.

Figure 6.1 shows an isometric view of our all-moving tail and Figure 6.2 gives a small demon-stration of the all-moving tail deflected relative to the tail. An engineering drawing can be seen inFigure D.4.

Figure 6.1: Isometric View of the All-Moving Tail

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Figure 6.2: View of the All-Moving Tail Deflected

6.2 Cockpit Layout

The cockpit will have a classical layout. It will have three chairs, two for the pilot and co-pilotand one directly behind the pilot for the load master. There is also room for a galley and lavatoryin the left corner, or possibly on a separate floor in the nose. The cockpit will be pressurized behinda locked door to the cabin.

The shape of the nose section is designed to resemble a slender cone. Considerations suchas the pilots’ vision angle are taken into account while deciding how slender the nose should be.The smallest angle between the pilot’s line of vision and the cockpit windscreen is known as thetransparency grazing angle. A minimum grazing angle of 30◦ is required. This is because should theangle fall below 30◦, the transparency of the glass will be greatly reduced to the extent that underadverse lighting conditions the pilot will only see the reflection of the instrument panel instead ofwhat is outside the aerocraft.

In Figure 6.3, an isometric view of the general layout of the cockpit can be seen.

6.3 Cargo Bay Layout

The cargo bay is rear loaded through the cargo bay doors, as seen in Section 6.4.A key feature of the cargo bay is the two exit doors; one on the port side close to the nose and

another aft on the starboard side. Although Federal Aviation Regulation (FAR) dictates the needfor only one door, in the interest of safety due to the placement of cargo, we recommend using thetwo door design.

Given the placement of the engines, the crew should be able to exit without injury undernormal operating conditions, as dictated by the FAR documents section 783. This can be seen inthe engineering drawing Figure D.1.

Drawings of the cargo bay can be seen in the isometric view, Figure 6.4, and an engineeringdrawing of the cargo inside the cargo bay in Figure 6.5. For an engineering drawing of the cargobay, please see Figure D.2.

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Figure 6.3: View of the General Layout of the Cockpit

The fuel tanks will be placed on the walls of fuselage anywhere there is space. Figure 6.5 alsoshows the position relative to the beginning of the fuselage.

Figure 6.4: Isometric View of Cargo in Cargo Bay

6.4 Cargo Bay Door

The cargo bay doors will open sideways from a hinge on the tail, a ramp will then extend fromthe fuselage to ground for deployment. As designed, the opening of the cargo bay doors allows for1 ft of clearance around the box while being loaded and unloaded. Figure 6.6 shows a solid model

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Figure 6.5: Engineering Drawing of Cargo in Cargo Bay

of the tail with the cargo bay doors opening at a 90◦ angle. For the engineering drawing pleaserefer to Figure D.6.

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Figure 6.6: Example of Cargo Bay Doors Opened

21

Chapter 7

Aerocraft Sizing and Sizing TradeStudies

Given our mission profile and requirements, we proceeded to determine what characteristicsour aerocraft should have, namely what restrictions there are on the thrust to weight ratio (T/W)and the wing loading to surface area (W/S) of our aerocraft. Subsequently, we performed a sizingtrade study to see if we should change our design for a lighter design.

7.1 Aerocraft Sizing Plot

There is little restriction on the maximum T/W and the minimum W/S. A high T/W corre-sponds to an oversized engine, and a low W/S corresponds to an oversized wing, both of which areundesirable. Thus, it is desirable to have the highest possible W/S while having the lowest possibleT/W.

Captured in Figure 7.1 are the requirements that the aeroplane needs:

1. to take off with a TOP of 66.7 which fulfills our balanced field length requirement.

2. to landing on a landing field of 3250 ft.

3. Climb gradient of 0.12 (7◦ climb).

4. Load factor of 2.5.s

For our initial design, a safe sizing was chosen to give a large margin on the landing and takeoffdistance. This is changed later during the trade-studies as we find that we can get a much lighterplane with a higher W/S and T/W, and stay in the acceptable bounds of the sizing plots.

7.2 Sizing Trade Study

The trade study is basically a perturbation of the two parameters, T/W, as well as W/S. For ourtrade study, we did a 20% perturbation on our baseline design using our tools for refined weightsestimation. We produced the following findings shown in Figure 7.2.

From Figure 7.2, the weight estimations, landing distance, and the TOP values for each con-figuration can be seen. Designs 1,4,7 and 8 fulfill both landing and takeoff requirements, but areoversized. Designs 2,3 and 6 fail the takeoff requirement. The only viable options are 5 and 9, anddesign 9 has a lower weight.

We can see the lines of constant weight and the configurations they correspond to in Figure 7.3.Thus, we understand from our trade studies that it would be best if we used design 9. Subsequentwork would be done on this configuration, as reflected in the refined weights estimate in Section 8.4.

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Figure 7.1: Sizing Plot

Figure 7.2: Trade Studies Matrix

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Figure 7.3: Carpet Plot

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Chapter 8

Weight Estimates

8.1 Initial Weight Estimates

An initial weights estimate based on the mission profile was required so that the design processcould be started. Roskam’s regression data for the Jet Military cargo class of aerocraft was used todetermine the relationship between the empty weight of the aerocraft to the takeoff weight of theaerocraft. Once this relation was established, an initial mission fuel fraction was calculated basedon the mission profile.

Using Breguet’s equations for range and loiter, as well as the historical data that Roskam hasfor the other portions of the mission, the following mission fuel fractions in Table 8.1 and 8.2 weregenerated.

Mission segment Warmup Taxi Take-off Climb Cruise Descent LandingFuel fraction 0.99 0.99 0.995 0.9789 0.9565 0.99 0.992

Table 8.1: Mission Fuel Fractions for a Transport Mission

Mission segment (Divert) Cruise LoiterFuel Fraction 0.9694 0.9691

Table 8.2: Mission Fuel Fractions for Diversion

Using the mission fuel fractions computed, as well as the relation that Roskam derived betweenthe empty weight and the takeoff weight of the military cargo transport plane, we then proceededto an iterative process in which we calculated the following results for our cargo plane:

Item Weight (lbs)Empty Aerocraft 120,000Available Fuel 54,800Trapped Fuel 3,300

Crew 615Payload 60,000

Gross Take-off Weight 239,000

Table 8.3: Initial Weight Estimate

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8.2 Sensitivity Studies

The sensitivity studies are essential in uncovering the design drivers. The main goal of thisexercise is to understand what factors drive the weight and ultimately the cost of the aerocraftdown. This was done using the initial weight estimate codes we had, by perturbing the parametersindividually and capturing their effect on the takeoff weight of the aerocraft. The results arecaptured in Table 8.4.

Parameter varied Absolute change in WTO (lbs) Relative change in WTO (%)Payload Weight 2.61 0.836

Cruise L/D -3730 -0.291Range 76.9 0.206

Empty Weight 2.09 1.12Fuel Consumption 81300 0.304

Flight Speed -98.8 -0.264

Table 8.4: Sensitivity Studies

As we can see from the relative change column, it is most desirable to have the lowest emptyweight, as it reduces the takeoff weight most significantly. Also, a higher L/D, flight speed, andlower fuel consumption rate are desirable.

Varying the flight speed and fuel consumption will depend heavily on the kind of turbo-fanengines we can find commercially, and that will be discussed in the Chapter 13.

In order to have a higher L/D, the aerocraft needs to cruise at the optimum altitude. Experiencetells us that the higher the plane cruises, the better the L/D. Thus, this will also depend on theengine performance as we will need to pick an engine that is able to give us a higher altitude.

8.3 Refined Mission Fuel Fraction

The following refined fuel fractions were calculated to be used in the iteration for a refinedweights estimate:

Mission Segment(I) Warm-up & Taxi Take-off Climb Cruise Descent LandingFuel Fraction 0.996 0.995 0.978 0.956 0.99 0.992

Table 8.5: Refined Mission Fuel Fraction (Segment I)

Mission Segment(II) Warm-up & Taxi Take-off Climb Cruise DescentFuel Fraction 0.996 0.995 0.978 0.952 0.99

Table 8.6: Refined Mission Fuel Fraction (Segment II)

Mission Segment(III) Climb Cruise (Divert) Loiter Descent LandingFuel Fraction 0.997 0.949 0.985 0.99 0.992

Table 8.7: Refined Mission Fuel Fraction (Segment III)

The whole mission is analyzed in Tables 8.5, 8.6 and 8.7. Mission segment I corresponds to theportion of the mission where the payload is being brought to the relief zone. Mission Segment II

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corresponds to the portion of the mission where the aerocraft returns from the relief zone. MissionSegment III corresponds to the requirement whereby the plane does a diversion to an alternatelanding site.

It should be noted that for both segments I and II, the cruise altitude is 45,000 ft to maximizethe L/D and improve fuel efficiency. For segment III, the cruise attitude is 10,000 ft because theaerocraft does not have enough endurance for a climb to optimal cruise altitude. Also, the cruisespeed is at Mach 0.30 and the loiter speed is at Mach 0.26 to improve efficiency as we are notrequired by mission specification to fly above Mach 0.80 for this portion of the mission.

8.4 Refined Weight Estimates

After the sizing and the trade studies are done (as described in Chapter 7), a refined weightsestimate was produced by analyzing the various weight groups of the aerocraft, as prescribed byRaymer. The refined weights estimation reflects the actual size of the wing according to the requiredW/S, as well as the actual weight of the engine selected that fulfills the T/W requirements. Thisestimation also makes use of the refined mission fuel fraction presented in the previous section.

Item Weight(lbs) Item Weight(lbs)Fuselage 24,400 Wing 22,570

Horizontal tail 2,100 Vertical tail 1,400Landing gear (nose) 3,400 Landing gear (main) 7,100Installed Engines 29,200 All Else 41,400Empty Weight 131,600Trapped Fuel 2,900 Crew 615

Operating Empty Weight 135,200Fuel Available 48,400 Payload 60,000

Gross Take Off Weight 243,500

Table 8.8: Refined Weights Estimates

These numbers in Table 8.8 are based on the sizing determined after the trade studies, and arethe weight estimation of the final design configuration.

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Chapter 9

Center of Gravity Location andExcursion

For stability issues, it is important to understand how the center of gravity (CG) shifts duringthe mission, so as to offset the effect using stability control systems, or shift the fuel tanks such thatthe CG excursion is minimal during flight. As such, an estimate of the CG location throughoutthe mission was calculated. The most forward and most aft locations are noted, to be used laterin the landing gear sizing. There are two CG excursion plots we should look at, one of the missionprofile, another of the loading of the plane.

9.1 CG Excursion During Mission

Figure 9.1: CG Excursion During Mission

As previously defined, (I) corresponds to the mission segment where the payload is transportedto the relief zone, (II) corresponds to the aerocraft returning, and (III) corresponds to the diversionmission.

As seen from Figure 9.1 the only anomaly occurs when the aerocraft has landed at the relief zone

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and unloads the payload. This would manifest itself as a large forward shift in the CG location.However, the fuel is adjusted to pull the CG back to its original location. With a quadricyclelanding gear, the aeroplane is more stable with a forward CG than an aft CG, so we opt to havethe counter-balance fuel moved to the main fuel tank before removing the payload.

Also, from Figure 9.1 we can see that the CG excursion during the flight is minimal. This isbecause the main fuel tank, where the aerocraft burns fuel from, is built at the CG of the plane.As fuel is burned, the CG of the aerocraft will not change much, keeping the CG excursion smallduring flight.

Worthy of note is the fact that the CG location of segment I and segment II to III are veryclose. This is a result of the choice of a favorable location for the aft fuel tank that acts as acounter-balance to the payload. This keeps the overall excursion to within 0.1 feet, which is highlydesirable.

9.2 Loading CG Excursion

As mentioned in Section 9.1, there is a need for an aft tank configuration in the aerocraft inorder to properly counter-balance the presence of the payload. Thus in the loading path, we havean additional concern that the aft tank should be loaded after the payload to prevent a longitudinaltip over.

Figure 9.2: CG Excursion At Loading

Figure 9.2 shows us the CG excursion at the different points during the loading process. Theconfiguration that corresponds to each station number are as follows:

1. Operational Empty Weight

2. Operational Empty Weight + Crew

3. Operational Empty Weight + Crew + Main Tank

4. Operational Empty Weight + Crew + Main Tank + Payload

5. Operational Empty Weight + Crew + Main Tank + Payload + Aft Tank

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From this study, we now know the most aft CG location to be 53 ft, and the most forward CGlocation to be 52 ft as measured from the nose of the aerocraft.

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Chapter 10

Wing Design and High Lift Systems

10.1 Aerofoil Selection

Our team of engineers performed a trade study of supercritical aerofoils to determine themost efficient lifting aerofoil for our Mach number of 0.85 at 45,000 ft. Using AVL, MATLAB,and a BATCH script, we were able to run a large selection of supercritical aerofoils found atangles of attack from -10◦ to +20◦. Using the Trefftz plots as well as aerodynamic wing loadingvectors outputted by AVL, we determined the most beneficial aerofoil for our aerocraft wing andhorizontal stabilizer was the NLF0215F. A sampling of various angle of attack executions for allaerofoils tested can be seen in Appendix G if needed. The aerofoil chosen can be seen below in adata point representation view in Figure 1.

Figure 10.1: NLF0215F Aerofoil View

10.2 Wing Design Characteristics

The wing geometry characteristics for the final design are shown below in Table 10.1. Allparameters of the wing were sized according to an iterative process taking the initial takeoff weight,W/S, and static margins. The value of 9 for the aspect ratio was chosen in order to maximize thewing span according to the reference area calculated through sizing of the W/S. It can be proventhrough aerodynamics that as the aspect ratio of the wing increases, the lift forces across the spanof the wing increases. Increased span-wise lift is highly desired for the FEMA conditions at takeoffand landing as well as reducing the amount of thrust needed for cruise. In addition, the wing spanof 143 ft is significantly less than the 200 ft aerocraft width constraint set forth by FEMA, whichis beneficial for our company because it will reduce excess weight and cost of materials.

An important parameter of the wing that might attract attention is the high wing structure withan anhedral of 5◦. This design feature is not necessarily typical in most carrier or cargo aerocraftsbut was thought to be a very important design to continue to incorporate into our final design.The reason for a high wing system is to allow for clearance between the ground and the engines aswell as the undercarriage of the wing in harsh environments prevalent in relief zones. Additionally,since the supporting structure is a wing box configuration, a high wing would put the wing box

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Reference Area 2257 ft2

AR 9Taper Ratio 0.4

Span 143 ftRoot Chord 22.62 ft

Leading Edge Sweep 30◦

Quarter Chord Sweep 27◦

Anhedral -5◦

Fixed Incidence 0◦

Table 10.1: Wing Geometry Characteristics

mostly out of the way of the interior of the fuselage for the payload and loading mechanisms. Anyother wing configuration would require the passing of the wing box directly through the fuselagewhich would require an increased length in aerocraft and added mass.

Some other important parameters for the wing include a mean aerodynamic chord (MAC) of16.8 ft, the y-direction distance of MAC of 30.54 ft, and distance of MAC from nose of 45.9 ft. Adetailed CAD drawing of the full span wing can be seen below in Figure 10.2.

Figure 10.2: Detailed View of Wing Full Span

10.3 High Lift Systems

In order to take off and land in the short distance required by FEMA, we need a CLmax ofabout 3 which can only be obtained with the help of the triple-slotted flap system and leading edgeslats, increasing the lift at these conditions by 1.9 and 0.4 respectively. The flaps run across 68% ofthe wing half-span while the slats are about 83% of the wing half-span. The high lift triple-slottedflap system is displayed in a more general sense below in Figure 10.3 [7, p.336]. A more detailedexplanation and CAD drawing of locations of the flaps will be presented below.

In the preliminary design stage, the intent was to use a leading edge slat to increase the CLmax

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Figure 10.3: General View of High Lift Systems

by about 0.4 and triple-slotted flaps to increase the CLmax by about 1.9. With these two wingmodifications intact, the wing can effectively have an increase of about 2.3 above the wing geometryCLmax . In addition, the all moving horizontal stabilizer discussed earlier will slightly increase thelift performance of the aerocraft by increasing its ability to pitch the aerocraft up or down.

We were able to determine the location of the flaps along the half span of the wing using a wingloading code provided by Professor Powell. After iterations of the code using our wing geometrywe were able to determine the inboard and outboard span-wise location of the trailing edge flapsbased on wing stalling at the particular Cl values. Figure 10.4 shows the plot used to determinespan-wise location of the triple-slotted flaps.

Figure 10.4: Sectional Lift Coefficient According to Normalized Wing Span Location

The leading edge slats are being placed across 83% of the half span wing because there are noother control surfaces placed on the leading edge to interfere with the slats. The slats will allowthe aerocraft wing to have a higher angle of attack which increases lift without experiencing stall.

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Chapter 11

Empennage and Control Surfaces

11.1 Empennage Characteristics

The main feature of the aerocraft’s empennage is the use of an all-moving T-tail. This design waschosen over a conventional tail so that the flow trailing the main wing would not create turbulenteffects over the horizontal stabilizers leading to a greater induced drag and instability. The T-tail allows for more stable maneuvers and pitch control during flight. A key characteristic of thevertical fin in this configuration is the minimal taper of 0.9 with a higher leading edge sweep of 35◦

to allow for less incident drag. From the previous preliminary designs, the height of the verticalfin has been drastically reduced, and the span of the horizontal stabilizer has been reduced as well.Specific values for important vertical fin and horizontal stabilizer characteristics are summarizedin Table 11.1 below.

Horizontal Stabilizer Vertical FinReference Area (ft2) 383.9 257.3

AR 4 1.9Root Chord (ft) 10.89 12.93

Span (ft) 39.2 22.11Taper Ratio 0.8 0.9

Leading Edge Sweep (◦) 35 35

Table 11.1: Horizontal and Vertical Tail Characteristics

A very unique and innovative design feature of the T-tail design on our aerocraft is the use ofan all-moving tail to increase the angle of attack that is induced by the vertical tail and stabilizer.There is a need for our aerocraft to be able to recover control in case of a one engine inoperativesituation. This is usually accomplished through the use of a yawing moment caused by rudders.Instead, the plane utilizes an all-moving vertical fin that acts as one complete rudder to reducethe amount of deflection required. In addition, the all-moving horizontal stabilizer will also helpimprove the controllability of the aerocraft during cruise. The vertical fin will be able to movearound its z-axis using a bar which runs through the entire fin to a hinge point in the middle ofthe horizontal stabilizer that will rotate and cause the fin to move. A 3-D view of the all movingmechanism using a rotating bar can be seen in Figure 6.2.

Since the vertical fin is the only moving mechanism around the z-axis, the horizontal stabilizerwill move through the same angle. Since the maximum angle deflected by the vertical fin will notbe too large, the rotation of the horizontal stabilizer away from the neutral position will not haveany real effects on the span wise coefficient of lift as well as the coefficient of drag.

The need for the taper ratio to be so high for the vertical fin was due to the fact that thereis not much drag penalty that results from flow around the aerofoil forming the vertical stabilizer.

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Another reason was to allow for a larger root chord of the horizontal stabilizers to be used higherup on the vertical tail which is optimal for laminar flow around it. The T-tail design also allowsfor less interference between the stabilizers and the cargo bay door which would be a problem if aconventional tail was used. Figure D.4 illustrates the design of the T-tail as attached to the end ofthe fuselage on top of the cargo bay door.

Other important characteristics of the empennage include the MAC, y-position of MAC, positionof MAC from nose, and volume coefficient used to size. The horizontal stabilizer has a MAC of 9.84ft, a y-position for MAC of 9.43 ft, distance of MAC from nose of 134.6 ft, and a volume coefficientof 0.75. The vertical fin has a MAC of 12.3 ft, a y-position for MAC of 5.43 ft, distance of MACfrom nose of 116.95, and a volume coefficient of 0.062. These dimensions in relation to the entireaerocraft can be seen more visually in the detailed three view CAD drawing presented in the earliersections.

11.2 Control Surfaces

Control surfaces of this FEMA mission aerocraft play a vital role in the functionality of theplane. Due to the unusual takeoff and landing terrain as well as possible unsafe weather conditions,it is necessary to implement the most advanced system of control surfaces on the main wing as wellas T-tail. The three main surfaces are ailerons, elevators, and rudders. Figure 11.1, shown below,illustrates where all surfaces are located in relation to the plane.

Figure 11.1: Detailed CAD Top View of Control Surface Locations

The ailerons are placed at about the last third of the wing (near the tip) on the trailing edgein order to allow for more control of the aerocraft’s ability to roll. The pilot is able to operatethe ailerons in order to roll for turn or to stabilize the aerocraft back to a natural state aftera small perturbation disturbance. The same idea is applied to the rudder which in our aerocraftencompasses the entire area of the vertical fin. The rudder is used to control the yaw of the aerocraftso that if a disturbance impacts the aerocraft, the pilot can correct it using a minor deflection inthe rudder to change the horizontal location of the nose. The elevator is located on the horizontalstabilizers to allow for more control of the pitch angle of the aerocraft so that the plane can eithergenerate more lift when in need or less when not. Table 11.2 summarizes the locations of all control

35

surfaces including flaps and slats in relation the inboard and outboard span location and chordfraction.

Flaps Slats Ailerons Elevator RudderInboard span location (normalized) 0.123 0.123 0.7 0.1 0

Outboard span location (normalized) 0.7 0.95 0.97 0.85 1Inboard chord fraction 0.7 0 0.7 0.7 0

Outboard chord fraction 1 0.15 1 1 1

Table 11.2: Control Surface Locations

11.3 One Engine Inoperative Requirements

While designing our T-tail and rudder system, we had to consider the requirement set by FEMAfor OEI. This situation occurs if one of the two engines becomes inactive and does not functionproperly. The resulting yawing moment must be stabilized using a maximum rudder deflection ofno more than 25◦. This requirement sized the length of the fuselage and geometric dimensions ofthe vertical fin.

There were two options to satisfy the required moment needed to counteract the OEI duringflight: make the vertical fin span longer and therefore the reference area larger, or increase thelength of the fuselage to increase the moment arm of the yawing forces generated by the rudder.Our engineering team chose to increase the length of the fuselage because there was a worry thatmaking the reference area of the vertical fin too large would make the span very large as well. Avertical fin that is too tall might have structural integrity issues. Therefore, we chose the saferoption of having a longer fuselage.

In conclusion, our current aerocraft configuration does satisfy the feasibility test set by OEI.The values used to analyze the OEI requirement can be seen in Appendix E.

36

Chapter 12

Landing Gear Design

Our aeroplane will employ a quadricycle landing gear, whereby the nose gear will consist oftwo twin nose wheels, and the main gear will consist of two four-wheel bogeys. The quadricyclearrangement is ideal for our purpose as it allows for the cargo floor to be very low to the ground.This means that loading and unloading of the cargo will be easier. The nose wheels will be placed25 ft from the nose, and the main wheels will be 66 ft from the nose. Figure 12.1 shows where thelanding gear will be positioned with respect to the fuselage.

Figure 12.1: Position of Landing Gear with Respect to Fuselage

The tires to be used are the Michelin Air X Radial Tires. The tire dimensions are detailed inTable 12.1.

Nose/Main Tire Diameter (ft) 3.08Nose/Main Tire Width (ft) 0.98

Table 12.1: Tire Dimensions

The main landing gear is located about 13 ft behind the most aft CG location which is locatedat 53.6 ft from the nose. At this distance, the vertical from the landing gear makes a 45◦ anglewith the main gear line and thus satisfies the 15◦ angle required for longitudinal stability. Theposition of the main landing gear also takes into consideration that a certain amount of clearanceis required for the tail section of the aerocraft to remain clear of ground during takeoff and landing.An angle of at least 15◦ between the landing gear and the tip of the tail is required for adequate

37

ground clearance. Calculations show that the aerocraft’s landing gear makes a 20◦ angle with thetail tip of the aerocraft, thus providing sufficient ground clearance.

The landing gear will be retracted into the fuselage when the aerocraft is not in takeoff orlanding mode. The space containing the nose landing gear will be of length 4.7 ft, width 2.9 ft andheight 3.6 ft. The space containing the main gears will be of length 7.8 ft, with width and heightthe same as that for the nose gears. The mechanism for the landing gear retraction is based ona four-bar linkage using three members that are connected by pivots. A diagonal arm called thedrag brace breaks in the middle for retraction. The gear retracts backward while the drag braceretracts forward, as shown in Figure 12.2. The advantage of this mechanism is that in the event of ahydraulic failure, aero loads will blow the gear down and activate the landing gear. This mechanismwill be used for both the nose and main gear. The retraction mechanism will be operated withthe use of a hydraulics actuation system. Hydraulic fluid will flow through a valve and into anactuator when a command is made, which will subsequently move a piston that will directly causethe retraction or deployment of the landing gear.

Figure 12.2: Landing Gear Retraction Mechanism

38

Chapter 13

Propulsion

In order to power the aerocraft based on the iterative estimates for gross takeoff weight andcalculated T/W as explained earlier, we chose a twin engine configuration; one turbo jet engine oneach half-span of the wing. The total required thrust to takeoff is 136,000 lbs, therefore, each engineis only responsible for half that force in normal operable conditions. The General Electric (GE)CF6-80E1A3 turbofan engine, shown in Figure 13.1, was chosen because it had a maximum thrustoutput of 72,000 lbs. This engine provided the closest characteristics to what the aerocraft needs tooperate with a safety cushion of about 7,300 lbs. The engine provides a specific fuel consumption(SFC) at sea level of 0.33 lb/(lbf-hour) with a dry weight of 11,000 lbs per engine. The diameteris 9.5 ft and the length is 14 ft.

Figure 13.1: General Electric (GE) CF6-80E1A3 Engine

The placement of the engines will have to be at least 9 ft from the fuselage since the enginediameter is 9.5 ft. An estimate of the center point of the engine location along the wing span is11 ft from the fuselage or 0.27 inboard half-span fraction. The 6.25 ft space between one end ofthe engine to the main fuselage will allow for more laminar flow characteristics in that region inorder to not create any circulation due to the colliding flow coming from the engine nacelle andfuselage. Table 13.1 displays some of the key features and dimensions of the GE CF6-80E1A3turbofan engine.

39

Maximum Diameter (in) 114Length (in) 168

Takeoff Thrust (lbf ) 72,000Dry Weight (lbs) 11,225

Specific Fuel Consumption (lb/(lbf*hour) 0.33Overall Pressure Ratio 32.4

Table 13.1: Engine Specifications

Since our wings will be high, the two engines will be mounted on the underside of the wings.This allows for easy access from the ground, for maintenance purposes. The engines will be placedalong the wing, away from the fuselage. The weight of the engines out along the wing provides a”span-loading effect”, which helps reduce wing weight.

40

Chapter 14

Performance Analysis

14.1 Stall Speed

At takeoff, the aerocraft has a wing loading of 108 pounds per square foot (psf) and a CLmax

of 3.0 resulting in a takeoff stall speed of 174 ft/s. During landing, due to the amount of fuel thatwas burnt getting to the destination, the weight of the aerocraft decreases. Consequently, W/S ofthe aerocraft decreases to about 98 psf. At a CLmax of 3.0, this will result in a stall speed of about167 ft/s at landing configuration.

14.2 Takeoff and Landing

At takeoff, the engines of the aerocraft are able to provide a maximum thrust of 144,000 lbs,giving a takeoff T/W of 0.591. This is more than sufficient to meet the minimum requirementsfor takeoff. With this amount of thrust and the use of high lift systems giving a CLmax of 3.0, theaerocraft is able to achieve a takeoff distance of about 2280 ft at a W/S of 108 psf.

During landing, the W/S decreases to about 98 psf due to the reduced weight of the aerocraftfrom the burning of the fuel. With the use of high lift systems giving a CLmax of 3.0, the aerocraftis able to attain a landing distance of about 3,200 ft without the use of thrust reversers. This iswithin the landing distance requirement of 3,250 ft. Table 14.1 summarises the takeoff and landingparameters of the aerocraft.

Takeoff LandingCLmax 3.0 3.0

e 0.75 0.7CDO

0.1255 0.1328L/D 4.3 4.0T/W 0.59 NAW/S 108 98

Distance (ft) 2,280 3,200Margin (w/o thrust rev. %) 24 1.5Margin (w/ thrust rev. %) NA 41

Table 14.1: Takeoff and Landing Parameters

41

14.3 Cruise, Climb and Flight Ceiling

The use of the General Electric CF6-80E1A3 engines has allowed us to fly the aerocraft at ahigher cruise altitude. We have chosen to fly the aerocraft at a cruising altitude of 45,000 ft. Theamount of thrust required will be less and hence reduce the fuel consumed. Our calculations showthat at 45,000 ft a thrust of about 12,000 lbs will be required for cruising flight. The engines areable to provide an estimated total thrust of 15,000 lbs at this altitude. Thus, there is 3,000 lbs ofexcess thrust which could be used for any maneuver corrections needed as the flight progresses.

For the climb segment, we have chosen a climb angle of 7◦. For simplicity purposes, we assumeda constant acceleration in the direction of the thrust vector and that the aerocraft will climb alonga straight line path until it reaches cruising altitude. Taking into considerations these assumptionsand the climb angle, the aerocraft will achieve a climb rate of 3,520 ft/min and reach cruisingaltitude of 45,000 ft in about 13 minutes, covering a distance of about 60 nm along the ground. Attakeoff, the engines are capable of producing an initial excess thrust of 55,000 lbs

The flight ceiling of the aerocraft is determined primarily by the capabilities of the engine toprovide enough thrust to keep the aerocraft at level flight. Data taken from Jane’s AerospaceEngines show that the CF6-80 engines can cruise at a maximum altitude of 45,000 ft at a speedof Mach 1.0. Since our aerocraft is cruising at a lower speed, there is excess thrust to allow theaerocraft to climb to a higher cruise altitude. However, due to a lack of sufficient data regardingengine parameters, we can only estimate that the flight ceiling imposed by the engine capabilitieswould be slightly higher at about 48,000 ft.

14.4 Trimmed Lift and Drag

Using the data acquired through our weights estimation and W/S sizing, we were able to sizethe wing appropriately and determine the max coefficient of lift (CLmax) of the aerocraft to be0.5263 at 0o angle of attack. Using the step up method to determine a more precise value for theparasite drag coefficient (CD0), we were able to figure the coefficient of drag (CD) at various stagesin flight as well as a lift to drag ratio (L/D). The step up method involved using a more complexmethod of building up mission fuel fractions at each changing point in the mission profiles. Usingthe value for CD0 and a Mach number of 0.85 at cruise condition as inputs into AVL, we were ableto output a Trefftz plot that displays the sectional coefficient of lift values across the wing andhorizontal stabilizer span as well as CL and CD values for the aerocraft. The supercritical aerofoilused in AVL analysis was the NLF0215F.

The plot of these span-wise values can be seen below in Figure 14.1 for cruise at an angle ofattack of 0◦. The values given by AVL correspond to the condition whereby the control surfaceswere trimmed in order to maintain the aerocraft’s stability at the specified angle of attack andspeed.

The corresponding trimmed lift and drag coefficients are 0.5263 and 0.03709 respectively. Inaddition to giving the values for the induced and parasitic drag, the AVL plot also shows the liftdistribution across the wings.

14.5 Stability

From the CG analysis of the whole mission profile, we are able to derive the static marginchanges through out the mission as well. The static margin is coupled to the CG excursion as thetwo have a very close relation. The fact that the CG excursion is small also means that the staticmargin stays within a tight range, and in our design we have our static margin to range from 6%to 7.5%. This means that the aeroplane is generally stable throughout the flight without being too

42

Figure 14.1: Trimmed Lift and Drag Data from AVL

difficult to manuever. For a more detailed presentation of the static margin analysis please refer toAppendix B.

Besides having the ability to determine the lift and drag coefficients, AVL is also able to producethe stability derivatives of the wing for the various angles of attack. By observing the coefficientsof the stability derivatives, we are able to tell if there exists static stability due to five differentparameters: the angle of attack, sideslip angle, roll rate, pitch rate and yaw rate. Table 14.2and 14.3 show the stability derivatives for the wing at zero angle of attack.

Alpha BetaZ force 5.2139 -4.4e-005Y force 0.000783 -0.27821

Rolling Moment, Cl -0.00026 -0.085709Pitching Moment, Cm 4.1704 -9e-005Yawing Moment, Cn -0.000438 0.091262

Table 14.2: Stability Derivatives due to Angle of Attack and Sideslip Angle

Roll Rate, p Pitch Rate, q Yaw Rate, rZ force 0.000321 -4.002 -4e-006Y force 0.20732 -0.00158 0.156

Rolling Moment, Cl -0.479 0.000172 0.147Pitching Moment, Cm 8e-005 -27.51 4.1e-005Yawing Moment, Cn -0.0109 0.001013 -0.0673

Table 14.3: Stability Derivatives due to Roll Rate, Pitch Rate and Yaw Rate

As can be seen from the tables, the stability derivatives are stable for all five parametersmentioned earlier. For example, the pitching moment coefficient due to the pitch rate is negative,implying stability. In conclusion, the aerocraft will exhibit static stability.

43

Chapter 15

Aero Loads

An analysis of the aero loads exerted on the aeroplane was done in order to determine its basicstrength and flight performance limits. The specific aero loads examined include maneuver, gust,and lifting surface loads. These are discussed in the following sections.

15.1 Maneuver and Gust Loads

The generation of lift during high-g maneuvers typically accounts for the greatest aero loads onthe aeroplane. At lower speeds the highest load factor an aeroplane may experience is limited bythe maximum lift available. For higher speeds the maximum load factor is limited to the chosenvalue based upon the expected use of the aeroplane. The flight envelope, or V-n diagram, ofthe aeroplane describes these basic flight performance limits. A V-n diagram for the aeroplane’sminimum cruise weight of 140,000 lbs is shown below in Figure 15.1. Similarly, a V-n diagram forthe aeroplane’s maximum cruise weight of 250,000 lbs is shown below in Figure 15.2. The flightconditions represented by the boundary of the flight envelope are the most severe structurally.Furthermore, the points located on the corners are the most critical, in practice, because theycorrespond to the highest loads produced on the aeroplane.

Figure 15.1: V-n Diagram for Minimum Cruise Weight

44

Figure 15.2: V-n Diagram for Maximum Cruise Weight

The first loading condition occurs at the highest possible angle of attack, which is obtainedin a pull up. The second loading condition corresponds to the positive low angle of attack andmaximum indicated airspeed at which the aeroplane will dive. At the most negative high angle ofattack the third loading condition occurs, which is obtained in low speed maneuvers. The fourthcritical loading condition corresponds to the negative low angle of attack, which occurs at highspeed pitch down maneuvers. These four angles of attack specific to the design of this aeroplaneare listed below in Table 15.1.

Point AOA (α◦)A 14D 2G -10F -6

Table 15.1: Critical Loading Angles of Attack

The flight envelopes in Figures 15.1 and 15.2 show the flight performance limits for various cases.These include flaps retracted and deployed for symmetric maneuvers, as well as gust loads. Gustloads were also considered because they can sometimes exceed the maneuver loads experienced byan aeroplane. These gust loads cause a change in the angle of attack, which affects the aeroplane’slift and ultimately the load factor.

15.2 Lifting Surface Loads

An analysis of the aerodynamic, inertial, and gravity loads acting on the wing was done in orderto aid in the structural arrangement of the wing components. A visualization of the aerodynamicloads can be seen below in Figure 15.3. Despite this information being considered when creatingthe initial structural arrangement, a more detailed analysis of the shear forces and moments will berequired to correctly size the various structural wing components. Preliminary work can be foundin Appendix F.

45

Figure 15.3: Aero Loads on Wings

46

Chapter 16

Load Path

The structural arrangement of the aeroplane was developed to define the major structuralcomponents and establish the most efficient load paths through the structure. The load pathlayout shows the expected location of these structural supports necessary to carry the specificloads of the aeroplane. Structurally, the aeroplane must be able to withstand empennage, landinggear, wing, and propulsion integration loads without major structural failures or fatigue problems.

The major fuselage loads will be carried by longerons running fore and aft. The longeronswill attach to the skin and prevent the fuselage from bending. Due to the loads the fuselage willexperience when carrying 60,000 lbs of cargo, longerons, which carry larger loads and help preventthe fuselage from bending, were chosen over a larger number of smaller stringers. Since longeronsare heavier, their weight has been minimized by designing the aeroplane so that they are kept asstraight as possible. Trade studies performed at a later stage in the design will be necessary todetermine the optimized layout of the longerons around the fuselage. Figure 16.1 below shows theload path layout.

Figure 16.1: Torsion Moment About the y-Axis for Critical Points With Maximum Weight

In order to withstand the large bending moment the wing produces as a result of the liftingforce, a wing box will be used to carry the load across the fuselage. The high wing design allowsfor the wing box to pass through the fuselage without encountering any clearance issues. Also, by

47

using the box to support the bending moment created by the wing, the fuselage is not subjected tothese loads, which allowed for a reduced fuselage weight. The wing itself will consist of a multisparstructure, typical of large aerocraft, with ribs located where the major loads occur in order totransfer the corresponding loads to the spars and skin.

The engine mounts on the wings will also require significant structural support due to thevarious loads it will have to withstand. These primarily include the thrust of the engine and weightof the engine, as well as the aero loads within the inlet duct since the aeroplane requires jet engines.

48

Chapter 17

Cost Analysis

For a preliminary cost analysis, our team relied on the DAPCA IV model as recommended byRaymer. This tool provided us with a quick way to analyze the various cost components involved inresearch and development, and production of the aerocraft. Using the DAPCA IV estimation, wemanaged to produce a cost analysis based on the empty weight of the aerocraft, the speed of cruise,and the amount of thrust required by the aerocraft. The results of this analysis are presented inTable 17.1.

Program Cost (Billions) (2008 USD)Engineering 2.256

Tooling 1.202Manufacturing 2.121

Materials 0.845Engine 0.902

Avionics 0.722RDT&E + flyaway 9.83

Table 17.1: Program Costs

From this cost analysis, a mark up on the production costs was done to obtain the market price.This increase needs to cover the research and development costs as well as provide a comfortableoverall profit margin for our company. Based on our company’s decision, we have produced amarket pricing strategy, as shown in Table 17.2.

Planned Price (Millions) (2008 USD) 285Contribution Margin (Millions) (2008 USD) 65.7

Quantity planned 35Quantity to break even 33

Profit Total (Millions) (2008 USD) 135

Table 17.2: Market Pricing Strategy

49

Chapter 18

Conclusions

The Spinning Cube Aviation design should be used for the FEMA relief and cargo transportmission. This design does fulfill all requirements provided by FEMA for transoceanic and reliefmission flights. Spinning Cube Aviation provides diligent and timely service at a low cost. Ourstrengths include: theoretical fluid dynamics analysis, theoretical stress analysis, theoretical sta-bility and inoperative-engine testing, computer-aided design, and model design. We recommendthis design with an all-moving T-tail and with two engines mounted under a high wing. With thisdesign solely addressing the FEMA concerns, we are able to reduce the cost of manufacturing andengineering for this aeroplane. Our company strengths, requirement fulfillments, and low cost arefactors resulting in an advantageous partnership between Federal Emergency Management Agencyand Spinning Cube Aviation.

50

Bibliography

[1] John D. Anderson. Fundamentals of Aerodynamics. McGraw-Hill, Boston, 4th edition, 2007.

[2] Malcolm J. Azburg and E. Eugene Larrabee. Airplane Stability and Control. Cambridge Uni-versity Press, Cambridge, 2nd edition, 2002.

[3] FAA. Federal Aviation Regulations. Department of Transportation Federal Aviation, Washing-ton, DC, 1993.

[4] Fred T. Jane. Jane’s aero-engines, 2007.

[5] Fred T. Jane. Jane’s all the world’s aircraft, 2008.

[6] m-selig ’at’ uiuc.edu. http://www.ae.uiuc.edu/m-selig/ads/coord database.html. 05.XI.2008.

[7] Daniel P. Raymer. Aircraft Design: A Conceptual Approach. American Institute of Aeronauticsand Astronautics, Inc., Reston, 4th edition, 2006.

[8] Dr. Jan Roskam. Parts I-XI. Design, Analysis, Research Corporation, Lawrence, KS, 4 edition,2005.

51

Appendix A

Configuration Comparison

Red Config E-2C Hawkeye SAC Y-8 Sukhoi SSJ-100WTO (lbs) 194,462 54,426 134,480 78,903WE (lbs) 99,160 40,484 76,060 70,548

T/W 0.21 0.09 0.03 -W/S (psf) 90 77.75 103 95.2

SL (ft) 2,889 1,440 7,135 4147STO (ft) 1,632 2,600 9,870 4190

AR 9 9.3 11.9 9.8Wing Span (ft) 140 81 125 90

Table A.1: Comparison Aeroplanes for Red Configuration

White Config C-5 Galaxy Kawasaki C-2 Boeing C-17WTO (lbs) 550,255 769,000 311,072 585,000WE (lbs) 249,660 380,000 134,040 276,500

T/W 0.404 0.22 0.35 0.154W/S (psf) 90 124 89 162

SL (ft) 3,250 3,820 7,875 3,000STO (ft) 3,064 9,800 7,545 7,740

AR 6.25 7.8 6.1 7.2Wing Span (ft) 200 223 145.7 165

Table A.2: Comparison Aeroplanes for White Configuration

52

Appendix B

Mission Fuel Fraction

Mff Weight (lbs) CG pos. (ft) Static Margin (%)Gross Takeoff 1 243500 53.29 7.41

Warmup 0.998 243000 53.29 6.8434Taxi 0.998 242500 53.29 6.8403

Takeoff 0.995 241300 53.29 6.8324Climb 0.97815 236000 53.30 6.7973Cruise 0.95562 225500 53.31 6.7226Descent 0.99 223300 53.31 6.7056Landing 0.992 221500 53.32 6.6919

Fuel adjust 1 221500 52.32 12.082payload drop 161500 53.37 6.3848

warmup 0.998 161200 53.37 6.3808taxi 0.998 160900 53.37 6.3767

takeoff 0.995 160000 53.38 6.3665climb 0.97815 156500 53.38 6.321cruise 0.95154 149000 53.40 6.2149

descent 0.99 147500 53.41 6.1927climb 0.99673 147000 53.41 6.1855

cruise divert 0.94925 140000 53.43 6.0668loiter 0.98581 137600 53.44 6.0331

descent 0.99 136200 53.44 6.0092landing 0.992 135100 53.45 5.9899

Xnp 54.5474Weight of Fuel A 26411

B 21974Weight of Fuel Total 48386

Table B.1: Mission Fuel Fraction at Various Stages

53

Appendix C

Centers of Gravity

54

posi

tion

ofcg

wei

ght

xposi

tion

Wei

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xz

xz

Fuse

lage

Nose

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3640

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11.9

560788

43498

Body

2749

13745

50

11.9

5687250

164252.7

5Tail

1402

7010

85

11.9

5595850

83769.5

Win

g*

2257

22570

56

17.7

1263920

399489

Hor.

Tail

383

2106.5

136

43.4

286484

91422.1

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261

1435.5

119

29.6

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75

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75

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75

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66

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75

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36

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5Luggage

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Main

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26415

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293

53

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21979

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55

Appendix D

Engineering Drawings

Figure D.1: Engineering Drawing of Assembled Plane

56

Figure D.2: Engineering Drawing of Fuselage

57

Figure D.3: Engineering Drawing of Nose

58

Figure D.4: Engineering Drawing of Tail

59

Figure D.5: Engineering Drawing of Wing

60

Figure D.6: Engineering Drawing of Fuselage Tail

61

Appendix E

One Engine Inoperative

Takeoff Thrust (lb) 68100Y-Distance from Fuselage to Engine (ft) 13.15

Critical Yawing Moment (lb*ft) 895000Total Yawing Moment (lb*ft) 1118600

Stall Velocity (ft/s) 161.5Minimum Control Speed (ft/s) 193.8

CL of Tail 1.264Lift per Unit Area (lbf/ft2) 54.60

Moment Arm (ft) 63Surface Area (ft2) 325.21

Effective Surface Area (ft2) 260.17

Table E.1: One Engine Inoperative

62

Appendix F

Distributed Aerodynamic, Inertia andGravity Loading Plots

Figure F.1: Normal Force Load Distribution

63

Figure F.2: Chordwise Longitudinal Load Distribution

Figure F.3: Spanwise Pitch Moment Distribution

64

Figure F.4: Inertia Load Distribution

65

Appendix G

Wing Aerofoil Trade Study

66

Figure G.1: Trefftz Plot for α = −10◦


67



68



69



70



71

Figure G.11: Trefftz Plot for α = 00◦

72



73



74



75



76



77



78



79



80



81



82

Appendix H

MATLAB Code

H.1 Powell’s Parasite Drag Coefficient Matlab Code

%% Military cargo jet parasite drag coefficient calculation%c=0.1628; % From Roskam, for military cargod=0.7316; % From Roskam, for military cargoWTO=184890; % lbs%Swet=10^(c+d*log10(WTO))%cf=0.0030; % From Roskam for jetsf=cf*Swet%wingLoading=72; % psfS=WTO/wingLoadingCD0=f/SAR=6.633;v = 562.25*1.687; %ft/srho = .000889; %lb/ft^3q = 0.5*rho*v^2 %psfe=0.8;G= .29145;ToverW = linspace(.35,1.0,25);WoverS=(((ToverW)-G)+sqrt((ToverW-G).^2-...((4*CD0)/(pi*e*AR))))./(2/(q*pi*e*AR));plot(WoverS,ToverW); xlabel(’Wing Load’);ylabel(’Thrust to weight’); title(’Climb sizing’);

WoverScruise=linspace(0,150,150);ToverWcruise = ((q*CD0)./(WoverScruise)) + (WoverScruise).*(1/(q*pi*e*AR));plot(WoverScruise,ToverWcruise); xlabel(’Wing Load’);ylabel(’Thrust to weight’); title(’Cruise sizing’); axis([0 150 0 1]);

H.2 Weights Sensitivity Matlab Code

%Weights Sensitivity

83

% in FPS unitsclear all%constantsW_per_crew = 175+30;%pounds%Sensitivity analysisformat long;A = -0.299; B = 0.8904; %Our regression data for military cargo%iteration throughfor i = 0:6

d_pl = 0; dLoD = 0; d_range = 0; d_empty = 0; dCj = 0; dV = 0;if i == 1

d_pl = 1;elseif i == 2

dLoD = 0.01;elseif i == 3

d_range = 1;elseif i == 5

dCj = 0.001;elseif i == 6

dV = 1;end

%inputsM = 0.85;V = 500+dV; %knotsloiter = 0.5;%hoursrange = 500+d_range; %nautical miles excluding diversionrangeD = 350;%nautical miles for diversionCrew_num = 3;W_payload = 60000+d_pl; %lbfW_cargo = 50000+d_pl;Thrust2Weight = 0.369;WingLoading = 72;e_cruise = 0.8;AR = 6.633*1.2;Cdo_cruise = 0.0152;

%cruise L/D%altitude - 30000ft or 9144 metersTemp_cruise = (15.04 - 0.00649*9144 + 273.15); %Temperature at cruise (in Kelvins)Press_cruise = 101.29* (Temp_cruise/288.08)^5.256 * 1000; %pressure at cruise in PaTemp_cruise = Temp_cruise * 1.8; %Temperature at cruise in RankinePress_cruise = Press_cruise * 0.02088545632547; %pressure at cruise in psfV_cruise = 0.85*sqrt(1.4*287*Temp_cruise/1.8)*3.2808399; %cruise speed in ft/sq = 0.5*Press_cruise/1716/Temp_cruise*V_cruise^2; %dynamic pressure

Cj_cruise = 0.7+dCj; LoD_cruise = 1/( (q*Cdo_cruise/WingLoading)+...(WingLoading/q/pi/AR/e_cruise))+dLoD;%cruise Cj and L/DCj_loiter = 0.5+dCj; LoD_loiter = LoD_cruise+1;%loiter Cj and L/D

%calculating fuel fractions

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ff1 = 0.99; %warmupff2 = 0.99; %taxiff3 = 0.995; %take-offff4 = 0.98; %climbff5 = 0.99; %descentff6 = 0.992; %landingffc = exp(-range*Cj_cruise/V/LoD_cruise);ffcd = exp(-rangeD*Cj_cruise/V/LoD_cruise);ffl = exp(-loiter*Cj_loiter/LoD_loiter);

mff1 = ff1*ff2*ff3*ff4*ff5*ff6*ffc;mff2 = ff4*ff5*ff6*ffcd*ffl/ff6;

%weight iterationW_crew = W_per_crew * Crew_num;Wto1s = 200000; %lbf - guesserr = 10;while err > 1

Wf1 = Wto1s*(1-mff1); %fuel burned in 1st legWb = Wto1s-Wf1;%weight after 1st legWa = Wb-W_cargo;%weight after dumping cargoWf2 = Wa*(1-mff1);%fuel burned in 2nd legWf3 = (Wa-Wf2)*(1-mff2);%fuel burned in the diversionWf = 1.06*(Wf1+Wf2+Wf3);%total fuel burnedWes = (0.07+(1.71*Wto1s^(-0.1))*(AR^0.1)*(Thrust2Weight^0.06)...*(WingLoading^(-0.1))*(M^0.05))*Wto1s;%raymer’s more precise...% regression for empty weightWto2 = (W_payload + W_crew)/(1-(Wf/Wto1s) - (Wes/Wto1s));err = abs(Wto2 - Wto1s);Wto1s = Wto2;

end

if i == 0Wto1 = Wto1s;We = Wes;

end

if i~=0&i~=4%absolute changesD = d_empty+d_pl+dLoD+d_range+dCj+dV;dWto(i) = (Wto1s - Wto1)/D;dWtos = Wto1s-Wto1;%relative changed_pl = d_pl/W_payload;dLoD = dLoD/LoD_cruise;d_range = d_range/range;dCj = dCj/Cj_cruise;dV = dV/V;rc(i) = (dWtos/Wto1)/(d_pl+dLoD+d_range+dCj+dV);end

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if i == 4d_empty = 1;Wto3s = (10^((log10(We+d_empty) + A)/B));Wto2s = (10^((log10(We) + A)/B));dWtoe = Wto3s - Wto2s;dWto(i) = dWtoe; d_empty = d_empty/We;rc(i) = (dWtoe/Wto2s)/d_empty;

endenddWto=dWto’rc=rc’

H.3 Preliminary Sizing Matlab Code

clear allAR = 6.633*1.2 ; %with winglete_cruise = 0.8;Cdo_cruise = 0.0152;

%Sizing to Take-off requirementTOP = 66.6;CLmax = 3;%this is max take off CLrho1 = 101325/(287*308.15); %air density at landing fieldrho2 = 101325/(287*(273+25)); %air density at normal conditionssigma = rho1/rho2;

WingLoadingD = linspace(0,160);

CLTO=CLmax;c=-2500;a=0.0149;b=8.134;TOP23=(-b+sqrt(b^2-4*a*c))/(2*a)

Thrust2Weight1 = WingLoadingD/TOP/sigma/CLTO;hold onplot(WingLoadingD, Thrust2Weight1)xlabel(’Wing Loading (psf)’)ylabel(’Thrust to weight ratio’)

%Sizing to landingCLmaxland = 3.2;Thrust2WeightD = linspace(0,1.3);%Wingloading2 = (3250-450)*(sigma*CLmaxland/80)*ones(100);Wingloading2 = (3250/1.67/0.66-450)/80*sigma*4*ones(100);%FAR 25 requirement + thrust reversersplot(Wingloading2, Thrust2WeightD)

%Sizing to cruise

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%altitude - 30000ft or 9144 metersTemp_cruise = (15.04 - 0.00649*9144 + 273.15);%Temperature at cruise (in Kelvins)Press_cruise = 101.29* (Temp_cruise/288.08)^5.256 * 1000;%pressure at cruise in PaTemp_cruise = Temp_cruise * 1.8; %Temperature at cruise in RankinePress_cruise = Press_cruise * 0.02088545632547;%pressure at cruise in psfV_cruise = 0.85*sqrt(1.4*287*Temp_cruise/1.8)*3.2808399;%cruise speed in ft/sq = 0.5*Press_cruise/1716/Temp_cruise*V_cruise^2; %dynamic pressureWingloading3 = q*sqrt(pi*AR*e_cruise*Cdo_cruise/3)*ones(100);plot(Wingloading3, Thrust2WeightD)

%Sizing to Manuever%consider max load factor to be 2.5n = 2.5;Thrust2Weight4 = (q*Cdo_cruise)./WingLoadingD ...+ n*WingLoadingD/(q*pi*e_cruise*AR);plot(WingLoadingD,Thrust2Weight4)

%Sizing to climb%consider the largest minimum climb gradient of 2.4%Thrust2Weight5 = 0.03+2*sqrt(Cdo_cruise/pi/AR/e_cruise)*ones(100);plot(WingLoadingD, Thrust2Weight5); axis([0 160 0 1]);

H.4 Preliminary Static Margin Matlab Code

clear allWf = 13;Lf = 110;Kf = .05;qhq = 0.9;Dalphah = 0.7;Dcl=6.3;Dclh=6.3;MAC = 26.36;

Xacw = 44/MAC;Xach = 110/MAC;Sw = 2754;Sh = 1150;Dcmfus = (180/pi)*(Kf*Wf^2*Lf)/(MAC*Sw);

xnp = (Dcl * Xacw - Dcmfus + ((qhq)*(Sh/Sw))*Dclh*Dalphah*Xach).../ (Dcl + ((qhq)*(Sh/Sw))*Dclh*Dalphah)xcg = 53;margin = xnp - (xcg/MAC)

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H.5 Preliminary Weights Estimate Matlab Code

% in FPS unitsclear all%constantsW_per_crew = 175+30;%pounds%inputsM = 0.85;V = 500; %knotsloiter = 0.5;%hoursrange = 500; %nautical miles excluding diversion & descentrangeD = 350;%nautical miles for diversionCrew_num = 3;W_payload = 60000; %lbfW_cargo = 50000;Thrust2Weight = 0.369;WingLoading = 72;e_cruise = 0.8;AR = 6.633*1.2; %with wingletCdo_cruise = 0.0152;Wto1 = 200000;%1st guess

%cruise L/D%altitude - 30000ft or 9144 metersTemp_cruise = (15.04 - 0.00649*9144 + 273.15);%Temperature at cruise (in Kelvins)Press_cruise = 101.29* (Temp_cruise/288.08)^5.256 * 1000;%pressure at cruise in PaTemp_cruise = Temp_cruise * 1.8;%Temperature at cruise in RankinePress_cruise = Press_cruise * 0.02088545632547;%pressure at cruise in psfV_cruise = 0.85*sqrt(1.4*287*Temp_cruise/1.8)*3.2808399;%cruise speed in ft/sq = 0.5*Press_cruise/1716/Temp_cruise*V_cruise^2; %dynamic pressure

Cj_cruise = 0.7; LoD_cruise = 1/( (q*Cdo_cruise/WingLoading)...+(WingLoading/q/pi/AR/e_cruise));%cruise Cj and L/DCj_loiter = 0.5; LoD_loiter = LoD_cruise+1;%loiter Cj and L/D%calculating fuel fractionsff1 = 0.99; %warmupff2 = 0.99; %taxiff3 = 0.995; %take-offff4 = 1.0065-0.0325*M; %climbff5 = 0.99; %descent; include 100nmff6 = 0.992; %landingffc = exp(-range*Cj_cruise/V/LoD_cruise);%cruise for 500nmffcd = exp(-rangeD*Cj_cruise/V/LoD_cruise);%cruise for 350nmffl = exp(-loiter*Cj_loiter/LoD_loiter);%loiter for 1/2 hour

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mff1 = ff1*ff2*ff3*ff4*ff5*ff6*ffc;mff2 = ff4*ff5*ff6*ffcd*ffl/ff6;

%weight iterationW_crew = W_per_crew * Crew_num;A = -0.299; B = 0.8904; %Our regression data for military cargoerr = 10;while err > 1,

Wf1 = Wto1*(1-mff1); %fuel burned in 1st legWb = Wto1-Wf1;%weight after 1st legWa = Wb-W_cargo;%weight after dumping cargoWf2 = Wa*(1-mff1);%fuel burned in 2nd legWf3 = (Wa-Wf2)*(1-mff2);%fuel burned in the diversionWf = 1.06*(Wf1+Wf2+Wf3);%total fuel burned

We = (0.07+(1.71*Wto1^(-0.1))*(AR^0.1)*(Thrust2Weight^0.06)...*(WingLoading^(-0.1))*(M^0.05))*Wto1;%raymer’s more precise regression for empty weightWto2 = W_crew+W_payload+Wf+We;err = abs(Wto2 - Wto1);Wto1 = Wto2;

end

H.6 Powell’s Inviscid Flapped Wing Loading Code

%% wingLoading.m - This is a matlab script that uses simple% lifting-line theory to compute the circulation% distribution, sectional lift and drag, and% total lift and drag on a tapered wing that% has aerodynamic twist.%% Inviscid properties (induced drag, induced angle% of attack, etc) are calculated by solving the% fundamental equation of finite-wing theory by% a Fourier-decomposition method.%% Written by Prof. Powell for Aero 481,% September, 2001.%% Last modified - 9/30/07%bOverCs=input(’Input the wing span, normalized by the root chord: ’);tipChord=input(’Input the tip chord, normalized by the root chord: ’);numberOfStations=100;alphaG=input(’Input the angle of attack of the wing (in deg): ’);flapStart =input([’Input the inboard flap edge’...’ location as a fraction of the half-span: ’]);flapEnd = input([’Input the outboard flap edge’...’ location as a fraction of the half-span: ’]);alphaL=input([’Input the zero-lift angle of’...

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’ attack of the unflapped portion (in deg): ’]);alphaLF = input(’Input the zero-lift angle’...’ of attack of the flapped portion (in deg): ’]);%for i=1:numberOfStations,

yOverCs(i)=0.9999*bOverCs/2*cos((i-1)*pi/(numberOfStations-1));cOverCs(i)=1-(1-tipChord)*abs(yOverCs(i)/(bOverCs/2));alpha(i)=alphaG*pi/180;if(abs(2*yOverCs(i)/bOverCs) >= flapStart &...

abs(2*yOverCs(i)/bOverCs) <= flapEnd)alphaL0(i)=alphaLF*pi/180;

elsealphaL0(i)=alphaL*pi/180;

endend%% Set up the values of theta at the spanwise stations%for i=1:numberOfStations,

theta(i)=acos(yOverCs(i)/(bOverCs/2));end%% Calculate the influence coefficients%for i=1:numberOfStations,

for n=1:numberOfStations,c(i,n)=(1/cOverCs(i)+pi/(2*bOverCs)*n/sin(theta(i)))*sin(n*theta(i));

endend%% Set the RHS vector for the fundamental equation%alpha_a=(alpha-alphaL0)’;%% Solve the matrix problem for the harmonic coefficients%disp(’ ’)disp(’Solving the matrix problem for the A_n’’s...Hang on’)disp(’ ’)a=c\alpha_a;%% Calculating the area and aspect ratio.%areaOverCsSquared = 0;for i=2:numberOfStations-1,

dyOverCs=abs(yOverCs(i+1)-yOverCs(i-1))/2;areaOverCsSquared = areaOverCsSquared + ...

dyOverCs*(cOverCs(i-1)+cOverCs(i+1))/2;endi=1;

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dyOverCs=abs(yOverCs(i+1)-yOverCs(i))/2;areaOverCsSquared = areaOverCsSquared+dyOverCs*cOverCs(i);i=numberOfStations;dyOverCs=abs(yOverCs(i)-yOverCs(i-1))/2;areaOverCsSquared = areaOverCsSquared+dyOverCs*cOverCs(i);%AR = bOverCs^2/areaOverCsSquared;%disp(’ ’)disp(’Done with the calculation. Hit any key to continue.’)pause;disp(’ ’)clc%% Set up the plot title string.%userName=getenv(’USER’);subTitle = sprintf(’%s -- (\\alpha = %4.2f, AR = %4.2f)’,...userName,alphaG,AR);%% Plot the circulation distribution along the span (Gamma/(c_s*U_inf))%disp(’ ’)disp(’Plotting Gamma vs y.’)disp(’ ’)%for i=1:numberOfStations,

Gamma(i)=0;end%for i=1:numberOfStations,

for n=1:numberOfStations,Gamma(i)=Gamma(i)+pi*a(n)*sin(n*theta(i));

endend%plot(yOverCs,Gamma,’r+’,yOverCs,Gamma,’r-’);myTitle = sprintf(’%s --- Circulation’,subTitle);title(myTitle);xlabel(’y/c_s’);ylabel(’Gamma/(c_s*U_{inf})’);print -dps gamma.ps%disp(’ ’)disp(’Done. Saved in gamma.ps. Hit any key when done viewing plot.’)disp(’ ’)pause;clc%% Plot the induced angle of attack along the span

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%disp(’ ’)disp(’Plotting alpha_i vs y.’)disp(’ ’)%for i=1:numberOfStations,

alpha_i(i)=0;end%for i=1:numberOfStations,

for n=1:numberOfStations,alpha_i(i)=alpha_i(i)-pi/(2*bOverCs)*n*a(n)*...sin(n*theta(i))/sin(theta(i));

endend%plot(yOverCs,alpha_i,’r+’,yOverCs,alpha_i,’r-’);myTitle = sprintf(’%s --- Induced Angle of Attack’,subTitle);title(myTitle);xlabel(’y/c_s’);ylabel(’alpha_i’);print -dps alphaI.ps%disp(’ ’)disp(’Done. Saved in alphaI.ps. Hit any key when done viewing plot.’)disp(’ ’)pause;clc%% Plot the sectional lift coefficient along the span%disp(’ ’)disp(’Plotting Cl vs y.’)disp(’ ’)%for i=1:numberOfStations,

cl(i)=0;end%for i=1:numberOfStations,

for n=1:numberOfStations,cl(i)=cl(i)+2*pi/cOverCs(i)*a(n)*sin(n*theta(i));

endend%plot(yOverCs,cl,’r+’,yOverCs,cl,’r-’);myTitle = sprintf(’%s --- Sectional Lift Coefficient’,subTitle);title(myTitle);xlabel(’y/c_s’);ylabel(’C_l’);

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print -dps cl.ps%disp(’ ’)disp(’Done. Saved in cl.ps. Hit any key when done viewing plot.’)disp(’ ’)pause;clc%% Plot the sectional induced drag coefficient along the span%disp(’ ’)disp(’Plotting Cdi vs y.’)disp(’ ’)%for i=1:numberOfStations,

cdi(i)=-cl(i)*alpha_i(i);end%plot(yOverCs,cdi,’r+’,yOverCs,cdi,’r-’);myTitle = sprintf(’%s --- Sectional Induced Drag Coefficient’,...subTitle);title(myTitle);xlabel(’y/c_s’);ylabel(’C_{d_i}’);print -dps cdi.ps%disp(’ ’)disp(’Done. Saved in cdi.ps. Hit any key when done viewing plot.’)disp(’ ’)pause;clc%CL = pi/4*2*pi/bOverCs*AR*a(1);%sum=0;for n=1:numberOfStations

sum = sum + n*(a(n)/a(1))^2;endCDi = CL^2/(pi*AR)*sum;%CD = CDi;%CLOverCD=CL/CD;%e=CL^2/(CD*pi*AR);%fprintf(’Wing aspect ratio AR = %4.2f\n’,AR);fprintf(’Wing lift coefficient CL = %6.4f\n’,CL);fprintf(’Wing induced drag coefficient CD_i = %6.4f\n’,CDi);fprintf(’Wing L/D = %4.2f\n’,CL/CD);

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fprintf(’Osswald efficiency e = %4.2f\n’,e);

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Appendix I

Calculations

I.1 Calculations for Stall Speed

Takeoff: Lift = Weight

0.5 ∗ ρ ∗ S ∗ V 2 ∗ CLmax = 243, 5000.5 ∗ 0.00238 ∗ 2257 ∗ V 2 ∗ 3.0 = 243, 500

V = 174 ft/s

Landing: Lift = Weight

0.5 ∗ ρ ∗ S ∗ V 2 ∗ CLmax = 223, 281.80.5 ∗ 0.00238 ∗ 2257 ∗ V 2 ∗ 3.0 = 223, 281.8

V = 166 ft/s

I.2 Calculations for Climb Rate

Assuming 7◦ climb angle,Distance traveled along aircraft horizontal axis = 45,000 / sin(7◦) = 369,248 ftAssuming constant acceleration along aircraft horizontal axis,

V 2 = U2 + 2 ∗ a ∗ s

7902 = 1742 + 2 ∗ a ∗ 369, 248a = 0.804 ft/s2

Time taken = (790− 174)/0.804= 766 s

= 12.8 min

Climb rate =45, 000

76660

= 3520 ft/min

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