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40 Solution Procedures Table 5-1. Maximum-effort solution. maximum effort variable initial increment tolerance horizontal velocity Vh 0.1V Δ 0.1Vɛ vertical rate of climb Vz 0.1V Δ 0.1Vɛ aircraft altitude HΔ Hɛ aircraft angular rate ˙ θ (pullup), ˙ ψ (turn) ΩΔ Ωɛ aircraft linear acceleration ax, ay, az GΔ Gɛ Table 5-2. Maximum-effort solution. maximum effort quantity best endurance maximum 1/ ˙w best range 99% maximum V/ ˙w high or low side, or 100% best climb or descent rate maximum Vz or 1/P best climb or descent angle maximum Vz/V or V/P ceiling maximum altitude power limit power margin, min(PavP G − PreqPG) =0 over all propulsion groups torque limit torque margin, min(Qlimit − Qreq) =0 over all limits wing stall lift margin, CLmax − CL =0 for designated wing rotor stall thrust margin, (CT /σ)max − CT /σ =0 for designated rotor Table 5-3. Trim solution. trim quantity target tolerance aircraft total force x, y, z components 0 Fɛ aircraft total moment x, y, z components 0 Mɛ aircraft load factor x, y, z components Flight State ɛ propulsion group power Flight State Pɛ power margin PavP G − PreqPG Flight State Pɛ rotor force lift, vertical, propulsive Flight State, component schedule Fɛ rotor thrust CT /σ Flight State Cɛ rotor thrust margin (CT /σ)max − CT /σ Flight State Cɛ rotor flapping βc, βs Flight State Aɛ rotor hub moment x (roll), y (pitch) Flight State Mɛ rotor torque Flight State Mɛ wing force lift Flight State, component schedule Fɛ wing lift coefficient CL Flight State Cɛ wing lift margin CLmax − CL Flight State Cɛ tail force lift Flight State Fɛ
Solution Procedures 41 Table 5-4. Trim solution. trim variable perturbation aircraft orientation θ (pitch), φ (roll) 100AΔ aircraft velocity Vh (horizontal velocity) V Δ aircraft velocity Vz (vertical velocity) V Δ aircraft velocity β (sideslip) 100AΔ aircraft angular rate ˙ θ (pullup), ˙ ψ (turn) ΩΔ aircraft control angle 100AΔ 5-1.7 Rotor-Flap Equations Evaluating the rotor hub forces may require solution of the flap equations E(v) =0. For tippath plane command, the thrust and flapping are known, so v =(θ0.75 θc θs) T . For no-feathering plane command, the thrust and cyclic pitch are known, so v =(θ0.75 βc βs) T . A Newton–Raphson solution method is used: from E(vn+1) ∼ = E(vn)+(dE/dv)(vn+1 − vn) =0, the iterative solution is vn+1 = vn − CE(vn) where C = f(dE/dv) −1 , including the relaxation factor f. The derivative matrix for axial flow can be used. Alternatively, the derivative matrix dE/dv can be obtained by numerical perturbation. Convergence of the Newton–Raphson iteration is tested in terms of |E|
Page 1 and 2: NASA/TP-2009-215402 NDARC NASA Desi
Page 3 and 4: NASA/TP-2009-215402 NDARC NASA Desi
Page 5 and 6: TABLE OF CONTENTS CHAPTER 1 - INTRO
Page 7: TABLE OF CONTENTS (cont.) CHAPTER 1
Page 10 and 11: viii LIST OF FIGURES (cont.) Figure
Page 13 and 14: Chapter 1 Introduction The NASA Des
Page 15 and 16: Introduction 3 of rotorcraft config
Page 17 and 18: Introduction 5 previous case DESIGN
Page 19 and 20: Introduction 7 4) Scully, M.; and F
Page 21 and 22: Chapter 2 Nomenclature The nomencla
Page 23 and 24: Nomenclature 11 Fuel Tanks Power Na
Page 25 and 26: Nomenclature 13 Motion aF AC aircra
Page 27 and 28: Chapter 3 Tasks The NDARC code perf
Page 29 and 30: Tasks 17 engine group is found (inc
Page 31 and 32: Tasks 19 3-4 Maps 3-4.1 Engine Perf
Page 33 and 34: Chapter 4 Operation 4-1 Flight Cond
Page 35 and 36: Operation 23 e) Input payload weigh
Page 37 and 38: Operation 25 Table 4-1. Mission seg
Page 39 and 40: Operation 27 horizontal ground dist
Page 41 and 42: Operation 29 climb for zero power m
Page 43 and 44: Operation 31 a) Horizontal velocity
Page 45 and 46: Operation 33 From the pressure p =
Page 47 and 48: Chapter 5 Solution Procedures The N
Page 49 and 50: Solution Procedures 37 Sizing Task
Page 51: Solution Procedures 39 relaxation i
Page 55 and 56: Solution Procedures 43 successive s
Page 57 and 58: Solution Procedures 45 initialize e
Page 59 and 60: Chapter 6 Cost Costs are estimated
Page 61 and 62: Cost 49 Table 6-1. DoD and CPI infl
Page 63 and 64: Cost 51 predicted base price (1994$
Page 65 and 66: Chapter 7 Aircraft The aircraft con
Page 67 and 68: Aircraft 55 The tilt control variab
Page 69 and 70: Aircraft 57 forward axes for descri
Page 71 and 72: Aircraft 59 For steady-state flight
Page 73 and 74: Aircraft 61 where Δz F = z F − z
Page 75 and 76: Aircraft 63 disk area); or the drag
Page 77 and 78: Aircraft 65 7-10 Performance Indice
Page 79 and 80: Aircraft 67 WEIGHT EMPTY STRUCTURE
Page 81 and 82: Chapter 8 Systems The systems compo
Page 83 and 84: Chapter 9 Fuselage There is one fus
Page 85 and 86: Fuselage 73 αe = αfus − αzl, w
Page 87 and 88: Chapter 10 Landing Gear There is on
Page 89 and 90: Chapter 11 Rotor The aircraft can h
Page 91 and 92: Rotor 79 propulsion group. The driv
Page 93 and 94: Rotor 81 plane command. The collect
Page 95 and 96: Rotor 83 or just CSF = WCHF with no
Page 97 and 98: Rotor 85 If μ is zero, the equatio
Page 99 and 100: Rotor 87 The velocity ratio is fW =
Page 101 and 102: Rotor 89 T/T ∞ 1.3 1.2 1.1 1.0 Ha
Page 103 and 104:
Rotor 91 TPP tilt / cyclic magnitud
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Rotor 93 with an average over the r
Page 107 and 108:
Rotor 95 (all equal to 1 for μz =0
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Rotor 97 κ 1.30 1.25 1.20 1.15 1.1
Page 111 and 112:
Rotor 99 (C T /σ) s c d mean 0.20
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Rotor 101 11-5.1.3 Twin Rotors For
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Rotor 103 The wake is a skewed cyli
Page 117 and 118:
Rotor 105 weight per lifting rotor;
Page 119 and 120:
Chapter 12 Force The force componen
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Chapter 13 Wing The aircraft can ha
Page 123 and 124:
Wing 111 denotes outboard edge, sub
Page 125 and 126:
Wing 113 13-3.1 Lift The wing lift
Page 127 and 128:
Wing 115 The wing interference at t
Page 129 and 130:
Chapter 14 Empennage The aircraft c
Page 131 and 132:
Empennage 119 14-4 Weights The tail
Page 133 and 134:
Chapter 15 Fuel Tank 15-1 Fuel Capa
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Fuel Tank 123 if Wfuel >Wfuel−max
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Chapter 16 Propulsion The propulsio
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Propulsion 127 If the sum of the fi
Page 141 and 142:
Chapter 17 Engine Group The engine
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Engine Group 131 The engine group p
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Engine Group 133 specific fuel cons
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Chapter 18 Referred Parameter Turbo
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Referred Parameter Turboshaft Engin
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Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Chapter 19 AFDD Weight Models This
Page 161 and 162:
AFDD Weight Models 149 The spar-cap
Page 163 and 164:
AFDD Weight Models 151 19-1.2 Aircr
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AFDD Weight Models 153 where w = nz
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AFDD Weight Models 155 units as use
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AFDD Weight Models 157 Table 19-9.
Page 171 and 172:
AFDD Weight Models 159 where fP = f
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AFDD Weight Models 161 The conversi
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AFDD Weight Models 163 19-12 Foldin
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AFDD Weight Models 165 error (%) er
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