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84 Rotor The force includes a term proportional to the rotor thrust and an input blockage factor fB =ΔT/T ≥ 0. This term accounts for blockage or download, as an alternative to including the drag of the fuselage or a lifting surface in the aircraft trim. For example, fB can model the tail-rotor blockage caused by operation near the vertical tail. The rotor loads in aircraft axes acting at the center of gravity are then: where Δz F = z F hub − zF cg. F F = C FS F S M F = C FS M S + Δz F F F The wind axis lift L and drag X are calculated from the net rotor-hub force F F and the rotor velocity v F . The velocity relative to the air gives the propulsive-force direction ep = v F /|v F | (no interference) and the velocity magnitude V = |v F |. The drag and lift components of the force are X = −e T p F F and L = |(I −epe T p )F F |, respectively. Thus XV = −(v F ) T F F and L 2 = |F F | 2 −|X| 2 . The rotor contribution to vertical force is the z-axis component of the force in inertial axes, FV = −k T C IF F F . 11–4 Aerodynamics The rotor velocity relative to the air is vF = vF AC + ωF ACΔzF in aircraft axes. The velocities in shaft axes are v S = C SF v F ⎛ =ΩR⎝ −μx ⎞ rμy ⎠ μz ω S = C SF ω F ⎛ ⎞ r ˙αx AC =Ω⎝ ˙αy ⎠ r ˙αz where ΩR is the rotor tip speed. The advance ratio μ, inflowratio λ, and shaft angle-of-attack α are defined as μ = μ 2 x + μ 2 y λ = λi + μz α = tan −1 (μz/μ) The blade velocity relative to the air has the maximum amplitude (advancing tip velocity) of μat = (1 + μ) 2 + μ 2 z, from which the advancing tip Mach number is Mat = Mtipμat, using the tip Mach number Mtip =(ΩR)/cs. The rotor thrust coefficient is defined as CT = T/ρA(ΩR) 2 . The dimensionless ideal induced velocity λi is calculated from μ, μz, and CT ; then the dimensional velocity is vi =ΩRλi. The ideal induced power is then Pideal = Tvi. Note that for these inflow velocities, the subscript “i” denotes “ideal.” The ideal induced velocity could be solved based on the reference velocity vh rather than the tip speed ΩR, but the advance ratio is required for other purposes as well. 11-4.1 Ideal Inflow The ideal wake-induced velocity is obtained from the momentum theory result of Glauert: λi = CT 2 λ2 sλ = + μ2 2 h λ2 + μ2 where λ = λi + μz, λ 2 h = |CT |/2 (λh is always positive) and s = sign CT . This expression is generalized to λi = λh sF(μ/λh,sμz/λh)
Rotor 85 If μ is zero, the equation for λi can be solved analytically. Otherwise, for non-axial flow, the equation is written as follows: λ = sλ2 h + μz λ2 + μ2 Using λ instead of λi as the independent variable simplifies implementation of the ducted fan model. A Newton–Raphson solution for λ gives: λin = λn+1 = λn − sλ 2 h λ 2 n + μ 2 λn − μz − λin 1+ λinλn/(λ 2 n + μ 2 ) f A relaxation factor of f =0.5is used to improve convergence. Three or four iterations are usually sufficient, using λ ∼ = sλ2 h (sλh + μz) 2 + μz + μ2 to start the solution. To eliminate the singularity of the momentum theory result at ideal autorotation, the expression 2 0.373μz +0.598μ λ = μz 2 − 0.991 is used when λ 2 h 1.5μ 2 +(2sμz +3λh) 2
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NASA/TP-2009-215402 NDARC NASA Desi
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NASA/TP-2009-215402 NDARC NASA Desi
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TABLE OF CONTENTS CHAPTER 1 - INTRO
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TABLE OF CONTENTS (cont.) CHAPTER 1
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viii LIST OF FIGURES (cont.) Figure
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Chapter 1 Introduction The NASA Des
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Introduction 3 of rotorcraft config
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Introduction 5 previous case DESIGN
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Introduction 7 4) Scully, M.; and F
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Chapter 2 Nomenclature The nomencla
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Nomenclature 11 Fuel Tanks Power Na
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Nomenclature 13 Motion aF AC aircra
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Chapter 3 Tasks The NDARC code perf
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Tasks 17 engine group is found (inc
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Tasks 19 3-4 Maps 3-4.1 Engine Perf
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Chapter 4 Operation 4-1 Flight Cond
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Operation 23 e) Input payload weigh
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Operation 25 Table 4-1. Mission seg
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Operation 27 horizontal ground dist
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Operation 29 climb for zero power m
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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 and 52: Solution Procedures 39 relaxation i
Page 53 and 54: Solution Procedures 41 Table 5-4. T
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: Rotor 83 or just CSF = WCHF with no
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
Page 105 and 106: Rotor 93 with an average over the r
Page 107 and 108: Rotor 95 (all equal to 1 for μz =0
Page 109 and 110: 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
Page 113 and 114: Rotor 101 11-5.1.3 Twin Rotors For
Page 115 and 116: 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
Page 121 and 122: 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
Page 135 and 136: Fuel Tank 123 if Wfuel >Wfuel−max
Page 137 and 138: Chapter 16 Propulsion The propulsio
Page 139 and 140: Propulsion 127 If the sum of the fi
Page 141 and 142: Chapter 17 Engine Group The engine
Page 143 and 144: Engine Group 131 The engine group p
Page 145 and 146: 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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Chapter 19 AFDD Weight Models This
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AFDD Weight Models 149 The spar-cap
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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.
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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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