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90 Rotor The forces acting on the hub are the thrust T , drag H, and side force Y (positive in z, x, yaxis directions, respectively). The aerodynamic analysis is conducted for a clockwise rotating rotor, with appropriate sign changes for lateral velocity, flapping, and force. The analysis is conducted in dimensionless form, based on the actual radius and rotational speed of the flight state. The inplane hub forces are produced by tilt of the thrust vector with the tip-path plane, plus forces in the tip-path plane, and profile terms (produced by the blade drag coefficient). The orientation of the tip-path axes relative to the shaft axes is then C PS = Xrβs Y−βc. Then ⎛ ⎝ CH CY CT ⎞ ⎠ = C SP ⎛ ⎝ 0 0 CT /C SP 33 ⎞ ⎛ ⎠ + rCY tpp 0 ⎝ CHtpp ⎞ ⎛ ⎠ + ⎝ CHo rCYo 0 The inplane forces relative to the tip-path plane can be neglected, or calculated by blade-element theory. Note that with tip-path plane command and CHtpp and CY tpp neglected, it is not necessary to solve for the rotor collective and cyclic pitch angles. In general the inplane forces relative to the tip-path plane are not zero, and may be significant, as for a rotor with large flap stiffness. Figures 11-3a and b show respectively the tip-path plane tilt and thrust vector tilt with cyclic pitch control (no-feathering plane tilt) as functions of flap stiffness (frequency), for several rotor thrust values. The difference between tip-path plane tilt (fig. 11-3a) and thrust vector tilt (fig. 11-3b) is caused by tilt of the thrust vector relative to the tip-path plane. The profile inplane forces can be obtained from simplified equations, or calculated by blade-element theory. The simplified method uses: CHo CYo = σ 8 cdmeanFH μx/μ −μy/μ where the mean drag coefficient cdmean is from the profile power calculation. The function FH accounts for the increase of the blade-section velocity with rotor edgewise and axial speed: CHo = 1 2 σcdU(r sin ψ + μ)dr = 1 2 σcd(u 2 T + u2 R + u2 P )1/2 (r sin ψ + μ)dr; so (from Harris) with V 2 = μ 2 + μ 2 z. FH =4 1 2π 2π 1 0 ∼= 1+V 2 0 ⎞ ⎠ 2 2 2 1/2 (r + μ sin ψ) +(μcos ψ) + μz (r sin ψ + μ) dr dψ 3μ + 1 4 μ3 V 2 − 1 (1 + V 2 ) 2 + μμ 2 z + 3 4 μ3 ln 11-4.3 Blade-Element Theory √ 1+V 2 +1 Blade-element theory is the basis for the solution for the collective and cyclic pitch angles (or flap angles) and evaluation of the rotor inplane hub forces. The section aerodynamics are described by lift varying linearly with angle-of-attack, cℓ = cℓαα (no stall), and a constant mean drag coefficient cdmean (from the profile power calculation). The analysis is conducted in dimensionless form (based on density ρ, rotor rotational speed Ω, and blade radius R of the flight state). So in the following σ, ν, and γ are for the actual R and Ω, and a =5.7 is the lift-curve slope used in the Lock number γ. The blade-section aerodynamic environment is described by the three components of velocity, from which the yaw and V
Rotor 91 TPP tilt / cyclic magnitude thrust tilt / cyclic magnitude 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 flap frequency ν (per-rev) Figure 11-3a. Tip-path plane tilt with cyclic pitch. CT /σ = 0.14 CT /σ = 0.10 CT /σ = 0.06 CT /σ = 0.02 0.0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 flap frequency ν (per-rev) Figure 11-3b. Thrust-vector tilt with cyclic pitch. CT /σ = 0.02 CT /σ = 0.06 CT /σ = 0.10 CT /σ = 0.14
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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
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Operation 33 From the pressure p =
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Chapter 5 Solution Procedures The N
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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 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: Rotor 89 T/T ∞ 1.3 1.2 1.1 1.0 Ha
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
Page 147 and 148: Chapter 18 Referred Parameter Turbo
Page 149 and 150: Referred Parameter Turboshaft Engin
Page 151 and 152: Referred Parameter Turboshaft Engin
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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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