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104 Rotor vm = κ(KT / √ 2) (T1 + T2)/2ρA. The interference velocities are calculated separately for the two rotors, with the correction factor ft: vint1 = ftκ T1/2ρA and vint2 = ftκ T2/2ρA. The sum vint1 + vint2 must take the required value. Below the non-overlap region, the component is in the wake of only one of the rotors, so the interference velocity from the other rotor is zero, and thus ft =1. Below the overlap region, the component is in the wake of both rotors, and the sum of the interference velocities equals vm if fth = KT / √ 2 √ τ1 + √ τ2 where τn = Tn/(T1 + T2) is the thrust ratio. For equal thrusts, fth = KT /2; orfth =1/ √ 2 for the nominal velocity. The expression ft = fth cos 2 χ+sin 2 χ gives the required correction factor, with ft =1 in edgewise flight. Optionally the correction for twin rotors can be omitted (ft =1); nominal (KT = √ 2); or use an input velocity factor in overlap region (KT ). 11–8 Drag The rotor component includes drag forces acting on the hub and spinner (at zF hub ) and on the pylon (at zF pylon ). The component drag contributions must be consistent. In particular, a rotor with a spinner (such as on a tiltrotor aircraft) would likely not have hub drag. The pylon is the rotor support and the nacelle is the engine support. The drag model for a tiltrotor aircraft with tilting engines would use the pylon drag (and no nacelle drag), since the pylon is connected to the rotor shaft axes; with non-tilting engines it would use the nacelle drag as well. The body axes for the drag analysis are rotated about the y-axis relative to the rotor shaft axes: C BF = C BS C SF , where C BS = Y−θref . The pitch angle θref can be input, or the rotation appropriate for a helicopter rotor or a propeller can be specified. a) Consider a helicopter rotor, with the shaft axes oriented z-axis up and x-axis downstream. It is appropriate that the angle-of-attack is α =0for forward flight, and α = −90 degree for hover, meaning that the body axes are oriented z-axis down and x-axis forward. Hence θref = 180 degree. b) Consider a propeller or tiltrotor, with the shaft axes oriented z-axis forward and x-axis up. It is appropriate that the angle-of-attack is α =0in cruise and α =90 degree for helicopter mode (with a tilting pylon), meaning that the body axes are oriented z-axis down and x-axis forward. Hence θref =90degree. The aerodynamic velocity relative to the air is calculated in component axes, v B . The angle-of-attack α and dynamic pressure q are calculated from v B . The reference areas for the drag coefficients are the rotor disk area A = πR 2 (for hub drag), pylon wetted area Spylon, and spinner wetted area Sspin; these areas are input or calculated as described previously. The hub drag can be fixed, specified as a drag area D/q; or the drag can be scaled, specified as a drag coefficient CD based on the rotor disk area A = πR 2 ; or the drag can be estimated based on the gross weight, using a squared-cubed relation or a square-root relation. Based on historical data, the drag coefficient CD =0.004 for typical hubs, CD =0.0024 for current low-drag hubs, and CD =0.0015 for faired hubs. For the squared-cubed relation: (D/q)hub = k(WMTO/1000) 2/3 (WMTO is the maximum takeoff gross weight; units of k are feet 2 /kilopound 2/3 or meter 2 /Megagram 2/3 ). Based on historical data, k =1.4 for typical hubs, k =0.8 for current low-drag hubs, and k =0.5 for faired hubs (English units). For the square-root relation: (D/q)hub = k WMTO/Nrotor (WMTO/Nrotor is the maximum takeoff gross
Rotor 105 weight per lifting rotor; units of k are feet 2 /pound 1/2 or meter 2 /kilogram 1/2 ); based on historical data (ref. 14), k =0.074 for single-rotor helicopters, k =0.049 for tandem-rotor helicopters (probably a blade number effect), k =0.038 for hingeless rotors, and k =0.027 for faired hubs (English units). The hub vertical drag can be fixed, specified as a drag area D/q; or the drag can be scaled, specified as a drag coefficient CD based on the rotor disk area A = πR 2 . The pylon forward-flight drag and vertical drag are specified as drag area or drag coefficient, based on the pylon wetted area. The spinner drag is specified as drag area or drag coefficient, based on the spinner wetted area. The drag coefficient for the hub or pylon at angle-of-attack α is CD = CD0 +(CDV − CD0)| sin α| Xd Optionally the variation can be quadratic (Xd =2). For sideward flight, CDhub = CD0 for the hub and CDpylon = CDV for the pylon. Then the total component drag force is The force and moment produced by the drag are D = qACDhub + qSpylonCDpylon + qSspinCDspin F F = edD M F = Δz F F F where Δz F = z F − z F cg (separate locations are defined for the rotor hub and for the pylon), and ed is the drag direction. The velocity relative to the air gives ed = −v F /|v F | (no interference). 11–9 Weights The rotor configuration determines where the weights occur in the weight statement, as summarized in table 11-3. The rotor group consists of blade assembly, hub and hinge, fairing/spinner, and blade-fold structure. The tail rotor (in empennage group) or the propeller/fan installation (in propulsion group) consists of the blade assembly, the hub and hinge, and the rotor/fan duct and rotor support. There are separate weight models for main rotors, tail rotors, and auxiliary-thrust systems (propellers). The tail-rotor model requires a torque calculated from the drive-system rated power and mainrotor rotational speed: Q = PDSlimit/Ωmr. The auxiliary-thrust model requires the design maximum thrust of the propeller. Table 11-3. Principal configuration designation. configuration weight statement weight model performance model main rotor rotor group rotor rotor tail rotor empennage group tail rotor rotor propeller propulsion group rotor, aux thrust rotor
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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
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Solution Procedures 39 relaxation i
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Solution Procedures 41 Table 5-4. T
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Solution Procedures 43 successive s
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Solution Procedures 45 initialize e
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Chapter 6 Cost Costs are estimated
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Cost 49 Table 6-1. DoD and CPI infl
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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
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: Rotor 103 The wake is a skewed cyli
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 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
Page 165 and 166: 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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