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100 Rotor c d mean c d mean 0.0350 0.0300 0.0250 0.0200 0.0150 0.0100 0.0050 CT /σ = 0.14 CT /σ = 0.12 CT /σ = 0.10 CT /σ = 0.08 cd comp 0.0000 0.00 0.10 0.20 0.30 0.40 0.50 Figure 11-9a. Mean drag coefficient for rotor in forward flight, high stall. 0.0350 0.0300 0.0250 0.0200 0.0150 0.0100 0.0050 0.0000 0.00 0.10 0.20 0.30 0.40 0.50 Figure 11-9b. Mean drag coefficient for rotor in forward flight, low stall. coefficient in hover, showing cdh without and with the separation term, and the total for the high stall and low stall cases. Figure 11-9 illustrates the mean drag coefficient in forward flight, showing the compressibility term cdcomp, and the growth in profile power with CT /σ and μ as the stall drag increment increases. μ μ
Rotor 101 11-5.1.3 Twin Rotors For twin rotors, the induced power is determined by the induced velocity of the rotor system, not the individual rotors. The induced power is still obtained using Pi = κPideal = κfDTvideal for each rotor, but the ideal induced velocity is calculated for an equivalent thrust CTe based on the thrust and geometry of both rotors. The profile power calculation is not changed for twin rotors. In hover, the twin-rotor induced velocity is vi = κtwin T/2ρAp, from the total thrust T and the projected disk area Ap =(2−m)A. The overlap fraction m is calculated from the rotor hub separation ℓ. A correction factor for the twin-rotor ideal power is also included. For a coaxial rotor, typically κtwin ∼ = 0.90. So the ideal inflow is calculated for CTe =(CT1 + CT 2)/(2 − m). In forward flight, the induced velocity of a coaxial rotor is vi = κtwinT/(2ρAV ), from the total thrust T and a span of 2R. The correction factor for ideal induced power (biplane effect) is κtwin ∼ = 0.88 to 0.81 for rotor separations of 0.06D to 0.12D. The ideal inflow is thus calculated for CTe = CT 1 + CT 2. The induced velocity of side-by-side rotors is vi = κtwinT/(2ρAeV ), from the total thrust T and a span of 2R+ℓ, hence Ae = A(1+ℓ/2R) 2 . The ideal inflow is thus calculated for CTe =(CT 1 +CT 2)/(1+ℓ/2R) 2 . The induced velocity of tandem rotors is vF = κtwin(TF /(2ρAV )+xRTR/(2ρAV )) for the front rotor and vR = κtwin(TR/(2ρAV )+xF TF /(2ρAV )) for the rear rotor. For large separation, xR ∼ = 0 and xF ∼ = 2; for the coaxial limit xR = xF =1is appropriate. Here xR = m and xF =2− m is used. To summarize, the model for twin-rotor ideal induced velocity uses CTe = x1CT 1 + x2CT 2 and the correction factor κtwin. In hover, xh =1/(2 − m); in forward flight of coaxial and tandem rotors, xf =1 for this rotor and xf = m or xf =2− m for the other rotor; in forward flight of side-by-side rotors, xf =1/(1 + ℓ/2R) 2 (x =1/2 if there is no overlap, ℓ/2R >1). The transition between hover and forward flight is accomplished using x = xf μ 2 + xhCλ 2 h μ 2 + Cλ 2 h with typically C =1to 4. This transition is applied to x for both rotors, and to κtwin. With a coaxial rotor in hover, the lower rotor acts in the contracted wake of the upper rotor. Momentum theory gives the ideal induced power for coaxial rotors with large vertical separation (ref. 13): Pu = Tuvu, v 2 u = Tu/2ρA for the upper rotor; and Pℓ =(¯αs/ √ τ)Tℓvℓ, v 2 ℓ = Tℓ/2ρA for the lower rotor. Here τ = Tℓ/Tu; ¯α is the average of the disk loading weighted by the induced velocity, hence a measure of nonuniform loading on the lower rotor (¯α =1.05 to 1.10 typically); and the momentum theory solution is ¯αs √ τ = 1 2τ 3/2 1 + 4(1 + τ) 2 ¯ατ − 1 The optimum solution for equal power of the upper and lower rotors is ¯αsτ =1, giving τ = Tℓ/Tu ∼ = 2/3. Hence for the coaxial rotor in hover the ideal induced velocity is calculated from CTe = CTu for the upper rotor and from CTe =(¯αs/ √ τ) 2 CTℓ for the lower rotor, with κtwin =1. Thus xh =1/(2−m) =1/2 and the input hover κtwin is not used, unless the coaxial rotor is modeled as a tandem rotor with zero longitudinal separation. 11-5.2 Table Performance Method The induced power is calculated from the ideal power: Pi = κPideal = κfDTvideal. The induced power factor κ is obtained from an input table (linearly interpolated) that can be a function of edgewise advance ratio μ or axial velocity ratio μz, and of blade loading CT /σ.
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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
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
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: Rotor 99 (C T /σ) s c d mean 0.20
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 159 and 160: Chapter 19 AFDD Weight Models This
Page 161 and 162: 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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