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102 Rotor The profile power is calculated from a mean blade drag coefficient: Po = ρA(ΩR) 3CPo = 3 σ ρA(ΩR) 8 cdFP . The mean drag coefficient cd, or alternatively cdFP = 8CPo/σ, is obtained from an input table (linearly interpolated) that can be a function of edgewise advance ratio μ and blade loading CT /σ. 11–6 Performance Indices Several performance indices are calculated for each rotor. The induced power factor is κ = Pi/Pideal. The rotor mean drag coefficient is cd =(8CPo/σ)/FP , using the function F (μ, μz) given previously. The rotor effective lift-to-drag ratio is a measure of the induced and profile power: L/De = VL/(Pi + Po). The hover figure of merit is M = TfDv/P. The propeller propulsive efficiency is η = TV/P. These two indices can be combined as a momentum efficiency: ηmom = T (V +w/2)/P , where w/2 =fW v/2 =fDv. 11–7 Interference The rotor can produce aerodynamic interference velocities at the other components (fuselage, wings, tails). The induced velocity at the rotor disk is κvi, acting opposite the thrust (z-axis of tip-path plane axes). So vP ind = −kP κvi, and vF ind = CFPvP ind . The total velocity of the rotor disk relative to the air . The direction consists of the aircraft velocity and the induced velocity from this rotor: vF total = vF −v F ind of the wake axis is thus eP w = −CPFvF total /|vF total | (for zero total velocity, ePw = −kP is used). The angle of the wake axis from the thrust axis is χ = cos−1 |(kP ) T eP w|. The interference velocity v F int at each component is proportional to the induced velocity v F ind (hence is in the same direction), with factors accounting for the stage of wake development and the position of the component relative to the rotor wake. The far-wake velocity is w = fW vi, and the contracted wake area is Ac = πR 2 c = A/fA. The solution for the ideal inflow gives fW and fA. For an open rotor, fW =2. For a ducted rotor, the inflow and wake depend on the wake area ratio fA, or on the ratio of the rotor thrust to total thrust: fT = Trotor/T . The corresponding velocity and area ratios at an arbitrary point on the wake axis are fw and fa, related by fa = μ 2 +(μz + fwλi) 2 (fVxμ) 2 +(fVzμz + λi) 2 Vortex theory for hover gives the variation of the induced velocity with distance z below the rotor disk: z/R v = v(0) 1+ 1+(z/R) 2 With this equation the velocity varies from zero far above the disk to v =2v(0) far below the disk. To use this expression in edgewise flow and for ducted rotors, the distance z/R is replaced by ζw/tR, where ζw is the distance along the wake axis, and the parameter t is introduced to adjust the rate of change (t small for faster transition to far-wake limit). Hence the velocity inside the wake is fwvi, where ⎧ ζw/tR ⎪⎨ 1+ 1+(ζw/tR) fw = fW fz = ⎪⎩ 2 ζw < 0 ζw/tR 1+(fW − 1) 1+(ζw/tR) 2 ζw > 0 and the contracted radius is Rc = R/ √ fa.
Rotor 103 The wake is a skewed cylinder, starting at the rotor disk and with the axis oriented by eP w. The interference velocity is required at the position zF B on a component. Whether this point is inside or outside the wake cylinder is determined by finding its distance from the wake axis, in a plane parallel to the rotor disk. The position relative to the rotor hub is ξP B = CPF (zF B − zF hub ); the corresponding point on the wake axis is ξP A = ePwζw. Requiring ξP B and ξP A have the same z value in the tip-path plane axes gives ζw = (kP ) T C PF (z F B − zF hub ) (k P ) T e P w from which fz, fw, fa, and Rc are evaluated. The distance r from the wake axis is then r 2 = (i P ) T (ξ P B − ξ P A) 2 + (j P ) T (ξ P B − ξ P A) 2 The transition from full velocity inside the wake to zero velocity outside the wake is accomplished in the distance sRc, using fr = ⎧ ⎨ 1 r ≤ Rc 1 − (r − Rc)/(sRc) ⎩ 0 r ≥ (1 + s)Rc (s =0for an abrupt transition, s large for always in wake). The interference velocity at the component (at z F B ) is calculated from the induced velocity vF ind , the factors fW fz accounting for axial development of the wake velocity, the factor fr accounting for immersion in the wake, and an input empirical factor Kint: v F int = Kint fW fzfrft v F ind An additional factor ft for twin rotors is included. Optionally the development along the wake axis can be a step function (fW fz =0, 1, fW above the rotor, on the rotor disk, and below the rotor disk, respectively); nominal (t =1); or use an input rate parameter t. Optionally the wake immersion can use the contracted radius Rc or the uncontracted radius R; can be a step function (s =0,sofr =1and 0 inside and outside the wake boundary); can be always immersed (s = ∞ so fr =1always); or can use an input transition distance s. Optionally the interference factor Kint can be reduced from an input value at low speed to zero at high speed, with linear variation over a specified speed range. To account for the extent of the wing or tail area immersed in the rotor wake, the interference velocity can be calculated at several of points along the span and averaged. The increment in position is Δz F B = CFB (0 Δy 0) T ; where Δy =(b/2)(−1+(2i − 1)/N ) for i =1to N, and b is the wing span. For twin main rotors (tandem, side-by-side, or coaxial), the performance may be calculated for the rotor system, but the interference velocity is still calculated separately for each rotor, based on its disk loading. At the component, the velocities from all rotors are summed, and the total used to calculate the angle-of-attack and dynamic pressure. This sum must give the interference velocity of the twin-rotor system, which requires the correction factor ft. Consider differential momentum theory to estimate the induced velocity of twin rotors in hover. For the first rotor, the thrust and area in the non-overlap region are (1 − m)T1 and (1 − m)A, hence the induced velocity is v1 = κ T1/2ρA; similarly v2 = κ T2/2ρA. In the overlap region the thrust and area are mT1 + mT2 and mA, hence the induced velocity is vm = κ (T1 + T2)/2ρA. So for equal thrust, the velocity in the overlap region (everywhere for the coaxial configuration) is √ 2 larger. The factor KT is introduced to adjust the overlap velocity:
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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
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 and 112: Rotor 99 (C T /σ) s c d mean 0.20
Page 113: Rotor 101 11-5.1.3 Twin Rotors For
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
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.
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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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