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138 Referred Parameter Turboshaft Engine Model no effect on PG. The model used for the efficiency variation is ηt ∼ = 1 −|(N/Nopt) − 1| XNη, where Nopt is the speed for peak efficiency, hence P (N) ηt(N) = P (Nspec) ηt(Nspec) = 1 −|(N/Nopt) − 1| XNη 1 −|(Nspec/Nopt) − 1| XNη Two approximations for the optimum turbine speed are used. The first is a linear expression in p = P/(P0Rδ √ θ): √ Nopt = Nspec θ KNoptA θM + KNoptB p δM and the second is a cubic function of p = P/(P0Cδ √ θ): √ Nopt = Nopt0C θ KNopt0 + KNopt1p + KNopt2p 2 + KNopt3p 3 [θM ] XNopt The second expression is based on a larger data sample. For power-available calculations, P = Pa(Nspec); for power-required calculations, P = Pq(N). 18–6 Power Available Given the flight condition and engine rating, the power available Pa is calculated as follows. The specific power and referred mass flow (at Nspec, relative to SP0 and ˙m0 for this rating) are approximated by functions of the ambient temperature ratio θ and inlet ram air ratios: SPa(Nspec) =SP0 θKspa ˙ma(Nspec) = ˙m0 δ/ √ θ Xspa δM θM e Kmfa Xmfa δM θM where the static lapse rate (Kspa, Kmfa) and ram air exponents (Xspa, Xmfa) are piecewise linear functions of θ. The power available is then SPa(Nspec) Pa(Nspec) =P0 SP0 ˙ma(Nspec) = P0 ˙m0 δ √ θ Kspae Kmfa Xspa+Xmfa δM θM This expression for ˙ma is used only to calculate Pa; elsewhere the ˙mq expression for performance at power required is used to obtain the mass flow at a power Pq. Finally Pa(N) =Pa(Nspec) 1 −|(N/Nopt) − 1| XNη 1 −|(Nspec/Nopt) − 1| XNη is the power available at turbine speed N. Installation losses Ploss are subtracted from Pa (Pav = Pa − Ploss), and then the mechanical limit is applied: Pav = min(Pav,PmechR). 18-6.1 Piecewise Linear Parameters Several parameters K are input as piecewise linear functions of the temperature ratio θ. One format of the input is a set of I regions, with the function in the i-th region given by K = K0i + K1iθ. The break point between the i and i − 1 regions is θbi = − K0i − K 0(i−1) K1i − K 1(i−1) Kbi = K0i + K1iθb
Referred Parameter Turboshaft Engine Model 139 for i =2to I. Another format is a set of I +1break points, with the values at the i-th point (θbi, Kbi). Then the coefficients between i and i +1are K0i = Kbiθ b(i+1) − K b(i+1)θbi θ b(i+1) − θbi K1i = −Kbi + K b(i+1) θ b(i+1) − θbi for i =1to I. The interpolation is performed using K = K0i + K1iθ for θ in the range θbi to θ b(i+1). Outside the defined regions, the linear expression is continued; hence θbi is used only for i =2to I. 18–7 Performance at Power Required The engine performance (mass flow, fuel flow, and gross jet thrust) is calculated for a specified power required Pq (which might equal the power available), flight condition, and engine rating. Installation losses Ploss are added to Preq (Pq = Preq + Ploss). The referred quantities (relative to SLS static MCP quantities) are approximated by cubic functions of q = Pq(Nspec)/(P0Cδ √ θ): ˙wreq = ˙w0C ˙mreq = ˙m0C δ √ θ δ/ √ θ Kffq0 + Kffq1q + Kffq2q 2 + Kffq3q 3 [θM ] −Xffq Kmfq0 + Kmfq1q + Kmfq2q 2 + Kmfq3q 3 [θM ] Xmfq Fg = Fg0C (δ) Kfgq0 + Kfgq1q + Kfgq2q 2 + Kfgq3q 3 [θM ] Xfgq at Nspec, with ˙w0C = sfc0CP0C. The mass flow and fuel flow are primarily functions of the gas power PG, and are assumed to be independent of ηt, hence independent of turbine speed. However, these equations are functions of Pq(Nspec), obtained from Pq(N) using Pq(Nspec) =Pq(N) 1 −|(Nspec/Nopt) − 1| XNη 1 −|(N/Nopt) − 1| XNη Then the installed net jet thrust FN and momentum drag Daux are calculated. 18–8 Scaling The parameters of the engine model can be defined for a specific engine, but it is also necessary to scale the parameters as part of the aircraft sizing task, in order to define an engine for a specified power. In addition, advanced technology must be represented in the model. Scaling and advanced technology are handled in terms of specific power and specific fuel consumption (at SLS static conditions, MCP, and Nspec). The engine model includes reference values of the engine performance parameters: P0R, SP0R, PmechR, sfc0C, SF0C, Nspec, Nopt0C. Mass flow and fuel flow are obtained from ˙m0R = P0R/SP0R and ˙w0C = sfc0CP0C. The reference power at each engine rating R defines a ratio to MCP: rp0R = P0R/P0C. Similarly for specific power and mechanical limits: rs0R = SP0R/SP0C, rm0R = PmechR/P0C. These ratios are kept fixed when the engine is scaled. The engine size is specified as takeoff power Pto = Peng, which is the power at rating R for SLS static conditions and specification turbine speed Nspec. Hence the MCP is P0C = Pto/rp0R, and the power at all other ratings follows.
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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$
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Chapter 7 Aircraft The aircraft con
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Aircraft 55 The tilt control variab
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Aircraft 57 forward axes for descri
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Aircraft 59 For steady-state flight
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Aircraft 61 where Δz F = z F − z
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Aircraft 63 disk area); or the drag
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Aircraft 65 7-10 Performance Indice
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Aircraft 67 WEIGHT EMPTY STRUCTURE
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Chapter 8 Systems The systems compo
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Chapter 9 Fuselage There is one fus
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Fuselage 73 αe = αfus − αzl, w
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Chapter 10 Landing Gear There is on
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Chapter 11 Rotor The aircraft can h
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Rotor 79 propulsion group. The driv
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Rotor 81 plane command. The collect
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Rotor 83 or just CSF = WCHF with no
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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 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: Referred Parameter Turboshaft Engin
Page 153 and 154: 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
Page 167 and 168: AFDD Weight Models 155 units as use
Page 169 and 170: AFDD Weight Models 157 Table 19-9.
Page 171 and 172: AFDD Weight Models 159 where fP = f
Page 173 and 174: AFDD Weight Models 161 The conversi
Page 175 and 176: AFDD Weight Models 163 19-12 Foldin
Page 177 and 178: AFDD Weight Models 165 error (%) er
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