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24 Operation For calculation of the time or distance in a mission segment, a headwind or tailwind can be specified. The wind velocity is a linear function of altitude h: Vw = ±(max(0,dwind + fwindh)), with the plus sign for a headwind and the minus sign for a tailwind. For example, California-to-Hawaii 85 th percentile winter quartile headwind profile is Vw =9.59+0.00149h (with altitude h in ft). Mission fuel reserves can be specified in several ways for each mission. Fuel reserves can be defined in terms of specific mission segments, for example 200 miles plus 20 minutes at speed for best endurance. Fuel reserves can be an input fraction of the fuel burned by all (except reserve) mission segments, so Wfuel =(1+fres)Wburn. Fuel reserves can be an input fraction of the fuel capacity, so Wfuel = Wburn + fresWfuel−cap. If more than one criterion for reserve fuel is specified, the maximum reserve is used. Time and distance in reserve segments are not included in endurance and range. To facilitate specification of range, range calculated for a group of segments (typically climb and descent segments) can be credited to a designated distance segment. For mission analysis, missions can be fixed or adjustable. In an adjustable mission, the fuel is input, so the time or distance in specified segments is adjusted based on the calculated fuel burned. If more than one segment is adjusted, all must be distance or all must be time or hold. Each segment can have only one special designation: reserve, adjustable, or range credit. A segment with a large distance, time, or altitude change can be split into several segments, for more accurate calculation of the performance and fuel burned. The number of segments n can be input or calculated from an input increment Δ: n =[x/Δ] + 1, where the brackets indicate integer truncation and x is the total distance, time, or altitude change. Then the change for each split segment is Δ=x/n. Table 4-1 summarizes the time T , distance D, and range dR calculations for each segment. The segment fuel burned is dWburn = T ˙w, where ˙w is the fuel flow. The horizontal velocity is Vh, and the vertical velocity (climb or descent) is Vc. The altitude at the start of the segment is h, and at the end of the segment (start of next segment) hend. The wind speed is Vw, and the ground speed is Vh − Vw. In an adjusted mission, the distances or times are changed at the end of the mission such that the sum of the fuel-burned increments will equal the difference between takeoff fuel weight (plus any added fuel) and the calculated mission fuel: dWburn = ˙wdT = ˙wdD/(Vh − Vw) =ΔWfuel. The increments are apportioned among the adjusted segments by the factor f, determined from the ratio of the input distances or times: dD = fΔD or dT = fΔT . Hence ΔD =ΔWfuel/ f ˙w/(Vh − W ) or ΔT =ΔWfuel/ f ˙w . For a segment that is a source of range credit, the range increment is set to zero and the distance D is added to Dother of the destination segment. For the destination segment, the range contribution remains fixed at the input value, but the time and hence fuel burned are calculated from (dist − Dother). It is necessary to separately accumulate Dother from earlier segments and Dother from later segments; Dother from later segments are estimated initially from the last iteration. At the end of the mission, the times and fuel burned are recalculated for all range credit destination segments. The segment time, distance, and fuel burned are evaluated by integrating over the segment duration. This integration can be performed by using the horizontal velocity, climb velocity, and fuel flow obtained for the flight state with the gross weight and altitude at the start of the segment, or at the middle of the segment, or the average of the segment start and segment end values (trapezoidal integration). The gross weight at the segment middle equals the gross weight at the segment start, less half the segment fuel burned (obtained from the previous mission iteration). The gross weight at the segment end equals the gross weight at the segment start, less the segment fuel burned. With trapezoidal integration, for the output the flight state is finally evaluated at the segment middle.
Operation 25 Table 4-1. Mission segment calculations. Segment kind Time T Distance D Range dR taxi time 0 D distance D/(Vh − Vw) dist D time time T (Vh − Vw) D hold time 0 D climb (h − hend)/Vc T (Vh − Vw) D spiral (h − hend)/Vc 0 D range credit source T D 0 destination D/(Vh − Vw) dist − Dother dist adjusted distance T + dD/(Vh − Vw) D + dD = D + fΔD Dnew time T + dT = T + fΔT D + dT (Vh − Vw) Dnew hold T + dT = T + fΔT 0 Dnew The mission endurance (block time), range, and fuel burned are E = T , R = dR, Wburn = dWburn (sum over all non-reserve segments). The reserve fuel from mission segments is Wres = dWburn (sum over all reserve segments). Optionally the reserve fuel is the maximum of that from mission segments and the fraction fresWburn, or the fraction fresWfuel−cap. The calculated mission fuel is then Wfuel = Wburn + Wres. 4–3 Takeoff Distance The takeoff distance can be calculated, either as ground run plus climb to clear an obstacle or accelerate-stop distance in case of engine failure. The obstacle height ho is typically 35 ft for commercial transport aircraft, or 50 ft for military aircraft and general aviation. This calculation allows determination of the balanced field length: engine failure at critical speed, such that the distance to clear the obstacle equals the distance to stop. Landing and VTOL takeoff calculations are not implemented, as these are best solved as an optimal control problem. The takeoff distance consists of a ground run, from zero ground speed to liftoff speed VLO, perhaps including engine failure at speed VEF; then rotation, transition, and climb; or decelerate to stop. Figure 4-1 describes the elements of the takeoff distance and the accelerate-stop distance, with the associated speeds. The ground is at angle γG relative to the horizontal (inertial axes), with γG positive for takeoff up hill. The takeoff profile is defined in terms of ground speed or climb speed, input as calibrated airspeed (CAS). The aircraft speed relative to the air is obtained from the ground speed, wind, and ground slope. The aircraft acceleration as a function of ground speed is integrated to obtain the ground distance, as well as the time, height, and fuel burned. Usually the speed increases from the start to liftoff (or engine failure), but the calculated acceleration depends on the flight-state specification. The analysis checks for consistency of the input velocity and the calculated acceleration (on the ground) and for consistency of the input height and input or calculated climb angle (during climb). The takeoff profile consists of a set of mission segments. The first segment is at the start of the takeoff, V =0. Subsequent segments correspond to the ends of the integration intervals. The last segment has the aircraft at the required obstacle height, or stopped on the ground. The mission can
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Page 5 and 6: TABLE OF CONTENTS CHAPTER 1 - INTRO
Page 7: TABLE OF CONTENTS (cont.) CHAPTER 1
Page 10 and 11: viii LIST OF FIGURES (cont.) Figure
Page 13 and 14: Chapter 1 Introduction The NASA Des
Page 15 and 16: Introduction 3 of rotorcraft config
Page 17 and 18: Introduction 5 previous case DESIGN
Page 19 and 20: Introduction 7 4) Scully, M.; and F
Page 21 and 22: Chapter 2 Nomenclature The nomencla
Page 23 and 24: Nomenclature 11 Fuel Tanks Power Na
Page 25 and 26: Nomenclature 13 Motion aF AC aircra
Page 27 and 28: Chapter 3 Tasks The NDARC code perf
Page 29 and 30: Tasks 17 engine group is found (inc
Page 31 and 32: Tasks 19 3-4 Maps 3-4.1 Engine Perf
Page 33 and 34: Chapter 4 Operation 4-1 Flight Cond
Page 35: Operation 23 e) Input payload weigh
Page 39 and 40: Operation 27 horizontal ground dist
Page 41 and 42: Operation 29 climb for zero power m
Page 43 and 44: Operation 31 a) Horizontal velocity
Page 45 and 46: Operation 33 From the pressure p =
Page 47 and 48: Chapter 5 Solution Procedures The N
Page 49 and 50: 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
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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
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Rotor 87 The velocity ratio is fW =
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Rotor 89 T/T ∞ 1.3 1.2 1.1 1.0 Ha
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Rotor 91 TPP tilt / cyclic magnitud
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Rotor 93 with an average over the r
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Rotor 95 (all equal to 1 for μz =0
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Rotor 97 κ 1.30 1.25 1.20 1.15 1.1
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Rotor 99 (C T /σ) s c d mean 0.20
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Rotor 101 11-5.1.3 Twin Rotors For
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Rotor 103 The wake is a skewed cyli
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Rotor 105 weight per lifting rotor;
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Chapter 12 Force The force componen
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Chapter 13 Wing The aircraft can ha
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Wing 111 denotes outboard edge, sub
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Wing 113 13-3.1 Lift The wing lift
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Wing 115 The wing interference at t
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Chapter 14 Empennage The aircraft c
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Empennage 119 14-4 Weights The tail
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Chapter 15 Fuel Tank 15-1 Fuel Capa
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Fuel Tank 123 if Wfuel >Wfuel−max
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Chapter 16 Propulsion The propulsio
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Propulsion 127 If the sum of the fi
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Chapter 17 Engine Group The engine
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Engine Group 131 The engine group p
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Engine Group 133 specific fuel cons
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Chapter 18 Referred Parameter Turbo
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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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