Aeronautical Engineer Data Book Episode 8 pps

Principles of propulsion 131 Military fighter (supersonic) 2 × 25 000 lbf (111.5 kN) reheat turbofan VTOL fighter (subsonic) 1 × 22 000 lbf (96.7 kN) turbofan Launch vehicle solid rocket boosters 2 × 2 700 000 lbf (12 MN) Fig. 8.7 Aircraft comparative power outputs ᎏᎏ   Section 9 Aircraft performance 9.1 Aircraft roles and operational profile Civil aircraft tend to be classified mainly by range. The way in which a civil aircraft operates is termed its operational profile. In the military field a more commonly used term is mission profile. Figure 9.1 shows a typical example and Table 9.1 some commonly used terms. 9.1.1 Relevant formula Relevant formulae used during the various stages of the operational profile are: Take-off ground roll S G = 1/(2gK A ).ln[K T + K A .V 2 LOF )/K T ]. This is derived from  V LOF [( ᎏ 2 1 ᎏ a)dV 2 ] 0 S Total take-off distance TO = (S G )(F p1 ) where F p1 is a ‘take-off’ plane form coefficient between about 1.1 and 1.4. V TRANS = (V LOF + V 2 )/2  1.15V S Rate of climb For small angles, the rate of climb (RC) can be determined from: (F – D)V 1 + ᎏ g V ᎏ ᎏ h d ᎏ V d RC = W where V/g. dV/dh is the correction term for flight acceleration 133 Aircraft performance Stepped cruise Descent Landing from 1500 ft and taxi in Range Mission time and fuel Block time and fuel Climb take-off to 1500 ft climb Taxi out and Transition to Fig. 9.1 A typical operational profile Table 9.1 Operational profile terms Take off Transition to climb Take-off climb V V V Take-off run available: operational length of the runway. Take-off distance available: length of runway including stopway (clear area at the end) and clearway (distance from end of stopway to the nearest 35 ft high obstruction). V s : aircraft stall speed in take-off configuration. V R : rotate speed. V 2 : take-off climb speed at 35 ft clearance height. mc : minimum speed for safe control. LOF : Lift off speed: speed as aircraft clears the ground. TRANS : average speed during the acceleration from V LOF to V 2 . ␥ : final climb gradient. ␥ c : best climb angle. 1st segment: first part of climb with undercarriage still down. 2nd segment: part of climb between ‘undercarriage up’ and a height above ground of 400 ft. 3rd segment: part of climb between 400 ft and 1500 ft. Climb from 1st segment: part of climb between 1500 ft to 1500 ft and 10 000 ft. cruise 2nd segment: part of climb from 10 000 ft to initial cruise altitude. V c : rate of climb. Cruise V T : cruise speed. Descent V mc : speed between cruise and 10 000 ft. (See Figure 9.2 for further details.) Landing Approach: from 50 ft height to flare height (h f ). Flare: deceleration from approach speed (V A ) to touch down speed V TD . Ground roll: comprising the free roll (no brakes) and the braked roll to a standstill.   134 Aeronautical Engineer’s Data Book V = V A V = 0 V = V F S B S FR S F S A Ground roll Approach distance Flare Free γ A γ A h f Radius Obstacle height Total landing distance Fig. 9.2 Approach and landing definitions W F = thrust g = acceleration due to gravity h = altitude RC = rate of climb S = reference wing area V = velocity W = weight f = fuel flow Flight-path gradient F – D γ = sin –1 ᎏ W Time to climb 2(h 2 – h 1 ) ∆t = ᎏᎏ (RC) 1 + (RC) 2 Distance to climb ∆S = V(∆t) Fuel to climb ∆Fuel = W f (∆t) Cruise The basic cruise distance can be determined by using the Breguet range equation for jet aircraft, as follows:     ᎏᎏ 135 Aircraft performance Cruise range R = L/D(V/sfc) ln(W 0 /W 1 ) where subscripts ‘0’ and ‘1’ stand for initial and final weight, respectively. Cruise fuel R/k –1) Fuel = W 0 –W 1 = W f (e where k, the range constant, equals L/D(V/sfc) and R = range. Cruise speeds Cruise speed schedules for subsonic flight can be determined by the following expressions. Optimum mach number (M DD ), optimum- altitude cruise First calculate the atmospheric pressure at altitude: W P = 0.7(M 2 DD )(C L DD )S where M 2 DD = drag divergence Mach number. Then input the value from cruise-altitude determination graph for cruise altitude. Optimum mach number, constant-altitude cruise Optimum occurs at maximum M(L/D). M =  S ᎏᎏ 0 W/ .7P 3 K ᎏᎏ C D min where K = parabolic drag polar factor P = atmospheric pressure at altitude Landing Landing distance calculations cover distance from obstacle height to touchdown and ground roll from touchdown to a complete stop.   136 Aeronautical Engineer’s Data Book Approach distance V 2 obs – V 2 TD S air =  ᎏᎏ + h obs  (L/D) 2g where V obs = speed at obstacle, V TD = speed at touchdown, h obs = obstacle height, and L/D = lift-to-drag ratio. Landing ground roll (W/S) A 2 (C D – µ BRK C L S gnd = ᎏᎏ ln1– ᎏᎏᎏ g ␳ (C D –µ BRK C L ) ((F/W)–µ BRK C Lmϫs ) 9.2 Aircraft range and endurance The main parameter is the safe operating range; the furthest distance between airfields that an aircraft can fly with sufficient fuel allowance for headwinds, airport stacking and possible diver- sions. A lesser used parameter is the gross still air range; a theoretical range at cruising height between airfields. Calculations of range are complicated by the fact that total aircraft mass decreases as a flight progresses, as the fuel mass is burnt (see Figure 9.3). Specific air range (r) is defined as distance/fuel used (in a short time). The equivalent endurance term is specific endurance (e). General expressions for range and endurance can be shown to follow the models in Table 9.2. Mass Initial mass m 0 Final mass m 1 Initial fuel mass Fuel Engines + structure + payload Unusable and m = m ( t ) or m = m ( x ) Total mass reserve fuel Distance Fig. 9.3 Range terminology Table 9.2 Range and endurance equations Specific range (r) Specific endurance (e) Propeller aircraft r = ␩ /fD e = ␩ /fDV Jet aircraft r = V/f j D e = 1/f j D Range (R) R =  m 0 =  m 0 m 1 ␩ ᎏ f d D m ᎏ m 1  ᎏ C C L ᎏ m ᎏ g d  ␩ ᎏᎏ f m ᎏ D R =  m 0 =  m 0 Vd V C ᎏ f ᎏ   m ᎏ g d m 1 ᎏ f j D m ᎏ m 1 m j ᎏ C D L ᎏ ᎏ Endurance (E) E =  m 0 ␩ ᎏ fD dm ᎏ V =  m 0  ᎏ C C L ᎏ m ᎏ g d  ␩ m m 1 m 1 ᎏ f ᎏ V D ᎏ E =  m 0 d =  m 0 ᎏ f ᎏ 1 d   m ᎏ g m m 1 ᎏ f j D m ᎏ m 1 j ᎏ C C D L ᎏ ᎏ 137 138 Aeronautical Engineer’s Data Book 9.3 Aircraft design studies Aircraft design studies are a detailed and itera- tive procedure involving a variety of theoretical and empirical equations and complex paramet- ric studies. Although aircraft specifications are built around the basic requirements of payload, range and performance, the design process also involves meeting overall criteria on, for example, operating cost and take-off weights. The problems come from the interdepen- dency of all the variables involved. In particu- lar, the dependency relationships between wing area, engine thrust and take-off weight are so complex that it is often necessary to start by looking at existing aircraft designs, to get a first impression of the practicality of a proposed design. A design study can be thought of as consisting of two parts: the initial ‘first approx- imations’ methodology, followed by ‘paramet- ric estimate’ stages. In practice, the processes are more iterative than purely sequential. Table 9.3 shows the basic steps for the initial ‘first approximations’ methodology, along with some general rules of thumb. Figure 9.4 shows the basis of the following stage, in which the results of the initial estimates are used as a basis for three alterna- tives for wing area. The process is then repeated by estimating three values for take-off Wing estimate Wing estimate Wing estimate area S 1 area S 3 area S 2 Choose suitable take-off mass Different engine possibilities/combinations Calculate performance criteria Fig. 9.4 A typical ‘parametric’ estimate stage 139 Table 9.3 The ‘first approximations’ methodology Estimated parameter Basic relationships Some ‘rules of thumb’ 1. Estimate the wing loading W/S. W/S = 0.5 ␳ V 2 C L in the ‘approach’ condition. Approach speed lies between 1.45 and 1.62 V stall . Approach C L lies between C Lmax /2.04 and C Lmax /2.72. 2. Check C L in the cruise. C L = ᎏ 0.98(W/S) ᎏ where q = 0.5 ␳ V 2 C L generally lies between 0.44 and 0.5. q 3. Check gust response at cruise speed. Gust response parameter = ᎏ ␣ ( 1 W wb . / A S) R ᎏ ␣ 1wb is the wing body lift curve slope obtained from data sheets. 4. Estimate size. Must comply with take-off and climb performance. Long range aircraft engines are sized to ‘top of climb’ requirements. 5. Estimate take-off wing s = kM 2 g 2 /(S w T.C LV2 ␴) 1.7 < C Lmax < 2.2 loading and T/W ratio as a function of C LV2 1.18 < C LV 2 < 1.53 6. Check the capability to Cruise L/D is estimated by comparisons with 17 < L/D < 21 climb (gust control) at existing aircraft data. in the cruise for most civil airliners. initial cruise altitude. F n /M CL = (L/D) –1 + (300/101.3V) (imperial units) 7. Estimate take-off mass M TO = M E + M PAY + M f 0.46 < ᎏ M O T E O M M ᎏ < 0.57 140 Aeronautical Engineer’s Data Book Wing area S 1 Wing area S 2 Design range be shown ‘within’ these design bounds Aircraft range Various engine options, take-off weights etc. can Fig. 9.5 Typical parametric plot showing design ‘bounds’ weight and engine size for each of the three wing area ‘conclusions’. The results are then plotted as parametric study plots and graphs showing the bounds of the various designs that fit the criteria chosen (Figure 9.5). 9.3.1 Cost estimates Airlines use their own (often very different) standardized methods of estimating the capital and operating cost of aircraft designs. They are complex enough to need computer models and all suffer from the problems of future uncer- tainty. 9.4 Aircraft noise Airport noise levels are influenced by FAR-36 which sets maximum allowable noise levels for subsonic aircraft at three standardized measure- ment positions (see Figure 9.6). The maximum allowable levels set by FAR-36 vary, depending on aircraft take-off weight (kg). [...]... 4.17 9.44 0.2 78 54.54 20.52 3.15 7.72 0. 288 51. 18 20.04 3.13 7 .85 0.231 93.5 28. 08 3 .8 8.43 0.235 93.5 28. 08 3 .8 8.43 0.235 391.6 55.57 8. 04 7 .89 0.279 112.3 32 .87 4. 08 9.62 0.195 3 38. 9 51.77 7. 68 7.91 0.239 182 .4 40.3 5.4 8. 9 0.2 28 Table 10.1 Continued Manufacturer Type Model Airbus A320– 200 Airbus A321– 200 Airbus A330– 200 Airbus A340– 300 Airbus A340– 500 Boeing 717– 200 Boeing 737– 80 0 Cadair Reg... 500 22 780 19 060 17 670 23 330 48 000 165 142 36 400 – 24 035 85 765 120 200 1 78 000 48 150 33 160 28 025 113 125 129 85 0 222 000 51 635 31 450 29 735 164 87 5 170 390 43 545 12 220 89 21 10 070 9965 31 675 61 680 14 690 15 921 15 200 21 540 41 480 19 9 58 6295 3006 4940 4530 13 663 17 100 5515 34 98 4750 286 5 11 585 31 975 9302 6355 6650 7417 22 673 35 83 0 11 1 08 780 5 10 165 83 32 24 593 190 423 58 000... 62.47 5.64 5.64 11. 08 65.6 5.64 5.64 11.63 33 3.61 3.61 4.3 38. 08 3.73 3.73 7.4 24. 38 27.93 27 .88 32.5 60.5 6. 08 6. 08 9.95 43 3.61 3.61 11.91 58. 65 6.02 6.02 9.74 46.7 3 .8 4.1 11.39 Wing: Area (m2) Span (m) MAC (m) Aspect ratio Taper ratio 122.4 33.91 4.29 9.39 0.24 122.4 33.91 4.29 9.39 0.24 363.1 58 7.26 9.26 0.251 363.1 58 7.26 9.26 0.251 437.3 61.2 8. 35 8. 56 0.22 92.97 28. 4 3 .88 8. 68 0.196 124.6 34.3... 960 132 400 58 965 17 350 13 659 14 535 16 81 0 39 415 195 043 55 566 30 343 30 685 1 18 954 134 081 84 200 25 200 18 999 18 620 33 130 59 000 Weight ratios: Ops empty/Max T/O Max payload/Max T/O Max fuel/Max T/O Max landing/Max T/O 0.562 0.261 0.256 0 .87 8 0.539 0.256 0.21 0 .82 6 0.523 0.1 58 0.4 78 0.77 0.479 0.1 78 0.412 0.701 0.467 0.141 0.423 0.647 0.613 0.236 0.212 0 .89 5 0.53 0. 188 0.263 0 .83 5 0.591 0.272... 24.5 25 10 .83 24.75 11 22.73 10. 28 17.45 10. 28 17.45 30 11 24.5 9.35 35 28 F1 0. 78 21.1 slats F2 0. 78 21.1 slats S2 0.665 S2 0.665 S2 0.625 S2 0.65 S2 0.599 S2 0.77 slats F2 0. 58 17. 08 none S2 0.7 slats F2 0. 58 17. 08 none S2 0.63 slats S2 0.72 8. 36 none S2 0.79 slats S2 0.66 10.6 slats/flaps slats slats slats slats slats 12.64 12.64 t21.5 6.26 1 .82 0.303 34 12.53 0.176 0.065 21.5 6.26 1 .82 0.303 34... 0 .89 5 0.53 0. 188 0.263 0 .83 5 0.591 0.272 0.276 0.922 0.603 0. 287 0.212 0.974 0.617 0.253 0.207 0.926 0.571 0.2 58 0.245 0.9 0.49 0.215 0.44 0.649 0.557 0.245 0.247 0.91 0.473 0.196 0.424 0.732 0.533 0.2 28 0.292 0 .80 8 Fuel (litres): Standard 23 86 0 23 700 139 090 141 500 195 620 13 89 2 26 024 80 80 5146 9640 13 365 150 387 22 107 152 1 08 40 9 38 Dimensions fuselage: Length (m) Height (m) Width (m) Finess... (kg): Ramp Max take-off Max landing 73 900 73 500 64 500 89 400 89 000 73 500 230 900 230 000 177 150 271 900 271 000 190 000 365 900 365 000 236 000 52 110 51 710 46 266 78 460 78 220 65 310 23 246 23 133 21 319 19 300 19 200 18 700 36 965 36 740 34 020 43 320 43 090 38 780 270 000 175 1 58 71 215 70 760 64 410 285 081 283 720 207 744 111 750 110 750 89 500 Zero-fuel Max payload Max fuel payload Design... 6.26 1 .82 0.303 34 15.2 0.176 0.079 47.65 9.44 1 .87 0.35 45 25.2 0.131 0.057 45.2 8. 45 1. 58 0.35 45 27.5 0.124 0.059 47.65 9.44 1 .87 0.35 45 27.5 0.109 0.049 19.5 4.35 0.97 0. 78 45 12 .8 0.21 0.095 23.13 6 1.56 0.31 35 17.7 0. 186 0.096 7.2 3.1 1.33 0.6 32 11.5 0.141 0. 081 12.3 3.3 0 .89 0.74 41 11.4 0.132 0.053 12.3 3.3 0 .89 0.74 41 13.6 0.132 0.064 56.2 8 1.14 0.4 45 25.9 0.144 0.067 21.4 4.7 1.03 0.77... 10.1 Civil aircraft – basic data Manufacturer Type Model Airbus A320– 200 Airbus A321– 200 Airbus A330– 200 Airbus A340– 300 Airbus A340– 500 Boeing 717– 200 Boeing 737– 80 0 Cadair Reg Jet 100ER Embraer Fokker Fokker Ilyushin EMB-145 F70 F100 II-96M Initial service date Engine manufacturer 1 988 CFMI 1993 CFMI 19 98 GE 1994 CFMI 2002 R-R 19 98 CFMI 1992 GE 1997 Allison 1 988 R-R 1 988 R-R Model/Type CFM56­... Hold volume (m3) Volume per passenger 179 220 380 440 440 110 189 52 50 79 119 375 182 405 214 150 – 6 38. 76 0.22 186 – 6 51.76 0.24 293 253 9 136 0.36 335 295 9 162.9 0.37 350 313 9 134.1 0.3 106 – 5 25 0.23 160 – 6 47.1 0.25 – – 4 14.04 0.27 – – 3 13.61 0.27 70 – – 12. 78 0.16 107 – – 16.72 0.14 335 312 9 143.04 0. 38 153 5 38. 03 0.21 323 293 10 194 0. 48 196 190 6 26.4 0.12 Mass (weight) (kg): Ramp . 20.04 28. 08 28. 08 55.57 32 .87 51.77 40.3 MAC (m) 4.29 4.29 7.26 7.26 8. 35 3 .88 4.17 3.15 3.13 3 .8 3 .8 8.04 4. 08 7. 68 5.4 Aspect ratio 9.39 9.39 9.26 9.26 8. 56 8. 68 9.44 7.72 7 .85 8. 43 8. 43 7 .89 . 0.647 0 .89 5 0 .83 5 0.922 0.974 0.926 0.9 0.649 0.91 0.732 0 .80 8 Fuel (litres): Standard 23 86 0 23 700 139 090 141 500 195 620 13 89 2 26 024 80 80 5146 9640 13 365 150 387 22 107 152 1 08 40 9 38 Dimensions. 17 940 23 330 85 765 113 125 164 87 5 9965 21 540 4530 286 5 7417 83 32 107 960 16 81 0 1 18 954 33 130 Operational empty 41 310 48 000 120 200 129 85 0 170 390 31 675 41 480 13 663 11 585 22 673 24