Aeronautical Engineer’s Data Book - part 6 pdf

130 Aeronautical Engineer’s Data Book Light airplane 200 hp (149.1 kW) piston engine Light helicopter 550 hp (410.1 kW) turboshaft B747-400 long-haul airliner 4 × 58 000 lbf (258.6 kN) turbofan Multi-role transport helicopter 2 × 1850 hp (1380.1kW) turboshafts Air combat helicopter 2 × 1550 hp (1156.3 kW) turboshafts Concorde SST 4 × 38 000 lbf (169.4 kN) turbojet with reheat Regional jet 2 × 7040 lbf(31.3 kN) turbofan High-wing commercial/military transport 2 × 1750 hp (1505 kW) turboprop B777-300 airliner 2 × 84 700 lbf (377 kN) turbofan 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 [...]... /Doug MD-9 0-3 0 McDon /Doug MD-11 Tupolev Tu-204 -2 00 160 5 1500 12 96 1434 163 9 1 965 18 56 2307 261 3 3033 3350 2135 29 26 3078 363 3 4031 2500 1440 1290 1210 1210 1335 1335 1321 1321 1 467 1458 2250 1 564 1 966 1 966 2234 2234 2130 177 148 /M0. 76 151 2.33 2. 86 2.32 23 16 1445 TBD/M0.89 2 .61 2.89 138 1 26 335/M0.85 320/M0. 76 1 26 1 36 119 128 320/M0.77 320/M0.77 365 /M0.93 365 /M0.93 365 /M0.93 3.1 3.23 160 0 160 0 2.21... 139 090 141 500 195 62 0 13 892 26 024 8080 51 46 964 0 13 365 150 387 22 107 152 108 40 938 Dimensions fuselage: Length (m) Height (m) Width (m) Finess ratio 37.57 4.14 3.95 9.51 44.51 4.14 3.95 11.27 57.77 5 .64 5 .64 10.24 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... 735 164 875 170 390 43 545 12 220 8921 10 070 9 965 31 67 5 61 68 0 14 69 0 15 921 15 200 21 540 41 480 19 958 62 95 30 06 4940 4530 13 66 3 17 100 5515 3498 4750 2 865 11 585 31 975 9302 63 55 66 50 7417 22 67 3 35 830 11 108 7805 10 165 8332 24 593 190 423 58 000 17 290 29 64 0 107 960 132 400 58 965 17 350 13 65 9 14 535 16 810 39 415 195 043 55 566 30 343 30 68 5 118 954 134 081 84 200 25 200 18 999 18 62 0 33... 0.252 0 .68 7 44 .6 15.1 5.11 0.3 34 21.3 0.245 0. 964 4.1 14.45 5.04 14.01 20.07 2;4 10.4 27.35 5.09 23.53 2;8 2;4 10 .6 24 .6 41 2;10 7.82 17 2;4 5.04 11.54 17.78 2;4 0.95 0.3 0.98 0.31 1.0 16 0.3 56 1.0 16 0.3 56 1.3 0.48 4.7 2. 06 3.8 1.5 4 1.5 5.1 1.7 5.1 1.7 6 2 .6 5.75 1.55 6. 5 2.7 6 2 .6 365 .51 62 7.77 0.2789 282.11 424.15 0. 361 3 3 06. 51 375.15 0.33 26 298.21 392.94 0.3418 349. 76 460 . 86 0.2915 410.09 68 9.48... F100 II-96M Initial service date Engine manufacturer 1988 CFMI 1993 CFMI 1998 GE 1994 CFMI 2002 R-R 1998 CFMI 1992 GE 1997 Allison 1988 R-R 1988 R-R Model/Type CFM 56 5A3 2 111.2 CFM 56 5B3 2 142 CF6­ 80E1A4 2 310 CFM5 6- 5 C4 4 151 Trent 553 4 235.8 1999 BMW R-R 715 CF34­ 3A1 2 41 AE3007A 2 97.9 CFM 56 7B24 2 107 2 31.3 Tay 62 0 2 61 .6 Tay 62 0 2 61 .6 No of engines Static thrust (kN) McDon /Doug MD-9 0-3 0... 0.3 1 06 – 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 1 96 190 6 26. 4 0.12 Mass (weight) (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 2 36 000 52 110 51 710 46 266 78 460 78 220 65 310 23 2 46 23... 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 0.1 76 0. 065 21.5 6. 26 1.82 0.303 34 15.2 0.1 76 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 0.1 86 0.0 96 7.2 3.1 1.33 0 .6 32 11.5 0.141 0.081... 3 86. 98 834 .67 0. 263 4 264 .1 5 56. 2 0.3 86 Undercarriage: Track (m) Wheelbase (m) Turning radius (m) No of wheels (nose; main) Main wheel diameter (m) Main wheel width (m) 9.44 6. 35 4.27 0.55 30 12.9 0.173 0.709 11.2 7 .6 5. 16 0. 56 17 12.9 0.219 0.902 21.72 10.04 4 .64 0.39 26 14.4 0.232 0.88 21.72 10.04 4 .64 0.39 26 16 0.232 0.978 96. 5 20.57 4.38 0.29 37.5 26. 5 0.2 46 0.812 33 12.24 4.54 0. 36 30 18 .6 0.294... McDon /Doug MD-11 Tupolev Tu-204 -2 00 19 96 1995 IAE 1990 GE 1997 Soloviev 2337 V2525-D5 PS-90A 4 164 .6 2 111.2 CF 6- 8 0 C2 DIF 3 274 2 157 Accommodation: Max seats (single class) Two class seating Three class seating No abreast 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 1 86 – 6 51. 76 0.24 293 253 9 1 36 0. 36 335 295 9 162 .9 0.37 350... 7 .6 16. 9 29 2;4 7 .6 16. 9 29 2;8 10.7 25.4 40 .6 2;10 10.7 28.53 4.88 17 .6 5.7 2;12 2;4 2;4 11.39 22. 86 2;4 1.143 0.4 06 1.27 0.455 1.0 16 0. 368 Nacelle: Length (m) Max width (m) 4.44 2.37 4.44 2.37 7 3.1 4.95 2.37 6. 1 3.05 6. 1 1.75 Performance Loadings: Max power Load (kg/kN) Max wing Load (kg/m2) Thrust/Weight ratio 330.49 60 0.49 0.3084 313.38 727.12 0.3253 370.97 63 3.43 0.2748 448 .68 7 46. 35 0.2272 3 86. 98 . GE CFMI R-R BMW CFMI GE Allison R-R R-R IAE GE Soloviev R-R Model/Type CFM5 6- CFM5 6- CF 6- CFM- Trent 715 CFM5 6- CF3 4- AE3007A Tay Tay 2337 V2525-D5 CF 6- 8 0 PS-90A 5A3 5B3 80E1A4 5 6- 5 C4 553. 60 .5 43 58 .65 46. 7 Height (m) 4.14 4.14 5 .64 5 .64 5 .64 3 .61 3.73 6. 08 3 .61 6. 02 3.8 Width (m) 3.95 3.95 5 .64 5 .64 5 .64 3 .61 3.73 6. 08 3 .61 6. 02 4.1 Finess ratio 9.51 11.27 10.24 11.08 11 .63 . Max. landing 64 500 73 500 177 150 190 000 2 36 000 46 266 65 310 21 319 18 700 34 020 38 780 175 158 64 410 207 744 89 500 Zero-fuel 60 500 71 500 165 142 178 000 222 000 43 545 61 68 0 19 958