Aircraft Performance Cruise PDF

Getting to Grips with Aircraft Performance CRUISE F. CRUISE 1. GENERAL 1.1. Introduction The main objective of the previous chapters is to comply with the airworthiness requirements of JAR/FAR 25 and JAR-OPS 1/FAR 121. This section...

Getting to Grips with Aircraft Performance CRUISE F. CRUISE 1. GENERAL 1.1. Introduction The main objective of the previous chapters is to comply with the airworthiness requirements of JAR/FAR 25 and JAR-OPS 1/FAR 121. This section deals with another objective. That of decreasing Direct Operating Costs (DOC). Direct Operating Costs include: Fixed costs (taxes, insurance, etc…), Flight-time related costs (crew, hourly maintenance costs, depreciation), Fuel-consumption related costs. The right choice of flight level and speed allows these DOCs to be minimized. In other words, as time and fuel consumption are closely related, cruise planning is established by making the right speed and flight level choices. In the following chapters, we will review some speed and altitude optimization criteria. 1.2. Specific Range The specific range (SR) is the distance covered per fuel unit. Basically speaking, the specific range is equal to: ground speed (GS) SR (Ground) = fuel consumption per hour (FF) Considering air distance, the specific range is equal to: true air speed (TAS) SR (Air) = fuel consumption per hour (FF) As TAS is expressed in nautical miles per hour (NM/h), and Fuel Flow (FF) in kilograms per hour (kg/h), the SR is expressed in NM/kg or NM/ton. Moreover, SR depends on aerodynamic characteristics (Mach and L/D), engine performance (Specific Fuel Consumption)1, aircraft weight (mg) and sound velocity at sea level (a0). 1 The Specific Fuel Consumption (SFC) is equal to the fuel flow (FF) divided by the available thrust. It is expressed in kg/h.N (kilogram per hour per Newton) and represents the fuel consumption per thrust unit. 127  CRUISE Getting to Grips with Aircraft Performance Aerodynamics ao ML D SR = SFC mg Engine T Weight T0 M. L/D Ê Ö SR Ê m Ê Ö SR Ì SFC Ê Ö SR Ì 2. SPEED OPTIMIZATION 2.1. All Engine Operating Cruise Speeds 2.1.1. Maximum Range Mach Number (MMR) Figure F1 illustrates the specific range as a function of Mach number for a given weight at a constant altitude. As a result, for a given weight, a maximum specific range value exists and the corresponding Mach number is called Maximum Range Mach number (MMR). SR (NM/ton) Given altitude, weight SRmax Maxi Range Mach MMR Figure F1: Maximum Range Mach Number 128 Getting to Grips with Aircraft Performance CRUISE The advantage of the Maximum Range Mach number is that the fuel consumption for a given distance is at its minimum. It also corresponds to the maximum distance an aircraft can fly with a given fuel quantity. During cruise, the aircraft’s weight decreases due to fuel burn. At the same time, the specific range increases, but MMR decreases (Figure F2). The Mach number must therefore be adjusted to correspond to weight changes during the entire flight at constant altitude. Figure F2: Maximum Range Mach Number versus Weight Pressure Altitude Influence Figure F3: Maximum Range Mach Number versus Pressure Altitude Variations of the maximum range Mach number are summarized as follows: PA = constant weight Ì ⇒ M MR Ì weight = constant PA Ê ⇒ M MR Ê 129  CRUISE Getting to Grips with Aircraft Performance 2.1.2. Long-Range Cruise Mach Number (MLRC) An alternative to MMR is to increase cruise speed with only a slight increase in fuel consumption. Typically, the long-range cruise Mach number (MLRC) provides this possibility. At the long-range cruise Mach number, the specific range corresponds to 99% of the maximum specific range (Figure F4). Economically speaking, the 1% loss compared to the maximum specific range is largely compensated by the cruise speed increase due to the flatness of the curve. MLRC > MMR SRlong range = 0.99 x SRmax range MLRC Figure F4: Long Range Cruise Mach Number Definition In relation to the Maximum Range Mach number, the long-range Cruise Mach number also decreases when weight decreases, as shown in Figure F5. 130 Getting to Grips with Aircraft Performance CRUISE MLRC Figure F5: Long Range Cruise Mach Number versus Weight PA = constant weight Ì ⇒ LRC Ì weight = constant PA Ê ⇒ LRC Ê 2.1.3. Economic Mach Number (MECON) Long-range Cruise Mach number was considered as a minimum fuel regime. If we consider the Direct Operating Cost instead, the Economic Mach number (MECON), can be introduced. As indicated in §1.1, DOCs are made up of fixed, flight-time related and fuel- consumption related costs. As a result, for a given trip, DOC can be expressed as: DOC = CC + CF.∆F + CT.∆T That is: CC = fixed costs CF = cost of fuel unit ∆F = trip fuel CT = time related costs per flight hour ∆T = trip time As DOCs are calculated per nautical mile, it is possible to plot fuel-related costs, flight-time related costs, and direct operating costs based on Mach number (Figure F6). 131  CRUISE Getting to Grips with Aircraft Performance MLRC Figure F6: Mach Number and Costs Minimum fuel costs correspond to the Maximum Range Mach number. The minimum DOC corresponds to a specific Mach number, referred to as Econ Mach (MECON). PA = constant weight Ì ⇒ M ECON Ì weight = constant PA Ê ⇒ M ECON Ê The MECON value depends on the time and fuel cost ratio. This ratio is called cost index (CI), and is usually expressed in kg/min or 100lb/h: Cost of time C T Cost Index (CI) = = Cost of fuel C F When CT is fixed and CF increases, it becomes interesting to decrease fuel consumption. Therefore, when CI decreases, Econ Mach decreases. CI Ê ⇒ MECON Ê CI Ì ⇒ MECON Ì The extreme CI values are: CI = 0: Flight time costs are null (fixed wages), so MECON = MMR (lowest boundary). CI = CImax: Flight time costs are high and fuel costs are low, so MECON = MAX SPEED in order to have a trip with a minimum flight time. The maximum speed is generally (MMO - 0.02) or (VMO - 10kt). For instance, a cost index of 30 kg/min means that the cost of one flight minute is the same as the cost of 30 kg of fuel. This does not mean the fuel flow is 30 kg/min. 132 Getting to Grips with Aircraft Performance CRUISE 2.1.4. Constant Mach Number The aircraft is often operated at a constant Mach number. MLRC Figure F7: Constant Mach Number Nevertheless, as the aircraft weight decreases, the gap between the selected Mach and the MMR increases. As a result, fuel consumption increases beyond the optimum. 3. ALTITUDE OPTIMIZATION 3.1. Optimum Cruise Altitude 3.1.1. At a Constant Mach Number In examining SR changes with the altitude at a constant Mach number, it is apparent that, for each weight, there is an altitude where SR is maximum. This altitude is referred to as “optimum altitude” (see Figure F8). PA Figure F8: Optimum Altitude Determination at Constant Mach Number 133  CRUISE Getting to Grips with Aircraft Performance When the aircraft flies at the optimum altitude, it is operated at the maximum lift to drag ratio corresponding to the selected Mach number (as in Figure F9). M < 0.76 M = 0.82 M = 0.84 M = 0.86 Figure F9: High Speed Polar Curve When the aircraft flies at high speed, the polar curve depends on the indicated Mach number, and decreases when Mach increases. So, for each Mach number, there is a different value of (CL/CD)max, that is lower as the Mach number increases. When the aircraft is cruising at the optimum altitude for a given Mach, CL is fixed and corresponds to (CL/CD)max of the selected Mach number. As a result, variable elements are weight and outside static pressure (Ps) of the optimum altitude. The formula expressing a cruise at optimum altitude is: Weight = constant Ps The optimum altitude curve, illustrated in Figure F10, is directly deduced from Figure F8. PA Figure F10: Optimum Altitude and Weight at Constant Mach Number 134 Getting to Grips with Aircraft Performance CRUISE Summary: For a given PA : optimum altitude Ê  weight Ì ⇒  specific range Ê  ISO Mach number optimum altitude curves are all quasi-parallel (Figure F11). PA Figure F11: ISO Mach Number Curves 3.1.2. Wind Influence The MMR (or MLRC or MECON) value varies with headwind or tailwind, due to changes in the ground SR. Figure F12 shows the Maximum Range Mach number versus wind variations. Given weight, PA Figure F12: MMR and wind influence 135  CRUISE Getting to Grips with Aircraft Performance As a result: Ground SR Ê  tailwind ⇒  M  MR Ì Ground SR Ì  headwind ⇒  M Ê  MR The wind force can be different at different altitudes. For a given weight, when cruise altitude is lower than optimum altitude, the specific range decreases (Figure F8). Nevertheless, it is possible that, at a lower altitude with a favorable wind, the ground specific range improves. When the favorable wind difference between the optimum altitude and a lower one reaches a certain value, the ground-specific range at lower altitude is higher than the ground-specific range at optimum altitude. As a result, in such conditions, it is more economical to cruise at the lower altitude. Figure F13 indicates the amount of favorable wind, necessary to obtain the same ground-specific range at altitudes different from the optimum: 136 Getting to Grips with Aircraft Performance CRUISE IN FLIGHT PERFORMANCE 3.05.15 P 7 CRUISE SEQ 020 REV 24 WIND ALTITUDE TRADE FOR CONSTANT SPECIFIC RANGE GIVEN : Weight : 68000 kg (150 000 lb) Wind at FL350 : 10 kt head FIND : Minimum wind difference to descend to FL310 : (26 − 3) = 23 kt RESULTS : Descent to FL310 may be considered provided the tail wind at this altitude is more than (23 − 10) = 13 kt. Figure F13: Optimum Altitude and Favorable Wind Difference 137  CRUISE Getting to Grips with Aircraft Performance 3.2. Maximum Cruise Altitude 3.2.1. Limit Mach Number at Constant Altitude Each engine has a limited Max-Cruise rating. This rating depends on the maximum temperature that the turbines can sustain. As a result, when outside temperature increases, maximum thrust decreases (see Figure F14). Thrust Given altitude Increasing weight drag m Max cruise thrust limit (ISA) (ISA + 15) Mach Mach2 Mach1 Figure F14: Influence of Temperature on Limit Mach Number at Given Altitude and Weight Figure F14 illustrates the maximum possible Mach number, as a function of temperature at a given altitude and weight. The change in limit Mach number at constant altitude can, therefore, be summed up as: For a given weight: Temperature Ò ⇒ Limit Mach number Ô For a given temperature: Weight Ò ⇒ Limit Mach number Ô 3.2.2. Maximum Cruise Altitude On the other hand, when an aircraft flies at a given Mach number, the higher the altitude, the more the thrust must be increased. The maximum cruise altitude is defined for a given weight, as the maximum altitude that an aircraft can maintain at maximum cruise thrust when the pilot maintains a fixed Mach number. 138 Getting to Grips with Aircraft Performance CRUISE. PA Non available area under ISA conditions Given Mach number PA2 PA1 ≤ ISA + 10 ISA + 20 weight m2 m1 Figure F15: Maximum Altitudes at Maximum Cruise Thrust From Figure F15, it can be deduced that: At m1, the maximum altitude is PA1 for temperatures less than ISA + 10 At m2, the maximum altitude is PA2 for temperatures less than ISA + 10, but PA1 for temperatures equal to ISA + 20. Maximum cruise altitude variations can be summed up as: weight Ê ⇒ Maximum cruise altitude Ì temperature Ê ⇒ maximum cruise altitude Ì Mach number Ê ⇒ maximum cruise altitude Ì Figure F16 illustrates how maximum and optimum altitudes are shown in an A330 FCOM: 139  CRUISE Getting to Grips with Aircraft Performance IN FLIGHT PERFORMANCE 3.05.15 P 6 CRUISE SEQ 055 REV 06 Figure F16: Maximum and Optimum Altitude 140 Getting to Grips with Aircraft Performance CRUISE 3.3. En route Maneuver Limits 3.3.1. Lift Range In level flight, lift balances weight and, when CL equals CLmax, the lift limit is reached. At this point, if the angle of attack increases, a stall occurs. Lift limit equation: mg = 0.7 S PS C Lmax M 2 CLmax M2 Drop of CLmax due to compressibility effects Flyable area Mach 2 Figure F17: CLmax M Curve versus Mach Number At a given weight, depending on the lift limit equation, each CLmax.M2 value corresponds to a static pressure (Ps) value. That is, a pressure altitude (PA). Therefore, there is a direct relationship between CLmax.M2 and PA. Figure F18 shows that, for a given PA, flight is possible between Mmin and Mmax. When PA increases, the Mach range decreases until it is reduced to a single point corresponding to the lift ceiling (PAmax). STALL STALL Figure F18: Lift Area Definition 141  CRUISE Getting to Grips with Aircraft Performance 3.3.2. Operating Maneuver Limitations 3.3.2.1. Buffet phenomenon Concerning the low Mach number limit, when speed decreases, the angle of attack must be increased in order to increase the lift coefficient, which keeps the forces balanced. Figure F19: Low Speed Stall In any case, it is not possible to indefinitely increase the angle of attack (AoA). At a high AoA, the airflow separates from the upper wing surface. If the AoA continues to increase, the point of airflow separation is unstable and rapidly fluctuates back and forth. Consequently, the pressure distribution changes constantly and also changes the lift’s position and magnitude. This effect is called buffeting and is evidenced by severe vibrations. When the AoA reaches a maximum value, the separation point moves further ahead and total flow separation of the upper surface is achieved. This phenomenon leads to a significant loss of lift, referred to as a stall. The high Mach number limit phenomenon is quite different. In fact, at high speed, compressibility effects produce shock waves on the upper wing surface. When Mach number, and/or AoA increase, the airflow separates from the upper surface behind the shock wave, which becomes unstable and induces buffeting of the same type as encountered in the low speed case. Figure F20: High Speed Airflow 142 Getting to Grips with Aircraft Performance CRUISE 3.3.2.2. Buffet limit When maneuvering, the aircraft is subject to a load factor expressed as: Lift n= Weight During turns, the load factor value mainly depends on the bank angle, as shown in Figure F21. In fact, in level flight, n = 1/cos(bank angle). Figure F21: Load Factor versus Bank Angle 0.7 S PS C Lmax M 2 At the lift limit, n= mg At a given pressure altitude (Ps) and given weight (mg), one load factor corresponds to each CL max M2. Therefore, a curve representing load factor versus Mach number will have the same shape as the one observed in Figure F17. In fact, the useful limit Mach numbers in operation are the ones for which buffeting occurs. Figure F22 represents the buffet limit, and for n = 1 (level straight flight), a minimum Mach appears for low speed buffet and a maximum Mach for high speed buffet. When n increases, the Mach number range decreases, so that when n = n max, Mmin = Mmax. So, nmax is the maximum admissible load factor at this weight and altitude, and the corresponding Mach number M allows the highest margin regarding buffet limit. 143  CRUISE Getting to Grips with Aircraft Performance Given Weight, PA M Figure F22: Load Factor and Lift Area 3.3.2.3. Pressure altitude effect Figure F23 illustrates the effects of pressure altitude on the lift area. It appears that, for a given weight: n max Ì Pressure altitude Ê lift range Ì When nmax = 1, the aircraft has reached the lift ceiling. For example, in Figure F23, PA3 corresponds to the lift ceiling at a given weight. PA0 PA1 PA PA2 PA3 Figure F23: Influence of Pressure Altitude on the Lift Limit At pressure altitude PA1 (Figure F23), nmax = 1.3. That is to say, it is possible to bear a load factor equal to 1.3, or make a 40° bank turn before buffeting occurs. 144 Getting to Grips with Aircraft Performance CRUISE In order to maintain a minimum margin against buffeting and ensure good aircraft maneuverability, it is necessary to determine an acceptable load factor limit below which buffeting shall never occur. This load factor limit is generally fixed to 1.3. This value is an operating limitation, but not a regulatory one. The corresponding altitude is called the “1.3g buffet limited altitude” or “buffet ceiling”. For a given Mach number, Figure F24 represents the 1.3g buffet limited altitude versus weight. At a given Mach number, when weight Ì Ö the buffet limited altitude Ê. PA Figure F24: 1.3g Buffet Limited Altitude As a result, the maximum recommended altitude indicated by the FMGS, depending on aircraft weight and temperature conditions, is the lowest of the: Maximum certified altitude, Maximum cruise altitude, 1.3g buffet limited altitude, Climb ceiling (see the “Climb” chapter). 3.3.2.4. A320 example Figure F25 shows how buffet limitations are illustrated in an A320 FCOM. 145  CRUISE Getting to Grips with Aircraft Performance OPERATING LIMITATIONS 3.01.20 P 5 GENERAL LIMITATIONS SEQ 001 REV 27 BUFFET ONSET R Figure F25: Buffet Onset Assumptions: Results: n = 1.3 Speed range: FL330 Mmin = M0.73 CG position: 31% Mmax = M0.82 Weight: 70 t In practice, for a given weight, the load factor limitation (1.3g) is taken into account as follows: At a fixed FL, the cruise Mach number range is determined for n = 1.3g, At a fixed cruise Mach number, the maximum FL (buffet ceiling) is determined for n = 1.3g. 146 Getting to Grips with Aircraft Performance CRUISE 3.4. Cruise Optimization: Step Climb Ideal cruise should coincide with optimum altitude. As a general rule, this altitude is not constant, but increases as weight decreases during cruise. On the other hand, ATC restrictions require level flight cruise. Aircraft must fly by segments of constant altitude which must be as close as possible to the optimum altitude. In accordance with the separation of aircraft between flight levels, the level segments are established at ± 2,000 feet from the optimum altitude. In general, it is observed that in such conditions: SR ≥ 99% SR max As a result, the following profile is obtained for a step climb cruise (Figure F26). Given Mach number Maximum thrust limited altitude Step Climb 2,000 ft under FL 290 4,000 ft above FL 290 or 2,000 ft in RVSM area Figure F26: A Step Climb Cruise Profile Flight levels are selected in accordance with temperature conditions. Usually, the first step is such that it starts at the first usable flight level, compatible with maximum cruise altitude. This is the case with the ISA condition cruise example in Figure F26. 4. FCOM CRUISE TABLE In the FCOM, cruise tables are established for several Mach numbers in different ISA conditions with normal air conditioning and anti-icing off. Aircraft performance levels are presented in Figure F27. 147  CRUISE Getting to Grips with Aircraft Performance IN FLIGHT PERFORMANCE 3.05.15 P 9 CRUISE SEQ 110 REV 31 R CRUISE - M.78 MAX. CRUISE THRUST LIMITS ISA N1 (%) MACH NORMAL AIR CONDITIONING CG=33.0% KG/H/ENG IAS (KT) ANTI-ICING OFF NM/1000KG TAS (KT) WEIGHT (1000KG) FL290 FL310 FL330 FL350 FL370 FL390 84.0.780 84.0.780 84.0.780 84.1.780 84.7.780 85.9.780 50 1276 180.9 302 1189 462 192.5 289 458 1112 204.0 277 1044 454 215.4 264 450 992 225.6 252 447 955 234.1 241 447 84.2.780 84.2.780 84.3.780 84.5.780 85.1.780 86.3.780 52 1288 179.2 302 1202 462 190.3 289 458 1127 201.4 277 1060 454 212.0 264 450 1011 221.3 252 447 977 229.0 241 447 84.4.780 84.5.780 84.6.780 84.8.780 85.5.780 86.9.780 54 1300 177.5 302 1216 462 188.1 289 458 1142 198.6 277 1079 454 208.4 264 450 1031 217.0 252 447 1003 223.1 241 447 84.7.780 84.8.780 84.9.780 85.2.780 85.9.780 87.6.780 56 1314 175.7 302 1231 462 185.9 289 458 1159 195.7 277 1097 454 204.8 264 450 1052 212.6 252 447 1036 216.0 241 447 84.9.780 85.1.780 85.2.780 85.6.780 86.4.780 88.3.780 58 1328 173.9 302 1246 462 183.6 289 458 1176 192.8 277 1117 454 201.3 264 450 1075 208.1 252 447 1070 209.0 241 447 85.2.780 85.3.780 85.6.780 85.9.780 86.9.780 89.2.780 60 1342 172.0 302 1262 462 181.3 289 458 1195 189.8 277 1137 454 197.6 264 450 1102 203.0 252 447 1110 201.5 241 447 85.5.780 85.6.780 85.9.780 86.3.780 87.6.780 90.1.780 62 1357 170.1 302 1279 462 178.8 289 458 1214 186.8 277 1158 454 194.1 264 450 1135 197.1 252 447 1153 194.0 241 447 85.7.780 85.9.780 86.2.780 86.7.780 88.2.780 64 1373 168.2 302 1297 462 176.4 289 458 1234 183.8 277 1182 454 190.2 264 450 1170 191.2 252 447 86.0.780 86.2.780 86.6.780 87.2.780 89.0.780 66 1389 166.2 302 1316 462 173.9 289 458 1254 180.9 277 1209 454 186.0 264 450 1209 185.0 252 447 86.2.780 86.5.780 86.9.780 87.8.780 89.8.780 68 1406 164.2 302 1335 462 171.4 289 458 1275 177.9 277 1242 454 181.0 264 450 1252 178.7 252 447 86.5.780 86.8.780 87.3.780 88.4.780 90.8.780 70 1424 162.1 302 1355 462 168.9 289 458 1299 174.6 277 1277 454 176.1 264 450 1298 172.3 252 447 86.8.780 87.1.780 87.7.780 89.0.780 72 1442 160.0 302 1375 462 166.4 289 458 1325 171.2 277 1314 454 171.1 264 450 87.1.780 87.5.780 88.2.780 89.8.780 74 1462 157.9 302 1397 462 163.9 289 458 1357 167.1 277 1356 454 165.7 264 450 87.4.780 87.8.780 88.8.780 90.5.780 76 1482 155.8 302 1419 462 161.3 289 458 1392 162.9 277 1400 454 160.5 264 450 LOW AIR CONDITIONING ENGINE ANTI ICE ON TOTAL ANTI ICE ON wFUEL = − 0.5 % wFUEL = + 2 % wFUEL = + 5 % Figure F27: Cruise table example 148