Getting to Grips with AC Performance PDF

 Flight Operations Support & Line Assistance Customer Services 1, rond-point Maurice Bellonte, BP 33 31707 BLAGNAC Cedex FRANCE Telephone (+33) 5 61 93 33 33...

 Flight Operations Support & Line Assistance Customer Services 1, rond-point Maurice Bellonte, BP 33 31707 BLAGNAC Cedex FRANCE Telephone (+33) 5 61 93 33 33 Telefax (+33) 5 61 93 29 68 Telex AIRBU 530526F SITA TLSBI7X getting to grips with aircraft performance January 2002 Getting to Grips with Aircraft Performance TABLE OF CONTENTS TABLE OF CONTENTS 1. INTRODUCTION 9 A. GENERAL 11 1. THE INTERNATIONAL STANDARD ATMOSPHERE (ISA) 11 1.1. STANDARD ATMOSPHERE MODELING 11 1.1.1. TEMPERATURE MODELING 11 1.1.2. PRESSURE MODELING 13 1.1.3. DENSITY MODELING 15 1.2. INTERNATIONAL STANDARD ATMOSPHERE (ISA) TABLE 15 2. ALTIMETRY PRINCIPLES 17 2.1. GENERAL 17 2.2. DEFINITIONS 18 2.3. EFFECTS OF ALTIMETER SETTING AND TEMPERATURE 20 2.3.1. ALTIMETER SETTING CORRECTION 20 2.3.2. TEMPERATURE CORRECTION 20 3. OPERATING SPEEDS 23 3.1. CALIBRATED AIR SPEED (CAS) 23 3.2. INDICATED AIR SPEED (IAS) 24 3.3. TRUE AIR SPEED (TAS) 24 3.4. GROUND SPEED (GS) 24 3.5. MACH NUMBER 25 3.6. TRUE AIR SPEED (TAS) VARIATIONS 26 4. FLIGHT MECHANICS 27 B. AIRCRAFT LIMITATIONS 29 1. FLIGHT LIMITATIONS 29 1.1. LIMIT LOAD FACTORS 29 1.2. MAXIMUM SPEEDS 30 1.3. MINIMUM SPEEDS 31 1.3.1. MINIMUM CONTROL SPEED ON THE GROUND: VMCG 31 1.3.2. MINIMUM CONTROL SPEED IN THE AIR: VMCA 32 1.3.3. MINIMUM CONTROL SPEED DURING APPROACH AND LANDING: VMCL 33 1.3.4. MINIMUM UNSTICK SPEED: VMU 34 1.3.5. STALL SPEED 35 2. MAXIMUM STRUCTURAL WEIGHTS 37 2.1. AIRCRAFT WEIGHT DEFINITIONS 37 2.2. MAXIMUM STRUCTURAL TAKEOFF WEIGHT (MTOW) 39 2.3. MAXIMUM STRUCTURAL LANDING WEIGHT (MLW) 39 2.4. MAXIMUM STRUCTURAL ZERO FUEL WEIGHT (MZFW) 39 2.5. MAXIMUM STRUCTURAL TAXI WEIGHT (MTW) 40 3. MINIMUM STRUCTURAL WEIGHT 40 4. ENVIRONMENTAL ENVELOPE 40 1 TABLE OF CONTENTS Getting to Grips with Aircraft Performance 5. ENGINE LIMITATIONS 41 5.1. THRUST SETTING AND EGT LIMITATIONS 41 5.2. TAKEOFF THRUST LIMITATIONS 42 C. TAKEOFF 43 1. INTRODUCTION 43 2. TAKEOFF SPEEDS 44 2.1. OPERATIONAL TAKEOFF SPEEDS 44 2.1.1. ENGINE FAILURE SPEED: VEF 44 2.1.2. DECISION SPEED: V1 44 2.1.3. ROTATION SPEED: VR 46 2.1.4. LIFT-OFF SPEED: VLOF 46 2.1.5. TAKEOFF CLIMB SPEED: V2 47 2.2. TAKEOFF SPEED LIMITS 48 2.2.1. MAXIMUM BRAKE ENERGY SPEED: VMBE 48 2.2.2. MAXIMUM TIRE SPEED: VTIRE 48 2.3. SPEED SUMMARY 48 3. RUNWAY LIMITATIONS 49 3.1. TAKEOFF DISTANCES 49 3.1.1. REGULATORY BACKGROUND 49 3.1.2. TAKEOFF DISTANCE (TOD) 50 3.1.3. TAKEOFF RUN (TOR) 52 3.1.4. ACCELERATE-STOP DISTANCE (ASD) 53 3.1.5. INFLUENCE OF V1 ON ACCELERATE-GO/STOP DISTANCES 55 3.2. AVAILABLE TAKEOFF LENGTHS 56 3.2.1. TAKEOFF RUN AVAILABLE (TORA) 56 3.2.2. TAKEOFF DISTANCE AVAILABLE (TODA) 56 3.2.3. ACCELERATE-STOP DISTANCE AVAILABLE (ASDA) 57 3.2.4. LOSS OF RUNWAY LENGTH DUE TO ALIGNMENT 58 3.2.5. INFLUENCE OF V1 ON THE RUNWAY-LIMITED TAKEOFF W EIGHT 61 4. CLIMB AND OBSTACLE LIMITATIONS 62 4.1. TAKEOFF FLIGHT PATH 62 4.1.1. DEFINITIONS 62 4.1.2. TAKEOFF SEGMENTS AND CLIMB REQUIREMENTS 62 4.1.3. MINIMUM AND MAXIMUM ACCELERATION HEIGHTS 64 4.1.4. TAKEOFF TURN PROCEDURE 65 4.2. OBSTACLE CLEARANCE 67 4.2.1. GROSS AND NET TAKEOFF FLIGHT PATHS 67 4.2.2. OBSTACLE CLEARANCE DURING A STRAIGHT TAKEOFF 68 4.2.3. OBSTACLE CLEARANCE DURING A TURN 68 4.2.4. LOSS OF GRADIENT DURING A TURN 69 4.2.5. TAKEOFF FLIGHT PATH WITH OBSTACLES 70 4.2.6. TAKEOFF FUNNEL 71 5. OUTSIDE ELEMENTS 74 5.1. WIND 74 5.2. PRESSURE ALTITUDE 75 5.2.1. EFFECT ON AERODYNAMICS 75 5.2.2. EFFECT ON ENGINES 76 5.2.3. SUMMARY 76 2 Getting to Grips with Aircraft Performance TABLE OF CONTENTS 5.3. TEMPERATURE 76 5.3.1. EFFECT ON AERODYNAMICS 76 5.3.2. EFFECT ON ENGINES 76 5.3.3. SUMMARY 77 5.4. RUNWAY SLOPE 77 5.5. RUNWAY CONDITIONS (DRY, DAMP, WET, CONTAMINATED) 77 5.5.1. DEFINITIONS 78 5.5.2. EFFECT ON PERFORMANCE 79 5.5.3. AIRCRAFT MANUFACTURER DATA 82 5.5.4. TAKEOFF PERFORMANCE ON W ET AND CONTAMINATED RUNWAYS 83 6. MAXIMUM TAKEOFF WEIGHT DETERMINATION 84 6.1. SPEED OPTIMIZATION PROCESS 84 6.2. REGULATORY TAKEOFF WEIGHT CHART (RTOW CHART) 85 7. FLEXIBLE AND DERATED TAKEOFF 87 7.1. FLEXIBLE TAKEOFF 87 7.1.1. DEFINITION 87 7.1.2. FLEXIBLE TAKEOFF AND RUNWAY STATE 88 7.1.3. FLEXIBLE TEMPERATURE DETERMINATION 89 7.1.4. FLEXIBLE TAKEOFF PROCEDURE 89 7.2. DERATED TAKEOFF 90 7.2.1. DEFINITION 90 7.2.2. MINIMUM CONTROL SPEEDS WITH DERATED THRUST 90 7.2.3. DERATED TAKEOFF AND RUNWAY STATE 91 7.2.4. DERATED TAKEOFF PROCEDURE 92 D. EN ROUTE LIMITATIONS 93 1. EN ROUTE FAILURE CASES 93 2. ENGINE FAILURE(S) 93 2.1. GENERAL DEFINITIONS 93 2.1.1. DRIFT DOWN PROCEDURE 93 2.1.2. GROSS AND NET DRIFT DOWN FLIGHT PATHS 94 2.1.3. TAKEOFF ALTERNATE AIRPORT 95 2.2. EN ROUTE OBSTACLE CLEARANCE – ONE ENGINE INOPERATIVE 96 2.2.1. LATERAL CLEARANCE 96 2.2.2. VERTICAL CLEARANCE 97 2.2.3. DIVERSION AIRFIELD 101 2.3. TWIN ENGINE AIRCRAFT 102 2.3.1. 60 MINUTE RULE 102 2.4. FOUR ENGINE AIRCRAFT 102 2.4.1. 90 MINUTE RULE 102 2.4.2. OBSTACLE CLEARANCE – TWO ENGINES INOPERATIVE 103 2.4.3. DIVERSION AIRFIELD – TWO ENGINES INOPERATIVE 104 3. IN-FLIGHT CABIN PRESSURIZATION FAILURE 105 3.1.1. OXYGEN SYSTEMS 105 3.1.2. PASSENGER OXYGEN REQUIREMENT 106 3.1.3. FLIGHT PROFILE 107 3.1.4. MINIMUM FLIGHT ALTITUDES 108 3.1.5. OBSTACLE CLEARANCE – CABIN PRESSURIZATION FAILURE 109 4. ROUTE STUDY 110 3 TABLE OF CONTENTS Getting to Grips with Aircraft Performance E. LANDING 111 1. INTRODUCTION 111 2. LANDING DISTANCE AVAILABLE (LDA) 111 2.1. WITH NO OBSTACLE UNDER LANDING PATH 111 2.2. WITH OBSTACLES UNDER LANDING PATH 111 3. LANDING PERFORMANCE 112 3.1. OPERATING LANDING SPEEDS 112 3.1.1. LOWEST SELECTABLE SPEED: VLS 113 3.1.2. FINAL APPROACH SPEED: VAPP 113 3.1.3. REFERENCE SPEED: VREF 114 3.2. ACTUAL LANDING DISTANCE (ALD) 114 3.2.1. MANUAL LANDING 114 3.2.2. AUTOMATIC LANDING 116 3.3. GO-AROUND PERFORMANCE REQUIREMENTS 117 3.3.1. APPROACH CLIMB 117 3.3.2. LANDING CLIMB 118 3.4. EXTERNAL PARAMETERS INFLUENCE 119 3.4.1. PRESSURE ALTITUDE 119 3.4.2. TEMPERATURE 119 3.4.3. RUNWAY SLOPE 119 3.4.4. RUNWAY CONDITIONS 120 3.4.5. AIRCRAFT CONFIGURATION 120 4. DISPATCH REQUIREMENTS 121 4.1. REQUIRED LANDING DISTANCE (RLD) 121 4.1.1. RLD DRY RUNWAYS 121 4.1.2. RLD W ET RUNWAYS 121 4.1.3. RLD CONTAMINATED RUNWAYS 122 4.1.4. RLD WITH AUTOMATIC LANDING (DRY) 122 4.2. GO-AROUND REQUIREMENTS 123 4.2.1. NORMAL APPROACH 123 4.2.2. CAT II OR CAT III APPROACH 123 4.3. CONCLUSION 123 5. IN-FLIGHT REQUIREMENTS 124 5.1. IN-FLIGHT FAILURE 124 5.2. OVERWEIGHT LANDING REQUIREMENTS 124 5.3. FUEL JETTISONING CONDITIONS 125 F. CRUISE 127 1. GENERAL 127 1.1. INTRODUCTION 127 1.2. SPECIFIC RANGE 127 2. SPEED OPTIMIZATION 128 2.1. ALL ENGINE OPERATING CRUISE SPEEDS 128 2.1.1. MAXIMUM RANGE MACH NUMBER (MMR) 128 2.1.2. LONG-RANGE CRUISE MACH NUMBER (MLRC) 130 2.1.3. ECONOMIC MACH NUMBER (MECON) 131 2.1.4. CONSTANT MACH NUMBER 133 4 Getting to Grips with Aircraft Performance TABLE OF CONTENTS 3. ALTITUDE OPTIMIZATION 133 3.1. OPTIMUM CRUISE ALTITUDE 133 3.1.1. AT A CONSTANT MACH NUMBER 133 3.1.2. W IND INFLUENCE 135 3.2. MAXIMUM CRUISE ALTITUDE 138 3.2.1. LIMIT MACH NUMBER AT CONSTANT ALTITUDE 138 3.2.2. MAXIMUM CRUISE ALTITUDE 138 3.3. EN ROUTE MANEUVER LIMITS 141 3.3.1. LIFT RANGE 141 3.3.2. OPERATING MANEUVER LIMITATIONS 142 3.4. CRUISE OPTIMIZATION: STEP CLIMB 147 4. FCOM CRUISE TABLE 147 G. CLIMB 149 1. FLIGHT MECHANICS 149 1.1. DEFINITIONS 149 1.2. CLIMB EQUATIONS 149 1.2.1. CLIMB GRADIENT (γ) 150 1.2.2. RATE OF CLIMB (RC) 151 1.2.3. SPEED POLAR 151 1.3. INFLUENCING PARAMETERS 152 1.3.1. ALTITUDE EFFECT 152 1.3.2. TEMPERATURE EFFECT 153 1.3.3. W EIGHT EFFECT 153 1.3.4. W IND EFFECT 153 2. CLIMB IN OPERATION 154 2.1. CLIMB MANAGEMENT 154 2.1.1. THRUST SETTING 154 2.1.2. ENERGY SHARING 154 2.1.3. CLIMB CEILING 155 2.2. CLIMB SPEEDS 155 2.2.1. CLIMB AT GIVEN IAS/MACH LAW 155 2.2.2. CLIMB AT MAXIMUM GRADIENT 156 2.2.3. CLIMB AT MAXIMUM RATE 156 2.2.4. CLIMB AT MINIMUM COST 156 2.3. FCOM CLIMB TABLE 157 2.4. CABIN CLIMB 158 H. DESCENT / HOLDING 159 1. FLIGHT MECHANICS 159 1.1. DEFINITIONS 159 1.2. DESCENT EQUATIONS 159 1.2.1. DESCENT GRADIENT (γ) 159 1.2.2. RATE OF DESCENT (RD) 160 1.2.3. SPEED POLAR 161 1.3. INFLUENCING PARAMETERS 161 1.3.1. ALTITUDE EFFECT 161 1.3.2. TEMPERATURE EFFECT 162 1.3.3. W EIGHT EFFECT 162 1.3.4. W IND EFFECT 163 5 TABLE OF CONTENTS Getting to Grips with Aircraft Performance 2. DESCENT IN OPERATION 164 2.1. THRUST SETTING 164 2.2. DESCENT SPEEDS 164 2.2.1. DESCENT AT GIVEN MACH/IAS LAW 164 2.2.2. DESCENT AT MINIMUM GRADIENT (DRIFT DOWN) 165 2.2.3. DESCENT AT MINIMUM RATE 165 2.2.4. DESCENT AT MINIMUM COST 165 2.2.5. EMERGENCY DESCENT 166 2.3. FCOM DESCENT TABLE 166 2.4. CABIN DESCENT 167 3. HOLDING 168 3.1. HOLDING SPEED 168 3.2. HOLDING IN OPERATION 169 I. FUEL PLANNING AND MANAGEMENT 171 1. JAR - FUEL PLANNING AND MANAGEMENT 171 1.1. FUEL POLICY 171 1.1.1. STANDARD FLIGHT PLANNING 171 1.1.2. ISOLATED AIRPORT PROCEDURE 175 1.1.3. UNREQUIRED DESTINATION ALTERNATE AIRPORT 175 1.1.4. DECISION POINT PROCEDURE 175 1.1.5. PRE-DETERMINED POINT PROCEDURE 177 1.1.6. ETOPS PROCEDURE 177 1.2. FUEL MANAGEMENT 179 1.2.1. MINIMUM FUEL AT LANDING AIRPORT 179 1.2.2. MINIMUM FUEL AT DESTINATION AIRPORT 179 2. FAR - FUEL PLANNING AND MANAGEMENT 181 2.1. DIFFERENT TYPES OF OPERATIONS 181 2.2. FUEL POLICY 182 2.2.1. DOMESTIC OPERATIONS 182 2.2.2. FLAG AND SUPPLEMENTAL OPERATIONS 184 2.2.3. ISOLATED AIRPORT PROCEDURE 186 2.2.4. UNREQUIRED DESTINATION ALTERNATE AIRPORT 186 2.2.5. REDISPATCH PROCEDURE 187 2.2.6. ETOPS PROCEDURE 188 2.2. FUEL MANAGEMENT 188 2.2.1 MINIMUM FUEL AT LANDING AIRPORT 188 J. APPENDIX 189 1. APPENDIX 1 : ALTIMETRY - TEMPERATURE EFFECT 189 2. APPENDIX 2 : TAKEOFF OPTIMIZATION PRINCIPLE 192 2.1. TAKEOFF CONFIGURATION 192 2.2. AIR CONDITIONING 193 2.3. TAKEOFF SPEED OPTIMIZATION 193 2.3.1. SPEED RATIOS: V1/VR AND V2/VS 193 2.3.2. V1/VR RATIO INFLUENCE 194 2.3.3. V2/VS RATIO INFLUENCE 197 2.4. RESULT OF THE OPTIMIZATION PROCESS 199 2.4.1. MAXIMUM TAKEOFF W EIGHT 199 6 Getting to Grips with Aircraft Performance TABLE OF CONTENTS 2.4.2. TAKEOFF SPEEDS 200 2.4.3. LIMITATION CODES 200 2.4.4. RTOW CHART INFORMATION 202 3. APPENDIX 3 : TAKEOFF PERFORMANCE SOFTWARE 203 3.1. P.E.P FOR WINDOWS 203 3.1.1. W HAT IS P.E.P. ? 203 3.1.2. TLO MODULE 204 3.2. LESS PAPER COCKPIT (LPC) 205 4. APPENDIX 4 : ABBREVIATIONS 206 7 Getting to Grips with Aircraft Performance INTRODUCTION 1. INTRODUCTION The safety of air transportation is a joint effort, regulated by the State on one hand, and practiced by the manufacturers, airlines and Air Traffic Controllers (ATC), on the other hand. The State is responsible for the supervision of civil aviation, to ensure that a high safety standard is maintained throughout the industry, and its primary means of enforcement is via the establishment and administration of written regulations. The control process encompasses a fixed set of rules to secure that all aircraft respect a minimum level of performance, which thereby leads to the definition of limitations. The "State administration" generally implies the civil aviation authority, which corresponds to the aircraft's country of registration. In the United States, for example, this role is devoted to the Federal Aviation Administration (FAA), whereas in France, it is the “Direction Générale de l’Aviation Civile” (DGAC). Every country has its own regulations, but the international aspect of air transportation takes into account the worldwide application of common rules. The International Civil Aviation Organization (ICAO) was therefore created in 1948, to provide a supranational council, to assist in defining the international minimum recommended standards. The Chicago Convention was signed on December 7, 1944, and has become the legal foundation for civil aviation worldwide. Although it is customary for each country to adopt the main airworthiness standards defined in conjunction with aircraft manufacturers (USA, Europe, Canada, etc.), every country has its own set of operational regulations. For instance, some countries (mainly European) have adopted JAR-OPS 1, while some others follow the US FAR 121. The "field of limitations" is therefore dependent upon an amalgamation of the following two realms: Airworthiness: Involving the aircraft's design (limitations, performance data etc….), in relation to JAR 25 or FAR 25. Operations: Involving the technical operating rules (takeoff and landing limitations, fuel planning, etc…), in relation to JAR-OPS 1 or FAR 121. Both airworthiness and operational regulations exist for all aircraft types. This brochure addresses "large aircraft”, which means aircraft with a maximum takeoff weight exceeding 5,700 kg. Airbus performance documentation is clearly divided into the two above-mentioned categories: Airworthiness and Operations. Airworthiness: The Airplane Flight Manual (AFM) is associated to the airworthiness certificate and contains certified performance data in compliance with JAR/FAR25. 9 INTRODUCTION Getting to Grips with Aircraft Performance Operations: The Flight Crew Operating Manual (FCOM) can be viewed as the AOM (aircraft-related portion of the Operations Manual), which contains all the necessary limitations, procedures and performance data for aircraft operation. The following table (Table 1) illustrates the large aircraft regulatory basis: ICAO EUROPE (JAA) USA (FAA) Annex 8 Airworthiness to the Chicago JAR1 25 FAR2 part 25 Convention Annex 6 Operating Rules to the Chicago JAR-OPS1 FAR part 121 Convention Table 1: Large Aircraft Requirements All aircraft of the Airbus family are JAR 25 and/or FAR 25 certified. On the other hand, compliance with the operating rules remains under the airline’s responsibility. This brochure is designed to address three different aspects of aircraft performance: The physical aspect : This brochure provides reminders on flight mechanics, aerodynamics, altimetry, influence of external parameters on aircraft performance, flight optimization concepts… The regulatory aspect : Description of the main JAR and FAR certification and operating rules, leading to the establishment of limitations. For a clear understanding, regulatory articles are quoted to assist in clarifying a given subject. In such cases, the text is written in italics and the article references are clearly indicated to the reader. The operational aspect : Description of operational methods, aircraft computer logics, operational procedures, pilot’s actions… 1 JAR: The Joint Airworthiness Requirements are under the European authority called the Joint Aviation Authority (JAA). 2 FAR: The Federal Aviation Regulations are under the US authority called the Federal Aviation Administration (FAA). 10 Getting to Grips with Aircraft Performance GENERAL A. GENERAL 1. THE INTERNATIONAL STANDARD ATMOSPHERE (ISA) 1.1. Standard Atmosphere Modeling The atmosphere is a gaseous envelope surrounding the earth. Its characteristics are different throughout the world. For this reason, it is necessary to adopt an average set of conditions called the International Standard Atmosphere (ISA). 1.1.1. Temperature Modeling The following diagram (Figure A1) illustrates the temperature variations in the standard atmosphere: Altitude (ft) (km) STRATOSPHERE 40000 12 TROPOPAUSE = 36089 ft subsonic jet transport 35000 10 cruise level 30000 25000 8 TROPOSPHERE 20000 6 15000 4 10000 2 5000 -56.5°C 15°C Sea level -60 -40 -20 0 20 40 60 Temperature (°C) Figure A1: ISA temperature The international reference is based on a sea-level temperature of 15°C at a pressure of 1013.25 hPa1. The standard density of the air at sea level is 1.225 kg/m3. 1 1013.25 hPa is equal to 29.92 in Hg, ‘hPa’ meaning hectoPascal and ‘in Hg’ inches of mercury. 11 GENERAL Getting to Grips with Aircraft Performance Temperature decreases with altitude at a constant rate of -6.5°C/1000m or -1.98°C/1000ft up to the tropopause. The standard tropopause altitude is 11,000 m or 36,089 feet. From the tropopause upward, the temperature remains at a constant value of -56.5°C. Therefore, the air which is considered as a perfect gas in the ISA model presents the following characteristics: At Mean Sea Level (MSL): ISA temperature = T0 = +15°C = 288.15 K Above MSL and below the tropopause (36,089 feet): ISA temperature (ºC) = T0 - 1.98 x [Alt(feet)/1000] For a quick determination of the standard temperature at a given altitude, the following approximate formula can be used: ISA temperature (ºC) = 15 - 2 x [Alt(feet)/1000] Above the tropopause (36,089 feet): ISA temperature = -56.5ºC = 216.65 K This ISA model is used as a reference to compare real atmospheric conditions and the corresponding engine/aircraft performance. The atmospheric conditions will therefore be expressed as ISA +/- ∆ISA at a given flight level. Example: Let’s consider a flight in the following conditions: Altitude = 33,000 feet Actual Temperature = -41ºC The standard temperature at 33,000 feet is : ISA = 15 - 2 x 33 = -51ºC, whereas the actual temperature is -41ºC, i.e. 10ºC above the standard. Conclusion: The flight is operated in ISA+10 conditions 12 Getting to Grips with Aircraft Performance GENERAL 1.1.2. Pressure Modeling To calculate the standard pressure P at a given altitude, the following assumptions are made: Temperature is standard, versus altitude. Air is a perfect gas. The altitude obtained from the measurement of the pressure is called pressure altitude (PA), and a standard (ISA) table can be set up (table A1). PAZp PRESSURE ALTITUDE (ft) (km) 40000 12 Zp PA==f(p) f(P) ISA table 10 30000 8 20000 6 4 10000 2 P 200 300 500 850 1013.25 (hPa) Figure A2: Pressure Altitude function of Pressure Pressure (hPa) Pressure altitude (PA) FL= PA/100 (feet) (meters) 200 38661 11784 390 250 34000 10363 340 300 30066 9164 300 500 18287 5574 180 850 4813 1467 50 1013 0 0 0 Table A1: Example of Tabulated Pressure Altitude Values 13 GENERAL Getting to Grips with Aircraft Performance Assuming a volume of air in static equilibrium, the aerostatic equation gives: dP = - ρgdh With ρ = air density at an altitude h g= gravity acceleration (9.80665 m/s2) dh = height of the volume unit dP = pressure variation on dh The perfect gas equation gives: P = RT ρ With R = universal gas constant (287.053 J/kg/K) Consequently: At Mean Sea Level (MSL): P0 = 1013.25 hPa Above MSL and below the tropopause (36,089 feet): g α αR0 P = P0 (1− h) T0 With P0 = 1013.25 hPa (standard pressure at sea level) T0 = 288.15 K (standard temperature at sea level) α = 0.0065 ºC/m g0 = 9.80665 m/s2 R = 287.053 J/kg/K h = Altitude (m) Note: For low altitudes, a reduction of 1 hPa in the pressure approximately corresponds to a pressure altitude increase of 28 feet. Above the tropopause (36,089 feet): − g 0 ( h −h1 ) RT1 P = P1e With P1 = 226.32 hPa (standard pressure at 11,000 m) T1 = 216.65 K (standard temperature at 11,000 m) 14 Getting to Grips with Aircraft Performance GENERAL h1 = 11,000 m g0 = 9.80665 m/s2 R = 287.053 J/kg/K h = Altitude (m) 1.1.3. Density Modeling To calculate the standard density ρ at a given altitude, the air is assumed to be a perfect gas. Therefore, at a given altitude, the standard density ρ (kg/m3) can be obtained as follows: P ρ= RT with R = universal gas constant (287.053 J/kg/K) P in Pascal T in Kelvin At Mean Sea Level (MSL): ρ0 = 1.225 kg/m3 1.2. International Standard Atmosphere (ISA) Table The International Standard Atmosphere parameters (temperature, pressure, density) can be provided as a function of the altitude under a tabulated form, as shown in Table A2: 15 GENERAL Getting to Grips with Aircraft Performance PRESSURE ALTITUDE TEMP. PRESSURE DENSITY Speed of ALTITUDE (Feet) (°C) RATIO σ = ρ/ρo sound (meters) hPa PSI In.Hg δ = P/Po (kt) 40 000 - 56.5 188 2.72 5.54 0.1851 0.2462 573 12 192 39 000 - 56.5 197 2.58 5.81 0.1942 0.2583 573 11 887 38 000 - 56.5 206 2.99 6.10 0.2038 0.2710 573 11 582 37 000 - 56.5 217 3.14 6.40 0.2138 0.2844 573 11 278 36 000 - 56.3 227 3.30 6.71 0.2243 0.2981 573 10 973 35 000 - 54.3 238 3.46 7.04 0.2353 0.3099 576 10 668 34 000 - 52.4 250 3.63 7.38 0.2467 0.3220 579 10 363 33 000 - 50.4 262 3.80 7.74 0.2586 0.3345 581 10 058 32 000 - 48.4 274 3.98 8.11 0.2709 0.3473 584 9 754 31 000 - 46.4 287 4.17 8.49 0.2837 0.3605 586 9 449 30 000 - 44.4 301 4.36 8.89 0.2970 0.3741 589 9 144 29 000 - 42.5 315 4.57 9.30 0.3107 0.3881 591 8 839 28 000 - 40.5 329 4.78 9.73 0.3250 0.4025 594 8 534 27 000 - 38.5 344 4.99 10.17 0.3398 0.4173 597 8 230 26 000 - 36.5 360 5.22 10.63 0.3552 0.4325 599 7 925 25 000 - 34.5 376 5.45 11.10 0.3711 0.4481 602 7 620 24 000 - 32.5 393 5.70 11.60 0.3876 0.4642 604 7 315 23 000 - 30.6 410 5.95 12.11 0.4046 0.4806 607 7 010 22 000 - 28.6 428 6.21 12.64 0.4223 0.4976 609 6 706 21 000 - 26.6 446 6.47 13.18 0.4406 0.5150 611 6 401 20 000 - 24.6 466 6.75 13.75 0.4595 0.5328 614 6 096 19 000 - 22.6 485 7.04 14.34 0.4791 0.5511 616 5 791 18 000 - 20.7 506 7.34 14.94 0.4994 0.5699 619 5 406 17 000 - 18.7 527 7.65 15.57 0.5203 0.5892 621 5 182 16 000 - 16.7 549 7.97 16.22 0.5420 0.6090 624 4 877 15 000 - 14.7 572 8.29 16.89 0.5643 0.6292 626 4 572 14 000 - 12.7 595 8.63 17.58 0.5875 0.6500 628 4 267 13 000 - 10.8 619 8.99 18.29 0.6113 0.6713 631 3 962 12 000 - 8.8 644 9.35 19.03 0.6360 0.6932 633 3 658 11 000 - 6.8 670 9.72 19.79 0.6614 0.7156 636 3 353 10 000 - 4.8 697 10.10 20.58 0.6877 0.7385 638 3 048 9 000 - 2.8 724 10.51 21.39 0.7148 0.7620 640 2 743 8 000 - 0.8 753 10.92 22.22 0.7428 0.7860 643 2 438 7 000 + 1.1 782 11.34 23.09 0.7716 0.8106 645 2 134 6 000 + 3.1 812 11.78 23.98 0.8014 0.8359 647 1 829 5 000 + 5.1 843 12.23 24.90 0.8320 0.8617 650 1 524 4 000 + 7.1 875 12.69 25.84 0.8637 0.8881 652 1 219 3 000 + 9.1 908 13.17 26.82 0.8962 0.9151 654 914 2 000 + 11.0 942 13.67 27.82 0.9298 0.9428 656 610 1 000 + 13.0 977 14.17 28.86 0.9644 0.9711 659 305 0 + 15.0 1013 14.70 29.92 1.0000 1.0000 661 0 - 1 000 + 17.0 1050 15.23 31.02 1.0366 1.0295 664 - 305 Table A2: International Standard Atmosphere (ISA) 16 Getting to Grips with Aircraft Performance GENERAL 2. ALTIMETRY PRINCIPLES 2.1. General An altimeter (Figure A4) is a manometer, which is calibrated following standard pressure and temperature laws. The ambient atmospheric pressure is the only input parameter used by the altimeter. Zp PA PR ESSU RE ALTITU DE PA = f(P) Zp = f(P) ISA table PA Zp amb amb IA Zi PA Zp set set P 1013.25 (hPa) Pamb Pset Figure A3: Ambient Pressure and Pressure Setting Figure A4: Altimeter Function on PFD Assuming the conditions are standard, the “Indicated Altitude” (IA) is the vertical distance between the following two pressure surfaces (Figure A3): The pressure surface at which the ambient pressure is measured (actual aircraft’s location), and The reference pressure surface, corresponding to the pressure selected by the pilot through the altimeter’s pressure setting knob. IA = f(Pamb) - f(Pset) IA = PAamb - PAset 17 GENERAL Getting to Grips with Aircraft Performance 2.2. Definitions QNH QFE 1013 Radio (AAL) Flight Altitude height Height Level QFE setting QNH setting Standard setting: 1013.25 hPa Figure A5: QNH and Pressure Altitude The pressure setting and the indicated altitude move in the same direction: Any increase in the pressure setting leads to an increase in the corresponding Indicated Altitude (IA). The aim of altimetry is to ensure relevant margins, above ground and between aircraft. For that purpose, different operational pressure settings can be selected through the altimeter’s pressure setting knob (Figure A5): QFE is the pressure at the airport reference point. With the QFE setting, the altimeter indicates the altitude above the airport reference point (if the temperature is standard). Note: The QFE selection is often provided as an option on Airbus aircraft. QNH is the Mean Sea Level pressure. The QNH is calculated through the measurement of the pressure at the airport reference point moved to Mean Sea Level, assuming the standard pressure law. With the QNH setting, the altimeter indicates the altitude above Mean Sea Level (if temperature is standard). Consequently, at the airport level in ISA conditions, the altimeter indicates the topographic altitude of the terrain. Standard corresponds to 1013 hPa. With the standard setting, the altimeter indicates the altitude above the 1013 hPa isobaric surface (if temperature is standard). The aim is to provide a vertical separation between aircraft while getting rid of the local pressure variations throughout 18 Getting to Grips with Aircraft Performance GENERAL the flight. After takeoff, crossing a given altitude referred to as Transition Altitude, the standard setting is selected. The Flight Level corresponds to the Indicated Altitude in feet divided by 100, provided the standard setting is selected. The Transition Altitude is the indicated altitude above which the standard setting must be selected by the crew. The Transition Level is the first available flight level above the transition altitude. The change between the QNH setting and Standard setting occurs at the transition altitude when climbing, and at the transition level when descending (Figure A6). take off approach climb descent 1013 1013 transition transition altitude level QNH sea level QNH QNH 1013 hPa Figure A6: Transition Altitude and Transition Level The transition altitude is generally given on the Standard Instrument Departure (SID) charts, whereas the transition level is usually given by the Air Traffic Control (ATC). 19 GENERAL Getting to Grips with Aircraft Performance 2.3. Effects of Altimeter Setting and Temperature The true altitude of an aircraft is rarely the same as the indicated altitude, when the altimeter setting is 1013 hPa. This is mainly due to the fact that the pressure at sea level is generally different from 1013 hPa, and/or that the temperature is different from ISA. 2.3.1. Altimeter Setting Correction In case of ISA temperature conditions, and a standard altimetric setting, the aircraft true altitude can be obtained from the indicated altitude provided the local QNH is known. True altitude = Indicated altitude + 28 x (QNH [hPa] - 1013) 2.3.2. Temperature Correction Flying at a given indicated altitude, the true altitude increases with the temperature (Figure A7). The relationship between true altitude and indicated altitude can be approximated as follows: T TA = IA TISA TA = True altitude IA = Indicated altitude T = Actual temperature (in Kelvin) TISA = Standard temperature (in Kelvin) An example is provided in Appendix 1 of this manual. 20 Getting to Grips with Aircraft Performance GENERAL 1013 ISA+ ∆ISA TA > IA 1013 ISA TA = IA 1013 ISA - ∆ISA TA < IA At a constant Indicated Altitude (IA), the True Altitude (TA) Ê when the Static Air Temperature (SAT) Ê Figure A7: Temperature effect on True Altitude, for a constant Indicated Altitude Conclusion: If the temperature is higher, you fly higher. If the temperature is lower, you fly lower. Temperature correction is important, when flying a departure or arrival procedure in very low temperature conditions. For that purpose, the following table (Table A3) is proposed in the FCOM: 21 GENERAL Getting to Grips with Aircraft Performance Table A3: True Altitude Correction versus Temperature 22 Getting to Grips with Aircraft Performance GENERAL 3. OPERATING SPEEDS Different speed types are used to operate an aircraft. Some of them enable the crew to manage the flight while maintaining some margins from critical areas, whereas others are mainly used for navigational and performance optimization purposes. This is why the following sections propose a review of the different speed types that are used in aeronautics. 3.1. Calibrated Air Speed (CAS) The Calibrated Air Speed (CAS) is obtained from the difference between the total pressure (Pt) and the static pressure (Ps). This difference is called dynamic pressure (q). As the dynamic pressure cannot be measured directly, it is obtained thanks to two probes (Figure A8). q = Pt - Ps Static probes (Stby+ F/O+ Capt.) symmetrical on the other side, to avoid sideslip errors Pitots (Stby + Capt.) F/O on the other side Figure A8: Pitot Tube and Static Probes To obtain the total pressure Pt, airflow is stopped by means of a forward- facing tube, called the pitot tube (Figure A9), which measures the impact pressure. This pressure measurement accounts for the ambient pressure (static aspect) at the given flight altitude plus the aircraft motion (dynamic aspect). The static pressure Ps is measured by means of a series of symmetrical static probes perpendicular to the airflow. This measurement represents the ambient pressure at the given flight altitude (static aspect). CAS = f (Pt-Ps) = f (q) Flying at a constant CAS during a climb phase enables the aerodynamic effect to remain the same as at sea level and, consequently, to eliminate speed variations. 23 GENERAL Getting to Grips with Aircraft Performance Total pressure pick-off: Pt Static port Ps Pi Ps0 Air flow CAS Dynamic: q = Pt - PS Static: PS Figure A9: CAS Determination Process 3.2. Indicated Air Speed (IAS) The Indicated Air Speed (IAS) is the speed indicated by the airspeed indicator. Whatever the flight conditions, if the pressure measurement were accurate, then the IAS should ideally be equal to the CAS. Nevertheless, depending on the aircraft angle of attack, the flaps configuration, the ground proximity (ground effect or not), the wind direction and other influent parameters, some measurement errors are introduced, mainly on the static pressure. This leads to a small difference between the CAS and the IAS values. This difference is called instrumental correction or antenna error (Ki). IAS = CAS + Ki 3.3. True Air Speed (TAS) An aircraft in flight moves in an air mass, which is itself in motion compared to the earth. The True Air Speed (TAS) represents the aircraft speed in a moving reference system linked to this air mass, or simply the aircraft speed in the airflow. It can be obtained from the CAS, using the air density (ρ ρ) and a compressibility correction (K). TAS = ( ρo/ρ ) K CAS 3.4. Ground Speed (GS) The ground speed (GS) represents the aircraft speed in a fixed ground reference system. It is equal to the TAS corrected for the wind component (Figure A10). Ground Speed = True Air Speed + Wind Component 24 Getting to Grips with Aircraft Performance GENERAL Wind TAS GS DA GS = Ground Speed DA = Drift Angle TAS = True Air Speed Figure A10: Ground Speed and Drift Angle 3.5. Mach Number The Mach Number is a comparison between the TAS and the speed of sound. TAS M= a With TAS = True Air Speed a = The speed of sound at the flight altitude The speed of sound in knots is: a(kt) = 39 SAT(K) With SAT = Static Air Temperature (ambient temperature)in Kelvin The speed of sound is solely dependent on temperature. Consequently, the Mach number can be expressed as follows: TAS (kt) M= 39 273 + SAT( ° C) Flying at a given Mach number in the troposphere: When the pressure altitude increases, the SAT decreases and thus the True Air Speed (TAS). Or : higher ⇒ slower 25 GENERAL Getting to Grips with Aircraft Performance Pt and Ps, respectively measured by the aircraft pitot tube and static probes, are also used to compute the Mach number. Therefore,  P − Ps  q M = f  t  = f    Ps   Ps  The TAS indicated on the navigation display of modern aircraft is then obtained from the Mach number: TAS ( Kt ) = 39M 273 + SAT (º C ) 3.6. True Air Speed (TAS) Variations FL 450 400 iso Mach 0.78 tropopause 350 300 Cross-over altitude 250 200 150 100 50 iso CAS 300 TAS (kt) 200 250 300 350 400 450 500 Figure A11: True Air Speed Variations – Climb profile 300 Kt / M0.78 The above graph (Figure A11) illustrates the TAS variations as a function of the pressure altitude for a climb at constant CAS (300 knots) and constant Mach (M0.78). The altitude at which a given CAS is equal to a given Mach number is called the cross-over altitude. 26 Getting to Grips with Aircraft Performance GENERAL 4. FLIGHT MECHANICS For a flight at constant speed in level flight, the drag force must balance the engine thrust. As a general rule, when engine thrust is higher than drag, the aircraft can use this excess thrust to accelerate and/or climb. On the other hand, when the thrust is insufficient to compensate for drag, the aircraft is forced to decelerate and/or descend. In flight, four forces are applied to an aircraft : Thrust, drag, lift and weight. If the aircraft is in steady level flight, the following balance is obtained (Figure A12): The thrust for steady level flight (T) is equal to drag (D = ½ ρ S V2 CD), Weight (mg) is equal to lift (L = ½ ρ S V2 CL). lift thrust drag weight = mg Figure A12: Balance of Forces for Steady Level Flight 4.1.1.1. Standard Lift Equation Weight = mg = ½ ρ S (TAS)2 CL (1) With m = Aircraft mass g = Gravitational acceleration ρ = Air density S = Wing area CL = lift coefficient The lift coefficient, CL, is a function of the angle of attack (α), the Mach number (M), and the aircraft configuration. 27 GENERAL Getting to Grips with Aircraft Performance 4.1.1.2. Standard Drag Equation Thrust = ½ ρ S (TAS)2 CD (2) With CD = Drag coefficient The drag coefficient, CD, is a function of the angle of attack (α), the Mach number (M) and the aircraft configuration. 4.1.1.3. Other Formulas As a function of the Mach number: Lift and drag equations may be expressed with the Mach number M. As a result, the equations are: Weight = 0.7 PS S M2 CL (3) Thrust = 0.7 PS S M2 CD (4) With Ps = Static Pressure As a function of P0: The pressure ratio δ is introduced into the lift and drag equations: Ps δ = (5) P0 With P0 = Pressure at Sea Level Ps = Pressure at Flight Level Therefore, the following equations are independent of pressure altitude: Weight = 0.7 P0 S M 2 C L (6) δ Thrust (7) = 0.7 P0 S M 2 C D δ 28 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS B. AIRCRAFT LIMITATIONS 1. FLIGHT LIMITATIONS During aircraft operation, the airframe must endure the forces generated from such sources as engine(s), aerodynamic loads, and inertial forces. In still air, when the aircraft is maneuvering, or during in flight turbulence, load factors (n) appear and thereby increase loads on the aircraft. This leads to the establishment of maximum weights and maximum speeds. 1.1. Limit Load Factors JAR 25.301 Subpart C FAR 25.301 Subpart C JAR 25.303 Subpart C FAR 25.303 Subpart C JAR 25.305 Subpart C FAR 25.305 Subpart C JAR 25.307 Subpart C FAR 25.307 Subpart C JAR 25.321 Subpart C FAR 25.321 Subpart C JAR 25.1531 Subpart G FAR 25.1531 Subpart G “JAR/FAR 25.301 Loads (a) Strength requirements are specified in terms of limit loads (the maximum loads to be expected in service) and ultimate loads (limit loads multiplied by prescribed factors of safety). Unless otherwise provided, prescribed loads are limit loads.” “JAR/FAR 25.321 Flight Loads (a) Flight Load Factors represent the ratio of the aerodynamic force component (acting normal to the assumed longitudinal axis of the airplane) to the weight of the airplane. A positive load factor is one in which the aerodynamic force acts upward with respect to the airplane.” Lift nz = Weight Except when the lift force is equal to the weight and nz=1 (for instance in straight and level flight), the aircraft’s apparent weight is different from its real weight (mg): Apparent weight = nz.m.g = Lift In some cases, the load factor is greater than 1 (turn, resource, turbulence). In other cases, it may be less than 1 (rough air). The aircraft's structure is obviously designed to resist such load factors, up to the limits imposed by regulations. 29 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance Consequently, load factor limits are defined so that an aircraft can operate within these limits without suffering permanent distortion of its structure. The ultimate loads, leading to rupture, are generally 1.5 times the load factor limits. “JAR/FAR 25.1531 Manoeuvring flight load factors Load factor limitations, not exceeding the positive limit load factors determined from the manoeuvring diagram in section 25.333 (b) must be established.” For all Airbus types, the flight maneuvering load acceleration limits are established as follows: Clean configuration……………………… -1g ≤ n ≤ +2.5g Slats extended……………………………. 0g ≤ n ≤ +2g 1.2. Maximum Speeds JAR 25.1501 Subpart G FAR 25.1501 Subpart G “JAR/FAR 25.1501 General (a) Each operating limitation specified in sections 25.1503 to 25.1533 and other limitations and information necessary for safe operation must be established.” JAR 25.1503 Subpart G FAR 25.1503 Subpart G JAR 25.1505 Subpart G FAR 25.1505 Subpart G JAR 25.1507 Subpart G FAR 25.1507 Subpart G JAR 25.1511 Subpart G FAR 25. 1511 Subpart G JAR 25.1515 Subpart G FAR 25.1515 Subpart G JAR 25.1517 Subpart G FAR 25.1517 Subpart G “JAR/FAR 25.1503 Airspeed Limitations: General When airspeed limitations are a function of weight, weight distribution, altitude, or Mach number, the limitations corresponding to each critical combination of these factors must be established.” 30 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS SPEED VALUE OPERATING DEFINITIONS EXAMPLES LIMIT SPEED FOR THE A320-200 JAR / FAR 25.1505 Subpart G VMO/MMO Maximum VMO or MMO are the speeds that may not be V = 350 kt (IAS) operating deliberately exceeded in any regime of flight MO MMO = M0.82 limit speed (climb, cruise, or descent). JAR / FAR 25.1511 Subpart G CONF1 230 kt CONF1+F 215 kt VFE V must be established so that it does not CONF2 200 kt Flap extended FE exceed the design flap speed. CONF3 185 kt speeds CONFULL 177 kt JAR / FAR 25.1515 Subpart G VLO: Landing Gear Operating Speed VLO may not exceed the speed at which it is VLO RET (landing gear safe both to extend and to retract the landing operating: retraction) gear. If the extension speed is not the same 220 kt (IAS) as the retraction speed, the two speeds must VLO / VLE be designated as VLO(EXT) and VLO(RET) VLO EXT (landing gear Landing gear respectively. operating: extension) speeds 250 kt (IAS) JAR / FAR 25.1515 Subpart G VLE (landing gear VLE: Landing Gear Extended Speed. extended) VLE may not exceed the speed at which it is 280 kt / M 0.67 safe to fly with the landing gear secured in the fully extended position. 1.3. Minimum Speeds 1.3.1. Minimum Control Speed on the Ground: VMCG JAR 25.149 Subpart B FAR 25.149 Subpart B “JAR/FAR 25.149 Minimum control speed (e) VMCG, the minimum control speed on the ground, is the calibrated airspeed during the take-off run, at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with the use of the primary aerodynamic controls alone (without the use of nose-wheel steering) to enable the take-off to be safely continued using normal piloting skill. 31 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance In the determination of VMCG, assuming that the path of the aeroplane accelerating with all engines operating is along the centreline of the runway, its path from the point at which the critical engine is made inoperative to the point at which recovery to a direction parallel to the centreline is completed, may not deviate more than 30 ft laterally from the centreline at any point.” Engine failure Vmcg Determination of V MCG: lateral deviation under 30 ft Figure B1: VMCG “VMCG must be established, with: The aeroplane in each take-off configuration or, at the option of the applicant, in the most critical take-off configuration; Maximum available take-off power or thrust on the operating engines; The most unfavourable centre of gravity; The aeroplane trimmed for take-off; and The most unfavourable weight in the range of take-off weights.” 1.3.2. Minimum Control Speed in the Air: VMCA JAR 25.149 Subpart B FAR 25.149 Subpart B “JAR/FAR 25.149 Minimum control speed (b) VMC[A] is the calibrated airspeed, at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative, and maintain straight flight with an angle of bank of not more than 5 degrees. (c)VMC[A] may not exceed 1.2 VS with Maximum available take-off power or thrust on the engines; The most unfavourable centre of gravity; The aeroplane trimmed for take-off; The maximum sea-level take-off weight 32 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS The aeroplane in the most critical take-off configuration existing along the flight path after the aeroplane becomes airborne, except with the landing gear retracted; and The aeroplane airborne and the ground effect negligible (d) During recovery, the aeroplane may not assume any dangerous attitude or require exceptional piloting skill, alertness, or strength to prevent a heading change of more than 20 degrees.” 5° max Heading change ≤ 20º Figure B2: VMCA 1.3.3. Minimum Control Speed during Approach and Landing: VMCL JAR 25.149 Subpart B FAR 25.149 Subpart B “JAR/FAR 25.149 Minimum control speed (f) VMCL, the minimum control speed during approach and landing with all engines operating, is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative, and maintain straight flight with an angle of bank of not more than 5º. VMCL must be established with: The aeroplane in the most critical configuration (or, at the option of the applicant, each configuration) for approach and landing with all engines operating; The most unfavourable centre of gravity; The aeroplane trimmed for approach with all engines operating; The most unfavourable weight, or, at the option of the applicant, as a function of weight. Go-around thrust setting on the operating engines (g) For aeroplanes with three or more engines, VMCL-2, the minimum control speed during approach and landing with one critical engine inoperative, is the calibrated airspeed at which, when a second critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with both engines still inoperative, and maintain straight flight with an angle of bank of not more than 5 degrees. VMCL-2 must be established with [the same conditions as VMCL, except that]: The aeroplane trimmed for approach with one critical engine inoperative 33 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance The thrust on the operating engine(s) necessary to maintain an approach path angle of 3 degrees when one critical engine is inoperative The thrust on the operating engine(s) rapidly changed, immediately after the second critical engine is made inoperative, from the [previous] thrust to: - the minimum thrust [and then to] - the go-around thrust setting (h) In demonstrations of VMCL and VMCL-2, … lateral control must be sufficient to roll the aeroplane from an initial condition of steady straight flight, through an angle of 20 degrees in the direction necessary to initiate a turn away from the inoperative engine(s) in not more than 5 seconds.” 20º 5º max Control in straight flight Turn away in less than 5 seconds Figure B3: VMCL and VMCL-2 1.3.4. Minimum Unstick Speed: VMU JAR 25.107 Subpart B FAR 25.107 Subpart B “JAR/FAR 25.107 Take-off speeds (d) VMU is the calibrated airspeed at and above which the aeroplane can safely lift off the ground, and continue the take-off…” During the flight test demonstration, at a low speed (80 - 100 kt), the pilot pulls the control stick to the limit of the aerodynamic efficiency of the control surfaces. The aircraft accomplishes a slow rotation to an angle of attack at which the maximum lift coefficient is reached, or, for geometrically-limited aircraft, until the tail strikes the runway (the tail is protected by a dragging device). Afterwards, the pitch is maintained until lift-off (Figure B4). Two minimum unstick speeds must be determined and validated by flight tests: - with all engines operatives : VMU (N) - with one engine inoperative : VMU (N-1) In the one-engine inoperative case, VMU (N-1) must ensure a safe lateral control to prevent the engine from striking the ground. It appears that : VMU (N) ≤ VMU (N-1) 34 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS Figure B4: VMU Demonstration (Geometrically-limited Aircraft) 1.3.5. Stall Speed Air velocity over the wing increases with the angle of attack, so that air pressure decreases and the lift coefficient increases.  Air pressure Ì Angle of Attack Ê Ö Air velocity over the wing Ê Ö  Lift coefficient Ê Therefore, the lift coefficient increases with the angle of attack. Flying at a constant level, this lift coefficient increase implies a decrease of the required speed. Indeed, the lift has to balance the aircraft weight, which can be considered as constant at a given time. Angle of Attack Ê Ö CL Ê Weight = ½ ρ S (TAS)2 CL = constant ρ = constant S = constant CL Ê Ö TAS Ì Lift = constant The speed cannot decrease beyond a minimum value. Above a certain angle of attack, the airflow starts to separate from the airfoil (Figure B5). V Figure B5: Airflow Separation 35 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance Figure B6 shows that the lift coefficient increases up to a maximum lift coefficient (CLmax), and suddenly decreases when the angle of attack is increased above a certain value. This phenomenon is called a stall and two speeds can be identified : - VS1g, which corresponds to the maximum lift coefficient (i.e. just before the lift starts decreasing). At that moment, the load factor is still equal to one (JAR 25 reference stall speed). - VS, which corresponds to the conventional stall (i.e. when the lift suddenly collapses). At that moment, the load factor is always less than one (FAR 25 reference stall speed). CL n = 1g C L MAX n < 1g Stall area (n ≤ 1g) Angle of Attack CAS V S1g VS Figure B6: CL versus Angle of Attack JAR 25.103 Subpart B “JAR 25.103 Stall speed (a) The reference stall speed VSR is a calibrated airspeed defined by the applicant. VSR may not be less than a 1-g stall speed. VSR is expressed as: VCLMAX VSR ≥ n zw Where: VCLMAX = [speed of maximum lift coefficient, i.e. VS1g] nzw = Load factor normal to the flight path at VCLMAX” Change 15 of JAR 25 (October 2000) introduced this notion of reference stall speed VSR, which is the same as Vs1g. In the previous version of JAR 25, a direct relationship between VS and VS1g was provided, in order to ensure the continuity between aircraft models certified at Vs, and aircraft models certified at VS1g. 36 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS For JAR, this rapport between Vs and Vs1g is: VS = 0.94 x VS1g As an example (refer to the “Takeoff” chapter): For aircraft models certified at VS (A300/A310), V2min = 1.2 VS For aircraft models certified at VS1g (Fly-By-Wire aircraft), V2min = 1.13 VS1g IMPORTANT: In Airbus operational documentation, as well as in this brochure, VSR is referred to as VS1g. FAR 25.103 Subpart B “FAR 25.103 Stalling speed (a) VS is the calibrated stalling speed, or the minimum steady flight speed, in knots, at which the airplane is controllable, with Zero thrust at the stalling speed, or […] with engines idling”. FAR 25 doesn’t make any reference to the 1-g stall speed requirement. Nevertheless, Airbus fly-by-wire aircraft have been approved by the FAA, under special conditions and similarly to JAA approval, with VS1g as the reference stall speed. 2. MAXIMUM STRUCTURAL WEIGHTS JAR 25.25 Subpart B FAR 25.25 Subpart B JAR 25.473 Subpart C FAR 25.473 Subpart C JAR-OPS 1.607 Subpart J AC 120-27C 2.1. Aircraft Weight Definitions Manufacturer’s Empty Weight (MEW) : The weight of the structure, power plant, furnishings, systems and other items of equipment that are considered an integral part of the aircraft. It is essentially a “dry” weight, including only those fluids contained in closed systems (e.g. hydraulic fluid). Operational Empty Weight (OEW) : The manufacturer’s weight empty plus the operator’s items, i.e. the flight and cabin crew and their baggage, unusable fuel, engine oil, emergency equipment, toilet chemicals and fluids, galley structure, catering equipment, seats, documents, etc… Dry Operating Weight (DOW) : The total weight of an aircraft ready for a specific type of operation excluding all usable fuel and traffic load. Operational Empty Weight plus items specific to the type of flight, i.e. catering, newspapers, pantry equipment, etc… 37 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance Zero Fuel Weight (ZFW) : The weight obtained by addition of the total traffic load (payload including cargo loads, passengers and passenger’s bags) and the dry operating weight. Landing Weight (LW) : The weight at landing at the destination airport. It is equal to the Zero Fuel Weight plus the fuel reserves. Takeoff Weight (TOW): The weight at takeoff at the departure airport. It is equal to the landing weight at destination plus the trip fuel (fuel needed for the trip), or to the zero fuel weight plus the takeoff fuel (fuel needed at the brake release point including reserves). TOW = DOW + traffic load + fuel reserves + trip fuel LW = DOW + traffic load + fuel reserves ZFW = DOW + traffic load Figure B7 shows the different aircraft’s weights, as defined in the regulations: Weight Taxi Weight taxi fuel TakeOff Weight (TOW) trip fuel Landing Weight (LW) fuel reserves Zero Fuel Weight (ZFW) total traffic load Dry Operating Weight (DOW) catering newspapers Operational Empty Weight (OEW) cabin equipment crews Manufacturer’s Empty Weight (MEW) propulsion systems structure Figure B7: Aircraft Weights 38 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS 2.2. Maximum Structural Takeoff Weight (MTOW) The takeoff weight (TOW) must never exceed a Maximum structural TOW (MTOW) which is determined in accordance with in flight structure resistance criteria, resistance of landing gear and structure criteria during a landing impact with a vertical speed equal to -1.83 m/s (-360 feet/min). 2.3. Maximum Structural Landing Weight (MLW) The landing weight (LW) is limited, assuming a landing impact with a vertical speed equal to -3.05 m/s (-600 feet/min). The limit is the maximum structural landing weight (MLW). The landing weight must comply with the relation: actual LW = TOW – Trip Fuel ≤ MLW or actual TOW ≤ MLW + Trip Fuel 2.4. Maximum Structural Zero Fuel Weight (MZFW) Bending moments, which apply at the wing root, are maximum when the quantity of fuel in the wings is minimum (see Figure B8). During flight, the quantity of fuel located in the wings, mWF, decreases. As a consequence, it is necessary to limit the weight when there is no fuel in the tanks. This limit value is called Maximum Zero Fuel Weight (MZFW). L L L L 2 2 2 2 mWFg mWFg mg mg Figure B8: wing bending relief due to fuel weight Therefore, the limitation is defined by: actual ZFW ≤ MZFW The takeoff fuel is the sum of the trip fuel and the fuel reserves. Consequently: actual TOW ≤ MZFW + Takeoff Fuel 39 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance 2.5. Maximum Structural Taxi Weight (MTW) The Maximum Taxi Weight (MTW) is limited by the stresses on shock absorbers and potential bending of landing gear during turns on the ground. Nevertheless, the MTW is generally not a limiting factor and it is defined from the MTOW, so that: MTW – Taxi Fuel > MTOW 3. MINIMUM STRUCTURAL WEIGHT JAR 25.25 Subpart B FAR 25.25 Subpart B The minimum weight is the lowest weight selected by the applicant at which compliance with each structural loading condition and each applicable flight requirement of JAR/FAR Part 25 is shown. Usually, the gusts and turbulence loads are among the criteria considered to determine that minimum structural weight. 4. ENVIRONMENTAL ENVELOPE JAR 25.1527 Subpart G FAR 25.1527 Subpart G “JAR/FAR 25.1527 The extremes of the ambient air temperature and operating altitude for which operation is allowed, as limited by flight, structural, powerplant, functional, or equipment characteristics, must be established.” The result of this determination is the so-called environmental envelope, which features the pressure altitude and temperature limits. Inside this envelope, the aircraft’s performance has been established and the aircraft systems have met certification requirements. The following Figure (B9) is an example of an A320 environmental envelope, published in the Flight Crew Operating Manual (FCOM). 40 Getting to Grips with Aircraft Performance AIRCRAFT LIMITATIONS Figure B9: A320 Environmental Envelope 5. ENGINE LIMITATIONS 5.1. Thrust Setting and EGT Limitations JAR 25.1521 Subpart G FAR 25.1521 Subpart G The main cause of engine limitations is due to the Exhaust Gas Temperature (EGT) limit (Figure B10). Figure B10: Engine Limitations 41 AIRCRAFT LIMITATIONS Getting to Grips with Aircraft Performance - The TakeOff (TOGA) thrust represents the maximum thrust available for takeoff. It is certified for a maximum time of 10 minutes, in case of engine failure at takeoff, or 5 minutes with all engines operative. - The Go Around (TOGA) thrust is the maximum thrust available for go- around. The time limits are the same as for takeoff. - The Maximum Continuous Thrust (MCT) is the maximum thrust that can be used unlimitedly in flight. It must be selected in case of engine failure, when TOGA thrust is no longer allowed due to time limitation. - The Climb (CL) thrust represents the maximum thrust available during the climb phase to the cruise flight level. Note that the maximum climb thrust is greater than the maximum cruise thrust available during the cruise phase. 5.2. Takeoff Thrust Limitations Figure B11 shows the influence of pressure altitude and outside air temperature on the maximum takeoff thrust, for a given engine type. At a given pressure altitude, temperature has no influence on engine takeoff thrust, below the so-called reference temperature (Tref) or flat rating temperature. Above this reference temperature, engine thrust is limited by the Exhaust Gas Temperature (EGT). The consequence is that the available thrust decreases as the temperature increases. On the other hand, at a given temperature, any increase in the pressure altitude leads to decreasing the available takeoff thrust. Tref Thrust (Tref depends on engine type) (daN) Tref (PA = 0) 23000 22000 21000 20000 19000 PA = 0 ft 18000 PA = 2000 ft 17000 PA = 8000 ft 16000 OAT (°C) 15000 -10 -5 0 5 10 15 20 25 30 35 40 Figure B11: TOGA thrust versus OAT and PA for a given engine type 42 Getting to Grips with Aircraft Performance TAKEOFF C. TAKEOFF 1. INTRODUCTION The possibility of engine failure during takeoff should always be considered, and the crew must be provided with the appropriate means of deciding on the safest procedure in the event of such a failure. Ground acceleration Rotation Airborne Acceleration Brake Start of Lift off release Rotation Figure C1: Takeoff Profile During the takeoff phase, the pilot must achieve the sufficient speed and angle of attack conditions to balance the aircraft’s lift and weight forces. At the end of the ground acceleration phase, the pilot pulls the stick to start the rotation. During this phase, acceleration is maintained and the angle of attack is increased in order to achieve a higher lift. The ground reactions progressively decrease until lift off. As mentioned above, the performance determination must take into account the possibility of an engine failure during the ground acceleration phase. For FAR/JAR certified aircraft, failure of the most critical engine must be considered. JAR 1.1 FAR 1.1 “JAR/FAR 1.1 : 'Critical Engine' means the engine whose failure would most adversely affect the performance or handling qualities of an aircraft”, i.e. an outer engine on a four engine aircraft. 43 TAKEOFF Getting to Grips with Aircraft Performance 2. TAKEOFF SPEEDS 2.1. Operational Takeoff Speeds 2.1.1. Engine Failure Speed: VEF JAR 25.107 Subpart B FAR 25.107 Subpart B “JAR/FAR 25.107 (a)(1) VEF is the calibrated airspeed at which the critical engine is assumed to fail. VEF must be selected by the applicant, but may not be less than VMCG.” 2.1.2. Decision Speed: V1 JAR 25.107 Subpart B FAR 25.107 Subpart B V1 is the maximum speed at which the crew can decide to reject the takeoff, and is ensured to stop the aircraft within the limits of the runway. “JAR/FAR 25.107 (a)(2) V1, in terms of calibrated airspeed, is selected by the applicant; however, V1 may not be less than VEF plus the speed gained with the critical engine inoperative during the time interval between the instant at which the critical engine is failed, and the instant at which the pilot recognises and reacts to the engine failure, as indicated by the pilot's initiation of the first action (e.g. applying brakes, reducing thrust, deploying speed brakes) to stop the aeroplane during accelerate-stop tests.” V1 can be selected by the applicant, assuming that an engine failure has occurred at VEF. The time which is considered between the critical engine failure at VEF, and th