STANDARD ATMOSPHERE, WEATHER AND AIRCRAFT MODEL
INTRODUCTION:
Lately, there has been a lot of concern in the aerospace industry about fuel needs and the polluting emissions generated by fuel consumption. There is a trend followed by many companies and airlines to deliver products that reduce fuel consumption. Many opportunities in saving fuel, thus polluting emissions, have been identified in the planning aircraft route. Airlines have ground teams that search and identify the best routes for a given flight. The avionics equipment in the cockpit that helps the pilot to plan and to maintain a route is the flight management system (FMS). The main tasks that a FMS performs according to Collins in [1] are flight guidance, control of the lateral and vertical aircraft paths, monitoring of the flight envelope, computing the optimal speed for every phase of the flight and providing automatic control of the engine thrust, etc. In this work when “optimal” is mentioned, it means the value of the parameters that gives as result the lowest cost of a given flight. Many different factors such as weather, traffic, or an emergency can change the predefined route given by the ground team. In these events, the crew has to determine a new route using navigation charts or existing FMS algorithms. FMS algorithms compute the “optimal flight altitude” and the “optimal speed”. However, these algorithms need to be improved to find better routes and important data such as weather conditions have to be improved in order to take advantage of favorable winds.
Environmental and economical background:
Since the first flight performed by the Wright brothers, the aerospace industry has been outstandingly developed. Starting from that unstable aircraft that flew 12 seconds, the aeronautical technology has improved and developed into impressive military aircraft able to cross continents without stopping such as the aircraft B2, or able to fly at speeds higher than sound speed such as the F-22. Research spacecraft have been built, and in some cases, they have even left the atmosphere, such is the case of the space shuttles and the International Space Station.However, the military industry is not the only one taking advantage of these developments. Civil aviation has also well developed, from small size aircraft used to deliver mail in which many pilots’ lives were lost, to bigger size and safer airplanes such as the A-380 and the 747. These aircraft allow people and cargo to travel between different destinations in a fast and effective way.
STANDARD ATMOSPHERE, WEATHER AND AIRCRAFT MODEL:
In this chapter, the International Standard Atmosphere (ISA) is described in terms of temperature, altitude and air density. The atmosphere model downloaded from Environment Canada, which is used to add the meteorological influence in the trajectory is described. Finally, the numerical aircraft model described by the PDB is explained and the way in which the interpolations are performed is shown at the end of this chapter.
The International Standard Atmosphere: The atmosphere is the mixture of gases that surround the earth. It is the transition between the land and outer space and it goes up to 100 km. Commercial flights are present from sea level up the troposphere (30,000 ft to 56,000 ft). The most important values that are analyzed in the atmosphere for any given flight are: temperature, pressure and air density. Temperature is important because it affects the thrust of the engines; it also has a strong influence on the speed of sound and, in combination with the pressure, it fixes the value of air density. Temperature has a “zigzag” variation through the atmosphere. The atmosphere cools down from sea level until a given altitude, then it heats up, colds down again to finally heat up until outer space is reached. Pressure is used to determine the altitude and the speed of the aircraft, and as mentioned above, helps to fix the density of air. Density is the mass of air per unit volume and is dependent on temperature and pressure. It is one of the most important parameters in aircraft performance because it affects lift, thrust, and airspeed.
Altitudes: There are many different altitudes, such as the geometric altitude, the absolute altitude, the pressure altitude, and the geopotential altitude. The geometric altitude is the altitude of an object above sea level. It is really important during climb, landing and approaching to high land such as mountains. The absolute altitude is the altitude from the center of the earth to the location of the object. The pressure altitude assumes a single pressure for every flight level. In this altitude, the crew must have the reference pressure provided by the ATC to locate the aircraft at a given altitude. Geopotential altitude is a transformation of the geographical altitude into an altitude that considers the reduction of the gravity caused by the increase altitude. It is mostly used for meteorological applications and it is described by equation (3.4), where hG is the geopotential altitude, r is the radius of the earth typically with a value of 6357 km and h is the geometric altitude of the airplane.
TRAJECTORY OPTIMIZATION:
In this chapter the way to determine the “optimal” Vertical Navigation (VNAV) is explained. Next the algorithm to find the “optimal” Lateral Navigation (LNAV) is exposed. Furthermore, the way of coupling these algorithms is explained to obtain the complete trajectory optimization.
Vertical navigation optimization: To find the optimal trajectory, flight trajectories with many speed/altitude combinations have to be calculated and compared. If “step climbs” are recommended they have to be calculated. Finally, all trajectories are compared and the one with the lowest cost is selected as the optimal VNAV trajectory. The total number of calculations needed to find the optimal VNAV trajectory is high. For example, for the L-1011 during climb, 20 KIAS speeds can be found, 13 MACH and 11 cruise altitudes, that gives 2860 possible trajectories. The search for the optimal between all these combinations in a limited time frame is a difficult and time consuming task.
Pre-optimal cruise optimization algorithm: The idea of the pre-optimal cruise optimization algorithm is to try to have a first guess of the optimal cruise altitude/MACH profile. This first guess is defined as the “optimal candidate”. This optimal candidate is the most important parameter in the algorithm because all the other calculations: climb, final cruise and descent explained in Chapter 4 are performed for the precruise couple and in its vicinity. The advantage of applying the method describe here for the L-1011 PDB for example will be, that, when the climb will be computed, instead of searching a crossover altitude in the 13 possible MACH speeds, this crossover altitude will be searched 3 or 5 speeds in order to find the climb cost. It can be interpreted as a reduction of 8 MACH crossovers for each KIAS climb. It is evident that a reduction in the number of possible optimal solutions is observed.
Pre-optimal cruise results versus the algorithm of reference:
In order to validate the pre-cruise initial solution, the algorithm was tested and compared with the algorithm developed by Gagné [18]. During this test, it was supposed that Gagné’s algorithm provided the optimal cruise profile. The comparison tests are shown in Table 5.1. These tests were performed in a 1324 nm flight, the distance of a Los Angeles – Minneapolis, with different weights. This flight was chosen as a test because is a commercial flight with a mean distance of a commercial flights in North America. It can be seen that in almost all weights, the optimal profile solution during cruise found by Gagné’s algorithm was exactly the same as our pre-cruise solution. Out of 9 cases, 3 cases highlighted in gray show different results.
Climb and descent KIAS/MACH selection:
After the selection of the pre-cruise speeds and altitudes, the climb computations are performed for all the available KIAS, and only 5 MACH: the pre-optimal MACH, the 2 before in the PDB and the 2 after the PDB. The maximal altitude calculated is the next one available in the PDB after the pre-optimal altitude found. As stated before, the number of combinations KIAS/MACH/altitudes and the calculation time are reduced. The results of these computations are tabulated in the algorithm. Tables contain the fuel consumption and the horizontal distance traveled are obtained and used within the algorithm. With these two tables, the ratio of nautical miles traveled per cost kilogram is calculated. Notice the term “cost kilogram”, this means that it is the cost defined by equation (2.17) where the cost index and the flight time are considered. The ratio with the maximum value is selected as the best climb profile.
FUEL CONSUMPTION AND EMISSIONS GENERATED DURING
A MISSED APPROACH:
Due to the proximity of airports to cities, very much attention has been given to the analysis and reduction of the following parameters: fuel burned emissions and noise produced in the landing phase of commercial aircraft as it was discussed in Chapter 1. During the descent phase, many problems may appear that can lead to the landing procedure being aborted, in which case the so-called missed approach or go-around procedure must be followed. This procedure may be expensive. Flight crews can vary their approach procedures and flap selections to match the flight’s objectives, which include fuel conservation, noise abatement and emissions reductions. Decisions on which type of approach to use vary with each airline, and sometimes even for each flight. The fuel required for a missed approach procedure during descent can burn up to 28 times the fuel consumed during a normal landing procedure [33] as specified in Boeing documentation.
CONCLUSION:
The algorithm described in this thesis was successfully implemented in two different aircrafts: The L-1011 and the Sukhoi RRJ 100. The L-1011 is meant to travel long distances while the Sukhoi RRJ 100 travels medium distances. The flight distances traveled by these aircraft represent the flights distance aimed in this thesis.
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Table des matières
INTRODUCTION
CHAPTER 1 LITERATURE REVIEW
Environmental and economical background
Technological implementations
Trajectory optimization
Missed approach
CHAPTER 2 A TYPICAL FLIGHT AND ITS COSTS
2.1 Typical flight
2.1.1 Climb
2.1.1.1 Constant KIAS climb from 2,000 ft to 10,000 ft .
2.1.1.2 Acceleration
2.1.1.3 Constant KIAS climb and the MACH crossover altitude
2.1.2 Constant MACH climb
2.1.2.1 Cruise
2.1.3 Descent
2.2 Total flight cost and the cost index
CHAPTER 3 STANDARD ATMOSPHERE, WEATHER AND AIRCRAFT MODEL
3.1 The International Standard Atmosphere
3.2 Altitudes
3.3 Airspeeds
3.4 Earth Model
3.5 Weather model
3.5.1 GRIB2 description
3.5.2 Data conversion
3.5.3 Meteorological data interpolation
3.6 Aircraft model and the Performance database
3.6.1 The performance database
3.6.2 The performance database interpolation
CHAPTER 4 FLIGHT TRAJECTORY CALCULATION
4.1 KIAS climb from 2,000 ft to 10,000 ft
4.2 Acceleration
4.3 Constant KIAS climb
4.4 Climb MACH
4.5 Descent distance estimation
4.6 Cruise
4.6.1 Step Climb
4.7 Final descent
CHAPTER 5 TRAJECTORY OPTIMIZATION
5.1 Vertical navigation optimization
5.1.1 Pre-optimal cruise optimization algorithm
5.1.2 Pre-optimal cruise results versus the algorithm of reference
5.1.3 Number of waypoints in the pre-optimal cruise algorithm
5.1.4 Climb and descent KIAS/MACH selection
5.1.5 Step climb procedure and selection
5.1.6 Optimal VNAV route selection
5.2 Lateral Navigation Optimization
5.2.1 Dijsktra’s Algorithm
5.2.2 The five routes algorithm
5.2.3 Coupling VNAV with five routes algorithm
CHAPTER 6 FUEL CONSUMPTION AND EMISSIONS GENERATED DURING
A MISSED APPROACH
6.1 Introduction
6.2 Methodology
6.2.1 Climb/Cruise/Descent CCD mode
6.2.2 Landing to Takeoff LTO mode
6.2.3 Crossover calculations
6.2.4 Full flight cost calculation
CHAPTER 7 ALGORITHM RESULTS
7.1 Flight calculations validity
7.2 Flight optimization results
7.2.1 L-1011 optimisation tests
7.2.2 Sukhoi Russian regional jet results.
7.3 The five routes algorithm results
7.4 Missed approach results
CONCLUSION
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