Alejandro Murrieta-Mendoza

Estimation of fuel consumption and polluting emissions generated during the missed approach procedure

This paper proposes a new method for estimate the fuel burned and the emissions generated such as CO2 and NOx during a missed approach procedure. This method use information from the air pollutant emissions inventory guidebook created by the Emission Inventory Guidebook from the European Environment agency to perform the computations. The descend phase was separated in two different mode, one composed by climb, cruise and descent, and the other by the landing to takeoff mode. The calculations are made with the help of an interpolation polynomial for the mode in function of distance and with the flight time for the mode in function of time. Missed approach calculations can be used as a decision tool to select between the costs of different routes and determine the most convenient in devices such as the Flight Management System or by ground automated systems assisting flight controllers.

Methodology for Vertical-Navigation Flight-Trajectory Cost Calculation Using a Performance Database

Trajectory optimization has been identified as an important way to reduce flight costs and polluting emissions. Due to the power capacity limitations in airborne devices such as the flight management system, a fast method should be implemented to calculate the full trajectory cost. Many flight management systems use a set of lookup tables with experimental data for each flight phase, and they are called performance databases. In this paper, the trajectory flight cost is calculated using a performance database instead of using classical equations of motion. The trajectory to be calculated is composed of climb, acceleration, cruise, descent, and deceleration. The influence of the crossover altitude during climb and descent, as well as step climbs in cruise, was considered. Lagrange linear interpolations were performed within the performance database discrete values to calculate the required values. By providing a takeoff weight, the initial and final coordinates, and the desired flight plan, the trajectory ...

Method to calculate aircraft VNAV trajectory cost using a performance database

Vertical Navigation (VNAV) trajectory optimization has been identified as a means to reduce fuel consumption. Due to the computing power limitations of devices such as Flight Management Systems (FMSs), it is very desirable to implement a fast method for calculating trajectory cost using optimization algorithms. Conventional trajectory optimization methods solve a set of differential equations called the aircraft equations of motions to find the optimal flight profile. Many FMSs do not use these equations, but rather a set of lookup tables with experimental, or pre-calculated data, called a Performance Database (PDB). This paper proposes a method to calculate a full trajectory flight cost using a PDB. The trajectory to be calculated is composed of climb, acceleration, cruise, descent and deceleration flight phases. The influence of the crossover altitude during climb and step climbs in cruise were considered for these calculations. Since the PDB is a set of discrete data, Lagrange linear interpolations were performed within the PDB to calculate the required values. Given a takeoff weight, the initial and final coordinates and the desired flight plan, the trajectory model provides the Top of Climb coordinates, the Top of Descent coordinates, the fuel burned and the flight time needed to follow the given flight plan. The accuracy of the trajectory costs calculated with the proposed method was validated for two aircraft; one with an aerodynamic model in FlightSIM, software developed by Presagis, and the other using the trajectory generated by the reference FMS.Copyright

Lateral Navigation Optimization Considering Winds and Temperatures for Fixed Altitude Cruise Using Dijsktra’s Algorithm

Optimizing the flight trajectory is a goal that will minimize fuel consumption and time related costs. Lateral Navigation (LNAV) has been investigated as part of identifying optimal trajectories. Winds and temperature have an important influence in the cost of a flight. Tail winds and low temperatures are desired, as both reduce flight costs. Implementing algorithms to locate where these favorable conditions exist close to the defined trajectory of a given flight will help to achieve optimal flight trajectories. These algorithms are to be implemented in an FMS using an aircraft model which is normally given in the form of a Performance Database (PDB). The approach given in this paper uses Dijsktra’s algorithm. This method is part of the graph-search techniques. The search area is defined by discretizing the cruise trajectory and defining adjacent waypoints, forming a grid where the possible trajectories are created. The algorithm requires the aircraft’s gross weight at the top of climb (TOC), the location of the top of descent (TOD), and the desired cruise speed and altitude. The related costs are calculated using the PDB’s model for two different commercial aircraft at a constant altitude and at a constant indicated mach. To minimize the costs, the algorithm considers the fuel burned, the flight time and the cost index (CI). The temperature and winds in the trajectory are obtained from the Canadian weather forecast (Environment Canada). Wind influence is taken into account by adding it to the ground speed, based on its direction regarding the aircraft’s trajectory heading. The effect of temperature is considered in the PDB. Generated trajectories are compared against the geodesic (or great circle) route.Copyright

Vertical Reference Flight Trajectory Optimization with the Particle Swarm Optimisation

The consumption of fossil fuels in order to power flights leads to undesirable pollution particles to be released to the atmosphere. Fuel also represents an important expense for airlines. For these reasons, it is of interest to reduce fuel burn for a given flight. In this article, the altitudes followed by a commercial aircraft during the cruise phase of a flight, also called vertical reference trajectory, were optimized in terms of fuel burn. The airspace was modelled under the form of a unidirectional graph. Fuel burn was computed using a numerical performance model. The weather forecast was obtained from the model delivered by Environment Canada. The selection of waypoints where to execute the changes in altitudes that provided the most economical flight cost in terms of fuel burn was determined using the particle swarm optimisation (PSO) algorithm. The trajectories provided by the algorithm developed in this paper were compared against simple geodesic trajectories to validate its optimization potential, and against as flown trajectories. Results have showed that up to 6.5% of fuel burn can be saved comparing against simple trajectories, and up to 3.1% was optimized comparing against as flown trajectories.

Four- and Three-Dimensional Aircraft Reference Trajectory Optimization Inspired by Ant Colony Optimization

A methodology of aircraft reference trajectory optimization inspired by the ant colony optimization is used in this paper to find the most efficient trajectory in terms of fuel burn and flight cost...

New Search Space Reduction Algorithm for Vertical Reference Trajectory Optimization

Burning the fuel required to sustain a given flight releases pollution such as carbon dioxide and nitrogen oxides, and the amount of fuel consumed is also a significant expense for airlines. It is desirable to reduce fuel consumption to reduce both pollution and flight costs. To increase fuel savings in a given flight, one option is to compute the most economical vertical reference trajectory (or flight plan). A deterministic algorithm was developed using a numerical aircraft performance model to determine the most economical vertical flight profile considering take-off weight, flight distance, step climb and weather conditions. This algorithm is based on linear interpolations of the performance model using the Lagrange interpolation method. The algorithm downloads the latest available forecast from Environment Canada according to the departure date and flight coordinates, and calculates the optimal trajectory taking into account the effects of wind and temperature. Techniques to avoid unnecessary calculations are implemented to reduce the computation time. The costs of the reference trajectories proposed by the algorithm are compared with the costs of the reference trajectories proposed by a commercial flight management system using the fuel consumption estimated by the FlightSim® simulator made by Presagis®.