Efficient scheduling of aircraft landings can improve runway throughput and reduce fuel burn. Currently, however, the most common conventional sequencing strategy is the first come, first served one, according to which aircraft are allowed to land in their order of arrival at the runway. The terminal area where most resequencing occurs is a very dynamic environment, so air traffic controllers cannot afford to spend a long time determining an alternative sequence. The goal of this research is to propose aircraft sequencing guidelines for fuel savings.

Outline

This thesis consists of four main parts. Part I presents the necessary background of this research. It gives an overview of air traffic demand scenarios and presents some technological solutions which can improve fuel burn efficiency. After reviewing the present inefficiency of operations, the leading idea of this research is presented.

Part II answers the question "how to model fuel burn?". It states the assumptions on which all simulations in the research are based, starting with the aircraft model, terminal area assumptions and optimization method overview. Single aircraft trajectory optimizations are performed and used as a base for fuel burn modeling. In the third part, which is the essence of this research, sequencing rules are extracted based on analysis of optimal sequencing. The differences between the first come, first served rules are investigated and the statistical performance of the proposed rules is examined. Finally, Part IV summarizes the research and provides suggestions for further study.

Background

At present, aviation accounts for about 3% of all carbon dioxide emissions [1]. Aviation emissions would not have been a discussion matter if it had not been for the continuously increasing demand for air travel. Considerable research has been done on finding new technology solutions which can reduce aircraft fuel burn and thus harmful emissions. Innovations such as lightweight materials, combustion system improvements and technologies which contribute to smooth laminar flow over the aircraft's body can lead to less fuel burn. However, hardware improvements are both cost and time consuming, so this research considers an operational approach only. The author's main goal is to find a substitute to the first come, first served rule commonly used for aircraft sequencing. The motive for this research is "making the most" of the available technology in use already by optimizing operations only without introducing any new hardware and/or software devices at air traffic control centers. The author does not aim at automation of the sequencing process, i.e. the system remains human-centered.

Literature review of the aircraft sequencing problem shows than even though the problem has been studied to some extent, most research is aimed at developing a real-time optimization algorithm and sequencing software rather than introducing something as simple as sequencing rules instead. Therefore, the approach taken in this research is rare, but as seen later can be extremely promising.

Fuel burn modeling

Furthermore, by referring to past research on environmentally-friendly aircraft sequencing, it is observed that for computational simplicity reasons, the fuel burn is mostly modeled by linear functions. Such an approach can contribute to finding analytical and computational solutions to the aircraft sequencing problem, but no prove has been found on its accuracy in the literature. Therefore, before the sequencing problem is formulated, there is a need to determine the fuel burn cost function, i.e. how each single aircraft's fuel burn by changes in the descent times. In order to do that, optimization of single aircraft descents is performed. The aircraft model used in this research is a point mass model. The trajectory is divided into several stages and optimization is performed using Sequential Quadratic Programming method. We consider heavy and medium aircraft as these types are most often used in civil aviation at hub airports which are likely to experience congestion and thus might benefit from improved aircraft sequencing. Here, past operations of the terminal area of Tokyo International Airport (Haneda Airport) are used to model the terminal area, which is shown in Figure 1.

With all the necessary assumptions being stated, optimization of the trajectory of single aircraft entering the terminal area is performed. First, the optimal descent time and the flight profile associated with it are found. Next, by introducing constraints on the desired deviation from the optimal descent time, the minimum fuel burn as a function of the descent time is determined (shown in Figure 2). The function obtained is used to model the fuel burn when aircraft have to be sped up or delayed in the landing sequence and it substitutes the linear function often used in the literature so far.

Sequencing rule extraction

With a function providing the relationship between fuel burn and flight time available, the next step to the actual sequencing can be made. Operational constraints such as minimum separation, earliest available arrival time, precedence constraints and constrained position shift (CPS) are considered. The minimum separation requirement guarantees that aircraft do not suffer from the wake vortices induced by leading aircraft. Earliest available arrival time accounts for congestions ahead and accumulated delays. Precedence constraints ensure that no overtaking of aircraft entering the terminal area at the same entry point occurs. The position shift constraint reflects the fact that no aircraft can be too far from its original position in the final sequence, i.e. an aircraft can skip ahead or back only a restricted number of positions.

Aircraft sequencing problem should answer two main questions:

1) What is the proposed sequencing? How is it different from the FCFS sequence?

2) How are the expected times of arrival (ETA) changed to achieve the proposed sequence?

It should be kept in mind that the goal of this research is not optimizing the aircraft sequence, but finding a sequence which excels the FCFS sequence in most cases. To do so, simulations are conducted according to the following flow:

1)Group aircraft in batches of 2, 3 or 4

2)Find the optimal sequence

3)Compare the optimal sequence with FCFS sequence

4)Investigate the conditions under which aircraft are swapped

5)Propose sequencing rules based on key swaps

6)Investigate the statistical performance of the rules by Monte-Carlo simulations

7)Finalize the rules

Simulations for ten aircraft entering the terminal area at random times in a predefined time interval are conducted. The ratio of aircraft at each entry waypoint and the ratio of heavy to medium aircraft resemble the actual traffic condition at the model airport. The optimal aircraft sequencing and scheduling is found under the constraints described earlier. A comparison of the optimal sequence and the first come, first served sequence in each simulation reveals the number of swaps in each case. The conditions under which swaps occurred are of interest for defining the swapping, thus sequencing rules.

Consider swapping a pair of aircraft. The swap influences the required separation necessary between the pair and the preceding aircraft as well as the separation between the pair and the following aircraft, i.e. four aircraft are considered to monitor the effect of the swap. The parameters which influence swapping are estimated arrival times of all four aircraft, their type (medium or heavy) and the earliest available arrival time. Analyzing the swaps, three rules are extracted. Their essence is shown in Table 1. The statistical performance of the proposed rules is verified by Monte-Carlo simulations. The fuel burn for each sequence is measured by a newly-introduced parameter f(par). If all aircraft could land at its estimated time of arrival, then the total fuel burn increase would be zero.

We are interested only in the fuel burn increase inferred by any delays, being positive or negative, because only this fuel burn increase above the nominal one, i.e. the fuel burn penalty for delays, can be influence by any sequencing decisions. If FCFS sequence required some aircraft to be delayed, then this delays cause some fuel burn increase, which sum is defined as fuelFCFS. Suppose the total fuel burn increase for all ten aircraft for certain sequencing is fuelseq. In such a case, f(par) is defined as:

In other words, f(par) shows how much fuel is necessary for the adjustments in a particular sequence compared to the fuel necessary when FCFS rule is applied. Positive values of f(par) indicate sequences which are worse than FCFS in terms of fuel burn and negative values indicate sequences which result in fuel saving compared to FCFS.

The average values of f(par) are shown in Table 2. Rule 2 has a slightly better average performance than Rule 1, but since it is more complicated than Rule 1, it is considered that Rule 1 excels overall. Therefore, a simultaneous application of Rule 1 and Rule 3 is suggested. For comparison, f(par) of the optimal sequence is -35%. Simulation results show an average f(par) of -17%, with f(par) for heavy aircraft of -12% and f(par) for medium aircraft of -22%.

Fuel savings by the simultaneous application of Rule 1 and Rule 3 are twice less than these by optimal sequencing. The main reason is that in the optimal solution the flight time can be adjusted very precisely to minimize the fuel burn and no aircraft arrives uselessly early. The flight time adjustments might play just an important role in the fuel burn as the sequencing itself. Besides, there are aircraft configurations which might be subject to both Rule 1 and Rule 3 resequencing, but because the possible resequencing groups overlap, only one of the rules is applied. However, even though the sequencing rules do not measure up to savings achieved through optimal sequencing, they are remarkably better than the conventional sequencing approach.

Summary

This research suggests guidelines for aircraft sequencing in order to minimize fuel burnt by aircraft in the terminal area. It makes use of information about aircraft type available to air traffic controllers on their radar screen. It was concluded that even though the guidelines do not result in absolute optimal aircraft sequencing, they can contribute to significant fuel savings. It was demonstrated that by a very simple change in the air traffic operations sufficient fuel improvement can be easily achieved. The author believes this research gives a valuable insight into the importance of air traffic operation procedures and their potential contribution to the environmental impact abatement of aviation.

1 J.A. Leggett, B. Elias, and D.T. Shedd, "Aviation and the European Union's Emission Trading Scheme", http://www.fas.org/sgp/crs/row/R42392.pdf, retrieved on 2012/5/30

Figure 1. Terminal area

Figure 2. Fuel burn vs. descent time

Table 1. Rules extracted from analyzing batches of 4 aircraft. ETA stands for estimated time of arrival, the figures "60" and "90" show the required separation.

Table 2. Average fuel parameters for the investigated sequencing rules

修士(工学)アンドレエバ森 アドリアナ フリストバ 提出の論文はFuel Saving Sequencing of Arrival Aircraft(燃料消費削減のための到着機シークエンシングに関する研究)と題し、英文で書かれ、9章からなっている。

航空輸送は今後、年5%近い成長が予想され、空港の混雑化と地球温暖化ガス排出の増加が懸念されている。地球温暖化ガス排出に関しては、燃料消費削減のために、空気抵抗低減、機体軽量化、エンジンの低燃費化、低炭素燃料などとともに、飛行経路の最適化が検討されている。このうち、飛行経路の最適化は混雑化する空域での航空管制とも密接に関連し、既存の機体を運航させる際の燃料消費削減策として早期の取り組みが期待されている。ただし、現状の航空管制は航空管制官の判断に依存し、混雑空港で全て自動化するには長期の開発と膨大な試験が必要とされる。筆者は、機体のサイズによって燃料消費特性が異なることに着目し、サイズの異なる航空機が混在して到着する際に、到着機の順番を変更することによって燃料消費を削減することが可能なことを最適化計算によって示し、現状の航空管制官による運用に取り入れることが容易な簡便なルールを最適化計算結果から導き、その効果をモンテカルロシミュレーションによって確認することを試みている。

第1章は序論で、航空管制に関する研究の背景を整理するとともに、研究の動機、目的を述べるとともに本論文の構成をまとめている。

第2章では航空管制の歴史的変遷と現状の方式を調査し、ターミナルエリアでは、航空機の後方乱気流の影響を避けるために既定の間隔をおいて滑走路に着陸させる必要があり、ターミナルエリアへの進入点を定め、進入点へ到着した航空機を到着順に管制していることを示し、その方式が、燃料消費の観点からは最適でない事を指摘している。

第3章では、到着機の順序付けに関する過去の研究を総括している。過去の研究事例は複数航空機の順位付けを実時間最適化問題として扱っており、現状の航空管制方式で直ちに取り入れることが困難なことを指摘し、単純なルール作りを提案することの意義を明確にしている。

第4章では、航空機の燃料消費特性のモデル化手法を説明している。すなわち、航空機を質点としてモデル化し、水平飛行から滑走路進入までの消費燃料を最小化するように飛行経路を算出する手法を最適化問題により定式化し、その数値計算手法を記述している。

第5章は、本論文で使用している最適化手法である逐次二次計画法(SQP:Sequential Quadratic Programming)に関して整理している。

第6章は、対象とする大型機(B747クラス)と、中型機(B737クラス)を仮定し、東京国際空港(羽田空港)への進入を想定したシナリオを説明している。

第7章は、単独の降下に関して消費燃料が最小となる最適解を分析している。最適解は、可能な限り高高度を飛行し、最大の経路角で直線的に降下する方式であることを確認した後、飛行時間を拘束した状態での最適降下に関しても計算を実施し、燃料消費量が飛行時間に関して二次関数として近似できることを示した。

第8章では、大型機と小型機が同数ずつ混在する状況において、着陸の最適な順序づけに関して検討している。順序付けの基本的な考え方は、大型機は最適な着陸飛行経路からずれた場合に燃料消費量が大きく増加するのに対して、小型機はその変化量が少なくて済むので、トータルな消費燃料に関して着陸順序の変更が効果的であるという点である。数機ごとの組に対して、最適な着陸順序を求め、それをもとに、単純な着陸順序のルールを提案し、その効果を50機に対するモンテカルロシミュレーションによって確認している。4機ごとに順位の入れ替えを単純なルールにより実施した場合には、到着順に管制した場合に発生する燃料増加量を17%削減することに成功している。最適な並べ替えを行った場合の削減量は35%であるので、その半分の効果を単純なルールで達成できていることになる。同時に考慮する機数を増やせばさらに効果は増すと予想されるが、管制官のワークロードの増加を同時に考慮することが必要であることも指摘している。

第9章では、本研究の成果をまとめると同時に、さらなる研究課題について述べている。

以上、要するに、本論文は、サイズの異なる航空機が混在して到着する際に、到着順を最適化する方法を定式化し、その解から、管制官が現場で活用できる簡単な到着順序の入れ替えルールを見出し、その効果をモンテカルロシミュレーションによって検証した。これらの成果は、航空工学上貢献するところが大きい。

よって本論文は博士(工学)の学位請求論文として合格と認められる。