Airbus, nonlinear dynamics, and the A380

By Hinke Osinga
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Etienne Coetzee at Airbus in Bristol; photograph by Hinke Osinga Interview with Etienne Coetzee,
Landing Gear Systems Engineer
Airbus, Bristol


by Hinke Osinga,
University of Bristol, UK
Etienne Coetzee at Airbus, Bristol.

Airbus is a global enterprise with industrial facilities in France, Germany, Spain and the UK; additional design and engineering satellite offices in the USA, Russia and China; fully-owned subsidiaries in the United States, China, Japan and the Middle East; spare parts centres in Hamburg, Frankfurt, Washington, Beijing, and Singapore; training centres in Toulouse, Miami, Hamburg and Beijing; and more than 130 field service offices around the world.

Airbus' industrial sites in France, Germany, Spain and the UK produce complete sections of aircraft, which are then transported to one of the final assembly lines in France and Germany. The company also relies on industrial co-operation and partnerships with major companies all over the world, and a network of some 1,500 suppliers in 30 countries.

The A380 aircraft

Since the first Airbus entered service in 1974, the product range has grown into four families of aircraft comprehensively covering the market from 107 to 555 seats. To date Airbus has sold more than 6,500 aircraft, has 266 customers/operators worldwide and has delivered nearly 4,500 aircraft. The newest member of the family, the A380, is the first true double-deck passenger airliner for the long-range market. This most spacious and efficient aircraft has seats for 555 passengers and is designed to allow for projected passenger growth worldwide without negatively impacting the environment.

  A380 aircraft in flight; Courtesy of Airbus UK
A380 in flight.
(Courtesy of Airbus UK)

Etienne Coetzee is an employee of Airbus UK in Bristol and has been working in the Landing Gear Systems (LGS) group for six years. The LGS group is generally responsible for the integration of all the landing gear systems, which includes the braking, steering, and extension/retraction systems. It is also responsible for ground maneuverability of the aircraft at low to medium speeds, and complements the work of the Handling Qualities and Flight Control groups in Toulouse. The LGS group is heavily involved in the development of the A380. The A380 may look like it is just a much bigger version of other Airbus aircraft, but it has the latest in major advanced technologies incorporated in its design, which makes it a very modern aircraft.

Front view of the A380; Courtesy of Airbus UK  

The LGS group provides part of the information needed to ensure that airports can accommodate this large aircraft with little or no need to adapt their runways, so that only alterations at the gates will be necessary in some cases. Etienne explains how the A380 team conducted major research. "They had to decide how many wheels the landing gear of the A380 should have, and where they should be positioned. We investigated the steering capabilities, how big the actuators should be, and so on."

Front view of the A380.
(Courtesy of Airbus UK)

A modeling career at Airbus

So how did Etienne get involved with Airbus? He was born in Pretoria, South Africa. As a child he lived in the US for three years, while his father was an airforce attaché in Washington. His dream was to become a pilot, but after a while he realized that he had a greater passion for engineering. So, he went to the University of Pretoria to study mechanical engineering. He obtained a BEng degree and left for Munich to work on light fighter aircraft at Daimler Chrysler Aerospace (now EADS). His research there focused on the aeroelastic tailoring of composite wings. In Munich he shared a house with students from the University of Bath in the UK. After they had returned to Bath he saw an opportunity to visit them and visit Airbus in Bristol at the same time.

Etienne really liked Bristol and he managed to organize a job within the Aeroelastics department of Airbus UK. "At the time I thought that landing gears were really boring and that wing design was the only real engineering challenge."

About six years ago, the LGS Modeling and Simulation group consisted of only two people, but with new projects, new people were required, and Etienne got assigned to this group as part of the A380 project. "I found to my surprise that landing gears are, in fact, amazingly difficult to design! The environment that the gears operate in is very harsh, and you also have highly nonlinear components on the gear such as tires, that makes the analysis of this system very complex. Our group models how all landing gears at Airbus operate on the aircraft, so we are in a unique position to gain a deep understanding of how everything works."

  Etienne in front of the A380 design office building; photograph by Hinke Osinga
Etienne in front of the A380 design office building.

Developing a good model for how the landing gear behaves on aircraft has taken years of testing. The model runs in a package called ADAMS, which is a completely integrated software environment for running simulations and visualizing how the aircraft behaves upon touchdown and during taxiing. This code is used to run lots of scenarios based on experimental data to check, for example, when control of the aircraft might be lost during certain maneuvers. Such studies are designed to support certification, to demonstrate that an aircraft satisfies all safety regulations. Etienne is working on improved and diverse methods for this purpose. He wants to demonstrate that the use of techniques from nonlinear dynamics is a potential future improvement in aircraft design.

Continued professional development and chaos theory

The southwest of England is the aerospace hub in the UK. Companies including Airbus and Rolls Royce are based there and developed a scheme with the University of Bristol and the University of the West of England (also based in Bristol) to promote personal development of their employees. Employees of Airbus are encouraged to attend the course Continued Professional Development in Aerospace (CPDA), which leads to an MSc degree. The CPDA course consists of four mandatory management modules and an options part with specialization in either management or technical skills. For Etienne, this opportunity meant that he was exposed to dynamical systems theory for the first time, during the class Nonlinear Flight Mechanics that was taught by Mark Lowenberg (Aero, Univeristy of Bristol) and Mikhail Goman (Computing, De Montfort University). "I think that this may have been the first time they taught that course, because their assignments were extremely difficult. I mean, I was trying to learn about strange attractors and Hopf bifurcations, and I had no idea what they were talking about." Despite the difficulty of the course, Etienne did realize that the landing gear on aircraft is inherently nonlinear and that he would be able to apply these rather abstract concepts. "I knew about hysteresis effects in landing gears and how difficult it is to design an effective anti-skid system due to the properties of the tires and brakes. I now know that the nonlinear effects are actually dominant."

 

 

Model of A320 in ADAMS package   Model of A320 in ADAMS package, frontal view
Model of the A320 in the ADAMS package.
A320 aircraft in flight; Courtesy of Airbus UK  

Even though Etienne was not sure how to apply what he had learnt about nonlinearity, he decided to choose his CPDA project on this topic. Supervised by Mark Lowenberg and Bernd Krauskopf (Engineering Mathematics, University of Bristol), he performed a nonlinear dynamics study of the landing gear on the A320 aircraft. The A320 is one of the most popular single-aisle jetliner aircraft offering around 150 seats. Etienne's project Nonlinear Aircraft Ground Dynamics, on the A320 landing gear system, fits in well with a European research project that looks at all aspects of aircraft on the ground, from the point of touchdown until the arrival at the gate.

A320 in flight.
(Courtesy of Airbus UK)

The tires on aircraft landing gear operate over a far larger envelope than that of cars. Aircraft tires can easily operate at slip angles of 20° and higher, as opposed to only 5° for typical car tires. These high-slip angles mean that the tires operate in the nonlinear area of the tire properties. "As you steer an aircraft around a corner, you must adjust the speed such that the loads on the tires are within the safety margins and the aircraft does not veer off the runway." The main interest lies in what are called high-speed runway exits. After landing, an aircraft must taxi away as quickly as possible to maximize the capacity of airports. Hence, it is an important question how fast an aircraft can turn corners without compromising safety.

It would have been possible to run a simulation in ADAMS using a specific thrust and steering angle and check whether it is safe or not. However, Etienne decided to try to use techniques from dynamical systems, especially the numerical continuation of different types of solutions. He managed to translate the basic ADAMS model into Matlab-SimMechanics and link it with the continuation package AUTO. With continuation he can extract, for example, specific relations between thrust levels and steering angles. "I was also able to check how the entire scenario depends on the steering rate, which was thought to influence the dynamics as well. I now know that, while it does have an effect, the steering rate is not always important."

  Overall stability diagram for the A320 with varying steering angle and fixed medium thrust level
Overall stability diagram for the A320 with varying steering angle and fixed medium thrust level.

In his thesis Etienne considers the aircraft moving at variable thrust and steering angle. This means that in his model the aircraft is going around in a circular fashion. "If this circular motion happens at constant speed, then I can think of this as an equilibrium that depends on the two parameters thrust and steering angle. With the use of AUTO I could trace the equilibrium solution in parameter space. In one parameter, you find saddle-node bifurcations, meaning that for fixed thrust certain steering angles are physically not possible, and Hopf bifurcations, where the equilibrium motion becomes unstable. With the continuation software I can find the stability boundaries directly." Enthusiastically, Etienne explains how one can then run simulations starting from data obtained by the continuation to investigate what exactly happens along the equilibrium branches and how stability is lost. "I was even able to identify a region where the aircraft moves around in a chaotic way!"

 

 

One-parameter bifurcation diagram of the behavior of the A320 as the steering angle varies using a fixed medium thrust level. The diagram shows the region where chaotic dynamics exist
  One-parameter bifurcation diagram of the behavior of the A320 as the steering angle varies using a fixed medium thrust level. The diagram shows the region where chaotic dynamics exist.  

Nonlinear dynamics may guide flight tests

While Etienne has not yet used his newly acquired nonlinear dynamics skills on the A380 to great extent, work is being done to expand and utilize these methods. As an example, Etienne mentions the `0.5 g lateral ground load regulation.' The regulations state that an aircraft must be capable of taking the load generated by a lateral force of 0.5 g due to a circular manoeuver.

Etienne at the A380 landing gear test rig; photograph by Hinke Osinga  

The Federal Aviation Administration has demonstrated from an operational test campaign that the 0.5 g load regulation is very conservative, and depends on the size and mass of the aircraft. Etienne explains that they are also coming to the same conclusions when they look at the results from some of their simulations. "In order to generate a 0.5 g force in the computer simulations, we need to specify unrealistic tire properties. It is physically not possible to get a large aircraft into a condition where it has to withstand such a force! We learnt from simulations that the bigger the aircraft, the smaller the lateral loads seem to be. With the results of the stability margins from my project I can work out the lateral loads, and my predictions correspond very well with the empirical data." In fact, Etienne believes that dynamical systems theory may well make it possible to prove analytically that 0.5 g loads cannot occur in a specified aircraft type under physically realistic maneuvers.

Etienne at the A380 landing gear test rig.

Dynamical systems techniques are already used for some work on the A380. "We recommended a specific flight test for the A380 based on our simulations and proved some skeptics wrong when we obtained a perfect match to our predictions!" Etienne is eager to tell everybody at Airbus UK about the use of nonlinear dynamics and he is slowly but surely making progress. "There are a lot of opportunities for seminars due to our Airbus Professionals Network, where we hold seminars that are open to all employees, and invite speakers who are experts in specific technical areas. I gave a talk at Airbus UK recently, and most of the attendees were certainly very interested."

Awareness will come gradually, and good computational tools are essential to ensure that others are confident in working with nonlinear methods. "It is important that we are able to use commercial tools for building our models and link this known computation environment with the new tools." Etienne envisages a Matlab front end linked with AUTO in a framework where the nonlinear methods automatically create the plots that make it easy to interpret the results. His group is currently working with the Mathworks to link their modeling codes with Matlab. "I am lucky to be working in such a talented environment. We do not take `no' for an answer. Everybody in our group has their own specialties, and together we overcome very difficult technical problems."

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