# Aircraft turning on the runway: how fast can they go?

02 November 2016
Professor Bernd Krauskopf with two essential tools to explain his work: models of a pushbike and an Airbus A300.

Planes don’t make money when they’re not in the air, so airlines want to know how fast they can move their passenger jets when they’re on the ground. But airliners’ tricycle design isn’t made for efficiency on the tarmac, and that’s where Professor Bernd Krauskopf’s mathematical modelling is providing valuable insights. He is part of an international collaboration with European airplane manufacturer Airbus that uses dynamical systems methods to find out how fast a plane can turn before it becomes unstable.

“Airports want planes on and off the runway as quickly as possible – at some airports, planes take off every 90 seconds,” says Professor Krauskopf. “So you need to get off the runway as soon as possible, and that means turning at reasonably high speed.”

Professor Krauskopf and colleagues are linking bifurcation analysis of nonlinear models to industry-validated aircraft models to ask three questions about aircraft moving on the ground: when is a turn stable? How can it become unstable? What happens when it’s not stable? The short answer to that last question is that the plane ends up stuck in the grass at the side of the tarmac, or worse, and airport operations are then thrown into chaos, explains Professor Krauskopf. “The whole goal is to know when you are close to stability loss so that you can avoid it,” he says, but admits, with a smile, that the “behaviour of the aircraft beyond stability is the most fun part of the work for me.”

The drivers for the research are safety, quicker turnaround times and the automation of airplane movements on the ground. Although many in-flight operations are computer-controlled, says Professor Krauskopf, ground operations are not. “The only time you can be sure the pilot is actually at the controls is on the ground. There is a drive to automate ground movements as well, for efficiency. In 10 to 15 years’ time, the pilot may be taken out of that loop as well.”

The list of variables involved in the research is lengthy – landing gear position, tyre friction, steering angle, aircraft weight, engine thrust and atmospheric conditions among them – but the insights are valuable to Airbus’ design evaluation processes. “Just looking at tyres, for example, we can explore in which direction and how strong the forces are on individual tyres,” says Professor Krauskopf. “You don’t want one tyre to wear out five times as quickly as other tyres, because that will take the plane out of operation. You can get some very useful operational information out of this line of study.”

This is applied maths of a very serious kind. But there is room for fun, too. The work has found a highly unstable turn that would see the aircraft spin out of control, skid backwards and then stop. Professor Krauskopf dubs this “the Blues Brothers approach” to parking at the gate to offload passengers. “So far, we have been unable to convince anyone of the practicality of this.”