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Stabilizing aircraft during takeoff and landing using math

Posted August 21, 2013
Stabilizing aircraft during takeoff and landing using math

Stabilizing aircraft during takeoff and landing using math
This is an example of runway marks left after a shimmy event. Credit: C.I.A.I.A.C., Madrid, Spain.

One of the lesser known concerns about commercial aircraft is their stability on the ground during taxiing, takeoff, and landing. During these processes, planes must maintain stability under various operating conditions. However, in some situations, the aircraft landing gear displays unwanted oscillations, which are referred to as shimmy oscillations.

In a paper published last month in the SIAM Journal on Applied Dynamical Systems, authors Chris Howcroft, Bernd Krauskopf, Mark Lowenberg, and Simon Neild study the dynamics of aircraft landing gear using nonlinear models. The dynamics of landing gear shimmy and the wheel-ground interaction are fundamentally nonlinear.

“Shimmy oscillations of aircraft landing gear have long been a problem, and their prediction and prevention remains an ongoing challenge in landing gear design,” explains author Chris Howcroft. “The issue is that a landing gear may display the desired behavior during ground take-off/landing manoeuvres over several hundred or so flights, but then suddenly oscillate given just the right—or rather, the wrong—conditions.”

Fortunately, mathematical models provide cost-effective ways to study the dynamics of the main landing gear (MLG) and determine the types of oscillations that may occur under different conditions. “The work we conducted clarifies under which conditions shimmy oscillations can be encountered in the MLG of a representative midsize passenger aircraft. We identified different types of shimmy oscillations and showed where they occur,” says Howcroft.

“Having the right mathematical model is really the key,” he adds. “Actual testing is extremely expensive; however, nonlinear analysis methods are very well suited to identifying these hard-to-find dynamics. They may also be employed to determine the shimmy characteristics before the aircraft has actually been built.”


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