Safety Envelope Determination for Impaired Aircraft During Landing Phase Based on Reachability Analysis

Abstract

The flight safety envelope can be viewed as a safe set which could ensure safety as long as the flight state keep within it. Once aircrafts are impaired, such as engine loss or a jammed elevator, dynamic characteristics of the aircrafts will be damaged and the flight safety envelope will shrink deeply. Unaware of these upset conditions, the flight system may operate under a conflicting envelope. Especially in landing phase, it is difficult to keep the flight state within the safety envelope and the accidents are generally associated with it. Therefore, study on estimation of the safety envelope under upset conditions, is critical to improve flight safety. In order to estimate the safety envelope, the reachability analysis based on the level set method is presented. The reachable set is obtained via computing the Hamilton-Jacobi partial differential equation (HJPDE), which is based on optimal control theory. Examples are provided using NASA’s generic transport model (GTM), and the results can be applied to flight safety risk assessment, providing theoretical guidance for the design of envelope protection systems.