Modeling of the Nonlinear Unsteady Pitching Moment Stall Characteristics from Cessna Citation II Flight Test Data

Abstract

One of the most widely applied identification methods for stall modelling from flight test data is based on Kirchoff’s method of flow separation. This approach has not lead to a satisfactory aerodynamic pitching moment model. The introduction of the so-called X-variable, representing the point of flow separation on the wing, interferes with identification of a pitch damping term, that is needed for dynamic stability. Moreover, flow separation is only a small contributor to the pitching moment, leading to a lack of physical interpretability. In general, Kirchoff methods lead to models incompatible with the nominal flight envelope. This paper presents a nonlinear unsteady model of the pitching moment using lag states of the angle of attack measurements, identified from flight test data collected with a Cessna Citation II. The model is formulated in terms of well-known stability derivatives and is a one-on-one extension of the nominal envelope model. Model regressors are selected from a large pool of candidates using Multivariate Orthogonal Function Modeling. The candidate pool is based on a newly formulated mathematical model, such that each model contribution has a clear physical interpretation. This has lead to a 𝐶𝑚𝛼 contribution depending on various lag states of the angle of attack, and pitch and downwash lag damping contributions as univariate splines. The model has good predictive abilities and can report a reduction of 55.9% in validation MSE compared to a Kirchoff based pitching moment model by van Ingen et al..