Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

TLDR

Aerodynamic forces and moments are expressed via indicial functions or internal state variables, with only linear terms considered in the examples. The study presents a theoretical investigation of aircraft aerodynamic model equations incorporating unsteady effects. The authors formulate aircraft unsteady aerodynamics as integro‑differential equations using indicial functions and as state‑space models with internal state variables, then apply these to a one‑degree‑of‑freedom harmonic motion and to longitudinal short‑period motion, modeling indicial functions as exponentials and state variables as linear, time‑invariant, first‑order differential equations. Both modeling approaches yield identical unsteady aerodynamic models.

Abstract

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.