Improved Harmonic Large-Angle Fuselage Aerodynamics Model

Abstract

Introduction F LIGHT vehicle simulation, guidance and control law design, and flight performance analysis methods commonly use aerodynamic models based on tabulated force and moment coefficients. Inputs for these models are generally derived from wind-tunnel test data and/or computational fluid dynamics (CFD) results. However, wind-tunnel data are often only available for a limited range of pitch and yaw angles, and CFD computations for a large number of arbitrary attitudes can be expensive. Rotorcraft simulation models require aerodynamic inputs at extreme attitudes and commonly use trigonometric high-angle models to provide smoothly varying data in these regimes.1,2 Other applications for extreme high-angle aerodynamic models are ground-handling simulations, where the wind may come from any azimuth, flight performance analysis at high angles,2 and trajectory analysis of tumbling bodies. This Engineering Note presents a trigonometric, quasi-steady, fuselage aerodynamics model that is valid at all aerodynamic angles with a range of ±180 deg yaw and ±90 deg pitch. This model is based on the C81 high-angle equation (HAE) model found in some rotorcraft simulations1 but with improvements to the usability of the original model. The HAE model uses aerodynamic coefficient inputs at key values of pitch and yaw angles that may come from wind-tunnel tests, CFD analysis, or other sources. A set of sinusoidal functions is used to estimate the values for all six wind-reference fuselage aerodynamic forces and moments at any combination of pitch angle and yaw angle. The HAE model is desirable in that the equations are continuous and easily computed, give the proper trends at all attitudes, include some cross-coupling effects, and require relatively few inputs. The quasi-steady nature of the HAE model makes it unsuitable for situations where time-dependent flow characteristics are significant. This model is not suitable where high accuracy is required and is not expected to capture sudden changes in flow characteristics at critical angles such as the onset of stall or slender forebody vortex shedding. To address this issue, a blending scheme is often used to transition between wind tunnel data (or other high-quality data) at low angles and the HAE model at high angles.1 This Note addresses three limitations with the Ref. 1 model. First, the original model assumes lateral–directional coefficients are con-