估算飞机气动导数的多维最小二乘方法研究

Calculating Aerodynamic Derivatives with Multi-Dimensions Least Square Method

给出了多维最小二乘法拟合经验曲线的格式。在基于总体布局参数的飞机操稳特性研究中,有些气动参数的估算还处于经验曲线阶段,本文用最小二乘法曲线拟合原理和空间多维理论建立了曲线的数学模型,尤其在开发软件过程中,利用所建立的数学模型可以更加简单、快速的估算飞机气动导数。最后对多种型号飞机进行算例分析,并与计算流体动力学(CFD)方法所求的气动导数、实际飞行试验数据进行对比,结果表明,用此方法对经验曲线所建立的数学模型,在飞机的气动导数估算中,其结果是合理可行的。

Introduce a format of the statistical curve fitted by multi - dimensions least square. In the stability and control performance based on geometry sizing study, some aerodynamic parameter is showed by statistical curve. With multi - dimensions least square method develop a mathematics model on statistical curve in this paper. Particularly in the developing airplane software process, estimating the aircraft aerodynamic derivatives can be more simply and quickly if use the mathematics model. Three examples for aerodynamic derivatives are given and a comparison among geometry sizing, computational fluid dynamics （CFD） and test data. The results show that the numerical calculation method based on geometry sizing is reasonable.