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Lateral dynamic flight stability of a model hoverfly in normal and inclined stroke-plane hovering

机译：正常和倾斜行程平面悬停时模型悬停的横向动态飞行稳定性

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Many insects hover with their wings beating in a horizontal plane ('normal hovering'), while some insects, e.g., hoverflies and dragonflies, hover with inclined stroke-planes. Here, we investigate the lateral dynamic flight stability of a hovering model hoverfly. The aerodynamic derivatives are computed using the method of computational fluid dynamics, and the equations of motion are solved by the techniques of eigenvalue and eigenvector analysis. The following is shown: The flight of the insect is unstable at normal hovering (stroke-plane angle equals 0) and the instability becomes weaker as the stroke-plane angle increases; the flight becomes stable at a relatively large stroke-plane angle (larger than about 24°). As previously shown, the instability at normal hovering is due to a positive roll-moment/side-velocity derivative produced by the 'changing-LEV-axial-velocity' effect. When the stroke-plane angle increases, the wings bend toward the back of the body, and the 'changing-LEV-axial-velocity' effect decreases; in addition, another effect, called the 'changing-relative-velocity' effect (the 'lateral wind', which is due to the side motion of the insect, changes the relative velocity of its wings), becomes increasingly stronger. This causes the roll-moment/side-velocity derivative to first decrease and then become negative, resulting in the above change in stability as a function of the stroke-plane angle.
机译：许多昆虫的翅膀在水平面上跳动（“正常盘旋”），而某些昆虫（例如，盘旋蝇和蜻蜓）盘旋在倾斜的行程平面上。在这里，我们研究了悬停模型Hoverfly的横向动态飞行稳定性。使用计算流体动力学方法计算空气动力学导数，并通过特征值和特征向量分析技术求解运动方程。如下图所示：昆虫的飞行在正常悬停时（飞行平面角等于0）不稳定，并且随着飞行平面角的增加，不稳定性变得更弱。飞行在相对较大的行程平面角（大于约24°）下变得稳定。如前所示，正常悬停时的不稳定性归因于“水平LEV轴向速度”效应产生的正侧倾角/侧向速度导数。当冲程平面角度增加时，机翼向身体后部弯曲，“水平LEV轴向速度变化”效应减小;此外，另一种称为“相对速度变化”效应（“侧向风”，这是由于昆虫的侧向运动改变了其翅膀的相对速度）而变得越来越强。这导致侧倾力矩/侧向速度导数先减小然后变为负值，从而导致上述稳定性随行程平面角的变化。

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