Despite significant interest in tailless flapping-wing micro aerial vehicle designs, tailed configurations are often favoured, as they offer many benefits, such as static stability and a simpler control strategy, separating wing and tail control. However, the tail aerodynamics are highly complex due to the interaction between the unsteady wing wake and tail, which is generally not modelled explicitly. We propose an approach to model the flapping-wing wake and hence the tail aerodynamics of a tailed flapping-wing robot. First, the wake is modelled as a periodic function depending on wing flap phase and position with respect to the wings. The wake model is constructed out of six low-order sub-models representing the mean, amplitude and phase of the tangential and vertical velocity components. The parameters in each sub-model are estimated from stereo-particle image velocimetry measurements using an identification method based on multivariate simplex splines. The computed model represents the measured wake with high accuracy, is computationally manageable and is applicable to a range of different tail geometries. The wake model is then used within a quasi-steady aerodynamic model, and combined with the effect of free-stream velocity, to estimate the forces produced by the tail. The results provide a basis for further modelling, simulation and design work, and yield insight into the role of the tail and its interaction with the wing wake in flapping-wing vehicles. It was found that due to the effect of the wing wake, the velocity seen by the tail is of a similar magnitude as the free stream and that the tail is most effective at 50–70% of its span.

中文翻译：

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扑翼微型飞行器机翼尾流和尾翼空气动力学建模

尽管对无尾扑翼微型飞行器的设计非常感兴趣，但尾翼配置往往受到青睐，因为它们提供了许多好处，例如静态稳定性和更简单的控制策略，分离机翼和尾翼控制。然而，由于不稳定的机翼尾流和尾部之间的相互作用，尾部空气动力学非常复杂，通常没有明确建模。我们提出了一种模拟扑翼尾流的方法，从而模拟尾翼扑翼机器人的尾部空气动力学。首先，尾流被建模为一个周期函数，取决于机翼襟翼相位和相对于机翼的位置。尾流模型由代表切向和垂直速度分量的平均值、幅度和相位的六个低阶子模型构成。每个子模型中的参数是使用基于多元单纯样条的识别方法从立体粒子图像测速测量中估计出来的。计算模型以高精度表示测量的尾流，在计算上是可管理的，并且适用于一系列不同的尾部几何形状。然后在准稳态空气动力学模型中使用尾流模型，并结合自由流速度的影响来估计尾部产生的力。结果为进一步建模、仿真和设计工作提供了基础，并深入了解了尾翼的作用及其与扑翼飞行器中机翼尾流的相互作用。发现由于机翼尾流的影响，