Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

叶片单元建模提供了一种快速分析方法，用于估计昆虫飞行过程中产生的空气动力，但此类模型尚未使用自由飞行昆虫记录的运动学数据进行严格测试。这主要是因为缺乏详细的自由飞行运动学数据，而且还因为现有叶片单元模型的分析限制意味着它们无法纳入昆虫飞行过程中发生的翅膀和身体的复杂三维运动。在这里，我们提出了一个叶片单元模型，该模型具有根据经验拟合的气动力系数，该模型结合了机动Eristalis食蚜蝇的完整三维机翼运动学，包括其机翼的扭转变形。将这两个自由参数拟合到包含N = 26 541 次翼拍的大型自由飞行数据集，拟合模型捕获了矢状面中行程平均力的大约 80% 的变化。我们通过对数据进行二次采样来测试模型的稳健性，发现占飞行序列 10% 的子样本的参数估计值几乎没有变化。我们提出的模型的简单性和通用性使得它可以很容易地应用于其他昆虫的运动学数据集，也可以用于昆虫飞行动力学的研究。