The added mass forces in insect flapping wings

The added mass forces of three-dimensional (3D) flapping wings of some representative insects, and the accuracy of the often used simple two-dimensional (2D) method, are studied. The added mass force of a flapping wing is calculated by both 3D and 2D methods, and the total aerodynamic force of the wing is calculated by the CFD method. Our findings are as following. The added mass force has a significant contribution to the total aerodynamic force of the flapping wings during and near the stroke reversals, and the shorter the stroke amplitude is, the larger the added mass force becomes. Thus the added mass force could not be neglected when using the simple models to estimate the aerodynamics force, especially for insects with relatively small stroke amplitudes. The accuracy of the often used simple 2D method is reasonably good: when the aspect ratio of the wing is greater than about 3.3, error in the added mass force calculation due to the 2D assumption is less than 9%; even when the aspect ratio is 2.8 (approximately the smallest for an insect), the error is no more than 13%.