Lyu Yu Zhu, Sun Mao
Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.
Phys Rev E. 2022 May;105(5-1):054403. doi: 10.1103/PhysRevE.105.054403.
Previous works on the flight dynamic stability of insects have focused on relatively large insects. Here, the longitudinal flight dynamic stability of two hovering miniature insects was computed. With the stability properties of the miniature insects from the present work and those of large insects from previous works, we studied the effects of insect size on the stability properties in the full range of insect sizes. The following results were obtained. Although the insects considered have a 30 000-fold difference in mass, their modal structure of flight stability is the same: an unstable oscillatory mode, a stable fast subsidence mode, and a stable slow subsidence mode; because of the unstable mode, the flight is unstable. An approximate analytical expression on the growth rate of the unstable mode as a function of insect mass (m) was derived. It shows that the time to double the initial values of disturbances (t_{d}) is proportional to the 0.17 power of the insect mass (m). That is, as m becomes smaller, t_{d} decreases (i.e., the instability becomes faster). This means that miniature insects need a faster nervous system to control the instability than larger insects. For example, the response time (represented by t_{d}) of a miniature insect, the gall midge (m≈0.05mg), needs to be faster by about 7 times than that of a larger insect, the hawk moth (m≈1600mg).
先前关于昆虫飞行动力学稳定性的研究主要集中在相对较大的昆虫上。在此，计算了两种悬停微型昆虫的纵向飞行动力学稳定性。结合本研究中微型昆虫以及先前研究中大型昆虫的稳定性特性，我们在昆虫大小的全范围内研究了昆虫大小对稳定性特性的影响。得到了以下结果。尽管所考虑的昆虫在质量上有30000倍的差异，但它们的飞行稳定性模态结构是相同的：一个不稳定振荡模态、一个稳定快速沉降模态和一个稳定缓慢沉降模态；由于存在不稳定模态，飞行是不稳定的。推导了不稳定模态增长率作为昆虫质量（m）函数的近似解析表达式。结果表明，扰动初始值翻倍的时间（(t_d)）与昆虫质量（m）的0.17次幂成正比。也就是说，随着m变小，(t_d)减小（即不稳定性变得更快）。这意味着微型昆虫比大型昆虫需要更快的神经系统来控制不稳定性。例如，微型昆虫瘿蚊（(m≈0.05mg)）的响应时间（以(t_d)表示）需要比大型昆虫天蛾（(m≈1600mg)）快约7倍。
