Aerodynamics of Passive Flight and Probability of Landing Sites

准确预测在重力和气动力影响下下降的物体的飞行范围和着陆点与许多工程和科学应用有关。实例包括预测重返大气层航天器的着陆位置，了解海洋幼虫的定居模式及其对海洋种群动态的影响。虽然下降运动遵循经典力学定律，但下降物体的流体介质与几何和材料特性之间的微妙相互作用使得准确的着陆点难以先验预测，因此最好作为概率处理。该奖项支持基础研究，旨在开发一个实验和数学上易于处理的框架，用于研究物体在流体介质中被动下降的力学与着陆点的概率结果之间的耦合。这项研究将借鉴在几个学科，包括固体-流体相互作用，动力系统和概率建模开发的技术。这种多学科的研究方法将与大洛杉矶地区的外展工作相结合，以帮助扩大代表性不足的群体在研究中的参与，并对工程和科学教育产生积极的影响。物体在流体介质中下落的下降运动通常是复杂的，即使是形状规则的物体，如硬币和卡片。对于这样的物体，已经确定了四种类型的下降轨迹：稳定，颤动，混乱或翻滚，这取决于物体和流体的性质。 该研究小组将通过精心设计的实验以及通过开发提高物理系统保真度的数学和计算模型，探索着陆点的概率分布对下降轨迹类型的依赖性。 研究工作还将侧重于建立一个物体应该满足的设计原则，以实现理想的着陆点分布。

Accurate prediction of the flight range and landing site of an object descending under the influence of gravitational and aerodynamic forces is relevant to many engineering and science applications. Examples range from forecasting the touchdown locations of re-entry space vehicles to understanding the settlement patterns of marine larvae and their influence on marine population dynamics. While the descent motion follows the laws of classical mechanics, the delicate interplay between the fluid medium and the geometric and material properties of the descending objects makes the exact landing site difficult to predict a priori and, thus, best treated as probabilistic. This award supports fundamental research that aims to develop an experimentally and mathematically tractable framework for studying the coupling between the mechanics of objects descending passively in a fluid medium and the probabilistic outcome of landing sites. This research will draw from techniques developed in several disciplines including solid-fluid interactions, dynamical systems, and probabilistic modeling. This multi-disciplinary research approach will be combined with outreach efforts in the greater Los Angeles area to help broaden the participation of underrepresented groups in research and positively impact engineering and science education.The descent motion of objects falling in a fluid medium is generally complex, even for regularly shaped objects such as coins and cards. For such objects, four types of descent trajectories have been identified: steady, fluttering, chaotic, or tumbling, depending on the object and fluid properties. This research team will explore the dependence of the probability distribution of landing sites on the type of descent trajectories through carefully designed experiments as well as by developing mathematical and computational models of increasing levels of fidelity to the physical systems. Research efforts will also focus on establishing design principles that an object should fulfill in order to achieve a desired distribution of landing sites.