On the Motion of Falling Leaves

TL;DR

This study systematically classifies the motion of falling leaves using experimental data, revealing key parameters affecting their paths and rotational stability, with potential applications in biology and meteorology.

Contribution

Introduces a new classification scheme for falling leaf trajectories and analyzes the dynamics and stability of their rotational motions based on extensive experiments.

Findings

Identified two critical Froude number values influencing rotational motion.

Classified falling leaf paths based on deviation and shape.

Found stable rotational motions around length and diagonal axes.

Abstract

This paper investigates the motion of falling leaves through modeling using papers and the corresponding data collected from more than four thousands experiments. Two series of experiments were designed in order to study the relationship between different parameters which can affect different paths of motion in leaves. In the first series of experiments, the shapes of the potential paths that falling papers can take were investigated as a whole. A new classification scheme was derived from these experiments, categorizing the motion of falling sheets of paper based on the deviation from the original point of release and the shape of the path they take on their descending journey. We believe this new classification scheme can be very useful with potential applications in various fields such as biology, meteorology, etc.; it can also build a foundation for further experiments. The second set of experiments was focused on the dynamics and shape of the motion of the falling paper itself. It was observed from these experiments that there should be two critical values for Froude number in the falling paper motion in regards to the rotational motion. We also found that the most stable and dominant rotational motions are those observed around the length axis as well as the ones along the diagonal axis.