Statistical Analysis of Relationships Among Samara Morphological Parameters and Transition Time

This paper is the continuation of our work on capturing the kinematics and dynamics of single-bladed Samara seeds undergoing auto-rotation. The existing literature and our prior work have focused on capturing aerodynamic characteristics under steady-state rotation conditions. We continue to explore the photogrammatry technique, with particular interests aimed at resolving the transition flight regime. Naturally occurring autorotation phenomena on single-bladed seeds offer avenues to optimize the autonomous vertical flight systems subjected to uncontrolled descent rates. These seeds show three distinct phases, namely free fall, transition, and steady-state rotation. The collective wisdom revolves around the vortex lift generation caused by the leading edge vortex under steady-state rotation conditions. Current understanding of this auto-rotation suggests that the spinning motion reduces the descent rate of these seeds allowing the wind to transport them further from their parent tree aiding in propagation methods. However the transition from free fall motion to the steady state phase is heavily unexplored. This flight phase is crucial in determining the flight dynamics and necessary blade characteristics to undergo a smooth fast transition, thus increasing flight-time and performance. The difference in transition time and transition length across the same species of seeds with different form factors is of interest. Prior work aimed to associate the vastly different transition dynamics for a statistically large sample size to identify the best and worst-performing seeds. The study was inconclusive in relating the transition dynamics with the nominal rotor blade nomenclature of pitch, aspect ratio, twist, and wing loading. This prompts the research question of what blade profiles differentiate these seeds. This current research employs general linear regression models such Analysis of Variance (ANOVA) to relate the transition-time to morphological parameters such as seed mass, blade area, and chord. In addition, it will identify the statistical significance of relationships between typical blade morphological parameters and transition-time and develop an analytical framework for evaluating significance of other kinematic and dynamic parameters to various performance characteristics such as the coefficients of lift and drag (CL and CD). While at large, the work in progress aims at capturing the transition flight dynamics, it is crucial in some of the priority areas involving vertical flight large-scale seed dispersal for terraforming, planetary explorations, and tornado modeling through naturally swirling leaves/vegetation.