Kinematics of Single-Winged Spinning Seeds: A Study on Mahogany and Buddha Coconut Samaras

Abstract

This study investigates the steady-state kinematics of single-winged spinning samaras and re-evaluates the simplifying assumptions commonly used in existing theoretical models. High-speed imaging was employed to quantify key parameters, including descent velocity, rotational speed, coning angle, pitching motion, and the precessional trajectory of the center of mass. The results show that all measured parameters exhibit significant temporal variation, contradicting the long-standing assumption that these quantities remain constant in steady-state flight. This variability reveals that commonly used steady-state simplifications in previous studies may overlook essential aerodynamic mechanisms governing natural samara descent. Despite this complexity, the observed sinusoidal variations in pitch, cone angle, and translational velocity, together with the nearly linear rotation rate, provide a physically grounded basis for reformulating the governing nonlinear differential equations into a simplified algebraic form. Such experimentally validated harmonic representations offer a more realistic alternative to traditional steady-state assumptions. The visualized trajectories of the center of mass, root tip, wingtip quarter-chord point, and wingtip trailing edge reveal the inherently coupled nature of samara motion and highlight the need for future experiments that capture full three-dimensional kinematics. Overall, this work advances the understanding of samara aerodynamics by emphasizing the importance of natural variability while identifying a tractable path toward more accurate modelling frameworks.

Figures (23)

• Figure 1: Front and back views of single-winged spinning samaras: (a), (b) represent the Buddha coconut samara, and (c), (d) represents mahogany samara
• Figure 2: Analytical modelling for the single-winged spinning samara with a non-inertial reference frame attached to the CM
• Figure 3: Velocity of the CM in the steady state with respect to the inertial reference frame $R$, represented by u, v, and w along the $X^R$, $Y^R$, and $Z^R$ directions, respectively (Data reconstructed from Varshney et al. Varshney2011TheMotion).
• Figure 4: a) The trajectory of the CM in the X$^R$-Y$^R$ plane is obtained by integrating the u and v component velocities as depicted in Fig.\ref{['Varsheny']}. b) The acceleration of the CM in the downward direction is derived from the w velocity plot, as illustrated in Fig.\ref{['Varsheny']} from Varshney et al. Varshney2011TheMotion.
• Figure 5: The schematic of the hold and release mechanism