A numerical model to investigate the stability of the vertical autorotation of a singlewinged samara is presented. This model is obtained after the method of small perturbations about an equilibrium state is applied on the nonlinear equations of motion of the samara. The aerodynamic stability derivatives of the wing are obtained by numerical differentiation. The model is used in order to study the influence of different parameters on the stability. Since the stability is highly dependent on the basic equilibrium state, the influence of the different parameters on the basic state is also presented and discussed. The theoretical model is validated by comparing its results with qualitative experimental results.

A derivation of a theoretical model for the vertical autorotation of a samara wing is presented. The dynamic effects are treated in an accurate manner. The aerodynamic effects are calculated by using the blade element/momentum theory. Because of basic differences between the mode of operation of a samara wing and other rotary wings, the model differs from existing rotary wing models. An experimental setup, aimed at verifying the theoretical model, is also described. Comparison between theoretical and experimental results are presented.

Summary 1. Autorotation of a single‐winged samara is a highly nonlinear phenomenon that represents a delicate equilibrium between gravity, inertia and aerodynamic effects. Therefore, in order to analyse this phenomenon, an accurate detailed model is necessary. Such a model has not been presented in the past. Recently the authors derived a detailed model which is briefly described in the paper. 2. The aerodynamic contributions present the most complicated part of the phenomenon. These contributions are treated using the blade‐element/momentuin method, with certain improvements and additions. These improvements are necessary due to inherent differences between samara wings and other rotary wing systems (aircraft propellers, helicopter rotors, etc.). 3. The cross‐sectional aerodynamics of the samara is characterized by relatively small Reynolds numbers, high angles of attack and rough surfaces. While these characteristics are different from other rotary wings, they are typical of the wing cross‐sections of insects and birds. Therefore the lift and drag coefficients, which are necessary for the analysis, are obtained using available data for insect and bird wings. 4. The results of the theoretical model are compared with experimental results of tlvo kinds. The first kind includes results for a samara of an Acer platanoides that were reported in the literature. In addition, a special experimental model of a samiira was built and tested. This model offers a simple way of varying the configuration in order to study (experimentally) the effect of different geometric parameters on the autorotation. 5. In the light of the uncertainty in the aerodynamic coefficients, it can be concluded that there is quite a good agreement between the theoretical and experimental results. Thus, after LTalidation, the theoretical model is used for a parametric study to find the influence of different parameters on the autorotation. The important results of this study are outlined below. 6. The spanwise flolv component and the tangential component of the induced velocity have a very small influence and thus can be neglected. 7. It is important to include in the analysis the effects of the axial induced velocity, the tip effect, and the drag of the root region. 8. Since chordwise variations of the centre of pressure location, as a function of the angle of attack, were seen in the past (based on over simplified analyses) as the mechanism which is responsible for the samara stability, this effect is also added to the model. While the influence of this effect on the pitch angle is large and small on the sinking rate, it results in an increase in the deviation between the theoretical and experimental results. 9. Autorotation is sensitive to the cross‐sectional aerodynamic coefficients. This sensitivity is critical since the available data on these coefficients is, to say the least, unsatisfactory and require significant improvement.

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A new analytical approach for modeling the pull-in condition of voltage controlled electrostatic actuators (VCEA) with a general single degree of freedom (DOF) and general shape is presented. The presented approach gives a more general view of the pull-in condition in electrostatic actuators. The pull-in condition for an electrostatic actuator is defined in the voltage and degree of freedom plane. Then a general algebraic equation, referred to as the pull-in equation, is derived for the actuator. The solution of this equation directly yields the pull-in condition. Several case studies are then presented and their pull-in characteristics are summarized.