Cubic scaling of thrust production with Strouhal number in tethered insect flight

A successful existing model for the scaling of the thrust coefficient of flapping wings was derived from Theodorsen’s theory, and results in a St² scaling and strong Reynolds number dependence. In the present work, we proposed a new model based on von Karman and Sears, that exhibits St³ scaling, the addition of reduced frequency, and limited Reynolds number dependence. Despite the significant differences in derivation and in algebraic form, the two models both exhibit comparable performance in modelling our sample data set, containing the thrust and wing kinematics of a large number (N=38) of individual mountain pine beetle specimens, recorded over 168 individual flights. The scaling of both models with Strouhal number produces similar thrust estimates across a limited range of Strouhal numbers near our experimental conditions, before diverging at large values (St > 10).

In addition to modelling thrust coefficient, our proposed model can provide an explicit estimate for circulation and circulation growth in the wake. Nevertheless, future work must investigate how scaling across reduced frequency and Reynolds number each masks the effect of the other term in these distinct models, as Theodorsen theory and von Karman and Sears theory share significant theoretical basis.