Response of cricket and spider motion-sensing hairs to airflow pulsations

Closed-form analytical solutions are presented for the angular displacement, velocity and acceleration of motion-sensing filiform hairs exposed to airflow pulsations of short time duration. The specific situations of interest correspond to a spider intentionally moving towards a cricket, or an insect unintentionally moving towards or flying past a spider. The trichobothria of the spider Cupiennius salei and the cercal hairs of the cricket Gryllus bimaculatus are explored. Guided by earlier work, the spatial characteristics of the velocity field due to a flow pulsation are approximated by the local incompressible flow field due to a moving sphere. This spatial field is everywhere modulated in time by a Gaussian function represented by the summation of an infinite Fourier series, thus allowing an exploration of the spectral dependence of hair motion. Owing to their smaller total inertia, torsional restoring constant and total damping constant, short hairs are found to be significantly more responsive than long hairs to a flow pulsation. It is also found that the spider trichobothria are underdamped, while the cercal hairs of the cricket are overdamped. As a consequence, the spider hairs are more responsive to sudden air motions. Analysis shows that while two spiders of different characteristic sizes and lunge velocities can generate pulsations with comparable energy content, the associated velocity fields display different patterns of spatial decay with distance from the pulsation source. As a consequence, a small spider lunging at a high velocity generates a smaller telltale far-field velocity signal than a larger spider lunging at a lower velocity. The results obtained are in broad agreement with several of the observations and conclusions derived from combined flow and behavioural experiments performed by Casas et al. for running spiders, and by Dangles et al. for spiders and a physical model of spiders lunging at crickets.