We develop a mathematical model to capture the web dynamics of slingshot spiders (Araneae: Theridiosomatidae), which utilize a tension line to deform their orb webs into conical springs to hunt flying insects. Slingshot spiders are characterized by their ultrafast launch speeds and accelerations (exceeding 1300 m/s(2)), however a theoretical approach to characterize the underlying spatiotemporal web dynamics remains missing. To address this knowledge gap, we develop a 2D-coupled damped oscillator model of the web. Our model reveals three key insights into the dynamics of slingshot motion. First, the tension line plays a dual role: enabling the spider to load elastic energy into the web for a quick launch (in milliseconds) to displacements of 10-15 body lengths, but also enabling the spider to halt quickly, attenuating inertial oscillations. Second, the dominant energy dissipation mechanism is viscous drag by the silk lines - acting as a low Reynolds number parachute. Third, the web exhibits underdamped oscillatory dynamics through a finely-tuned balance between the radial line forces, the tension line force and viscous drag dissipation. Together, our work suggests that the conical geometry and tension-line enables the slingshot web to act as both an elastic spring and a shock absorber, for the multi-functional roles of risky predation and self-preservation.
