  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.
