https://arxiv.org/abs/2007.00926

Projectile Trajectory of Penguin's Faeces and Rectal Pressure Revisited
Hiroyuki Tajima, Fumiya Fujisawa

We discuss a trajectory of penguins' faeces after the powerful shooting due to their strong rectal pressure. Practically, it is important to see how far faeceses reach when penguins expel them from higher places. Such information is useful for keepers to avoid the direct hitting of faeceses. We estimate the upper bound for the maximum flight distance by solving the Newton's equation of motion. Our results indicate that the safety zone should be 1.34 meters away from a penguin trying to poop in typical environments. In the presence of the viscous resistance, the grounding time and the flying distance of faeces can be expressed in terms of Lambert {\it W} function. Furthermore, we address the penguin's rectal pressure within the hydrodynamical approximation combining Bernoulli's theorem and Hagen-Poiseuille equation for viscosity corrections. We found that the calculated rectal pressure is larger than the estimation in the previous work.