about 4. The robustness of this number with respect to initial and boundary conditions suggested the quantity to be a universal constant and was thus named formation number. The phenomenon of 'pinch-off', or detachment, from the feeding starting jet is observed in a wide range of flows observed in nature. For instance, it was shown that biological systems such as the human heart or swimming and flying animals generate vortex rings with a stroke-to-diameter ratio close to the formation number of about 4, hence giving ground to the existence of an optimal vortex ring formation process in terms of propulsion, thrust generation and mass transport. In particular, the squid lolliguncula brevis was shown to propel itself by periodically emitting vortex rings at a stroke-ratio close to 4. Moreover, in another study by Gharib et al (2006), the formation number was used as an indicator to monitor the health of the human heart and identify patients with dilated cardiomyopathy. Other examples Vortex ring state in helicopters Air vortices can form around the main rotor of a helicopter, causing a dangerous condition known as vortex ring state (VRS) or "settling with power". In this condition, air that moves down through the rotor turns outward, then up, inward, and then down through the rotor again. This re-circulation of flow can negate much of the lifting force and cause a catastrophic loss of altitude. Applying more power (increasing collective pitch) serves to further accelerate the downwash through which the main-rotor is descending, exacerbating the condition. In the human heart A vortex ring is formed in the left ventricle of the human heart during cardiac relaxation (diastole), as a jet of blood enters through the mitral valve. This phenomenon was initially observed in vitro and subsequently strengthened by analyses based on color Doppler mapping and magnetic resonance imaging. Some recent studies have also confirmed the presence of a vortex ring during rapid filling phase of diastole and implied that the process of vortex ring formation can influence mitral annulus dynamics. Bubble rings Releasing air underwater forms bubble rings, which are vortex rings of water with bubbles (or even a single donut-shaped bubble) trapped along its axis line. Such rings are often produced by scuba divers and dolphins. Separated vortex rings There has been research and experiments on the existence of separated vortex rings (SVR) such as those formed in the wake of the pappus of