As I read with interest “Dynamics of a skydiver’s epic free fall,” the Quick Study by José Colino, Antonio Barbero, and Francisco Tapiador (Physics Today, April 2014, page 64), I encountered several important errors from the aerodynamic standpoint that need to be clarified.
First, in the paragraph just above the subhead “A closer look at Baumgartner’s jump,” the authors state that “since the [shock] wave propagates at the speed of sound, the diver will eventually cross that disruptive shock.” Shock waves always propagate faster than the upstream speed of sound. In fact, what we call a detached shock wave, which forms upstream of a blunt body flying at supersonic speeds, travels at roughly the same velocity as the blunt body itself.
Second, the authors state that “shock waves form where subsonic and supersonic flows meet.” That is true only when downstream boundary conditions require that a supersonic flow slow to subsonic speeds. When a subsonic flow accelerates to a supersonic flow, the region where the flow is sonic is not a shock wave but a sonic line or sheet. Accordingly, the thin regions marked in blue in panel b of the figure are sonic sheets, not “shock waves” as the authors state. The sheets delimit the subsonic region between the shock and the diver’s head, and the supersonic region around the chest and the rest of the diver’s body.
Unlike shock waves, sonic sheets are isentropic. Of course, even though it is supersonic, the flow formed downstream of the sonic sheets marked in blue is slower than the incoming flow. Nevertheless, the unsteady and complex boundary layers formed around the chest and backpack wrapped in fluttering fabrics create a forest of small, low-intensity shock waves that eventually accommodate the air speed to that of the object in contact with it.
Furthermore, in describing panel b of the figure, the authors say the detached shock wave at the diver’s front is positioned “downstream” of him. That turns the established language of fluid dynamics upside down: “Upstream” is in the opposite direction to the incoming flow relative to the object (or to the axes used to describe the motion), and “downstream” is behind the object, in the direction of the flow.
My above comments aside, I truly congratulate Colino and coauthors for their illuminating study on the free fall of a diver; I will surely use it in my undergraduate classes.
