How Terminal Is Terminal Velocity?

Several years ago the authors of the present piece wrote a MONTHLY article [1] describing the velocity dependence of aerodynamic drag. Recently, a science reporter for the Guardian newspaper, who found this reference, solicited our help in writing an article about how a 102-year-old woman from Turin could fall out of a fourth floor window and survive [2]. In particular, the reporter wanted to know about the role of terminal velocity in her survival. An internet search found many webpages dealing with terminal velocity, but none relevant to understanding whether terminal velocity is reached during falls from relatively low heights. We also found an interesting posting from a Coast Guard officer in New York Harbor inquiring about the chance of survival when a person falls from a 230-foot bridge into water and wanting to know how fast the person would hit the water. We also learned about a popular book, New York Dead by Stuart Woods [3], in which a character, a popular TV newscaster, plummets twelve stories onto a heap of dirt twenty yards away and survives. The book contains a discussion and speculation about how the character survived the fall. One idea is that the character was “saved by terminal velocity.” An important part of the plotline of another popular novel, Angels and Demons by Dan Brown [4], is devoted to a character falling from a helicopter. It raises the question of how a two foot-by-two foot piece of cloth could slow one’s speed by 25%. Clearly there are many practical and interesting aspects to studying people’s falling through the air. In this self-contained short addendum to [1], we explain why terminal velocity played no role in the falls from the fourth through twelfth story windows. We explicitly