So here we are at the end of the twentieth century and at the end of our discussion of the history of aerodynamics and its impact on flying machines. Some final comments may add to our perspective on that history.

There are three themes whose threads have been running through this history of aerodynamics. First, the discipline of aerodynamics – the fundamental understanding of the physical nature of aerodynamic flows and the gradual evolution of the basic governing equations – developed quite independently of any drive toward practical applications such as flying machines. The period from early Greek science through the Middle Ages generated a few basic thoughts, such as the concept of a continuum, the recognition that an object moving through the air experienced some type of aerodynamic “resistance,” da Vinci's quantitative understanding of the continuity equation, and his careful observations of separated-flow patterns in water. Major advances came during the seventeenth century with the rise of serious experimental work in western Europe, particularly the development of rational mechanics by Newton. Human understanding of the physical sciences began to flower, as did the beginnings of a comprehension of aerodynamics. With Newtonian mechanics as a springboard, the intellectual giants of the eighteenth and nineteenth centuries, men such as Bernoulli, Euler, d' Alembert, Lagrange, Laplace, and Helmholtz, built an intellectual framework for aerodynamics that led to stunning quantitative breakthroughs: the Euler equations for an inviscid flow and the Navier-Stokes equations for a viscous flow. By the middle of the nineteenth century those equations embodied a full, rational under-standing of the fundamental physics of aerodynamic flows. The only problem was that those equations were too complicated to be solved! All of that intellectual progress took place quite independently of any desire to design flying machines. The men involved in that progress were, for the most part, intellectuals simply pursuing a basic understanding of nature.