History of the Theory of Lift: A Mathematical War in the Background of the Great War (Part I)

When the Wright brothers made their historic record in December 1903 of the first powered flight, there was no workable theory of lift. Even the most basic question in aeronautics on how much lift a wing produces could not be answered in a principled way. The Wrights had simply built their airplane by trial-and-error. The emergence of this new machine (the airplane) posed danger to countries in political tension. Whoever reveals the mystery of lift first and arrives at a constructive way of designing airplanes will be able to build better ones in shorter times, and hence dominate the sky. And whoever dominates the sky will have an unfair advantage in the battle. The branch of science that could shed light on how a wing produces lift is fluid mechanics; and the two leading countries at the time were Britain and Germany. So, right before, during, and after the Great War, there was a parallel mathematical war between the two countries to develop a theory of lift. The Cambridge school of mathematical physics, led by Rayleigh, Lamb, Taylor, and Bairstow, had developed the discontinuity theory of lift. In contrast, the Gottingen school of technical mechanics, led by Prandtl, Kutta, Munk, and Betz, had developed the circulation theory of lift. While the German lost the actual war, they won the mathematical war; the circulation theory of lift has dominated to become routinely taught in every single aeronautical school throughout the world including Cambridge. In this two-part lecture, I will discuss some of the historical details of this mathematical war in the background of tensions due to war, politics and press. We will discuss how the German training in technical schools (Technische Hochschule) provided freedom/advantage in accepting assumptions about the nature of air that the Cambridge school of mathematical physics could not tolerate (e.g., neglecting viscosity). Hence, they responded differently to the same technical problems (e.g., the German invention of the Kutta condition to handle the non-uniqueness of Euler’s equation). I will discuss Their different perspectives on the ideal-flow concept and Navier-Stokes’ equations. This story represents a unique incident in the history of science where both physicists and engineers played chess with Nature to unravel the mystery of a natural phenomenon: lift. The engineering sense of urgency allowed Prandtl and his fellow engineers to make the right move in the game that the best renowned physicists of the time (e.g., Einstein) could not do.