Secrets in Math: How do we Fly?

Abstract

This article covers the history of flight from 1400s  to the modern era, focusing on d'Alembert's paradox and explanations of how lift is  created. It is unnerving to think that it wasn't until 2008 that  scientists were finally able to answer the question of how planes remain in the air. D'Alembert's paradox has been troubling mathematicians and aeronautic experts for years. It was a simple statement made in 1749, but the implications have affected the field of fluid dynamics until recently. The statement made by d'Alembert essentially concluded that there is no mathematical explanation for the physical observation of drag on any solid object moving through a fluid, making airborne flight an unexplainable enigma. However, in 2008, a paper was published finally providing a coherent resolution to d'Alembert's paradox as well as fully explaining how lift and drag is created (Hoffman and Johnson, 2008; 2009). After disproving the previous theories provided by Prandtl and Kutta-Zhukovsy, Hoffman and Johnson built on the work of d'Alembert and Stokes, and were able to identify the instability mechanism which their predecessors overlooked. Using this mechanism, they were able to explain what causes the net drag acting on the wing. Now with this understanding, airplane developers can take greater steps to improving the design of airplane wings and make air travel much more efficient.