The Joukowsky transform is a conformal mapping of a disk to an airfoil shape. The wiki page says that "it was historically used to understand some principles of airfoil design". That's kind of a vague statement and I'd like to know more about precisely how it was used. I know that early work on theoretical fluid mechanics before digital computers were available used potential theory and other techniques from complex analysis. Was complex analysis integral to the design and engineering of aircraft before computers, or was it a theoretical and conceptual tool used to help understand fluid mechanics but not used directly in the design of aircraft?

I'm asking this because I occasionally encounter people rolling their eyes at learning about imaginary numbers, and I like being able to tell them that an important historical application of complex numbers was the defeat of the Nazi menace in the skies. I'd like to make sure I'm being truthful there.