Inversion

QUOTE

Carl Jacobi once said…

“Invert, always invert.”

CONCEPT

Inversion

Inversion is a problem-solving technique that involves approaching a problem or situation by looking at it from the opposite perspective. By considering what we want to avoid or what could go wrong, we can gain new insights and identify potential solutions that might have otherwise been overlooked.

Inverting a problem can help break conventional thinking patterns, expose hidden assumptions, and reveal possible obstacles. It encourages individuals to think critically and creatively, reducing the likelihood of being blindsided by unforeseen challenges or undesirable outcomes.

STORY

You Can Increase ... And You Can Decrease

In the early 20th century, aviation was a rapidly growing field, with engineers and inventors racing to build faster, more efficient, and safer aircraft. One of the most significant challenges they faced was designing a reliable and effective airfoil—the shape of an airplane's wing—which would generate enough lift to keep the plane in the air.

At the time, most designers focused on increasing lift by experimenting with different wing shapes, materials, and configurations. However, a German engineer named Ludwig Prandtl took a different approach.

Instead of focusing solely on maximizing lift, Prandtl asked: "What factors are causing a decrease in lift or preventing the aircraft from staying in the air?"

By inverting the problem, Prandtl identified a crucial factor: induced drag, which is a byproduct of lift that increases with the angle of attack (the angle between the wing and the airflow). He realized that reducing induced drag was just as important as increasing lift for the overall performance and efficiency of an aircraft.

Prandtl's insight led him to develop a new wing design—the elliptical wing planform.

His new design reduced induced drag, allowing aircraft to fly faster and more efficiently while still generating the necessary lift. The elliptical wing planform was eventually adopted by several aircraft, including the iconic British Supermarine Spitfire, which played a crucial role in World War II.