What is elliptic lift distribution and why is it optimal for minimum induced drag?

• A. Elliptic distribution yields uniform downwash and minimizes induced drag for a given total lift and span.
• B. Elliptic distribution yields non-uniform downwash and maximizes induced drag.
• C. Elliptic distribution reduces lift.
• D. Elliptic distribution applies only to rectangular wings.

Answer: (C)

Elliptic lift distribution means the lift per unit span follows an elliptical (half-ellipse) shape along the wing span, which makes the induced downwash nearly uniform across the span. This uniform downwash is key: when every section of the wing experiences the same induced angle of attack, the wing’s overall energy radiated into wingtip vortices is minimized. The result, from lifting-line theory, is the smallest possible induced drag for a given total lift and wingspan because the spanwise lift distribution matches the most efficient way to spread out and cancel the wingtip vortex effects. In other words, it makes the Oswald efficiency factor as close to 1 as possible, reducing induced drag.

This isn’t about reducing lift or about a specific planform like a rectangular wing; it’s about how lift is distributed along the span to minimize energy lost to induced vortices. The elliptic distribution is an ideal optimum; real wings may approximate it but don’t have to be rectangular to benefit from the concept.