Aeronautical Sciences

Recent Progress in Aeronautical Sciences: Exquisite Stability of Insect Flight and a New Theory of Lift

-

B2 L5 R5220

In this talk, I will present a special variational principle that we revived from the history of analytical mechanics: Hertz’ principle of least curvature. Using this principle, we developed a general (dynamical) closure condition that is, unlike the Kutta condition, derived from first principles. In contrast to the classical theory, the proposed variational theory is not confined to sharp-edged airfoils, i.e., it allows, for the first time, theoretical computation of lift over arbitrarily smooth shapes, thereby generalizing the century-old lift theory of Kutta and Zhukovsky. Moreover, the new variational condition reduces to the Kutta condition in the special case of a sharp-edged airfoil, which challenges the widely accepted concept regarding the viscous nature of the Kutta condition. We also generalized this variational principle to Navier-Stokes’, thereby discovering the fundamental quantity that Nature minimizes in every incompressible flow.

Mathematical Control Theory in Aeronautical Engineering: Boosted Maneuverability in Stall and Unconventional Stability of Insect Flight

Haithem Taha, Visiting Professor, Computer, Electrical and Mathematical Sciences and Engineering, KAUST

-

B9 L2 H2

The great Russian Mathematician Vladimir Arnold once said, “Mathematics is the part of physics where experiments are cheap”. In this talk, I will present two modern applications in aeronautical engineering where simple, but rigorous, mathematical control theory led to game-changing results exploiting nonlinearities and time-variation rather than obviating them.