Prandtl’s Boundary-Layer Theory as a Basis for Improving Aerodynamic Shapes

The boundary layer theory, developed by Ludwig Prandtl , revolutionized our understanding of fluid flows and became a powerful tool for optimizing aerodynamic shapes. At large Reynolds numbers, viscosity can be neglected outside a narrow boundary layer ; therefore, the Euler equation s and the potential theory can be used to calculate the pressure distribution on the surface of solids . In particular, analytic formulae for the drag -to-lift ratio of the optimal wing and special -shaped bodies of revolution, which ensure the flow pattern without boundary -layer separation , were proposed and used to solve the inverse problems of searching for the optimal shapes of vehicles . Analytical formulae and examples of calculations with given values of the range and mass of an aircraft are presented.