# Abstract

References are presented into a new mathematical theory for the generation of lift and drag on a body moving

through a slightly viscous incompressible fluid such as air and water, as well as a large variety of applications.

The new resolution of d’Alembert’s paradox offers a new explanation of the generation of both drag and lift in incompressible flow, which is fundamentally different from the accepted explanation by Kutta-Zhukowsky of lift and Prandtl of drag. The new resolution is based on computation and analysis of turbulent solutions of the incompressible Navier-Stokes equations with slip/small friction boundary conditions as a model of a turbulent boundary layer. The combined computation/analysis shows that both drag and lift originate from a mechanism of instability at rear separation generating swirls of low-pressure streamwise vorticity, a mechanism discovered by computation and not described in the classical literature of fluid mechanics based on analytical mathematics. The swirls at separation are similar in nature to the familiar vortex generated in a bathtub drain:

and is developed in a variety of applications including:

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- Why Birds Can Fly
- Why a Helicopter Can Fly
- Why Paragliding Is Possible
- Why Wingsuit Flying Is Possible
- Why a Propoeller Gives Thrust
- Why a Frisbee Flies So Well
- Why It Is Possible to Sail
- Why Phelp’s Dolphin Kick Works
- How a Boomerang Flies
- How a Wing Paddle Works
- How a Wind Turbine Works
- Why a Topspin Tennis Ball Curves Down
- Aerodynamics of Discus Throw

“I’m proud to say that after extensive aero development of the Chevrolet-Volt, and more to come, we have achieved a vehicle that had a coefficient of drag that is more 30% lower in drag than the original concept. It’s not easy, but it is a necessity,” says Ed Welburn, VP, GM Global Design.

“I’m proud to say that after extensive aero development of the Chevrolet-Volt, and more to come, we have achieved a vehicle that had a coefficient of drag that is more 30% lower in drag than the original concept. It’s not easy, but it is a necessity,” says Ed Welburn, VP, GM Global Design.