## måndag 30 maj 2016

### New Theory of Flight: Time Line

Potential flow around circular cylinder with zero drag and lift (left).
Real flow with non-stationary turbulent 3d rotational slip separation and non-zero drag (right).

The New Theory of Flight published in J Mathematical Fluid Mechanics, can put be into the following time line:

1750 formulation by Euler of the Euler equations describing incompressible flow with vanishing viscosity expressing Newton's 2nd law and incompressibility in Euler coordinates of a fixed Euclidean coordinate system.

1752 d'Alembert's Paradox as zero drag and lift of potential flow around a wing defined as stationary flow which is
1. incompressible
2. irrotational
3. of vanishing viscosity
4. satisfies slip boundary condition
as exact solution of the Euler equations.

1904 resolution of d'Alembert's paradox of zero drag by Prandtl stating that potential flow is unphysical, because 4. violates a requirement that real flow must satisfy
• no slip boundary condition.
1904 resolution of d'Alembert's paradox of zero lift by Kutta-Zhukovsky stating that potential flow is unphysical, because 2. violates that a sharp trailing edge in real flow creates
• rotational flow.
2008 resolution of d'Alembert's paradox of zero drag and lift by Hoffman-Johnson stating that potential flow is unphysical, because
• potential flow it is unstable at separation and develops into non-stationary turbulent 3d rotational slip separation as a viscosity solution of the Euler equations with substantial drag and lift.
Recall that d'Alembert's paradox had to be resolved, in one way or the other, to save theoretical fluid mechanics from complete collapse, when the Wright brothers managed to get their Flyer off ground into sustained flight in 1903 with a 10 hp engine.

Prandtl, named the Father of Modern Fluid Mechanics, discriminated the potential solution by an ad hoc postulate that 4. was unphysical (without touching 2.) and obtained drag without lift.

Kutta-Zhukovsky, named Fathers of Modern Aero Dynamics, discriminated the potential solution by an ad hoc postulate that 2. was unphysical (without touching 4.) and obtained lift without drag.

Hoffman-Johnson showed without ad hoc postulate that the potential solution is unstable at separation and develops into non-stationary turbulent 3d rotational slip separation causing drag and lift.

The length of the time-line 1750-1752-1904-2008 is remarkable from scientific point of view. Little happened between 1752 and 1904 and between 1904 and 2008, and what happened in 1904 was not in touch with reality. For detailed information, see The Secret of Flight.

1946 Nobel Laureate Hinshelwood made the following devastating analysis:
• D’Alembert’s paradox separated fluid mechanics from its start into theoretical fluid mechanics explaining phenomena which cannot be observed and practical fluid mechanics or hydraulics observing phenomena which cannot be explained.
The only glimpse in the darkness was offered by the mathematician Garret Birkhoff in his 1950 book Hydrodynamics, by asking if any potential flow is stable, a glimpse of light that was directly blown out by a devastating critique of the book from fluid dynamics community, which made Birkhoff remove his question in the 2nd edition of the book and to never return to hydrodynamics.

The 2008 resolution of d'Alembert's Paradox leading into the New Theory of Flight by Hoffman-Johnson,  has been met with complete silence/full oppression by the fluid mechanics community still operating under the paradigm of Hinshelwoods analysis.