söndag 10 januari 2010

The Mathematical Secret of Flight II

My article with Johan Hoffman The Mathematical Secret of Flight has now been delivered for publication in Nordisk Matematisk Tidskrift. We present the first correct mathematical/physical explanation of how a wing is capable of generating a lift/drag quotient of size 10-20, which enables birds and aeroplanes to fly.  

The secret of flight is revealed in the above figure. Can you see it?

We show that existing explanations are either incorrect, such as Kutta-Zhukovsky's circulation theory, or trivial, such as lower pressure above the wing than below.

The new explanation of flight is a spin-off of our Resolution of d'Alembert's Paradox
based on identifying the instability mechanism of potential flow changing the zero-lift pressure distribution of potential flow to turbulent lifting flow with some drag. We show that both lift and drag can accurately be predicted by computing, on a laptop, turbulent solutions of the Navier-Stokes equations with a slip boundary condition modeling the small skin friction of slightly viscous flow.

The new mathematical theory of flight is also presented as the knol Why It Is Possible to Fly
with so far 7.250 pageviews.

I invite proponents of conventional explanations of flight, to scrutinize our new explanation
and if rejected to defend their own favorite theory. I believe that it is the duty of scientists to 
engage into scientific discussion in areas of expertize, and I hope that the present denial and silence will be replaced by a constructive open debate, for example as comments to this post.

1 kommentar:

  1. Thanks for this eye-opener. I have so far only had to discuss whether lift is caused by downwash or increased airspeed on the top surface. I was happy to read Ingelmann-Sundbergs articles as they provided an explanation suited for an engineer (me). I never went beyond this and will try to do so now.
    For the engineer it is sufficient to understand that lift is generated (mostly) on the top surface and it acts on the skin from where it is transferred to the ribs and then to the spar and ulimately to the wing-fuselage junction where the lift is reacted.
    The downwash explanation is correct from an impulse point of view, but it gives no real understanding of how to design an efficient wing.