M DV/DT

DKE/DT

DPE/DT

DU/DT=alpha Del^2U

Navier-Stokes

Viscosity

Heat

Entropy

Everything else is an obsolete math model that relies on crap assumptions. Navier-Stokes is the only approach that starts from first principles. Problem is there is no known closed form solution to the equations. A computer and descretized model is needed to obtain a solution, and then you need an appropriate turbulence model for the regime you are in if you want to look at transition and turbulence. You also need the control volume/solution space to be big enough that all energy is dissipated as heat. In other words it's not a continuum and momentum is NOT conserved. It's dissipated!!!! WHY IS THIS SO HARD???? They can't find the momentum which doesn't exist.....because it becomes heat! The temperature of the air goes up, a very tiny amount. So does entropy. Everything else is just a work around....and a bad one. But that is the aerodynamics we teach undergrads and a lot of grad students....because deriving Navier-Stokes and applying the equations is beyond most of them. So we teach them garbage, and they are never told it's all bunk. There is an entire bunk book, bunk teaching, and bunk spewing industry built around this.

I almost had a seizure when I saw Mclean with that picture of vorticity and Biot Savart.....fortunately he was correct in tearing it apart. I've calmed down now. I thought he was going to be defending it. The biggest problem with aerodynamics is the over-mathification of the field, without using sound physics and thermodynamic principles or even understanding such things exist. If I hear the word continuum one more time I'm going to scream! Of course the stupid integrals don't exist, but even if they did they would still be crap. I kept shouting Reynolds number! viscosity!!! HEAT!!!!!! he never got there. Aerodynamicist like to throw those terms out....And that whole Pradtl pancake thing....good grief. No viscous loss, no dissipation of momentum as heat. That pressure field only goes so far before being dissipated.

I also think these guys spend so much time looking at airflow in a wind tunnel they forget the airplane is moving through the fluid, not the other way around. You have to burn fuel to make that happen, and it all winds up as heat in the end. Even gliders....the sun heats the ground, the glider takes some of the energy from the thermal and then spreads it around as it descends. We are all riding the potential energy wave and spreading entropy hither and yon.

I think this is where Mclean was going....at least I hope so. But Aero guys are strange-you never can tell.

Fuel costs money.

Pops is right....money makes airplanes fly.

QED

I can't believe I got drawn into this.....I'm weak...must be the fever.