Peter wrote:
I reckon the answer to this old puzzle is simply that there is no simple answer.
Indeed. This Wiki-page is quite nice actually. It sees the thing from several perspectives.
I like this picture of the Kutta condition.
What is not mentioned (but can be found is text books) is that when starting at zero velocity on a real foil/wing, the flow starts out as the picture above. Then the separation point moves with the flow and, and it develops into the picture below: A working airfoil with the correct flow condition. So, understanding lift without understanding circulation in a fluid continuum, forget it. Then you also have to understand the difference of sucking and blowing, as well as other concepts, viscosity for instance, and in the end also turbulence, and how it works in correlation with viscosity.
Another thing is that the answer can always be measured, and in most cases also calculated. There is no profound reason to “understand” lift, whatever that actually is supposed to mean. It’s better to just shut up and measure it or calculate it 
That’s the only way to get results no matter how you look at it.
I just looked at my previous Uni modules on “Aerodynamics topic”, the fundamental laws are simply Newton laws (plain classic mechanics no relativity or quantum physics) for conservation of mass, momentum, energy the math tools varies a bit: Navier-Stokes/Euler/Lagrange equations, Dimensional analysis, Helmholtz’ theorems, Biot-Savart law, Bernoulli theorems, asymptotic expansions and boundary layer methods
As suggested by @mh, I think the most comprehensive starter books on flying & aerodynamics are by John D Anderson (Fundamentals of Aerodynamics & Introduction to Flight), he puts lot of history, design into perspective and there is load of maths but they are kept to simple form, he also does the advanced Aeronautical Engineering courses at the Maryland university, also I concur stick and rudder as pilot aerodynamics for anyone flying between VS0 and VNE on kts
Just a note “Bernoulli theorems” they were briefly mentioned in “Aerodynamic module” in my studies (few pages and never used to solve anything), but they are used used all day along in “Aerodynamics – Hydrodynamics module”, the main application being plumbing for dam water supply I recall the painful full set was:
MEC431–Continuum Mechanics
MEC432-Fluid mechanics
MEC578-Aerodynamics
MEC564-Compressible aerodynamics
MEC561-Fluid-structure interactions
MEC555-Turbulence and vortex dynamics
MEC568-Structural dynamics
MEC552-Computational fluid dynamics
MEC585-Turbulent flows: dynamics and numerical simulations
MEC594-Aerodynamics and hydrodynamics
Peter wrote:
One physicist told me that the number of people around the world who truly understand Einstein’s theories of relativity can be counted in the hundreds, at most. That’s perhaps 0.1% of how many are taught the stuff at universities.
I would absolutely agree with this. I did a bit of general relativity during my masters year and managed to get just about enough to get through the relevant exam. Whilst I had a bit of understanding at high level I was very aware how far it was beyond me to get into the mathematical details. I would say really understanding the mechanics of this is extremely rare.
getting the high level approximations which work pretty well for real life is much more manageable.
People look for simple ways to explain things – especially for the media, especially these days when everything has to fit into one handy soundbite – but I reckon the answer to this old puzzle is simply that there is no simple answer.
One physicist told me that the number of people around the world who truly understand Einstein’s theories of relativity can be counted in the hundreds, at most. That’s perhaps 0.1% of how many are taught the stuff at universities.
Well, it’s been said that Kelly Johnson could actually see the air but he was a one-off…
Capitaine wrote:
There is the question of how well one needs to understand something to use it.
An excellent point! In medicine we very often do things because they work, without really understanding why. The science behind the inner workings of the human body and its interactions with medicines is so astronomically complex that I don’t think we will ever reach a point where we understand in full how our bodies really work…
I see this is a holy thread resurrection Batman and I was the OP! Wheels of time.
The substantial money prize to complete the Navier-Stokes partial differential equations on fluid dynamics is still there for the taking for over a century just round the corner at Oxford.
The Kutta-Zhukovski condition ignores the physics negation of circulation theory to come up with some mathematical work arounds.
This non-pilot article on Bernoulli vs Newton is quite good.
https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/
There is the question of how well one needs to understand something to use it. I’m not ashamed to admit I don’t really understand how, say, gravity works: the effects are obvious, but how does it really work? “Yes, but why” used to be my favourite expression (I must have been an annoying child )
mh many thanks – stick and rudder gets looked at quite often, the book is very good at explaining what the aircraft is doing – so good both on theory and practice.
I thought an edit with a quote from Langewiesche would be on point (no pun intended)
“Trying to understand the piloting of airplanes by concentrating on Bernoulli and Prandtl is like trying to catch on to tennis by studying just exactly how the rubber molecules behave in a tennis ball when the ball hits the court and just exactly how the catgut behaves in the racket when the ball strikes: instead of simply observing that it bounces!”
Hey Robert,
if you are interested in aerodynamics beyond the knowledge a pilot needs to fly, I may recommend Fundamentals of Aerodynamics by John Anderson.
In general, with Navier-Stokes you can describe every flow. But Navier-Stokes isn’t that handy outside the numerical world. (Even with numeric flow calculations, Navier-Stokes equations are not trivial to hanlde). You have to make some assumptions about your flow, to get an equation, that you can actually handle (i.e. inviscid flow, incompressible flows, etc.).
And this is with all other models, too. You have to make some assumptions on your flow to begin with (and you have to keep it in mind) . For instance for Kutta-Jhoukowski, the flow has to be in a steady state (d/dt = 0), inviscid, incompressible and non-rotating to begin with. Or Bernoulli, which is true for incompressible, inviscid flow, only. So you can’t use all of these for calculations in any flow.
Then, you have to know what you want to describe. Kutta-Jhoukowski and Blasius can’t calculate any drag, for instance. Biot-Savart or Bernoulli can not calculate lift or drag, and so on.
For a pilot, Newtons laws of motion are perfect suitable to describe what happens, as described by Wolfgang Langewiesche in his book ‘stick and rudder’. (You probably know this one :-)
Cheers,
