The problem with Bernoulli:
There is no problem with Bernoulli's equation. Given a flow pattern - faster over the top (on average) and typically slower under the bottom results in lower pressures above (on average) and higher on the bottom. The total differences in pressures time the wing area equal the force applied on the wing and equal the force of lift. Period. The problem, however, is explaining the flow pattern - why is flow over the top faster than flow along the bottom? That's when the wheels come off. An obvious (and correct) explanation is to talk about circulation and the Kutta condition (velocity at the trailing edge must be finite) - this gives you a good math model of the flow / pressures / lift. But, to explain circulation, at a minimum you need to show the vector sum of the undisturbed and circulation flow fields. And, the discussion quickly degenerates into vector calculus - I assume I'm not the only one that struggles with that. As a result, people have come up with semi-plausible sounding nonsense that they blame on Bernoulli such as the difference in distances, looks like a ventrui, pressure does not fully explain lift, air bounces off the bottom, Bernoulli 60% vs Newton 40%... All that is nothing less than 100% unadulterated male bovine excrement. So, while Bernoulli's equation is quite useful, explanations of lift that invoke Bernoulli tend to be nothing more than fairy tales for pilots.
If the fairy tales were correct, the "weight" that an airplane (or quad copter) exerts on the ground would be reduced due to the low pressure on top of the airfoil due to the shape as the speed of the airfoil increases. Right? Guess what:
The problem with Newton:
The simplistic but totally wrong fairy tales have been told and retold for so long by so many sources (including the FAA) that people have come to believe them and won't accept a factual explanation. (Which may include Bernoulli properly applied.) The other problem being that to describe the flow fields in detail, the math gets really messy and nowadays one resorts to computational fluid dynamics. And, the inner workings of CFD are somewhat on the less than intuitive side.
Bottom line:
Tradition.
We have taught fairy tales for so long, that we will accept nothing less than a fairy tale. We even believe that experts in fluid dynamics / aerodynamics don't understand how an airplane wing generates lift. One can (and I have) provide a reasonably intuitive non-mathematical explanation that is consistent with real life and the laws of physics, but no one is really interested.
But don't listen to me. How about this:
"AEROSPACE PROFESSOR SEMINAR SERIES
How does an aircraft wing generate lift?
This talk covers common misconceptions, including equal transit-time theory and the Venturi effect, and presents some explanations that appeal to physical intuition, including flow turning and streamline curvature.
Krzysztof Fidkowski is an associate professor in the Aerospace Engineering Department at the University of Michigan. His research interests include development of robust solution techniques for computational fluid dynamics, error estimation, computational geometry management, parallel computation, large-scale model reduction, and design under uncertainty. His teaching interests are in undergraduate aerodynamics and numerical methods, and in graduate computational fluid dynamics."
Geoff "Who should really proofread before clicking on the post button" Thorpe
