I think the lecturer that you link to did himself a disservice by mentioning the concept of a centripetal force.
That's unpractical in the following sense: while it is true that whenever there is a centripetal force the resulting motion is curvilinear, there is logically no reason to reverse the causal relation and posit: Here we notice a curvilinear motion, let's attribute that to a centripetal force.
I recommend that you drop the idea of attributing the air flow to some centripetal force.
About wing lift
The particular cross section of a wing is good for efficiency, but simpler shapes can produce lift too.
In most cases optimizing for fuel efficiency is the way to go.
There is one class of aircraft where the wings are not optimized for fuel efficiency, but for versatility: aircrafts that are built for aerobatics.
For aerobatics performance you want wings that can readily produce lift both when they are right side up and when they are upside down.
Aerobatics aircraft wings are very flat; if the top of the wings would be curved like normal wings then flying upside down would be more difficult. The wings are almost like flat boards. Those wings will certainly leave a lot of turbulance in their wake, which of course is wasted energy. Normal aircraft wings are designed to minimize energy waste, that is the reason for the shape of the cross section
This demonstrates that the primary mechanism of wings producing lift is the angle of attack. Every wing, be it a normal wing or an aerobatics wing must have an angle of attack in order to produce lift at all.
Of course, understanding angle of attack is very straightforward. For instance, when you are in car traveling at highway speed stick your hand out the window. You feel the lift.
The whole issue of wing lift should always be discussed in terms of the following two separate issues:
- What is it that produces lift: angle of attack
- How do you optimize lift/drag ratio: that requires thorough understanding of aerodynamics
Let me elaborate on the implications of angle of attack. Using the example of a hand sticking out of car window: you hold your hand at an angle such that you try to optimize lift/drag ratio. At that angle of attack two things are happening: compression of the air moving underneath, rarefaction of the air moving over the hand. The compression and the rarefaction are counterparts. While the compression is very palpable the rarefaction is something you will not readily notice. However, the rarefaction is as important, if not more important. As long as the air flow over the hand doesn't become detached it will be deflected downwards, just as the compressed air moving underneath is deflected downwards. If the angle of attack is too large the air flow over the wing does become detached, it becomes turbulent, resulting in catastrophic loss of lift.
A webpage with a description of the design of the Mudry CAP 232 aerobatics aircraft
The Cap wing [... ] uses a symmetrical airfoil cross section [...].
The CAP wing has the same curvature on the top and the bottom
surfaces. [...] this CAP symmetrical wing works equally well whether
the angle of attack is [...] upright or inverted. And the stall speed
is the same both ways. This makes axial rolling more precise.