In my previous reply, I overlooked this sentence, which gets to the heart of the misunderstanding:
> It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_.
Given a situation where Bernoulli is applicable (steady-state flow and inignificant compressibility effects), if you were to measure the airflow velocity and pressure fields around the wing, you would find both that they conform to Bernoulli, and that the pressure summed over the whole wing would account for the entirety of its lift.
Alternatively, if you were to calculate the rate of change of momentum of the entire airflow affected by the wing, you would find that this also accounts for the entirety of its lift. This works even in those cases where Bernoulli is not applicable.
So we have two different approaches to calculating the lift, and summing them would give the wrong answer.
Both approaches can themselves be explained in more fundamental terms, and in both cases, it comes down to Newtonian mechanics.
Neither approach allows us to calculate what the airflow looks like and how the presence of the wing shapes it, so neither approach offers a complete explanation. For that, we need Navier-Stokes, which is also reducible to Newtonian mechanics.
What's wrong with many attempted explanations of lift, by either principle, is that they don't get the details right: they try to simplify the issues to the point where they are simply wrong.
That is a fair point, but to be clear, it does nothing to rehabilitate the notion that Newton and Bernoulli provide independent components of lift that have to be added (or, for that matter, that one is right and therefore the other is wrong, which is another common misunderstanding that has shown up elsewhere.)
Great because I maintain that Newton and Bernoulli are emphatically not independent perspectives and any explanation that ignores one or the other is incomplete :)
We have been here before :( You can have a complete explanation without Bernoulli, or including it. It is not a necessary component of a rigorous explanation.
> It's simply not _enough_ to say that it's purely angle-of-attack or geometry, and it's definitely not enough to say it's just pressure difference caused by Bernoulli, it's _both at once_.
Given a situation where Bernoulli is applicable (steady-state flow and inignificant compressibility effects), if you were to measure the airflow velocity and pressure fields around the wing, you would find both that they conform to Bernoulli, and that the pressure summed over the whole wing would account for the entirety of its lift.
Alternatively, if you were to calculate the rate of change of momentum of the entire airflow affected by the wing, you would find that this also accounts for the entirety of its lift. This works even in those cases where Bernoulli is not applicable.
So we have two different approaches to calculating the lift, and summing them would give the wrong answer.
Both approaches can themselves be explained in more fundamental terms, and in both cases, it comes down to Newtonian mechanics.
Neither approach allows us to calculate what the airflow looks like and how the presence of the wing shapes it, so neither approach offers a complete explanation. For that, we need Navier-Stokes, which is also reducible to Newtonian mechanics.
What's wrong with many attempted explanations of lift, by either principle, is that they don't get the details right: they try to simplify the issues to the point where they are simply wrong.