I understand that the Bernoulli effect is a flawed explanation for the cause of lift, and does not cause much at all, but how much?
Is there any experimental data on the force caused by the Bernoulli effect? Maybe implicitly through data of the pressure difference between the top and underside of an aeroplane's wings. After that, I assume I could (crudely approximating the pressure to be acting perpendicularly to the flight direction) use $\Delta P A$ to work out the net force on the plane.
Perhaps there is another way to quantitatively analyse the extent to which the Bernoulli effect causes lift.
Edit: see this short cartoon (content similar to Mike Dunlavey's answer).