NASA: Predicting Stall of Wing Difficult

The New Theory of Flight is based on computational solution of the Navier-Stokes equations with slip boundary condition, which allows realistic simulation of the airflow around a wing at all angles of attack. In particular the stall angle with sudden loss of lift and increase of drag, can be accurately predicted, as well as maximal lift obtained just before stall.

On the other hand, in the text-book theory of flight based on Kutta-Zhukovsky circulation theory of lift, stall angle and maximal lift are outside the range of the mathematical model, as evidenced by NASA:

• Predicting the stall point (the angle at which the wing stalls) is very difficult mathematically. Engineers usually rely on wind tunnel tests to determine the stall point. But the test must be done very carefully, matching all the important similarity parameters of the actual flight hardware.

The fact that stall is outside the text-book theory of flight is probably viewed as both surprising and alarming by the students to which NASA directs its information. The general public enjoying air transportation is however not disturbed with this fact as part of the information from the captain before take-off.

In any case, the pilot needs to know the stall angle and maximal lift and mathematical prediction when available, offers clear advantages as compared to the alternative of direct trial and error with a real airplane.

PS NASA supplies the following info, which does not help to reduce fear of flying:

• As an object moves through the air, air molecules stick to the surface. This creates a layer of air near the surface called a boundary layer that, in effect, changes the shape of the object. The flow turning reacts to the edge of the boundary layer just as it would to the physical surface of the object. 
• To make things more confusing, the boundary layer may lift off or "separate" from the body and create an effective shape much different from the physical shape. The separation of the boundary layer explains why aircraft wings will abruptly lose lift at high angles to the flow. This condition is called a wing stall.