As a high school student, I am trying to learn more about airfoils and the theory behind it.

I started off with analyzing the NACA0012 airfoil on Autodesk CFD. I modified the lower surface as shown in the image below (the modified airfoil simulation at Angle of Attack=9 degrees).

I simulated the NACA0012 airfoil and the modified airfoil at Reynolds number 1 million (with inlet velocity of 48.655 m/s, chord length of 0.304 8m (1 foot), air density=1.20473 kg/m3, coeff of viscosity= 1.817×10-5 Pa). My simulations were incompressible flow simulations. The modified airfoil at AoA=9 I know that the NACA 0012 airfoil has its center of pressure at quarter chord point at low angles of attack by the thin airfoil theory.

In the case of my modified airfoil, I find that the centre of pressure moves from 0.596 chord length to 0.259 chord length as I vary the angle of attack from 0 to 10. I have attached an image of the center of pressure location below. The baseline airfoil is the NACA0012 airfoil and I have measured location of center of pressure from the trailing edge.

enter image description here

I also read that beyond the viscous fluid layer, near a solid, the fluid behaves like a frictionless fluid. Based on this theory, I assume that at low angles of attack, the fluid slows down and pressure increases by Bernoulli's principle beyond the viscous layer as shown in the image below.

enter image description here

I think this idea reasonably explains why the centre of pressure is closer to the trailing edge:the high pressure fluid exerts more force near the trailing edge as compared to the NACA0012 airfoil, which moves the center of pressure toward the trailing edge.

enter image description here

The NACA 0012 airfoil at AOA 0 for comparison.

Based on the viscous boundary layer theory or any other theory that I am unaware of, is it possible to explain the reason for the centre of pressure moving toward the quarter chord point at higher angles of attack? I am thinking that the viscous layer is thicker at higher angles of attack and hence the freestream fluid velocity does not decrease as much as it does at angle of attack zero. I am pretty sure this is incorrect and there is a lot more going on. Would someone mind explaining what other factors are at play or what other topics I need to know to answer this question?

Appreciate any help.

  • $\begingroup$ How do you calculate the centre of pressure - using paper and a pen? Then think about what changes to make it move. $\endgroup$
    – Solar Mike
    Jan 1 at 9:45
  • 2
    $\begingroup$ You would probably get a more thorough answer on the Aviation SE site. $\endgroup$
    – Eric S
    Jan 1 at 16:46

1 Answer 1


Theories are developed to represent something happening in reality, in a form of mathematical model. Theory is not the benchmark, reality is. You cannot use a theory to prove something which is happening in reality, but can only develop a theory so that this reality can be represented correctly. Sometimes, using a specific theory to gain reasoning for a different real occurence can lead your mind getting confused and not reaching any satisfying conclusion.

I don't know much about boundary layer and its relation to the movement of center of pressure with changing angles of attack, but I know this that as soon as you start increasing the angle of attack for any type of airfoil, then most of the pressure forces and shear forces are experienced at the airfoil's front (near the leading edge) rather than at the back (trailing edge), as proven by extensive experiements. This ofcourse has to do with the changing airflow around the airfoil, when increasing the angle of attack. Look at the figure below (taken from this link).

enter image description here

This asserts that the center of pressure should move forward because most of the amount of forces are now acting forward, and by definition, center of pressure is the location where the net forces on the complete airfoil act.

  • $\begingroup$ It also intuitively makes sense looking at stream line diagrams or videos for the same airfoil over various AOA. As AOA increases, it presents a larger obstruction Larger and a larger "hump" in the flow behind the leading edge as the stream lines try to find their way back to the airfoil surface. $\endgroup$
    – DKNguyen
    Jan 1 at 19:37

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