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Comment by quibono | Hacker News Reader

> With a simple rectangular wing, the center of pressure is 1/4 of the way along the wing from the leading edge

Is there a nice way to derive this? I find it interesting it's not the exact center though I guess it makes sense given the angle of the surface.

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> Is there a nice way to derive this? “It has been found both experimentally and theoretically that, if the aerodynamic force is applied at a location 1/4 chord back from the leading edge on most low speed airfoils, the magnitude of the aerodynamic moment remains nearly constant with angle of attack. Engineers call the location where the aerodynamic moment remains constant the aerodynamic center (ac) of the airfoil” [1].

As you go faster, it goes from quarter chord to half. For a rectangle, the chord length is equal to the airfoil length.

Why quarter? It comes from thin-airfoil theory [2]. (Unintuitively, it holds across atmospheres.)

[1] https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...

[2] http://aero-comlab.stanford.edu/aa200b/lect_notes/thinairfoi...

I was asking myself the same question. I would love to see a derivation from e.g. the Navier Stokes equation for this. I think, intuitively, when you draw the streamlines under the rectangular wings, the applied force should be related to the curvature of the streamlines (which is larger at the beginning of the wing).

I made some simple 2D Navier-Stokes solver here where you can use the mouse to draw a section of a wing:

https://alexander-barth.github.io/FluidSimDemo-WebAssembly/

The color represents the pressure (I should add a proper color bar!)

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