Shape and 2D Lift Relationship

[thatjazzdude89]

TL;DR Summary

How does the geometric shape of an airfoil effect 2D lift coefficient?

I’m aware that this is a simple question to a very complex question. However, I’m curious as to how to calculate a lift coefficient simply using a 2 dimensional equation or a series of 2 dimensional equations, such as the NACA equations. I’m somewhat familiar with the lift line theory, but to be honest it seems very complex and I am not aware of a simple and practical way to apply it. By this I mean; I would like to take the NACA or 2D airfoil equations and plug them into another set of equations to arrive at a usable result for overall wing design. I apologize for any ignorance on my part; I’m a community college graduate who enjoys designing RC aircraft as a hobby, so I have not taken any aerodynamics classes or training. Thanks for any assistance.

 

[FactChecker]

Sorry, it doesn't get simpler-- it gets more complicated. In fact, that is why the wind tunnels are still so busy. Even the Navier-Stokes Computational Fluid Dynamics (CFD) calculations that supercomputer use are not completely reliable. The flight tests of a newly designed airplane are done in cautious steps to check that the aerodynamics calculations look ok to proceed to the next test step.

 

[boneh3ad]

Sorry, it doesn't get simpler-- it gets more complicated. In fact, that is why the wind tunnels are still so busy. Even the Navier-Stokes Computational Fluid Dynamics (CFD) calculations that supercomputer use are not completely reliable. The flight tests of a newly designed airplane are done in cautious steps to check that the aerodynamics calculations look ok to proceed to the next test step.

Keeps food on my table.

 

[harsh_raj]

That sounds interesting, AN EQUATION FOR LIFT!!

But its not that simple, even slight modification in airfoil shape changes its aerodynamics significantly, ultimately deciding its application.
For example, NACA C4 series are used in subsonic compressor blades because they are thick and provide good pressure disrribution. Whereas, DCA (Double Circular Airfoil) are used in transonic rotors because they are thin.
So changing shape of airfoil changes lots of things, a simple equation might not able to caplture all this.

Maybe a machine learning model with lots of data for various airfoils at different mach no. and AOA can be little help here.