What is the formula for calculating the coefficient of lift for an airfoil?

[thetexan]

TL;DR Summary

Elements of Cl

A C of L curve for a particular airfoil is calculated based on what?

I know AOA is a part of it but is there a formula for CL itself? For example...

CL= L / rho * 1/2 * V^2 * S

Which is fine.

but...

L = CL * rho * 1/2 * V^2 * S

gets a value for CL from somewhere, right?

I assume it’s calculated from some formula based on shape or camber and thickness and other factors and AOA.

if that’s true does anyone know the formula and the elements of the calculation?

for example the formula for lift includes the elements of density, velocity, and surface area and CL. What I’m looking for are the elements used in the calculation of CL itself. If that's possible.

thanks,
Tex

 

[Baluncore]

There are a few ways to get the pressures on the different parts of an airfoil. You could mount a model in a wind tunnel; You could use a finite element method; or a Joukowsky transform to turn the airfoil into a cylinder with rotation of the flow. https://en.wikipedia.org/wiki/Joukowsky_transform

Once the pressures on the surface are known they can be resolved into vertical and horizontal components and integrated over the profile, to give the lift and the drag.

 

[boneh3ad]

Ultimately, the most common way would be integrating the pressure coefficient across the surface and then splitting the resultant into its vertical and horizontal components. Still, you need to calculate $C_p$ to do that, and in general there is no "formula" to calculate these sorts of things. You have to either perform CFD of some kind, use various "simpler" theories for approximate answers, or measure it experimentally. Also note, I used the word "simpler" instead of "simple" here. None of these things are simple enough to allow calculation from a formula.

 

[thetexan]

So is the only way CL is determined on a particular airfoil by experimentation? Then those numbers made into a graph?

Is there not a CL formula like the lift formula?
I was under the impression (I don’t remember where I got it) that there was a formula that involved camber ratios and other stuff.
Tex

 

[jrmichler]

A classic book on the subject is Theory of Wing Sections, by Abbott and Von Doenhoff: https://www.amazon.com/dp/0486605868/?tag=pfamazon01-20.

It should answer all of your questions. Of course, it will take a while to fully understand it...