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

In summary, the conversation discusses the calculation of the lift coefficient (CL) for a particular airfoil and the elements involved in the calculation. It is mentioned that the pressures on the surface of the airfoil can be obtained through various methods such as wind tunnel testing, finite element method, or a Joukowsky transform. The lift coefficient can then be determined by integrating the pressure coefficient across the surface and splitting it into vertical and horizontal components. It is noted that there is no simple formula for calculating the lift coefficient and it often requires experimentation or the use of more complex theories. The book "Theory of Wing Sections" by Abbott and Von Doenhoff is recommended as a comprehensive resource on the subject.
  • #1
thetexan
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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
 
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  • #2
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.
 
  • #3
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.
 
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  • #4
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
 
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1. What is an airfoil?

An airfoil is a shape designed to produce lift when moving through a fluid, such as air. It is commonly used in the design of wings for aircraft and blades for wind turbines.

2. What is the coefficient of lift?

The coefficient of lift is a dimensionless number that represents the amount of lift produced by an airfoil at a specific angle of attack. It is a crucial factor in determining the performance and stability of an aircraft or other aerodynamic device.

3. How is the coefficient of lift calculated?

The formula for calculating the coefficient of lift is: CL = L / (1/2 * ρ * V2 * A), where L is the lift force, ρ is the density of the fluid, V is the velocity of the air, and A is the reference area of the airfoil.

4. What factors affect the coefficient of lift?

The coefficient of lift can be affected by several factors, including the shape and size of the airfoil, the angle of attack, the airspeed, the density and viscosity of the fluid, and the surface roughness of the airfoil.

5. Why is the coefficient of lift important?

The coefficient of lift is important because it determines the amount of lift that an airfoil can produce, which is crucial for the flight and performance of an aircraft. It also helps engineers and designers to optimize the shape and design of airfoils for different applications.

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