# Lift equation

1. Feb 2, 2005

### BigStelly

Hello All....
I am just wondering about something.

The lift equation is,

$$L= \frac {C_L \rho A V^2} 2$$

where $$C_L=$$ coeficient of lift
$$\rho=$$ air density
$$A=$$ area of wingspan
$$V=$$ velocity of the aircraft

Does anyone have idea on what the typical coeficient of lift is? I know its calculated based on angle of attack and whatnot but does anyone know how this is done? any help greatly appreciated!

edit: fixed latex

Last edited by a moderator: Feb 3, 2005
2. Feb 2, 2005

### Andrew Mason

I think it must be derived empirically. It would depend on the wing design and the way air flows around the wing. That is, I think, why aerospace engineers have wind tunnels. They design a wing and test it to find its lift coefficient. They can then determine how the lift varies as a function of velocity and air density/temperature. Put it this way, would you want to fly in an airplane whose lift coefficient was based on an engineer's calculation or would you prefer one whose lift was determined from testing?

AM

3. Feb 3, 2005

### anders

I think I read somewhere that a very approximate value for the lift coefficient of a flat plate is

L=1.05*sin(2*a)

where a is the angle of attack (I have to say again that this is just a ballpark figure).

Also, the lift-coefficient can be determined analytically for some very simple wing-shapes. It can be determined with good accuracy using numerical methods for arbitrary shapes. Also, the lift-coefficient is dependent on the reynolds-number (there is more info on reynolds-numbers on www.wikipedia.com).

4. Mar 8, 2007

### mrbeachbum

Analytical Derivation for Coeffient of Lift

The lift equation pictured above is used for calculating the lift of a known airfoil under various conditions (an airfoil is by definition the 2-D geometry of a given wing). This is used more for sizing a wing, and not to find the coeffient of lift. The total lift of a particular wing is also affected by the Aspec Ratio, the span of a wing squared divided by the total area.

If you want to determine the Coeffient of lift for a new airfoil, you have to first determine the flow field around the given geometry. Notice: the velocity around the airfoil is a function of the angle of attack. In addition, the velocity immediately over the surface is not the only one that needs to be known, the entire flow field must be defined. There are many vortex and recirculation phenomena which need to be accounted for when designing (or determining the performance of) an airfoil. Once the velocity around the airfoil is known, the pressure over the surface can be found using the Bernoulli equation. This is not a simple exercise. Most aerodynamics courses spend the bulk of their time covering this material.

Wind tunnels are also used, but they are being replaced by Computational Fluid Dynamics, in which the above is calculated on a computer. This is also quite difficult for lay-men, as the average CFD software package is at least \$5,000. The software package also have many inherent assumptions about the user, like a thorough understanding of grid generation, aerodynamics, and thermodynamics.

The easiest way to find the coefficient of lift is to look it up, and use a pre-defined airfoil.

If you look up NACA and NASA airfoils, you will find everything you need.

5. Oct 24, 2007

### white flock

Coefficient of lift

Sorry i had ot takemy work off

Last edited: Oct 24, 2007