Calculating Lift Based on Experimental Test Results
In 1915, the U.S. Congress created the National Advisory Committee on Aeronautics (NACA -- a precursor of NASA). During the 1920s and 1930s, NACA conducted extensive wind tunnel tests on hundreds of airfoil shapes (wing cross-sectional shapes). The data collected allows engineers to predictably calculate the amount of lift and drag that airfoils can develop in various flight conditions.The lift coefficient of an airfoil is a number that relates its lift-producing capability to air speed, air density, wing area and angle of attack -- the angle at which the airfoil is oriented with respect to the oncoming air flow (we'll discuss this in greater detail later in the article). The lift coefficient of a given airfoil depends upon the angle of attack.
 Image courtesy NASA The lift-curve slope of a NACA airfoil |
Here is the standard equation for calculating lift using a lift coefficient:
 |
|
L = lift Cl = lift coefficient (rho) = air density V = air velocity A = wing area |
As an example, let's calculate the lift of an airplane with a wingspan of 40 feet and a chord length of 4 feet (wing area = 160 sq. ft.), moving at a speed of 100 mph (161 kph) at sea level (that's 147 feet, or 45 meters, per second!). Let's assume that the wing has a constant cross-section using an NACA 1408 airfoil shape, and that the plane is flying so that the angle of attack of the wing is 4 degrees.
We know that:
- A = 160 square feet
- (rho) = 0.0023769 slugs / cubic foot (at sea level on a standard day)
- V = 147 feet per second
- Cl = 0.55 (lift coefficient for NACA 1408 airfoil at 4 degrees AOA)
- Lift = 0.55 x .5 x .0023769 x 147 x 147 x 160
- Lift = 2,260 lbs
Try your hand at airfoil design on NASA's Web site using a virtual wind tunnel.
