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)

So let's calculate the lift:

• 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.