Airfoil Lift Coefficient

I believe the answer to your query is pretty well explained in two previous questions on the lift coefficient and reference area. The basic point of this latter discussion is that you measure the lift force in the wind tunnel using a force balance and compute the lift coefficient from it by the following equation:

One difference that will be important to you is that the variables change slightly when considering an airfoil as opposed to a wing or complete aircraft, for which the above equation is written. Instead of a reference area, an airfoil has a reference length. This l ref is the length of the airfoil from leading to trailing edge, a quantity called the chord and represented by c. If using English units, this length is input in feet, or in meters if using the Metric system. Also, we typically change the lift coefficient to lowercase letters to indicate that we are calculating the lift on a two-dimensional airfoil section rather than a three-dimensional wing. The above equation therefore becomes

You may notice that the units don't quite work out since we are replacing the area Sref with the length c. It is assumed that c is multiplied by a unit span dimension (1 foot or 1 meter) to make the units work out properly. This is why the lift on an airfoil section is referred to as the lift per unit span.
- answer by Jeff Scott, 14 July 2002

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