Dimensionless Forces

We use dimensionless force and moment coefficients defined by:

L = 0.5 ρ V2 S CL(Re, M, shape)
M = 0.5 ρ V2 S c Cm(Re, M, shape)

CL is called the lift coefficient, Cm the moment coefficient. The length2 term in our first dimensionless parameter has been replaced by the area, S. This area could be anything we choose (the contact area of the nose wheel, the wing planform area, the fuselage cross-sectional area). In a particular application people generally agree on a reference area. For car drag coefficients the frontal area is often used. For aircraft the wing area is a common reference area. The c (for chord) in the moment coefficient definition is similarly agreed upon. This "agreement" on reference area is very important as can be seen in advertisements for cars. (Automobile drag coefficients are usually based on frontal area and numbers like 0.4 are sometimes mentioned in car ads. But, the drag coefficient means nothing by itself. If we chose the reference area to be the floor area of the Fremont GM plant, we would have very low drag coefficients.)