Lift Coefficient - Section Lift Coefficient

Lift coefficient may also be used as a characteristic of a particular shape (or cross-section) of an airfoil. In this application it is called the section lift coefficient It is common to show, for a particular airfoil section, the relationship between section lift coefficient and angle of attack. It is also useful to show the relationship between section lift coefficient and drag coefficient.

The section lift coefficient is based on two-dimensional flow - the concept of a wing with infinite span and non-varying cross-section, the lift of which is bereft of any three-dimensional effects. It is not relevant to define the section lift coefficient in terms of total lift and total area because they are infinitely large. Rather, the lift is defined per unit span of the wing In such a situation, the above formula becomes:

where is the chord length of the airfoil.

The section lift coefficient for a given angle of attack can be approximated using the thin airfoil theory, or determined from wind tunnel tests on a finite-length test piece, with end-plates designed to ameliorate the three-dimensional effects associated with the trailing vortex wake structure.

Note that the lift equation does not include terms for angle of attack — that is because the mathematical relationship between lift and angle of attack varies greatly between airfoils and is, therefore, not constant. (In contrast, there is a straight-line relationship between lift and dynamic pressure; and between lift and area.) The relationship between the lift coefficient and angle of attack is complex and can only be determined by experimentation or complicated analysis. See the accompanying graph. The graph for section lift coefficient vs. angle of attack follows the same general shape for all airfoils, but the particular numbers will vary. The graph shows an almost linear increase in lift coefficient with increasing angle of attack, up to a maximum point, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is the stall angle of the airfoil.

The lift coefficient is a dimensionless number.

Note that in the graph here, there is still a small but positive lift coefficient with angles of attack less than zero. This is true of any airfoil with camber (asymmetrical airfoils). On a cambered airfoil at zero angle of attack the pressures on the upper surface are lower than on the lower surface.