Airfoil Pressure Distributions

7.5.1 Pressure Coefficient

In measurements or calculations of the flow about airfoils, the surface pressure data are conventionally presented in terms of the pressure coefficient Cp. In incompressible flow, the definition of Cp follows from Bernoulli’s equation, that is,

then substituting into Eq. 7.28 gives

Note that C* is the pressure coefficient at the point on the airfoil when sonic conditions are first achieved, that is, M00 = M*. This point is generally not known a priori and is usually predicted on the basis of the minimum pressure coefficient found from incompressible flow. For this, the well-known Karman-Tsien relation [see Abbott & von Doenhoff (1949)] can be used where the compressible value CPM is related to the incompressible value CPi using