Center of Pressure—Aerodynamic Center

The center of pressure (c. p.) is the point about which the moment of the aerodynamic forces is zero.

The aerodynamics center (a. c.), also called neutral point, is the point about which the moment of the aerodynamic forces is independent of incidence.

2.7.1 Results for the Circular Cylinder

The reference length for the circular cylinder is the diameter c = 2a.

The pressure coefficient on the cylinder can be obtained from the velocity derived earlier

where Г (a) = 4n Ua sin a. See Fig. 2.16 for the two cases a = 0 and a = §.

The lift coefficient is

Ci (a) = 4п sin a (2.58)

This is a purely theoretical result, as real flow effects will dramatically change the flow field, compared to that shown in Fig. 2.9, even for small incidence angles. From the inviscid flow point of view, however, the cylinder at low incidence (near a = 0) has a lift slope which is twice the result we will find in thin airfoil theory. The maximum lift that could be achieved theoretically with the small flap device is Clmax = 4п, a very large number, when compared with high lift profiles, as we will see. This result corresponds to a = п.. See Fig.2.17.

Fig. 2.17 Ideal cylinder-with-flap lift curve

The drag coefficient for the cylinder, as for all airfoils in inviscid, incompressible flow is (d’Alembert paradox)

Cd = 0 (2.60)

In frictionless flow, the contact force between the fluid and the obstacle is normal to the surface. Hence, the center O of the cylinder is the center of pressure, i. e. Cm, o = 0 for all a’s. This result indicates that O is also the aerodynamic center.