Center of Pressure

Let D be an arbitrary point along the chord, the moment at D reads

xd / a

Cm, D — Cm, o + Cl — (Cm, o)^_0 – 2 + 4

Setting the result to zero gives the location of the center of pressure, i. e.

xc. p. = 1 _ в (Cm, o)a=0 = 1 + 1 fC <m dx (4 53)

c 2 4a 2 a 0 c c

In general, the center of pressure will go to when a goes to zero, and will be close to the mid-chord for large incidences.

Application:

• location of the center of pressure for a flat plate and symmetric profiles: Xcc~ = 1

• location of the center of pressure for a parabolic plate of camber <: = 1 _

2 d 1

3 c a’

4.5.1 Aerodynamic Center

Taking the partial derivative da of Cm, D and setting the result to zero, gives the location of the aerodynamic center, that is

xa. c.

c

this is in sharp contrast to subsonic flow, where the aerodynamic center is located at the quarter-chord. This phenomena has been responsible for many accidents in the early days of supersonic flights. The Franco-British Concorde transport aircraft was handling the change of location of the aerodynamic center, during the transonic acceleration, by moving fuel from a tank located in the front fuselage area to a tank located in the tail area of the fuselage and doing the reverse for return to subsonic and landing, Fig.4.8.