Center of Pressure Location

Variables

What it means

The center of pressure (CP) is the point on an airfoil or wing where the total aerodynamic force (lift and drag) can be considered to act. Its location moves with angle of attack. The formula relates the CP to the aerodynamic centre (AC, fixed point where moment is independent of α) and the pitching moment coefficient. In subsonic flow, the CP moves forward as α increases; for symmetrical airfoils, the CP and AC coincide. Understanding CP location is important for structural design and for calculating pitching moments. It is used in stability analysis and in control surface sizing. The formula is derived from the definition of aerodynamic coefficients.

Worked example

Common mistakes

• Center of pressure location: x_cp = x_ac − (C_m,ac / C_L).
• x_ac: Aerodynamic centre location (usually at quarter‑chord).
• C_m,ac: Pitching moment coefficient about aerodynamic centre.
• C_L: Lift coefficient.
• For symmetric airfoils, C_m,ac = 0, so x_cp = x_ac.

Applications

The center of pressure location, x_cp = x_ac − (C_m,ac / C_L), gives the point where the resultant lift force acts. It shifts with angle of attack and Mach number. Engineers use this location to determine the aerodynamic centre and to calculate the pitching moment about the center of gravity. The CP location is critical for static stability and control surface sizing. By understanding CP movement, aerospace engineers can design the aircraft CG position to ensure acceptable stability and handling qualities, and can size elevators and horizontal stabilisers effectively.

• Longitudinal static stability analysis
• Control surface sizing (elevator, stabilator)
• CG position and trim calculations
• Pitching moment and manoeuvre load analysis
• Design of variable‑geometry wings (sweep effects on CP)