Center of Pressure

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

The center of pressure (CP), denoted $O_{c,p}$ , is the point of application of the resultant aerodynamic force. Due to the axial symmetry of the vehicle, the center of pressure lies on the vehicle's longitudinal axis. Its position depends on the vehicle's shape and flight conditions (angle of attack, Mach number, etc.). In general, the center of pressure does not coincide with the center of mass.

Core Elements

Relationship Between Center of Pressure and Center of Mass

When the resultant aerodynamic force $\mathbf{R}$ acting at the center of pressure is translated to the center of mass $O_{c,g}$ , the force translation principle requires an additional moment — the stability moment $\mathbf{M}_{st}$ :

\mathbf{M}_{st} = \mathbf{R} \times (x_p - x_g)\mathbf{x}_1^0

where $x_p$ and $x_g$ are the distances from the center of pressure and center of mass to the nose tip of the rocket, respectively.

Effect of Center-of-Pressure Position on Stability

Condition	Effect	Stability
CP behind center of mass ( $x_p > x_g$ )	Aerodynamic moment reduces angle of attack	Statically stable
CP ahead of center of mass ( $x_p < x_g$ )	Aerodynamic moment increases angle of attack	Statically unstable
CP coincides with center of mass ( $x_p = x_g$ )	No moment	Neutrally stable

Determination of Center-of-Pressure Position

The center-of-pressure position is typically expressed using the center-of-pressure coefficient $x_{cp}$ :

x_{cp} = \frac{x_p}{l_k}

where $l_k$ is the reference length. The center-of-pressure coefficient is determined through wind tunnel testing or CFD computations and varies with Mach number and angle of attack.

Application Value

The center-of-pressure position is a critical parameter in vehicle aerodynamic layout design. For ballistic missiles and launch vehicles, the center of pressure must be behind the center of mass to achieve statically stable flight. For vehicles requiring maneuvering flight, control surface deflections can be used to shift the center-of-pressure position. During the reentry phase of cislunar space missions, the center-of-pressure position determines the trim angle of attack and lift-to-drag ratio of the reentry vehicle.

References

Zheng W, An X Y, Zhou X, He R Z. Aerospace Flight Mechanics[M]. National University of Defense Technology, 2026.
Jia P R, Chen K J, et al. Long-Range Rocket Ballistics[M]. National University of Defense Technology Press.