Aerodynamic Coefficient

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

Definition

The aerodynamic coefficient is a dimensionless parameter derived from aerodynamic forces, used to characterize the aerodynamic properties of a vehicle. The aerodynamic forces (drag $X$ , lift $Y$ , side force $Z$ ) are nondimensionalized using the dynamic pressure $q$ and reference area $S_M$ :

C_x = \frac{X}{q S_M}, \quad C_y = \frac{Y}{q S_M}, \quad C_z = \frac{Z}{q S_M}

where the dynamic pressure $q = \frac{1}{2}\rho v^2$ , with $\rho$ being the atmospheric density and $v$ the flight velocity.

Core Elements

Drag Coefficient $C_x$

Drag always acts opposite to the flight velocity direction and exists whenever there is relative motion between the vehicle and the atmosphere. The drag coefficient can be decomposed as:

C_x = C_{x0} + C_{x\alpha}(\alpha^2 + \beta^2)

where $C_{x0}$ is the zero-lift drag coefficient (at $\alpha = \beta = 0$ ) and $C_{x\alpha}$ is the induced drag coefficient.

Lift Coefficient $C_y$

Lift acts perpendicular to the velocity direction within the vehicle's plane of symmetry, primarily generated by the angle of attack $\alpha$ . Within the small-angle-of-attack range:

C_y = C_y^\alpha \cdot \alpha

where $C_y^\alpha$ is the derivative of the lift coefficient with respect to the angle of attack, a key parameter in aerodynamic design.

Side Force Coefficient $C_z$

The side force acts perpendicular to both the velocity direction and the plane of symmetry, primarily generated by the sideslip angle $\beta$ :

C_z = C_z^\beta \cdot \beta

For axisymmetric vehicles, $C_y^\alpha = -C_z^\beta$ .

Relationships Between Coefficients

Coefficient	Body Frame Representation	Velocity Frame Representation
Axial force	$C_{x1}$	—
Normal force	$C_{y1} = C_{y1}^\alpha \cdot \alpha$	—
Drag	—	$C_x$
Lift	—	$C_y = C_y^\alpha \cdot \alpha$

Application Value

Aerodynamic coefficients are the core parameters for aerodynamic force calculations, determining the aerodynamic characteristics of a vehicle under various flight conditions. During powered-phase trajectory design, the drag coefficient directly affects velocity losses. During reentry, the lift-to-drag ratio determines the vehicle's maneuverability and deceleration characteristics. Aerodynamic coefficients are typically obtained through wind tunnel testing or CFD computations.

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.