Zero-Angle-of-Attack Reentry

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

Definition

Zero-angle-of-attack reentry refers to a reentry mode in which the total angle of attack $\eta = 0$ , the velocity direction is aligned with the vehicle's longitudinal axis, and the lift $L = 0$ . It is also known as ballistic reentry or zero-lift reentry. For a statically stable reentry vehicle, when an angle of attack exists, the stability moment reduces it until the velocity direction aligns with the longitudinal axis and the vehicle ceases to experience lift.

Core Elements

Equations of Motion

During zero-angle-of-attack reentry, since $L = 0$ (i.e., $Y = Z = 0$ ), the planar reentry equations of motion simplify to:

\left\{\begin{array}{l} \frac{\mathrm{d}v}{\mathrm{d}t} = -\frac{X}{m} - g\sin\Theta \\ \frac{\mathrm{d}\Theta}{\mathrm{d}t} = \left(\frac{v}{r} - \frac{g}{v}\right)\cos\Theta \\ \frac{\mathrm{d}r}{\mathrm{d}t} = v\sin\Theta \\ \frac{\mathrm{d}\beta_e}{\mathrm{d}t} = \frac{v}{r}\cos\Theta \end{array}\right.

Compared to lifting reentry, the equations lack the lift term $Y/(mv)$ , and the motion is entirely determined by initial conditions and drag.

Ballistic Characteristics

Characteristic	Description
Large impact point dispersion	No lift control during reentry; deviations cannot be corrected
Narrow reentry corridor	The reentry angle must be strictly limited to the allowable range
High peak load factor	No lift buffer; deceleration is severe
Lower total aerodynamic heating	Steep trajectory; shorter range and time experienced

Comparison with Lifting Reentry

Comparison Item	Zero-Angle-of-Attack Reentry	Lifting Reentry
Lift	$L = 0$	$L > 0$
Trajectory control	None	Adjustable via lift
Peak load factor	Higher	Lower
Thermal protection design	Relatively simple	Relatively complex
Impact point precision	Low	Higher

Passive Phase Trajectory Differences

The passive-phase trajectory considering atmospheric drag differs from the ideal elliptical trajectory in the following ways:

Velocities at corresponding points are unequal: $v_{\text{ascending}}(r) > v_{\text{descending}}(r)$
The descending arc is steeper than the ascending arc: $|\Theta_{\text{descending}}(r)| > |\Theta_{\text{ascending}}(r)|$
The minimum velocity point is not at the trajectory apex but on the descending arc
The passive-phase range depends on the vehicle mass

Application Value

Zero-angle-of-attack reentry is the simplest reentry mode, applicable to ballistic missile warheads and early return spacecraft. Although it suffers from large impact point dispersion and a narrow reentry corridor, the absence of lift generation or control results in lower total aerodynamic heating, making the thermal protection problem easier to address and the structural design simpler. Ballistic reentry spacecraft were the first category of reentry vehicles developed.

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.