Powered Phase Turning Process

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

Definition

The powered phase turning process is the complete maneuver of a vehicle from vertical liftoff ( $\theta = 90°$ ) to the desired flight-path angle at engine cutoff ( $\theta = \theta_k^*$ ). The turn is achieved by generating a normal force perpendicular to the velocity vector. The normal force is primarily provided by aerodynamic lift and the normal component of thrust, with its magnitude depending on the angle of attack $\alpha$ .

Core Elements

Three Phases of the Turn

Phase	Pitch Program Angle	Angle of Attack	Characteristics
Vertical Segment	$\varphi_{pr} = 90°$	$\alpha \approx 0$	Vertical ascent, rapid transit through dense atmosphere
Turning Segment	Gradually decreasing from 90°	$\alpha \neq 0$	Generates normal force, velocity vector turns
Aiming Segment	Constant	$\alpha \approx 0$	Maintains desired velocity direction

Generation of Normal Force

From the normal acceleration equation:

\dot{\theta} = \frac{1}{mv}(P_e + C_y^\alpha q S_M)\alpha + \frac{g}{v}\cos\theta

To change the direction of the velocity vector, a normal force perpendicular to the velocity vector must be provided. Although gravity can reduce $\theta$ , its magnitude is small and it cannot be independently controlled, so it cannot serve as the primary turning force. The normal force is mainly generated by aerodynamic lift and the normal component of thrust, and its magnitude is proportional to the angle of attack $\alpha$ .

Relationship Between Angle of Attack and Control Deflection Angle

Under the instantaneous balance assumption, the angle of attack is determined by the control deflection angle:

\alpha = -\frac{\sqrt{2}P(x_g - x_c)}{2Y_1^\alpha(x_g - x_p)}\delta_\varphi

The control deflection angle $\delta_\varphi$ is determined by the difference between the actual pitch angle and the program angle.

Turning Characteristics of Stable and Unstable Rockets

Type	$x_g - x_p$	Angle of Attack Sign	Turning Characteristics
Statically Stable Rocket	$< 0$	$\delta_\varphi$ and $\alpha$ have the same sign	Naturally stable, requires continuous control to turn
Statically Unstable Rocket	$> 0$	$\delta_\varphi$ and $\alpha$ have opposite signs	Requires control system to maintain stability, fast turning response

Application Value

The turning process is the core content of powered-phase flight program design. The turning segment design directly affects cutoff parameters, flight loads, aerodynamic loads, and structural stress. Excessive turning rate leads to load factor exceedance, while insufficient turning rate increases gravity losses. The optimal turning program must balance velocity increment losses against structural loads.

References

郑伟, 安雪滢, 周祥, 何睿智. 空天飞行力学[M]. 国防科技大学, 2026.
贾沛然, 陈克俊, 等. 远程火箭弹道学[M]. 国防科技大学出版社.