Free-Flight Phase

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The free-flight phase is the flight phase of a ballistic missile between the end of the powered phase and the beginning of the reentry phase. During this phase, if the warhead is not equipped with a propulsion system or control system, it coasts entirely on the energy acquired at the powered-phase terminal, following a trajectory that approximates an ellipse intersecting the Earth. The free-flight phase can be regarded as a special case of the orbital phase -- unpowered flight of a vehicle in Earth's gravitational field.

Core Elements

Motion Characteristics

The motion during the free-flight phase is fundamentally elliptical orbital motion under the two-body problem. After acquiring a certain velocity and position at the powered-phase terminal, the warhead flies along an elliptical arc under Earth's gravity until it reenters the atmosphere.

  • The ballistic trajectory is a portion of an ellipse, with the perigee typically below the Earth's surface
  • Flight altitude can reach hundreds to thousands of kilometers (for intercontinental missiles)
  • Flight time constitutes the majority of the total flight duration

Relationship with the Orbital Phase

The free-flight phase can be viewed as a special orbital phase:

  • Similarities: Both undergo conic-section motion under central gravitational attraction, governed by the same equations of motion
  • Differences: The free-flight trajectory intersects the Earth (the perigee of the ellipse is below the surface), so the vehicle will eventually meet the Earth; in contrast, the orbital phase trajectory remains entirely in orbit around Earth

Passive Phase

The free-flight phase and reentry phase of a ballistic missile are collectively referred to as the passive phase, because the warhead generally has no propulsion during these two phases. The trajectory characteristics of the passive phase (range, flight time, impact accuracy) are primarily determined by the powered-phase terminal parameters.

Modern Warhead Free-Flight Maneuvering

With technological advances, many modern warheads perform maneuvering flight during the free-flight phase to improve penetration probability. Such maneuvering can be regarded as a special case of orbital maneuvering, making the warhead trajectory more difficult to predict and increasing the difficulty of defense.

Application Value

Free-flight phase trajectory analysis is one of the core topics in long-range rocket ballistics. The relationship between free-flight trajectory parameters and powered-phase terminal parameters, the calculation of passive-phase range and flight time, and the derivation of trajectory error coefficients are all fundamental to ballistic missile design and accuracy analysis.

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.