Load Factor

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

Definition

The load factor is the resultant of all real external forces acting on a rocket excluding gravity, denoted as $\mathbf{N}$ . The acceleration produced by the load factor is the apparent acceleration $\dot{\mathbf{W}}$ . The load factor is a critical parameter for vehicle structural strength design and instrumentation selection.

\mathbf{N} = m\dot{\mathbf{W}}

Core Elements

Load Factor Components in the Body Frame

The load factor is decomposed into three components in the body frame:

Component	Symbol	Direction	Physical Meaning
Axial load factor	$N_{x1}$	Along the vehicle longitudinal axis	Resultant of engine thrust and aerodynamic drag
Normal load factor	$N_{y1}$	Perpendicular to the longitudinal axis, within the plane of symmetry	Resultant of lift and normal thrust component
Lateral load factor	$N_{z1}$	Perpendicular to the plane of symmetry	Resultant of side force and lateral thrust component

\begin{bmatrix} N_{x1} \\ N_{y1} \\ N_{z1} \end{bmatrix} = m \begin{bmatrix} \dot{W}_{x1} \\ \dot{W}_{y1} \\ \dot{W}_{z1} \end{bmatrix}

Load Factor Coefficient

The load factor coefficient is defined as the ratio of the load factor to the rocket's ground weight:

\begin{bmatrix} n_{x1} \\ n_{y1} \\ n_{z1} \end{bmatrix} = \frac{1}{g_0} \begin{bmatrix} \dot{W}_{x1} \\ \dot{W}_{y1} \\ \dot{W}_{z1} \end{bmatrix}

where $g_0$ is the standard gravitational acceleration at sea level. The load factor coefficient is a dimensionless quantity representing the multiple of the load factor relative to ground-level gravity.

Relationship Between Load Factor and Apparent Acceleration

The apparent acceleration is the quantity directly measured by the accelerometer in an inertial measurement unit (IMU), equal to the acceleration produced by all external forces except gravity. The load factor equals the apparent acceleration multiplied by the vehicle mass.

Application Value

The load factor is the core input parameter for vehicle structural strength design. The airframe structure, instrumentation, and payload must withstand the maximum load factor during powered-phase flight. For ballistic missiles, the load factor coefficient determines the structural strength requirements for the warhead during reentry. For launch vehicles, the load factor coefficient influences the design of payloads such as satellites. During powered-phase flight, the maximum axial load factor typically occurs just before first-stage engine cutoff.

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.