Characteristic Velocity

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

Definition

Characteristic velocity $v_{ch}$ is the sum of the absolute values of all velocity impulses in an orbital maneuver, i.e., $v_{ch} = \sum|\Delta v_i|$ . Characteristic velocity is the core metric for evaluating the fuel consumption of an orbital maneuver and directly determines the amount of propellant the spacecraft must carry.

Core Elements

Basic Definition

v_{ch} = |\Delta v_1| + |\Delta v_2| + \cdots + |\Delta v_n|

The relationship between characteristic velocity and actual fuel consumption is given by the Tsiolkovsky rocket equation:

\frac{\Delta m}{m_0} = 1 - \exp\left(-\frac{v_{ch}}{I_{sp} g_0}\right)

Characteristic Velocity for Typical Orbit Transfers

Transfer Scheme	Characteristic Velocity
Hohmann transfer	$v_{ch} = \Delta v_1 + \Delta v_2$
Bi-elliptic transfer	$v_{ch} = \Delta v_1 + \Delta v_2 + \Delta v_3$
Infinite bi-elliptic transfer	$v_{ch} = (\sqrt{2}-1)\left(\sqrt{\mu/r_1} + \sqrt{\mu/r_2}\right)$

Characteristic Velocity for Orbit Adjustment

For orbit adjustment maneuvers, the total characteristic velocity of two tangential impulses:

v_{ch} = |\Delta v_{t1}| + |\Delta v_{t2}|

When $\Delta a$ and $\Delta e$ have the same sign:

v_{ch} = na\frac{|\Delta a|/a - e|\Delta e|}{2}

When $\Delta a$ and $\Delta e$ have opposite signs:

v_{ch} = na\frac{|\Delta a|/a + e|\Delta e|}{2}

Minimum Energy Condition

For orbit adjustments, the most energy-efficient scheme is to apply the velocity impulse tangentially at the orbit's perigee.

Application Value

Characteristic velocity is the core parameter for comparing orbital maneuver schemes. During the design phase, the scheme with the least fuel consumption is selected by comparing the characteristic velocities of different transfer options. Characteristic velocity is also directly used to determine the spacecraft's propellant budget and is an important input for mission analysis and spacecraft design.

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.