Delta-v

In general physics, delta-v is simply the change in velocity.

Depending on the situation delta-v can be referred to as a spatial vector ($\Delta \mathbf{v}\,$ ) or scalar ($\Delta{v}\,$ ). In both cases it is equal to the acceleration (vector or scalar) integrated over time:

$\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt$

(vector version)

$\Delta{v} = {v}_1 - {v}_0 = \int^{t_1}_{t_0} {a} \, dt$

(scalar version)

where:

• $\mathbf{v_0}\,$

or ${v_0}\,$
is initial velocity vector or scalar at time $t_0\,$

,

• $\mathbf{v_1}\,$

or ${v_1}\,$
is target velocity vector or scalar at time $t_1\,$

.

Astrodynamics

In astrodynamics delta-v is a scalar measure for the amount of "effort" needed to carry out an orbital maneuver, i.e., to change from one orbit to another. A delta-v is typically provided by the thrust of a rocket engine. The time-rate of delta-v is the magnitude of the acceleration, i.e., the thrust per kilogram total current mass, produced by the engines. The actual acceleration vector is found by adding the gravity vector to the vector representing the thrust per kilogram.

Without gravity, delta-v is, in the case of thrust in the direction of the velocity, simply the change in speed. However, in a gravitational field, orbits which are not circular involve changes in speed without requiring any delta-v, while gravity drag can cause the change of speed to be less than delta-v.

When applying delta-v in the direction of the velocity and against gravity the specific orbital energy gained per unit delta-v is equal to the instantaneous speed. For a burst of thrust during which both the acceleration produced by the thrust, and the gravity, are constant, the specific orbital energy gained per unit delta-v is the mean value of the speed before and the speed after the burst.

The rocket equation shows that the required amount of propellant can dramatically increase, and that the possible payload can dramatically decrease, with increasing delta-v. Therefore in modern spacecraft propulsion systems considerable study is put into reducing the total delta-v needed for a given spaceflight, as well as designing spacecraft that are capable of producing a large delta-v.

For examples of the first, see Hohmann transfer orbit, gravitational slingshot; also, a large thrust reduces gravity drag.

For the second some possiblities are:

• staging
• large specific impulse
• since a large thrust can not be combined with a very large specific impulse, applying different kinds of engine in different parts of the spaceflight (the ones with large thrust for the launch from Earth).
• reducing the "dry mass" (mass without propellant) while keeping the capability of carrying much propellant, by using light, yet strong, materials; when other factors are the same, it is an advantage if the propellant has a high density, because the same mass requires smaller tanks.

Delta-v is also required to keep satellites in orbit and is expended in orbital stationkeeping maneuvers.

See also

• Delta-v budget
• Gravity drag
• Orbital maneuver
• Orbital stationkeeping
• Spacecraft propulsion
• Specific impulse
• Tsiolkovsky rocket equation

External links

• http://www.pma.caltech.edu/~chirata/deltav.html