Delta-v

Delta-v (literally "change in velocity"), symbolised as Δv and pronounced delta-vee, as used in spacecraft flight dynamics, is a measure of the impulse that is needed to perform a maneuver such as launch from, or landing on a planet or moon, or in-space orbital maneuver. It is a scalar that has the units of speed. As used in this context, it is not the same as the physical change in velocity of the vehicle.

Delta-v is produced by reaction engines, such as rocket engines and is proportional to the thrust per unit mass, and burn time, and is used to determine the mass of propellant required for the given maneuver through the Tsiolkovsky rocket equation.

For multiple maneuvers, delta-v sums linearly.

For interplanetary missions delta-v is often plotted on a porkchop plot which displays the required mission delta-v as a function of launch date.

Definition

where

Specific cases

In the absence of external forces:

where a is the coordinate acceleration.

When thrust is applied in a constant direction this simplifies to:

Delta-v (disambiguation)

Delta V may refer to:

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Delta-v (physics)

In general physics, delta-v is simply a change in velocity. The Greek uppercase letter delta is the standard mathematical symbol to represent change in some quantity.

Depending on the situation, delta-v can be either a spatial vector (Δv) or scalar (Δv). In either case it is equal to the acceleration (vector or scalar) integrated over time:

where:

Change in velocity is useful in many cases, such as determining the change in momentum, where :, where , is momentum and m is mass.