Delta-v

Delta-v (more known as "change in velocity"), symbolized as ∆v and pronounced delta-vee, as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or landing on a planet or moon, or an 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 said spacecraft. A simple example might be the case of a conventional rocket-propelled spacecraft, which achieves thrust by burning fuel. Such a spacecraft's delta-v, then, would be the change in velocity that spacecraft can achieve by burning its entire fuel load. Delta-v is produced by reaction engines, such as rocket engines, and is proportional to the thrust per unit mass and the burn time. It 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. where () is the instantaneous thrust at time . () is the instantaneous mass at time . In the absence of external forces: where is the coordinate acceleration. When thrust is applied in a constant direction (/ is constant) this simplifies to: which is simply the magnitude of the change in velocity. However, this relation does not hold in the general case: if, for instance, a constant, unidirectional acceleration is reversed after (_1 − _0)/2 then the velocity difference is 0, but delta-v is the same as for the non-reversed thrust. For rockets, "absence of external forces" is taken to mean the absence of gravity and atmospheric drag, as well as the absence of aerostatic back pressure on the nozzle, and hence the vacuum I_sp is used for calculating the vehicle's delta-v capacity via the rocket equation. In addition, the costs for atmospheric losses and gravity drag are added into the delta-v budget when dealing with launches from a planetary surface.