Delta-v

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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 (<math>\Delta \mathbf{v}\,</math>) or scalar (<math>\Delta{v}\,</math>). In both cases it is equal to the acceleration (vector or scalar) integrated over time:

<math>\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt</math> (vector version)

<math>\Delta{v} = {v}_1 - {v}_0 = \int^{t_1}_{t_0} {a} \, dt</math> (scalar version)

where:

<math>\mathbf{v_0}\,</math> or <math>{v_0}\,</math> is initial velocity vector or scalar at time <math>t_0\,</math>,
<math>\mathbf{v_1}\,</math> or <math>{v_1}\,</math> is target velocity vector or scalar at time <math>t_1\,</math>.

1 Astrodynamics
2 Delta-v's around the Solar System
- 2.1 Acronyms used
3 Games
4 See also
5 References

[edit] 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 change of delta-v is the magnitude of the acceleration caused by the engines, i.e., the thrust per kilogram total current mass. The actual acceleration vector is found by adding the gravity vector and the vectors representing any other forces acting on the object to the vector representing the thrust per kilogram.

When designing a satellite, delta-v is used as an indicator of how much fuel will be required. Actual fuel usage is more difficult to compute because the mass of a thrusting satellite is constantly changing because fuel is being burned and exhausted through the rocket nozzle. The delta-v achieved by burning the first kilogram of fuel is generally less than the delta-v achieved by burning the last kilogram. There are also other complicating factors such as engine efficiency not being a constant. The total delta-v needed is a good starting point for early design decisions since consideration of the added complexities are deferred to later times in the design process.

Without gravity or other external forces, delta-v, in the case of thrust in the direction of the velocity, is simply the change in speed. However, gravity can change an object's speed without any delta-v from an engine, so gravity can cause the change in speed to be less or more than the delta-v. Notice the somewhat subtle usage: delta-v is the change in velocity caused by thrusting of the engine and does not generally equal the total change in velocity, which includes changes due to all other forces.

It is not possible to determine delta-v requirements by considering only the total energy in the initial and final orbits. For example, most spacecraft are launched in an orbit with inclination fairly near to the latitude at the launch site, to take advantage of the earth's rotational surface speed. If it is necessary, for mission-based reasons, to put the spacecraft in an orbit of different inclination, a substantial delta-v is required, though the kinetic and potential energies in the final orbit and the launch orbit are equal.

When rocket thrust is applied in short bursts the other sources of acceleration may be negligible, and the speed change of one burst may be simply approximated by the delta-v. The total delta-v to be applied can then simply be found by addition of each of the delta-vs needed at the discrete burns, even though between bursts the magnitude and direction of the velocity changes due to gravity, e.g. in an elliptic orbit.

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, and Interplanetary Superhighway; also, a large thrust reduces gravity drag.

For the second some possibilities 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). The reason to use high thrust at launch is that the loss to gravity can be minimized; once in space, high specific impulse saves fuel.
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.