Delta-v

In physics, delta-v refers to a difference in speed.

Depending on the delta-v situation you can refer to it as a vector (Δ Δ v{displaystyle Delta mathbf {v} ,}) or a climbing (Δ Δ v{displaystyle Delta {v},}). In both cases it is equal to the acceleration (vector or scaling) integrated in time:

Δ Δ v=v1− − v0=∫ ∫ t0t1adt{displaystyle Delta mathbf {v} =mathbf {v} _{1-}mathbf {v} _{0}=int _{t_{0}}}}{t_{1}}}{mathbf {a} ,dt} (vector version)

Δ Δ v=v1− − v0=∫ ∫ t0t1adt{displaystyle Delta {v}={v}_{1}-{v}_{0}={t_{0}}}{t_{1}}{a}{a},dt} (scalar version)

where:

• v0{displaystyle mathbf {v_{0}} ,} or v0{displaystyle {v_{0}},} is the initial speed vector or climbing at the moment t0{displaystyle t_{0},},
• v1{displaystyle mathbf {v_{1}} ,} or v1{displaystyle {v_{1}},} is the target of speed vector or scale at the moment t1{displaystyle t_{1},}.

Astrodynamics

In astrodynamics delta-v is a scalar measure for the amount of "stress" necessary to carry out an orbital maneuver, that is, the change from one orbit to another. Delta-v is normally given by the thrust of a rocket motor. The time value of delta-v is the amount of acceleration, that is, the thrust per kilogram of rocket mass at that moment. The real value of the acceleration is the sum of the gravity vector and the thrust vector.

Without gravity delta-v is, in the case of thrust in the velocity direction, simply the change in velocity. However, in a gravitational field, non-circular orbits incorporate changes in velocity without requiring any delta-v, while gravity can cause the velocity to be less than delta-v.

The Tsiolskovski rocket equation shows that the required amount of propellant can be increased dramatically, and the payload can also be drastically reduced if a higher delta-v is required. Therefore, in modern spacecraft propulsion systems, there is considerable study of ways to reduce the total delta-v required for a given spaceflight, as well as spacecraft designs capable of achieving high delta-v.

For the first, see the Hohmann transfer orbit and the gravitational spin; Furthermore, high thrust reduces the loss due to gravity.

For the second the possibilities are:

• Use several phases
• Specific impulse
• Since a high thrust cannot be combined with a high specific impulse, different motor techniques are used to different parts of the space path (those that have the greatest thrust to launch from the ground).
• Reduce the "vacuum mass" (non-propellant mass) by maintaining the ability to carry a lot of propellant, using light but resistant materials; when the other factors are equal, it is better for the propellant to have greater density since the same mass requires smaller tanks.

Delta-v is also needed to maintain satellites in orbit and is spent on station orbital maintenance maneuvers.

Launch

• To ship to low-earth orbit — it is not only required from 0 to 7.8 km/s, but also from 1.5 to 2 km/s due to atmospheric friction and gravitational loss.
• Reentered from LEO.

Delta-v required for station maintenance

Interplanetary Delta-V