Delta-v budget

Delta-v budget (or velocity change budget) is an astrogation term used in astrodynamics and aerospace industry for velocity change (or delta-v) requirements for the various propulsive tasks and orbital maneuvers over phases of a space mission.

Sample delta-v budget will enumerate various classes of maneuvers, delta-v per maneuver, number of maneuvers required over the time of the mission.

In the absence of an atmosphere, the delta-v is typically the same for changes in orbit in either direction; in particular, gaining and losing speed cost an equal effort.

Because the delta-v needed to achieve the mission usually varies with the relative position of the gravitating bodies, launch windows are often calculated from porkchop plots that show delta-v plotted against the launch time.

General principles

From the rocket equation, the delta-v of a rocket is logarithmically related to the mass ratio of the vehicle, minimising the delta-v budget as far as possible is usually very important to avoid the necessity for infeasibly big and expensive rockets.

The simplest budget can be calculated with Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bi-elliptic transfer can give a lower delta-v.

A more complex transfer occurs when the orbits are not coplanar, in that case there is an additional delta-v necessary to change the plane of the orbit, the velocity of the vehicle needs a substantial change and the delta-v is usually high. These plane changes can be almost free in some cases if the gravity and mass of a planetary body is used to perform the deflection. In other cases boosting up to a relatively high altitude apoapsis, low speed before performing the plane change can give lower total delta-v.

The slingshot effect can be used in some cases to give a boost of speed/energy; if a vehicle goes past a planetary or lunar body, it is possible to pick up (or lose) much of that body's orbital speed relative to the Sun or a planet.

Another effect is the Oberth effect- this can be used to greatly decrease the delta-v needed, as using propellant at low potential energy/high speed multiplies up the effect of a burn. Thus for example the delta-v for a Hohmann transfer from Earth's orbital radius to Mars' orbital radius is many kilometres per second, but the incremental burn from LEO over and above that to reach Earth escape velocity is far less than if the burn to reach a Mars transfer orbit is performed outside the Earth's gravity.

Because the slingshot effect and Oberth effect depend on the position and motion of bodies, the delta-v budget changes with launch time. These can be plotted on a porkchop plot.

Course corrections usually also require some propellant budget. Propulsion systems never provide precisely the right propulsion in precisely the right direction at all times and navigation also introduces some uncertainty. Some propellant needs to be reserved to correct variations from the optimum trajectory.

Launch/landing budget

The delta-v requirements for sub-orbital spaceflight can be surprisingly low. For the Ansari X Prize altitude of 100 km, Space Ship One required a delta-v of roughly 1.4 km/s. To reach low earth orbit of the space station of 300 km, the delta-v is over six times higher about 9.4 km/s. Because of the exponential nature of the rocket equation the orbital rocket needs to be considerably bigger.

• Launch to LEO — this not only requires an increase of velocity from 0 to 7.8 km/s, but also typically 1.5–2 km/s for atmospheric drag and gravity drag
• Re-entry from LEO — the delta-v required is the orbital maneuvering burn to lower perigee into the atmosphere, atmospheric drag takes care of the rest.

Stationkeeping budget

Earth–Moon space budget

Delta-v needed to move inside Earth–Moon system (speeds lower than escape velocity) are given in km/s units. This table assumes that the Oberth Effect is being used, possible with chemical propulsion but not with current electrical propulsion.

The return to LEO figures assume that a heat shield and aerobraking/aerocapture is used to reduce the speed by up to 3.2 km/s. The heat shield increases the mass, possibly by 15%. Where a heat shield is not used the higher from LEO Delta-v figure applies.

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Interplanetary budget

The spacecraft is assumed to be using chemical propulsion and the Oberth Effect.

According to Marsden and Ross, "The energy levels of the Sun-Earth L₁ and L₂ points differ from those of the Earth-Moon system by only 50 m/s (as measured by maneuver velocity)."^[7]

Delta-vs between Earth and Mars

Delta-v's in km/s for various orbital maneuvers^[5][8] using conventional rockets. Red arrows show where optional aerobraking can be performed in that particular direction, black numbers give delta-v in km/s that apply in either direction. Lower delta-v transfers than shown can often be achieved, but involve rare transfer windows or take significantly longer, see: fuzzy orbital transfers. Not all possible links are shown.

Electric propulsion vehicles going from Mars C3=0 to Earth C3=0 without using the Oberth Effect need to use a much larger deltaV of about 6km/s. The hohmann transfer from Earth C3=0 to Mars C3=0 without using the oberth effect is about 5.5km/s.^[9]

Abbreviations used

Near earth object

Near earth objects are asteroids that are in orbits that are within the orbit of Mars. The delta-v to return from them are usually quite small, sometimes as low as 60m/s, using aerobraking on Earths atmosphere (substantial reentry shields would be required).^[10]

However, the delta-v to reach them is usually rather higher, over 3.8 km/s,^[10] which is still less than the delta-v to reach the moon's surface.

However, the orbital phasing can be problematic; once rendezvous has been achieved, low delta-v return windows can be fairly far apart (more than a year, often many years), depending on the body.

In general bodies that are much further away or closer to the Sun than the Earth have more frequent windows for travel, but usually have larger delta-v's.

See also

• Bi-elliptic transfer
• Gravity assist
• Hohmann transfer
• The Oberth effect
• Tsiolkovsky rocket equation

References

External links

• Javascript Delta V calculator
• Decorative Delta-V Map
• Delft University DeltaV page

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