Delta-v (velocity increment) budget
The Δv (pronounce delta-v) budget provides information on the types of maneuvres to be performed, their number and their size (in terms of velocity change to be accomplished). An example Δv budget is given in the next table.
A Δv budget usually stems from orbital analysis. However, the following data subdivided over three broad categories may help you to generate a preliminary Δv budget for the mission at hand without the need for time-consuming calculations.The three categories are:
- Launch into Low Earth Orbit (LEO)
- Impulsive shot manoeuvres
- Constant low thrust space manoeuvres
All values given are taken from lecture notes "Aerospace Design & Systems Engineering Elements I, Part: Spacecraft (bus) Design and Sizing", B.T.C. Zandbergen, TU-Delft, LR, November 2015.
Given the preliminary character of the data, it is advised to add a proper margin to this data.
Launch into Low Earth Orbit (LEO)
Table: Required Δv for launch into LEO
Launch into LEO (including drag and gravity loss)
Moon surface into Low Lunar Orbit (LLO)
LLO to Moon surface
Mars surface to Low Mars Orbit (LMO)
Low Mars orbit to Mars surface
9.2-10.2 (depending on vehicle size and ascent trajectory)
2.0-2.6 km/s (2.2 km/s for Apollo ascent stage)
1.6-2.9 km/s (2.5 km/s for Apollo descent stage)
4.7 km/s (including effect of atmospheric drag
Impulsive shot space manoeuvres
Next table provides typical Δv value(s) for impulsive shot space manoeuvres. These are manouevres wherein the effect of burn time is considered negligible. In reality, with increasing burn times, gravity loss will increase.
Table: Typical Δv value(s) for impulsive shot space manoeuvres
MTO to Mars orbit insertion:
Highly elliptical orbit
LEO to solar escape
- 50-55 m/s per year
- 100-400 m/s/year
- 30-100 m/s
Orbit control: Drag compensation
- < 100 m/s per year max. (<25 m/s average)
- < 25 m/s per year max. (< 5 m/s average)
- < 7.5 m/s per year max.
Attitude control: 3-axis control
2-6 m/s per year
Constant low thrust space manoeuvres
Because of gravity loss, low thrust-to-weight (T/W) propulsion systems suffer a loss in performance equivalent to increasing the effective mission Δv. For example, the impulsive Δv for a high T/W transfer from LEO to GEO is 4.2 km/s; for a low T/W transfer, the effective Δv is about 5.9 km/s. However, even with gravity losses, low T/W propulsion systems can still out-perform high T/W impulsive systems, because the very high specific impulse of some low T/W systems (greater than 1000 s) more than compensates for the increase in effective Δv.
Table: Typical Δv value(s) for constant low thrust (acceleration < 0.001 m/s2) orbit transfer (propellant mass is negligible)
LEO (200 km altitude) to GEO (no plane change)
a is 0.001 m/s2: ~55 days
LEO (200 km altitude) to GEO (including 28o plane change)
a is 0.001 m/s2: ~70 days
LEO to MEO (19150 km altitude; no plane change)
a is 0.001 m/s2: ~44 days
LEO to Earth escape for different values of initial acceleration-to-local gravitational acceleration:
LEO to Lunar orbit
LEO to Mars orbit
Next figure illustrates the effect of the thrust-to-weight ratio (as a measure for the vehicle acceleration) on mission Δv for low thrust LEO to GEO transfer. With decreasing thrust-to weight ratio, the mission Δv increases.
Figure: Low thrust LEO-to-GEO orbit transfer (one-way only) including 28.5 degrees plane change (launch from Eastern Test Range)
Note: A thrust-to-weight ratio of 0.1 corresponds to an initial acceleration of about 1 m/s2.
Travel time calculation example:
Taking a(n) initial thrust-to-weight (T/W) ratio of 0.001 (initial acceleration of 0.01m/s2 ) to achieve a velocity increment of 5.9 km/s and assuming a constant acceleration leads to a transfer or travel time of about 6.8 days. For a spacecraft with an initial weight of 20000 N (~2000 kg mass), we find for the required thrust level a value of 20 N. Assuming a specific impulse of 2000 s this gives then a mass flow of ~ 1g/s. Multiplying by the travel time, this gives a propellant mass of 616 kg. On the other hand, using the rocket equation, we find an initial-to-empty mass ratio of 1.34 or an empty mass of 1489 kg. This leads to a propellant mass of 511 kg, which is ~ 100 kg below the propellant mass estimated assuming a constant acceleration. Since mass flow of propellant is constant, we find for the travel time 511 kg / 1 g/s = 511000 s = 5.91 days.