Delta-v (velocity increment) budget

The 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 delta-v budget is given in the next table.

A delta-v budget usually stems from oribital analysis. However, the following data subdivided over three broad categories may help you to generate a preliminary Dv budget for the mission at hand without the need for time-consuming calculations.

Given the preliminary character of the data, it is advised to add a proper margin to this data. Note that in case you require more accurate data (for instance to be able to reduce the design margin), the values given can be verified through orbit analysis in the later stages of the design. Fundamentals of orbit analysis and design are treated in amongs others TU-Delfts' course AE1801.

Launch into Low Earth Orbit (LEO)


Table: Required Delta V for launch into LEO

Manoeuvre

Delta V, km/s

Launch into LEO (including drag and gravity loss)

9.5

Impulsive shot manoeuvres


Table: Typical Delta V value(s) for impulsive shot space manoeuvres

Manoeuvre

Delta V, km/s

Orbit transfer:
LEO to GEO
LEO to GEO
GTO to GEO (1)
GTO to GEO (2)
LEO to Earth escape
LEO to Lunar Transfer Orbit (LTO)
LEO to lunar orbit
GTO to lunar orbit
LEO to LTO
LEO to Mars orbit
LEO to solar escape
Low Lunar Orbit to Descent
Moon to Low Lunar Orbit (LLO)
Mars to Low Mars Orbit (LMO)


3.95 (no plane change required)
4.2 (including plane change of 28 deg)
1.5 (no plane change required)
1.8 (incl. plane change of 28 deg.)
3.2
3.1
3.9
1.7
3.1
5.7
8.7
0.022
2.312
4.1

Orbit control:

  • Station-keeping (GEO)
  • Station-keeping in Moon orbit
  • Station-keeping in L1/L2



50-55 m/s per year
100-400 m/s/year
30-100 m/s  

Orbit control: Drag compensation

  • alt.: 400-500 km
  • alt.: 500-600 km
  • alt.: >600 km


< 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

Auxiliary tasks:

  • Spin-up or despin
  • Stage or booster separation
  • Momentum wheel unloading



5-10 m/s per manoeuvre
5-10 m/s per manoeuvre
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 DV. For example, the impulsive DV for a high T/W transfer from LEO to GEO is 4.2 km/s; for a low T/W transfer, the effective DV 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 Dv. Table: Typical DV value(s) for constant low thrust (acceleration < 0.001 m/s2) orbit transfer (propellant mass is negligible)

 Manoeuvre

Delta V, km/s

Transfer time

LEO (200 km altitude) to GEO (no plane change)

 4.71

 a is 0.001 m/s2:
 ~55 days

LEO (200 km altitude) to GEO (including 28 deg. plane change)

 5.97

 a is 0.001 m/s2:
 ~70 days

LEO to MEO (19150 km altitude; no plane change)

 3.83

 a is 0.001 m/s2:
  ~44 days

LEO to Earth escape for different values of initial acceleration-to-local gravitational acceleration:

  • 10-2
  • 10-3
  • 10-4
  • 10-5



 5.82
 6.66
 7.08
 7.43

 

LEO to Lunar orbit
GTO to Lunar orbit

 ~8
 3.6-4.5

 months-year  
 250- 450 days

LEO to Mars orbit

 ~15

 ~2.2 years 

- Transfer or trip time for constant thrust spiral is is calculated by dividing total propellant mass by mass flow. Total propellant mass is calculated using the rocket equation also known as Tsiolkowsky's equation. In case of negligible propellant mass (constant acceleration), transfer time can be calculated by dividing the velocity change by the acceleration.

- DV for LEO to GEO transfer orbit calculated using T.N. Edelbaum's equation: DV = SQRT(V1 2 - 2 V1 V2 cos (pi/2 delta-i ) + V2 2 )  where V1 is circular velocity initial orbit, V2 is circular velocity final orbit, and delta-i is plane change in degrees.

- Values for LEO to Earth escape taken from Rocket Propulsion and Spaceflight dynamics, by Cornelisse, Schoyer & Wakker, for jet exhaust to initial circular velocity ratio equal to 10.

- Value for GTO to Lunar orbit taken from SMART-1, by D. Racca

- Value for LEO to Low Lunar Orbit taken from Optimized Low-Thrust Orbit Transfer for Space Tugs, by Pukniel

- Value for LEO to Mars orbit taken from NASA-JPL.

 

 

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 511kg / 1 g/s = 511000 s = 5.91 days.

 

Naam auteur: B.T.C. Zandbergen
© 2014 TU Delft

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