Mission Delta V Budget

Mission Delta-V Budget (space-systems/mission-design/mission-delta-v-budget)

Use when the task is a spacecraft mission delta-v budget: summing the launch insertion, orbit transfer, plane change, station keeping, and deorbit contributions, applying a margin allocation, and converting the budgeted delta-v into propellant mass with the Tsiolkovsky rocket equation from the dry mass and the specific impulse.

Units convention (stated once): delta-v in m/s, masses in kg, specific impulse in seconds, g0 = 9.80665 m/s^2 (standard gravity), margin as a fraction (0.15 means 15 percent). No km/s or tonne mixing anywhere.

Domain quick reference

• Total delta-v budget: dv_total = sum of the contributions, each a positive magnitude in m/s. The classic low earth orbit to geostationary orbit mission sums launch insertion of about 1600 m/s (orbit circularization after the launch vehicle injection), the coplanar Hohmann transfer of about 3816 m/s, station keeping of about 50 m/s per year, and a deorbit burn of about 150 m/s, for a nominal total of about 5616 m/s before margin.
• Margin allocation: dv_budget = dv_total * (1 + margin_fraction). A 10 percent margin on the 5616 m/s example gives 6177.6 m/s; the margin covers modeling uncertainty, dispersions, and off-nominal maneuvers.
• Tsiolkovsky rocket equation: dv = Isp * g0 * ln(m0 / mf), with m0 the initial (wet) mass and mf the final (dry) mass. A mass ratio of e at 300 s specific impulse gives exactly 2941.995 m/s.
• Propellant mass: m_prop = m_dry * (exp(dv / (Isp * g0)) - 1). The example budget of 6177.6 m/s with a 1500 kg dry mass and a 310 s specific impulse (bipropellant class) needs about 9945 kg of propellant, so the wet mass is about 11445 kg.
• Wet mass: m0 = m_dry + m_prop, the initial mass the propulsion subsystem must accelerate. The propellant fraction m_prop / m0 for the example is about 0.87, typical of a large chemical delta-v budget.
• Plane change: an inclination change between orbits adds its own contribution, roughly 2 * v * sin(delta_i / 2); a 28.5 degree plane change at geostationary transfer orbit speed adds about 1800 m/s on top of the coplanar transfer, which is why inclined injection is preferred.
• Budget verdict: the budget closes when the budgeted delta-v (nominal plus margin) is at most the available delta-v of the propulsion subsystem; a negative reserve is a design failure, not a rounding detail.
• ECSS-E-ST-10C (systems engineering general requirements) frames mission analysis and the delta-v budget within the ECSS lifecycle; ECSS standards are free to download from https://ecss.nl/standards/ (name + paraphrase + link only).

Workflow

1. List the delta-v contributions in m/s: launch insertion, orbit transfer (Hohmann or other), plane change, station keeping over the mission life, and the deorbit or disposal burn.
2. Sum the contributions with sum_delta_v to get the nominal total; a contribution is never subtracted from the budget.
3. Apply the margin allocation with apply_margin (typically 5 to 15 percent for a pre-critical design budget) to get the budgeted delta-v.
4. Convert the budgeted delta-v into propellant mass with propellant_mass from the dry mass and the specific impulse, and get the wet mass with wet_mass.
5. Build the MissionDeltaVBudget with the contributions, margin, dry mass, and specific impulse; use fits to check the budget against the available delta-v of the propulsion subsystem.
6. Sanity-check the result: a low earth orbit to geostationary orbit mission with margin lands near 6 km/s budgeted, and the propellant fraction of a chemical spacecraft with several km/s of budget sits above 0.8.

Pitfalls

• Summing the margin twice: the margin allocation is applied to the nominal total once, and the margined total feeds the rocket equation; adding margin again inside the propellant conversion inflates the tank sizing.
• Forgetting a contribution: station keeping accumulates over the mission life (about 50 m/s per year for geostationary, more for constellations), and omitting the deorbit or disposal burn understates the budget and can miss the 25-year disposal rule.
• Using the nominal total for propellant sizing: the propellant mass must come from the budgeted delta-v (nominal plus margin), or any dispersion eats the reserve.
• Confusing dry mass and wet mass: the rocket equation works from the dry (final) mass; feeding the wet mass as mf understates the propellant requirement.
• Mixing units: a delta-v in km/s or a specific impulse in newtons per kilogram of fuel flow breaks the exponential; keep m/s and seconds.
• Treating the margin as optional: the founder mandate is a budget with margin; a zero-margin budget is a point estimate, not a budget.
• Ignoring the plane change: a coplanar Hohmann transfer is not the mission delta-v; the inclination change adds its own contribution and often dominates for high-inclination targets.

Behavior contract (gate 3)

The delta-v summation, margin allocation, Tsiolkovsky conversion, and budget class logic is exercised by the gate 3 contract test: scripts/test_mission_delta_v_budget.py against scripts/mission_delta_v_budget_logic.py (stdlib unittest, offline). Run from the repo root: python3 skills/space-systems/mission-design/mission-delta-v-budget/scripts/test_mission_delta_v_budget.py

Compliance

• Standards referenced, not reproduced: ECSS-E-ST-10C (systems engineering general requirements) frames mission analysis and the delta-v budget within the ECSS lifecycle, and the Tsiolkovsky rocket equation above is common astrodynamics methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.