Propellant Tank Sizing

Propellant Tank Sizing (space-systems/subsystems/propellant-tank-sizing)

Use when the task is sizing a spacecraft propellant tank from the propellant mass budget of the propulsion bus: converting the propellant mass into the liquid volume with the propellant density, adding the ullage volume for the required ullage fraction, computing the total spherical tank volume and its radius, sizing the membrane wall thickness from the burst pressure and the material allowable, estimating the tank shell mass, and sizing the pressurant gas mass for the regulated or blowdown pressurization scheme. This leaf implements the standard tank sizing chain in pure Python, stdlib only. It pairs with space-systems/mission-design/mission-delta-v-budget upstream, the leaf that converts the mission budget into the propellant mass this sizing consumes, and with space-systems/subsystems/thermal-design, the other spacecraft bus sizing sibling.

Domain quick reference

• Propellant volume: V_p = m / rho, where m is the propellant mass and rho the propellant density at the reference temperature.
• Ullage volume: the ullage fraction u is a fraction of the TOTAL tank volume, so V_ullage = V_p * u / (1 - u). The propellant occupies the remaining (1 - u) of the tank.
• Tank volume: V_t = V_p / (1 - u), the sum of the propellant and ullage volumes.
• Sphere radius: r = (3 * V_t / (4 * pi))^(1/3) for a spherical tank.
• Burst pressure: p_burst = burst_factor * MEOP, with burst factor 2.0 a typical proof margin over the maximum expected operating pressure.
• Wall thickness (thin-walled sphere membrane): t = p_burst * r / (2 * sigma_ult), from the hoop stress balance 2 * sigma * t / r = p.
• Shell mass: m_shell = 4 * pi * r^2 * t * rho_material * f_boss, where f_boss covers bosses and welds.
• Tank mass fraction: m_shell / m_propellant, the sanity metric that gates the bus design against a typical 0.20 budget.
• Pressurant mass (ideal gas): m_gas = P * V_ullage / (R * T), at the operating pressure of the scheme. A regulated system holds MEOP; a blowdown system starts at MEOP and falls to MEOP / ratio.
• Blowdown pressure range: p_initial = MEOP, p_final = MEOP / ratio for a given blowdown ratio.
• Units are SI throughout: kg, m3, m, Pa, K. The helium gas constant is 2077.0 J/(kg K).
• ECSS frames the spacecraft engineering context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the propellant budget: propellant_mass_kg from the mission delta-v work and propellant_density_kg_m3 for the chosen propellant (hydrazine is about 1008 kg/m3).
2. Choose the ullage fraction (typically 0.06 of the total volume) and convert mass to volume with propellant_volume_m3.
3. Add the gas volume with ullage_volume_m3 and close the total with tank_volume_m3, then get the sphere radius with sphere_radius_m.
4. Set the pressure case: meop_pa, the burst factor (typically 2.0) and the material ultimate, then burst_pressure_pa and wall_thickness_m.
5. Estimate the structure: shell_mass_kg with the material density (Ti-6Al-4V is about 4430 kg/m3) and the boss factor (typically 1.10).
6. Size the pressurant: pressurant_mass_kg at the MEOP for a regulated system or at the initial pressure for blowdown, and blowdown_pressure_range for the blowdown scheme.
7. Run analyze with the full input dict to get every quantity plus the tank mass fraction and the "tank-sizing-pass" or "tank-sizing-fail" verdict against the typical 0.20 budget.
8. Confirm the deterministic checks with the contract test scripts/test_propellant_tank_sizing.py.

The ullage fraction, burst factor and boss factor are documented typical values; they are program inputs and must come from the actual tank specification, not from this leaf.

Worked example

Hydrazine monopropellant tank: mass 100 kg, density 1008 kg/m3, ullage fraction 0.06, MEOP 2.0 MPa, burst factor 2.0, Ti-6Al-4V ultimate 900 MPa, material density 4430 kg/m3, helium pressurant at 293 K, regulated scheme at the MEOP.

• Propellant volume: 100 / 1008 = 0.099206 m3.
• Ullage volume: 0.099206 * 0.06 / 0.94 = 0.0063323 m3.
• Tank volume: 0.099206 / 0.94 = 0.105539 m3.
• Sphere radius: (3 * 0.105539 / (4 * pi))^(1/3) = 0.29319 m.
• Burst pressure: 2.0 * 2.0 = 4.0 MPa; wall thickness: 4e6 * 0.29319 / (2 * 900e6) = 6.5153e-4 m = 0.6515 mm.
• Shell mass: 4 * pi * 0.29319^2 * 6.5153e-4 * 4430 * 1.10 = 3.4296 kg.
• Tank mass fraction: 3.4296 / 100 = 0.0343, well inside the 0.20 budget, so the verdict is "tank-sizing-pass".
• Pressurant mass (regulated at MEOP): 2e6 * 0.0063323 / (2077 * 293) = 0.020811 kg of helium.
• Blowdown case: ratio 2.5 at the same MEOP gives p_initial 2.0 MPa and p_final 0.8 MPa; the pressurant is sized at the initial pressure, so the gas mass is the same 0.020811 kg with these inputs.
• Fail construction: keeping the same radius and thickness but a material density of 30000 kg/m3 raises the shell to about 23.2 kg, fraction 0.232 above 0.20, so the verdict flips to "tank-sizing-fail".

Pitfalls

• Taking the typical values as the design: the ullage fraction, burst factor, and boss factor are documented typicals (0.06, 2.0, 1.10) that must come from the actual tank specification; the leaf itself says they are program inputs.
• Adding ullage the wrong way: the ullage fraction is a fraction of the TOTAL tank volume, so V_ullage = V_p * u / (1 - u), not u times the propellant volume.
• Sizing the wall from MEOP instead of burst pressure: the membrane thickness uses p_burst = burst_factor * MEOP; a burst-factor slip of 1.0 (rejected by validation) halves the wall and the shell mass.
• Confusing the pressurization schemes: a regulated system holds MEOP while a blowdown system starts at MEOP and falls to MEOP / ratio, with the pressurant sized at the initial pressure; picking the wrong scheme changes the gas mass and the pressure case.
• Judging the bus on the raw shell alone: the gate is the tank mass fraction m_shell / m_propellant against the 0.20 budget (0.0343 in the worked example), so a heavy propellant load can mask an overbuilt tank and vice versa.
• Sizing pressurant with the wrong gas constant: helium is 2077.0 J/(kg K); a nitrogen or other-gas constant silently rescales the pressurant mass.

Verification

• Confirm propellant_volume_m3(100, 1008) returns 0.099206 m3.
• Confirm analyze returns a tank volume of 0.105539 m3, a radius of 0.29319 m, a wall thickness of 6.5153e-4 m and a shell mass of 3.4296 kg for the worked example inputs.
• Confirm the sphere round-trip: sphere_radius_m then 4/3 * pi * r^3 recovers the tank volume.
• Confirm the blowdown range p_final = MEOP / ratio and that the blowdown pressurant mass is computed at the initial pressure.
• Confirm the verdict flips to "tank-sizing-fail" only when the tank mass fraction exceeds 0.20.
• Confirm every non-positive mass, density, pressure, temperature, radius and thickness, burst factors at or below 1.0, ullage fractions outside (0, 1), an unknown pressurization mode and blowdown without a ratio raise ValueError.
• Run the contract test offline: python3 scripts/test_propellant_tank_sizing.py (49 tests, deterministic).

Related leaves

• space-systems/mission-design/mission-delta-v-budget: upstream leaf that converts the mission budget into the propellant mass this tank sizing consumes.
• space-systems/subsystems/thermal-design: the thermal control sizing sibling of the spacecraft bus, paired on the same spacecraft.
• space-systems/subsystems/solar-array-sizing: the power side of the bus mass and volume trade around the tank.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_propellant_tank_sizing.py

The test covers the worked-example sizing contract (volumes, radius, burst pressure, wall thickness, shell mass, pressurant mass within the stated tolerances), ullage fraction edges, sphere volume round trip, boss factor effect, the regulated and blowdown pressurant sizing, the blowdown pressure range, the fail-verdict construction and its 0.20 boundary, the documented-default analyze path, and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: ECSS is a free ESA download (ecss.nl/standards); the tank sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.