Cold Gas Thruster

Cold Gas Thruster (propulsion/rocket/cold-gas-thruster)

Use when the task is sizing and assessing a cold gas thruster for spacecraft reaction control: a high pressure inert gas plenum, often nitrogen, discharges through a choked nozzle throat and produces a small thrust for attitude control. This leaf implements the standard cold gas RCS model in pure Python, stdlib only: choked nozzle mass flow from the plenum pressure and temperature, thrust from the mass flow and specific impulse, tank gas mass from the ideal gas law, isothermal blowdown of the plenum, operating time to a minimum usable pressure, and the total impulse available over the blowdown. It pairs with propulsion/rocket/rocket-engine-cycle for the feed cycle context this thruster class replaces on small spacecraft, and with propulsion/rocket/nozzle-design for the throat and expansion geometry. The boundary is strict: this leaf is the gas thruster flow and blowdown model, not a tank structural sizer and not an attitude control law.

Domain quick reference

• Choked mass flow: m_dot = P * A* / sqrt(T) * CF_CONST, where CF_CONST = sqrt(gamma/R * (2/(gamma+1))^((gamma+1)/(gamma-1))). For nitrogen with gamma = 1.4 and R = 296.8 J/(kg K), CF_CONST = 0.039746. The throat is choked while the plenum pressure ratio stays above the critical value, which holds for cold gas blowdown.
• Thrust from mass flow and specific impulse: F = m_dot * Isp * g0 with g0 = 9.80665 m/s^2. The specific impulse of a cold gas thruster is low, typically 40 to 75 s for nitrogen, because the stored gas is never heated.
• Tank gas mass: m = P * V / (R * T) from the ideal gas law. A 25 MPa, 0.03 m3 nitrogen plenum at 293 K holds about 8.62 kg.
• Isothermal blowdown: the tank is thin walled and the discharge is slow, so the gas stays near the wall temperature. Mass flow is proportional to pressure and the pressure decays exponentially: p(t) = p0 * exp(-t / tau) with tau = m_tank / m_dot0. Blowdown from 25 MPa with a 0.5 mm throat gives tau about 757 s.
• Operating time: t = tau * ln(p0 / p_min) to reach the minimum usable pressure p_min at which the thrust stays controllable.
• Total impulse: I = Isp * g0 * (m0 - m_final), the momentum of the expelled gas at the fixed specific impulse. Blowing the worked plenum down to 2 MPa yields about 5058 Ns.
• Cold gas thrusters suit small spacecraft RCS duty: simple, safe, low thrust, modest total impulse; hydrazine and electric options carry far more impulse per kilogram when the mission demands it.
• Units are SI throughout: Pa, m3, K, m, kg/s, N, s, Ns.
• ECSS frames the spacecraft propulsion context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the plenum state: pressure P0 in Pa, volume V in m3, temperature T in K, throat diameter d in m, specific impulse Isp in s and the minimum usable pressure p_min in Pa.
2. Compute the throat area A* = pi * d^2 / 4.
3. Get the initial choked mass flow with choked_mass_flow(P0, T, A*) and the thrust with thrust(m_dot, Isp). The mass flow scales linearly with plenum pressure.
4. Compute the tank gas mass with tank_gas_mass(P0, V, T) and the blowdown time constant with blowdown_time_constant(m, m_dot0).
5. Sample the pressure history with pressure_at_time(P0, t, tau) at any requested time, and find the operating time with operating_time(P0, p_min, tau).
6. Compute the gas mass left at p_min with tank_gas_mass(p_min, V, T) and the total impulse with total_impulse(Isp, m0, m_final).
7. For a one-call sizing, run size_thruster(P0, V, T, d, Isp, p_min, t_query) and read all nine outputs from the result dict.
8. Confirm the deterministic checks with the contract test scripts/test_cold_gas_thruster.py.

Worked example

A nitrogen cold gas RCS plenum: P0 = 25 MPa, V = 0.03 m3, T = 293 K, throat diameter 0.5 mm, Isp = 65 s, p_min = 2 MPa.

• Throat area: A* = pi/4 * (0.5e-3)^2 = 1.9635e-7 m2.
• Initial mass flow: m_dot0 = 25e6 * 1.9635e-7 / sqrt(293) * 0.039746 = 0.011398 kg/s.
• Thrust: F = 0.011398 * 65 * 9.80665 = 7.265 N.
• Tank gas mass: m0 = 25e6 * 0.03 / (296.8 * 293) = 8.6244 kg.
• Time constant: tau = 8.6244 / 0.011398 = 756.7 s.
• Pressure at 30 s: p = 25e6 * exp(-30 / 756.7) = 24.028 MPa.
• Operating time: t = 756.7 * ln(25 / 2) = 1911.1 s.
• Mass at p_min: m_final = 2e6 * 0.03 / (296.8 * 293) = 0.68995 kg.
• Total impulse: I = 65 * 9.80665 * (8.6244 - 0.68995) = 5057.7 Ns.
• At p_min the flow and thrust scale with pressure: m_dot_min = 0.000912 kg/s and F_min = 0.581 N, both about 8% of the initial values.

Verification

• Confirm choked_mass_flow(25e6, 293, 1.9635e-7) returns 0.011398 kg/s and thrust(0.011398, 65) returns 7.265 N.
• Confirm tank_gas_mass(25e6, 0.03, 293) returns 8.6244 kg, blowdown_time_constant(8.6244, 0.011398) returns 756.7 s and pressure_at_time(25e6, 30, 756.7) returns 24.028 MPa.
• Confirm operating_time(25e6, 2e6, 756.7) returns 1911.1 s and total_impulse(65, 8.6244, 0.68995) returns 5057.7 Ns.
• Confirm the mass flow doubles when the plenum pressure doubles, and that the pressure decay shape p(tau) = p0 / e holds.
• Confirm every non-positive pressure, temperature, volume, area, mass flow, tank mass and isp, every p_min at or above p0, and every negative query time raises ValueError.
• Run the contract test offline: python3 scripts/test_cold_gas_thruster.py (30 tests, deterministic).

Related leaves

• propulsion/rocket/rocket-engine-cycle: the pressure-fed and pump-fed feed cycle context this cold gas thruster class replaces for small spacecraft.
• propulsion/rocket/nozzle-design: throat and expansion geometry and the exit flow terms for chemical thrusters.
• propulsion/rocket/thrust-vector-control: larger engines steered mechanically, the alternative to small RCS thrusters for attitude control.
• space-systems/subsystems/propellant-tank-sizing: the plenum tank that stores the gas, sized as a pressure vessel.
• propulsion/electric/hall-thruster and the electric pack: the high impulse electric alternative for long life station keeping.

Pitfalls

• Using a high Isp for the cold gas budget: the specific impulse of a cold gas thruster is low, typically 40 to 75 s for nitrogen because the stored gas is never heated - quoting a chemical-thruster Isp inflates the total impulse and undersizes the plenum.
• Treating the blowdown as adiabatic: the model assumes isothermal blowdown (thin-walled tank, slow discharge, gas near the wall temperature), which gives the exponential p(t) = p0 * exp(-t / tau); a fast, adiabatic discharge follows a different pressure history.
• Reporting the initial thrust as the available thrust: at the minimum usable pressure the flow and thrust scale with pressure, so F_min = 0.581 N is about 8% of the 7.265 N initial value - the RCS sizing must hold across the blowdown, not at p0.
• Setting p_min at or above the plenum pressure: operating_time needs p_min below p0 for the logarithm to exist; p_min at or above p0 raises ValueError, as do negative query times.
• Computing the total impulse from the initial mass alone: the impulse is Isp * g0 * (m0 - m_final) over the expelled gas, so the gas left in the tank at p_min (0.690 kg of 8.624 kg in the example) must be subtracted, not included.
• Using the model beyond its boundary: this leaf is the gas thruster flow and blowdown model, not a tank structural sizer and not an attitude control law - the plenum tank belongs to space-systems/subsystems/propellant-tank-sizing.

Behavior contract (gate 3)

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

python3 scripts/test_cold_gas_thruster.py

The test covers the worked-example contract (mass flow 0.011398 kg/s, thrust 7.265 N, tank mass 8.6244 kg, time constant 756.7 s, pressure 24.028 MPa at 30 s, operating time 1911.1 s, total impulse 5057.7 Ns), the linear scaling of mass flow with pressure, the isothermal exponential decay shape, the size_thruster chain with all nine output keys, and ValueError rejection of non-positive pressure, temperature, volume, throat area, mass flow, tank mass and isp, p_min at or above p0, and negative query times.

Compliance

• Standards referenced, not reproduced: ECSS E-ST-35 is a free ESA download (ecss.nl/standards); the cold gas thruster relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.