Solid Rocket Motor

Solid Rocket Motor (propulsion/rocket/solid-rocket-motor)

Use when the task is solid propellant rocket motor design and ballistics: burn-rate law, chamber pressure equilibrium, grain geometry and web thickness, mass flow through the throat, thrust, and total impulse. This leaf is the ballistic core of the rocket pack; it pairs with propulsion/rocket/nozzle-design (exit flow and thrust terms downstream of the chamber) and with propulsion/rocket/combustion-chamber-design, propulsion/rocket/propellant-selection, and propulsion/rocket/rocket-sizing.

Domain quick reference

• Burn-rate law (Vieille / St. Robert): the regression rate of the burning surface is r = a * p^n, with pressure exponent n typically 0.2 to 0.5 for composite propellants and coefficient a set so that rates of 2 to 8 mm/s result at operating pressure.
• Chamber pressure equilibrium: the pressure settles where the mass generated by the burning surface, rho_p * A_b * r, equals the choked mass flow through the throat, p_c * A_t / c*. Solving gives p_c = (rho_p * a * A_b * c* / A_t)^(1/(1-n)). The exponent is singular at n = 1: no finite equilibrium exists in that limiting case.
• Grain geometry: the web is the thickness of propellant consumed normal to the burning surface; burn time is web / r. For a tubular grain the inner-bore burn area is pi * D_inner * L, ignoring end faces.
• Burn progression: a burn area that grows as the web burns is progressive, one that holds is neutral, one that shrinks is regressive. Progressive grains raise pressure and thrust over the burn; regressive grains decay; neutral grains hold a plateau.
• Mass flow: m_dot = p_c * A_t / c* (choked throat), equal at equilibrium to rho_p * A_b * r.
• Thrust: F = Isp * g0 * m_dot, with g0 = 9.80665 m/s^2.
• Total impulse: I_t = F * t_b, or equivalently Isp * g0 * m_prop.
• Characteristic velocity: c* = sqrt(R * T_c / (gamma * (2/(gamma+1))^((gamma+1)/(gamma-1)))); typical AP/HTPB values near 1550 to 1600 m/s.
• Typical composite propellant (AP/HTPB): ammonium perchlorate oxidizer in a hydroxyl-terminated polybutadiene binder, density about 1700 to 1850 kg/m^3, sea-level specific impulse about 240 to 260 s.
• Units are SI throughout: Pa, m, m^2, m/s, kg/s, K, N, N*s.
• ECSS space-systems standards frame the rocket propulsion context; the ballistics relations above are standard engineering methodology, summary-only.

Workflow

1. Collect the propellant data: density rho_p, burn-rate coefficient a and exponent n, and the chamber temperature, gamma, and gas constant R for the characteristic velocity.
2. Compute the characteristic velocity with characteristic_velocity.
3. Choose the grain geometry and throat area; get the burn area with tubular_grain_burn_area (or the equivalent for the chosen geometry) and the web thickness.
4. Solve the equilibrium chamber pressure with equilibrium_chamber_pressure.
5. Get the operating burn rate with burn_rate at that pressure.
6. Compute the mass flow with mass_flow (or burn_mass_flow as the burn-side cross-check) and the thrust with thrust_from_isp.
7. Estimate the burn time with web_burn_time and the total impulse with total_impulse, cross-checked by total_impulse_from_propellant.
8. Judge the grain with burn_area_verdict from the initial and final burn areas (progressive, neutral, or regressive).
9. Confirm the deterministic checks with the contract test scripts/test_solid_rocket_motor.py.

Worked example

A tubular AP/HTPB grain with rho_p = 1800 kg/m^3, a = 2.0e-5 m/s per Pa^n, n = 0.3, inner-bore burn area A_b = 0.14 m^2, throat area A_t = 1.0e-4 m^2, and c* = 1600 m/s:

• Equilibrium pressure: p_c = (1800 * 2.0e-5 * 0.14 * 1600 / 1.0e-4) ^(1/0.7), about 10.2 MPa.
• Burn rate at equilibrium: r = a * p_c^n, about 2.5 mm/s.
• Mass flow: p_c * A_t / c*, about 0.64 kg/s (the burn side rho_p * A_b * r matches within rounding).
• Thrust at Isp = 250 s: F = 250 * 9.80665 * 0.64, about 1.57 kN.
• Burn time for a 20 mm web: t_b = 0.02 / 0.0025, about 7.9 s.
• Total impulse: F * t_b, about 12.4 kN*s, matching Isp * g0 * m_prop with the propellant mass rho_p * A_b * web = 5.04 kg.

A grain whose inner bore grows as it burns gives a growing burn area and is progressive; a sliver or rod geometry that loses surface is regressive; a star or wagon-wheel geometry cut for constant surface is neutral.

Related leaves

• propulsion/rocket/nozzle-design: exit Mach, choked mass flow, exit velocity, and thrust with the pressure term downstream of the chamber.
• propulsion/rocket/combustion-chamber-design: chamber geometry and structural sizing around the ballistic solution.
• propulsion/rocket/propellant-selection: propellant families and their burn-rate and impulse properties.
• propulsion/rocket/rocket-sizing: motor selection and sizing inside the full launch vehicle mass and performance loop.

Pitfalls

• Assuming a neutral grain stays neutral as the web burns: the burn area verdict must be re-checked for the geometry - a tubular bore that grows with web is progressive, a sliver or rod that loses surface is regressive, and only a star or wagon-wheel cut for constant surface is neutral.
• Setting the pressure exponent near unity: the equilibrium solution p_c = (rho_p * a * A_b * c* / A_t)^(1/(1-n)) is singular at n = 1 - no finite chamber pressure exists in that limiting case, and the module rejects it rather than returning a huge pressure.
• Balancing the chamber on the throat side alone: equilibrium requires the burn-side mass flow rho_p * A_b * r to equal the choked throat flow p_c * A_t / c*; the worked example cross-checks both sides (about 0.64 kg/s each), so a mismatch between them means an input error, not a motor quirk.
• Mixing burn-rate coefficient units: with r = a * p^n the coefficient a is expressed per Pa^n (2.0e-5 m/s per Pa^n in the example) - a coefficient tabulated in other pressure units shifts the whole pressure equilibrium.
• Feeding zero burn area or zero throat area: both raise rejection because the equilibrium has no physical content - a zero throat with a burning grain would pressurize without bound.
• Reporting thrust without the impulse check: total_impulse from F * t_b must match Isp * g0 * m_prop (about 12.4 kN*s both ways in the example); the propellant-mass route catches thrust or burn-time slips.

Behavior contract (gate 3)

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

python3 scripts/test_solid_rocket_motor.py

The test covers the burn-rate law and exponent thresholds, the characteristic velocity band, the chamber pressure equilibrium identity (burn-side mass flow equals choked throat mass flow), the n = 1 limiting case, zero burn area and zero throat area rejection, mass flow, thrust, total impulse from thrust and from propellant mass, tubular grain burn area, web burn time, and the burn progression verdict.

Compliance

• Standards referenced, not reproduced: ECSS is a free ESA download (ecss.nl/standards); solid propellant ballistics is standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.