# Combustion Chamber Design > Use when you must size and assess the combustion chamber of a rocket engine: compute the characteristic velocity (c-star) from the chamber pressure, the throat area, and the propellant mass flow, estimate the theoretical c-star from the chamber temperature, the molecular weight, and the specific heat ratio, size the throat area from the propellant flow and the chamber pressure, compute the thrust coefficient and the thrust from the chamber pressure and the throat area, and derive the chamber volume from L-star, the contraction ratio from the chamber area and the throat, and the vacuum specific impulse from the thrust and the mass flow. Produces the chamber sizing dict that feeds the nozzle-design and the engine balance. Trigger: rocket combustion chamber, characteristic velocity, c-star, thrust coefficient, contraction ratio, chamber pressure, chamber volume, L-star, throat area. - Skill: `ashfordeou/combustion-chamber-design` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/combustion-chamber-design` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/combustion-chamber-design/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/combustion-chamber-design --- # Combustion Chamber Design (propulsion/rocket/combustion-chamber-design) Use when the task is rocket combustion chamber design: the characteristic velocity, the throat area, the thrust coefficient, the contraction ratio, the chamber volume from L-star, and the vacuum specific impulse of the chamber upstream of the nozzle throat. ## Domain quick reference - Characteristic velocity (defining relation): c-star = Pc * At / mdot with Pc the chamber pressure in Pa, At the throat area in m^2, and mdot the propellant mass flow in kg/s; c-star has units of m/s and measures the combustion quality of the chamber. Worked: LOX/RP-1 at 7.0 MPa, throat area 0.02 m^2, and 80 kg/s gives c-star = 7e6 * 0.02 / 80 = 1750 m/s, a typical delivered value. - Theoretical c-star from gas properties: c-star = sqrt(gamma * R * Tc) / (gamma * sqrt((2 / (gamma + 1))^((gamma + 1) / (gamma - 1)))) with R = 8314 / Mw the gas constant from the molecular weight Mw in kg/kmol and Tc the chamber temperature in K. Worked: LOX/RP-1 at Tc = 3670 K, Mw = 23, gamma = 1.20 gives about 1776 m/s. The ratio of delivered to theoretical c-star is the c-star efficiency, 0.92 to 0.98; 1750 / 1776 = 0.985 in the worked case. - Throat area from the propellant flow: At = mdot * c-star / Pc. Worked: 80 * 1750 / 7e6 = 0.02 m^2, closing the loop with the defining relation. - Thrust coefficient: Cf = F / (Pc * At) with F the thrust in N; Cf is about 1.4 to 1.6 at sea level and 1.8 to 2.0 in vacuum depending on the expansion. Worked: 252 kN over 7.0 MPa and 0.02 m^2 gives Cf = 252000 / 140000 = 1.8, a vacuum-class value. Thrust from the coefficient: F = Cf * Pc * At. - Vacuum specific impulse: Isp = F / (mdot * g0) with g0 = 9.80665 m/s^2. Worked: 252000 / (80 * 9.80665) = 321.2 s, consistent with LOX/RP-1 vacuum performance. - Contraction ratio: epsilon_c = Ac / At with Ac the chamber cross section area, typically 2 to 5 for liquid engines. Worked: Ac = 0.07 m^2 over At = 0.02 m^2 gives epsilon_c = 3.5. - Chamber volume from L-star: Vc = L-star * At with L-star the characteristic chamber length in m, typically 0.5 to 1.5 m for liquid propellants; L-star sets the residence time for complete combustion. Worked: L-star = 0.9 m gives Vc = 0.018 m^3. - Throat radius: for a circular throat, r = sqrt(At / pi). Worked: At = 0.02 m^2 gives r = 0.0798 m, about 80 mm. - Theoretical c-star depends only on the gas (Tc, Mw, gamma), not on the chamber pressure; raising Pc raises the achievable thrust at fixed throat area but not the ideal c-star. ## Workflow 1. Fix the design point: chamber pressure Pc, propellant mass flow mdot, and the propellant gas properties Tc, Mw, gamma. 2. Compute the theoretical c-star with theoretical_cstar and the delivered c-star with characteristic_velocity once the throat area is known; the ratio gives the c-star efficiency. 3. Size the throat area with throat_area_from_flow(mdot, c-star, Pc); this At is the interface to the nozzle downstream. 4. Compute the thrust coefficient with thrust_coefficient, or the thrust with thrust_from_cf, and the vacuum specific impulse with vacuum_specific_impulse. 5. Select the chamber cross section and compute the contraction ratio with contraction_ratio and the chamber volume with chamber_volume(L-star, At). 6. Check the throat radius with nozzle_throat_radius for the mechanical layout, then pass At, Pc, and the gas properties to the nozzle-design leaf for the expansion downstream of the throat. ## Pitfalls - Routing the nozzle downstream of the throat here: area ratio, exit Mach, expansion, and the diverging section belong to the nozzle-design leaf; this leaf stops at the throat and hands over At. - Routing propellant choice here: mixture ratio, density impulse, and storability belong to propellant-selection; this leaf consumes the chosen propellant's Tc, Mw, and gamma. - Routing the rocket equation here: delta-v, mass ratio, and staging belong to rocket-sizing and rocket-staging; the Isp from this leaf feeds those leaves. - Routing gas turbine combustor questions here: stoichiometric fuel-air-ratio and adiabatic flame temperature for continuous-flow jet engine combustors belong to combustor-design; a rocket chamber is a different device with c-star bookkeeping. - Confusing the two c-star values: c-star = Pc * At / mdot is the measured defining value; the gas-property formula is the ideal ceiling, and their ratio is the c-star efficiency, 0.92 to 0.98. - Using psi instead of Pa or bar: c-star, Cf, and At sizing are only consistent in Pa, m^2, kg/s, and N; a pressure in bar silently shifts every result by 1e5. - Forgetting g0 in the specific impulse: Isp = F / (mdot * g0), so a 252000 N thrust at 80 kg/s gives 321 s, not 3150 s. - Accepting a contraction ratio at or below 1: the chamber must converge into the throat, so Ac must exceed At and contraction_ratio raises ValueError otherwise. - Sizing the volume without L-star: Vc = L-star * At, so a small throat at fixed L-star gives a small chamber and a short residence time, which lowers the c-star efficiency. ## Behavior contract (gate 3) The combustion chamber sizing logic is exercised by the gate 3 contract test: scripts/test_combustion_chamber_design.py against scripts/combustion_chamber_design_logic.py (stdlib unittest, offline). Run: python3 scripts/test_combustion_chamber_design.py ## Compliance - ECSS is cited as reference only for the space systems propulsion context; the characteristic velocity, thrust coefficient, L-star, and contraction ratio relations are standard rocket propulsion methodology, paraphrased here. No proprietary or copyrighted text is reproduced. - compliance: STANDARDS-REF, gated: false.