Bipropellant O/F Ratio
Size oxidizer and fuel flow rates from a mixture ratio and total propellant flow.
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The engineering
The mixture ratio r is the ratio of oxidizer to fuel mass flow feeding the chamber. It sets the flame temperature, the combustion products, and therefore Isp — so once you pick r from a combustion analysis, this card splits a known total flow into the two feed lines (or scales a total from one measured line).
The performance-optimum r is almost always fuel-rich of stoichiometric: lighter product molecules mean higher exhaust velocity even at lower temperature. LOX/RP-1 burns stoichiometric near 3.4 but flies around 2.3–2.6; LOX/LH2 is stoichiometric at 8.0 yet typically runs 5–6. If your tank volumes come out lopsided, remember oxidizer is usually the heavier, denser side of the split.
Sanity check: fuel fraction plus oxidizer fraction always sum to 1, and mixture ratio times fuel flow must reproduce oxidizer flow.
Where this math comes from
Robert Goddard flew the first liquid-fueled rocket in 1926 on gasoline and liquid oxygen, feeding both by pressure and learning by explosion how much the proportions mattered. The German rocket program under Walter Thiel systematized mixture-ratio tuning on the A-4/V-2, trading peak temperature for cooler, more manageable fuel-rich operation.
George P. Sutton codified the modern treatment in Rocket Propulsion Elements (first edition 1949), where the mixture ratio r and its relation to characteristic velocity and specific impulse became the standard bench formulation every propulsion engineer still uses.
- 1926Robert H. GoddardFirst liquid-propellant rocket flight — gasoline and LOX proportioned by hand.
- 1942Walter Thiel / A-4 teamSystematic fuel-rich mixture tuning on the V-2 engine.
- 1949George P. SuttonRocket Propulsion Elements codifies O/F ratio and its link to Isp.
- 1971NASA SP-8087Design monograph standardizes mixture-ratio distribution and injector practice.
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