# Info

Oxidizer-to-fuel ratio (O/F) Figure 4.23. The less the weight ratio, the less the oxidizer carried.

ratio. There is a discontinuity in the oxidizer-to-fuel ratio curve between the rocket-derived propulsion value of 6 and where airbreathing propulsion begins, at a value of 4. The airbreathing propulsion cycles move down to the right, reducing in weight ratio and oxidizer-to-fuel ratio to values 2.5 and 0.5, respectively. From equation (3.1) we have the relationship in equation (4.12a). Equation (4.12a) directly links the weight ratio to orbit to a function of the oxidizer-to-fuel ratio and the weight of fuel divided by the operational weight empty (dry weight plus trapped fluids, crew and payload). So the fuel-to-OWE ratio is multiplied by one plus the oxidizer-to-fuel ratio to produce the weight ratio. If the fuel-to-OWE ratio is approximately constant, then there is a direct benefit to incorporating airbreathing propulsion. The gross weight is reduced and the total engine thrust is reduced, greatly reducing the size, complexity and cost of the propulsion system. If the fuel-weight-to-OWE ratio is approximately constant then increased engine and turbopump size and weight is a consequence of continuing with rocket propulsion systems. In synthesis,

Rearranging equation (4.12a) we have equation (4.12b). Remember in this equation the oxidizer/fuel ratio is the oxidizer/fuel ratio carried on the launcher with its associated weight ratio, not the rocket engine oxidizer-to-fuel ratio. The importance of equations (4.12a,b) and of the graph is that it shows the gross weight is a function of one airframe parameter, OWE, and of two propulsion parameters, and that the gross weight is directly proportional to the carried oxidizer-to-fuel ratio. Reduce the carried oxidizer and the gross weight and resultant engine thrust decrease proportionately. Beginning with the rocket point in Figure 4.23 at a weight ratio of 8.1 to the ACES weight ratio of 3.0 a straight line constructed between these points has all of the hydrogen-fueled propulsion system lying along that line, except the air augmented rocket and ram rocket. The reason these two do not lie on the curve is that the engine oxidizer-to-fuel ratio is essentially unchanged and the reduction in weight ratio comes from the air entrained in the ejector system. Thus

Analyzing the data in Figure 4.23, the result is a value for Wfuel/OWE equal to 1.05 ± 0.06. So, regardless of the propulsion system, the quantity of fuel carried by a hydrogen-fueled launcher that achieves LEO lies between 99% and 111% of the OWE. This only holds true only for a hydrogen/oxygen propulsion system with a six-to-one oxygen/fuel ratio and a stoichiometric air/fuel ratio of 35.4 to one. A hydrogen/oxygen rocket with a seven-to-one oxidizer/fuel ratio will have a different value. This is an important result of the governing equations, as it fixes the fuel weight regardless of the propulsion system and focuses on the real problem,

 Fuel Hydrogen Hydrogen Kerosene Methane Hydrazine UDMHa Oxidizer 