carried oxidizer to fuel ratio (oxygen and hydrogen) must be reduced to 5 or less. That means at least an airbreathing rocket or airbreathing PDR to achieve that threshold.

The weight ratio, hence the takeoff gross weight, is a direct result of the pro-pellant weight with respect to the OWE. The propellant weight is a direct function of the oxidizer-to-fuel ratio (O/F):

This equation set (4.14) is equations (4.12a) and (4.12b) repeated. 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/fuel ratio. The importance of the set (4.14) is that the gross weight is a function of one airframe parameter, OWE, and 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 4.29 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 continuous hydrogen-fueled propulsion system lying along that line. Except for the PDR, the PDEs lie below the continuous propulsion curve, hence their fuel weight to OWE ratio is less than one.

The PDR is essentially equivalent to the rocket in terms of weight ratio to orbital velocity. The PDE/ramjet is equivalent to a rocket-ramjet system and lies inline with the thermally integrated KLIN cycle at a higher oxidizer-to-fuel ratio and lower weight ratio. So the PDE/ramjet has an oxidizer-to-fuel ratio about one unit greater than the KLIN cycle and about one-half unit less in terms of weight ratio. In terms of characteristics the PDE/ramjet appears to be more like a thermally integrated rocket/turbojet than the airbreathing rocket propulsion systems. In terms of the impact on operational systems, the next set of charts will size launchers to the same mission and payload so these propulsion system differences can be evaluated in terms of launcher system size and weight.

The PDE/ram-scramjet jet is equivalent to the thermally integrated airbreathing rocket-ram-scramjet systems and lies to the left (greater O/F ratio) of the thermally integrated ram-scramjet cycles at a slightly lesser weight ratio to orbital speed near the RBCC propulsion systems of Yamanaka (scram-LACE), Builder (ejector ram-scramjet) and Rudakov (deeply cooled-ram-scramjet). From the cycle analysis the PDE appears to have performance advantages and disadvantages with respect to the continuous cycles (lesser weight ratio but greater oxidizer-to-fuel ratio) that must be evaluated on launcher-sizing programs. These three propulsion configurations were evaluated in detail. When deciding the thrust-to-weight ratio, cost of development,

and payload capability for all these various configurations must be examined without bias to determine the best overall configuration to build. These ideas require further parametric investigation to finalize the comparison.

So, while most conventional propulsion systems have fuel weight approximately equal to the OWE, the PDE propulsion systems have fuel weights that are less than the OWE, hence the advantage of PDE systems. This is a simple and fundamental relationship to judge hydrogen/oxygen propellant SSTO results. As shown in Table 4.6 for other fuels, the ratio will not be one.

In determining the launcher size for each propulsion system concept, an important parameter is the installed engine thrust-to-weight ratio. A non-gimbaled (that is fixed and not steerable by pivoting the engine) rocket engine for space operation could have an engine thrust-to-weight ratio as large as 90. For a large gimbaled engine, such as the Space Shuttle main engine (SSME) that value is about 55 for the installed engine. And this value will be the reference value. The liftoff thrust generally determines the maximum engine thrust for the vehicle. For a given vehicle thrust-to-weight ratio at liftoff or takeoff, the weight of the engines is a function of the required vehicle thrust-to-weight ratio at liftoff, the thrust margin, the weight ratio and the OWE. Thus:

TWTO = vehicle thrust-to-weight ratio at takeoff; ETWR = engine thrust-to-weight ratio; WR = weight ratio to achieve orbit speed; OWE = vehicle operational weight empty.

The weight ratio is the total mission weight ratio including all maneuvering propellant. For vertical liftoff the launcher thrust-to-weight ratio is at least 1.35. For horizontal takeoff the launcher thrust-to-weight ratio is in the 0.75 to 0.90 range. Usually if the horizontal takeoff thrust-to-weight ratio exceeds one, there is a significant weight penalty (Czysz and Vandenkerckhove, 2000). The engine thrust-to-weight ratio has been a constant source of controversy and discussion for airbreath-ing engines. One approach to avoid the arguments before the sizing procedure begins, and that has stopped the sizing process in the past, is to find a suitable relationship for determining the engine thrust-to-weight ratio. For the authors' efforts, that procedure is to assume the total installed engine weight is a constant equal to the all-rocket launcher. The resulting engine thrust-to-weight ratio for all other propulsion systems can then be determined as:

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