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Kuchemann's tau

Figure 3.25. Size-determining parameter group correlates with Kiichemann's tau.

Kuchemann's tau

Figure 3.25. Size-determining parameter group correlates with Kiichemann's tau.

values of tau less than 0.24, and one for values greater than 0.24. The shaded rectangle represents typical SSTO solution space for both rocket and airbreathing propulsion systems. The reason the solution space is so narrow is that, whatever the propulsion system, the quantity of hydrogen fuel is approximately the same, and therefore the volumes for the different propulsion systems are quite similar. With liquid oxygen 15.2 time more dense than liquid hydrogen, the presence or absence of liquid oxygen has a significant weight impact, but a lesser volume impact. The Kv term is a function of tau and the configuration concept and details of this formulation can be found in [Curran and Murthy, 2000]. Nominally Kv has a value of 0.4 for a wide range of tau and configurations. The Kv term is a correlation term that defines the maximum volume available for propellant as a function of vehicle size as defined by the planform area. The correlation is based on analyzing the results of hypersonic design studies from the author's experience that spans from 20 tons to 500 tons gross weight vehicles.

The ICI term consists of two elements, the propulsion index (7p) and the structural index (Istr), see equation (3.4). For an entire spectrum of propulsion systems the Ip depends mainly on turbopumps: the Ip value for a given turbopump level of performance is almost constant. Assuming a Space Shuttle main engine (SSME) propulsion system, the propulsion index for an SSTO vehicle is 4.3. For a spectrum of propulsion systems from the SSME to an airbreather that must operate to Mach 14, and that must be installed on SSTO vehicles, the propulsion index is 4.1 ± 0.2. The structural index is the total structural weight divided by the wetted area of the vehicle. This index is remarkably consistent over the passage of

Figure 3.26. All-rocket available design space is limited.

time. In 1968, the projected 1983 weight of an insulated, aluminum structure that is, both the structure and the propellant tank, was 3.5 lb/ft2 (17.1 kg/m2) [HyFac, 1970]. In 1993, NASA's estimated weight of an insulated, aluminum structure for a hypersonic waverider aircraft, that is, both the structure and the propellant tank, was 3.5 lb/ft2 (17.1 kg/m2) [Pegg and Hunt, 1993]. Using these values, the estimated range for the current value of ICI is 9 to 11. This then gives us a boundary to establish the practicality of SSTO vehicles with today's industrial capability. If the value ICI is 9 to 11 or less, the concept is practical in terms of current industrial capability. If the value of ICI of a configuration/propulsion system is greater than the boundary value, then it is doubtful the concept is practical in terms of the current industrial capability The distance the concept under consideration is from the ICI boundary is a measure of the margin, or lack of margin, with respect to the current state of the art, perhaps more meaningful than less quantitative indices such as the popular ''technology readiness level''.

Based on these definitions, the solution space is presented graphically as a function of planform area (on the ordinate), and ICI (on the abscissa), with lines of constant payload and tau forming the graphical results map. Three propulsion systems are presented for the SSTO to LEO mission (100 nautical miles or 200 km orbital altitude), with payloads varying from zero to 10 metric tons. Kiichemann's tau ranges from 0.063 to 0.20. The three propulsion systems evaluated are:

(1) All-rocket, topping cycle similar to the P&W XLR-129 or the US SSME. For hydrogen/oxygen propellants is a hypersonic glider analogous to FDL-7C/D, Figure 3.26.

(2) Rocket plus ejector ram/scramjet operating as an airbreathing system to Mach number 8, then transitioning to rocket to orbit. For hydrogen/oxygen propellants, the airbreather configuration shown in Figure 3.27.

(3) Rocket plus ejector ram/scramjet operating as an airbreathing system to Mach number 12 then transitioning to rocket to orbit. For hydrogen/oxygen propel-lants, the airbreather configuration shown in Figure 3.28.

Figure 3.26 presents the solution map for the all-rocket configuration. The bottom scale is for ICI in English units for Ip and Istr and the top scale is for ICI in SI units. The left scale is in English units and the right scale is in SI units for the planform area. The vertical bar is the ICI boundary for the all-rocket, topping cycle similar to SSME. Note that most of the design space is to the right of the ICI boundary at 9.0 to 9.5, that is, beyond the current state of the art. A kerosene-fueled supersonic cruise vehicle like Concorde has a low value of tau, about 0.035. A hydrocarbon-fueled hypersonic cruise vehicle would have a larger value of tau, about 0.063. If the designer of a SSTO chose to pattern the design after a cruise vehicle, with a low value of tau, the design would not converge, no matter what resources were expended. Note that as the payload increases, the available design space increases. One of the

SSTO Combined Cycle. Air Breathing to M = 8

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