ENGINEERING NOTES 1177into Earth orbit is independent of launch vehicle size and equals the cost of every 4 kw installed into an electric upper stage, also independent of size. It is important to realize that neither payload cost nor the cost of an electric stage can be expected to be independent of size; the results obtained by means of this simplification can therefore not be of general validity. However, this simple-minded assumption will be found of considerable help in illustrating the method. A circular orbit around Jupiter with an altitude of 20 planetary radii is to be established. Under these conditions, the diagram shown in Fig. 4 may be constructed. As in the previous figures, the payload is plotted along the ordinate whereas the initial mass capability of the ballistic system is plotted along the bottom abscissa. In order to obtain the performance boundary for systems of equal cost, rather than systems of equal initial mass, the horizontal scale at the top of the diagram, which is determined by the tradeoff ratio, has been used for the performance of the hybrid vehicles. Under these conditions, along any vertical line ballistic and hybrid systems exhibit the same recurrent cost. For the hypothetical cost assumptions used in this Note, a hybrid system which equals the cost of a ballistic system must be based on a launch vehicle whose initial mass capability is approximately 48% of the initial mass capability of the ballistic counterpart, i.e., the tradeoff ratio is 0.48. Comparing Fig. 4 to Fig. 1, it becomes evident that the equal performance boundary has been modified by the inclusion of the equal cost groundrule. Specifically, the area of ballistic superior performance has been enlarged in such a way as to roughly double the magnitude of the payload maximum. The shaded line indicates the physical limit of capability for the ballistic system. Below this line, the ballistic system is capable of performing the mission but, outside the area B, requires more trip time than the hybrid system. To further aid in the comparison, the hybrid performance lines for the longest (1000 days) and shortest (600 days) ballistic trip times are also shown in the diagram as broken lines inside H, the area of superior hybrid performance. Concluding RemarksA method has been developed which allows one to compare the performances of space propulsion systems of widely differing characteristics. Biased comparisons can be avoided by systematically arranging and selecting the groundrules of the comparison before they are fed into the analysis. Meaningful results can be obtained in, spite of the large range of uncertainties attached to some of the performance parameters by adopting the use of scaling laws which reflect major trends or other relationships of interest rather than scattered performance estimates. This Note has intentionally been limited to a description of the method. Quantitative conclusions may be obtained by exercising the use of realistic performance and cost inputs whenever available. NomenclatureA = constant d...

Isothermal vapor-liquid equilibrium data have been measured tor the dimethyl ether/methanol system at 10 temperatures from 0.00 to 180.00 °C, and at pressures to 6.7 MPa, by a vapor-recirculating method. Barker's method of data reduction has been used to test the thermodynamic consistency of Isotherms below the critical temperature of dimethyl ether (128.8 °C). The results of the experiments have been compared with predictions of two cubic equations of state, the RedHch-Kwong and Peng-Robinson equations. With Interaction parameters calculated by fitting the Isotherm at 100 °C, these equations predict the liquid-and vapor-phase compositions to within about 3 mol % over most of the experimental range.

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Vapor-liquid equilibrium measurements have been performed on mixtures of krypton + ethane at eleven temperatures, between 150 and 296 K, and at pressures up to 6.9 MPa. Five isotherms lie at temperatures where both components are subcritical and six were measured between their critical temperatures, up to the mixture critical point. Excess Gibbs energies were estimated at subcritical temperatures by using the methods of Barker and the maximum likelihood principle. The experimental results were compared with predictions of the Redlich-Kwong and Peng-Robinson equations of state. A perturbation theory treatment due to Gubbins et al. proved much better in achieving good agreement with experiment.

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Gas-and liquid-phase equilibria in 2 4, 1,1-N2H2(CHS)2, their mixtures, and the solubilities of He(g) and N2(g) in the liquid mixtures have been measured. Excess volume of mixing of the mixtures has been determined as a function of composition. AG°, AH0, and 50 of vaporization have been obtained for the pure liquids. The measurements of vapor pressure and of liquid and gas compositions for the binary liquids have yielded the excess molar thermodynamic properties. An equation of the form AH -Xixja + bx 1 + cxj) for the molar heat of solution in terms of the mole fractions, xi, has been shown to be very convenient and useful and accounts for deviations from regularity. In the dilute regions, this equation assumes the "regular" form AH = axix%. The solubilities of He(g) and N2(g) in the liquid mixtures were measured at various temperatures and pressures. It was found that the ternary "regular behavior" is obeyed for the dissolved gases and that the atmospheric solubility K (in mole fraction) follows the linear relationship log K = e + fxx in a wide terminal composition range. AG°, AH0, and AS0 of solution have been computed for He and N2 and have been closely estimated for Ar. The values of all the useful thermodynamic properties have been tabulated at convenient compositions of the liquid phase. Deviations from ideality have been briefly discussed from a molecular point of view.i.e., the observed vapor pressure of these compounds(1) E. T.

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