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High altitude operation of internal combustion engines requires multiple stages of turbo-compression to maintain sea level density at the engine intake to maintain rated power. Aurora Flight Sciences Corporation has selected a set of automotive turbo-compressor components for the Rotax engine chosen for high altitude performance of the Theseus aircraft. Prior to construction and testing, Aurora predicted the system performance by power and RPM matching, using factory component performance data in the form of a spreadsheet. They concluded that their system could be controlled by a single wastegate control over the entire design altitude range of the Theseus aircraft. The slow nature of their spreadsheet interpolation scheme made impractical any future dynamic system analysis. This prompted the present study, which was to find an alternative and faster method for system performance analysis. This dissertation describes a procedure for converting the component performance map data to a set of algebraic empirical equations which are accurate to within a few percent and are well-behaved as the RPM reduces to zero or the pressure ratio approaches unity. The accuracy of the models has been tested by comparing the calculated dependent variables with their measured counterparts. Subsequently, an iterative solution was developed to calculate the operating points at all altitudes where power and RPM are matched. The single waste gate configuration did not perform well in the analysis and was, therefore, replaced with a series of multiple pressure regulators, which has several advantages. First, it allows each stage to be started sequentially as altitude increases. Second, it provides more power due to higher temperatures and mass flows in the downstream turbines. Third, the system need not be actively controlled, since this method uses passive control. Only the engine throttle valve is needed for power adjustments. Overspeeding and compressor stall are also avoided, by carefully selecting the pressure regulator settings. With the single waste gate controller, all stages have identical mass flow rate and thus must be started simultaneously. The end product of the present analysis is a graphical display of the operating points of each stage as plotted on the component performance maps.