Regression Analysis of Launch Vehicle Payload Capability for Interplanetary Missions
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Abstract
During the conceptual design of interplanetary space missions, it is common for engineers and mission planners to
perform launch system trades. This paper provides an analytical means for facilitating these trades rapidly and
efficiently using polynomial equations derived from payload planner’s guides. These equations model expendable
launch vehicles’ maximum payload capability as a function of vis-viva energy (C3). This paper first presents the
motivation and method for deriving these polynomial equations. Next, 34 polynomials are derived for vehicles
among nine launch vehicle series: Atlas V, Delta IV, Falcon 9, and Taurus, as well as H-IIA, Long March, Proton,
Soyuz, and Zenit. The quality of fit of these polynomials are assessed, and it is found that the maximum 95th
percentile model fit error for all 34 vehicles analyzed is 4.43% with a mean of 1.44%, and the minimum coefficient
of determination (R²) is 0.99967. As a result, the equations are suitable for launch vehicle trade studies in conceptual
design and beyond. A realistic example of such a trade for the Mars Reconnaissance Orbiter mission is provided.
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2010-09
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