Regression Analysis of Launch Vehicle Payload Capability for Interplanetary Missions
- Paper number
IAC-10,D2,1,11,x7556
- Author
Mr. Jarret Lafleur, Georgia Institute of Technology, United States
- Coauthor
Ms. Marcie Wise, Georgia Institute of Technology, United States
- Coauthor
Dr. Joseph Saleh, Georgia Institute of Technology, United States
- Year
2010
- Abstract
A common requirement in systems analysis and conceptual design for new spacecraft is the capability to perform rapid, parametric assessments of launch vehicle options. Such assessments allow engineers to incorporate launch vehicle considerations into cost, mass, and orbit performance trade studies early during conceptual design and development. Such launch vehicle analysis is traditionally accomplished through manual references to sources such as launch-vehicle-specific payload planner's guides. This method can be time consuming and is not conducive to parametric exploration and trade studies. In this paper, least-squares polynomial regressions for payload capability are derived for a large set of expendable launch vehicles to enable more efficient launch option analyses for interplanetary mission applications. The equations derived in this paper model expendable launch vehicles' maximum payload capability as a function of vis-viva energy (C3). Fourth-order polynomials are chosen in order to minimize prediction error while also maintaining a compact representation of the data. To determine the polynomial coefficients for each launch vehicle, a standardized fitting process is used consisting of (1) digitizing the data contained in plots from payload planner's guides, (2) performing a least-squares polynomial regression on this data, and (3) checking the regression quality of fit through statistical tests on the coefficient of determination (R-squared value) and model fit error distribution. This process is carried out for 34 vehicles from a variety of interplanetary-capable launch vehicle series including Atlas V, Delta IV, Falcon 9, Taurus, H-IIA, Long March, Proton, Zenit, and Soyuz. The maximum 95th percentile model fit error for all 34 vehicles analyzed is 4.43\%, with a mean of 1.44\%, and the minimum R-squared value is 0.99967. As a result, the equations here derived are suitable for launch vehicle trade studies in conceptual design phases and beyond. A realistic example of such a trade for the Mars Reconnaissance Orbiter (MRO) mission is provided. This example illustrates a scenario in which a mission planner has information regarding payload mass and mission C3 requirements and uses the regressions to compare the payload capabilities of several different launch vehicles. To illustrate how this can facilitate launch vehicle selection decisions, a launch margin versus cost Pareto frontier for MRO is produced and discussed. Overall, the capabilities enabled by this work provide a powerful tool for the mission planner and project manager in making efficient, informed trades and decisions on launch options early during design and development phases for a variety of interplanetary mission applications.
- Abstract document
- Manuscript document
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