Response Surface Equations for Expendable Launch Vehicle Payload Mass Capability

Abstract

Systems analysis and conceptual design for new spacecraft commonly require the capability to perform rapid, parametric assessments of launch vehicle options. Such assessments allow engineers to incorporate launch vehicle considerations in first-order cost, mass, and orbit performance trades early during conceptual design and development phases. This paper demonstrates an efficient approach to la unch vehicle analysis and selection using response surface equations (RSEs) derived directly from launch vehicle payload planner’s guides. These RSEs model payload capability as a f unction of circular orbit altitude and inclination. Following presentation of the RSE fit ting method and statistical goodness of fit tests, the RSE and model fit error statistics for t he Pegasus XL are derived and presented as an example. In total, 43 RSEs are derived for the following launch vehicles and their derivatives: Pegasus, Taurus, Minotaur, and Falcon series as well as the Delta IV, Atlas V, and the foreign Ariane and Soyuz vehicles. Ranges of validity and model fit error statistics with respect to the original planner’s guide data a re provided for each of the 43 fits. Across all launch vehicles fit, the resulting RSEs have a maximum 90 th percentile model fit error of 4.39% and a mean 90 th percentile model fit error of 0.97%. In addition, of the 43 RSEs, the lowest R≤ value is 0.9715 and the mean is 0.9961. As a result, these equations are sufficiently accurate and well-suited for use in conceptual desi gn trades. Examples of such trades are provided, including demonstrations using the RSEs to (1) select a launch vehicle given an orbit inclination and altitude, (2) visualize orbit altitude and inclination constraints given a spacecraft mass, and (3) calculate the sensitivity of orbital parameters to mass growth. Suited for a variety of applications, the set of RS Es provides a tool to the aerospace engineer allowing efficient, informed launch option trades a nd decisions early during design.