Title:
Response Surface Equations for Expendable Launch Vehicle Payload Capability
Response Surface Equations for Expendable Launch Vehicle Payload Capability
Author(s)
Fleming, Elizabeth S.
Lafleur, Jarret M.
Saleh, Joseph H.
Lafleur, Jarret M.
Saleh, Joseph H.
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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 launch 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 function of circular orbit altitude and
inclination. Following presentation of the RSE fitting method and statistical goodness of fit
tests, the RSE and model fit error statistics for the 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 are provided for each of the 43 fits. Across
all launch vehicles fit, the resulting RSEs have a maximum 90th percentile model fit error of
4.39% and a mean 90th percentile model fit error of 0.97%. In addition, of the 43 RSEs, the
lowest R^2 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 design 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 RSEs provides a tool to the aerospace engineer
allowing efficient, informed launch option trades and decisions early during design.
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Date Issued
2009-09
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Text
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Paper
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