Extension and enhancement of the Allen-Eggers analytical ballistic entry trajectory solution

Zachary R. Putnam, Robert D. Braun

Research output: Contribution to journalArticle


The closed-form analytical solution to the equations of motion for ballistic entry developed by Allen and Eggers is presented using modern nomenclature and is extended and enhanced through several new developments. A method of choosing an appropriate constant flight-path angle is identified.Analytical limits are proposed that bound the domain of applicabilityof the approximation.Closed-formexpressions for range andtime are developedthat are consistentwiththe assumptions in theAllen-Eggers approximation. Collectively, the improvements address key weaknesses in the original approximate solution.Assessment of the accuracy of the approximate solution relative to the planar equations ofmotion shows that the extended and enhanced Allen-Eggers solution provides good accuracy across a wide range of ballistic coefficients at Earth with initial flight-path angles steeper than about-7 deg. In some instances, the expression developed for range-to-go may be accurate enough for use in onboard real-time guidance and targeting systems.

Original languageEnglish (US)
Pages (from-to)414-430
Number of pages17
JournalJournal of Guidance, Control, and Dynamics
Issue number3
StatePublished - Mar 1 2015
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

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