Title:
Extension and Enhancement of the Allen-Eggers Analytic Solution for Ballistic Entry Trajectories
Extension and Enhancement of the Allen-Eggers Analytic Solution for Ballistic Entry Trajectories
Author(s)
Putnam, Zachary R.
Braun, Robert D.
Braun, Robert D.
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Abstract
The closed-form analytic solution to the equations of motion for ballistic entry developed
by Allen and Eggers is extended and enhanced with a method of choosing an appropriate
constant flight-path angle, limits based on the equations of motion and acceptable ap-
proximation error are proposed that bound the domain of applicability, and closed-form
expressions for range and time-dependency. The expression developed for range to go
exhibits error that may low enough for onboard drag-modulation guidance and targeting
systems. These improvements address key weaknesses in the original approximate solution.
Results show that the extended and enhanced Allen-Eggers solution provides good accuracy across a range of ballistic coefficients entries at Earth with initial flight-path angles
steeper than -7 deg.
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Date Issued
2014-06
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Text
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Paper
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