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

Zachary R. Putnam, Robert D. Braun

Research output: Contribution to journalArticle

Abstract

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
Volume38
Issue number3
DOIs
StatePublished - Mar 1 2015
Externally publishedYes

Fingerprint

flight paths
Flight paths
Ballistics
entry
ballistics
Enhancement
trajectory
flight
Trajectories
trajectories
Trajectory
augmentation
Approximate Solution
Terminology
nomenclature
approximation
Range of data
targeting
Equations of motion
Angle

ASJC Scopus subject areas

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

Cite this

Extension and enhancement of the Allen-Eggers analytical ballistic entry trajectory solution. / Putnam, Zachary R.; Braun, Robert D.

In: Journal of Guidance, Control, and Dynamics, Vol. 38, No. 3, 01.03.2015, p. 414-430.

Research output: Contribution to journalArticle

@article{dcd0f817742b42cbb220b80966b3e823,
title = "Extension and enhancement of the Allen-Eggers analytical ballistic entry trajectory solution",
abstract = "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.",
author = "Putnam, {Zachary R.} and Braun, {Robert D.}",
year = "2015",
month = "3",
day = "1",
doi = "10.2514/1.G000846",
language = "English (US)",
volume = "38",
pages = "414--430",
journal = "Journal of Guidance, Control, and Dynamics",
issn = "0731-5090",
publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",
number = "3",

}

TY - JOUR

T1 - Extension and enhancement of the Allen-Eggers analytical ballistic entry trajectory solution

AU - Putnam, Zachary R.

AU - Braun, Robert D.

PY - 2015/3/1

Y1 - 2015/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84931360835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84931360835&partnerID=8YFLogxK

U2 - 10.2514/1.G000846

DO - 10.2514/1.G000846

M3 - Article

AN - SCOPUS:84931360835

VL - 38

SP - 414

EP - 430

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 3

ER -