The Journal of the Astronautical Sciences

, Volume 65, Issue 4, pp 470–489 | Cite as

Analytical Assessment of Drag-Modulation Trajectory Control for Planetary Entry

  • Zachary R. PutnamEmail author
  • Robert D. Braun


Discrete-event drag-modulation trajectory control is assessed for planetary entry using the closed-form Allen-Eggers solution to the equations of motion. A control authority metric for drag-modulation trajectory control systems is derived. Closed-form analytical relationships are developed to assess range divert capability and to identify jettison condition constraints for limiting peak acceleration and peak heat rate. Closed-form relationships are also developed for drag-modulation systems with an arbitrary number of stages.


Entry EDL Drag modulation Mars 



sensed acceleration magnitude, Earth g






hypersonic drag coefficient


base of the natural logarithm


acceleration due to gravity, m/s2


altitude, m


atmospheric scale height, m


integer index


stagnation-point convective heating constant, kg1/2/m


mass, kg





\(\dot {Q}\)

stagnation-point convective heat rate, W/cm2


effective nose radius, m


planetary radius, m


range, km


aerodynamic reference area, m2


velocity magnitude, m/s


velocity magnitude at jettison, m/s


ballistic coefficient, kg/m2


flight-path angle, positive above local horizontal, rad


Allen-Eggers constant flight-path angle, rad

\(\bar {\gamma }\)

Euler-Mascheroni constant


atmospheric density, kg/m3


atmospheric density at jettison, kg/m3



This work was supported in part by a NASA Space Technology Research Fellowship.

Compliance with Ethical Standards

Conflict of Interest Statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© American Astronautical Society 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Aerospace Engineering SciencesUniversity of Colorado BoulderBoulderUSA

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