Advertisement

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
Article
  • 106 Downloads

Abstract

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.

Keywords

Entry EDL Drag modulation Mars 

Notation

a

sensed acceleration magnitude, Earth g

b

exponent

C

constant

CD

hypersonic drag coefficient

e

base of the natural logarithm

g

acceleration due to gravity, m/s2

h

altitude, m

H

atmospheric scale height, m

i

integer index

k

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

m

mass, kg

n

integer

N

integer

\(\dot {Q}\)

stagnation-point convective heat rate, W/cm2

r

effective nose radius, m

R

planetary radius, m

s

range, km

Sref

aerodynamic reference area, m2

V

velocity magnitude, m/s

Vi

velocity magnitude at jettison, m/s

β

ballistic coefficient, kg/m2

γ

flight-path angle, positive above local horizontal, rad

γ

Allen-Eggers constant flight-path angle, rad

\(\bar {\gamma }\)

Euler-Mascheroni constant

ρ

atmospheric density, kg/m3

ρi

atmospheric density at jettison, kg/m3

Notes

Acknowledgements

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.

References

  1. 1.
    Allen, H.J., Eggers, A.J.: A study of the motion and aerodynamic heating of ballistic missiles entering the Earth’s atmosphere at high supersonic speeds. Tech. Rep. NACA-TR-1381, Ames Aeronautical Laboratory, Washington DC (1958)Google Scholar
  2. 2.
    Bairstow, S.H., Barton, G.H.: Orion reentry guidance with extended range capability using predguid. In: AIAA Guidance, Navigation, and Control Conference, pp. 1–17. Hilton Head, South Carolina (2007)Google Scholar
  3. 3.
    Barbera, F.J.: Closed-form solution for ballistic vehicle motion. J. Spacecr. Rocket. 18(1), 52–57 (1981)CrossRefGoogle Scholar
  4. 4.
    Bose, D. M., Shidner, J., Winski, R., Zumwalt, C., Cheatwood, F. M., Hughes, S.J.: The hypersonic inflatable aerodynamic decelerator (HIAD) mission applications study. In: AIAA Aerodynamic Decelerator Systems (ADS) Conference. American Institute of Aeronautics and Astronautics, Reston, Virginia (2013)Google Scholar
  5. 5.
    Braun, R. D., Manning, R.M.: Mars exploration entry, descent, and landing challenges. J. Spacecr. Rocket. 44(2), 310–323 (2007)CrossRefGoogle Scholar
  6. 6.
    Citron, S. J., Meir, T.C.: An analytic solution for entry into planetary atmospheres. AIAA J. 3(3), 470–475 (1965)CrossRefzbMATHGoogle Scholar
  7. 7.
    Cohen, M.J.: Some closed form solutions to the problem of re-entry of lifting and non-lifting vehicles. In: 2nd Aerospace Sciences Meeting. Northhampton College of Advanced Technology, American Institute of Aeronautics and Astronautics, New York, NY (1965)Google Scholar
  8. 8.
    Dutta, S., Bowes, A.L., Cianciolo, A.D., Glass, C.E., Powell, R.W.: Guidance scheme for modulation of drag devices to enable return from low Earth orbit. In: AIAA Atmospheric Flight Mechanics. AIAA, Grapevine, TX (2017)Google Scholar
  9. 9.
    Dyakonov, A., Schoenenberger, M., Scallion, W., Van Norman, J., Novak, L.A., Tang, C.Y.: Aerodynamic interference due to MSL reaction control system. In: 41st AIAA Thermophysics conference, pp. 1–16. San Antonio, TX (2009)Google Scholar
  10. 10.
    Dyakonov, A.A., Glass, C.E., Desai, P.N., Van norman, J.W.: Analysis of effectiveness of phoenix entry reaction control system. J. Spacecr. Rocket. 48(5), 746–755 (2011)CrossRefGoogle Scholar
  11. 11.
    Hall, J.L., Le, A.K.: Aerocapture trajectories for spacecraft with large towed ballutes. In: AAS/AIAA Space Flight Mechanics Meeting. Santa Barbara, CA (2001)Google Scholar
  12. 12.
    Johnson, W.R., Lyons, D.T.: Titan ballute aerocapture using a perturbed TitanGRAM model. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit. Providence, RI (2004)Google Scholar
  13. 13.
    Kuo, Z.S., Liu, K.C., Chang, Y.S.: Explicit guidance of ballistic entry using improved matched asymptotic expansions. Trans. Jpn. Soc. Aeronaut. Space Sci. 50(168), 121–127 (2007)CrossRefGoogle Scholar
  14. 14.
    Levy, L.L.: The Use of Drag Modulation to Limit the Rate at Which Deceleration Increases During Nonlifting Entry. Tech. Rep. NASA TN D-1037, Ames Research Center, Washington, DC (1961)Google Scholar
  15. 15.
    Loh, W.H.T.: A higher order theory of ballistic entry. In: American Astronautical Society Eighth Annual Meeting, pp. 529–540. American Astronautical Society 8th Annual Meeting, Washington, DC (1962)Google Scholar
  16. 16.
    McRonald, A.D.: A lightweight inflatable hypersonic drag device for planetary entry. In: Association Aeronautique De France Conference. Arcachon, France (1999)Google Scholar
  17. 17.
    Miller, B.P.: Approximate velocity, position and time relationship for ballistic re-entry. ARS J. 31(3), 437–438 (1961)CrossRefGoogle Scholar
  18. 18.
    Miller, K.L., Gulick, D., Lewis, J., Trochman, B., Stein, J., Lyons, D.T., Wilmoth, R.G.: Trailing ballute aerocapture: concept and feasibility assessment. In: 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. Huntsville, AL (2003)Google Scholar
  19. 19.
    Phillips, R.L., Cohen, C.B.: Use of drag modulation to reduce deceleration loads during atmospheric entry. ARS J. 29(6), 414–422 (1959)CrossRefGoogle Scholar
  20. 20.
    Putnam, Z.R., Braun, R.D.: Drag-modulation flight-control system options for planetary aerocapture. J. Spacecr. Rocket. 51(1), 139–50 (2014)CrossRefGoogle Scholar
  21. 21.
    Putnam, Z.R., Braun, R.D.: Precision landing at mars using Discrete-Event drag modulation. J. Spacecr. Rocket. 51(1), 128–138 (2014)CrossRefGoogle Scholar
  22. 22.
    Putnam, Z.R., Braun, R.D.: Extension and enhancement of the Allen-Eggers solution for ballistic entry trajectories. Journal of Guidance, Control, and Dynamics (2015)Google Scholar
  23. 23.
    Randall, D.E.: Influence of staging on re-entry trajectory characteristics. J. Spacecr. Rocket. 7(3), 370–372 (1970)CrossRefGoogle Scholar
  24. 24.
    Robinson, A., Besonie, A.: On the problems of re-entry into the Earth’s atmosphere. J. Astronaut. Sci. 7(1), 7–21 (1960)Google Scholar
  25. 25.
    Rose, P.H., Hayes, J.E.: Drag modulation and celestial mechanics. In: 7th Annual Meeting of the American Astronautical Society. Dallas, TX (1961)Google Scholar
  26. 26.
    Venkatapathy, E., Arnold, J., Fernandez, I., Hamm, K. R., Kinney, D., Laub, B., Makino, A., McGuire, M.K., Peterson, K., Prabhu, D., Empey, D., Dupzyk, I., Huynh, L., Hajela, P., Gage, P., Howard, A.R., Andrews, D.: Adaptive deployable entry and placement technology (ADEPT): a feasibility study for human missions to Mars. In: 21st AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar. American Institute of Aeronautics and Astronautics, Reston, Virigina (2012)Google Scholar
  27. 27.
    Vinh, N.X., Johannesen, J.R., Mease, K.D., Hanson, J.M.: Explicit guidance of drag-modulated aeroassisted transfer between elliptical orbits. J. Guid. Control. Dyn. 9(3), 274–280 (1986)CrossRefGoogle Scholar
  28. 28.
    Warden, R.V.: Ballistic re-entries with a varying w/CD A. ARS J. 31(2), 208–213 (1961)CrossRefGoogle Scholar
  29. 29.
    Werner, M., Woollard, B., Tadanki, A., Pujari, S.R., Braun, R.D., Lock, R., Nelessen, A., Woolley, R.: Development of an earth smallsat flight test to demonstrate viability of mars aerocapture. In: 55th AIAA Aerospace Sciences Meeting, pp. 1–16. AIAA, American Institute of Aeronautics and Astronautics, Grapevine, TX (2017)Google Scholar
  30. 30.
    Westhelle, C.H., Masciarelli, J.P.: Assessment of aerocapture flight at titan using a drag-only device. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, pp. 1–7. Austin, TX (2003)Google Scholar

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

Personalised recommendations