Skip to main content
SpringerLink
Log in

Determining Dynamic Stability of a Re-entry Capsule at Free Fall

  • Original article
  • Published:
Aerotecnica Missili & Spazio Aims and scope Submit manuscript

Abstract

Re-entry capsules, designed with blunt-body shapes to endure hypersonic air velocities and heat, encounter instability in the low subsonic regime during the final descent phase. Ensuring a controlled descent with the appropriate attitude for deploying deceleration systems becomes paramount. To address this challenge, we employ a cost-effective approach to investigate the dynamic stability of a typical re-entry capsule in free fall. This study involves formulating the aerodynamic model of the system and hypothesizing associated coefficients. A meticulously designed and instrumented prototype is dynamically scaled and subjected to low altitude drop tests to recreate the desired scenario. Subsequently, the data collected during these tests is processed, and stability derivatives are estimated using system identification techniques. Our research contributes to a deeper understanding of the dynamic stability of re-entry capsules during free fall, shedding light on their behavior and providing insights essential for improving their performance and safety during descent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

The data that support the findings of this study are highly confidential in nature, as they are associated with an upcoming space program. Due to security and confidentiality considerations, access to the data is restricted. However, researchers interested in accessing the data may submit requests for access to the corresponding author, subject to approval and in accordance with the policies and guidelines set by Aerotecnica Missili & Spazio.

Abbreviations

\({A}_{ref}\) :

Reference area of the model (m2)

\({C}_{l\dot{\beta }}+{C}_{lp}\) :

Yaw damping coefficient

\({C}_{l}\) :

Yaw coefficient

\({C}_{l\beta }\) :

Yaw coefficient due to sideslip angle

\({C}_{m\dot{\alpha }}+{C}_{mq}\) :

Pitch damping coefficient

\({C}_{m}\) :

Pitch coefficient

\({C}_{m\alpha }\) :

Pitch coefficient due to angle of attack

\({C}_{n}\) :

Roll coefficient

\({C}_{nr}\) :

Roll damping coefficient

\({C}_{n\beta }\) :

Roll coefficient due to sideslip angle

\({C}_{x}\) :

X-axis force coefficient

\({C}_{x\alpha }\) :

X-axis force coefficient due to angle of attack

\({C}_{y}\) :

Y-axis force coefficient

\({C}_{y\beta }\) :

Y-axis force coefficient due to sideslip angle

\({C}_{z}\) :

Z-axis force coefficient

\({C}_{z\alpha }\) :

Z-axis force coefficient due to angle of attack

\({I}_{xx}\) :

X-axis moment of inertia (kg m2)

\({I}_{yy}\) :

Y-axis moment of inertia (kg m2)

\({I}_{zz}\) :

Z-axis moment of inertia (kg m2)

\({g}_{x}\) :

X-axis acceleration due to gravity in the inertial frame (m/s2)

\({g}_{y}\) :

Y-axis acceleration due to gravity in the inertial frame (m/s2)

\({g}_{z}\) :

Z-axis acceleration due to gravity in the inertial frame (m/s2)

\({l}_{CG}\) :

Distance between nose and C.G. (m)

\({m}_{1}\) :

Mass reading from balance 1 (kg)

\({m}_{2}\) :

Mass reading from balance 2 (kg)

\(\dot{p}\) :

X-axis angular acceleration (rad/s2)

\({p}^{*}\) :

X-axis normalized angular rate (rad)

\(\overline{q }\) :

Dynamic pressure (Pa)

\(\dot{q}\) :

Y-axis angular acceleration (rad/s2)

\({q}^{*}\) :

Y-axis normalized angular rate (rad)

\(\dot{r}\) :

Z-axis angular acceleration (rad/s2)

\({r}^{*}\) :

Z-axis normalized angular rate (rad)

\(\dot{u}\) :

Xi-axis acceleration in the inertial frame (m/s2)

\(\dot{v}\) :

Yi-axis acceleration in the inertial frame (m/s2)

\(\dot{w}\) :

Zi-axis acceleration in the inertial frame (m/s2)

\({{\varvec{V}}}_{{\varvec{x}}}\) :

X-axis velocity vector in body frame (m/s)

\({{\varvec{V}}}_{{\varvec{y}}}\) :

Y-axis velocity vector in body frame (m/s)

\({{\varvec{V}}}_{{\varvec{z}}}\) :

Z-axis velocity vector in body frame (m/s)

\(\dot{\alpha }\) :

Angle of attack rate (rad/s)

\({\alpha }_{t}\) :

Total angle (rad)

\(\dot{\beta }\) :

Side-slip angle rate (rad/s)

\(h\) :

Height of the string (m)

\(I\) :

Total moment of inertia (kg m2)

\(M\) :

Mach number

\(T\) :

Time period of one oscillation (s)

\(V\) :

Magnitude of the velocity vector in body frame (m/s)

\(d\) :

Reference diameter of the model (m)

\(g\) :

Acceleration due to gravity (m/s2)

\(l\) :

Length of the model (m)

\(m\) :

Total mass of the model (kg)

\(p\) :

X-axis angular rate (rad/s)

\(q\) :

Y-axis angular rate (rad/s)

\(r\) :

Z-axis angular rate (rad/s)

\(t\) :

Time period (s)

\(\alpha\) :

Angle of attack (rad)

\(\beta\) :

Side-slip angle (rad)

References

  1. DuBose, H.C.: Static and dynamic stability of blunt bodies. Advisory Group Aeronaut Res Develop Paris (France) 347 (1961)

  2. Rom, J., Zorea, C.: Effect of a spike on the drag and on the aerodynamic stability of blunt bodies in supersonic flow. J. Spacecr. Rocket. 7(8), 1017–1019 (1970). https://doi.org/10.2514/3.30094

    Article  Google Scholar 

  3. Guglieri, G., Quagliotti, F.: Low speed dynamic tests on a capsule configuration. Aerosp. Sci. Technol. 4(6), 383–390 (2000). https://doi.org/10.1016/S1270-9638(00)01066-X

    Article  Google Scholar 

  4. Murphy, K., Borg, S., Watkins, A., Cole, D., and Schwartz, R.: Testing of the crew exploration vehicle in NASA langley's unitary plan wind tunnel. In: 45th AIAA Aerospace Sciences Meeting and Exhibit, (2007). https://doi.org/10.2514/6.2007-1005

  5. Murphy, K., Brauckmann, G., Bell, J., Rhode, M., Owens, D.B., Wilson, T., Bibb, K., Chan, D., Walker, E., “Orion crew module aerodynamic testing. In: 29th AIAA Applied Aerodynamics Conference, (2011). https://doi.org/10.2514/6.2011-3502

  6. Bibb, K., Brauckmann, G., Walker, E., and Robinson, P.: Development of the Orion crew module static aerodynamic database, Part I: Hypersonic. In: 29th AIAA Applied Aerodynamics Conference, (2011). https://doi.org/10.2514/6.2011-3506

  7. Desikan, S.L.N., Patil, M.M., Subramanian, S.: Understanding of flow features over a typical crew module at Mach 4. Aeronaut. J. 119(1216), 727–746 (2015). https://doi.org/10.1017/S0001924000010794

    Article  Google Scholar 

  8. Aubuchon, V.V., Owens, D.B., Carvajal, O., Lumb, S.B.: Dynamic stability of the boeing CST-100. AIAA Atmospheric Flight Mechanics Conference, 2017. https://doi.org/10.2514/6.2017-1399

  9. Baillion, M.: Blunt bodies dynamic derivatives, special course on capsule aerodynamics. AGARD Report 808, (1997)

  10. Murman, S., Aftosmis, M.: Dynamic analysis of atmospheric-entry probes and capsules. In: 45th AIAA Aerospace Sciences Meeting and Exhibit (2007). https://doi.org/10.2514/6.2007-74

  11. Mitcheltree, R.A., Wilmoth, R.G., Cheatwood, F.M., Brauckmann, G.J., Greene, F.A.: Aerodynamics of Stardust sample return capsule. J. Spacecr. Rocket. 36(3), 429–435 (1999). https://doi.org/10.2514/2.3463

    Article  Google Scholar 

  12. Potturi, A.S., and Peroomian, O.: Dynamic stability analysis of the orion crew module through computational fluid dynamics. In: 46th AIAA Fluid Dynamics Conference (2016). https://doi.org/10.2514/6.2016-3200

  13. Teramoto, S., Hiraki, K., Fujii, K.: Numerical analysis of dynamic stability of a reentry capsule at transonic speeds. AIAA J. 39(4), 646–653 (2001). https://doi.org/10.2514/2.3463

    Article  Google Scholar 

  14. Karatekin, Ö., Charbonnier, J.M., Wang, F., Dehant, V.: Dynamic stability of atmospheric entry probes. Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science (2004)

  15. Fujita, K., Inatani, Y., Hiraki, K.: Attitude stability of blunt-body capsules in hypersonic rarefied regime. J. Spacecr. Rocket. 41(6), 925–931 (2004). https://doi.org/10.2514/1.3588

    Article  Google Scholar 

  16. Mehta, R.C.: Computations of flowfield over reentry modules at high speed”, computational simulations and applications. IntechOpen (2011). https://doi.org/10.5772/24259

    Article  Google Scholar 

  17. Kaushikh, K., Arunvinthan, S., Pillai, S.N.: Aerodynamics and aerothermodynamics of undulated re-entry vehicles. Acta Astronaut. 142, 95–102 (2018). https://doi.org/10.1016/j.actaastro.2017.10.024

    Article  Google Scholar 

  18. Soumya, N., Nair, A.P., Brinda, V., Sheela, D.S., Lalithambika, V.R., Dhekane, M.V.: Attitude control schemes for crew module atmospheric re-entry experiment mission. IFAC-PapersOnLine 51(1), 627–632 (2018). https://doi.org/10.1016/j.ifacol.2018.05.105

    Article  Google Scholar 

  19. Nomura, M., Fujita, K., Nagai, H.: Computational study of aerodynamic characteristics on reentry capsule aft-body shape in transonic flow. 2018 AIAA Atmospheric Flight Mechanics Conference, (2018). https://doi.org/10.2514/6.2018-0290

  20. Winchenbach, G.L., Chapman, G.T., Hathaway, W.H., Ramsey, A., Berner, C.: Dynamic stability of blunt atmospheric entry configurations. J. Spacecr. Rocket. 39(1), 49–55 (2002). https://doi.org/10.2514/2.3781

    Article  Google Scholar 

  21. Albisser, M.: Identification of aerodynamic coefficients from free flight data. Ph.D. Dissertation, Université de Lorraine (2015)

  22. Owens, D.B., Aubuchon, V.: Overview of orion crew module and launch abort vehicle dynamic stability. In: 29th AIAA Applied Aerodynamics Conference, (2011). https://doi.org/10.2514/6.2011-3504

  23. Kazemba, C., Braun, R., Clark, I., Schoenenberger, M.: Survey of blunt body dynamic stability in supersonic flow. AIAA Atmospheric Flight Mechanics Conference (2012). https://doi.org/10.2514/6.2012-4509

    Article  Google Scholar 

  24. Bibi, A., Maqsood, A., Go, T.H.: Review on analysis & modeling of dynamic stability characteristics of atmospheric entry vehicles. NUST J. Eng. Sci. 7(1), 15–21 (2015). https://doi.org/10.24949/Fnjes.v7i1.121

    Article  Google Scholar 

  25. Kazemba, C.D., Braun, R.D., Clark, I.G., Schoenenberger, M.: Survey of blunt-body supersonic dynamic stability. J. Spacecr. Rocket. 54(1), 109–127 (2016). https://doi.org/10.2514/1.A33552

    Article  Google Scholar 

  26. Inatani, Y.: Reentry capsule for sample return from asteroids in the planetary exploration missions. J. Phys. (2018). https://doi.org/10.1088/1742-6596/1005/1/012049

    Article  Google Scholar 

  27. Nomura, M., Robbe, A., Fujita, K., Nagai, H.: Reentry capsule dynamic instability with different aft-body shape in transonic flow. In: AIAA Scitech 2019 Forum, (2019). https://doi.org/10.2514/6.2019-0018

  28. Kobayashi, K., Ohmichi, Y., Kanazaki, M.: Modal decomposition analysis of subsonic unsteady flow around an atmospheric entry capsule with forced oscillation. AIAA Scitech 2019 Forum, (2019). https://doi.org/10.2514/6.2019-1851

  29. Gainer, T.G., Hoffman, S.: Summary of transformation equations and equations of motion used in free flight and wind tunnel data reduction and analysis. NASA Technical Report, (1972)

  30. Etkin, B.: Dynamics of atmospheric flight. Wiley, New York (1972)

    Google Scholar 

  31. Demuth, H., Beale, M.: Neural network toolbox: user’s guide: for use with Matlab. MathWorks Incorporated, (1992)

  32. Jategaonkar, R.V.: Flight vehicle system identification: a time-domain methodology. Am Institut. Aeronaut Astronaut. Inc. (2015). https://doi.org/10.2514/4.102790

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the guidance and motivation provided by Mr. K. Srinivasan of the Wind Tunnel Data Division, Wind Tunnel Group, Aeronautics Entity, Vikram Sarabhai Space Centre. This work was supported by Vikram Sarabhai Space Centre, Indian Space Research Organisation.

Author information

Authors and Affiliations

  1. Department of Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, KA, India

    C. Priyant Mark & Winston Netto

Authors
  1. C. Priyant Mark
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Winston Netto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Priyant Mark.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mark, C.P., Netto, W. Determining Dynamic Stability of a Re-entry Capsule at Free Fall. Aerotec. Missili Spaz. 103, 101–116 (2024). https://doi.org/10.1007/s42496-023-00180-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42496-023-00180-7

Keywords

Search

Navigation