Skip to main content
SpringerLink
Log in

Monte Carlo simulation of stage separation dynamics of a multistage launch vehicle

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This paper provides the formulation used for studing the cold and hot separating stages of a multistage launch vehicle. Monte Carlo simulation is employed to account for the off nominal design parameters of the bodies undergoing separation to evaluate the risk of failure for the separation event. All disturbances, effect of dynamic unbalance, residual thrust, separation disturbance caused by the separation mechanism and misalignment in cold and hot separation are analyzed to find out nonoccurrence of collision between the separation bodies. The results indicate that the current design satisfies the separation requirements.

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

Similar content being viewed by others

Abbreviations

a 0 :

acceleration of coordinate system (m/s2)

u, υ, w :

components of body linear velocity along x, y and z axes (m/s)

p, q, r :

components of body angular velocity about x, y, z axes ((°)/s)

C :

coning angle (°)

u*:

critical velocity (m/s)

ρ 1 :

gas density (kg/m3)

T :

lateral angular tip-off rate ((°)/s)

m :

mass(kg)

M a :

matchnumber

P k :

pressure in vessel (Pa)

P a :

pressure in nozzle (Pa)

P 02 :

pressure between shock and first stage (Pa)

P M :

pressure between two stages (Pa)

I xy , I xz , I yz :

products of inertia in yaw, roll and pitch planes (kg · m2)

r :

radius of stage one (m)

R 1,2 :

relative distance between CG (center of gravity) of stages 1,2 and coordinate system (m)

I x , I y , I z :

roll, pitch and yaw moments of inertial, respectively (kg · m2)

S a :

surface of nozzle (m2)

T k :

temperature in vessel (K)

T M :

temperature between two stages (K)

t :

time (s)

u 1 :

velocity (m/s)

V M :

volume of space between two stages (m3)

ψ, γ, φ :

yaw, roll and pitch angles (°).

References

  1. Chubb W. The collision boundary between the two separating stages of the SA-4 saturn vehicle[R]. NASA-TND-598, August 1961.

  2. Palmer G D, Mitchell D H. Spring separation of spacecraft[R]. NASA-CR-64009, 1963.

  3. Dwork M. Coning effects caused by separation of spin stabilized stages[J]. AIAA Journal, 1963, 1(11):2639–2640.

    Article  Google Scholar 

  4. Wilke R O. Comments on coning effects caused by separation of spin stabilized stages[J]. AIAA Journal, 1964, 2(7):1358.

    Article  Google Scholar 

  5. Puglisi A G. Saturn IB/S-IVB stage separation controllability report[R]. Douglas Report SM-46758, 1964.

  6. Decker J P, Pierpont P K. Aerodynamic separation characteristics of conceptual parallel-staged reusable launch vehicle at Mach 3 to 6[R]. NASA-TMX-1051, January 1965.

  7. Decker J P. Aerodynamic abort-separation characteristics of a parallel staged reusable launch vehicle from Mach 0.60 to 1.20[R]. NASA-TMX-1174, November 1965.

  8. Decker J P, Gera J. An exploratory study of parallel-stage separation of reusable launch vehicles[R]. NASA-TND-4765, 1968.

  9. Christensen K L, Narahara R M. Spacecraft separation[J]. Space Aeronautics, 1966, 46(7):74–82.

    Google Scholar 

  10. Mitchell D H, Palmer G D. Analysis and simulation of a high accuracy spacecraft separation system[J]. Journal of Spacecraft and Rockets, 1966, 3(4):458–463.

    Article  Google Scholar 

  11. Waterfall A P. A theoretical study of the multi-spring stage separation system of the black arrow satellite launcher[R]. Royal Aerospace Establishment, TR-682016, Farnborough Hants, UK, August 1968.

  12. Bolster W J, Googins G C. Design, development and testing of a series of air-launched sounding rockets[J]. Journal of Spacecraft and Rockets, 1969, 6(4):460–465.

    Article  Google Scholar 

  13. Longren D R. Stage separation dynamics of spin stabilized rockets[J]. Journal of Spacecraft and Rockets, 1970, 7(4):434–439.

    Article  Google Scholar 

  14. Hurley M J, Jr, Carrie G W. Stage separation of parallel-staged shuttle vehicles: a capability assessment[J]. Journal of Spacecraft and Rockets, 1972, 9(10):764–771.

    Article  Google Scholar 

  15. Su M W, Mullen C R, Jr. Plume impingement force during tandem stage separation at high altitudes[J]. Journal of Spacecraft and Rockets, 1972, 9(9):715–717.

    Article  Google Scholar 

  16. Subramanyam J D A. Separation dynamics analysis for a multistage rocket[C]. In: Kobayashi S (ed). Proceedings of the International Symposium of Space Science and Technology, Tokyo: AGNE Publishing, 1973, 383–390.

    Google Scholar 

  17. Kalesnikof K S. Dynamic separation[M]. 1977 (in Russian).

  18. Saxena S K. Upper stage jet impingement on separated booster[J]. Aeronautical Journal, 1979, 616:71–74.

    Google Scholar 

  19. Lochan R, Adimurthy V, Kumar K. Separation dynamics of strap-on boosters[J]. Journal of Guidance, Control and Dynamics, 1992, 15(1):137–143.

    Article  Google Scholar 

  20. Lochan R. Dynamics of bodies separating from launch vehicles[D]. Ph D Dissertation. Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, May 1993.

    Google Scholar 

  21. Lochan R, Adimurthy V, Kumar K. Separation dynamics of ullage rockets[J]. Journal of Guidance, Control and Dynamics, 1994, 17(3):426–434.

    Article  Google Scholar 

  22. Lochan R, Adimurthy V. Separation dynamics of strap-on boosters in the atmosphere[J]. Journal of Guidance, Control and Dynamics, 1997, 20(4):633–639.

    Article  MATH  Google Scholar 

  23. Cheng S C. Payload fairing separation dynamics[J]. Journal of Spacecraft and Rockets, 1999, 36(4):511–515.

    Google Scholar 

  24. Reubush D E, Martin J G, Robinson J S, et al. Hyper-X stage separation-simulation development and results[C]. In: 10th International Space Planes and Hypersonic Systems and Technologies Conference, Kyoto, Japan, April 2001.

  25. Jeyakumar D, Biswas K K. Design and analysis of the stage separation system of a massive liquid rocket stage[C]. In: Proceedings of the International Conference on Modelling Simulation and Optimization for Design of Multidisciplinary Engineering Systems, Goa, India, 2003.

  26. Jeyakumar D, Biswas K K. Stage separation system design and dynamic analysis of ISRO launch vehicles[J]. Journal of Aerospace Sciences and Technologies, 2003, 55(3):211–222.

    Google Scholar 

  27. Jeyakumar D, Biswas K K. Stage separation dynamic analysis of upper stage of a multistage launch vehicle using retro rocket[J]. Mathematical and Computer Modelling, 2005, 41(8/9): 849–866.

    Article  MATH  MathSciNet  Google Scholar 

  28. Mitchell D H. Flight separation mechanism[R]. NASA-SP-8056, 1970.

  29. Logan J W. DSV-3E first-second stage separation analysis[R]. Rept SM-46446, Douglas Aircraft co, April 1965.

  30. Ball K J, Osborne G F. Space vehicle dynamics[M]. Oxford: Oxford University Press, 1967.

    Google Scholar 

  31. Orlik-Rukemann K J, Iyengar S. Example of dynamic interference effects between two oscillating vehicles[J]. Journal of Spacecraft and Rockets, 1973, 10(9):617–619.

    Article  Google Scholar 

  32. Xue Yu. Separation between stages of multistage carrier rocket[R]. FTD-ID (RS) T-1143-83, Sept 1983.

  33. Naftel J C, Wilhite A W, Cruz C I. Analysis of separation of a two-stage winged launch vehicle[C]. In: 24th AIAA Aerospace Sciences Meeting, Reno, NV, Jan 1986.

  34. Papoulis A. Probability, random variables, and stochastic processes[M]. McGraw-Hill, 1991.

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, K. N. Toosi University of Technology, P. O. Box 16765-3381, Tehran, Iran

    J. Roshanian & M. Talebi

Authors
  1. J. Roshanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Talebi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Roshanian.

Additional information

(Communicated by CHEN Li-qun)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roshanian, J., Talebi, M. Monte Carlo simulation of stage separation dynamics of a multistage launch vehicle. Appl. Math. Mech.-Engl. Ed. 29, 1411–1426 (2008). https://doi.org/10.1007/s10483-008-1103-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-1103-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation