Development of a sensitivity analysis tool for the trajectory of multistage launch vehicles

Abstract

The primary objective of this work is to create a highly accurate sensitivity analysis tool for multi-stage launch vehicle trajectories. This tool is designed to assess the impact of various parameters on the trajectory and performance of multi-stage launch vehicles. To achieve this, we have developed high-fidelity simulation software that considers all translational and angular movements by modelling the six-degrees-of-freedom (6DOF) equations of motion. The validation of this software is based on experimental data. An essential aspect of this work is the utilization of the developed sensitivity analysis tool to determine how different parameters affect the trajectory of multi-stage launch vehicles. Through the sensitivity analysis conducted using the developed tool, it is possible to identify which parameters are of critical importance during the design phase. We apply a generic mission profile for the Minotaur-I launcher to obtain parametric dependencies of the flight path. Through a comprehensive parametric study, we evaluate a range of critical parameters, including gross lift-off weight, a specific impulse of each stage, pitch-over manoeuvre initial time and angle, and ignition impulse of each stage. These parameters significantly influence the trajectory, performance, and reliability of the launch vehicle for mission design and success. The results of the sensitivity analysis underscore that even minor variations in these parameters can result in substantial deviations from the nominal insertion altitude. The acceptability of errors in specific impulse changes varies across stages, with maximum changes of 6.07%, and the fourth stage showing less sensitivity at 0.13%. However, it's important to note that variations in the parameters of the first stage tend to be challenging to rectify once they occur, with maximum changes in specific impulses reaching 75.57%. Another noteworthy discovery is that the acceptability of changes in pitch-over manoeuvre initiation times depends on the rate of change; they can be deemed either acceptable or unacceptable based on this factor, with changes ranging between 17.90% and 98.38%.

Keywords

• Launch vehicles
• Sensitivity analysis
• Trajectory design

References

1. Castro, M. P. (2015). AFRC Core Simulation Overview (No. AFRC-E-DAA-TN23131).
2. Stewart, S. M., Ward, L., & Strand, S. Distributed GN&C Flight Software Simulation for Spacecraft Cluster Flight. In Proceedings of the 37th Annual AAS Guidance and Control Conference, AAS, 14-32.
3. Leslie, R., Geyer, D., Cunningham, K., Glaab, P., Kenney, P., & Madden, M. (1998). LaSRS++-An object-oriented framework for real-time simulation of aircraft. In AIAA Modeling and Simulation Technologies Conference and Exhibit, 382-388. https://doi.org/10.2514/6.1998-4529
4. Phys.org. (2004). Marshall Center names flight simulator 2004 'Software of the Year'. https://phys.org/news/2004-07-marshall-center-flight-simulator-software.html
5. Zwack, M. R., Dees, P. D., Thomas, H. D., Polsgrove, T. P., & Holt, J. B. (2017). Program to Optimize Simulated Trajectories II (POST2) Surrogate Models for Mars Ascent Vehicle (MAV) Performance Assessment (No. NASA/TM-2017-219842).
6. Anton, P. S., Raman, R., Osburg, J., & Kallimani, J. G. (2009). An Update of the Nation’s Long-Term Strategic Needs for NASA’s Aeronautics Test Facilities. The RAND Corporation, Santa Monica, CA.
7. NASA. (2008). OTIS 3.2 Software Released. https://ntrs.nasa.gov/api/citations/20050215610/downloads/20050215610.pdf
8. Cremaschi, F., Weikert, S., Schäff, S., & Wiegand, A. (2018). ASTOS, a reconfigurable software for design of mega constellations, operation of Flying Laptop and end-of-life disposal. In 2018 SpaceOps Conference (p. 2496).

9. AGI website (2018). http://www.agi.com/home.
10. Kirkpatrick, D. (1999). Space mission analysis and design, 8. Torrance: Microcosm.
11. Aguirre, M. A. (2012). Introduction to space systems: design and synthesis, 27. Springer Science & Business Media.
12. Sarafin, T. P., & Larson, W. J. (1995). Spacecraft structures and mechanisms: from concept to launch. Springer Dordrecht
13. Cornelisse, J. W., Schöyer, H. F. R., & Wakker, K. F. (1979). Rocket Propulsion and Spaceflight Dynamics. Aerospace Engineering Series. Pitman.
14. Diederiks-Verschoor, I. H. (2008). An introduction to space law. Kluwer Law International.
15. Mastroddi, F., Stella, F., Polli, G. M., & Giangi, M. (2008). Sensitivity analysis for the dynamic aeroelasticity of a launch vehicle. Journal of Spacecraft and Rockets, 45(5), 999-1009. https://doi.org/10.2514/1.30725
16. McGhee, D. S., Peck, J. A., & McDonald, E. J. (2012). Probabilistic Sensitivity Analysis for Launch Vehicles with Varying Payloads and Adapters for Structural Dynamics and Loads. In 14th AIAA Non-Deterministic Approaches Conference, M11-0845.
17. Yang, S. S. (2020). Sensitivity Analysis of Major Cost Parameters on the Launch Cost of Reusable Vehicles. Journal of the Korean Society of Propulsion Engineers, 24(2), 35-42. https://doi.org/10.6108/KSPE.2020.24.2.035
18. Jodei, J., Ebrahimi, M., & Roshanian, J. (2009). Multidisciplinary design optimization of a small solid propellant launch vehicle using system sensitivity analysis. Structural and Multidisciplinary Optimization, 38, 93-100. https://doi.org/10.1007/s00158-008-0260-5
19. Kresse, W., & Danko, D. M. (Eds.). (2012). Springer handbook of geographic information, 118-120. Berlin, Springer.
20. Chang, K. T. (2008). Introduction to geographic information systems (Vol. 4). Boston: McGraw-Hill.
21. Cai, G., Chen, B. M., & Lee, T. H. (2011). Unmanned rotorcraft systems. Springer Science & Business Media.
22. Hotine, M. (1991). Geodetic coordinate systems. In Differential Geodesy, 65-89. Berlin, Heidelberg: Springer Berlin Heidelberg.
23. Seemkooei, A. A. (2002). Comparison of different algorithms to transform geocentric to geodetic coordinates. Survey Review, 36(286), 627-633.
24. Janota, A., Šimák, V., Nemec, D., & Hrbček, J. (2015). Improving the precision and speed of Euler angles computation from low-cost rotation sensor data. Sensors, 15(3), 7016-7039. https://doi.org/10.3390/s150307016
25. Tewari, A. (2011). Advanced control of aircraft, spacecraft and rockets. John Wiley & Sons.
26. Stevens, B. L., Lewis, F. L., & Johnson, E. N. (2015). Aircraft control and simulation: dynamics, controls design, and autonomous systems. John Wiley & Sons.
27. Christodoulou, N. S. (2009). An algorithm using Runge-Kutta methods of orders 4 and 5 for systems of ODEs. International Journal of Numerical Methods and Applications, 2(1), 47-57.
28. Malys, S., Wong, R., & True, S. A. (2016). The WGS 84 terrestrial reference frame in 2016. In Eleventh Meeting of the International Committee on GNSS, ICG-11, 6-11.
29. International Civil Aviation Organization (2002). World Geodetic System, 1984 (WGS-84) Manual.
30. Amin, M. M., El-Fatairy, S. M., & Hassouna, R. M. (2002). A Better Match of the EGM96 Harmonic Model for the Egyptian Territory Using Collocation. Port-Said Engineering Research Journal PSERJ, 6(2), 1-16.
31. Markley, F. L., & Crassidis, J. L. (2014). Fundamentals of Spacecraft Attitude Determination and Control. Space Technology Library. Springer New York
32. Atmosphere, U. S. (1976). US standard atmosphere. National Oceanic and Atmospheric Administration.
33. Sutton, G. P., & Biblarz, O. (2016). Rocket propulsion elements. John Wiley & Sons.
34. Tewari, A. (2007). Atmospheric and space flight dynamics. Birkhũser Boston.
35. Buckley, M. S., Weis, C. S., Marina, L. L., Morris, L. C., & Schoneman, S. (1998). The Orbital/Suborbital Program (OSP)" Minotaur" Space Launch Vehicle: Using Surplus ICBM Motors to Achieve Low Cost Space Lift for Small Satellites.
36. Minotaur (2020). Minotaur I User’s Guide. Northrop Group.
37. Suresh, B. N., & Sivan, K. (2015). Integrated design for space transportation system, 142-143. New Delhi: Springer India.
38. Sooy, T. J., & Schmidt, R. Z. (2005). Aerodynamic predictions, comparisons, and validations using missile datcom (97) and aeroprediction 98 (ap98). Journal of Spacecraft and Rockets, 42(2), 257-265. https://doi.org/10.2514/1.7814
39. Morante, D., Sanjurjo Rivo, M., & Soler, M. (2021). A survey on low-thrust trajectory optimization approaches. Aerospace, 8(3), 88. https://doi.org/10.3390/aerospace8030088
40. Borg, L. (2023). Concept investigation into metal plasma source for high powered space applications.