混合火箭近年來備受矚目，然而有關三節皆採用混合引擎的運載火箭的研究文獻相對稀缺。為了填補這一研究領域的空白，本論文不僅將深入介紹火箭的運動方程式及其所受的各種作用力，更將提供詳盡的資訊，以豐富對混合火箭運行機制的理解。接著，在MATLAB的Simulink環境下進行的模擬步驟和假設約束將被仔細闡述，以協助讀者理解模擬過程中所使用的方法和技術。這包括模型的建立、參數的設定以及模擬的運行過程，從而為後續深入的模擬分析打下基礎。最後，本論文將回歸主題，即混合運載火箭的入軌模擬，討論在沒有額外控制器和攻角一直保持零度的情況下，自行設計一架全新的混合火箭，並引入額外的約束條件，以更貼近實際操作環境。透過窮舉法和蒙地卡羅方法，我們將深入研究火箭各參數對酬載入軌結果的影響，並探討如何找到最佳的模擬結果，這有望為混合火箭的設計和性能優化提供實用的指南。

Hybrid rockets have attracted increasing attention in recent years; however, research literature on launch vehicles employing hybrid engines for all three stages is relatively scarce. To address this gap in the research field, this paper not only delves into the motion equations of rockets and the various forces they experience but also provides detailed information to enhance understanding of the operational mechanisms of hybrid rockets. Subsequently, the simulation steps and assumed constraints carried out in the MATLAB Simulink environment will be carefully elucidated, aiding readers in comprehending the methods and techniques employed during the simulation process. This encompasses model construction, parameter configuration, and the simulation execution process, laying the groundwork for subsequent in-depth simulation analyses.
In conclusion, this paper returns to its main theme, the trajectory simulation of hybrid launch vehicles. It discusses the design of a novel hybrid rocket with no additional controllers and a constant zero-degree angle of attack. Additional constraints are introduced to better mimic real operational environments. Through exhaustive methods and Monte Carlo simulations, we will thoroughly investigate the impact of various rocket parameters on payload trajectory results. The aim is to explore how to achieve the optimal simulation results, providing practical guidance for the design and performance optimization of hybrid rockets.

[1] M. J. Turner, Rocket and spacecraft propulsion: principles, practice and new developments. Springer Science & Business Media, 2008.
[2] C. B. Christensen, B. Dunn, H. Nguyen Le, R. Puleo, and C. Mullins, "Start-up Space: Update on Record Investment and Global Trends in Commercial Space Ventures and its Implications on the Expansion of Space Commerce," in ASCEND 2023, 2023, p. 4601.
[3] "Space Economy Report, 9th ed," Euroconsult: Courbevoie, France.
[4] "Start-Up Space Report 2022," BryceTech: Alexandria, VA, USA, 2022.
[5] "Smallsats by the Numbers 2023," BryceTech: Alexandria, VA, USA, 2023.
[6] "2022 State of the Satellite Industry Report;," BryceTech: Alexandria, VA, USA, 2022.
[7] "2022 Orbital Launches Year in Review," BryceTech: Alexandria, VA, USA, 2023.
[8] E. L. Petersen et al., "Solid propellant rocket motor having self-extinguishing propellant grain and systems therefrom," ed: Google Patents, 2012.
[9] M. Gruntman, Blazing the trail: the early history of spacecraft and rocketry. AIAA, 2004.
[10] A. B. Van Riper, Rockets and missiles: the life story of a technology. JHU Press, 2007.
[11] G. P. Sutton and O. Biblarz, Rocket propulsion elements. John Wiley & Sons, 2016.
[12] A. Karabeyoglu, "Hybrid rocket propulsion for future space launch," Department of Aeronautics and Astronautics, Stanford University, Aero/Astro 50th Year Anniversary, 2008.
[13] G. Cai, H. Zhu, D. Rao, and H. Tian, "Optimal design of hybrid rocket motor powered vehicle for suborbital flight," Aerospace Science and Technology, vol. 25, no. 1, pp. 114-124, 2013.
[14] F. d. S. Costa and R. Vieira, "Preliminary analysis of hybrid rockets for launching nanosats into LEO," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 32, pp. 502-509, 2010.
[15] L. Casalino, F. Letizia, and D. Pastrone, "Optimization of hybrid upper-stage motor with coupled evolutionary/indirect procedure," Journal of Propulsion and Power, vol. 30, no. 5, pp. 1390-1398, 2014.
[16] M. A. Karabeyoglu and D. Altman, "Dynamic modeling of hybrid rocket combustion," Journal of Propulsion and Power, vol. 15, no. 4, pp. 562-571, 1999.
[17] W. H. Knuth, M. J. Chiaverini, J. A. Sauer, and D. J. Gramer, "Solid-fuel regression rate behavior of vortex hybrid rocket engines," Journal of Propulsion and power, vol. 18, no. 3, pp. 600-609, 2002.
[18] M. Karabeyoglu, D. Altman, and B. J. Cantwell, "Combustion of liquefying hybrid propellants: Part 1, general theory," Journal of Propulsion and Power, vol. 18, no. 3, pp. 610-620, 2002.
[19] G. Cai, P. Zeng, X. Li, H. Tian, and N. Yu, "Scale effect of fuel regression rate in hybrid rocket motor," Aerospace Science and Technology, vol. 24, no. 1, pp. 141-146, 2013.
[20] C. Oztan and V. Coverstone, "Utilization of additive manufacturing in hybrid rocket technology: A review," Acta astronautica, vol. 180, pp. 130-140, 2021.
[21] K. K. Kuo and M. J. Chiaverini, Fundamentals of hybrid rocket combustion and propulsion. American Institute of Aeronautics and Astronautics, 2007.
[22] F. Barato, "Review of Alternative Sustainable Fuels for Hybrid Rocket Propulsion," Aerospace, vol. 10, no. 7, p. 643, 2023.
[23] C. Oiknine, "New perspectives for hybrid propulsion," in 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2006, p. 4674.
[24] M. J. Chiaverini, N. Serin, D. K. Johnson, Y.-C. Lu, K. K. Kuo, and G. A. Risha, "Regression rate behavior of hybrid rocket solid fuels," Journal of Propulsion and Power, vol. 16, no. 1, pp. 125-132, 2000.
[25] F. Barato, N. Bellomo, and D. Pavarin, "Integrated approach for hybrid rocket technology development," Acta Astronautica, vol. 128, pp. 257-261, 2016.
[26] K. K. Kuo, "Challenges of hybrid rocket propulsion in the 21st century," Fundamentals of hybrid rocket combustion and propulsion, vol. 18, pp. 593-638, 2007.
[27] A. Okninski, W. Kopacz, D. Kaniewski, and K. Sobczak, "Hybrid rocket propulsion technology for space transportation revisited-propellant solutions and challenges," FirePhysChem, vol. 1, no. 4, pp. 260-271, 2021.
[28] M. Bouziane, A. E. d. M. Bertoldi, P. Hendrick, and M. Lefebvre, "Experimental investigation of the axial oxidizer injectors geometry on a 1-kN paraffin-fueled hybrid rocket motor," FirePhysChem, vol. 1, no. 4, pp. 231-243, 2021.
[29] A. Mazzetti, L. Merotto, and G. Pinarello, "Paraffin-based hybrid rocket engines applications: A review and a market perspective," Acta Astronautica, vol. 126, pp. 286-297, 2016.
[30] Y.-S. Chen and B. Wu, "Development of a small launch vehicle with hybrid rocket propulsion," in 2018 Joint Propulsion Conference, 2018, p. 4835.
[31] T. Marquardt and J. Majdalani, "Review of classical diffusion-limited regression rate models in hybrid rockets," Aerospace, vol. 6, no. 6, p. 75, 2019.
[32] S. A. Whitmore, Z. W. Peterson, and S. D. Eilers, "Closed-loop precision throttling of a hybrid rocket motor," Journal of Propulsion and Power, vol. 30, no. 2, pp. 325-336, 2014.
[33] G. Story, T. Abel, S. Claflin, O. Park, J. Arves, and D. Kearney, "Hybrid propulsion demonstration program 250K hybrid motor," in 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2003, p. 5198.
[34] A. Karabeyoglu, G. Zilliac, B. J. Cantwell, S. DeZilwa, and P. Castellucci, "Scale-up tests of high regression rate paraffin-based hybrid rocket fuels," Journal of propulsion and power, vol. 20, no. 6, pp. 1037-1045, 2004.
[35] A. Chandler, E. Jens, B. Cantwell, and G. S. Hubbard, "Visualization of the liquid layer combustion of paraffin fuel for hybrid rocket applications," in 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2012, p. 3961.
[36] K.-H. Shin, C. Lee, S. Y. Chang, and J. Y. Koo, "The enhancement of regression rate of hybrid rocket fuel by various methods," in 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005, p. 359.
[37] O. Orlandi et al., "Toward advanced solid fuels for hybrid propulsion," in Space Propulsion Conference, 2010.
[38] L. Galfetti, L. Merotto, M. Boiocchi, F. Maggi, and L. De Luca, "Ballistic and rheological characterization of paraffin-based fuels for hybrid rocket propulsion," in 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2011, p. 5680.
[39] M. Kanazaki, H. Yoda, K. Chiba, K. Kitagawa, and T. Shimada, "Design methodology of a hybrid rocket-powered launch vehicle for suborbital flight," Journal of aerospace engineering, vol. 30, no. 6, p. 04017071, 2017.
[40] F. M. Villanueva, H. Linshu, A. F. Rafique, and T. Rahman, "Small launch vehicle trajectory profile optimization using hybrid algorithm," in Proceedings of 2013 10th International Bhurban Conference on Applied Sciences & Technology (IBCAST), 2013: IEEE, pp. 163-168.
[41] 呂奕廷, "火箭升空 射出台灣太空夢," 2018.
[42] 彭婉玲, "[參與共好] ARRC 的一小步, 台灣的一大步——MIT 火箭起飛不是夢," 神農坡雜誌, no. 23, pp. 24-29, 2023.
[43] 陳學民, "探空火箭計畫--蘭摩爾探針系統," 2010.
[44] F. Morgado, A. Marta, and P. Gil, "Multistage rocket preliminary design and trajectory optimization using a multidisciplinary approach," Structural and Multidisciplinary Optimization, vol. 65, no. 7, p. 192, 2022.
[45] G. W. Collins, The foundations of celestial mechanics. 2004.
[46] J. R. Wertz, Spacecraft attitude determination and control. Springer Science & Business Media, 2012.
[47] D. A. Vallado, Fundamentals of astrodynamics and applications. Springer Science & Business Media, 2001.
[48] J. Ries, R. Eanes, C. Shum, and M. Watkins, "Progress in the determination of the gravitational coefficient of the Earth," Geophysical research letters, vol. 19, no. 6, pp. 529-531, 1992.
[49] V. A. Chobotov, Orbital mechanics. Aiaa, 2002.
[50] A. Tewari, Atmospheric and space flight dynamics. Springer, 2007.
[51] H. Moritz, "Geodetic reference system 1980," Journal of Geodesy, vol. 74, no. 1, pp. 128-133, 2000.
[52] K. R. Britting, Inertial navigation systems analysis. 2010.
[53] R. Boynton, "Precise measurement of mass," in 60th Annual Conference of the Society of Allied Weight Engineers, 2001, vol. 204.
[54] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55. Tenth Printing," 1972.
[55] R. Cooper, "Nuclear propulsion for space vehicles," Annual Review of Nuclear Science, vol. 18, no. 1, pp. 203-228, 1968.
[56] C. Charles, "Plasmas for spacecraft propulsion," Journal of Physics D: Applied Physics, vol. 42, no. 16, p. 163001, 2009.
[57] K. Tsiolkovsky, "Reactive Flying Machines," Izdatel’stvo Akademii Nauk SSSR: Moscow, Russia, 1954.
[58] A. Darrin and B. L. O'Leary, Handbook of space engineering, archaeology, and heritage. CRC Press, 2009.
[59] L. Hillion, J.-D. Parisse, and A. Mangeot, "Preliminary sizing and study of a hybrid rocket based combined cycle," Frontiers in Space Technologies, vol. 4, p. 1103981, 2023.
[60] "Encyclopedia Astronautica." http://www.astronautix.com/index.html (accessed.
[61] U. Walter and U. Walter, "Atmospheric and ascent flight," Astronautics: The Physics of Space Flight, pp. 121-163, 2018.
[62] N. Oceanic and A. Administration, "US standard atmosphere, 1976," Technical Report, 1976.
[63] U. S. C. o. E. t. t. S. Atmosphere, U. S. A. Force, U. S. W. Bureau, U. S. N. Oceanic, and A. Administration, US standard atmosphere. National Oceanic and Amospheric [sic] Administration, National Aeronautics …, 1962.
[64] D. Anderson, J. C. Tannehill, R. H. Pletcher, R. Munipalli, and V. Shankar, Computational fluid mechanics and heat transfer. CRC press, 2020.
[65] G. Karniadakis, A. Beskok, and N. Aluru, Microflows and nanoflows: fundamentals and simulation. Springer Science & Business Media, 2006.
[66] D. F. Elger, B. A. LeBret, C. T. Crowe, and J. A. Roberson, Engineering fluid mechanics. John Wiley & Sons, 2020.
[67] A. Sommerfeld, Ein beitrag zur hydrodynamischen erklaerung der turbulenten fluessigkeitsbewegungen. 1909.
[68] D. Halliday, R. Resnick, and J. Walker, Fundamentals of physics. John Wiley & Sons, 2013.
[69] E. D. Martin, A study of laminar compressible viscous pipe flow accelerated by an axial body force, with application to magnetogasdynamics. National Aeronautics and Space Administration, 1961.
[70] F. J. Regan, Dynamics of atmospheric re-entry. Aiaa, 1993.
[71] J. H. Lienhard, A heat transfer textbook. Phlogistron, 2005.
[72] N. Space, "National Aeronautics and Space Administration," Retrieved from National Aeronautics and Space Administration: www. nasa. gov, 1977.
[73] E. L. Houghton and P. W. Carpenter, Aerodynamics for engineering students. Elsevier, 2003.
[74] L. M. Milne-Thomson, Theoretical aerodynamics. Courier Corporation, 1973.
[75] L. J. Clancy, "Aerodynamics," (No Title), 1975.
[76] P. A. Chambre and S. A. Schaaf, Flow of rarefied gases. Princeton University Press, 2017.
[77] M. Reilly and N. R. L. W. DC, "Equations of powered rocket ascent and orbit trajectory," NRL Report, vol. 8237, pp. 75-83, 1979.
[78] H. D. Curtis, Orbital mechanics for engineering students. Butterworth-Heinemann, 2013.
[79] "Proton-K." http://www.astronautix.com/p/proton-k.html (accessed.
[80] D. M. Gaspar, "A Tool for Preliminary Design of Rockets," Instituto Superior Tecnico, Masters Thesis, 2014.
[81] A. Y. Mission, "PROTON LauNch SySTem miSSiON PLaNNeR’S Guide," 2009.
[82] "N2O4/UDMH." http://www.astronautix.com/n/n2o4udmh.html (accessed.
[83] G. A. Crowell Sr, "The descriptive geometry of nose cones," URL: http://www. myweb. cableone. net/cjcrowell/NCEQN2. doc, 1996.
[84] P. A. Ritter, "Optimization and design for heavy lift launch vehicles," 2012.
[85] "Europa I." http://www.astronautix.com/e/europai.html (accessed.
[86] D. P. Kroese, T. Brereton, T. Taimre, and Z. I. Botev, "Why the Monte Carlo method is so important today," Wiley Interdisciplinary Reviews: Computational Statistics, vol. 6, no. 6, pp. 386-392, 2014.