## 1 Introduction  
Since the beginning of the space race, a variety of launch vehicles have been developed to transport a satellite to Earth's orbit or beyond, astronauts to the Moon, or scientific instruments and cargo to the International Space Station. Launch vehicles or launchers can be classified according to their mass capabilities such as heavy-lift, medium-lift, and small-lift, while ballistic missiles have been transformed into space launch vehicles; for example, Delta IV from the heavy-lift launch vehicle category was derived from the Thor intermediate-range ballistic missile, which was the first operational ballistic missile of the United States Air Force (USAF); and the small-lift Falcon-9 was derived from many of today's launch vehicles to avoid the cost and simplify the design process [1]. Traditionally, small satellites and light-weight satellites have been launched into space as secondary payloads on larger launch vehicles. However, the secondary payload approach did not provide specific requirements such as launch timing and orbital characteristics for many small satellites. Therefore, smaller launch vehicles for a wide range of applications for small satellite missions have been started to be developed. With the increased number of small satellites developed and launched yearly, there has been a strong need to reduce launch costs and lower handling and preparation times. HRM stands out as a strong candidate to meet these needs with advantages such as increased safety, throttle control, environmentally friendly propellants, simplified design, cost-effectiveness, combustion efficiency, ease of testing and handling, and potential for reusable components, making them attractive for specific applications. Several pioneering companies have been at the forefront of advancing hybrid rocket propulsion technology, fusing the advantages of both solid and liquid propulsion methods. Virgin Galactic, renowned for its suborbital space tourism endeavors, has also delved into hybrid rocket technology for its SpaceShipTwo suborbital spacecraft [2]. Notably, ARCA Space Corporation has been working diligently on hybrid rocket technology with aspirations to create launch vehicles and spacecraft capable of deploying payloads to various orbits [3]. Beyond these, ExPace, a subsidiary of China Aerospace Science and Industry Corporation (CASIC), has made strides in the hybrid propulsion sector, particularly with the Kuiazhou series of rockets, contributing to China's space endeavors [4]. Additionally, Nammo, a European aerospace and defense company, has demonstrated commitment to hybrid rocket technology, joining the ranks of innovative entities aiming to revolutionize propulsion in both civil and military applications [5]. The HANBIT-TLV suborbital rocket serves as a precursor to the company's upcoming commercial satellite launcher, the Hanbit-Nano [6]. This two-stage small satellite launcher is meticulously designed to transport payloads weighing up to 50 kg to a 500 km sun-synchronous orbit. These companies, among others, symbolize cutting-edge progress in hybrid rocket propulsion, which has domain-rich potential to transform space access and exploration paradigms. The results from a comparison of the advantages and disadvantages of SRMs, LRMs, and HRMs shown in Table 1. Articles by [PERSON] and [PERSON] (1991), [PERSON] and [PERSON] (1992), [PERSON] and [PERSON] (1998), [PERSON] and [PERSON] (2001), [PERSON] (2002), [PERSON] (2003), [PERSON] (2003), [PERSON] (2007), [PERSON] et al. (2009), [PERSON] et al. (2012), [PERSON] et al. (2012), [PERSON] (2014), [PERSON] et al. (2015), [PERSON] et al. (2015), [PERSON] et al. (2017), [PERSON] (2019), [PERSON] et al. (2022), [PERSON] and [PERSON] (2022), and [PERSON] (2022) present very detailed studies on HRMs and their historical developments. HRMs have been extensively studied due to their unique design combining solid and liquid propulsion elements [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27].