## 1 Introduction
Their historical development spans decades, with significant advancements in understanding combustion dynamics, performance optimization, and safety enhancements. These studies have contributed to the broader field of rocket propulsion, offering innovative solutions and insights into efficient and reliable space propulsion technologies. In Table 1, the items indicated with a \"+\" sign on the table represent advantages, those with a \"\(-\)\" sign indicate disadvantages, and \"N/A\" signifies the absence of either advantages or disadvantages. According to Table 1, solid rocket propulsion offers advantages in simplicity and reliability due to minimal moving parts, featuring stable propellants ideal for extended storage and fixed thrust profiles as seen in boosters. However, a drawback is their lack of throttle control, impeding precise adjustments, and once ignited, they are not easily shut down. This contrasts with liquid propulsion, which provides precise throttle control and restart capabilities for intricate missions like orbital maneuvers. Liquid propellants enhance fuel efficiency and performance with high specific impulse allowing for a variety of propellant combinations. Nonetheless, the complexity of liquid motors leads to increased manufacturing and maintenance costs, and volatile propellants demand cautious handling due to potential degradation. On another point, hybrid propulsion amalgamates solid safety with liquid control, excelling in throttle adaptability and potentially higher efficiency, and some hybrid propellants are environmentally friendlier. The superior density-specific impulse (\(\rho-I_{sp}\)) values exhibited by solid propellants render them highly suitable for deployment in compact stages, which are particularly well-suited for the initial phases of a launch vehicle. Their inherent reliability, devoid of the need for pumps and valves, is a noteworthy characteristic [7]. However, this commendable performance and shutoff control capability may not extend effectively to upper stages due to the limitations associated with lower \(I_{sp}\) of around 210-250 s. In contrast, liquid rocket motors (LRMs) circumvent these challenges by offering higher \(I_{sp}\) and the added advantage of flexible stop-and-restart capabilities. Typically, liquid oxygen (LOX) serves as the oxidizer (\(O\)), while either liquid hydrogen (LH2) or RP-1 functions as the fuel (\(F\)), influencing propellant performance significantly [3]. Hybrid rocket motors (HRMs) share performance similarities with storable or semiconyro LCMs. With oxygen (\(Ox\)) stored separately from \(F\), HRMs boast the ability to be shut off and restarted akin to LRMs, along with the capacity for throttling within a broad thrust (\(T\)) range [3]. Combining advantageous features of both solid rocket motors (SRMs) and LRMs, HRMs have garnered considerable attention in contemporary technologies, primarily due to their merits in terms of high safety, simplicity, cost-effectiveness, stop-and-restart capability, throttling ability, and the utilization of environmentally friendly propellant combinations. Despite these advantages, HRMs exhibit certain drawbacks, including a low solid \(F\) regression rate and intricacies related to the coupling between mixture-ratio values and thrust levels. Notwithstanding these issues, the successful utilization of HRMs in SpaceShipOne, marking the first private manned space flight, underscores their potential and applicability [4]. The distinctive characteristics of HRMs, such as the separate storage of solid and liquid oxidizers, contribute to enhanced safety and cost-effectiveness throughout the manufacturing, storage, transportation, and operational processes [10]. The specified features indicate that HRMs are advantageous compared to solid and liquid rocket motors, and the importance of their use is highlighted in conjunction with evolving technology.