## 1 Introduction  
A Launch Vehicle (LV) design requires complex decisions to be made from the start of the design phase. Mission designers must decide on inter-related factors, which include the most feasible engine design and propellants to reach the mission's requirements, environmental impact, manufacturing processes, overall cost and the availability and skillset of human resource required to manufacture, test and deploy a launch vehicle [1]. These factors are all inter-connected, highlighting the intricacies involved in making major decisions at an early stage of the design process. A typical rocket engine uses solid, liquid or hybrid propellants. Compared to solid or hybrid propellants, liquid propellants have the following advantages: (1) relatively high energy density, which leads to a higher Specific Impulse (\(I_{sp}\)), resulting in increased engine efficiency; (2) propellant storage tanks require a reasonably low volume; (3) engine throttling (if required) is easily achieved by varying the propellant flow rate in order to control the thrust; (4) allowance for multiple burns as the engine can be repeatedly shut down and restarted [2]. Liquid Propellant Rocket Engines (LPREs) are classified by their propellant feed system: either pressure fed or pump fed. Mission designers prefer pump-fed LPREs due to the higher combustion chamber pressure (\(p_{c}\)) produced. Higher \(p_{c}\) results in a relatively smaller engine; therefore, the payload carrying capacity of the overall LVincreases. However, pump-fed engines, also known as turbopump engines, come with varying complexities. There are three types of turbopump LPRE cycles: Gas Generator (GG), Staged Combustion (SC) and Expander. GG and SC cycles contain a secondary combustion chamber where tapped-off fuel and oxidizers are ignited. The resulting exhaust gases are used to power the turbine. This turbine powers the pumps, which raise the propellant pressure to the required \(p_{c}\). In SC, the exhaust gases are redirected back to the main chamber for complete combustion. Expander cycles do not contain a secondary combustion chamber. Such engines are only used for cryogenic propellants as their heat of vaporization is greater; therefore, more energy can be extracted and used in mechanical work. Thus, Expander cycle LPREs are only used as upper stage engines in LVs. Hence, for single-stage LVs or first-stage engines, there is often a tradeoff between GG and SC engines: SC engines typically achieve higher \(p_{c}\); therefore, the LV can carry greater payloads. However, this increase in payload comes at the expense of greater design complexity. The design phase for an LV consists of three stages: conceptual, preliminary and detailed design. The propellant pair and engine cycle are finalized in the conceptual design phase. The mission designer's main aim is to maximize the LPRE performance while simultaneously minimizing the overall LV weight in order to increase the payload [3]. According to [PERSON] [4], the Life-Cycle Cost (LCC) of an LV follows the Pareto Principle: 80% of a vehicle's LCC is finalized at the conceptual design stage.Thus, any changes in the preliminary or detailed design stages do not result in exponential improvements. Therefore, to minimize the risk of major revisions at a later stage in the design cycle, research recommends a thorough analysis of all major sub-systems and components at the conceptual design phase [5]. The use of multiple trade-off studies during the conceptual design stage enables mission designers to quantitatively determine the effect of mission requirements on the engine's performance and overall LV size. Such studies aid mission designers in understanding the effect of interconnected variables such as propellant mass, LV weight, \(p_{c}\), thrust and manufacturing complexity [6]. Trade-off studies rely on mathematical tools to model the propulsion sub-systems and provide LV mass estimates.