1. Optimal Sizing for a Reusable Launch Vehicle
Optimal sizing refers to determining the stage weight of a multi-stage rocket that satisfies the mission requirements for given properties while minimizing the Gross Lift-Off Weight (GLOW) of the rocket. Despite numerous sizing approaches for an expendable launch vehicle, studies on a reusable launch vehicle (RLV) are scarce.
This research proposes an optimal sizing method for an RLV for the first time. The method regards the propellant required for the landing of a reusable stage as the structure mass during ascent and accordingly decomposes the structure fraction into two terms for ascent and descent, respectively. Afterward, it establishes an optimization problem (sizing module) corresponding to the given velocity losses. To precisely estimate the velocity losses, this research incorporates trajectory optimization with the sizing module and solves iteratively the two problems until convergence.
Fig. 1: Mass configuration of an RLV
2. Cost Awareness Design
Over the past few decades, the development of launch vehicles has been generally led by the government with the primary concerns of mission success, national security, and technological advancements. However, with the advent of the new space era, numerous private companies have emerged as technologies have matured and the demand for space transportation has increased. It has naturally brought about a paradigm shift in space development from government-led to private company-led. As a result, cost plays a key role in rocket design as private companies strive to maximize profits by reducing the costs incurred to develop, manufacture, and operate launch vehicles.
Fig. 2: A four step design procedure for an RLV
For an expendable launch vehicle, it is reasonable to assume that the launch cost is proportional to the GLOW, and thus the minimum GLOW guarantees the minimum launch cost. However, in the case of an RLV, reducing the GLOW does not always decrease the launch cost during its life cycle. Fig. 3 illustrates a situation where the launch cost of an RLV designed for the minimum GLOW (left) becomes more expensive with an increasing reuse number than the one designed for the minimum cost (right).
This research introduces a four-step design procedure aimed at minimizing the launch cost of an RLV. It involves establishing a parametric cost model using cost estimation relationships (CER) to evaluate the life cycle cost of an RLV. This model serves as the objective function of the optimization problem. The procedure integrates the sizing and trajectory modules, thereby finding the expendable stage weight that minimizes the life cycle cost for a given reusable stage weight in a single process. The proposed procedure begins with selecting the range of interest for reusable stage weight and discretizing the range into n search points, and then solves the semi-integrated optimization problem n times. After obtaining cost data corresponding to each search point, the procedure identifies the optimal point representing the minimum cost.
Fig. 3: Possible cost reduction from cost-awareness design
Fig. 4: Launch sequence of an RLV
3. Rocket family design
There has been an increasing demand for various types of launchers capable of carrying a wide variety of satellites, spacecraft, and cargo to space. As a result, various rocket companies, such as Space X, Blue Origins, and Rocket Labs, are operating or developing more than one type of launcher simultaneously.
Leveraging commonalities is one of the most profitable strategies when developing multiple rockets since the components, such as engines, fairings, and stage structures, incur significant costs. That is, sharing compatible components enables manufacturers to operate the same product line for different rockets and avoid additional development for the components, resulting in cost and time savings.
In this work, we develop a sizing procedure for a two-members rocket family capable of fulfilling multiple missions considering the commonalities between the members. The procedure aims to take full advantage of sharing a common part across multiple rockets whose payload capability differs entirely, ultimately leading to cost and time savings in designing a rocket family.
A case study on a rocket family that involves an existing RLV, Falcon 9, and a preliminary designed expendable launch vehicle demonstrates the effectiveness of the proposed procedure. It shows that each vehicle saves costs of approximately 5~13% depending on the number of launches and reuses by sharing the compatible stage.
Fig. 5: Commonality check between two rockets