Two-stage launch vehicles have an optimum velocity for first stage separation that maximizes payload mass
the verdict
INSUFFICIENT LEANING
refutedsupported
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The retrieved literature touches on optimal staging concepts and factors influencing staging velocity and vehicle mass, but provides only partial support without fully establishing that first-stage separation velocity is optimized specifically to maximize payload mass.
The vertical-takeoff–horizontal-landing (VTHL) two-stage-to-orbit (TSTO) system is a kind of novel launch vehicle in which a reusable first stage can take off vertically like a rocket and land horizontally like an airplane. The advantage of the VTHL TSTO vehicle is that the launch costs can be reduced significantly due to its reusable first stage. This paper presents an application of multidisciplinary analysis optimization on preliminary sizing in conceptual design of the VTHL TSTO vehicle. The VTHL TSTO concept is evaluated by multidisciplinary analysis, including geometry, propulsion, aerodynamics, mass, trajectory, and static stability. The preliminary sizing of the VTHL TSTO vehicle is formulated as a multidisciplinary optimization problem. The focus of this paper is to investigate the impacts of the first-stage reusability and propellant selection on the staging altitude and velocity, size, and mass of the VTHL TSTO vehicles. The observations from the results show that the velocity and altitude of the optimal staging point are determined mainly by the reusability of the first stage, which in turn affects the size and mass of the upper stage and the first stage. The first stage powered by hydrocarbon fuel has a lower dry mass compared with that powered by liquid hydrogen.
Abstract A rocket must carry the fuel it expels in order to accelerate its structure and payload. The rocket equation relates the change in speed to the fuel mass expelled. To launch a spacecraft into Earth orbit requires a multi-stage rocket, since otherwise the mass of fuel required would be prohibitive. While the details vary among historical and current launch vehicles, the advantages and physical principles of staging can be demonstrated by analysing the simpler case of a two-stage rocket in free space. I show that a two-stage rocket produces a higher payload speed than a single-stage rocket with the same fuel and structural mass, and introduce the concept of optimal staging to maximise this speed. I also examine how mechanical energy extracted from the expelled fuel is distributed between the stages, payload capsule, and exhaust. A surprising result is that the two-stage rocket deposits more energy into the exhaust stream than its single-stage counterpart. I suggest further investigations that are appropriate for advanced high school or undergraduate students of physics or aerospace engineering. Supplementary materials are provided online for classroom use.
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