Space Trajectories. Launcheur Staging

A space launcher consists of propulsion stages capable of reaching an orbital speed of at least 8 km/s. Propulsion is anaerobic, as ambient oxygen becomes insufficient above 30 km altitude. All the fuel required is carried by the launcher at lift-off, resulting in a very high mass. Rocket propulsion uses propellants (solids) or ergols (liquids with an oxidizer and a reducer stored separately). We use the term ergols for simplicity's sake.

A single-stage launcher is penalized by the dry mass retained until injection into orbit. Staging consists in dividing the propellants into stages (between 2 and 4) with their own engines, tanks, structures and equipment. The stages are jettisoned at the end of combustion to lighten the launcher's remaining mass. Design choices concern the number of stages, their dimensions, general architecture, propellant technologies (propellants, engines) and structural technologies (steel, aluminum, stainless steel, carbon), propellant masses and thrust levels. These choices determine the development of the launcher, which takes several years. It is very difficult to call them into question at a later date, and a poor initial estimate can result in an under-performing launcher, or even a dead end. Margins must be sufficient to anticipate unfavorable cases, without leading to an oversized launcher. These margins depend on the uncertainties involved in modeling the launcher during the preliminary design phase.

The specifications define one or more reference missions characterized by a given payload mass to be brought into a given orbit. It may or may not impose certain technological choices (e.g. to reuse existing boosters) and authorize launcher versatility (number of boosters, last stage) for very dissimilar reference missions.

The preliminary design of a launcher involves several disciplines: propulsion, architecture, aerodynamics, trajectory, piloting, thermics and ground resources. The aim is to find the least-cost launcher for the specified mission. Overall launcher optimization is a difficult problem, involving both continuous (masses, thrust, etc.) and discrete variables (number of stages, propellant types, etc.). Multi-disciplinary approaches (MDOs) tackle this problem in many different ways, but are often complex to implement.

This article describes the standard methods used at the start of a preliminary project. The aim is to define propellant masses and thrust levels. The first part introduces the formulation of staging and trajectory problems. The classical method presented in the second part is based on impulse modeling to decouple these two problems, then proceed by iterations. The coupled method presented in Part 3 solves both problems simultaneously. It can handle versatile configurations...