The paper presents engineering models, optimization algorithms and design results from a Multidisciplinary Design Optimization (MDO) research in the framework of ESA's PRESTIGE PhD program. The application focuses on the conceptual design of classical unmanned Expendable Launch Vehicles, and results are presented from sensitivity studies and validation tests on European launchers (Ariane-5 ECA and VEGA). Relatively simple models and a mixed global/local optimization approach allow obtaining reasonable results with limited computational effort. A critical analysis of the results also leads to the identification of the most critical modeling aspects to be improved to allow for early preliminary design applications. Nomenclature α = engine mixture ratio ε = nozzle expansion ratio θ = pitch angle ψ = yaw angle µ = mean value σ = standard deviation A e = nozzle exhaust area AoA = total angle of attack a = orbit semiaxiscore boosters configuration CpL = cost per launch e = orbit eccentricity GTOW = gross take-off weight i = orbit inclination I sp = specific impulse, nominal conditions (i.e. nozzle optimal expansion) 2 I sp,vac = specific impulse in vacuum I sp,sea = specific impulse at sea level L/D = length over diameter ratio LSP = launch success probability MR = Engine mixture ratio M = Mach number M prop = Propellant mass (usable propellant only) M dry = Dry mass = inert mass + unused propellants mass N s = number of stages N bs = number of booster sets N b,j = number of boosters for j-th boosters set n ax = axial acceleration p cc = chamber pressure PL = payload PLSF = payload scaling factor q dyn = dynamic pressure q heat = heat flux SET = single engine type configuration (i.e. same engine type for all stages) T nom = total thrust, nominal conditions (i.e. nozzle optimal expansion) T ,vac = total thrust in vacuum T sea = total thrust at sea level

The upper atmosphere of Mars is constantly perturbed by small-scale gravity waves propagating from below. As gravity waves strongly affect the large-scale dynamics and thermal state, constraining their statistical characteristics is of great importance for modeling the atmospheric circulation. We present a new data set of density perturbation amplitudes derived from accelerometer measurements during aerobraking of the European Space Agency’s Trace Gas Orbiter. The obtained data set presents features found by three previous orbiters: the lower thermosphere polar warming in the winter hemisphere, and the lack of links between gravity wave activity and topography. In addition, the orbits allowed for demonstrating a very weak diurnal variability in wave activity at high latitudes of the southern winter hemisphere for the first time. The estimated vertical damping rates of gravity waves agree well with theoretical predictions. No clear anticorrelation between perturbation amplitudes and the background temperature has been found. This indicates differences in dissipation mechanisms of gravity waves in the lower and upper thermosphere.

The main goal of this paper is to analyze different methodologies and to quantitatively compare a set of algorithms for multi-objective global optimization, as an initial step toward a multidisciplinary design optimization framework for space transportation systems. Through a comparative analysis based on mathematical benchmarks, hierarchies among several stochastic techniques are proposed. This leads to the identification of two algorithms as the most promising for multidisciplinary design optimization applications: the nondominated sorting genetic algorithm-II (NSGA-II) and an improved version of particle swarm optimization. Then a significant advantage of the latter is highlighted on the problem of trajectory optimization for expendable launch vehicles. In this applicative scenario, the paper also aims at proving the capability of global methods to correctly assess the performance of expendable launch vehicles. Environmental, dynamical, and guidance models for the optimization of ascent trajectories are therefore introduced. Results for seven performance optimization test cases show that global techniques provide comparable payload masses with respect to traditional gradient-based methods. In addition to the trajectory models, historical linear regressions simulating an expendable launch vehicle's design cycle are described. The focus is in this case on the definition of a simple model as a test bench for the verification of the effectiveness of global methods on multidisciplinary design optimization problems, rather than on the quality of the design results. Three widely different expendable launch vehicle design optimization problems are successfully solved by applying the improved particle swarm optimization algorithm. This demonstrates the suitability of the developed global optimization architecture and algorithms for search-space exploration in multidisciplinary design optimization, paving the way for more detailed modeling and more realistic applications

The paper presents in details the engineering models and optimization algorithms for a Multidisciplinary Design Optimization research framework developed within ESA's PRES-TIGE PhD program. The application focuses on the conceptual design of classical unmanned Expendable Launch Vehicles, with future extensions to the early preliminary detail level and to more complex systems such as manned and reusable vehicles. Results are presented from the validation of the disciplinary models and optimization algorithms. Besides, sensitivity analyses and Multidisciplinary Analysis and Optimization runs on European test cases (Ariane-5 ECA and VEGA) show how relatively simple models and a mixedglobal/local optimization approach allow to obtain reasonable results for conceptual level design (10 to 20% errors on global performance figures) with very limited computational effort.

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