Analysis and optimization of an air-launch-to-orbit separation

• We define a new safety criteria based on a dedicated flight simulator.
• We show that a classic screening method can underestimate uncertainty factors.
• We develop a new method reducing this risk and we validate it with a test function.
• We use this method for the sensitivity analysis of an air-launch-to-orbit separation.
• We optimize the separation trajectory to improve the safety of the system.

In an air-launch-to-orbit, a space rocket is launched from a carrier aircraft. Air-launch-to-orbit appears as particularly interesting for nano- and microsatellites which are generally launched as secondary loads, that is, placed in the conventional launch vehicle׳s payload section with a larger primary satellite. In an air-launch-to-orbit, a small satellite can be launched alone as a primary load, away from a carrier aircraft, aboard a smaller rocket vehicle, and in doing so, benefit from more flexible dates and trajectories. One of the most important phases of the mission is the separation between the carrier aircraft and the space rocket. A flight simulator including a large number of factors of uncertainties has been especially developed to study the separation, and a safety criteria has been defined with respect to store collision avoidance. It is used for a sensitivity analysis and an optimization of the possible trajectories. The sensitivity analysis first requires a screening method to select unessential factors that can be held constant. The Morris method is amongst the most popular screening methods. It requires limited calculations, but may result in keeping constant an essential factor which would greatly affect the results of the sensitivity analysis. This paper shows that this risk can be important in spite of recent improvements of the Morris method. It presents an adaptation of this method which divides this risk by a factor of ten on a standard test function. It is based on the maximum of the elementary effects instead of their average. The method focuses the calculations on the factors with a low impact, checking the convergence of this set of factors, and uses two different factor variations instead of one. This adaptation of the Morris method is used to limit the amount of the air-launch-to-orbit simulations and simplify the uncertainty domain for analysis by Sobol׳s method. The aerodynamic perturbations due to wind, the parameters defining the trajectory, the interactions, and the mass characteristics of the systems are detected as factors with a high impact. The parameters of the trajectory are finally optimized with a stochastic gradient method. It shows that the separation is safer with a low speed, a low climb angle, and a high vertical acceleration of the aircraft. A trajectory offering such a separation will be tested with an air-launch-to-orbit demonstrator from the French space agency CNES and the French aerospace laboratory ONERA.