Modeling and Optimization in Space Engineering by Giorgio Fasano & János D. Pintér

Author:Giorgio Fasano & János D. Pintér
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

7.6.1.2 VEGA Performance Map

Adding a level of complexity it is possible to compute the performance map of a different launcher, VEGA, in polar circular orbit at different altitudes. The problem is still related to the maximization of the payload mass, but there are some important differences in the model that require modifications also in the transcription method. The polar orbit has an inclination of 90° and the vehicle could pass over the north or south pole, where the inertial velocities EoM, in particular the longitudinal component, are not defined (see also Sect. 7.4.4). This configuration cannot be analyzed by the solver; therefore a different set of equation of motion is required, namely inertial Cartesian. The application of this set to the entire trajectory is not efficient due to the poor scaling of the velocity and position components. A better approach would be to apply the Cartesian EoM only in the phases that cross the pole, whereas the other phases are modeled with inertial velocities EoM.

Additionally, VEGA presents a restartable upper stage, and for orbit altitude higher than 300 km, the implementation of a two burn strategy is beneficial. This leads to the presence of a coast arc with a duration dependent on the final orbit altitude, e.g., 1,800 s for an orbit altitude of 700 km. This long ballistic phase presents no attitude control, it is a simple transfer to the apoapsis, but the numeric integration required by the multiple shooting method is quite time consuming due to the long duration. A performance improvement can be achieved with a collocation method applied only to this long phase: the advantages of both methods can be appreciated, the accuracy of multiple shooting and the fast computation of the collocation.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.