Journal of Applied Mathematics
Volume 2012 (2012), Article ID 714627, 19 pages
Research Article

Computation of the Added Masses of an Unconventional Airship

1Laboratoire IBISC, Université d'Evry Val d'Essonne, 40 Rue du Pelvoux, 91025 Evry, France
2Lab of Mathematical Engineering, Polytechnic School, 2078 La Marsa, Tunisia

Received 5 June 2012; Revised 9 August 2012; Accepted 10 August 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Naoufel Azouz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a modelling of an unmanned airship. We are studying a quadrotor flying wing. The modelling of this airship includes an aerodynamic study. A special focus is done on the computation of the added masses. Considering that the velocity potential of the air surrounding the airship obeys the Laplace's equation, the added masses matrix will be determined by means of the velocity potential flow theory. Typically, when the shape of the careen is quite different from that of an ellipsoid, designers in preprocessing prefer to avoid complications arising from mathematical analysis of the velocity potential. They use either complete numerical studies, or geometric approximation methods, although these methods can give relatively large differences compared to experimental measurements performed on the airship at the time of its completion. We tried to develop here as far as possible the mathematical analysis of the velocity potential flow of this unconventional shape using certain assumptions. The shape of the careen is assumed to be an elliptic cone. To retrieve the velocity potential shapes, we use the spheroconal coordinates. This leads to the Lamé's equations. The whole system of equations governing the interaction air-structure, including the boundary conditions, is solved in an analytical setting.