Estimation of the virtual masses of a large unconventional airship based on purely analytical method to aid in the preliminary design

Abstract

This paper presents preliminary results of the modeling of a large autonomous quad-rotor airship, with flying wing shape. This airship is supposed to be a flexible body. This study promotes an entirely analytical methodology with some assumptions. In this study and as first assumption, the shape of the careen is supposed to be an elliptic cone. To retrieve the velocity potential shapes, this paper solved the Laplace’s equation by using the sphero-conal coordinates. This leads to the Lamé’s equations. The whole system equations governing the interaction of air–structure, including the boundary conditions, is solved in an analytical setting. This paper opted for a modeling and determination of the added masses of a flexible airship by an analytical method illustrated by a comparison with a geometric method. This analytical method includes the study of complex functions which are the Lamé functions. This paper provides an analytical way to estimate an aerodynamic phenomenon which acts on the airship and in particular on its envelope and known as the phenomenon of added masses or virtual masses, as well as the means of defining it and the calculation analytically for the case of the flexible airship. Considering that the calculation of the added masses is very difficult and the numerical methods increase the number of degrees of freedom, the analytical method established in this paper has become a solution of calculations of these virtual masses. This paper includes an application for determining the added masses of a new generation MC500 airship. This paper allows defining an analytical method which determines the added masses of an airship, which helps the automation engineer to develop a control strategy to stabilize this airship.