Modeling of Apparent Mass for a Buoyant Vehicle Including Dynamic Buoyancy Effects

Abstract

Methods are presented for modeling apparent mass effects for buoyant vehicles including dynamic buoyancy. Apparent mass and virtual mass are terms used to describe the additional inertia of the flow induced in the fluid surrounding a vehicle accelerates. Apparent mass effects become significant when the density of the vehicle is near the density of the surrounding air. Dynamic buoyancy is an effect where forces and moments are applied to the vehicle due to acceleration of the surrounding fluid. A static method is considered where the additional momentum of the virtual mass is included along with that of the vehicle. A dynamic method is also considered where additional degrees of freedom are used to represent the momentum of the virtual mass. This method was presented in an earlier paper, but is expanded to include dynamic buoyancy effects. Dynamic buoyancy is significant to the dynamic method because the effect occurs not only between the vehicle and the wind but also between the vehicle and virtual mass. A detailed description of the transformation of an inertia matrix from one reference frame to another is included, as it is necessary to describe the interaction of multiple masses defined relative to different reference frames. Considerations are also discussed for implementing these methods for rotating earth models where the earth reference frame is moving relative to an inertial reference frame.