  Motivated by the study of the potential use of blowing and venting operations
of ballast tanks in manned submarines as a complementary or alternative control
system for manoeuvring, we first propose a mathematical model for these
operations. Then we consider the coupling of blowing and venting with the
Feldman, variable mass, coefficient based hydrodynamic model for the equations
of motion. The final complete model is composed of a system of twenty-four
nonlinear ordinary differential equations. In a second part, we carry out a
rigorous mathematical analysis of the model: existence of a solution is proved.
As one of the possible applications of this model in naval engineering
problems, we consider the problem of roll control in an emergency rising
manoeuvre by using only blowing and venting. To this end, we formulate a
suitable constrained, nonlinear, optimal control problem where controls are
linked to the variable aperture of blowing and venting valves of each of the
tanks. Existence of a solution for this problem is also proved. Finally, we
address the numerical resolution of the control problem by using a descent
algorithm. Numerical experiments seem to indicate that, indeed, an appropriate
use of blowing and venting operations may help in the control of this emergency
manoeuvre.
