MATHEMATICAL MODEL AND SIMULATION OF FREE BALLOON LIFTOFF IN THE PRESENCE OF SURFACE WINDS

A mathematical model of free balloon launches in windy conditions is based on the conservation linear momentum horizontal and vertical axes. Linear equations are represented by a set four nonlinear first-order ODEs. Some ODEs were solved analytically, while Riccati ODE with variable coefficients for acceleration was using numerical solvers. Transient aerodynamic lift drag caused slip flow over envelope. It takes ten half times to reach 90.9% wind velocity step function response. launch condition developed terms minimum required envelope temperature which net aerostatic overcomes inert weight balloon. Perturbation analysis used explore changes lift. Simulations performed cases without distortion enhanced cooling due forced convection. Since all takeoffs downwind, obstacle clearance becomes an issue rapid loss Balloons may stop climbing even start descending shortly after liftoff despite intense heating representing real hazard.