Google Gravity Balloon !free! -

[ V = \frac{m_{air}}{\rho_{strat}} \approx \frac{30 \text{ kg}}{0.088 \text{ kg/m}^3} \approx 340 \text{ m}^3 ]

The optimization problem: maximize the number of user-hours connected given constraints on battery (solar recharge rate), wind prediction error, and balloon longevity. This became a partially observable Markov decision process (POMDP) with >10^6 state variables. google gravity balloon

Mathematically, the pressure differential (\Delta P) is limited by the meridional stress (\sigma) in the lobes: [ \Delta P = \frac{2 \sigma t}{R_{curv}} ] where (t) is film thickness and (R_{curv}) is lobe radius. By keeping (R_{curv}) small (many lobes), Loon could handle (\Delta P) up to 200 Pa without bursting. Unlike airships or drones, Loon had no propulsion. How do you steer a balloon? You change its altitude to catch different wind currents. The stratosphere has multiple layers of wind moving in different directions (e.g., west-to-east at 20 km, east-to-west at 25 km). By keeping (R_{curv}) small (many lobes), Loon could