Flight-Height Optimized: Physics-Informed Planning for Precision Drone Seeding

Hand planting is slow, variable, and risky in windy, rocky coastal or bushland terrain. We reframe aerial seeding as an environment-aware optimization that selects drone height, airspeed, and heading to maximize per-cell hit rate while maintaining throughput over large areas. Central to our approach is a physics-based drop model: we compute the exact fall time under quadratic drag, predict mean horizontal drift by coupling vehicle motion with wind at release height, and model random spread using an Ornstein-Uhlenbeck turbulence process whose time scale increases with altitude. We then couple the latter with an error budget that accounts for timing, heading, and wind-direction uncertainty, yielding finite-time dispersion that is operationally realistic. Compared with altitude-only rules or heading-agnostic heuristics common in the restoration literature, our formulation makes the environment explicit-wind speed, wind direction, and turbulence intensity enter transparently-and produces reproducible, parameter-tuned operating points rather than ad-hoc settings. We provide equation-level details for local calibration and a lightweight dashboard that visualizes recall, drift distance, and recommended settings balancing hit rate and coverage speed in real time. In this scheme, the optimizer selects height, speed, and heading of the drone to center the expected impact on the target while reducing variance under the prevailing turbulence and relative wind angle.