Air ducts are integral to modern buildings but are challenging to access for inspection. Small quadrotor drones offer a potential solution, as they can navigate both horizontal and vertical sections and smoothly fly over debris. However, hovering inside air ducts is problematic due to the airflow generated by the rotors, which recirculates inside the duct and destabilizes the drone, whereas hovering is a key feature for many inspection missions. In this article, we map the aerodynamic forces that affect a hovering drone in a duct using a robotic setup and a force/torque sensor. Based on the collected aerodynamic data, we identify a recommended position for stable flight, which corresponds to the bottom third for a circular duct. We then develop a neural network-based positioning system that leverages low-cost time-offlight sensors. By combining these aerodynamic insights and the data-driven positioning system, we show that a small quadrotor drone (here, 180 mm) can hover and fly inside small air ducts, starting with a diameter of 350 mm. These results open a new and promising application domain for drones.