Distributed tactile sensing for multi-force detection is crucial for various aerial robot interaction tasks. However, current contact sensing solutions on drones only exploit single end-effector sensors and cannot provide distributed multi-contact sensing. Designed to be easily mounted at the bottom of a drone, we propose an optical tactile sensor that features a large and curved soft sensing surface, a hollow structure and a new illumination system. Even when spaced only 2 cm apart, multiple contacts can be detected simultaneously using our software pipeline, which provides real-world quantities of 3D contact locations (mm) and 3D force vectors (N), with an accuracy of 1.5 mm and 0.17 N respectively. We demonstrate the sensor's applicability and reliability onboard and in real-time with two demos related to i) the estimation of the compliance of different perches and subsequent re-alignment and landing on the stiffer one, and ii) the mapping of sparse obstacles. The implementation of our distributed tactile sensor represents a significant step towards attaining the full potential of drones as versatile robots capable of interacting with and navigating within complex environments.