Touchscreen technologies will most probably replace current instrument panels in future aeronautical cockpits. However, while safety and performance require interactive instruments to maximize the perception, action and collaboration spaces offered to pilots, the literature highlights the limits of touch-based interaction regarding these aspects. Our objective is thus to explore how tangible embodied interaction (TEI), associated with a touch-based flight deck device, could address this issue. In this paper, we contribute a structured design space for pilot-system interactions based on an analysis of the design properties of physical interaction as described in the literature, and on relevant usability, safety and industrial requirements.