The Energy System Transition in Aviation research project of the Aeronautics Research Center Niedersachsen (NFL) searches for potentially game-changing technologies to reduce the carbon footprint of aviation by promoting and enabling new propulsion and drag reduction technologies. The greatest potential for aerodynamic drag reduction is seen in laminar flow control by boundary layer suction. While most of the research so far has been on partial laminarization by application of Natural Laminar Flow (NLF) and Hybrid Laminar Flow Control (HLFC) to wings, complete laminarization of wings, tails and fuselages promises much higher gains. The potential drag reduction and suction requirements, including the necessary compressor power, are calculated on component level using a flow solver with viscid/inviscid coupling and a 3D Reynolds-Averaged Navier-Stokes (RANS) solver. The effect on total aircraft drag is estimated for a state-of-the-art mid-range aircraft configuration using preliminary aircraft design methods, showing that total cruise drag can be halved compared to today's turbulent aircraft.