Current high temperature superconducting (HTS) wires exhibit high current densities enabling their use in electrical rotating machinery. The possibility of designing high power density superconducting motors operating at reasonable temperatures allows for new applications in mobile systems in which size and weight represent key design parameters. Thus, all-electric aircrafts represent a promising application for HTS motors. The design of such a complex system as an aircraft consists of a multi-variable optimization that requires computer models and advanced design procedures. This paper presents a specific sizing model of superconducting propulsion motors to be used in aircraft design. The model also takes into account the cooling system. The requirements for this application are presented in terms of power and dynamics as well as a load profile corresponding to a typical mission. We discuss the design implications of using a superconducting motor on an aircraft as well as the integration of the electrical propulsion in the aircraft, and the scaling laws derived from physics-based modeling of HTS motors