Aviation researchers are increasingly focusing on unconventional vehicle designs with tightly integrated propulsion systems to improve overall aircraft performance and reduce environmental impact. Properly analyzing these types of vehicle and propulsion systems requires multidisciplinary models that include many design variables and physics-based analysis tools. This need poses a challenge from a propulsion modeling standpoint because current state-of-the-art thermodynamic cycle analysis tools are not well suited to integration into vehicles level models or to the application of efficient gradient-based optimization techniques that help to counteract the increased computational costs. Therefore, the objective of this research effort was to investigate the development a new thermodynamic cycle analysis code, called pyCycle, to address this limitation and enable design optimization of these new vehicle concepts. This paper documents the development, verification, and application of this code to the design optimization of an advanced turbofan engine. The results of this study show that pyCycle models compute thermodynamic cycle data within 0.03% of an identical Numerical Propulsion System Simulation (NPSS) model. pyCycle also provides more accurate gradient information in three orders of magnitude less computational time by using analytic derivatives. The ability of pyCycle to accurately and efficiently provide this derivative information for gradient-based optimization was found to have a significant benefit on the overall optimization process with wall times at least seven times faster than using finite difference methods around existing tools. The results of this study demonstrate the value of using analytic derivatives for optimization of cycle models, and provide a strong justification for integrating derivatives into other important engineering analyses.Aerospace 2019, 6, 87 2 of 36 design process with cycle analysis serving as the key analysis method for initializing, guiding the development of, and then ultimately confirming the final engine design [6].Cycle analysis techniques have been studied since the conception of the gas turbine engine in the 1930s. While the fundamental equations governing cycle analysis are rooted in the laws of thermodynamics for a steady one-dimensional flow, the implementation of these equations has changed substantially over the years. These different implementations, predominantly in the form of various computer codes, can be organized into several major eras as shown in Figure 1. This history was pieced together from several sources [6][7][8] with incomplete or conflicting information, so it should be noted that the dates defining the start and end of these eras are approximate.