Purpose – Extend the Blade Element Momentum Theory (BEMT) such that rotors with pronounced cone and axis angle (tilt or yaw) can be calculated. Derive an equation for the speed ratio (lambda) as a function of Tip Speed Ratio (TSR), radius, blade, cone and axis angle. This converts the BEMT into an Unsteady BEMT or UBEMT. Present the Wagner rotor as one such rotor geometry. --- Methodology – Literature review and calculations. --- Findings – The UBEMT can be used to calculate highly unconventional rotor geometries. --- Research Limitations – Although the aerodynamic coefficients used in the UBEMT are from measurements in steady flow conditions, they can be used with success. --- Practical Implications – Also conventional Horizontal Axis Wind Turbines (HAWT) with noticeable cone and axis angle should be calculated with the UBEMT. The accuracy of power calculations of these HAWTs can be slightly improved. --- Originality – Analytic equations for rotors with cone and axis angle have barely been discussed.

Parametric models have been widely used in pertinent literature for reconstructing, modifying and representing a wide range of airfoil and/or hydrofoil profile geometries. Design spaces corresponding to these models can be exploited for modeling and profile-shape optimization under various performance criteria. Accuracy requirements, along with the need for modeling local features, often lead to high-dimensional design spaces that hinder the process of shape optimization and design through analysis. In this work, we propose a shape-informed dimensional reduction approach that attempts to tackle this deficiency by producing low-dimensional latent design spaces that can be efficiently used in shape representation and optimization. Furthermore, geometric moments are introduced in an attempt to cost-effectively capture analysis-relevant information that is generally expensive to produce. Specifically, geometric integral properties, although intrinsic features of the shape, are quite commonly related to performance indicators employed in performance optimization and therefore provide a cost-effective physics-informed component in the description of the design in the latent space. To this end, we employ the generalized Karhunen-Loeve expansion to produce a shape- and physics-informed subspace retaining the highest possible geometric variance and robustness, that is, lack of invalid designs. At the same time, a series of shape discretizations, encoding the foil's shape profile, are examined with regards to their effect on the resulting latent space's quality and efficiency. Our results demonstrate a significant reduction in the dimensionality of the original design space while maintaining a high representational capacity and a large percentage of valid geometries that facilitate fast convergence to optimal solutions in performance-based optimization.