Superconducting electric propulsion systems, characterized by high power densities and efficiencies, provide a possibility to zero carbon emission for future aviation. Stacks of high temperature superconductor (HTS) coated conductors (CCs) have become an alternative for high field magnets applied to superconducting machines, given their excellent field trapping ability and thermal stability. High-frequency ripple fields always exist in high-speed electric machines. Most research work regarding HTS trapped field stacks (TFSs) was focused on their magnetization methods and amplitude of trapped flux density; however, their performance in the high-frequency environment remains unclear. Despite several numerical models established for flat HTS TFSs, a comprehensive analysis of curved ones is still lacking, which possess geometrical applicability for cylindrical rotating shafts. Aimed at exploring the electromagnetic properties of curved HTS TFSs applied to high-speed rotating machines, a 3D numerical model considering both the multilayer structure and the Jc(B) dependence of HTS CCs has been built. Current and magnetic flux density distributions, as well as loss properties of a curved HTS TFS have been studied in detail, under perpendicular and cross fields with varying frequencies ranging from 50 Hz to 20 kHz. Results have shown that, the widely adopted 2D-axisymmetric models are inapplicable to study the electromagnetic distributions of TFSs because of the emergence of the electromagnetic crisscross defined in this paper. High-frequency ripple fields can drive induced current towards the periphery of the HTS TFS due to the skin effect, leading to a fast rise of AC loss and even an irreversible demagnetization of the stack. This paper has qualified and quantified the highfrequency electromagnetic hehaviours of curved HTS TFSs, providing a useful reference for their loss controlling and anti-demagnetization design in high-speed propulsion machines.