Efficient co-design of eVTOL aircraft via adaptive time-grid refinement strategy

The co-design of electric vertical takeoff and landing (eVTOL) aircraft faces significant computational challenges due to deeply coupled multidisciplinary interactions. In direct transcription, traditional uniform grids often perform poorly: they introduce redundant nodes in smooth regions while providing insufficient resolution during high‑gradient transient phases, leading to unnecessarily large nonlinear programming problems and high computational costs. To improve discretization efficiency, we propose the relative improvement rate guided strategy (RIRGS), an adaptive time‑grid refinement method that dynamically identifies and refines key segments based on relative changes in the control trajectory across successive iterations. To validate its performance, we apply RIRGS to the eVTOL take‑off co‑design problem. RIRGS not only produces physically feasible optimal designs and trajectories, but also reduces the number of nodes by approximately 80% compared to a uniform grid, shortens the solution time by over 90%, and maintains comparable accuracy. Furthermore, compared with existing non‑uniform discretization strategies, RIRGS achieves convergence with fewer iterations and fewer nodes, demonstrating superior adaptability and computational efficiency.