Directional sensitivity of wind current alignment in wheel over point geometry: development and validation of ATMM-W through percentage change

Accurate wheel over point determination is critical for safe course alterations, particularly in confined waters where small trajectory errors rapidly reduce lateral clearance. The conventional Advance Transfer Mathematical Model offers a practical geometric method for estimating wheel over distance, but it assumes still water conditions where heading equals course over ground. In operational environments, current set and wind induced drift modify the vessel ground velocity vector, so the alteration realised on the ground track differs from the planned heading alteration, creating a direct source of wheel over point error and increased cross track distance after the turn. This study develops Advance Transfer Mathematical Model-Weather as a weather corrected extension of the existing model by applying vector composition of ship speed through water, current velocity, and wind induced drift in an East North reference frame to compute an effective alteration angle representing the ground track change. Validation using a Wärtsilä full mission ship simulator with Electronic Chart Display and Information System integration under steady environmental conditions shows consistent reductions in post turn cross track distance for both port and starboard alterations, with maximum improvement reaching 60 percent, supporting integration into operational passage planning and decision support tools.