Is there a range at which a battleship can see incoming shells early enough to manoeuvre out of their path?
Short answerAt less than roughly 8,000 yards in World War II conditions, a battleship is not going to dodge correctly aimed heavy shells before impact.
NotesHeavy shells take time to travel, but a battleship also takes time and distance to change course. Inside about 8,000 yards, the geometry leaves too little opportunity to manoeuvre clear of a correct solution. A miss at that distance is more likely to come from an aiming error than a successful last-second dodge. Close-range capital-ship combat gives fire-control quality and the opening salvo such importance. Manoeuvre can still disrupt an enemy's solution over time, but it does not make a battleship agile enough to evade each visible shell group.