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Siege

The trebuchet swings on its own equations of motion, beam, counterweight on its hanger and stone in its sling, and lets go at the angle you set; a test holds its energy steady through the throw to a millionth. Every missile flies with the drag of a sphere or a bolt in still air, and comes down where that flight says. The castles are dry-laid stone and timber, solved as a slice through the wall, held up by nothing but weight and friction: a castle left alone stands exactly as built, and every siege is won within par in the tests by aiming with only the settings a player has. Ours: how hard a block must be struck to crack, the slice's depth, the onager's skein as a simple spring, the bombard's powder as a fixed energy per kilogram, and stone coming to rest a little sooner than a plain solver lets it.