Abstract: A safety helmet has a hard outer shell having front and rear edges. A bowl-shaped liner with front and rear edges and a peak between the edges is contoured to fit snugly in the shell so that the front and rear edges of the liner are adjacent to the front and rear edges of the shell. The liner has an interior surface contoured generally to fit a wearer's head and a corrugated exterior surface, the tips of the liner corrugations contacting the shell along multiple lines of contact. The corrugations in at least a central zone of the liner adjacent to the peak extend fore and aft between the front and rear edges of the liner such that the corrugations define valleys that are spaced from the shell to provide air passages in the helmet extending from the front of the helmet to an array of through-holes in the liner and to a vent opening in the shell adjacent to the rear edge of the liner. A valve is provided to control air flow through the passages and the through-holes.