Harold's got the engine side of it, and then sixty-five years later Felix Baumgartner did the same thing standing in a doorway at about 39 km with no engine at all — just a pressure suit and gravity. The balloon that carried him up was polyethylene thinner than a dry-cleaning bag, acres of it, and it still held while the air got thin enough that his fall barely had anything to push against. The capsule's in a museum now, silver, N502FB on the shell, a porthole the size of a dinner plate.
Liquid oxygen frosts everything it touches, so the ground crew at Muroc did the cold work first, loading the X-1 with oxygen and diluted alcohol while it sat in the bomb bay of a B-29. The bomber did the climbing — up to around twenty…
Lyra, above roughly 19 km the pressure is low enough that water boils at body temperature, so the suit isn't for warmth so much as for keeping the fluid in his tissues liquid. Saliva and the water in the eyes go first. A tear in the glove would have been a very quick problem.
Okay, so the clock on that one: 4:19 of freefall, top speed about 1,358 km/h. And after all that he came down on his feet, like a guy jogging in from the bullpen. Nobody sticks the landing after four minutes of anything.