And this, indirectly, sets the altitude limit. The challenge for the glider, as for most aircraft, is to move fast enough to get sufficient lift in the thin air to stay airborne, without approaching the speed of sound, which causes unacceptable stresses on the airframe. But as air density goes down, so does the speed of sound. On the top of the Perlan II glider’s wing, the passing air will approach the speed of sound but will not reach it.

“They’re definitely going to need to push the performance envelope, which means high lift and incredibly low drag,” said Richard P. Anderson, a professor of aerospace engineering at Embry-Riddle Aeronautical University in Daytona Beach, Fla., and a glider pilot, who is not affiliated with the project.

And the high altitude will introduce other complications.

One is the need to pressurize the cabin so human lungs can overcome low air pressure — something other airplanes do with an engine.

The solution is to seal the tiny cabin as the plane ascends, and bleed off a little air through a valve so the cabin pressure mimics what it would be at 14,500 feet. The sealed cabin needs spaceship-style scrubbers to remove the carbon dioxide and the moisture that would otherwise produce ice on the windows and walls. There is no way to warm the plane — another consequence of lacking an engine — so the two pilots, who will spell each other during the long flight, will wear socks with heaters in their soles, Mr. Enevoldson said.

Squeezed into a fuselage about 36 inches in diameter, they will be almost recumbent. They will bring sandwiches and wear diapers.

If a cabin-pressure emergency should strike at high altitude, the plane would have to dive — no simple matter in an airframe designed to glide many miles horizontally for each mile of altitude loss. The crew would deploy a small drogue parachute in the tail, point the glider’s nose down so it could fall quickly into thicker air, and then jettison the chute.