Ordinarily, Felix Baumgartner would not need a lot of practice in the science of falling.

He has jumped off two of the tallest buildings in the world, as well as the statue of Christ in Rio de Janeiro (a 95-foot leap for which he claimed a low-altitude record for parachuting). He has sky-dived across the English Channel. He once plunged into the black void of a 623-foot-deep cave, which he formerly considered the most difficult jump of his career.

But now Fearless Felix, as his fans call him, has something more difficult on the agenda: jumping from a helium balloon in the stratosphere at least 120,000 feet above Earth. Within about half a minute, he figures, he would be going 690 miles per hour and become the first skydiver to break the speed of sound. After a free fall lasting five and a half minutes, his parachute would open and land him about 23 miles below the balloon.

At least, that’s the plan, although no one really knows what the shock wave will do to his body as it exceeds the speed of sound. The jump, expected sometime this year, would break one of the most venerable aerospace records. For half a century, no one has surpassed (one person died trying) the altitude record set by Joe Kittinger as part of an Air Force program called Project Excelsior.

In 1960, Mr. Kittinger, then a 32-year-old Air Force pilot, jumped from a balloon 102,800 feet above the New Mexico desert. Today, at 81, Mr. Kittinger is a retired colonel and part of the Red Bull Stratos team working on Mr. Baumgartner’s jump, which is being financed by the energy-drink company.