Riders and runners passed along the drive, arching their heads to stare at the scene of Mr. Alfonso, in a blue, gray and white Fuji racing uniform, discussing changes to the prosthetics with Mr. Rheinstein and his team. Mr. Alfonso and Mr. Rheinstein decided to change the arm to make it shorter and retest it later in the afternoon.

“Unfortunately, I don’t think the happy ending is going to come right away,” Mr. Rheinstein said.

Indeed, learning to ride with the new arms will take time and training, as Mr. Alfonso adapts his highly developed riding style and gear. Despite state-of-the-art electronic shifters from Shimano, which allow him to change gears by lightly tapping a switch, using the prosthetics “will be hard,” he said.

Mr. Alfonso knows he needs to adapt if he is going to win medals, and eventually his competitive drive will take over, he said. “Because winning means always going forward,” he said. “Going forward, leading, always.” At 34, he quite likely has two shots left at the Paralympics, in 2012 and 2016.

His facial reconstruction has not gone easily, either. His body rejected a chin implant, and doctors removed it on Thursday. Final, outpatient surgery for touchups to his rebuilt nose are to be done in a few days.

With so little time for Mr. Alfonso to adapt to the prosthetics and train before the July race in Canada, Ms. Lea petitioned last month for an exemption to the strict equipment rules; after a back and forth, the international body that oversees paracycling granted her request, though it remains unclear whether the exemption will extend beyond July.

In any case, the prosthetics will allow Mr. Alfonso to compete in official bike races, from London to Saturday mornings in Central Park, something he is keen to do. But on this afternoon in Central Park, as the Hanger team left to tweak his new arms, Mr. Alfonso returned to his old position and set off for a quick loop of the park drive.

He rode slowly at first, blending with the other cyclists out for an afternoon ride in the spring sun and looking entirely at ease. After a while, his legs began pumping strongly. He gripped the sides of his upturned handlebars with his bare arms, rose from the saddle and powered up Cat’s Paw hill.

He was in total control of the bike, and he left every other rider behind.