Midvale College is told that a wealthy man, Mr. Astorbilt (Arthur O'Connell), will give a large donation, but he has a strange request — he challenges the school to build a man-powered flying machine. If they succeed by a certain date, they get the donation, otherwise it will go to a rival school.
Merlin Jones (Kirk) designs a lightweight airplane, powered by a propeller driven by bicycle pedals. Recognizing that even his football-jock friends won't be strong enough for such a feat, he develops a strength elixir (based on adrenaline), which should give the power that a man would need to get off the ground.
To get the jocks' support, he creates "an honest way to cheat", adapting the recently-discovered sleep-learning method to help them pass a particularly hard history course. Once the jocks are asleep, a timer starts a phonograph album, with the sound of Jennifer reading their lessons to them. This backfires in class, however — asked to give an oral report, the jocks speak, but Jennifer's voice comes out. Eventually it works out in the students' favor.
Jones gets their help, and the great day comes. The pilot drinks the elixir, then pedals off into the sky, winning the contest. Unfortunately, the "wealthy donor" is last seen fleeing from men in white coats, who want to take him back to the local mental hospital.
This production marks both Tommy Kirk's and Annette Funicello's last film for Walt Disney. Actor Mark Goddard, who plays Haywood (and is perhaps best known as Major Don West on television's Lost in Space), made his feature film debut in this movie.
The screen credit for writing reads, "Screenplay by Tom and Helen August", which were the pseudonyms for Alfred Lewis Levitt & Helen Levitt, two writers who were blacklisted.