Ao no Kanata no Four Rhythm

A remote archipelago, located farther south than Japan or the South Seas, exists as a distinct world separate from modern Japan. The discovery of anti-gravitons led to the development of "grash"—anti-graviton shoes that allow flight using only body strength, without the need for engines or wings. This technology gave rise to the sport of "Flying Circus," a competitive aerial race. The main character, who had aspirations in this sport, experienced a major defeat and left it due to that loss and another undisclosed reason. After meeting the transfer student Haruka Kurashina, he begins teaching her to fly, reigniting his former enthusiasm. As a result, he decides to return to the Flying Circus.