Harrier than who?
Space Harrier takes place in a surreal world in which the ground has a checkerboard pattern. The enemies include prehistoric animals, Chinese dragons, and alien pods. The player is forced forward along the levels, running or flying left & right around enemy fire, while shooting back with fireballs.
Like After Burner, Space Harrier was among the first arcade game to feature a console in which the player sits, and which moves according to the joystick movement. There is also a non-moving sit-down version and a standard upright version. Space Harrier is a good throwback for those of us who were around when 3D style games were new. I'm guessing younger players wouldn't find too much enjoyment in the game, however.