An Ultimate disc is a wing you can catch. 𐃏 It has no tail, no fuselage, and no static stability whatsoever — by the standards of a fixed-wing aircraft it should tumble within the first few metres. Instead it flies a hundred, because it carries its stabiliser as angular momentum. This treatise works through the mechanics in four movements: the disc as a rigid body, the aerodynamic forces on it, the gyroscopic dance that shapes every throw, and the resulting flight envelope. The canonical sources are Hummel’s flight simulations (Hummel, Sarah Ann, 2003), the Manchester wind-tunnel programme of Potts and Crowther (Potts, Jonathan R. and Crowther, William J., 2002), and Lorenz’s instrumented discs (Lorenz, Ralph D., 2005).1