Minimum induced loss propellers (and windmills) are the rotor analogues of elliptically loaded wings, characterized by minimum kinetic energy loss for a specified disc loading, number of blades, and flight (or wind) speed; they approximate most nearly an “actuator disc,” given the constraints of single rotation and blade number. Beginning in 1979 the author, his students, friends, and clients have produced a series of surprisingly efficient propellers (and anti-propellers) for various applications ranging from the CHRYSALIS and GOSSAMER ALBATROSS human powered airplanes to 50 kW horizontal axis wind turbines. Minimum induced loss rotor design may be carried out readily with a pocket scientific calculator, but off-design performance prediction requires something more, for instance the HELICE code and a small computer. Design and performance algorithms are given in Part I. A brief account of some applications is given in a companion paper with the subtitle Part II - Applications.