Propeller theory is the science governing the design of efficient propellers. A propeller is the most common propulsor on ships, and on small aircraft. History In the second half of the nineteenth century, several theories were developed. The momentum theory or disk actuator theory – a theory describing a mathematical model of an ideal propeller – was developed by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and Robert Edmund Froude (1889). The propeller is modelled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. This disc creates a flow around the propeller. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the propeller, torque and induced velocity. Friction is not included. The blade element theory (BET) is a mathematical process originally designed by William Froude father of Robert Edmund Froude (1878), David W. Taylor (1893) and Stefan Drzewiecki to determine the behaviour of propellers. It involves breaking an airfoil down into several small parts then determining the forces on them. These forces are then converted into accelerations, which can be integrated into velocities and positions. Theory of operation A propeller imparts momentum to a fluid which causes a force to act on the ship. The ideal efficiency of any propulsor is that of an actuator disc in an ideal fluid. This is called the Froude efficiency and is a natural limit which cannot be exceeded by any device, no matter how good it is. Any propulsor which has virtually zero slip in the water, whether this is a very large propeller or a huge drag device, approaches 100% Froude efficiency. The essence of the actuator-disc theory is that if the slip is defined as the ratio of fluid velocity increase through the disc to vehicle velocity, the Froude efficiency is equal to 1/(slip + 1). Thus a lightly loaded propeller with a large swept area can have a high Froude efficiency. An actual propeller has blades made up of sections of helicoidal surfaces which can be thought to 'screw' through the fluid (hence the common reference to propellers as "screws"). Actually the blades are twisted airfoils or hydrofoils and each section contributes to the total thrust. Two to five blades are most common, although designs which are intended to operate at reduced noise will have more blades and one-bladed ones with a counterweight have also been