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.
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.
1) Leading edge 2) Face 3) Fillet area 4) Hub or Boss 5) Hub or Boss Cap 6) Trailing edge 7) Back 8) Propeller shaft 9) Stern tube bearing 10) Stern tube A propeller imparts momentum to a fluid which causes a force to act on the ship.
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.
[2] Thus a lightly loaded propeller with a large swept area can have a high Froude efficiency.
Actually the blades are twisted airfoils or hydrofoils and each section contributes to the total thrust.
An alternative design is the controllable-pitch propeller (CPP, or CRP for controllable-reversible pitch), where the blades are rotated normally to the drive shaft by additional machinery – usually hydraulics – at the hub and control linkages running down the shaft.
It also eliminates the need for a reversing gear and allows for more rapid change to thrust, as the revolutions are constant.
The downsides of a CPP/CRP include: the large hub which decreases the torque required to cause cavitation, the mechanical complexity which limits transmission power and the extra blade shaping requirements forced upon the propeller designer.
The blades freely move through an entire circle on an axis at right angles to the shaft.
This allows hydrodynamic and centrifugal forces to 'set' the angle the blades reach and so the pitch of the propeller.
A propeller that turns clockwise to produce forward thrust, when viewed from aft, is called right-handed.
Larger vessels often have twin screws to reduce heeling torque, counter-rotating propellers, the starboard screw is usually right-handed and the port left-handed, this is called outward turning.
The individual airfoil-shaped blades turn as the propeller moves so that they are always generating lift in the vessel's direction of movement.
This type of propeller can reverse or change its direction of thrust very quickly.
A more serious situation can exist if a multi-engine aircraft loses power to one of its engines, in particular the one which is positioned on the side that enhances the P-factor.
This power plant is called the critical engine and its loss will require more control compensation by the pilot.
Geometric pitch is the distance an element of an airplane propeller would advance in one revolution if it were moving along a helix having an angle equal to that between the chord of the element and a plane perpendicular to the propeller axis.
The force (F) experienced by a foil is determined by its area (A), fluid density (ρ), velocity (V) and the angle of the foil to the fluid flow, called angle of attack (
The effect of the flow over and the circulation around the foil is to reduce the velocity over the face and increase it over the back of the blade.
The forces generated by the bubble collapse can cause permanent damage to the surfaces of the blade.
Taking an arbitrary radial section of a blade at r, if revolutions are N then the rotational velocity is
This analysis is simplified and ignores a number of significant factors including interference between the blades and the influence of tip vortices.
The thrust, T, and torque, Q, depend on the propeller's diameter, D, revolutions, N, and rate of advance,
Thrust and velocity, at the same Froude number, give thrust power: For torque: When a propeller is added to a ship its performance is altered; there is the mechanical losses in the transmission of power; a general increase in total resistance; and the hull also impedes and renders non-uniform the flow through the propeller.
Producing the following: The terms contained within the brackets are commonly grouped as the quasi-propulsive coefficient (
is produced from small-scale experiments and is modified with a load factor for full size ships.